research article localization of outdoor mobile robots...
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Research ArticleLocalization of Outdoor Mobile Robots Using Curb Features inUrban Road Environments
Hyunsuk Lee1 Jooyoung Park2 and Woojin Chung1
1 Department of Mechanical Engineering Korea University Anam-dong Seongbuk-gu Seoul 136-713 Republic of Korea2Department of Control and Instrumentation Korea University Anam-dong Seongbuk-gu Seoul 136-713 Republic of Korea
Correspondence should be addressed to Woojin Chung smartrobotkoreaackr
Received 12 December 2013 Revised 13 February 2014 Accepted 13 February 2014 Published 8 April 2014
Academic Editor Leo Chen
Copyright copy 2014 Hyunsuk Lee et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
Urban road environments that have pavement and curb are characterized as semistructured road environments In semistructuredroad environments the curb provides useful information for robot navigation In this paper we present a practical localizationmethod for outdoor mobile robots using the curb features in semistructured road environments The curb features are especiallyuseful in urban environment where the GPS failures take place frequently A curb extraction is conducted on the basis of the KernelFisher Discriminant Analysis (KFDA) to minimize false detection We adopt the Extended Kalman Filter (EKF) to combine thecurb information with odometry and Differential Global Positioning System (DGPS) The uncertainty models for the sensors arequantitatively analyzed to provide a practical solution
1 Introduction
Outdoor environments have irregular shapes and changesin geometry and illumination due to the weather conditionTherefore environmental uncertainty is relatively highThereare numerous studies for autonomous navigation of mobilerobot in outdoor environments Typical examples are theautonomous vehicles that were developed through DARPAGrandUrban Challenges [1 2] Most of the vehicles wereequipped with a variety of high cost sensors in order toovercome various uncertainties
The aim of this work is to develop a practical localizationmethod for outdoor mobile robots In particular this studyfocuses on surveillance robots in urban road environmentsA localization method using a small number of sensors isproposed instead of using multiple high cost sensors
The fusion of a global positioning system (GPS) andinertial measurement unit (IMU) has been widely used forthe outdoor localization of mobile robots [3 4] Howeverit is difficult to ensure the accurate pose estimation indense urban environment where GPS signal is degraded bythe multipath errors and satellite blockage Therefore theuse of environmental features has been studied to enhancethe precision of the estimated robot pose in dense urban
environment [5 6] In [7] a 3D representation of the localenvironment is used to detect obstruction of the GPS signalswhich is blocked by buildings In [8 9] the extracted linefeatures of buildings are used to estimate the robot positionHowever the available information regarding buildings issparse in many places and the slow update rate limits theperformance of localization In [10] the road centerlineis extracted to correct the lateral position of the vehiclein mountainous forested paths However the correction ofthe heading error is not considered by the extracted roadcenterline
Generally urban road environments are paved and thecurbs act as the boundaries of the roads Therefore urbanroad environments are characterized as semistructured roadenvironments In semistructured road environments thecurb provides useful information for robot navigationThere-fore the curb features have been widely used for navigationstrategies and localization methods In [11] Wijesoma et alpropose amethod based on EKF for detection and tracking ofthe curbsThe range and angle of the curbs are obtained froman LRF measurement However quantitative performanceanalysis of the curb detection was not clearly shown In[12 13] the curb on one side of the road is extracted usinga vertical LRF for vehicle localization The lateral error of
Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2014 Article ID 368961 12 pageshttpdxdoiorg1011552014368961
2 Mathematical Problems in Engineering
a vehicle is reduced by map matching approach using theextracted curb point However the correction of the headingangle is not considered because there is no angle informationof the curb
A method for traversable region detection using roadfeatures such as road surface curbs and obstacles is pro-posed in our previous works [14ndash16] The curb features arederived by the geometric features of the road to obtain curbcandidates In order to extract the correct curb among thecurb candidates a validation gate is derived from principalcomponent analysis (PCA)The curb extraction is performedsuccessfully in a road environment However there was afundamental limitation on PCA The validation gate doesnot consider the classification of the curb and noncurbdata Consequently false detection where noncurb data areextracted as curbs may occur The precision of estimatedpose is decreased when the false detection data are usedfor localization Therefore it is important to reduce the falsedetection rate
The contribution of this paper can be summarized by twoschemes The first contribution is the robust curb extractionscheme by using a single Laser Range Finder (LRF) Inorder to reduce the number of false detection of the curbsthe classification of the curb data and the noncurb datais conducted by using Kernel Fisher Discriminant Analysis(KFDA) in [17ndash19] On the basis of our previous worksgeometrical features of the curb are defined The secondcontribution is the integrated localization scheme using curbfeatures on the basis of quantitative sensor uncertainty mod-els In particular the uncertaintymodel for the extracted curbis quantitatively determined from experiments ExtendedKalman Filter (EKF) is exploited to combine the curb featureswith odometry and Differential Global Positioning System(DGPS) information The extracted curbs enable accurateestimation of the pose of the robot even when the temporalGPS blackout takes place
The remainder of this paper is organized as followsA method for curb extraction is presented in Section 2Section 3 describes the localization method for an outdoormobile robot using the extracted curb It also introducesthe uncertainty models for the sensor measurements Theexperimental results of the proposedmethod are presented inSection 4 Finally the conclusion of this research is presentedin Section 5
2 Road Feature Extraction
21 System Configuration Figure 1 shows the configurationof the mobile robot and the LRF coordinate configurationA single onboard LRF with a tilting angle of 120572
119905is used to
extract road features such as the road surface and curbsThe following list shows the nomenclature for road featureextraction The variables are described with respect to therobot coordinate frame
119908119903 road width
120572119905 nominal tilt angle of LRF
120579119891 angle between the detected road surface points
and 119884119877-axis
119889119891 horizontal look-ahead distance from the robot to
the road surface points(119909C119877 119910C119877) coordinates of the right curb edge (pointC)120579C119877 angle between the right curb and 119884
119877-axis
(119909C119871 119910C119871) coordinates of the left curb edge (point B)120579C119871 angle between the left curb and 119884
119877-axis
22 Road Feature Detection A road feature detection schemewas proposed in our previous works [14 15] The previousworks on road feature detection are briefly reviewed Thefirst step for the road feature detection is the road surfaceextraction In order to identify the road surface the LRFmeasurements in expected road region 119877
119910are selected as
candidates for the road surface 119871119903 Multiple line segments
are constructed by combining consecutive data points of 119871119903
The angle of the road surface is parallel with the 119883119877-axis
in the ideal case Therefore the range data 119871119903are saved as
road surface points 119871119891if the angle of the line segment is
within threshold 120579119890 The road surface is extracted as a line
by using the least square method The extracted road surfaceprovides 120579
119891and 119889
119891from the robotThe overall algorithm can
be summarized in Algorithm 1Figure 2 shows the ideal model of a semistructured road
environment The geometrical features of the road can beused to extract the curb features The curb has the followingfour attributes
(Att 1) The angular difference between the curb ori-entation (120579
119888) and road surface angle (120579
119891) is close to
90∘(Att 2) The gap between the horizon distance of theroad surface (119889
119891) and the 119910 value of the curb point (B
or C) is close to 0(Att 3) The angular difference between the left curb( AB) and the right curb ( CD) is close to 0(Att 4)The difference between the roadwidth and thegap between two curbs is close to 0 It is assumed thatthe road width is known
It is commonly assumed that the robot navigates parallelto the curb It is reasonable to assume that the robot ismovingalong the road without significant change of orientationin most cases Moreover the vertical surfaces of the curbare perpendicular to the road surface When we scan theroad environments using the LRF the road features arecomposed of straight lines with different orientations Inorder to distinguish different line segments that correspondto the road surface the curbs and the sidewalk it is helpfulto assume that the robotrsquos heading direction points forwardalong the road The road width is assumed to be known bygiven map information
Thefirst attribute is used to select the curb candidatesTheline segments that satisfy the following condition are selectedas the curb candidates
1198861=
120587
2
plusmn 120576 (1)
Mathematical Problems in Engineering 3
(1) 119871119894larr the LRF measurement
(2) 119871119884119894
larr 119910 coordinate of the LRF measurement(3)119873 larrThe number of the LRF measurement points(4)119877119884larr Expected 119910 range of the road surface points
(5) for 119894 larr 1 to119873
(6) if 119871119884119894
isin 119877119884 then
(7) 119871119903larr save 119871
119894as candidate for the road surface
(8) 120579119903larr angle of candidate for the road surface
(9) 119872 larrThe number of candidates for the road surface(10) end if(11) end for(12) for 119895 larr 1 to119872
(13) if 10038171003817100381710038171003817120579119903119895
10038171003817100381710038171003817le 120579119890 then
(14) 119871119891larr save 119871
119903119895as the road surface
(15) end if(16) end for(17) return (119871
119891)
Algorithm 1 Road surface extraction
LRF coordinate
Robot coordinate
Curb
Curb
Road
A
B
C
DF
ZL
YL
df
120572tXL
XR
YR
ZR
120579f
wr
O
Figure 1 The configuration of a robot and installation of a LRF
where 1198861= |120579119891minus 120579119888| 120576 = tolerance
Once the curb candidates are determined attributes 2 3and 4 are used to extract the correct curb out of the curbcandidatesThe attribute values 119886
2 1198863 and 119886
4that correspond
to each attribute are numerically calculated for the pair ofright and left curb candidates as follows
1198862= 119889119891minus avg (119910C119877 119910C119871)
1198863= 120579C119877 minus 120579C119871
1198864= 119908119903minus 119908119888
(2)
CurbRoadLRF
A
B C
D
Extracted road surface
Figure 2 Ideal model of semiconstructed environment (blue dottedline LRF data red line extracted road surface)
119908119888is the gap between the right and left curb points (119908
119888=
119909C119877 minus 119909C119871) When a curb exists on only one side 1198862and
1198863are computed from the curb candidates for one side 119886
4is
assumed to be 0 The data vector of the curb candidates isgiven as follows
x119894= [1198862
1198863
1198864]
119879
(3)
23 Curb Extraction Using Kernel Fisher Discriminant Anal-ysis (KFDA) KFDA is applied to extract the correct curbfrom the curb candidates KFDA aims to find a discriminantfunction for optimal data classification Therefore the dis-criminant function can be used to classify the curb candidatesas curb and noncurb class The curb extraction is conductedby the following procedure First the training data withclass information are selected The discriminant function isderived from the offline computation of the training dataWhen the discriminant function is obtained classificationof the curb candidates is carried out by the discriminantfunction in real time
4 Mathematical Problems in Engineering
The discriminant function 120572 is defined as a vector tomaximize the following object function in the kernel featurespaceF Consider the following
119869 (120572) =
120572119879119878Φ
119861120572
120572119879119878Φ
119882120572
(4)
The ldquobetween-class variance matrixrdquo 119878Φ119861and the ldquowithin-
class variance matrixrdquo 119878Φ119882are defined as follows
119878Φ
119861= sum
119888
ℓ119888(120581119888120581119879
119888minus 120581120581119879)
119878Φ
119882= 119870119870
119879minus sum
119888
ℓ119888120581119888120581119888
119879
(5)
with 120581119888
= (1ℓ119888) sum119894isin119888
119870119894119895and 120581 = (1ℓ)sum
119894119870119894119895 ℓ is the
number of total training samples and ℓ119888is the number of class
samplesTraining data 119909
1 1199092 119909
ℓ consist of data with obvious
class information Each sample xtraining119894 isin R3 belongs to oneof two classes that include curb and noncurb class In order toobtain equivalent effects on classification the components ofeach sample should be normalized Consider the following
x(119896)119894
=
x(119896)119894
minus 120583(119896)
120590(119896)
(6)
Here 120583(119896) and 120590(119896) are themean and standard deviation of
each attribute respectivelyThe training data that aremappedto the kernel feature space are represented by an ℓ times ℓmatrix119870 The Gaussian kernel is used for mapping the data ontokernel feature spaceF Consider the following
119870119894119895= 119896 (x
119894 x119895) = exp(minus
10038171003817100381710038171003817x119894minus x119895
10038171003817100381710038171003817
2
21205902
) (7)
120590 is the control parameter that needs to be tuned toimprove classification performance [19] If 120590 is too small theoverfitting problem may take place Although the classifi-cation accuracy with respect to the training data increasesthe classification performance with respect to the test databecomes poor under the occurrence of the overfitting If 120590is too large the underfitting problem may take place Theclassification performance will not be satisfactory at all caseswhen the underfitting takes place Therefore 120590 should becarefully selected In this paper 120590 is manually tuned underthe consideration of experimental performances
The discriminant function that maximizes the objectfunction in (4) is derived by an eigenvalue problem In orderto project the training data onto a one-dimensional (1D)solution space the eigenvector that corresponds to the largesteigenvalue is defined as the discriminant function 120572 for dataclassificationThe discriminant function 120572 is given by an ℓtimes1
vector Consider the following
119878Φ
119861120572 = 120582119878
Φ
119882120572 (8)
The classification of the training data is conducted byan inner product of the data matrix 119870 and the discriminant
function120572The projected training data119910training are distributedin the 1D solution space Consider the following
119910training = 120572 sdot 119870 (9)
The class of test data can be predicted by using thediscriminant function 120572 The test data denote the curbcandidates The test data xtest is projected to the 1D solutionspace as shown in the following equation
119910test = sum
119894
120572119894119896 (xtraining119894 xtest) (10)
The class properties of the training data are used to predictthe class of the test data 119910test The Mahalanobis distancesbetween each class and the test data are computed by thefollowing equation
119889 (119910test 120583Φ
119888) =
(119910test minus 120583Φ
119888)
2
(120590Φ
119888)2
(11)
where 120583Φ
119888and 120590
Φ
119888denote the mean and standard deviation
of the class distribution respectively The class of the testdata is determined as the class with the smallest Mahalanobisdistance When the test data are classified as the curb classthey are extracted as the curb
3 Outdoor Localization Using Curb Feature
31 System Design This paper adopts EKF to estimate therobot pose using curb features EKF is a well-known methodfor mobile robot localization and sensor fusion [20ndash22]When the initial pose of the robot and adequate observationsare provided the pose of the robot can be estimated bycorrecting the odometry error The EKF process consists of aprediction step and an update step in sampling time 119896 DGPSand an LRF are used to correct odometry errors Figure 3shows a block diagram of the localization process
32 Measurement Uncertainty Model The GPS error mainlyoccurs due to the following two factors One is the pseu-dorange errors caused by systematic factors Another is thegeometric constellation of satellites In this paper DGPS isused to minimize the pseudorange errors The uncertaintymodel for DGPS is computed under the consideration of theldquodilution of precisionrdquo in relation to the geometric constella-tion of satellites and the pseudorange error or so-called ldquouser-equivalent range errorrdquo [23] Consider the following
RDGPS119896 = [
1205902
119909120590119909119910
120590119909119910
1205902
119910
]1205902
UERE (12)
The error covarianceRDGPS119896 is given as (12)The elementsof the covariance matrix are provided by the DGPS receiverin real time
Several studies were proposed to define the error covari-ance of line features [24 25] However the uncertaintymodels are appropriate for a static condition or a low-speeddriving condition on a flat surface However the outdoor
Mathematical Problems in Engineering 5
DGPS
Robot
Laser rangefinder
Position(xDGPS yDGPS )
Incrementaldisplacement
(ΔsΔ120579)
Curb information
Map
PredictionCorrectedrobot pose
Localizer
1st measurementcorrection
2nd measurementcorrection
(R120572Rr)
(W120572iWri)
xminusk
Pminusk
x+k2x+k1
zDGPS k
RDGPS k
zcurb k
Rcurb k
P+k2P+k1
Figure 3 A block diagram of localization process
Extracted curb
Actual curb
120572i
ri120579i
di
Figure 4 Noise model of the extracted curb
mobile robots are usually driven in the uneven terrain Themeasurement noise of the extracted curb occurs due to thewobble of the robot Therefore the uncertainty model forthe curb needs to be defined by experiments under resultantdriving conditions
In order to define the error covariance Rcurb we considerthe noise model of the extracted curb as shown in Figure 4The information of the extracted curb contains estimationerrors in the range and angle Therefore the angle andrange measurements for the extracted curb are composed ofthe ldquotruerdquo angle 120579
119894and the ldquotruerdquo range 119889
119894 along with the
estimation errors Consider the following
120572119894= 120579119894+ 120576120572119894
119903119894= 119889119894+ 120576119903119894
(13)
where 120576120572119894
and 120576119903119894are the estimation errors for a curb and
have random variances 1205902120572and 120590
2
119903 respectively The ground
truth of the curb locations can be measured by an additionalLRF which is attached to the side of the robot Because theadditional LRF is directly facing the curb the range data fromthe additional LRF provide reliable geometric informationof the curb during robotrsquos movement The measurement ofthe curb from the additional LRF is more accurate than theforward-pointing tilted LRF because the number of rangedata points that correspond to the curb is much larger Thecurb is represented as a straight line by the application of theleast square method The ground truth implies the relativerange and orientation of the curb The estimation errorsare computed for the extracted curbs Therefore the errorcovariance of the curb is defined by the distribution of theestimation errors By using a large number of measurementsof the estimation errors 120576
120572and 120576
119903 the error covariance is
calculated as follows
Rcurb = [
1205902
120572120590120572119903
120590119903120572
1205902
119903
] = [
119864 (120576120572120576119879
120572) 119864 (120576
120572120576119879
119903)
119864 (120576119903120576119879
120572) 119864 (120576
119903120576119879
119903)
] (14)
The covariance matrices are experimentally defined asconstant values for the left and right curbs
33 Extended Kalman Filter Localization Using Curb FeatureThe odometry data from the wheel encoders are used topredict the robot pose By using the incremental distanceΔ119904119896minus1
and orientationΔ120579119896minus1
the predicted robot pose is givenby the following equation
xminus119896= 119891 (x
119896minus1 u119896minus1
) =
[
[
[
[
[
[
119909minus
119896minus1+ Δ119904119896minus1
cos(120579minus
119896minus1+
Δ120579119896minus1
2
)
119910minus
119896minus1+ Δ119904119896minus1
sin(120579minus
119896minus1+
Δ120579119896minus1
2
)
120579minus
119896minus1+ Δ120579119896minus1
]
]
]
]
]
]
(15)
6 Mathematical Problems in Engineering
Extracted curb(from 1st estimated robot perspective)
Actual curb(curb line map)
W
R
Wri
W120572i
Rrk
R120572k
W+
k1
Wy+k1
Wx+k1
Figure 5 Extracted curb features and a line map with respect to theglobal coordinate frame
The state vector xminus119896= [119909minus
119896119910minus
119896
120579minus
119896]
119879
is the predicted robotpose at sampling time 119896 When the initial pose of the robot isgiven the robot pose is represented by 119909 119910 and 120579 in a globalcoordinate frameTheuncertainty of the predicted robot poseconsistently increases because of the accumulative errors ofthe odometry
In order to correct the odometry error the first measure-ment correction is performed using DGPS measurementsThe update frequency is set to 1Hz on the basis of theDGPS measurement frequency When the available positionmeasurement is provided the observation vector is given inglobal coordinates Consider the following
zDGPS119896 = [119909DGPS119896 119910DGPS119896]119879
(16)
The observation model for the current state is describedas follows
hDGPS (xminus
119896 119896) = [119909
minus
119896119910minus
119896]
119879
(17)
The measurement Jacobian matrixH119896is given as follows
HDGPS119896 =120597h (xminus119896 119896)
120597xminus119896
= [
1 0 0
0 1 0] (18)
zcurb119896 = [120572119896
119903119896]
119879
(19)
The second measurement correction is conducted byusing the curb features The observation vector for theextracted curb is given by (19) When the curbs are extractedon both sides there are two measurement vectors for the leftand right curbs as shown in Figure 5 The sequence of thesecond measurement correction is from the right curb to theleft curbThe update rate is 5Hz if the curbs are continuouslyextracted
The robot pose is corrected by comparing the curb withthe map The extracted curb is matched with the 119894th line ofthe curb map The observation model for the 119894th line 119882z
119894=
[119882120572119894
119882119903119894]
119879
and the robot pose at time 119896 is given by thefollowing equation
hcurb (x+
1198961 119896 119894)
= [
119882120572119894minus120579+
1198961
119882119903119894minus 119909+
1198961cos 119882120572
119894+ 119910+
1198961sin 119882120572
119894
]
(20)
The Jacobian matrixH119896is defined as follows
Hcurb119896 =120597h (x+1198961
119896 119894)
120597x+1198961
= [
0 0 minus1
minus cos 119882120572119894minus sin 119882120572
1198940
]
(21)
The consistency of EKF relies on the observation modelIf an erroneous sensor observation is provided the systemdoes not provide a consistent result Therefore the outliersthat lie outside of the uncertainty bounds should be rejectedA normalized innovation squared (NIS) test is implementedin order to confirm the consistency of the filter NIS valuehas a 120594
2 distribution with respect to 119899 degrees of freedomConsider the following
NIS119896= (z119896minus h (x+
119896 119896))
119879Sminus1119896
(z119896minus h (x+
119896 119896)) le 120594
2 (22)
where S119896is the innovation matrix which is defined as S
119896=
H119896Pminus119896H119879119896+R119896 The NIS value for valid measurements should
be within the threshold of the 1205942 distribution However the
erroneous measurements are discarded when the NIS valuelies outside the threshold boundary A threshold value thatcorresponds to a 95 confidence region is used for outlierrejection
4 Experimental Results
41 Experimental Setup Figure 6 shows the sensor systemattached to the mobile robot The outdoor mobile robotis a Pioneer P3-AT a commercial outdoor platform ofMobileRobots The wheel encoders attached to the drivingmotors provide odometry information SICK LMS-100 wasused to detect the curb The LRF was tilted by 5∘ towardthe ground A Novatel DGPS system was used to measurethe global position The robot was equipped with a roverantenna and a base stationwas located on the roof of a nearbybuilding The ldquotruerdquo value for the curb and the ground truthwere measured using an additional LRF (HOKUYO URG-04lx) attached to the side of the robot
The experiment was performed in Korea University inSeoul Korea as shown in Figure 7 The robot was drivenmanually along the yellow dashed line from ldquoSrdquo to ldquoGrdquoThe curbs along the experimental path are represented assolid green lines The target environment has semistructuredgeometry that is composed of paved roads and curbs inmost of the region Furthermore there are tall buildings andtunnels that degrade the DGPS precisionThe travel distancealong the experimental path was 775m and average speed ofthe robot was 05ms
Mathematical Problems in Engineering 7
DGPS baseDGPS rover
Pioneer P3-AT
LaptopLaser range
finder
Communicate
Figure 6 Sensor system attached to mobile robot
Reference pathCurb map
SG
Figure 7 Experimental environment
42 Curb Extraction Results The curb extraction process ina semistructured road environment is shown in Figure 8Figure 8(a) shows the road environment where the experi-ment was performed The red dotted line represents the scanarea of the tilted LRF Figure 8(b) shows the extracted roadsurface on the basis of the scanned LRF data in the roadenvironment When the road surface is extracted the linesegments that satisfy attribute 1 in Section 22 are selected asthe curb candidates Figure 8(c) shows the line segments thatcorrespond to the curb candidates The first and the secondcandidates for each side of the curbs are represented by blueand green lines respectively There are two candidates oneach sideTherefore four pairs of candidates can be extractedas curbs (R1 L1) (R1 L2) (R2 L1) and (R2 L2) The classprediction results for each pair of curb candidates are listedin Table 1 The pairs of candidates (R1 L1) and (R1 L2)are classified as the curb class Finally candidate (R1 L1) isextracted as the curbs as shown in Figure 8(d) which hasthe smallest Mahalanobis distance with respect to the curb
Table 1 Class prediction for pairs of curb candidates
Candidates Mahalanobis distance Class predictionCurb class Noncurb class
1198831(R1 L1) 00005 1634922 True Curb
1198832(R1 L2) 19779 2025195 True Curb
1198833(R2 L1) 1056307 41180 False Curb
1198834(R2 L2) 1102497 32296 False Curb
Table 2 Classification results including confusion matrix
Instance PCA KFDAClass correct 4338 913 4683 986Class incorrect 413 87 68 14Total 4751 100 4751 100
Classified as Classified asTrue curb False curb True curb False curb
True curb 3524(971)
106(29)
3566(982)
64(18)
False curb 307(274)
814(726)
4(04)
1117(996)
class If the LRF data that correspond to the vertical surfaceare detected the proposed method will perform successfullydespite the small and less distinct curbs
The curb extraction was performed while the robotnavigates through the experimental path Figure 9 showsthe curb mapping result from the curb extraction The curbmap is shown in the right bottom in Figure 9 The extractedcurbs are denoted by the magenta dots The results indicatethat most of the curbs along the experimental path weresuccessfully extracted In order to demonstrate the robust-ness of the proposed method comparison of classificationperformance between our previousmethod and the proposedmethod is summarized in Table 2 The accuracy of the curbextractionwith PCAwas 913 for 4751 scanned datasetsTheaccuracy was improved to 986 with the proposed KFDAA confusion matrix is presented below The conventionalmethod and the proposed method show 971 and 982of true positive rate respectively The curb extraction isperformed successfully by the application of both methodsHowever the most important factor in the curb extraction isto reduce the false detection rate False detection is that thenoncurb data are misclassified as the curb dataThe accuracyof the estimated pose can be decreased when the false curbsare used for localization The false detection rate was 274with PCA The false detection rate was reduced to 04 withthe proposed KFDA The result implies that most of thenoncurb data were classified as noncurb data correctly
43 Uncertainty Measurement Results The DGPS measure-ments are represented by red dots along the experimentalpath in Figure 10(a) The areas with large DGPS errors arerepresented by AndashF Figure 10(b) shows the standard devia-tion of the DGPS measurements The standard deviation ofthe DGPS is about 2m in open area There were temporalblackouts in areas B D and E due to satellite blockage
8 Mathematical Problems in Engineering
(a)
0 1 2 3
0
1
2
3
4
5
6
7
Detected road surface
minus1minus2
minus1
minus2minus3minus4minus5minus6
y(m
)
x (m)
(b)
0 1 2 3
0
1
2
3
4
5
6
7
minus1minus2
minus1
minus2minus3minus4minus5minus6
y(m
)
x (m)
R2
L1 R1
L2
(c)
Extracted curbs
0 1 2 3
0
1
2
3
4
5
6
7
minus1minus2
minus1
minus2minus3minus4minus5minus6
y(m
)
x (m)
(d)
Figure 8 Curb extraction results (a) Road environment (b) Road surface detection (c) Curb feature candidates on both sides (d) Extractedcurb
0 50 100 150
0
50
100
150
y(m
)
x (m)
minus50
minus50minus100
Figure 9 Curb mapping result on experimental path
Mathematical Problems in Engineering 9
Reference pathDGPS measurements
SG
A
B
DE
C
F
(a)
0 5 10 15 20 25 300
2
4
6
8
Time (min)
Dist
ance
(m)
A B C D E F
120590DGPS
(b)
Figure 10 (a) DGPS measurement and (b) DGPS uncertainty measurement (1120590 bound)
CurbAdditional LRF
Figure 11 Additional LRF for ground truth of the curbs
The uncertainty measurements in areas B D and E werealmost infinite as shown in Figure 10(b) Furthermore largeDGPS errors occurred in areas A C and F due to thedegraded satellite signals In particular measurement errorswere 21m on average in area F The standard deviation thatwas measured in area F was 64m on average The resultimplies that the regional properties ofDGPSwere obtained bymeasuring the DGPS uncertainty in real time However theprecision of the localization only by DGPS can be decreasedwhen the robot navigates near the buildings
The curb estimation errors are considered in order todefine the error covariance The most accurate result forthe quantitative curb uncertainty is obtained by measuringthe estimation errors in experimental environments Theestimation errors were measured while the robot navigatesthrough the road with curbs Ground truth for the curb wasprovided by an additional LRF that is attached to the sideof the robot as shown in Figure 11 Ground truth of thecurb was provided by line feature from the additional LRFdata Experiments were conducted in order to measure theestimation errors prior to the localization experiment The
Table 3 Error covariance of extracted curb
Range std 120590119903
Angle std 120590120572
Correlation 120590119903120572
Right curb 01620m 00575 rad 00035msdotradLeft curb 01614m 00649 rad minus00034msdotrad
following results show the estimation errors for the range andangle of the extracted curb
Figure 12 shows the histogram of the curb estimationerrors for each sideThe number of the estimation error mea-surements is approximately 5000 The covariance matrix ofthe curb was computed from the distributions of estimationerrors The elements of error covariance for each side of thecurb are listed in Table 3
The covariance representation for the extracted curbs isshown in Figure 13 The extracted curbs are represented byblue lines and the error bounds for the curbs are representedby green dotted lines The resultant curbs exist within theerror bounds with 95 confidence
44 Outdoor Localization Results The localization results areshown in Figure 14 The proposed method was comparedwith the conventional framework for outdoor localizationthat combines DGPS measurement with odometry The bluedash-dot line represents the localization results correctedonly by the DGPS measurements The estimated paths showsome difference with respect to the reference path (yellowdotted line) in area AndashF due to theDGPS errorsThemagentaline represents the localization results corrected byDGPS andthe extracted curb When the curb information is appliedthe results show that the robot position well matches thereference path even if the DGPS errors are large or a blackoutoccurs (area AndashF) It is clear that the curb information plays adominant role The following part presents the localizationerrors in area AndashF as shown in Figure 14 The localizationerrors were compared with the conventional framework thatcombines DGPS measurement with odometry The ground
10 Mathematical Problems in Engineering
0
100
200
300Histogram of left curb range errors
Estimation error (m)
N(c
ount
)
040302010minus01minus02minus03minus04
0
100
200
300
400Histogram of left curb angle errors
Estimation error (rad)
N(c
ount
)
010050minus005minus01
(a)
Estimation error (m)
0
200
400
600
800Histogram of right curb range errors
N(c
ount
)
040302010minus01minus02minus03minus04
0
200
400
600
800Histogram of right curb angle errors
Estimation error (rad)
N(c
ount
)
010050minus005minus01
(b)
Figure 12 Distribution of estimation errors for (a) left and (b) right curbs
0 1 2 3
0
1
2
3
4
5
6
7
Range dataExtracted curbCovariance (95 confidence)
minus1minus2
minus1
minus2minus3minus4minus5minus6
y(m
)
x (m)
Figure 13 Extracted curbs and covariance representation
truth was computed using the additional LRF attached to theside of the robot
Figure 15 shows the lateral errors of the localizationresults The position errors when using the fusion of theodometry and DGPS are shown in Figure 15(a) The lateralerrors in each areawere usually greater than 1m In particularthe maximum error in area F was 5m In contrast thelocalization result which was corrected by odometry DGPSand curb information shows that the lateral errors werewithin 06m across the entire area as shown in Figure 15(b)
SG
A
B
DE
C
F
Reference pathEKF (odometry + DGPS)EKF (odometry + DGPS + curb)
Figure 14 Localization results in semistructured road environment
Therefore the proposed method shows robust performancein terms of lateral position estimation errors despite the largeDGPS errorsTheheading errors of the localization results arerepresented in Figure 16 The result that was corrected usingonly the DGPS data is shown in Figure 16(a) The headingerrors were greater than 1∘ on averageThe variancewas largerthan 2∘ However when the curb information is used forcorrection the heading errors were remarkably decreasedFurthermore the errors rarely exceed 3∘ in the entire areaIn experiments the proposed method showed precise androbust performance for the lateral and heading errors despitethe large DGPS errors and a temporal blackout
Mathematical Problems in Engineering 11
0
1
2
3
4
5
Late
ral e
rror
s (m
)
A B C D E FSection
EKF (odometry + DGPS)
minus1
minus2
minus3
minus4
(a)
A B C D E F
0
1
2
3
4
5
Late
ral e
rror
s (m
)Section
EKF (odometry + DGPS + curb)
minus1
minus2
minus3
minus4
(b)
Figure 15 Lateral errors (a) corrected by DGPS and (b) corrected by DGPS and extracted curb
A B C D E FSection
EKF (odometry + DGPS)
0
5
10
15
Ang
ular
erro
rs (d
eg)
minus5
minus10
(a)
A B C D E F
0
5
10
15
Ang
ular
erro
rs (d
eg)
Section
EKF (odometry + DGPS + curb)
minus5
minus10
(b)
Figure 16 Heading errors (a) corrected by DGPS and (b) corrected by DGPS and extracted curb
5 Conclusion
This paper presents a localization method for outdoor robotsusing curb features in semistructured road environmentsA reliable curb extraction scheme is proposed to classifythe curb candidates as curb and noncurb classes Mostof the curbs in an experimental path are extracted withhigh accuracy An EKF-based localization is also proposed
to combine the extracted curbs with odometry and DGPSmeasurements The uncertainty models of the sensors aredefined by experiments to provide a practical solution forlocalization From experimental results the robustness of theproposed method is demonstrated in real road experimentsThe curb features can correct significantly the lateral positionand heading errors in dense area where the DGPS signal getsdegraded by buildings
12 Mathematical Problems in Engineering
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This research was supported in part by the MKE (TheMinis-try of Knowledge Economy) Korea under the HumanResources Development Program for Convergence RobotSpecialists Support Program supervised by the NIPA(National IT Industry Promotion Agency) (NIPA-2013-H1502-13-1001) This work was also supported by theNational Research Foundation of Korea (NRF) Grant fundedby Korea Government (MEST) (2013-029812)
References
[1] S Thrun M Montemerlo H Dahlkamp et al ldquoStanley therobot that won the DARPA Grand Challengerdquo Journal of FieldRobotics vol 23 no 9 pp 661ndash692 2006
[2] M Buehler K Lagnemma and S Singh The DARPA UrbanChallenge Autonomous Vehicles in City Traffic Springer NewYork NY USA 2009
[3] A Soloviev ldquoTight coupling of GPS laser scanner and iner-tial measurements for navigation in urban environmentsrdquo inProceedings of the IEEEION Position Location and NavigationSymposium pp 511ndash525 Monterey Calif USA May 2008
[4] S Panzieri F Pascucci and G Ulivi ldquoAn outdoor navigationsystem using GPS and inertial platformrdquo IEEEASME Transac-tions on Mechatronics vol 7 no 2 pp 134ndash142 2002
[5] E-J Jung andD-J Yi ldquoTask-oriented navigation algorithms foran outdoor environment with colored borders and obstaclesrdquoIntelligent Service Robotics vol 6 no 2 pp 69ndash77 2013
[6] S Kim J Kang andM Jin Chung ldquoProbabilistic voxelmappingusing an adaptive confidence measure of stereo matchingrdquoIntelligent Service Robotics vol 6 no 2 pp 89ndash99 2013
[7] M Joerger and B Pervan ldquoRange-domain integration of GPSand laser-scanner measurements for outdoor navigationrdquo inProceedings of the 19th International Technical Meeting of theSatellite Division of The Institute of Navigation (ION GNSS rsquo06)pp 1115ndash1123 Fort Worth Tex USA September 2006
[8] M Hentschel O Wulf and B Wagner ldquoA GPS and laser-basedlocalization for urban and non-urban outdoor environmentsrdquoin Proceedings of the IEEERSJ International Conference on Intel-ligent Robots and Systems pp 149ndash154 Nice France September2008
[9] A Georgiev and P K Allen ldquoLocalizationmethods for amobilerobot in urban environmentsrdquo IEEE Transactions on Roboticsvol 20 no 5 pp 851ndash864 2004
[10] Y Morales T Tsubouchi and S Yuta ldquoVehicle localizationin outdoor mountainous forested paths and extension of two-dimensional road centerline maps to three-dimensional mapsrdquoAdvanced Robotics vol 24 no 4 pp 489ndash513 2010
[11] W SWijesoma K R S Kodagoda andA P Balasuriya ldquoRoad-boundary detection and tracking using ladar sensingrdquo IEEETransactions onRobotics andAutomation vol 20 no 3 pp 456ndash464 2004
[12] M Jabbour and P Bonnifait ldquoGlobal localization robust toGPS outages using a vertical ladarrdquo in Proceedings of the 9th
International Conference on Control Automation Robotics andVision pp 1ndash6 December 2006
[13] P Bonnifait M Jabbour and V Cherfaoui ldquoAutonomousnavigation in urban areas using GIS-managed informationrdquoInternational Journal of Vehicle Autonomous Systems vol 6 no5 pp 83ndash103 2008
[14] Y Shin D Kim H Lee J Park and W Chung ldquoAutonomousnavigation of a surveillance robot in harsh outdoor environ-mentsrdquo Advances in Mechanical Engineering vol 2013 ArticleID 837484 15 pages 2013
[15] Y Shin C Jung andWChung ldquoDrivable road region detectionusing a single laser range finder for outdoor patrol robotsrdquo inProceedings of the IEEE Intelligent Vehicles Symposium (IV rsquo10)pp 877ndash882 San Diego Calif USA June 2010
[16] D Kim and W Chung ldquoLocalization of outdoor mobile robotsusing road featuresrdquo in Proceedings of the 8th International Con-ference on Ubiquitous Robots and Ambient Intelligence (URAIrsquo11) pp 363ndash365 Incheon Republic of Korea November 2011
[17] S Mika G Ratsch J Weston B Scholkopf and K MullerldquoFisher discriminant analysis with kernelsrdquoNeural Networks forSignal Processing vol 9 pp 41ndash48 1999
[18] S Mika G Ratsch and K R Muller ldquoA mathematical pro-gramming approach to the kernel fisher algorithmrdquo Advancesin Neural Information Processing vol 13 pp 591ndash597 2001
[19] G Camps-Valls and L Bruzzone Kernel Methods for RemoteSensing Data Analysis JohnWiley amp Sons New York NY USA2009
[20] R E Kalman ldquoA new approach to linear filtering and predictionproblemsrdquo Journal of Basic Engineering vol 82 no 1 pp 35ndash451960
[21] R E Kalman and R S Bucy ldquoNew results in linear filtering andprediction theoryrdquo Journal of Basic Engineering vol 83 no 3pp 95ndash108 1961
[22] J J Leonard and H F Durrant-Whyte Directed Sonar Sensingfor Mobile Robot Navigation Kluwer Academic DordrechtTheNetherlands 1992
[23] B W Parkinson and J J Spilker Global Positioning SystemTheory and ApplicationsThe American Institute of Aeronauticsand Astronautics Washington DC USA 1996
[24] K O Arras and R Y Siegwart ldquoFeature extraction and sceneinterpretation for map-based navigation and map buildingrdquo in12th Mobile Robots Conference vol 3210 of Proceedings of SPIEpp 42ndash53 Pittsburgh Pa USA January 1998
[25] S T Pfister S I Roumeliotis and J W Burdick ldquoWeighted linefitting algorithms for mobile robot map building and efficientdata representationrdquo in Proceedings of the IEEE InternationalConference on Robotics and Automation pp 1304ndash1311 Septem-ber 2003
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
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Mathematical Problems in Engineering
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Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
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Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
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Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
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CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
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Operations ResearchAdvances in
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Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
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Algebra
Discrete Dynamics in Nature and Society
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Decision SciencesAdvances in
Discrete MathematicsJournal of
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Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
2 Mathematical Problems in Engineering
a vehicle is reduced by map matching approach using theextracted curb point However the correction of the headingangle is not considered because there is no angle informationof the curb
A method for traversable region detection using roadfeatures such as road surface curbs and obstacles is pro-posed in our previous works [14ndash16] The curb features arederived by the geometric features of the road to obtain curbcandidates In order to extract the correct curb among thecurb candidates a validation gate is derived from principalcomponent analysis (PCA)The curb extraction is performedsuccessfully in a road environment However there was afundamental limitation on PCA The validation gate doesnot consider the classification of the curb and noncurbdata Consequently false detection where noncurb data areextracted as curbs may occur The precision of estimatedpose is decreased when the false detection data are usedfor localization Therefore it is important to reduce the falsedetection rate
The contribution of this paper can be summarized by twoschemes The first contribution is the robust curb extractionscheme by using a single Laser Range Finder (LRF) Inorder to reduce the number of false detection of the curbsthe classification of the curb data and the noncurb datais conducted by using Kernel Fisher Discriminant Analysis(KFDA) in [17ndash19] On the basis of our previous worksgeometrical features of the curb are defined The secondcontribution is the integrated localization scheme using curbfeatures on the basis of quantitative sensor uncertainty mod-els In particular the uncertaintymodel for the extracted curbis quantitatively determined from experiments ExtendedKalman Filter (EKF) is exploited to combine the curb featureswith odometry and Differential Global Positioning System(DGPS) information The extracted curbs enable accurateestimation of the pose of the robot even when the temporalGPS blackout takes place
The remainder of this paper is organized as followsA method for curb extraction is presented in Section 2Section 3 describes the localization method for an outdoormobile robot using the extracted curb It also introducesthe uncertainty models for the sensor measurements Theexperimental results of the proposedmethod are presented inSection 4 Finally the conclusion of this research is presentedin Section 5
2 Road Feature Extraction
21 System Configuration Figure 1 shows the configurationof the mobile robot and the LRF coordinate configurationA single onboard LRF with a tilting angle of 120572
119905is used to
extract road features such as the road surface and curbsThe following list shows the nomenclature for road featureextraction The variables are described with respect to therobot coordinate frame
119908119903 road width
120572119905 nominal tilt angle of LRF
120579119891 angle between the detected road surface points
and 119884119877-axis
119889119891 horizontal look-ahead distance from the robot to
the road surface points(119909C119877 119910C119877) coordinates of the right curb edge (pointC)120579C119877 angle between the right curb and 119884
119877-axis
(119909C119871 119910C119871) coordinates of the left curb edge (point B)120579C119871 angle between the left curb and 119884
119877-axis
22 Road Feature Detection A road feature detection schemewas proposed in our previous works [14 15] The previousworks on road feature detection are briefly reviewed Thefirst step for the road feature detection is the road surfaceextraction In order to identify the road surface the LRFmeasurements in expected road region 119877
119910are selected as
candidates for the road surface 119871119903 Multiple line segments
are constructed by combining consecutive data points of 119871119903
The angle of the road surface is parallel with the 119883119877-axis
in the ideal case Therefore the range data 119871119903are saved as
road surface points 119871119891if the angle of the line segment is
within threshold 120579119890 The road surface is extracted as a line
by using the least square method The extracted road surfaceprovides 120579
119891and 119889
119891from the robotThe overall algorithm can
be summarized in Algorithm 1Figure 2 shows the ideal model of a semistructured road
environment The geometrical features of the road can beused to extract the curb features The curb has the followingfour attributes
(Att 1) The angular difference between the curb ori-entation (120579
119888) and road surface angle (120579
119891) is close to
90∘(Att 2) The gap between the horizon distance of theroad surface (119889
119891) and the 119910 value of the curb point (B
or C) is close to 0(Att 3) The angular difference between the left curb( AB) and the right curb ( CD) is close to 0(Att 4)The difference between the roadwidth and thegap between two curbs is close to 0 It is assumed thatthe road width is known
It is commonly assumed that the robot navigates parallelto the curb It is reasonable to assume that the robot ismovingalong the road without significant change of orientationin most cases Moreover the vertical surfaces of the curbare perpendicular to the road surface When we scan theroad environments using the LRF the road features arecomposed of straight lines with different orientations Inorder to distinguish different line segments that correspondto the road surface the curbs and the sidewalk it is helpfulto assume that the robotrsquos heading direction points forwardalong the road The road width is assumed to be known bygiven map information
Thefirst attribute is used to select the curb candidatesTheline segments that satisfy the following condition are selectedas the curb candidates
1198861=
120587
2
plusmn 120576 (1)
Mathematical Problems in Engineering 3
(1) 119871119894larr the LRF measurement
(2) 119871119884119894
larr 119910 coordinate of the LRF measurement(3)119873 larrThe number of the LRF measurement points(4)119877119884larr Expected 119910 range of the road surface points
(5) for 119894 larr 1 to119873
(6) if 119871119884119894
isin 119877119884 then
(7) 119871119903larr save 119871
119894as candidate for the road surface
(8) 120579119903larr angle of candidate for the road surface
(9) 119872 larrThe number of candidates for the road surface(10) end if(11) end for(12) for 119895 larr 1 to119872
(13) if 10038171003817100381710038171003817120579119903119895
10038171003817100381710038171003817le 120579119890 then
(14) 119871119891larr save 119871
119903119895as the road surface
(15) end if(16) end for(17) return (119871
119891)
Algorithm 1 Road surface extraction
LRF coordinate
Robot coordinate
Curb
Curb
Road
A
B
C
DF
ZL
YL
df
120572tXL
XR
YR
ZR
120579f
wr
O
Figure 1 The configuration of a robot and installation of a LRF
where 1198861= |120579119891minus 120579119888| 120576 = tolerance
Once the curb candidates are determined attributes 2 3and 4 are used to extract the correct curb out of the curbcandidatesThe attribute values 119886
2 1198863 and 119886
4that correspond
to each attribute are numerically calculated for the pair ofright and left curb candidates as follows
1198862= 119889119891minus avg (119910C119877 119910C119871)
1198863= 120579C119877 minus 120579C119871
1198864= 119908119903minus 119908119888
(2)
CurbRoadLRF
A
B C
D
Extracted road surface
Figure 2 Ideal model of semiconstructed environment (blue dottedline LRF data red line extracted road surface)
119908119888is the gap between the right and left curb points (119908
119888=
119909C119877 minus 119909C119871) When a curb exists on only one side 1198862and
1198863are computed from the curb candidates for one side 119886
4is
assumed to be 0 The data vector of the curb candidates isgiven as follows
x119894= [1198862
1198863
1198864]
119879
(3)
23 Curb Extraction Using Kernel Fisher Discriminant Anal-ysis (KFDA) KFDA is applied to extract the correct curbfrom the curb candidates KFDA aims to find a discriminantfunction for optimal data classification Therefore the dis-criminant function can be used to classify the curb candidatesas curb and noncurb class The curb extraction is conductedby the following procedure First the training data withclass information are selected The discriminant function isderived from the offline computation of the training dataWhen the discriminant function is obtained classificationof the curb candidates is carried out by the discriminantfunction in real time
4 Mathematical Problems in Engineering
The discriminant function 120572 is defined as a vector tomaximize the following object function in the kernel featurespaceF Consider the following
119869 (120572) =
120572119879119878Φ
119861120572
120572119879119878Φ
119882120572
(4)
The ldquobetween-class variance matrixrdquo 119878Φ119861and the ldquowithin-
class variance matrixrdquo 119878Φ119882are defined as follows
119878Φ
119861= sum
119888
ℓ119888(120581119888120581119879
119888minus 120581120581119879)
119878Φ
119882= 119870119870
119879minus sum
119888
ℓ119888120581119888120581119888
119879
(5)
with 120581119888
= (1ℓ119888) sum119894isin119888
119870119894119895and 120581 = (1ℓ)sum
119894119870119894119895 ℓ is the
number of total training samples and ℓ119888is the number of class
samplesTraining data 119909
1 1199092 119909
ℓ consist of data with obvious
class information Each sample xtraining119894 isin R3 belongs to oneof two classes that include curb and noncurb class In order toobtain equivalent effects on classification the components ofeach sample should be normalized Consider the following
x(119896)119894
=
x(119896)119894
minus 120583(119896)
120590(119896)
(6)
Here 120583(119896) and 120590(119896) are themean and standard deviation of
each attribute respectivelyThe training data that aremappedto the kernel feature space are represented by an ℓ times ℓmatrix119870 The Gaussian kernel is used for mapping the data ontokernel feature spaceF Consider the following
119870119894119895= 119896 (x
119894 x119895) = exp(minus
10038171003817100381710038171003817x119894minus x119895
10038171003817100381710038171003817
2
21205902
) (7)
120590 is the control parameter that needs to be tuned toimprove classification performance [19] If 120590 is too small theoverfitting problem may take place Although the classifi-cation accuracy with respect to the training data increasesthe classification performance with respect to the test databecomes poor under the occurrence of the overfitting If 120590is too large the underfitting problem may take place Theclassification performance will not be satisfactory at all caseswhen the underfitting takes place Therefore 120590 should becarefully selected In this paper 120590 is manually tuned underthe consideration of experimental performances
The discriminant function that maximizes the objectfunction in (4) is derived by an eigenvalue problem In orderto project the training data onto a one-dimensional (1D)solution space the eigenvector that corresponds to the largesteigenvalue is defined as the discriminant function 120572 for dataclassificationThe discriminant function 120572 is given by an ℓtimes1
vector Consider the following
119878Φ
119861120572 = 120582119878
Φ
119882120572 (8)
The classification of the training data is conducted byan inner product of the data matrix 119870 and the discriminant
function120572The projected training data119910training are distributedin the 1D solution space Consider the following
119910training = 120572 sdot 119870 (9)
The class of test data can be predicted by using thediscriminant function 120572 The test data denote the curbcandidates The test data xtest is projected to the 1D solutionspace as shown in the following equation
119910test = sum
119894
120572119894119896 (xtraining119894 xtest) (10)
The class properties of the training data are used to predictthe class of the test data 119910test The Mahalanobis distancesbetween each class and the test data are computed by thefollowing equation
119889 (119910test 120583Φ
119888) =
(119910test minus 120583Φ
119888)
2
(120590Φ
119888)2
(11)
where 120583Φ
119888and 120590
Φ
119888denote the mean and standard deviation
of the class distribution respectively The class of the testdata is determined as the class with the smallest Mahalanobisdistance When the test data are classified as the curb classthey are extracted as the curb
3 Outdoor Localization Using Curb Feature
31 System Design This paper adopts EKF to estimate therobot pose using curb features EKF is a well-known methodfor mobile robot localization and sensor fusion [20ndash22]When the initial pose of the robot and adequate observationsare provided the pose of the robot can be estimated bycorrecting the odometry error The EKF process consists of aprediction step and an update step in sampling time 119896 DGPSand an LRF are used to correct odometry errors Figure 3shows a block diagram of the localization process
32 Measurement Uncertainty Model The GPS error mainlyoccurs due to the following two factors One is the pseu-dorange errors caused by systematic factors Another is thegeometric constellation of satellites In this paper DGPS isused to minimize the pseudorange errors The uncertaintymodel for DGPS is computed under the consideration of theldquodilution of precisionrdquo in relation to the geometric constella-tion of satellites and the pseudorange error or so-called ldquouser-equivalent range errorrdquo [23] Consider the following
RDGPS119896 = [
1205902
119909120590119909119910
120590119909119910
1205902
119910
]1205902
UERE (12)
The error covarianceRDGPS119896 is given as (12)The elementsof the covariance matrix are provided by the DGPS receiverin real time
Several studies were proposed to define the error covari-ance of line features [24 25] However the uncertaintymodels are appropriate for a static condition or a low-speeddriving condition on a flat surface However the outdoor
Mathematical Problems in Engineering 5
DGPS
Robot
Laser rangefinder
Position(xDGPS yDGPS )
Incrementaldisplacement
(ΔsΔ120579)
Curb information
Map
PredictionCorrectedrobot pose
Localizer
1st measurementcorrection
2nd measurementcorrection
(R120572Rr)
(W120572iWri)
xminusk
Pminusk
x+k2x+k1
zDGPS k
RDGPS k
zcurb k
Rcurb k
P+k2P+k1
Figure 3 A block diagram of localization process
Extracted curb
Actual curb
120572i
ri120579i
di
Figure 4 Noise model of the extracted curb
mobile robots are usually driven in the uneven terrain Themeasurement noise of the extracted curb occurs due to thewobble of the robot Therefore the uncertainty model forthe curb needs to be defined by experiments under resultantdriving conditions
In order to define the error covariance Rcurb we considerthe noise model of the extracted curb as shown in Figure 4The information of the extracted curb contains estimationerrors in the range and angle Therefore the angle andrange measurements for the extracted curb are composed ofthe ldquotruerdquo angle 120579
119894and the ldquotruerdquo range 119889
119894 along with the
estimation errors Consider the following
120572119894= 120579119894+ 120576120572119894
119903119894= 119889119894+ 120576119903119894
(13)
where 120576120572119894
and 120576119903119894are the estimation errors for a curb and
have random variances 1205902120572and 120590
2
119903 respectively The ground
truth of the curb locations can be measured by an additionalLRF which is attached to the side of the robot Because theadditional LRF is directly facing the curb the range data fromthe additional LRF provide reliable geometric informationof the curb during robotrsquos movement The measurement ofthe curb from the additional LRF is more accurate than theforward-pointing tilted LRF because the number of rangedata points that correspond to the curb is much larger Thecurb is represented as a straight line by the application of theleast square method The ground truth implies the relativerange and orientation of the curb The estimation errorsare computed for the extracted curbs Therefore the errorcovariance of the curb is defined by the distribution of theestimation errors By using a large number of measurementsof the estimation errors 120576
120572and 120576
119903 the error covariance is
calculated as follows
Rcurb = [
1205902
120572120590120572119903
120590119903120572
1205902
119903
] = [
119864 (120576120572120576119879
120572) 119864 (120576
120572120576119879
119903)
119864 (120576119903120576119879
120572) 119864 (120576
119903120576119879
119903)
] (14)
The covariance matrices are experimentally defined asconstant values for the left and right curbs
33 Extended Kalman Filter Localization Using Curb FeatureThe odometry data from the wheel encoders are used topredict the robot pose By using the incremental distanceΔ119904119896minus1
and orientationΔ120579119896minus1
the predicted robot pose is givenby the following equation
xminus119896= 119891 (x
119896minus1 u119896minus1
) =
[
[
[
[
[
[
119909minus
119896minus1+ Δ119904119896minus1
cos(120579minus
119896minus1+
Δ120579119896minus1
2
)
119910minus
119896minus1+ Δ119904119896minus1
sin(120579minus
119896minus1+
Δ120579119896minus1
2
)
120579minus
119896minus1+ Δ120579119896minus1
]
]
]
]
]
]
(15)
6 Mathematical Problems in Engineering
Extracted curb(from 1st estimated robot perspective)
Actual curb(curb line map)
W
R
Wri
W120572i
Rrk
R120572k
W+
k1
Wy+k1
Wx+k1
Figure 5 Extracted curb features and a line map with respect to theglobal coordinate frame
The state vector xminus119896= [119909minus
119896119910minus
119896
120579minus
119896]
119879
is the predicted robotpose at sampling time 119896 When the initial pose of the robot isgiven the robot pose is represented by 119909 119910 and 120579 in a globalcoordinate frameTheuncertainty of the predicted robot poseconsistently increases because of the accumulative errors ofthe odometry
In order to correct the odometry error the first measure-ment correction is performed using DGPS measurementsThe update frequency is set to 1Hz on the basis of theDGPS measurement frequency When the available positionmeasurement is provided the observation vector is given inglobal coordinates Consider the following
zDGPS119896 = [119909DGPS119896 119910DGPS119896]119879
(16)
The observation model for the current state is describedas follows
hDGPS (xminus
119896 119896) = [119909
minus
119896119910minus
119896]
119879
(17)
The measurement Jacobian matrixH119896is given as follows
HDGPS119896 =120597h (xminus119896 119896)
120597xminus119896
= [
1 0 0
0 1 0] (18)
zcurb119896 = [120572119896
119903119896]
119879
(19)
The second measurement correction is conducted byusing the curb features The observation vector for theextracted curb is given by (19) When the curbs are extractedon both sides there are two measurement vectors for the leftand right curbs as shown in Figure 5 The sequence of thesecond measurement correction is from the right curb to theleft curbThe update rate is 5Hz if the curbs are continuouslyextracted
The robot pose is corrected by comparing the curb withthe map The extracted curb is matched with the 119894th line ofthe curb map The observation model for the 119894th line 119882z
119894=
[119882120572119894
119882119903119894]
119879
and the robot pose at time 119896 is given by thefollowing equation
hcurb (x+
1198961 119896 119894)
= [
119882120572119894minus120579+
1198961
119882119903119894minus 119909+
1198961cos 119882120572
119894+ 119910+
1198961sin 119882120572
119894
]
(20)
The Jacobian matrixH119896is defined as follows
Hcurb119896 =120597h (x+1198961
119896 119894)
120597x+1198961
= [
0 0 minus1
minus cos 119882120572119894minus sin 119882120572
1198940
]
(21)
The consistency of EKF relies on the observation modelIf an erroneous sensor observation is provided the systemdoes not provide a consistent result Therefore the outliersthat lie outside of the uncertainty bounds should be rejectedA normalized innovation squared (NIS) test is implementedin order to confirm the consistency of the filter NIS valuehas a 120594
2 distribution with respect to 119899 degrees of freedomConsider the following
NIS119896= (z119896minus h (x+
119896 119896))
119879Sminus1119896
(z119896minus h (x+
119896 119896)) le 120594
2 (22)
where S119896is the innovation matrix which is defined as S
119896=
H119896Pminus119896H119879119896+R119896 The NIS value for valid measurements should
be within the threshold of the 1205942 distribution However the
erroneous measurements are discarded when the NIS valuelies outside the threshold boundary A threshold value thatcorresponds to a 95 confidence region is used for outlierrejection
4 Experimental Results
41 Experimental Setup Figure 6 shows the sensor systemattached to the mobile robot The outdoor mobile robotis a Pioneer P3-AT a commercial outdoor platform ofMobileRobots The wheel encoders attached to the drivingmotors provide odometry information SICK LMS-100 wasused to detect the curb The LRF was tilted by 5∘ towardthe ground A Novatel DGPS system was used to measurethe global position The robot was equipped with a roverantenna and a base stationwas located on the roof of a nearbybuilding The ldquotruerdquo value for the curb and the ground truthwere measured using an additional LRF (HOKUYO URG-04lx) attached to the side of the robot
The experiment was performed in Korea University inSeoul Korea as shown in Figure 7 The robot was drivenmanually along the yellow dashed line from ldquoSrdquo to ldquoGrdquoThe curbs along the experimental path are represented assolid green lines The target environment has semistructuredgeometry that is composed of paved roads and curbs inmost of the region Furthermore there are tall buildings andtunnels that degrade the DGPS precisionThe travel distancealong the experimental path was 775m and average speed ofthe robot was 05ms
Mathematical Problems in Engineering 7
DGPS baseDGPS rover
Pioneer P3-AT
LaptopLaser range
finder
Communicate
Figure 6 Sensor system attached to mobile robot
Reference pathCurb map
SG
Figure 7 Experimental environment
42 Curb Extraction Results The curb extraction process ina semistructured road environment is shown in Figure 8Figure 8(a) shows the road environment where the experi-ment was performed The red dotted line represents the scanarea of the tilted LRF Figure 8(b) shows the extracted roadsurface on the basis of the scanned LRF data in the roadenvironment When the road surface is extracted the linesegments that satisfy attribute 1 in Section 22 are selected asthe curb candidates Figure 8(c) shows the line segments thatcorrespond to the curb candidates The first and the secondcandidates for each side of the curbs are represented by blueand green lines respectively There are two candidates oneach sideTherefore four pairs of candidates can be extractedas curbs (R1 L1) (R1 L2) (R2 L1) and (R2 L2) The classprediction results for each pair of curb candidates are listedin Table 1 The pairs of candidates (R1 L1) and (R1 L2)are classified as the curb class Finally candidate (R1 L1) isextracted as the curbs as shown in Figure 8(d) which hasthe smallest Mahalanobis distance with respect to the curb
Table 1 Class prediction for pairs of curb candidates
Candidates Mahalanobis distance Class predictionCurb class Noncurb class
1198831(R1 L1) 00005 1634922 True Curb
1198832(R1 L2) 19779 2025195 True Curb
1198833(R2 L1) 1056307 41180 False Curb
1198834(R2 L2) 1102497 32296 False Curb
Table 2 Classification results including confusion matrix
Instance PCA KFDAClass correct 4338 913 4683 986Class incorrect 413 87 68 14Total 4751 100 4751 100
Classified as Classified asTrue curb False curb True curb False curb
True curb 3524(971)
106(29)
3566(982)
64(18)
False curb 307(274)
814(726)
4(04)
1117(996)
class If the LRF data that correspond to the vertical surfaceare detected the proposed method will perform successfullydespite the small and less distinct curbs
The curb extraction was performed while the robotnavigates through the experimental path Figure 9 showsthe curb mapping result from the curb extraction The curbmap is shown in the right bottom in Figure 9 The extractedcurbs are denoted by the magenta dots The results indicatethat most of the curbs along the experimental path weresuccessfully extracted In order to demonstrate the robust-ness of the proposed method comparison of classificationperformance between our previousmethod and the proposedmethod is summarized in Table 2 The accuracy of the curbextractionwith PCAwas 913 for 4751 scanned datasetsTheaccuracy was improved to 986 with the proposed KFDAA confusion matrix is presented below The conventionalmethod and the proposed method show 971 and 982of true positive rate respectively The curb extraction isperformed successfully by the application of both methodsHowever the most important factor in the curb extraction isto reduce the false detection rate False detection is that thenoncurb data are misclassified as the curb dataThe accuracyof the estimated pose can be decreased when the false curbsare used for localization The false detection rate was 274with PCA The false detection rate was reduced to 04 withthe proposed KFDA The result implies that most of thenoncurb data were classified as noncurb data correctly
43 Uncertainty Measurement Results The DGPS measure-ments are represented by red dots along the experimentalpath in Figure 10(a) The areas with large DGPS errors arerepresented by AndashF Figure 10(b) shows the standard devia-tion of the DGPS measurements The standard deviation ofthe DGPS is about 2m in open area There were temporalblackouts in areas B D and E due to satellite blockage
8 Mathematical Problems in Engineering
(a)
0 1 2 3
0
1
2
3
4
5
6
7
Detected road surface
minus1minus2
minus1
minus2minus3minus4minus5minus6
y(m
)
x (m)
(b)
0 1 2 3
0
1
2
3
4
5
6
7
minus1minus2
minus1
minus2minus3minus4minus5minus6
y(m
)
x (m)
R2
L1 R1
L2
(c)
Extracted curbs
0 1 2 3
0
1
2
3
4
5
6
7
minus1minus2
minus1
minus2minus3minus4minus5minus6
y(m
)
x (m)
(d)
Figure 8 Curb extraction results (a) Road environment (b) Road surface detection (c) Curb feature candidates on both sides (d) Extractedcurb
0 50 100 150
0
50
100
150
y(m
)
x (m)
minus50
minus50minus100
Figure 9 Curb mapping result on experimental path
Mathematical Problems in Engineering 9
Reference pathDGPS measurements
SG
A
B
DE
C
F
(a)
0 5 10 15 20 25 300
2
4
6
8
Time (min)
Dist
ance
(m)
A B C D E F
120590DGPS
(b)
Figure 10 (a) DGPS measurement and (b) DGPS uncertainty measurement (1120590 bound)
CurbAdditional LRF
Figure 11 Additional LRF for ground truth of the curbs
The uncertainty measurements in areas B D and E werealmost infinite as shown in Figure 10(b) Furthermore largeDGPS errors occurred in areas A C and F due to thedegraded satellite signals In particular measurement errorswere 21m on average in area F The standard deviation thatwas measured in area F was 64m on average The resultimplies that the regional properties ofDGPSwere obtained bymeasuring the DGPS uncertainty in real time However theprecision of the localization only by DGPS can be decreasedwhen the robot navigates near the buildings
The curb estimation errors are considered in order todefine the error covariance The most accurate result forthe quantitative curb uncertainty is obtained by measuringthe estimation errors in experimental environments Theestimation errors were measured while the robot navigatesthrough the road with curbs Ground truth for the curb wasprovided by an additional LRF that is attached to the sideof the robot as shown in Figure 11 Ground truth of thecurb was provided by line feature from the additional LRFdata Experiments were conducted in order to measure theestimation errors prior to the localization experiment The
Table 3 Error covariance of extracted curb
Range std 120590119903
Angle std 120590120572
Correlation 120590119903120572
Right curb 01620m 00575 rad 00035msdotradLeft curb 01614m 00649 rad minus00034msdotrad
following results show the estimation errors for the range andangle of the extracted curb
Figure 12 shows the histogram of the curb estimationerrors for each sideThe number of the estimation error mea-surements is approximately 5000 The covariance matrix ofthe curb was computed from the distributions of estimationerrors The elements of error covariance for each side of thecurb are listed in Table 3
The covariance representation for the extracted curbs isshown in Figure 13 The extracted curbs are represented byblue lines and the error bounds for the curbs are representedby green dotted lines The resultant curbs exist within theerror bounds with 95 confidence
44 Outdoor Localization Results The localization results areshown in Figure 14 The proposed method was comparedwith the conventional framework for outdoor localizationthat combines DGPS measurement with odometry The bluedash-dot line represents the localization results correctedonly by the DGPS measurements The estimated paths showsome difference with respect to the reference path (yellowdotted line) in area AndashF due to theDGPS errorsThemagentaline represents the localization results corrected byDGPS andthe extracted curb When the curb information is appliedthe results show that the robot position well matches thereference path even if the DGPS errors are large or a blackoutoccurs (area AndashF) It is clear that the curb information plays adominant role The following part presents the localizationerrors in area AndashF as shown in Figure 14 The localizationerrors were compared with the conventional framework thatcombines DGPS measurement with odometry The ground
10 Mathematical Problems in Engineering
0
100
200
300Histogram of left curb range errors
Estimation error (m)
N(c
ount
)
040302010minus01minus02minus03minus04
0
100
200
300
400Histogram of left curb angle errors
Estimation error (rad)
N(c
ount
)
010050minus005minus01
(a)
Estimation error (m)
0
200
400
600
800Histogram of right curb range errors
N(c
ount
)
040302010minus01minus02minus03minus04
0
200
400
600
800Histogram of right curb angle errors
Estimation error (rad)
N(c
ount
)
010050minus005minus01
(b)
Figure 12 Distribution of estimation errors for (a) left and (b) right curbs
0 1 2 3
0
1
2
3
4
5
6
7
Range dataExtracted curbCovariance (95 confidence)
minus1minus2
minus1
minus2minus3minus4minus5minus6
y(m
)
x (m)
Figure 13 Extracted curbs and covariance representation
truth was computed using the additional LRF attached to theside of the robot
Figure 15 shows the lateral errors of the localizationresults The position errors when using the fusion of theodometry and DGPS are shown in Figure 15(a) The lateralerrors in each areawere usually greater than 1m In particularthe maximum error in area F was 5m In contrast thelocalization result which was corrected by odometry DGPSand curb information shows that the lateral errors werewithin 06m across the entire area as shown in Figure 15(b)
SG
A
B
DE
C
F
Reference pathEKF (odometry + DGPS)EKF (odometry + DGPS + curb)
Figure 14 Localization results in semistructured road environment
Therefore the proposed method shows robust performancein terms of lateral position estimation errors despite the largeDGPS errorsTheheading errors of the localization results arerepresented in Figure 16 The result that was corrected usingonly the DGPS data is shown in Figure 16(a) The headingerrors were greater than 1∘ on averageThe variancewas largerthan 2∘ However when the curb information is used forcorrection the heading errors were remarkably decreasedFurthermore the errors rarely exceed 3∘ in the entire areaIn experiments the proposed method showed precise androbust performance for the lateral and heading errors despitethe large DGPS errors and a temporal blackout
Mathematical Problems in Engineering 11
0
1
2
3
4
5
Late
ral e
rror
s (m
)
A B C D E FSection
EKF (odometry + DGPS)
minus1
minus2
minus3
minus4
(a)
A B C D E F
0
1
2
3
4
5
Late
ral e
rror
s (m
)Section
EKF (odometry + DGPS + curb)
minus1
minus2
minus3
minus4
(b)
Figure 15 Lateral errors (a) corrected by DGPS and (b) corrected by DGPS and extracted curb
A B C D E FSection
EKF (odometry + DGPS)
0
5
10
15
Ang
ular
erro
rs (d
eg)
minus5
minus10
(a)
A B C D E F
0
5
10
15
Ang
ular
erro
rs (d
eg)
Section
EKF (odometry + DGPS + curb)
minus5
minus10
(b)
Figure 16 Heading errors (a) corrected by DGPS and (b) corrected by DGPS and extracted curb
5 Conclusion
This paper presents a localization method for outdoor robotsusing curb features in semistructured road environmentsA reliable curb extraction scheme is proposed to classifythe curb candidates as curb and noncurb classes Mostof the curbs in an experimental path are extracted withhigh accuracy An EKF-based localization is also proposed
to combine the extracted curbs with odometry and DGPSmeasurements The uncertainty models of the sensors aredefined by experiments to provide a practical solution forlocalization From experimental results the robustness of theproposed method is demonstrated in real road experimentsThe curb features can correct significantly the lateral positionand heading errors in dense area where the DGPS signal getsdegraded by buildings
12 Mathematical Problems in Engineering
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This research was supported in part by the MKE (TheMinis-try of Knowledge Economy) Korea under the HumanResources Development Program for Convergence RobotSpecialists Support Program supervised by the NIPA(National IT Industry Promotion Agency) (NIPA-2013-H1502-13-1001) This work was also supported by theNational Research Foundation of Korea (NRF) Grant fundedby Korea Government (MEST) (2013-029812)
References
[1] S Thrun M Montemerlo H Dahlkamp et al ldquoStanley therobot that won the DARPA Grand Challengerdquo Journal of FieldRobotics vol 23 no 9 pp 661ndash692 2006
[2] M Buehler K Lagnemma and S Singh The DARPA UrbanChallenge Autonomous Vehicles in City Traffic Springer NewYork NY USA 2009
[3] A Soloviev ldquoTight coupling of GPS laser scanner and iner-tial measurements for navigation in urban environmentsrdquo inProceedings of the IEEEION Position Location and NavigationSymposium pp 511ndash525 Monterey Calif USA May 2008
[4] S Panzieri F Pascucci and G Ulivi ldquoAn outdoor navigationsystem using GPS and inertial platformrdquo IEEEASME Transac-tions on Mechatronics vol 7 no 2 pp 134ndash142 2002
[5] E-J Jung andD-J Yi ldquoTask-oriented navigation algorithms foran outdoor environment with colored borders and obstaclesrdquoIntelligent Service Robotics vol 6 no 2 pp 69ndash77 2013
[6] S Kim J Kang andM Jin Chung ldquoProbabilistic voxelmappingusing an adaptive confidence measure of stereo matchingrdquoIntelligent Service Robotics vol 6 no 2 pp 89ndash99 2013
[7] M Joerger and B Pervan ldquoRange-domain integration of GPSand laser-scanner measurements for outdoor navigationrdquo inProceedings of the 19th International Technical Meeting of theSatellite Division of The Institute of Navigation (ION GNSS rsquo06)pp 1115ndash1123 Fort Worth Tex USA September 2006
[8] M Hentschel O Wulf and B Wagner ldquoA GPS and laser-basedlocalization for urban and non-urban outdoor environmentsrdquoin Proceedings of the IEEERSJ International Conference on Intel-ligent Robots and Systems pp 149ndash154 Nice France September2008
[9] A Georgiev and P K Allen ldquoLocalizationmethods for amobilerobot in urban environmentsrdquo IEEE Transactions on Roboticsvol 20 no 5 pp 851ndash864 2004
[10] Y Morales T Tsubouchi and S Yuta ldquoVehicle localizationin outdoor mountainous forested paths and extension of two-dimensional road centerline maps to three-dimensional mapsrdquoAdvanced Robotics vol 24 no 4 pp 489ndash513 2010
[11] W SWijesoma K R S Kodagoda andA P Balasuriya ldquoRoad-boundary detection and tracking using ladar sensingrdquo IEEETransactions onRobotics andAutomation vol 20 no 3 pp 456ndash464 2004
[12] M Jabbour and P Bonnifait ldquoGlobal localization robust toGPS outages using a vertical ladarrdquo in Proceedings of the 9th
International Conference on Control Automation Robotics andVision pp 1ndash6 December 2006
[13] P Bonnifait M Jabbour and V Cherfaoui ldquoAutonomousnavigation in urban areas using GIS-managed informationrdquoInternational Journal of Vehicle Autonomous Systems vol 6 no5 pp 83ndash103 2008
[14] Y Shin D Kim H Lee J Park and W Chung ldquoAutonomousnavigation of a surveillance robot in harsh outdoor environ-mentsrdquo Advances in Mechanical Engineering vol 2013 ArticleID 837484 15 pages 2013
[15] Y Shin C Jung andWChung ldquoDrivable road region detectionusing a single laser range finder for outdoor patrol robotsrdquo inProceedings of the IEEE Intelligent Vehicles Symposium (IV rsquo10)pp 877ndash882 San Diego Calif USA June 2010
[16] D Kim and W Chung ldquoLocalization of outdoor mobile robotsusing road featuresrdquo in Proceedings of the 8th International Con-ference on Ubiquitous Robots and Ambient Intelligence (URAIrsquo11) pp 363ndash365 Incheon Republic of Korea November 2011
[17] S Mika G Ratsch J Weston B Scholkopf and K MullerldquoFisher discriminant analysis with kernelsrdquoNeural Networks forSignal Processing vol 9 pp 41ndash48 1999
[18] S Mika G Ratsch and K R Muller ldquoA mathematical pro-gramming approach to the kernel fisher algorithmrdquo Advancesin Neural Information Processing vol 13 pp 591ndash597 2001
[19] G Camps-Valls and L Bruzzone Kernel Methods for RemoteSensing Data Analysis JohnWiley amp Sons New York NY USA2009
[20] R E Kalman ldquoA new approach to linear filtering and predictionproblemsrdquo Journal of Basic Engineering vol 82 no 1 pp 35ndash451960
[21] R E Kalman and R S Bucy ldquoNew results in linear filtering andprediction theoryrdquo Journal of Basic Engineering vol 83 no 3pp 95ndash108 1961
[22] J J Leonard and H F Durrant-Whyte Directed Sonar Sensingfor Mobile Robot Navigation Kluwer Academic DordrechtTheNetherlands 1992
[23] B W Parkinson and J J Spilker Global Positioning SystemTheory and ApplicationsThe American Institute of Aeronauticsand Astronautics Washington DC USA 1996
[24] K O Arras and R Y Siegwart ldquoFeature extraction and sceneinterpretation for map-based navigation and map buildingrdquo in12th Mobile Robots Conference vol 3210 of Proceedings of SPIEpp 42ndash53 Pittsburgh Pa USA January 1998
[25] S T Pfister S I Roumeliotis and J W Burdick ldquoWeighted linefitting algorithms for mobile robot map building and efficientdata representationrdquo in Proceedings of the IEEE InternationalConference on Robotics and Automation pp 1304ndash1311 Septem-ber 2003
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
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Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
Mathematical Problems in Engineering 3
(1) 119871119894larr the LRF measurement
(2) 119871119884119894
larr 119910 coordinate of the LRF measurement(3)119873 larrThe number of the LRF measurement points(4)119877119884larr Expected 119910 range of the road surface points
(5) for 119894 larr 1 to119873
(6) if 119871119884119894
isin 119877119884 then
(7) 119871119903larr save 119871
119894as candidate for the road surface
(8) 120579119903larr angle of candidate for the road surface
(9) 119872 larrThe number of candidates for the road surface(10) end if(11) end for(12) for 119895 larr 1 to119872
(13) if 10038171003817100381710038171003817120579119903119895
10038171003817100381710038171003817le 120579119890 then
(14) 119871119891larr save 119871
119903119895as the road surface
(15) end if(16) end for(17) return (119871
119891)
Algorithm 1 Road surface extraction
LRF coordinate
Robot coordinate
Curb
Curb
Road
A
B
C
DF
ZL
YL
df
120572tXL
XR
YR
ZR
120579f
wr
O
Figure 1 The configuration of a robot and installation of a LRF
where 1198861= |120579119891minus 120579119888| 120576 = tolerance
Once the curb candidates are determined attributes 2 3and 4 are used to extract the correct curb out of the curbcandidatesThe attribute values 119886
2 1198863 and 119886
4that correspond
to each attribute are numerically calculated for the pair ofright and left curb candidates as follows
1198862= 119889119891minus avg (119910C119877 119910C119871)
1198863= 120579C119877 minus 120579C119871
1198864= 119908119903minus 119908119888
(2)
CurbRoadLRF
A
B C
D
Extracted road surface
Figure 2 Ideal model of semiconstructed environment (blue dottedline LRF data red line extracted road surface)
119908119888is the gap between the right and left curb points (119908
119888=
119909C119877 minus 119909C119871) When a curb exists on only one side 1198862and
1198863are computed from the curb candidates for one side 119886
4is
assumed to be 0 The data vector of the curb candidates isgiven as follows
x119894= [1198862
1198863
1198864]
119879
(3)
23 Curb Extraction Using Kernel Fisher Discriminant Anal-ysis (KFDA) KFDA is applied to extract the correct curbfrom the curb candidates KFDA aims to find a discriminantfunction for optimal data classification Therefore the dis-criminant function can be used to classify the curb candidatesas curb and noncurb class The curb extraction is conductedby the following procedure First the training data withclass information are selected The discriminant function isderived from the offline computation of the training dataWhen the discriminant function is obtained classificationof the curb candidates is carried out by the discriminantfunction in real time
4 Mathematical Problems in Engineering
The discriminant function 120572 is defined as a vector tomaximize the following object function in the kernel featurespaceF Consider the following
119869 (120572) =
120572119879119878Φ
119861120572
120572119879119878Φ
119882120572
(4)
The ldquobetween-class variance matrixrdquo 119878Φ119861and the ldquowithin-
class variance matrixrdquo 119878Φ119882are defined as follows
119878Φ
119861= sum
119888
ℓ119888(120581119888120581119879
119888minus 120581120581119879)
119878Φ
119882= 119870119870
119879minus sum
119888
ℓ119888120581119888120581119888
119879
(5)
with 120581119888
= (1ℓ119888) sum119894isin119888
119870119894119895and 120581 = (1ℓ)sum
119894119870119894119895 ℓ is the
number of total training samples and ℓ119888is the number of class
samplesTraining data 119909
1 1199092 119909
ℓ consist of data with obvious
class information Each sample xtraining119894 isin R3 belongs to oneof two classes that include curb and noncurb class In order toobtain equivalent effects on classification the components ofeach sample should be normalized Consider the following
x(119896)119894
=
x(119896)119894
minus 120583(119896)
120590(119896)
(6)
Here 120583(119896) and 120590(119896) are themean and standard deviation of
each attribute respectivelyThe training data that aremappedto the kernel feature space are represented by an ℓ times ℓmatrix119870 The Gaussian kernel is used for mapping the data ontokernel feature spaceF Consider the following
119870119894119895= 119896 (x
119894 x119895) = exp(minus
10038171003817100381710038171003817x119894minus x119895
10038171003817100381710038171003817
2
21205902
) (7)
120590 is the control parameter that needs to be tuned toimprove classification performance [19] If 120590 is too small theoverfitting problem may take place Although the classifi-cation accuracy with respect to the training data increasesthe classification performance with respect to the test databecomes poor under the occurrence of the overfitting If 120590is too large the underfitting problem may take place Theclassification performance will not be satisfactory at all caseswhen the underfitting takes place Therefore 120590 should becarefully selected In this paper 120590 is manually tuned underthe consideration of experimental performances
The discriminant function that maximizes the objectfunction in (4) is derived by an eigenvalue problem In orderto project the training data onto a one-dimensional (1D)solution space the eigenvector that corresponds to the largesteigenvalue is defined as the discriminant function 120572 for dataclassificationThe discriminant function 120572 is given by an ℓtimes1
vector Consider the following
119878Φ
119861120572 = 120582119878
Φ
119882120572 (8)
The classification of the training data is conducted byan inner product of the data matrix 119870 and the discriminant
function120572The projected training data119910training are distributedin the 1D solution space Consider the following
119910training = 120572 sdot 119870 (9)
The class of test data can be predicted by using thediscriminant function 120572 The test data denote the curbcandidates The test data xtest is projected to the 1D solutionspace as shown in the following equation
119910test = sum
119894
120572119894119896 (xtraining119894 xtest) (10)
The class properties of the training data are used to predictthe class of the test data 119910test The Mahalanobis distancesbetween each class and the test data are computed by thefollowing equation
119889 (119910test 120583Φ
119888) =
(119910test minus 120583Φ
119888)
2
(120590Φ
119888)2
(11)
where 120583Φ
119888and 120590
Φ
119888denote the mean and standard deviation
of the class distribution respectively The class of the testdata is determined as the class with the smallest Mahalanobisdistance When the test data are classified as the curb classthey are extracted as the curb
3 Outdoor Localization Using Curb Feature
31 System Design This paper adopts EKF to estimate therobot pose using curb features EKF is a well-known methodfor mobile robot localization and sensor fusion [20ndash22]When the initial pose of the robot and adequate observationsare provided the pose of the robot can be estimated bycorrecting the odometry error The EKF process consists of aprediction step and an update step in sampling time 119896 DGPSand an LRF are used to correct odometry errors Figure 3shows a block diagram of the localization process
32 Measurement Uncertainty Model The GPS error mainlyoccurs due to the following two factors One is the pseu-dorange errors caused by systematic factors Another is thegeometric constellation of satellites In this paper DGPS isused to minimize the pseudorange errors The uncertaintymodel for DGPS is computed under the consideration of theldquodilution of precisionrdquo in relation to the geometric constella-tion of satellites and the pseudorange error or so-called ldquouser-equivalent range errorrdquo [23] Consider the following
RDGPS119896 = [
1205902
119909120590119909119910
120590119909119910
1205902
119910
]1205902
UERE (12)
The error covarianceRDGPS119896 is given as (12)The elementsof the covariance matrix are provided by the DGPS receiverin real time
Several studies were proposed to define the error covari-ance of line features [24 25] However the uncertaintymodels are appropriate for a static condition or a low-speeddriving condition on a flat surface However the outdoor
Mathematical Problems in Engineering 5
DGPS
Robot
Laser rangefinder
Position(xDGPS yDGPS )
Incrementaldisplacement
(ΔsΔ120579)
Curb information
Map
PredictionCorrectedrobot pose
Localizer
1st measurementcorrection
2nd measurementcorrection
(R120572Rr)
(W120572iWri)
xminusk
Pminusk
x+k2x+k1
zDGPS k
RDGPS k
zcurb k
Rcurb k
P+k2P+k1
Figure 3 A block diagram of localization process
Extracted curb
Actual curb
120572i
ri120579i
di
Figure 4 Noise model of the extracted curb
mobile robots are usually driven in the uneven terrain Themeasurement noise of the extracted curb occurs due to thewobble of the robot Therefore the uncertainty model forthe curb needs to be defined by experiments under resultantdriving conditions
In order to define the error covariance Rcurb we considerthe noise model of the extracted curb as shown in Figure 4The information of the extracted curb contains estimationerrors in the range and angle Therefore the angle andrange measurements for the extracted curb are composed ofthe ldquotruerdquo angle 120579
119894and the ldquotruerdquo range 119889
119894 along with the
estimation errors Consider the following
120572119894= 120579119894+ 120576120572119894
119903119894= 119889119894+ 120576119903119894
(13)
where 120576120572119894
and 120576119903119894are the estimation errors for a curb and
have random variances 1205902120572and 120590
2
119903 respectively The ground
truth of the curb locations can be measured by an additionalLRF which is attached to the side of the robot Because theadditional LRF is directly facing the curb the range data fromthe additional LRF provide reliable geometric informationof the curb during robotrsquos movement The measurement ofthe curb from the additional LRF is more accurate than theforward-pointing tilted LRF because the number of rangedata points that correspond to the curb is much larger Thecurb is represented as a straight line by the application of theleast square method The ground truth implies the relativerange and orientation of the curb The estimation errorsare computed for the extracted curbs Therefore the errorcovariance of the curb is defined by the distribution of theestimation errors By using a large number of measurementsof the estimation errors 120576
120572and 120576
119903 the error covariance is
calculated as follows
Rcurb = [
1205902
120572120590120572119903
120590119903120572
1205902
119903
] = [
119864 (120576120572120576119879
120572) 119864 (120576
120572120576119879
119903)
119864 (120576119903120576119879
120572) 119864 (120576
119903120576119879
119903)
] (14)
The covariance matrices are experimentally defined asconstant values for the left and right curbs
33 Extended Kalman Filter Localization Using Curb FeatureThe odometry data from the wheel encoders are used topredict the robot pose By using the incremental distanceΔ119904119896minus1
and orientationΔ120579119896minus1
the predicted robot pose is givenby the following equation
xminus119896= 119891 (x
119896minus1 u119896minus1
) =
[
[
[
[
[
[
119909minus
119896minus1+ Δ119904119896minus1
cos(120579minus
119896minus1+
Δ120579119896minus1
2
)
119910minus
119896minus1+ Δ119904119896minus1
sin(120579minus
119896minus1+
Δ120579119896minus1
2
)
120579minus
119896minus1+ Δ120579119896minus1
]
]
]
]
]
]
(15)
6 Mathematical Problems in Engineering
Extracted curb(from 1st estimated robot perspective)
Actual curb(curb line map)
W
R
Wri
W120572i
Rrk
R120572k
W+
k1
Wy+k1
Wx+k1
Figure 5 Extracted curb features and a line map with respect to theglobal coordinate frame
The state vector xminus119896= [119909minus
119896119910minus
119896
120579minus
119896]
119879
is the predicted robotpose at sampling time 119896 When the initial pose of the robot isgiven the robot pose is represented by 119909 119910 and 120579 in a globalcoordinate frameTheuncertainty of the predicted robot poseconsistently increases because of the accumulative errors ofthe odometry
In order to correct the odometry error the first measure-ment correction is performed using DGPS measurementsThe update frequency is set to 1Hz on the basis of theDGPS measurement frequency When the available positionmeasurement is provided the observation vector is given inglobal coordinates Consider the following
zDGPS119896 = [119909DGPS119896 119910DGPS119896]119879
(16)
The observation model for the current state is describedas follows
hDGPS (xminus
119896 119896) = [119909
minus
119896119910minus
119896]
119879
(17)
The measurement Jacobian matrixH119896is given as follows
HDGPS119896 =120597h (xminus119896 119896)
120597xminus119896
= [
1 0 0
0 1 0] (18)
zcurb119896 = [120572119896
119903119896]
119879
(19)
The second measurement correction is conducted byusing the curb features The observation vector for theextracted curb is given by (19) When the curbs are extractedon both sides there are two measurement vectors for the leftand right curbs as shown in Figure 5 The sequence of thesecond measurement correction is from the right curb to theleft curbThe update rate is 5Hz if the curbs are continuouslyextracted
The robot pose is corrected by comparing the curb withthe map The extracted curb is matched with the 119894th line ofthe curb map The observation model for the 119894th line 119882z
119894=
[119882120572119894
119882119903119894]
119879
and the robot pose at time 119896 is given by thefollowing equation
hcurb (x+
1198961 119896 119894)
= [
119882120572119894minus120579+
1198961
119882119903119894minus 119909+
1198961cos 119882120572
119894+ 119910+
1198961sin 119882120572
119894
]
(20)
The Jacobian matrixH119896is defined as follows
Hcurb119896 =120597h (x+1198961
119896 119894)
120597x+1198961
= [
0 0 minus1
minus cos 119882120572119894minus sin 119882120572
1198940
]
(21)
The consistency of EKF relies on the observation modelIf an erroneous sensor observation is provided the systemdoes not provide a consistent result Therefore the outliersthat lie outside of the uncertainty bounds should be rejectedA normalized innovation squared (NIS) test is implementedin order to confirm the consistency of the filter NIS valuehas a 120594
2 distribution with respect to 119899 degrees of freedomConsider the following
NIS119896= (z119896minus h (x+
119896 119896))
119879Sminus1119896
(z119896minus h (x+
119896 119896)) le 120594
2 (22)
where S119896is the innovation matrix which is defined as S
119896=
H119896Pminus119896H119879119896+R119896 The NIS value for valid measurements should
be within the threshold of the 1205942 distribution However the
erroneous measurements are discarded when the NIS valuelies outside the threshold boundary A threshold value thatcorresponds to a 95 confidence region is used for outlierrejection
4 Experimental Results
41 Experimental Setup Figure 6 shows the sensor systemattached to the mobile robot The outdoor mobile robotis a Pioneer P3-AT a commercial outdoor platform ofMobileRobots The wheel encoders attached to the drivingmotors provide odometry information SICK LMS-100 wasused to detect the curb The LRF was tilted by 5∘ towardthe ground A Novatel DGPS system was used to measurethe global position The robot was equipped with a roverantenna and a base stationwas located on the roof of a nearbybuilding The ldquotruerdquo value for the curb and the ground truthwere measured using an additional LRF (HOKUYO URG-04lx) attached to the side of the robot
The experiment was performed in Korea University inSeoul Korea as shown in Figure 7 The robot was drivenmanually along the yellow dashed line from ldquoSrdquo to ldquoGrdquoThe curbs along the experimental path are represented assolid green lines The target environment has semistructuredgeometry that is composed of paved roads and curbs inmost of the region Furthermore there are tall buildings andtunnels that degrade the DGPS precisionThe travel distancealong the experimental path was 775m and average speed ofthe robot was 05ms
Mathematical Problems in Engineering 7
DGPS baseDGPS rover
Pioneer P3-AT
LaptopLaser range
finder
Communicate
Figure 6 Sensor system attached to mobile robot
Reference pathCurb map
SG
Figure 7 Experimental environment
42 Curb Extraction Results The curb extraction process ina semistructured road environment is shown in Figure 8Figure 8(a) shows the road environment where the experi-ment was performed The red dotted line represents the scanarea of the tilted LRF Figure 8(b) shows the extracted roadsurface on the basis of the scanned LRF data in the roadenvironment When the road surface is extracted the linesegments that satisfy attribute 1 in Section 22 are selected asthe curb candidates Figure 8(c) shows the line segments thatcorrespond to the curb candidates The first and the secondcandidates for each side of the curbs are represented by blueand green lines respectively There are two candidates oneach sideTherefore four pairs of candidates can be extractedas curbs (R1 L1) (R1 L2) (R2 L1) and (R2 L2) The classprediction results for each pair of curb candidates are listedin Table 1 The pairs of candidates (R1 L1) and (R1 L2)are classified as the curb class Finally candidate (R1 L1) isextracted as the curbs as shown in Figure 8(d) which hasthe smallest Mahalanobis distance with respect to the curb
Table 1 Class prediction for pairs of curb candidates
Candidates Mahalanobis distance Class predictionCurb class Noncurb class
1198831(R1 L1) 00005 1634922 True Curb
1198832(R1 L2) 19779 2025195 True Curb
1198833(R2 L1) 1056307 41180 False Curb
1198834(R2 L2) 1102497 32296 False Curb
Table 2 Classification results including confusion matrix
Instance PCA KFDAClass correct 4338 913 4683 986Class incorrect 413 87 68 14Total 4751 100 4751 100
Classified as Classified asTrue curb False curb True curb False curb
True curb 3524(971)
106(29)
3566(982)
64(18)
False curb 307(274)
814(726)
4(04)
1117(996)
class If the LRF data that correspond to the vertical surfaceare detected the proposed method will perform successfullydespite the small and less distinct curbs
The curb extraction was performed while the robotnavigates through the experimental path Figure 9 showsthe curb mapping result from the curb extraction The curbmap is shown in the right bottom in Figure 9 The extractedcurbs are denoted by the magenta dots The results indicatethat most of the curbs along the experimental path weresuccessfully extracted In order to demonstrate the robust-ness of the proposed method comparison of classificationperformance between our previousmethod and the proposedmethod is summarized in Table 2 The accuracy of the curbextractionwith PCAwas 913 for 4751 scanned datasetsTheaccuracy was improved to 986 with the proposed KFDAA confusion matrix is presented below The conventionalmethod and the proposed method show 971 and 982of true positive rate respectively The curb extraction isperformed successfully by the application of both methodsHowever the most important factor in the curb extraction isto reduce the false detection rate False detection is that thenoncurb data are misclassified as the curb dataThe accuracyof the estimated pose can be decreased when the false curbsare used for localization The false detection rate was 274with PCA The false detection rate was reduced to 04 withthe proposed KFDA The result implies that most of thenoncurb data were classified as noncurb data correctly
43 Uncertainty Measurement Results The DGPS measure-ments are represented by red dots along the experimentalpath in Figure 10(a) The areas with large DGPS errors arerepresented by AndashF Figure 10(b) shows the standard devia-tion of the DGPS measurements The standard deviation ofthe DGPS is about 2m in open area There were temporalblackouts in areas B D and E due to satellite blockage
8 Mathematical Problems in Engineering
(a)
0 1 2 3
0
1
2
3
4
5
6
7
Detected road surface
minus1minus2
minus1
minus2minus3minus4minus5minus6
y(m
)
x (m)
(b)
0 1 2 3
0
1
2
3
4
5
6
7
minus1minus2
minus1
minus2minus3minus4minus5minus6
y(m
)
x (m)
R2
L1 R1
L2
(c)
Extracted curbs
0 1 2 3
0
1
2
3
4
5
6
7
minus1minus2
minus1
minus2minus3minus4minus5minus6
y(m
)
x (m)
(d)
Figure 8 Curb extraction results (a) Road environment (b) Road surface detection (c) Curb feature candidates on both sides (d) Extractedcurb
0 50 100 150
0
50
100
150
y(m
)
x (m)
minus50
minus50minus100
Figure 9 Curb mapping result on experimental path
Mathematical Problems in Engineering 9
Reference pathDGPS measurements
SG
A
B
DE
C
F
(a)
0 5 10 15 20 25 300
2
4
6
8
Time (min)
Dist
ance
(m)
A B C D E F
120590DGPS
(b)
Figure 10 (a) DGPS measurement and (b) DGPS uncertainty measurement (1120590 bound)
CurbAdditional LRF
Figure 11 Additional LRF for ground truth of the curbs
The uncertainty measurements in areas B D and E werealmost infinite as shown in Figure 10(b) Furthermore largeDGPS errors occurred in areas A C and F due to thedegraded satellite signals In particular measurement errorswere 21m on average in area F The standard deviation thatwas measured in area F was 64m on average The resultimplies that the regional properties ofDGPSwere obtained bymeasuring the DGPS uncertainty in real time However theprecision of the localization only by DGPS can be decreasedwhen the robot navigates near the buildings
The curb estimation errors are considered in order todefine the error covariance The most accurate result forthe quantitative curb uncertainty is obtained by measuringthe estimation errors in experimental environments Theestimation errors were measured while the robot navigatesthrough the road with curbs Ground truth for the curb wasprovided by an additional LRF that is attached to the sideof the robot as shown in Figure 11 Ground truth of thecurb was provided by line feature from the additional LRFdata Experiments were conducted in order to measure theestimation errors prior to the localization experiment The
Table 3 Error covariance of extracted curb
Range std 120590119903
Angle std 120590120572
Correlation 120590119903120572
Right curb 01620m 00575 rad 00035msdotradLeft curb 01614m 00649 rad minus00034msdotrad
following results show the estimation errors for the range andangle of the extracted curb
Figure 12 shows the histogram of the curb estimationerrors for each sideThe number of the estimation error mea-surements is approximately 5000 The covariance matrix ofthe curb was computed from the distributions of estimationerrors The elements of error covariance for each side of thecurb are listed in Table 3
The covariance representation for the extracted curbs isshown in Figure 13 The extracted curbs are represented byblue lines and the error bounds for the curbs are representedby green dotted lines The resultant curbs exist within theerror bounds with 95 confidence
44 Outdoor Localization Results The localization results areshown in Figure 14 The proposed method was comparedwith the conventional framework for outdoor localizationthat combines DGPS measurement with odometry The bluedash-dot line represents the localization results correctedonly by the DGPS measurements The estimated paths showsome difference with respect to the reference path (yellowdotted line) in area AndashF due to theDGPS errorsThemagentaline represents the localization results corrected byDGPS andthe extracted curb When the curb information is appliedthe results show that the robot position well matches thereference path even if the DGPS errors are large or a blackoutoccurs (area AndashF) It is clear that the curb information plays adominant role The following part presents the localizationerrors in area AndashF as shown in Figure 14 The localizationerrors were compared with the conventional framework thatcombines DGPS measurement with odometry The ground
10 Mathematical Problems in Engineering
0
100
200
300Histogram of left curb range errors
Estimation error (m)
N(c
ount
)
040302010minus01minus02minus03minus04
0
100
200
300
400Histogram of left curb angle errors
Estimation error (rad)
N(c
ount
)
010050minus005minus01
(a)
Estimation error (m)
0
200
400
600
800Histogram of right curb range errors
N(c
ount
)
040302010minus01minus02minus03minus04
0
200
400
600
800Histogram of right curb angle errors
Estimation error (rad)
N(c
ount
)
010050minus005minus01
(b)
Figure 12 Distribution of estimation errors for (a) left and (b) right curbs
0 1 2 3
0
1
2
3
4
5
6
7
Range dataExtracted curbCovariance (95 confidence)
minus1minus2
minus1
minus2minus3minus4minus5minus6
y(m
)
x (m)
Figure 13 Extracted curbs and covariance representation
truth was computed using the additional LRF attached to theside of the robot
Figure 15 shows the lateral errors of the localizationresults The position errors when using the fusion of theodometry and DGPS are shown in Figure 15(a) The lateralerrors in each areawere usually greater than 1m In particularthe maximum error in area F was 5m In contrast thelocalization result which was corrected by odometry DGPSand curb information shows that the lateral errors werewithin 06m across the entire area as shown in Figure 15(b)
SG
A
B
DE
C
F
Reference pathEKF (odometry + DGPS)EKF (odometry + DGPS + curb)
Figure 14 Localization results in semistructured road environment
Therefore the proposed method shows robust performancein terms of lateral position estimation errors despite the largeDGPS errorsTheheading errors of the localization results arerepresented in Figure 16 The result that was corrected usingonly the DGPS data is shown in Figure 16(a) The headingerrors were greater than 1∘ on averageThe variancewas largerthan 2∘ However when the curb information is used forcorrection the heading errors were remarkably decreasedFurthermore the errors rarely exceed 3∘ in the entire areaIn experiments the proposed method showed precise androbust performance for the lateral and heading errors despitethe large DGPS errors and a temporal blackout
Mathematical Problems in Engineering 11
0
1
2
3
4
5
Late
ral e
rror
s (m
)
A B C D E FSection
EKF (odometry + DGPS)
minus1
minus2
minus3
minus4
(a)
A B C D E F
0
1
2
3
4
5
Late
ral e
rror
s (m
)Section
EKF (odometry + DGPS + curb)
minus1
minus2
minus3
minus4
(b)
Figure 15 Lateral errors (a) corrected by DGPS and (b) corrected by DGPS and extracted curb
A B C D E FSection
EKF (odometry + DGPS)
0
5
10
15
Ang
ular
erro
rs (d
eg)
minus5
minus10
(a)
A B C D E F
0
5
10
15
Ang
ular
erro
rs (d
eg)
Section
EKF (odometry + DGPS + curb)
minus5
minus10
(b)
Figure 16 Heading errors (a) corrected by DGPS and (b) corrected by DGPS and extracted curb
5 Conclusion
This paper presents a localization method for outdoor robotsusing curb features in semistructured road environmentsA reliable curb extraction scheme is proposed to classifythe curb candidates as curb and noncurb classes Mostof the curbs in an experimental path are extracted withhigh accuracy An EKF-based localization is also proposed
to combine the extracted curbs with odometry and DGPSmeasurements The uncertainty models of the sensors aredefined by experiments to provide a practical solution forlocalization From experimental results the robustness of theproposed method is demonstrated in real road experimentsThe curb features can correct significantly the lateral positionand heading errors in dense area where the DGPS signal getsdegraded by buildings
12 Mathematical Problems in Engineering
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This research was supported in part by the MKE (TheMinis-try of Knowledge Economy) Korea under the HumanResources Development Program for Convergence RobotSpecialists Support Program supervised by the NIPA(National IT Industry Promotion Agency) (NIPA-2013-H1502-13-1001) This work was also supported by theNational Research Foundation of Korea (NRF) Grant fundedby Korea Government (MEST) (2013-029812)
References
[1] S Thrun M Montemerlo H Dahlkamp et al ldquoStanley therobot that won the DARPA Grand Challengerdquo Journal of FieldRobotics vol 23 no 9 pp 661ndash692 2006
[2] M Buehler K Lagnemma and S Singh The DARPA UrbanChallenge Autonomous Vehicles in City Traffic Springer NewYork NY USA 2009
[3] A Soloviev ldquoTight coupling of GPS laser scanner and iner-tial measurements for navigation in urban environmentsrdquo inProceedings of the IEEEION Position Location and NavigationSymposium pp 511ndash525 Monterey Calif USA May 2008
[4] S Panzieri F Pascucci and G Ulivi ldquoAn outdoor navigationsystem using GPS and inertial platformrdquo IEEEASME Transac-tions on Mechatronics vol 7 no 2 pp 134ndash142 2002
[5] E-J Jung andD-J Yi ldquoTask-oriented navigation algorithms foran outdoor environment with colored borders and obstaclesrdquoIntelligent Service Robotics vol 6 no 2 pp 69ndash77 2013
[6] S Kim J Kang andM Jin Chung ldquoProbabilistic voxelmappingusing an adaptive confidence measure of stereo matchingrdquoIntelligent Service Robotics vol 6 no 2 pp 89ndash99 2013
[7] M Joerger and B Pervan ldquoRange-domain integration of GPSand laser-scanner measurements for outdoor navigationrdquo inProceedings of the 19th International Technical Meeting of theSatellite Division of The Institute of Navigation (ION GNSS rsquo06)pp 1115ndash1123 Fort Worth Tex USA September 2006
[8] M Hentschel O Wulf and B Wagner ldquoA GPS and laser-basedlocalization for urban and non-urban outdoor environmentsrdquoin Proceedings of the IEEERSJ International Conference on Intel-ligent Robots and Systems pp 149ndash154 Nice France September2008
[9] A Georgiev and P K Allen ldquoLocalizationmethods for amobilerobot in urban environmentsrdquo IEEE Transactions on Roboticsvol 20 no 5 pp 851ndash864 2004
[10] Y Morales T Tsubouchi and S Yuta ldquoVehicle localizationin outdoor mountainous forested paths and extension of two-dimensional road centerline maps to three-dimensional mapsrdquoAdvanced Robotics vol 24 no 4 pp 489ndash513 2010
[11] W SWijesoma K R S Kodagoda andA P Balasuriya ldquoRoad-boundary detection and tracking using ladar sensingrdquo IEEETransactions onRobotics andAutomation vol 20 no 3 pp 456ndash464 2004
[12] M Jabbour and P Bonnifait ldquoGlobal localization robust toGPS outages using a vertical ladarrdquo in Proceedings of the 9th
International Conference on Control Automation Robotics andVision pp 1ndash6 December 2006
[13] P Bonnifait M Jabbour and V Cherfaoui ldquoAutonomousnavigation in urban areas using GIS-managed informationrdquoInternational Journal of Vehicle Autonomous Systems vol 6 no5 pp 83ndash103 2008
[14] Y Shin D Kim H Lee J Park and W Chung ldquoAutonomousnavigation of a surveillance robot in harsh outdoor environ-mentsrdquo Advances in Mechanical Engineering vol 2013 ArticleID 837484 15 pages 2013
[15] Y Shin C Jung andWChung ldquoDrivable road region detectionusing a single laser range finder for outdoor patrol robotsrdquo inProceedings of the IEEE Intelligent Vehicles Symposium (IV rsquo10)pp 877ndash882 San Diego Calif USA June 2010
[16] D Kim and W Chung ldquoLocalization of outdoor mobile robotsusing road featuresrdquo in Proceedings of the 8th International Con-ference on Ubiquitous Robots and Ambient Intelligence (URAIrsquo11) pp 363ndash365 Incheon Republic of Korea November 2011
[17] S Mika G Ratsch J Weston B Scholkopf and K MullerldquoFisher discriminant analysis with kernelsrdquoNeural Networks forSignal Processing vol 9 pp 41ndash48 1999
[18] S Mika G Ratsch and K R Muller ldquoA mathematical pro-gramming approach to the kernel fisher algorithmrdquo Advancesin Neural Information Processing vol 13 pp 591ndash597 2001
[19] G Camps-Valls and L Bruzzone Kernel Methods for RemoteSensing Data Analysis JohnWiley amp Sons New York NY USA2009
[20] R E Kalman ldquoA new approach to linear filtering and predictionproblemsrdquo Journal of Basic Engineering vol 82 no 1 pp 35ndash451960
[21] R E Kalman and R S Bucy ldquoNew results in linear filtering andprediction theoryrdquo Journal of Basic Engineering vol 83 no 3pp 95ndash108 1961
[22] J J Leonard and H F Durrant-Whyte Directed Sonar Sensingfor Mobile Robot Navigation Kluwer Academic DordrechtTheNetherlands 1992
[23] B W Parkinson and J J Spilker Global Positioning SystemTheory and ApplicationsThe American Institute of Aeronauticsand Astronautics Washington DC USA 1996
[24] K O Arras and R Y Siegwart ldquoFeature extraction and sceneinterpretation for map-based navigation and map buildingrdquo in12th Mobile Robots Conference vol 3210 of Proceedings of SPIEpp 42ndash53 Pittsburgh Pa USA January 1998
[25] S T Pfister S I Roumeliotis and J W Burdick ldquoWeighted linefitting algorithms for mobile robot map building and efficientdata representationrdquo in Proceedings of the IEEE InternationalConference on Robotics and Automation pp 1304ndash1311 Septem-ber 2003
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Differential EquationsInternational Journal of
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Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
4 Mathematical Problems in Engineering
The discriminant function 120572 is defined as a vector tomaximize the following object function in the kernel featurespaceF Consider the following
119869 (120572) =
120572119879119878Φ
119861120572
120572119879119878Φ
119882120572
(4)
The ldquobetween-class variance matrixrdquo 119878Φ119861and the ldquowithin-
class variance matrixrdquo 119878Φ119882are defined as follows
119878Φ
119861= sum
119888
ℓ119888(120581119888120581119879
119888minus 120581120581119879)
119878Φ
119882= 119870119870
119879minus sum
119888
ℓ119888120581119888120581119888
119879
(5)
with 120581119888
= (1ℓ119888) sum119894isin119888
119870119894119895and 120581 = (1ℓ)sum
119894119870119894119895 ℓ is the
number of total training samples and ℓ119888is the number of class
samplesTraining data 119909
1 1199092 119909
ℓ consist of data with obvious
class information Each sample xtraining119894 isin R3 belongs to oneof two classes that include curb and noncurb class In order toobtain equivalent effects on classification the components ofeach sample should be normalized Consider the following
x(119896)119894
=
x(119896)119894
minus 120583(119896)
120590(119896)
(6)
Here 120583(119896) and 120590(119896) are themean and standard deviation of
each attribute respectivelyThe training data that aremappedto the kernel feature space are represented by an ℓ times ℓmatrix119870 The Gaussian kernel is used for mapping the data ontokernel feature spaceF Consider the following
119870119894119895= 119896 (x
119894 x119895) = exp(minus
10038171003817100381710038171003817x119894minus x119895
10038171003817100381710038171003817
2
21205902
) (7)
120590 is the control parameter that needs to be tuned toimprove classification performance [19] If 120590 is too small theoverfitting problem may take place Although the classifi-cation accuracy with respect to the training data increasesthe classification performance with respect to the test databecomes poor under the occurrence of the overfitting If 120590is too large the underfitting problem may take place Theclassification performance will not be satisfactory at all caseswhen the underfitting takes place Therefore 120590 should becarefully selected In this paper 120590 is manually tuned underthe consideration of experimental performances
The discriminant function that maximizes the objectfunction in (4) is derived by an eigenvalue problem In orderto project the training data onto a one-dimensional (1D)solution space the eigenvector that corresponds to the largesteigenvalue is defined as the discriminant function 120572 for dataclassificationThe discriminant function 120572 is given by an ℓtimes1
vector Consider the following
119878Φ
119861120572 = 120582119878
Φ
119882120572 (8)
The classification of the training data is conducted byan inner product of the data matrix 119870 and the discriminant
function120572The projected training data119910training are distributedin the 1D solution space Consider the following
119910training = 120572 sdot 119870 (9)
The class of test data can be predicted by using thediscriminant function 120572 The test data denote the curbcandidates The test data xtest is projected to the 1D solutionspace as shown in the following equation
119910test = sum
119894
120572119894119896 (xtraining119894 xtest) (10)
The class properties of the training data are used to predictthe class of the test data 119910test The Mahalanobis distancesbetween each class and the test data are computed by thefollowing equation
119889 (119910test 120583Φ
119888) =
(119910test minus 120583Φ
119888)
2
(120590Φ
119888)2
(11)
where 120583Φ
119888and 120590
Φ
119888denote the mean and standard deviation
of the class distribution respectively The class of the testdata is determined as the class with the smallest Mahalanobisdistance When the test data are classified as the curb classthey are extracted as the curb
3 Outdoor Localization Using Curb Feature
31 System Design This paper adopts EKF to estimate therobot pose using curb features EKF is a well-known methodfor mobile robot localization and sensor fusion [20ndash22]When the initial pose of the robot and adequate observationsare provided the pose of the robot can be estimated bycorrecting the odometry error The EKF process consists of aprediction step and an update step in sampling time 119896 DGPSand an LRF are used to correct odometry errors Figure 3shows a block diagram of the localization process
32 Measurement Uncertainty Model The GPS error mainlyoccurs due to the following two factors One is the pseu-dorange errors caused by systematic factors Another is thegeometric constellation of satellites In this paper DGPS isused to minimize the pseudorange errors The uncertaintymodel for DGPS is computed under the consideration of theldquodilution of precisionrdquo in relation to the geometric constella-tion of satellites and the pseudorange error or so-called ldquouser-equivalent range errorrdquo [23] Consider the following
RDGPS119896 = [
1205902
119909120590119909119910
120590119909119910
1205902
119910
]1205902
UERE (12)
The error covarianceRDGPS119896 is given as (12)The elementsof the covariance matrix are provided by the DGPS receiverin real time
Several studies were proposed to define the error covari-ance of line features [24 25] However the uncertaintymodels are appropriate for a static condition or a low-speeddriving condition on a flat surface However the outdoor
Mathematical Problems in Engineering 5
DGPS
Robot
Laser rangefinder
Position(xDGPS yDGPS )
Incrementaldisplacement
(ΔsΔ120579)
Curb information
Map
PredictionCorrectedrobot pose
Localizer
1st measurementcorrection
2nd measurementcorrection
(R120572Rr)
(W120572iWri)
xminusk
Pminusk
x+k2x+k1
zDGPS k
RDGPS k
zcurb k
Rcurb k
P+k2P+k1
Figure 3 A block diagram of localization process
Extracted curb
Actual curb
120572i
ri120579i
di
Figure 4 Noise model of the extracted curb
mobile robots are usually driven in the uneven terrain Themeasurement noise of the extracted curb occurs due to thewobble of the robot Therefore the uncertainty model forthe curb needs to be defined by experiments under resultantdriving conditions
In order to define the error covariance Rcurb we considerthe noise model of the extracted curb as shown in Figure 4The information of the extracted curb contains estimationerrors in the range and angle Therefore the angle andrange measurements for the extracted curb are composed ofthe ldquotruerdquo angle 120579
119894and the ldquotruerdquo range 119889
119894 along with the
estimation errors Consider the following
120572119894= 120579119894+ 120576120572119894
119903119894= 119889119894+ 120576119903119894
(13)
where 120576120572119894
and 120576119903119894are the estimation errors for a curb and
have random variances 1205902120572and 120590
2
119903 respectively The ground
truth of the curb locations can be measured by an additionalLRF which is attached to the side of the robot Because theadditional LRF is directly facing the curb the range data fromthe additional LRF provide reliable geometric informationof the curb during robotrsquos movement The measurement ofthe curb from the additional LRF is more accurate than theforward-pointing tilted LRF because the number of rangedata points that correspond to the curb is much larger Thecurb is represented as a straight line by the application of theleast square method The ground truth implies the relativerange and orientation of the curb The estimation errorsare computed for the extracted curbs Therefore the errorcovariance of the curb is defined by the distribution of theestimation errors By using a large number of measurementsof the estimation errors 120576
120572and 120576
119903 the error covariance is
calculated as follows
Rcurb = [
1205902
120572120590120572119903
120590119903120572
1205902
119903
] = [
119864 (120576120572120576119879
120572) 119864 (120576
120572120576119879
119903)
119864 (120576119903120576119879
120572) 119864 (120576
119903120576119879
119903)
] (14)
The covariance matrices are experimentally defined asconstant values for the left and right curbs
33 Extended Kalman Filter Localization Using Curb FeatureThe odometry data from the wheel encoders are used topredict the robot pose By using the incremental distanceΔ119904119896minus1
and orientationΔ120579119896minus1
the predicted robot pose is givenby the following equation
xminus119896= 119891 (x
119896minus1 u119896minus1
) =
[
[
[
[
[
[
119909minus
119896minus1+ Δ119904119896minus1
cos(120579minus
119896minus1+
Δ120579119896minus1
2
)
119910minus
119896minus1+ Δ119904119896minus1
sin(120579minus
119896minus1+
Δ120579119896minus1
2
)
120579minus
119896minus1+ Δ120579119896minus1
]
]
]
]
]
]
(15)
6 Mathematical Problems in Engineering
Extracted curb(from 1st estimated robot perspective)
Actual curb(curb line map)
W
R
Wri
W120572i
Rrk
R120572k
W+
k1
Wy+k1
Wx+k1
Figure 5 Extracted curb features and a line map with respect to theglobal coordinate frame
The state vector xminus119896= [119909minus
119896119910minus
119896
120579minus
119896]
119879
is the predicted robotpose at sampling time 119896 When the initial pose of the robot isgiven the robot pose is represented by 119909 119910 and 120579 in a globalcoordinate frameTheuncertainty of the predicted robot poseconsistently increases because of the accumulative errors ofthe odometry
In order to correct the odometry error the first measure-ment correction is performed using DGPS measurementsThe update frequency is set to 1Hz on the basis of theDGPS measurement frequency When the available positionmeasurement is provided the observation vector is given inglobal coordinates Consider the following
zDGPS119896 = [119909DGPS119896 119910DGPS119896]119879
(16)
The observation model for the current state is describedas follows
hDGPS (xminus
119896 119896) = [119909
minus
119896119910minus
119896]
119879
(17)
The measurement Jacobian matrixH119896is given as follows
HDGPS119896 =120597h (xminus119896 119896)
120597xminus119896
= [
1 0 0
0 1 0] (18)
zcurb119896 = [120572119896
119903119896]
119879
(19)
The second measurement correction is conducted byusing the curb features The observation vector for theextracted curb is given by (19) When the curbs are extractedon both sides there are two measurement vectors for the leftand right curbs as shown in Figure 5 The sequence of thesecond measurement correction is from the right curb to theleft curbThe update rate is 5Hz if the curbs are continuouslyextracted
The robot pose is corrected by comparing the curb withthe map The extracted curb is matched with the 119894th line ofthe curb map The observation model for the 119894th line 119882z
119894=
[119882120572119894
119882119903119894]
119879
and the robot pose at time 119896 is given by thefollowing equation
hcurb (x+
1198961 119896 119894)
= [
119882120572119894minus120579+
1198961
119882119903119894minus 119909+
1198961cos 119882120572
119894+ 119910+
1198961sin 119882120572
119894
]
(20)
The Jacobian matrixH119896is defined as follows
Hcurb119896 =120597h (x+1198961
119896 119894)
120597x+1198961
= [
0 0 minus1
minus cos 119882120572119894minus sin 119882120572
1198940
]
(21)
The consistency of EKF relies on the observation modelIf an erroneous sensor observation is provided the systemdoes not provide a consistent result Therefore the outliersthat lie outside of the uncertainty bounds should be rejectedA normalized innovation squared (NIS) test is implementedin order to confirm the consistency of the filter NIS valuehas a 120594
2 distribution with respect to 119899 degrees of freedomConsider the following
NIS119896= (z119896minus h (x+
119896 119896))
119879Sminus1119896
(z119896minus h (x+
119896 119896)) le 120594
2 (22)
where S119896is the innovation matrix which is defined as S
119896=
H119896Pminus119896H119879119896+R119896 The NIS value for valid measurements should
be within the threshold of the 1205942 distribution However the
erroneous measurements are discarded when the NIS valuelies outside the threshold boundary A threshold value thatcorresponds to a 95 confidence region is used for outlierrejection
4 Experimental Results
41 Experimental Setup Figure 6 shows the sensor systemattached to the mobile robot The outdoor mobile robotis a Pioneer P3-AT a commercial outdoor platform ofMobileRobots The wheel encoders attached to the drivingmotors provide odometry information SICK LMS-100 wasused to detect the curb The LRF was tilted by 5∘ towardthe ground A Novatel DGPS system was used to measurethe global position The robot was equipped with a roverantenna and a base stationwas located on the roof of a nearbybuilding The ldquotruerdquo value for the curb and the ground truthwere measured using an additional LRF (HOKUYO URG-04lx) attached to the side of the robot
The experiment was performed in Korea University inSeoul Korea as shown in Figure 7 The robot was drivenmanually along the yellow dashed line from ldquoSrdquo to ldquoGrdquoThe curbs along the experimental path are represented assolid green lines The target environment has semistructuredgeometry that is composed of paved roads and curbs inmost of the region Furthermore there are tall buildings andtunnels that degrade the DGPS precisionThe travel distancealong the experimental path was 775m and average speed ofthe robot was 05ms
Mathematical Problems in Engineering 7
DGPS baseDGPS rover
Pioneer P3-AT
LaptopLaser range
finder
Communicate
Figure 6 Sensor system attached to mobile robot
Reference pathCurb map
SG
Figure 7 Experimental environment
42 Curb Extraction Results The curb extraction process ina semistructured road environment is shown in Figure 8Figure 8(a) shows the road environment where the experi-ment was performed The red dotted line represents the scanarea of the tilted LRF Figure 8(b) shows the extracted roadsurface on the basis of the scanned LRF data in the roadenvironment When the road surface is extracted the linesegments that satisfy attribute 1 in Section 22 are selected asthe curb candidates Figure 8(c) shows the line segments thatcorrespond to the curb candidates The first and the secondcandidates for each side of the curbs are represented by blueand green lines respectively There are two candidates oneach sideTherefore four pairs of candidates can be extractedas curbs (R1 L1) (R1 L2) (R2 L1) and (R2 L2) The classprediction results for each pair of curb candidates are listedin Table 1 The pairs of candidates (R1 L1) and (R1 L2)are classified as the curb class Finally candidate (R1 L1) isextracted as the curbs as shown in Figure 8(d) which hasthe smallest Mahalanobis distance with respect to the curb
Table 1 Class prediction for pairs of curb candidates
Candidates Mahalanobis distance Class predictionCurb class Noncurb class
1198831(R1 L1) 00005 1634922 True Curb
1198832(R1 L2) 19779 2025195 True Curb
1198833(R2 L1) 1056307 41180 False Curb
1198834(R2 L2) 1102497 32296 False Curb
Table 2 Classification results including confusion matrix
Instance PCA KFDAClass correct 4338 913 4683 986Class incorrect 413 87 68 14Total 4751 100 4751 100
Classified as Classified asTrue curb False curb True curb False curb
True curb 3524(971)
106(29)
3566(982)
64(18)
False curb 307(274)
814(726)
4(04)
1117(996)
class If the LRF data that correspond to the vertical surfaceare detected the proposed method will perform successfullydespite the small and less distinct curbs
The curb extraction was performed while the robotnavigates through the experimental path Figure 9 showsthe curb mapping result from the curb extraction The curbmap is shown in the right bottom in Figure 9 The extractedcurbs are denoted by the magenta dots The results indicatethat most of the curbs along the experimental path weresuccessfully extracted In order to demonstrate the robust-ness of the proposed method comparison of classificationperformance between our previousmethod and the proposedmethod is summarized in Table 2 The accuracy of the curbextractionwith PCAwas 913 for 4751 scanned datasetsTheaccuracy was improved to 986 with the proposed KFDAA confusion matrix is presented below The conventionalmethod and the proposed method show 971 and 982of true positive rate respectively The curb extraction isperformed successfully by the application of both methodsHowever the most important factor in the curb extraction isto reduce the false detection rate False detection is that thenoncurb data are misclassified as the curb dataThe accuracyof the estimated pose can be decreased when the false curbsare used for localization The false detection rate was 274with PCA The false detection rate was reduced to 04 withthe proposed KFDA The result implies that most of thenoncurb data were classified as noncurb data correctly
43 Uncertainty Measurement Results The DGPS measure-ments are represented by red dots along the experimentalpath in Figure 10(a) The areas with large DGPS errors arerepresented by AndashF Figure 10(b) shows the standard devia-tion of the DGPS measurements The standard deviation ofthe DGPS is about 2m in open area There were temporalblackouts in areas B D and E due to satellite blockage
8 Mathematical Problems in Engineering
(a)
0 1 2 3
0
1
2
3
4
5
6
7
Detected road surface
minus1minus2
minus1
minus2minus3minus4minus5minus6
y(m
)
x (m)
(b)
0 1 2 3
0
1
2
3
4
5
6
7
minus1minus2
minus1
minus2minus3minus4minus5minus6
y(m
)
x (m)
R2
L1 R1
L2
(c)
Extracted curbs
0 1 2 3
0
1
2
3
4
5
6
7
minus1minus2
minus1
minus2minus3minus4minus5minus6
y(m
)
x (m)
(d)
Figure 8 Curb extraction results (a) Road environment (b) Road surface detection (c) Curb feature candidates on both sides (d) Extractedcurb
0 50 100 150
0
50
100
150
y(m
)
x (m)
minus50
minus50minus100
Figure 9 Curb mapping result on experimental path
Mathematical Problems in Engineering 9
Reference pathDGPS measurements
SG
A
B
DE
C
F
(a)
0 5 10 15 20 25 300
2
4
6
8
Time (min)
Dist
ance
(m)
A B C D E F
120590DGPS
(b)
Figure 10 (a) DGPS measurement and (b) DGPS uncertainty measurement (1120590 bound)
CurbAdditional LRF
Figure 11 Additional LRF for ground truth of the curbs
The uncertainty measurements in areas B D and E werealmost infinite as shown in Figure 10(b) Furthermore largeDGPS errors occurred in areas A C and F due to thedegraded satellite signals In particular measurement errorswere 21m on average in area F The standard deviation thatwas measured in area F was 64m on average The resultimplies that the regional properties ofDGPSwere obtained bymeasuring the DGPS uncertainty in real time However theprecision of the localization only by DGPS can be decreasedwhen the robot navigates near the buildings
The curb estimation errors are considered in order todefine the error covariance The most accurate result forthe quantitative curb uncertainty is obtained by measuringthe estimation errors in experimental environments Theestimation errors were measured while the robot navigatesthrough the road with curbs Ground truth for the curb wasprovided by an additional LRF that is attached to the sideof the robot as shown in Figure 11 Ground truth of thecurb was provided by line feature from the additional LRFdata Experiments were conducted in order to measure theestimation errors prior to the localization experiment The
Table 3 Error covariance of extracted curb
Range std 120590119903
Angle std 120590120572
Correlation 120590119903120572
Right curb 01620m 00575 rad 00035msdotradLeft curb 01614m 00649 rad minus00034msdotrad
following results show the estimation errors for the range andangle of the extracted curb
Figure 12 shows the histogram of the curb estimationerrors for each sideThe number of the estimation error mea-surements is approximately 5000 The covariance matrix ofthe curb was computed from the distributions of estimationerrors The elements of error covariance for each side of thecurb are listed in Table 3
The covariance representation for the extracted curbs isshown in Figure 13 The extracted curbs are represented byblue lines and the error bounds for the curbs are representedby green dotted lines The resultant curbs exist within theerror bounds with 95 confidence
44 Outdoor Localization Results The localization results areshown in Figure 14 The proposed method was comparedwith the conventional framework for outdoor localizationthat combines DGPS measurement with odometry The bluedash-dot line represents the localization results correctedonly by the DGPS measurements The estimated paths showsome difference with respect to the reference path (yellowdotted line) in area AndashF due to theDGPS errorsThemagentaline represents the localization results corrected byDGPS andthe extracted curb When the curb information is appliedthe results show that the robot position well matches thereference path even if the DGPS errors are large or a blackoutoccurs (area AndashF) It is clear that the curb information plays adominant role The following part presents the localizationerrors in area AndashF as shown in Figure 14 The localizationerrors were compared with the conventional framework thatcombines DGPS measurement with odometry The ground
10 Mathematical Problems in Engineering
0
100
200
300Histogram of left curb range errors
Estimation error (m)
N(c
ount
)
040302010minus01minus02minus03minus04
0
100
200
300
400Histogram of left curb angle errors
Estimation error (rad)
N(c
ount
)
010050minus005minus01
(a)
Estimation error (m)
0
200
400
600
800Histogram of right curb range errors
N(c
ount
)
040302010minus01minus02minus03minus04
0
200
400
600
800Histogram of right curb angle errors
Estimation error (rad)
N(c
ount
)
010050minus005minus01
(b)
Figure 12 Distribution of estimation errors for (a) left and (b) right curbs
0 1 2 3
0
1
2
3
4
5
6
7
Range dataExtracted curbCovariance (95 confidence)
minus1minus2
minus1
minus2minus3minus4minus5minus6
y(m
)
x (m)
Figure 13 Extracted curbs and covariance representation
truth was computed using the additional LRF attached to theside of the robot
Figure 15 shows the lateral errors of the localizationresults The position errors when using the fusion of theodometry and DGPS are shown in Figure 15(a) The lateralerrors in each areawere usually greater than 1m In particularthe maximum error in area F was 5m In contrast thelocalization result which was corrected by odometry DGPSand curb information shows that the lateral errors werewithin 06m across the entire area as shown in Figure 15(b)
SG
A
B
DE
C
F
Reference pathEKF (odometry + DGPS)EKF (odometry + DGPS + curb)
Figure 14 Localization results in semistructured road environment
Therefore the proposed method shows robust performancein terms of lateral position estimation errors despite the largeDGPS errorsTheheading errors of the localization results arerepresented in Figure 16 The result that was corrected usingonly the DGPS data is shown in Figure 16(a) The headingerrors were greater than 1∘ on averageThe variancewas largerthan 2∘ However when the curb information is used forcorrection the heading errors were remarkably decreasedFurthermore the errors rarely exceed 3∘ in the entire areaIn experiments the proposed method showed precise androbust performance for the lateral and heading errors despitethe large DGPS errors and a temporal blackout
Mathematical Problems in Engineering 11
0
1
2
3
4
5
Late
ral e
rror
s (m
)
A B C D E FSection
EKF (odometry + DGPS)
minus1
minus2
minus3
minus4
(a)
A B C D E F
0
1
2
3
4
5
Late
ral e
rror
s (m
)Section
EKF (odometry + DGPS + curb)
minus1
minus2
minus3
minus4
(b)
Figure 15 Lateral errors (a) corrected by DGPS and (b) corrected by DGPS and extracted curb
A B C D E FSection
EKF (odometry + DGPS)
0
5
10
15
Ang
ular
erro
rs (d
eg)
minus5
minus10
(a)
A B C D E F
0
5
10
15
Ang
ular
erro
rs (d
eg)
Section
EKF (odometry + DGPS + curb)
minus5
minus10
(b)
Figure 16 Heading errors (a) corrected by DGPS and (b) corrected by DGPS and extracted curb
5 Conclusion
This paper presents a localization method for outdoor robotsusing curb features in semistructured road environmentsA reliable curb extraction scheme is proposed to classifythe curb candidates as curb and noncurb classes Mostof the curbs in an experimental path are extracted withhigh accuracy An EKF-based localization is also proposed
to combine the extracted curbs with odometry and DGPSmeasurements The uncertainty models of the sensors aredefined by experiments to provide a practical solution forlocalization From experimental results the robustness of theproposed method is demonstrated in real road experimentsThe curb features can correct significantly the lateral positionand heading errors in dense area where the DGPS signal getsdegraded by buildings
12 Mathematical Problems in Engineering
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This research was supported in part by the MKE (TheMinis-try of Knowledge Economy) Korea under the HumanResources Development Program for Convergence RobotSpecialists Support Program supervised by the NIPA(National IT Industry Promotion Agency) (NIPA-2013-H1502-13-1001) This work was also supported by theNational Research Foundation of Korea (NRF) Grant fundedby Korea Government (MEST) (2013-029812)
References
[1] S Thrun M Montemerlo H Dahlkamp et al ldquoStanley therobot that won the DARPA Grand Challengerdquo Journal of FieldRobotics vol 23 no 9 pp 661ndash692 2006
[2] M Buehler K Lagnemma and S Singh The DARPA UrbanChallenge Autonomous Vehicles in City Traffic Springer NewYork NY USA 2009
[3] A Soloviev ldquoTight coupling of GPS laser scanner and iner-tial measurements for navigation in urban environmentsrdquo inProceedings of the IEEEION Position Location and NavigationSymposium pp 511ndash525 Monterey Calif USA May 2008
[4] S Panzieri F Pascucci and G Ulivi ldquoAn outdoor navigationsystem using GPS and inertial platformrdquo IEEEASME Transac-tions on Mechatronics vol 7 no 2 pp 134ndash142 2002
[5] E-J Jung andD-J Yi ldquoTask-oriented navigation algorithms foran outdoor environment with colored borders and obstaclesrdquoIntelligent Service Robotics vol 6 no 2 pp 69ndash77 2013
[6] S Kim J Kang andM Jin Chung ldquoProbabilistic voxelmappingusing an adaptive confidence measure of stereo matchingrdquoIntelligent Service Robotics vol 6 no 2 pp 89ndash99 2013
[7] M Joerger and B Pervan ldquoRange-domain integration of GPSand laser-scanner measurements for outdoor navigationrdquo inProceedings of the 19th International Technical Meeting of theSatellite Division of The Institute of Navigation (ION GNSS rsquo06)pp 1115ndash1123 Fort Worth Tex USA September 2006
[8] M Hentschel O Wulf and B Wagner ldquoA GPS and laser-basedlocalization for urban and non-urban outdoor environmentsrdquoin Proceedings of the IEEERSJ International Conference on Intel-ligent Robots and Systems pp 149ndash154 Nice France September2008
[9] A Georgiev and P K Allen ldquoLocalizationmethods for amobilerobot in urban environmentsrdquo IEEE Transactions on Roboticsvol 20 no 5 pp 851ndash864 2004
[10] Y Morales T Tsubouchi and S Yuta ldquoVehicle localizationin outdoor mountainous forested paths and extension of two-dimensional road centerline maps to three-dimensional mapsrdquoAdvanced Robotics vol 24 no 4 pp 489ndash513 2010
[11] W SWijesoma K R S Kodagoda andA P Balasuriya ldquoRoad-boundary detection and tracking using ladar sensingrdquo IEEETransactions onRobotics andAutomation vol 20 no 3 pp 456ndash464 2004
[12] M Jabbour and P Bonnifait ldquoGlobal localization robust toGPS outages using a vertical ladarrdquo in Proceedings of the 9th
International Conference on Control Automation Robotics andVision pp 1ndash6 December 2006
[13] P Bonnifait M Jabbour and V Cherfaoui ldquoAutonomousnavigation in urban areas using GIS-managed informationrdquoInternational Journal of Vehicle Autonomous Systems vol 6 no5 pp 83ndash103 2008
[14] Y Shin D Kim H Lee J Park and W Chung ldquoAutonomousnavigation of a surveillance robot in harsh outdoor environ-mentsrdquo Advances in Mechanical Engineering vol 2013 ArticleID 837484 15 pages 2013
[15] Y Shin C Jung andWChung ldquoDrivable road region detectionusing a single laser range finder for outdoor patrol robotsrdquo inProceedings of the IEEE Intelligent Vehicles Symposium (IV rsquo10)pp 877ndash882 San Diego Calif USA June 2010
[16] D Kim and W Chung ldquoLocalization of outdoor mobile robotsusing road featuresrdquo in Proceedings of the 8th International Con-ference on Ubiquitous Robots and Ambient Intelligence (URAIrsquo11) pp 363ndash365 Incheon Republic of Korea November 2011
[17] S Mika G Ratsch J Weston B Scholkopf and K MullerldquoFisher discriminant analysis with kernelsrdquoNeural Networks forSignal Processing vol 9 pp 41ndash48 1999
[18] S Mika G Ratsch and K R Muller ldquoA mathematical pro-gramming approach to the kernel fisher algorithmrdquo Advancesin Neural Information Processing vol 13 pp 591ndash597 2001
[19] G Camps-Valls and L Bruzzone Kernel Methods for RemoteSensing Data Analysis JohnWiley amp Sons New York NY USA2009
[20] R E Kalman ldquoA new approach to linear filtering and predictionproblemsrdquo Journal of Basic Engineering vol 82 no 1 pp 35ndash451960
[21] R E Kalman and R S Bucy ldquoNew results in linear filtering andprediction theoryrdquo Journal of Basic Engineering vol 83 no 3pp 95ndash108 1961
[22] J J Leonard and H F Durrant-Whyte Directed Sonar Sensingfor Mobile Robot Navigation Kluwer Academic DordrechtTheNetherlands 1992
[23] B W Parkinson and J J Spilker Global Positioning SystemTheory and ApplicationsThe American Institute of Aeronauticsand Astronautics Washington DC USA 1996
[24] K O Arras and R Y Siegwart ldquoFeature extraction and sceneinterpretation for map-based navigation and map buildingrdquo in12th Mobile Robots Conference vol 3210 of Proceedings of SPIEpp 42ndash53 Pittsburgh Pa USA January 1998
[25] S T Pfister S I Roumeliotis and J W Burdick ldquoWeighted linefitting algorithms for mobile robot map building and efficientdata representationrdquo in Proceedings of the IEEE InternationalConference on Robotics and Automation pp 1304ndash1311 Septem-ber 2003
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
Mathematical Problems in Engineering 5
DGPS
Robot
Laser rangefinder
Position(xDGPS yDGPS )
Incrementaldisplacement
(ΔsΔ120579)
Curb information
Map
PredictionCorrectedrobot pose
Localizer
1st measurementcorrection
2nd measurementcorrection
(R120572Rr)
(W120572iWri)
xminusk
Pminusk
x+k2x+k1
zDGPS k
RDGPS k
zcurb k
Rcurb k
P+k2P+k1
Figure 3 A block diagram of localization process
Extracted curb
Actual curb
120572i
ri120579i
di
Figure 4 Noise model of the extracted curb
mobile robots are usually driven in the uneven terrain Themeasurement noise of the extracted curb occurs due to thewobble of the robot Therefore the uncertainty model forthe curb needs to be defined by experiments under resultantdriving conditions
In order to define the error covariance Rcurb we considerthe noise model of the extracted curb as shown in Figure 4The information of the extracted curb contains estimationerrors in the range and angle Therefore the angle andrange measurements for the extracted curb are composed ofthe ldquotruerdquo angle 120579
119894and the ldquotruerdquo range 119889
119894 along with the
estimation errors Consider the following
120572119894= 120579119894+ 120576120572119894
119903119894= 119889119894+ 120576119903119894
(13)
where 120576120572119894
and 120576119903119894are the estimation errors for a curb and
have random variances 1205902120572and 120590
2
119903 respectively The ground
truth of the curb locations can be measured by an additionalLRF which is attached to the side of the robot Because theadditional LRF is directly facing the curb the range data fromthe additional LRF provide reliable geometric informationof the curb during robotrsquos movement The measurement ofthe curb from the additional LRF is more accurate than theforward-pointing tilted LRF because the number of rangedata points that correspond to the curb is much larger Thecurb is represented as a straight line by the application of theleast square method The ground truth implies the relativerange and orientation of the curb The estimation errorsare computed for the extracted curbs Therefore the errorcovariance of the curb is defined by the distribution of theestimation errors By using a large number of measurementsof the estimation errors 120576
120572and 120576
119903 the error covariance is
calculated as follows
Rcurb = [
1205902
120572120590120572119903
120590119903120572
1205902
119903
] = [
119864 (120576120572120576119879
120572) 119864 (120576
120572120576119879
119903)
119864 (120576119903120576119879
120572) 119864 (120576
119903120576119879
119903)
] (14)
The covariance matrices are experimentally defined asconstant values for the left and right curbs
33 Extended Kalman Filter Localization Using Curb FeatureThe odometry data from the wheel encoders are used topredict the robot pose By using the incremental distanceΔ119904119896minus1
and orientationΔ120579119896minus1
the predicted robot pose is givenby the following equation
xminus119896= 119891 (x
119896minus1 u119896minus1
) =
[
[
[
[
[
[
119909minus
119896minus1+ Δ119904119896minus1
cos(120579minus
119896minus1+
Δ120579119896minus1
2
)
119910minus
119896minus1+ Δ119904119896minus1
sin(120579minus
119896minus1+
Δ120579119896minus1
2
)
120579minus
119896minus1+ Δ120579119896minus1
]
]
]
]
]
]
(15)
6 Mathematical Problems in Engineering
Extracted curb(from 1st estimated robot perspective)
Actual curb(curb line map)
W
R
Wri
W120572i
Rrk
R120572k
W+
k1
Wy+k1
Wx+k1
Figure 5 Extracted curb features and a line map with respect to theglobal coordinate frame
The state vector xminus119896= [119909minus
119896119910minus
119896
120579minus
119896]
119879
is the predicted robotpose at sampling time 119896 When the initial pose of the robot isgiven the robot pose is represented by 119909 119910 and 120579 in a globalcoordinate frameTheuncertainty of the predicted robot poseconsistently increases because of the accumulative errors ofthe odometry
In order to correct the odometry error the first measure-ment correction is performed using DGPS measurementsThe update frequency is set to 1Hz on the basis of theDGPS measurement frequency When the available positionmeasurement is provided the observation vector is given inglobal coordinates Consider the following
zDGPS119896 = [119909DGPS119896 119910DGPS119896]119879
(16)
The observation model for the current state is describedas follows
hDGPS (xminus
119896 119896) = [119909
minus
119896119910minus
119896]
119879
(17)
The measurement Jacobian matrixH119896is given as follows
HDGPS119896 =120597h (xminus119896 119896)
120597xminus119896
= [
1 0 0
0 1 0] (18)
zcurb119896 = [120572119896
119903119896]
119879
(19)
The second measurement correction is conducted byusing the curb features The observation vector for theextracted curb is given by (19) When the curbs are extractedon both sides there are two measurement vectors for the leftand right curbs as shown in Figure 5 The sequence of thesecond measurement correction is from the right curb to theleft curbThe update rate is 5Hz if the curbs are continuouslyextracted
The robot pose is corrected by comparing the curb withthe map The extracted curb is matched with the 119894th line ofthe curb map The observation model for the 119894th line 119882z
119894=
[119882120572119894
119882119903119894]
119879
and the robot pose at time 119896 is given by thefollowing equation
hcurb (x+
1198961 119896 119894)
= [
119882120572119894minus120579+
1198961
119882119903119894minus 119909+
1198961cos 119882120572
119894+ 119910+
1198961sin 119882120572
119894
]
(20)
The Jacobian matrixH119896is defined as follows
Hcurb119896 =120597h (x+1198961
119896 119894)
120597x+1198961
= [
0 0 minus1
minus cos 119882120572119894minus sin 119882120572
1198940
]
(21)
The consistency of EKF relies on the observation modelIf an erroneous sensor observation is provided the systemdoes not provide a consistent result Therefore the outliersthat lie outside of the uncertainty bounds should be rejectedA normalized innovation squared (NIS) test is implementedin order to confirm the consistency of the filter NIS valuehas a 120594
2 distribution with respect to 119899 degrees of freedomConsider the following
NIS119896= (z119896minus h (x+
119896 119896))
119879Sminus1119896
(z119896minus h (x+
119896 119896)) le 120594
2 (22)
where S119896is the innovation matrix which is defined as S
119896=
H119896Pminus119896H119879119896+R119896 The NIS value for valid measurements should
be within the threshold of the 1205942 distribution However the
erroneous measurements are discarded when the NIS valuelies outside the threshold boundary A threshold value thatcorresponds to a 95 confidence region is used for outlierrejection
4 Experimental Results
41 Experimental Setup Figure 6 shows the sensor systemattached to the mobile robot The outdoor mobile robotis a Pioneer P3-AT a commercial outdoor platform ofMobileRobots The wheel encoders attached to the drivingmotors provide odometry information SICK LMS-100 wasused to detect the curb The LRF was tilted by 5∘ towardthe ground A Novatel DGPS system was used to measurethe global position The robot was equipped with a roverantenna and a base stationwas located on the roof of a nearbybuilding The ldquotruerdquo value for the curb and the ground truthwere measured using an additional LRF (HOKUYO URG-04lx) attached to the side of the robot
The experiment was performed in Korea University inSeoul Korea as shown in Figure 7 The robot was drivenmanually along the yellow dashed line from ldquoSrdquo to ldquoGrdquoThe curbs along the experimental path are represented assolid green lines The target environment has semistructuredgeometry that is composed of paved roads and curbs inmost of the region Furthermore there are tall buildings andtunnels that degrade the DGPS precisionThe travel distancealong the experimental path was 775m and average speed ofthe robot was 05ms
Mathematical Problems in Engineering 7
DGPS baseDGPS rover
Pioneer P3-AT
LaptopLaser range
finder
Communicate
Figure 6 Sensor system attached to mobile robot
Reference pathCurb map
SG
Figure 7 Experimental environment
42 Curb Extraction Results The curb extraction process ina semistructured road environment is shown in Figure 8Figure 8(a) shows the road environment where the experi-ment was performed The red dotted line represents the scanarea of the tilted LRF Figure 8(b) shows the extracted roadsurface on the basis of the scanned LRF data in the roadenvironment When the road surface is extracted the linesegments that satisfy attribute 1 in Section 22 are selected asthe curb candidates Figure 8(c) shows the line segments thatcorrespond to the curb candidates The first and the secondcandidates for each side of the curbs are represented by blueand green lines respectively There are two candidates oneach sideTherefore four pairs of candidates can be extractedas curbs (R1 L1) (R1 L2) (R2 L1) and (R2 L2) The classprediction results for each pair of curb candidates are listedin Table 1 The pairs of candidates (R1 L1) and (R1 L2)are classified as the curb class Finally candidate (R1 L1) isextracted as the curbs as shown in Figure 8(d) which hasthe smallest Mahalanobis distance with respect to the curb
Table 1 Class prediction for pairs of curb candidates
Candidates Mahalanobis distance Class predictionCurb class Noncurb class
1198831(R1 L1) 00005 1634922 True Curb
1198832(R1 L2) 19779 2025195 True Curb
1198833(R2 L1) 1056307 41180 False Curb
1198834(R2 L2) 1102497 32296 False Curb
Table 2 Classification results including confusion matrix
Instance PCA KFDAClass correct 4338 913 4683 986Class incorrect 413 87 68 14Total 4751 100 4751 100
Classified as Classified asTrue curb False curb True curb False curb
True curb 3524(971)
106(29)
3566(982)
64(18)
False curb 307(274)
814(726)
4(04)
1117(996)
class If the LRF data that correspond to the vertical surfaceare detected the proposed method will perform successfullydespite the small and less distinct curbs
The curb extraction was performed while the robotnavigates through the experimental path Figure 9 showsthe curb mapping result from the curb extraction The curbmap is shown in the right bottom in Figure 9 The extractedcurbs are denoted by the magenta dots The results indicatethat most of the curbs along the experimental path weresuccessfully extracted In order to demonstrate the robust-ness of the proposed method comparison of classificationperformance between our previousmethod and the proposedmethod is summarized in Table 2 The accuracy of the curbextractionwith PCAwas 913 for 4751 scanned datasetsTheaccuracy was improved to 986 with the proposed KFDAA confusion matrix is presented below The conventionalmethod and the proposed method show 971 and 982of true positive rate respectively The curb extraction isperformed successfully by the application of both methodsHowever the most important factor in the curb extraction isto reduce the false detection rate False detection is that thenoncurb data are misclassified as the curb dataThe accuracyof the estimated pose can be decreased when the false curbsare used for localization The false detection rate was 274with PCA The false detection rate was reduced to 04 withthe proposed KFDA The result implies that most of thenoncurb data were classified as noncurb data correctly
43 Uncertainty Measurement Results The DGPS measure-ments are represented by red dots along the experimentalpath in Figure 10(a) The areas with large DGPS errors arerepresented by AndashF Figure 10(b) shows the standard devia-tion of the DGPS measurements The standard deviation ofthe DGPS is about 2m in open area There were temporalblackouts in areas B D and E due to satellite blockage
8 Mathematical Problems in Engineering
(a)
0 1 2 3
0
1
2
3
4
5
6
7
Detected road surface
minus1minus2
minus1
minus2minus3minus4minus5minus6
y(m
)
x (m)
(b)
0 1 2 3
0
1
2
3
4
5
6
7
minus1minus2
minus1
minus2minus3minus4minus5minus6
y(m
)
x (m)
R2
L1 R1
L2
(c)
Extracted curbs
0 1 2 3
0
1
2
3
4
5
6
7
minus1minus2
minus1
minus2minus3minus4minus5minus6
y(m
)
x (m)
(d)
Figure 8 Curb extraction results (a) Road environment (b) Road surface detection (c) Curb feature candidates on both sides (d) Extractedcurb
0 50 100 150
0
50
100
150
y(m
)
x (m)
minus50
minus50minus100
Figure 9 Curb mapping result on experimental path
Mathematical Problems in Engineering 9
Reference pathDGPS measurements
SG
A
B
DE
C
F
(a)
0 5 10 15 20 25 300
2
4
6
8
Time (min)
Dist
ance
(m)
A B C D E F
120590DGPS
(b)
Figure 10 (a) DGPS measurement and (b) DGPS uncertainty measurement (1120590 bound)
CurbAdditional LRF
Figure 11 Additional LRF for ground truth of the curbs
The uncertainty measurements in areas B D and E werealmost infinite as shown in Figure 10(b) Furthermore largeDGPS errors occurred in areas A C and F due to thedegraded satellite signals In particular measurement errorswere 21m on average in area F The standard deviation thatwas measured in area F was 64m on average The resultimplies that the regional properties ofDGPSwere obtained bymeasuring the DGPS uncertainty in real time However theprecision of the localization only by DGPS can be decreasedwhen the robot navigates near the buildings
The curb estimation errors are considered in order todefine the error covariance The most accurate result forthe quantitative curb uncertainty is obtained by measuringthe estimation errors in experimental environments Theestimation errors were measured while the robot navigatesthrough the road with curbs Ground truth for the curb wasprovided by an additional LRF that is attached to the sideof the robot as shown in Figure 11 Ground truth of thecurb was provided by line feature from the additional LRFdata Experiments were conducted in order to measure theestimation errors prior to the localization experiment The
Table 3 Error covariance of extracted curb
Range std 120590119903
Angle std 120590120572
Correlation 120590119903120572
Right curb 01620m 00575 rad 00035msdotradLeft curb 01614m 00649 rad minus00034msdotrad
following results show the estimation errors for the range andangle of the extracted curb
Figure 12 shows the histogram of the curb estimationerrors for each sideThe number of the estimation error mea-surements is approximately 5000 The covariance matrix ofthe curb was computed from the distributions of estimationerrors The elements of error covariance for each side of thecurb are listed in Table 3
The covariance representation for the extracted curbs isshown in Figure 13 The extracted curbs are represented byblue lines and the error bounds for the curbs are representedby green dotted lines The resultant curbs exist within theerror bounds with 95 confidence
44 Outdoor Localization Results The localization results areshown in Figure 14 The proposed method was comparedwith the conventional framework for outdoor localizationthat combines DGPS measurement with odometry The bluedash-dot line represents the localization results correctedonly by the DGPS measurements The estimated paths showsome difference with respect to the reference path (yellowdotted line) in area AndashF due to theDGPS errorsThemagentaline represents the localization results corrected byDGPS andthe extracted curb When the curb information is appliedthe results show that the robot position well matches thereference path even if the DGPS errors are large or a blackoutoccurs (area AndashF) It is clear that the curb information plays adominant role The following part presents the localizationerrors in area AndashF as shown in Figure 14 The localizationerrors were compared with the conventional framework thatcombines DGPS measurement with odometry The ground
10 Mathematical Problems in Engineering
0
100
200
300Histogram of left curb range errors
Estimation error (m)
N(c
ount
)
040302010minus01minus02minus03minus04
0
100
200
300
400Histogram of left curb angle errors
Estimation error (rad)
N(c
ount
)
010050minus005minus01
(a)
Estimation error (m)
0
200
400
600
800Histogram of right curb range errors
N(c
ount
)
040302010minus01minus02minus03minus04
0
200
400
600
800Histogram of right curb angle errors
Estimation error (rad)
N(c
ount
)
010050minus005minus01
(b)
Figure 12 Distribution of estimation errors for (a) left and (b) right curbs
0 1 2 3
0
1
2
3
4
5
6
7
Range dataExtracted curbCovariance (95 confidence)
minus1minus2
minus1
minus2minus3minus4minus5minus6
y(m
)
x (m)
Figure 13 Extracted curbs and covariance representation
truth was computed using the additional LRF attached to theside of the robot
Figure 15 shows the lateral errors of the localizationresults The position errors when using the fusion of theodometry and DGPS are shown in Figure 15(a) The lateralerrors in each areawere usually greater than 1m In particularthe maximum error in area F was 5m In contrast thelocalization result which was corrected by odometry DGPSand curb information shows that the lateral errors werewithin 06m across the entire area as shown in Figure 15(b)
SG
A
B
DE
C
F
Reference pathEKF (odometry + DGPS)EKF (odometry + DGPS + curb)
Figure 14 Localization results in semistructured road environment
Therefore the proposed method shows robust performancein terms of lateral position estimation errors despite the largeDGPS errorsTheheading errors of the localization results arerepresented in Figure 16 The result that was corrected usingonly the DGPS data is shown in Figure 16(a) The headingerrors were greater than 1∘ on averageThe variancewas largerthan 2∘ However when the curb information is used forcorrection the heading errors were remarkably decreasedFurthermore the errors rarely exceed 3∘ in the entire areaIn experiments the proposed method showed precise androbust performance for the lateral and heading errors despitethe large DGPS errors and a temporal blackout
Mathematical Problems in Engineering 11
0
1
2
3
4
5
Late
ral e
rror
s (m
)
A B C D E FSection
EKF (odometry + DGPS)
minus1
minus2
minus3
minus4
(a)
A B C D E F
0
1
2
3
4
5
Late
ral e
rror
s (m
)Section
EKF (odometry + DGPS + curb)
minus1
minus2
minus3
minus4
(b)
Figure 15 Lateral errors (a) corrected by DGPS and (b) corrected by DGPS and extracted curb
A B C D E FSection
EKF (odometry + DGPS)
0
5
10
15
Ang
ular
erro
rs (d
eg)
minus5
minus10
(a)
A B C D E F
0
5
10
15
Ang
ular
erro
rs (d
eg)
Section
EKF (odometry + DGPS + curb)
minus5
minus10
(b)
Figure 16 Heading errors (a) corrected by DGPS and (b) corrected by DGPS and extracted curb
5 Conclusion
This paper presents a localization method for outdoor robotsusing curb features in semistructured road environmentsA reliable curb extraction scheme is proposed to classifythe curb candidates as curb and noncurb classes Mostof the curbs in an experimental path are extracted withhigh accuracy An EKF-based localization is also proposed
to combine the extracted curbs with odometry and DGPSmeasurements The uncertainty models of the sensors aredefined by experiments to provide a practical solution forlocalization From experimental results the robustness of theproposed method is demonstrated in real road experimentsThe curb features can correct significantly the lateral positionand heading errors in dense area where the DGPS signal getsdegraded by buildings
12 Mathematical Problems in Engineering
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This research was supported in part by the MKE (TheMinis-try of Knowledge Economy) Korea under the HumanResources Development Program for Convergence RobotSpecialists Support Program supervised by the NIPA(National IT Industry Promotion Agency) (NIPA-2013-H1502-13-1001) This work was also supported by theNational Research Foundation of Korea (NRF) Grant fundedby Korea Government (MEST) (2013-029812)
References
[1] S Thrun M Montemerlo H Dahlkamp et al ldquoStanley therobot that won the DARPA Grand Challengerdquo Journal of FieldRobotics vol 23 no 9 pp 661ndash692 2006
[2] M Buehler K Lagnemma and S Singh The DARPA UrbanChallenge Autonomous Vehicles in City Traffic Springer NewYork NY USA 2009
[3] A Soloviev ldquoTight coupling of GPS laser scanner and iner-tial measurements for navigation in urban environmentsrdquo inProceedings of the IEEEION Position Location and NavigationSymposium pp 511ndash525 Monterey Calif USA May 2008
[4] S Panzieri F Pascucci and G Ulivi ldquoAn outdoor navigationsystem using GPS and inertial platformrdquo IEEEASME Transac-tions on Mechatronics vol 7 no 2 pp 134ndash142 2002
[5] E-J Jung andD-J Yi ldquoTask-oriented navigation algorithms foran outdoor environment with colored borders and obstaclesrdquoIntelligent Service Robotics vol 6 no 2 pp 69ndash77 2013
[6] S Kim J Kang andM Jin Chung ldquoProbabilistic voxelmappingusing an adaptive confidence measure of stereo matchingrdquoIntelligent Service Robotics vol 6 no 2 pp 89ndash99 2013
[7] M Joerger and B Pervan ldquoRange-domain integration of GPSand laser-scanner measurements for outdoor navigationrdquo inProceedings of the 19th International Technical Meeting of theSatellite Division of The Institute of Navigation (ION GNSS rsquo06)pp 1115ndash1123 Fort Worth Tex USA September 2006
[8] M Hentschel O Wulf and B Wagner ldquoA GPS and laser-basedlocalization for urban and non-urban outdoor environmentsrdquoin Proceedings of the IEEERSJ International Conference on Intel-ligent Robots and Systems pp 149ndash154 Nice France September2008
[9] A Georgiev and P K Allen ldquoLocalizationmethods for amobilerobot in urban environmentsrdquo IEEE Transactions on Roboticsvol 20 no 5 pp 851ndash864 2004
[10] Y Morales T Tsubouchi and S Yuta ldquoVehicle localizationin outdoor mountainous forested paths and extension of two-dimensional road centerline maps to three-dimensional mapsrdquoAdvanced Robotics vol 24 no 4 pp 489ndash513 2010
[11] W SWijesoma K R S Kodagoda andA P Balasuriya ldquoRoad-boundary detection and tracking using ladar sensingrdquo IEEETransactions onRobotics andAutomation vol 20 no 3 pp 456ndash464 2004
[12] M Jabbour and P Bonnifait ldquoGlobal localization robust toGPS outages using a vertical ladarrdquo in Proceedings of the 9th
International Conference on Control Automation Robotics andVision pp 1ndash6 December 2006
[13] P Bonnifait M Jabbour and V Cherfaoui ldquoAutonomousnavigation in urban areas using GIS-managed informationrdquoInternational Journal of Vehicle Autonomous Systems vol 6 no5 pp 83ndash103 2008
[14] Y Shin D Kim H Lee J Park and W Chung ldquoAutonomousnavigation of a surveillance robot in harsh outdoor environ-mentsrdquo Advances in Mechanical Engineering vol 2013 ArticleID 837484 15 pages 2013
[15] Y Shin C Jung andWChung ldquoDrivable road region detectionusing a single laser range finder for outdoor patrol robotsrdquo inProceedings of the IEEE Intelligent Vehicles Symposium (IV rsquo10)pp 877ndash882 San Diego Calif USA June 2010
[16] D Kim and W Chung ldquoLocalization of outdoor mobile robotsusing road featuresrdquo in Proceedings of the 8th International Con-ference on Ubiquitous Robots and Ambient Intelligence (URAIrsquo11) pp 363ndash365 Incheon Republic of Korea November 2011
[17] S Mika G Ratsch J Weston B Scholkopf and K MullerldquoFisher discriminant analysis with kernelsrdquoNeural Networks forSignal Processing vol 9 pp 41ndash48 1999
[18] S Mika G Ratsch and K R Muller ldquoA mathematical pro-gramming approach to the kernel fisher algorithmrdquo Advancesin Neural Information Processing vol 13 pp 591ndash597 2001
[19] G Camps-Valls and L Bruzzone Kernel Methods for RemoteSensing Data Analysis JohnWiley amp Sons New York NY USA2009
[20] R E Kalman ldquoA new approach to linear filtering and predictionproblemsrdquo Journal of Basic Engineering vol 82 no 1 pp 35ndash451960
[21] R E Kalman and R S Bucy ldquoNew results in linear filtering andprediction theoryrdquo Journal of Basic Engineering vol 83 no 3pp 95ndash108 1961
[22] J J Leonard and H F Durrant-Whyte Directed Sonar Sensingfor Mobile Robot Navigation Kluwer Academic DordrechtTheNetherlands 1992
[23] B W Parkinson and J J Spilker Global Positioning SystemTheory and ApplicationsThe American Institute of Aeronauticsand Astronautics Washington DC USA 1996
[24] K O Arras and R Y Siegwart ldquoFeature extraction and sceneinterpretation for map-based navigation and map buildingrdquo in12th Mobile Robots Conference vol 3210 of Proceedings of SPIEpp 42ndash53 Pittsburgh Pa USA January 1998
[25] S T Pfister S I Roumeliotis and J W Burdick ldquoWeighted linefitting algorithms for mobile robot map building and efficientdata representationrdquo in Proceedings of the IEEE InternationalConference on Robotics and Automation pp 1304ndash1311 Septem-ber 2003
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
6 Mathematical Problems in Engineering
Extracted curb(from 1st estimated robot perspective)
Actual curb(curb line map)
W
R
Wri
W120572i
Rrk
R120572k
W+
k1
Wy+k1
Wx+k1
Figure 5 Extracted curb features and a line map with respect to theglobal coordinate frame
The state vector xminus119896= [119909minus
119896119910minus
119896
120579minus
119896]
119879
is the predicted robotpose at sampling time 119896 When the initial pose of the robot isgiven the robot pose is represented by 119909 119910 and 120579 in a globalcoordinate frameTheuncertainty of the predicted robot poseconsistently increases because of the accumulative errors ofthe odometry
In order to correct the odometry error the first measure-ment correction is performed using DGPS measurementsThe update frequency is set to 1Hz on the basis of theDGPS measurement frequency When the available positionmeasurement is provided the observation vector is given inglobal coordinates Consider the following
zDGPS119896 = [119909DGPS119896 119910DGPS119896]119879
(16)
The observation model for the current state is describedas follows
hDGPS (xminus
119896 119896) = [119909
minus
119896119910minus
119896]
119879
(17)
The measurement Jacobian matrixH119896is given as follows
HDGPS119896 =120597h (xminus119896 119896)
120597xminus119896
= [
1 0 0
0 1 0] (18)
zcurb119896 = [120572119896
119903119896]
119879
(19)
The second measurement correction is conducted byusing the curb features The observation vector for theextracted curb is given by (19) When the curbs are extractedon both sides there are two measurement vectors for the leftand right curbs as shown in Figure 5 The sequence of thesecond measurement correction is from the right curb to theleft curbThe update rate is 5Hz if the curbs are continuouslyextracted
The robot pose is corrected by comparing the curb withthe map The extracted curb is matched with the 119894th line ofthe curb map The observation model for the 119894th line 119882z
119894=
[119882120572119894
119882119903119894]
119879
and the robot pose at time 119896 is given by thefollowing equation
hcurb (x+
1198961 119896 119894)
= [
119882120572119894minus120579+
1198961
119882119903119894minus 119909+
1198961cos 119882120572
119894+ 119910+
1198961sin 119882120572
119894
]
(20)
The Jacobian matrixH119896is defined as follows
Hcurb119896 =120597h (x+1198961
119896 119894)
120597x+1198961
= [
0 0 minus1
minus cos 119882120572119894minus sin 119882120572
1198940
]
(21)
The consistency of EKF relies on the observation modelIf an erroneous sensor observation is provided the systemdoes not provide a consistent result Therefore the outliersthat lie outside of the uncertainty bounds should be rejectedA normalized innovation squared (NIS) test is implementedin order to confirm the consistency of the filter NIS valuehas a 120594
2 distribution with respect to 119899 degrees of freedomConsider the following
NIS119896= (z119896minus h (x+
119896 119896))
119879Sminus1119896
(z119896minus h (x+
119896 119896)) le 120594
2 (22)
where S119896is the innovation matrix which is defined as S
119896=
H119896Pminus119896H119879119896+R119896 The NIS value for valid measurements should
be within the threshold of the 1205942 distribution However the
erroneous measurements are discarded when the NIS valuelies outside the threshold boundary A threshold value thatcorresponds to a 95 confidence region is used for outlierrejection
4 Experimental Results
41 Experimental Setup Figure 6 shows the sensor systemattached to the mobile robot The outdoor mobile robotis a Pioneer P3-AT a commercial outdoor platform ofMobileRobots The wheel encoders attached to the drivingmotors provide odometry information SICK LMS-100 wasused to detect the curb The LRF was tilted by 5∘ towardthe ground A Novatel DGPS system was used to measurethe global position The robot was equipped with a roverantenna and a base stationwas located on the roof of a nearbybuilding The ldquotruerdquo value for the curb and the ground truthwere measured using an additional LRF (HOKUYO URG-04lx) attached to the side of the robot
The experiment was performed in Korea University inSeoul Korea as shown in Figure 7 The robot was drivenmanually along the yellow dashed line from ldquoSrdquo to ldquoGrdquoThe curbs along the experimental path are represented assolid green lines The target environment has semistructuredgeometry that is composed of paved roads and curbs inmost of the region Furthermore there are tall buildings andtunnels that degrade the DGPS precisionThe travel distancealong the experimental path was 775m and average speed ofthe robot was 05ms
Mathematical Problems in Engineering 7
DGPS baseDGPS rover
Pioneer P3-AT
LaptopLaser range
finder
Communicate
Figure 6 Sensor system attached to mobile robot
Reference pathCurb map
SG
Figure 7 Experimental environment
42 Curb Extraction Results The curb extraction process ina semistructured road environment is shown in Figure 8Figure 8(a) shows the road environment where the experi-ment was performed The red dotted line represents the scanarea of the tilted LRF Figure 8(b) shows the extracted roadsurface on the basis of the scanned LRF data in the roadenvironment When the road surface is extracted the linesegments that satisfy attribute 1 in Section 22 are selected asthe curb candidates Figure 8(c) shows the line segments thatcorrespond to the curb candidates The first and the secondcandidates for each side of the curbs are represented by blueand green lines respectively There are two candidates oneach sideTherefore four pairs of candidates can be extractedas curbs (R1 L1) (R1 L2) (R2 L1) and (R2 L2) The classprediction results for each pair of curb candidates are listedin Table 1 The pairs of candidates (R1 L1) and (R1 L2)are classified as the curb class Finally candidate (R1 L1) isextracted as the curbs as shown in Figure 8(d) which hasthe smallest Mahalanobis distance with respect to the curb
Table 1 Class prediction for pairs of curb candidates
Candidates Mahalanobis distance Class predictionCurb class Noncurb class
1198831(R1 L1) 00005 1634922 True Curb
1198832(R1 L2) 19779 2025195 True Curb
1198833(R2 L1) 1056307 41180 False Curb
1198834(R2 L2) 1102497 32296 False Curb
Table 2 Classification results including confusion matrix
Instance PCA KFDAClass correct 4338 913 4683 986Class incorrect 413 87 68 14Total 4751 100 4751 100
Classified as Classified asTrue curb False curb True curb False curb
True curb 3524(971)
106(29)
3566(982)
64(18)
False curb 307(274)
814(726)
4(04)
1117(996)
class If the LRF data that correspond to the vertical surfaceare detected the proposed method will perform successfullydespite the small and less distinct curbs
The curb extraction was performed while the robotnavigates through the experimental path Figure 9 showsthe curb mapping result from the curb extraction The curbmap is shown in the right bottom in Figure 9 The extractedcurbs are denoted by the magenta dots The results indicatethat most of the curbs along the experimental path weresuccessfully extracted In order to demonstrate the robust-ness of the proposed method comparison of classificationperformance between our previousmethod and the proposedmethod is summarized in Table 2 The accuracy of the curbextractionwith PCAwas 913 for 4751 scanned datasetsTheaccuracy was improved to 986 with the proposed KFDAA confusion matrix is presented below The conventionalmethod and the proposed method show 971 and 982of true positive rate respectively The curb extraction isperformed successfully by the application of both methodsHowever the most important factor in the curb extraction isto reduce the false detection rate False detection is that thenoncurb data are misclassified as the curb dataThe accuracyof the estimated pose can be decreased when the false curbsare used for localization The false detection rate was 274with PCA The false detection rate was reduced to 04 withthe proposed KFDA The result implies that most of thenoncurb data were classified as noncurb data correctly
43 Uncertainty Measurement Results The DGPS measure-ments are represented by red dots along the experimentalpath in Figure 10(a) The areas with large DGPS errors arerepresented by AndashF Figure 10(b) shows the standard devia-tion of the DGPS measurements The standard deviation ofthe DGPS is about 2m in open area There were temporalblackouts in areas B D and E due to satellite blockage
8 Mathematical Problems in Engineering
(a)
0 1 2 3
0
1
2
3
4
5
6
7
Detected road surface
minus1minus2
minus1
minus2minus3minus4minus5minus6
y(m
)
x (m)
(b)
0 1 2 3
0
1
2
3
4
5
6
7
minus1minus2
minus1
minus2minus3minus4minus5minus6
y(m
)
x (m)
R2
L1 R1
L2
(c)
Extracted curbs
0 1 2 3
0
1
2
3
4
5
6
7
minus1minus2
minus1
minus2minus3minus4minus5minus6
y(m
)
x (m)
(d)
Figure 8 Curb extraction results (a) Road environment (b) Road surface detection (c) Curb feature candidates on both sides (d) Extractedcurb
0 50 100 150
0
50
100
150
y(m
)
x (m)
minus50
minus50minus100
Figure 9 Curb mapping result on experimental path
Mathematical Problems in Engineering 9
Reference pathDGPS measurements
SG
A
B
DE
C
F
(a)
0 5 10 15 20 25 300
2
4
6
8
Time (min)
Dist
ance
(m)
A B C D E F
120590DGPS
(b)
Figure 10 (a) DGPS measurement and (b) DGPS uncertainty measurement (1120590 bound)
CurbAdditional LRF
Figure 11 Additional LRF for ground truth of the curbs
The uncertainty measurements in areas B D and E werealmost infinite as shown in Figure 10(b) Furthermore largeDGPS errors occurred in areas A C and F due to thedegraded satellite signals In particular measurement errorswere 21m on average in area F The standard deviation thatwas measured in area F was 64m on average The resultimplies that the regional properties ofDGPSwere obtained bymeasuring the DGPS uncertainty in real time However theprecision of the localization only by DGPS can be decreasedwhen the robot navigates near the buildings
The curb estimation errors are considered in order todefine the error covariance The most accurate result forthe quantitative curb uncertainty is obtained by measuringthe estimation errors in experimental environments Theestimation errors were measured while the robot navigatesthrough the road with curbs Ground truth for the curb wasprovided by an additional LRF that is attached to the sideof the robot as shown in Figure 11 Ground truth of thecurb was provided by line feature from the additional LRFdata Experiments were conducted in order to measure theestimation errors prior to the localization experiment The
Table 3 Error covariance of extracted curb
Range std 120590119903
Angle std 120590120572
Correlation 120590119903120572
Right curb 01620m 00575 rad 00035msdotradLeft curb 01614m 00649 rad minus00034msdotrad
following results show the estimation errors for the range andangle of the extracted curb
Figure 12 shows the histogram of the curb estimationerrors for each sideThe number of the estimation error mea-surements is approximately 5000 The covariance matrix ofthe curb was computed from the distributions of estimationerrors The elements of error covariance for each side of thecurb are listed in Table 3
The covariance representation for the extracted curbs isshown in Figure 13 The extracted curbs are represented byblue lines and the error bounds for the curbs are representedby green dotted lines The resultant curbs exist within theerror bounds with 95 confidence
44 Outdoor Localization Results The localization results areshown in Figure 14 The proposed method was comparedwith the conventional framework for outdoor localizationthat combines DGPS measurement with odometry The bluedash-dot line represents the localization results correctedonly by the DGPS measurements The estimated paths showsome difference with respect to the reference path (yellowdotted line) in area AndashF due to theDGPS errorsThemagentaline represents the localization results corrected byDGPS andthe extracted curb When the curb information is appliedthe results show that the robot position well matches thereference path even if the DGPS errors are large or a blackoutoccurs (area AndashF) It is clear that the curb information plays adominant role The following part presents the localizationerrors in area AndashF as shown in Figure 14 The localizationerrors were compared with the conventional framework thatcombines DGPS measurement with odometry The ground
10 Mathematical Problems in Engineering
0
100
200
300Histogram of left curb range errors
Estimation error (m)
N(c
ount
)
040302010minus01minus02minus03minus04
0
100
200
300
400Histogram of left curb angle errors
Estimation error (rad)
N(c
ount
)
010050minus005minus01
(a)
Estimation error (m)
0
200
400
600
800Histogram of right curb range errors
N(c
ount
)
040302010minus01minus02minus03minus04
0
200
400
600
800Histogram of right curb angle errors
Estimation error (rad)
N(c
ount
)
010050minus005minus01
(b)
Figure 12 Distribution of estimation errors for (a) left and (b) right curbs
0 1 2 3
0
1
2
3
4
5
6
7
Range dataExtracted curbCovariance (95 confidence)
minus1minus2
minus1
minus2minus3minus4minus5minus6
y(m
)
x (m)
Figure 13 Extracted curbs and covariance representation
truth was computed using the additional LRF attached to theside of the robot
Figure 15 shows the lateral errors of the localizationresults The position errors when using the fusion of theodometry and DGPS are shown in Figure 15(a) The lateralerrors in each areawere usually greater than 1m In particularthe maximum error in area F was 5m In contrast thelocalization result which was corrected by odometry DGPSand curb information shows that the lateral errors werewithin 06m across the entire area as shown in Figure 15(b)
SG
A
B
DE
C
F
Reference pathEKF (odometry + DGPS)EKF (odometry + DGPS + curb)
Figure 14 Localization results in semistructured road environment
Therefore the proposed method shows robust performancein terms of lateral position estimation errors despite the largeDGPS errorsTheheading errors of the localization results arerepresented in Figure 16 The result that was corrected usingonly the DGPS data is shown in Figure 16(a) The headingerrors were greater than 1∘ on averageThe variancewas largerthan 2∘ However when the curb information is used forcorrection the heading errors were remarkably decreasedFurthermore the errors rarely exceed 3∘ in the entire areaIn experiments the proposed method showed precise androbust performance for the lateral and heading errors despitethe large DGPS errors and a temporal blackout
Mathematical Problems in Engineering 11
0
1
2
3
4
5
Late
ral e
rror
s (m
)
A B C D E FSection
EKF (odometry + DGPS)
minus1
minus2
minus3
minus4
(a)
A B C D E F
0
1
2
3
4
5
Late
ral e
rror
s (m
)Section
EKF (odometry + DGPS + curb)
minus1
minus2
minus3
minus4
(b)
Figure 15 Lateral errors (a) corrected by DGPS and (b) corrected by DGPS and extracted curb
A B C D E FSection
EKF (odometry + DGPS)
0
5
10
15
Ang
ular
erro
rs (d
eg)
minus5
minus10
(a)
A B C D E F
0
5
10
15
Ang
ular
erro
rs (d
eg)
Section
EKF (odometry + DGPS + curb)
minus5
minus10
(b)
Figure 16 Heading errors (a) corrected by DGPS and (b) corrected by DGPS and extracted curb
5 Conclusion
This paper presents a localization method for outdoor robotsusing curb features in semistructured road environmentsA reliable curb extraction scheme is proposed to classifythe curb candidates as curb and noncurb classes Mostof the curbs in an experimental path are extracted withhigh accuracy An EKF-based localization is also proposed
to combine the extracted curbs with odometry and DGPSmeasurements The uncertainty models of the sensors aredefined by experiments to provide a practical solution forlocalization From experimental results the robustness of theproposed method is demonstrated in real road experimentsThe curb features can correct significantly the lateral positionand heading errors in dense area where the DGPS signal getsdegraded by buildings
12 Mathematical Problems in Engineering
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This research was supported in part by the MKE (TheMinis-try of Knowledge Economy) Korea under the HumanResources Development Program for Convergence RobotSpecialists Support Program supervised by the NIPA(National IT Industry Promotion Agency) (NIPA-2013-H1502-13-1001) This work was also supported by theNational Research Foundation of Korea (NRF) Grant fundedby Korea Government (MEST) (2013-029812)
References
[1] S Thrun M Montemerlo H Dahlkamp et al ldquoStanley therobot that won the DARPA Grand Challengerdquo Journal of FieldRobotics vol 23 no 9 pp 661ndash692 2006
[2] M Buehler K Lagnemma and S Singh The DARPA UrbanChallenge Autonomous Vehicles in City Traffic Springer NewYork NY USA 2009
[3] A Soloviev ldquoTight coupling of GPS laser scanner and iner-tial measurements for navigation in urban environmentsrdquo inProceedings of the IEEEION Position Location and NavigationSymposium pp 511ndash525 Monterey Calif USA May 2008
[4] S Panzieri F Pascucci and G Ulivi ldquoAn outdoor navigationsystem using GPS and inertial platformrdquo IEEEASME Transac-tions on Mechatronics vol 7 no 2 pp 134ndash142 2002
[5] E-J Jung andD-J Yi ldquoTask-oriented navigation algorithms foran outdoor environment with colored borders and obstaclesrdquoIntelligent Service Robotics vol 6 no 2 pp 69ndash77 2013
[6] S Kim J Kang andM Jin Chung ldquoProbabilistic voxelmappingusing an adaptive confidence measure of stereo matchingrdquoIntelligent Service Robotics vol 6 no 2 pp 89ndash99 2013
[7] M Joerger and B Pervan ldquoRange-domain integration of GPSand laser-scanner measurements for outdoor navigationrdquo inProceedings of the 19th International Technical Meeting of theSatellite Division of The Institute of Navigation (ION GNSS rsquo06)pp 1115ndash1123 Fort Worth Tex USA September 2006
[8] M Hentschel O Wulf and B Wagner ldquoA GPS and laser-basedlocalization for urban and non-urban outdoor environmentsrdquoin Proceedings of the IEEERSJ International Conference on Intel-ligent Robots and Systems pp 149ndash154 Nice France September2008
[9] A Georgiev and P K Allen ldquoLocalizationmethods for amobilerobot in urban environmentsrdquo IEEE Transactions on Roboticsvol 20 no 5 pp 851ndash864 2004
[10] Y Morales T Tsubouchi and S Yuta ldquoVehicle localizationin outdoor mountainous forested paths and extension of two-dimensional road centerline maps to three-dimensional mapsrdquoAdvanced Robotics vol 24 no 4 pp 489ndash513 2010
[11] W SWijesoma K R S Kodagoda andA P Balasuriya ldquoRoad-boundary detection and tracking using ladar sensingrdquo IEEETransactions onRobotics andAutomation vol 20 no 3 pp 456ndash464 2004
[12] M Jabbour and P Bonnifait ldquoGlobal localization robust toGPS outages using a vertical ladarrdquo in Proceedings of the 9th
International Conference on Control Automation Robotics andVision pp 1ndash6 December 2006
[13] P Bonnifait M Jabbour and V Cherfaoui ldquoAutonomousnavigation in urban areas using GIS-managed informationrdquoInternational Journal of Vehicle Autonomous Systems vol 6 no5 pp 83ndash103 2008
[14] Y Shin D Kim H Lee J Park and W Chung ldquoAutonomousnavigation of a surveillance robot in harsh outdoor environ-mentsrdquo Advances in Mechanical Engineering vol 2013 ArticleID 837484 15 pages 2013
[15] Y Shin C Jung andWChung ldquoDrivable road region detectionusing a single laser range finder for outdoor patrol robotsrdquo inProceedings of the IEEE Intelligent Vehicles Symposium (IV rsquo10)pp 877ndash882 San Diego Calif USA June 2010
[16] D Kim and W Chung ldquoLocalization of outdoor mobile robotsusing road featuresrdquo in Proceedings of the 8th International Con-ference on Ubiquitous Robots and Ambient Intelligence (URAIrsquo11) pp 363ndash365 Incheon Republic of Korea November 2011
[17] S Mika G Ratsch J Weston B Scholkopf and K MullerldquoFisher discriminant analysis with kernelsrdquoNeural Networks forSignal Processing vol 9 pp 41ndash48 1999
[18] S Mika G Ratsch and K R Muller ldquoA mathematical pro-gramming approach to the kernel fisher algorithmrdquo Advancesin Neural Information Processing vol 13 pp 591ndash597 2001
[19] G Camps-Valls and L Bruzzone Kernel Methods for RemoteSensing Data Analysis JohnWiley amp Sons New York NY USA2009
[20] R E Kalman ldquoA new approach to linear filtering and predictionproblemsrdquo Journal of Basic Engineering vol 82 no 1 pp 35ndash451960
[21] R E Kalman and R S Bucy ldquoNew results in linear filtering andprediction theoryrdquo Journal of Basic Engineering vol 83 no 3pp 95ndash108 1961
[22] J J Leonard and H F Durrant-Whyte Directed Sonar Sensingfor Mobile Robot Navigation Kluwer Academic DordrechtTheNetherlands 1992
[23] B W Parkinson and J J Spilker Global Positioning SystemTheory and ApplicationsThe American Institute of Aeronauticsand Astronautics Washington DC USA 1996
[24] K O Arras and R Y Siegwart ldquoFeature extraction and sceneinterpretation for map-based navigation and map buildingrdquo in12th Mobile Robots Conference vol 3210 of Proceedings of SPIEpp 42ndash53 Pittsburgh Pa USA January 1998
[25] S T Pfister S I Roumeliotis and J W Burdick ldquoWeighted linefitting algorithms for mobile robot map building and efficientdata representationrdquo in Proceedings of the IEEE InternationalConference on Robotics and Automation pp 1304ndash1311 Septem-ber 2003
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
Mathematical Problems in Engineering 7
DGPS baseDGPS rover
Pioneer P3-AT
LaptopLaser range
finder
Communicate
Figure 6 Sensor system attached to mobile robot
Reference pathCurb map
SG
Figure 7 Experimental environment
42 Curb Extraction Results The curb extraction process ina semistructured road environment is shown in Figure 8Figure 8(a) shows the road environment where the experi-ment was performed The red dotted line represents the scanarea of the tilted LRF Figure 8(b) shows the extracted roadsurface on the basis of the scanned LRF data in the roadenvironment When the road surface is extracted the linesegments that satisfy attribute 1 in Section 22 are selected asthe curb candidates Figure 8(c) shows the line segments thatcorrespond to the curb candidates The first and the secondcandidates for each side of the curbs are represented by blueand green lines respectively There are two candidates oneach sideTherefore four pairs of candidates can be extractedas curbs (R1 L1) (R1 L2) (R2 L1) and (R2 L2) The classprediction results for each pair of curb candidates are listedin Table 1 The pairs of candidates (R1 L1) and (R1 L2)are classified as the curb class Finally candidate (R1 L1) isextracted as the curbs as shown in Figure 8(d) which hasthe smallest Mahalanobis distance with respect to the curb
Table 1 Class prediction for pairs of curb candidates
Candidates Mahalanobis distance Class predictionCurb class Noncurb class
1198831(R1 L1) 00005 1634922 True Curb
1198832(R1 L2) 19779 2025195 True Curb
1198833(R2 L1) 1056307 41180 False Curb
1198834(R2 L2) 1102497 32296 False Curb
Table 2 Classification results including confusion matrix
Instance PCA KFDAClass correct 4338 913 4683 986Class incorrect 413 87 68 14Total 4751 100 4751 100
Classified as Classified asTrue curb False curb True curb False curb
True curb 3524(971)
106(29)
3566(982)
64(18)
False curb 307(274)
814(726)
4(04)
1117(996)
class If the LRF data that correspond to the vertical surfaceare detected the proposed method will perform successfullydespite the small and less distinct curbs
The curb extraction was performed while the robotnavigates through the experimental path Figure 9 showsthe curb mapping result from the curb extraction The curbmap is shown in the right bottom in Figure 9 The extractedcurbs are denoted by the magenta dots The results indicatethat most of the curbs along the experimental path weresuccessfully extracted In order to demonstrate the robust-ness of the proposed method comparison of classificationperformance between our previousmethod and the proposedmethod is summarized in Table 2 The accuracy of the curbextractionwith PCAwas 913 for 4751 scanned datasetsTheaccuracy was improved to 986 with the proposed KFDAA confusion matrix is presented below The conventionalmethod and the proposed method show 971 and 982of true positive rate respectively The curb extraction isperformed successfully by the application of both methodsHowever the most important factor in the curb extraction isto reduce the false detection rate False detection is that thenoncurb data are misclassified as the curb dataThe accuracyof the estimated pose can be decreased when the false curbsare used for localization The false detection rate was 274with PCA The false detection rate was reduced to 04 withthe proposed KFDA The result implies that most of thenoncurb data were classified as noncurb data correctly
43 Uncertainty Measurement Results The DGPS measure-ments are represented by red dots along the experimentalpath in Figure 10(a) The areas with large DGPS errors arerepresented by AndashF Figure 10(b) shows the standard devia-tion of the DGPS measurements The standard deviation ofthe DGPS is about 2m in open area There were temporalblackouts in areas B D and E due to satellite blockage
8 Mathematical Problems in Engineering
(a)
0 1 2 3
0
1
2
3
4
5
6
7
Detected road surface
minus1minus2
minus1
minus2minus3minus4minus5minus6
y(m
)
x (m)
(b)
0 1 2 3
0
1
2
3
4
5
6
7
minus1minus2
minus1
minus2minus3minus4minus5minus6
y(m
)
x (m)
R2
L1 R1
L2
(c)
Extracted curbs
0 1 2 3
0
1
2
3
4
5
6
7
minus1minus2
minus1
minus2minus3minus4minus5minus6
y(m
)
x (m)
(d)
Figure 8 Curb extraction results (a) Road environment (b) Road surface detection (c) Curb feature candidates on both sides (d) Extractedcurb
0 50 100 150
0
50
100
150
y(m
)
x (m)
minus50
minus50minus100
Figure 9 Curb mapping result on experimental path
Mathematical Problems in Engineering 9
Reference pathDGPS measurements
SG
A
B
DE
C
F
(a)
0 5 10 15 20 25 300
2
4
6
8
Time (min)
Dist
ance
(m)
A B C D E F
120590DGPS
(b)
Figure 10 (a) DGPS measurement and (b) DGPS uncertainty measurement (1120590 bound)
CurbAdditional LRF
Figure 11 Additional LRF for ground truth of the curbs
The uncertainty measurements in areas B D and E werealmost infinite as shown in Figure 10(b) Furthermore largeDGPS errors occurred in areas A C and F due to thedegraded satellite signals In particular measurement errorswere 21m on average in area F The standard deviation thatwas measured in area F was 64m on average The resultimplies that the regional properties ofDGPSwere obtained bymeasuring the DGPS uncertainty in real time However theprecision of the localization only by DGPS can be decreasedwhen the robot navigates near the buildings
The curb estimation errors are considered in order todefine the error covariance The most accurate result forthe quantitative curb uncertainty is obtained by measuringthe estimation errors in experimental environments Theestimation errors were measured while the robot navigatesthrough the road with curbs Ground truth for the curb wasprovided by an additional LRF that is attached to the sideof the robot as shown in Figure 11 Ground truth of thecurb was provided by line feature from the additional LRFdata Experiments were conducted in order to measure theestimation errors prior to the localization experiment The
Table 3 Error covariance of extracted curb
Range std 120590119903
Angle std 120590120572
Correlation 120590119903120572
Right curb 01620m 00575 rad 00035msdotradLeft curb 01614m 00649 rad minus00034msdotrad
following results show the estimation errors for the range andangle of the extracted curb
Figure 12 shows the histogram of the curb estimationerrors for each sideThe number of the estimation error mea-surements is approximately 5000 The covariance matrix ofthe curb was computed from the distributions of estimationerrors The elements of error covariance for each side of thecurb are listed in Table 3
The covariance representation for the extracted curbs isshown in Figure 13 The extracted curbs are represented byblue lines and the error bounds for the curbs are representedby green dotted lines The resultant curbs exist within theerror bounds with 95 confidence
44 Outdoor Localization Results The localization results areshown in Figure 14 The proposed method was comparedwith the conventional framework for outdoor localizationthat combines DGPS measurement with odometry The bluedash-dot line represents the localization results correctedonly by the DGPS measurements The estimated paths showsome difference with respect to the reference path (yellowdotted line) in area AndashF due to theDGPS errorsThemagentaline represents the localization results corrected byDGPS andthe extracted curb When the curb information is appliedthe results show that the robot position well matches thereference path even if the DGPS errors are large or a blackoutoccurs (area AndashF) It is clear that the curb information plays adominant role The following part presents the localizationerrors in area AndashF as shown in Figure 14 The localizationerrors were compared with the conventional framework thatcombines DGPS measurement with odometry The ground
10 Mathematical Problems in Engineering
0
100
200
300Histogram of left curb range errors
Estimation error (m)
N(c
ount
)
040302010minus01minus02minus03minus04
0
100
200
300
400Histogram of left curb angle errors
Estimation error (rad)
N(c
ount
)
010050minus005minus01
(a)
Estimation error (m)
0
200
400
600
800Histogram of right curb range errors
N(c
ount
)
040302010minus01minus02minus03minus04
0
200
400
600
800Histogram of right curb angle errors
Estimation error (rad)
N(c
ount
)
010050minus005minus01
(b)
Figure 12 Distribution of estimation errors for (a) left and (b) right curbs
0 1 2 3
0
1
2
3
4
5
6
7
Range dataExtracted curbCovariance (95 confidence)
minus1minus2
minus1
minus2minus3minus4minus5minus6
y(m
)
x (m)
Figure 13 Extracted curbs and covariance representation
truth was computed using the additional LRF attached to theside of the robot
Figure 15 shows the lateral errors of the localizationresults The position errors when using the fusion of theodometry and DGPS are shown in Figure 15(a) The lateralerrors in each areawere usually greater than 1m In particularthe maximum error in area F was 5m In contrast thelocalization result which was corrected by odometry DGPSand curb information shows that the lateral errors werewithin 06m across the entire area as shown in Figure 15(b)
SG
A
B
DE
C
F
Reference pathEKF (odometry + DGPS)EKF (odometry + DGPS + curb)
Figure 14 Localization results in semistructured road environment
Therefore the proposed method shows robust performancein terms of lateral position estimation errors despite the largeDGPS errorsTheheading errors of the localization results arerepresented in Figure 16 The result that was corrected usingonly the DGPS data is shown in Figure 16(a) The headingerrors were greater than 1∘ on averageThe variancewas largerthan 2∘ However when the curb information is used forcorrection the heading errors were remarkably decreasedFurthermore the errors rarely exceed 3∘ in the entire areaIn experiments the proposed method showed precise androbust performance for the lateral and heading errors despitethe large DGPS errors and a temporal blackout
Mathematical Problems in Engineering 11
0
1
2
3
4
5
Late
ral e
rror
s (m
)
A B C D E FSection
EKF (odometry + DGPS)
minus1
minus2
minus3
minus4
(a)
A B C D E F
0
1
2
3
4
5
Late
ral e
rror
s (m
)Section
EKF (odometry + DGPS + curb)
minus1
minus2
minus3
minus4
(b)
Figure 15 Lateral errors (a) corrected by DGPS and (b) corrected by DGPS and extracted curb
A B C D E FSection
EKF (odometry + DGPS)
0
5
10
15
Ang
ular
erro
rs (d
eg)
minus5
minus10
(a)
A B C D E F
0
5
10
15
Ang
ular
erro
rs (d
eg)
Section
EKF (odometry + DGPS + curb)
minus5
minus10
(b)
Figure 16 Heading errors (a) corrected by DGPS and (b) corrected by DGPS and extracted curb
5 Conclusion
This paper presents a localization method for outdoor robotsusing curb features in semistructured road environmentsA reliable curb extraction scheme is proposed to classifythe curb candidates as curb and noncurb classes Mostof the curbs in an experimental path are extracted withhigh accuracy An EKF-based localization is also proposed
to combine the extracted curbs with odometry and DGPSmeasurements The uncertainty models of the sensors aredefined by experiments to provide a practical solution forlocalization From experimental results the robustness of theproposed method is demonstrated in real road experimentsThe curb features can correct significantly the lateral positionand heading errors in dense area where the DGPS signal getsdegraded by buildings
12 Mathematical Problems in Engineering
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This research was supported in part by the MKE (TheMinis-try of Knowledge Economy) Korea under the HumanResources Development Program for Convergence RobotSpecialists Support Program supervised by the NIPA(National IT Industry Promotion Agency) (NIPA-2013-H1502-13-1001) This work was also supported by theNational Research Foundation of Korea (NRF) Grant fundedby Korea Government (MEST) (2013-029812)
References
[1] S Thrun M Montemerlo H Dahlkamp et al ldquoStanley therobot that won the DARPA Grand Challengerdquo Journal of FieldRobotics vol 23 no 9 pp 661ndash692 2006
[2] M Buehler K Lagnemma and S Singh The DARPA UrbanChallenge Autonomous Vehicles in City Traffic Springer NewYork NY USA 2009
[3] A Soloviev ldquoTight coupling of GPS laser scanner and iner-tial measurements for navigation in urban environmentsrdquo inProceedings of the IEEEION Position Location and NavigationSymposium pp 511ndash525 Monterey Calif USA May 2008
[4] S Panzieri F Pascucci and G Ulivi ldquoAn outdoor navigationsystem using GPS and inertial platformrdquo IEEEASME Transac-tions on Mechatronics vol 7 no 2 pp 134ndash142 2002
[5] E-J Jung andD-J Yi ldquoTask-oriented navigation algorithms foran outdoor environment with colored borders and obstaclesrdquoIntelligent Service Robotics vol 6 no 2 pp 69ndash77 2013
[6] S Kim J Kang andM Jin Chung ldquoProbabilistic voxelmappingusing an adaptive confidence measure of stereo matchingrdquoIntelligent Service Robotics vol 6 no 2 pp 89ndash99 2013
[7] M Joerger and B Pervan ldquoRange-domain integration of GPSand laser-scanner measurements for outdoor navigationrdquo inProceedings of the 19th International Technical Meeting of theSatellite Division of The Institute of Navigation (ION GNSS rsquo06)pp 1115ndash1123 Fort Worth Tex USA September 2006
[8] M Hentschel O Wulf and B Wagner ldquoA GPS and laser-basedlocalization for urban and non-urban outdoor environmentsrdquoin Proceedings of the IEEERSJ International Conference on Intel-ligent Robots and Systems pp 149ndash154 Nice France September2008
[9] A Georgiev and P K Allen ldquoLocalizationmethods for amobilerobot in urban environmentsrdquo IEEE Transactions on Roboticsvol 20 no 5 pp 851ndash864 2004
[10] Y Morales T Tsubouchi and S Yuta ldquoVehicle localizationin outdoor mountainous forested paths and extension of two-dimensional road centerline maps to three-dimensional mapsrdquoAdvanced Robotics vol 24 no 4 pp 489ndash513 2010
[11] W SWijesoma K R S Kodagoda andA P Balasuriya ldquoRoad-boundary detection and tracking using ladar sensingrdquo IEEETransactions onRobotics andAutomation vol 20 no 3 pp 456ndash464 2004
[12] M Jabbour and P Bonnifait ldquoGlobal localization robust toGPS outages using a vertical ladarrdquo in Proceedings of the 9th
International Conference on Control Automation Robotics andVision pp 1ndash6 December 2006
[13] P Bonnifait M Jabbour and V Cherfaoui ldquoAutonomousnavigation in urban areas using GIS-managed informationrdquoInternational Journal of Vehicle Autonomous Systems vol 6 no5 pp 83ndash103 2008
[14] Y Shin D Kim H Lee J Park and W Chung ldquoAutonomousnavigation of a surveillance robot in harsh outdoor environ-mentsrdquo Advances in Mechanical Engineering vol 2013 ArticleID 837484 15 pages 2013
[15] Y Shin C Jung andWChung ldquoDrivable road region detectionusing a single laser range finder for outdoor patrol robotsrdquo inProceedings of the IEEE Intelligent Vehicles Symposium (IV rsquo10)pp 877ndash882 San Diego Calif USA June 2010
[16] D Kim and W Chung ldquoLocalization of outdoor mobile robotsusing road featuresrdquo in Proceedings of the 8th International Con-ference on Ubiquitous Robots and Ambient Intelligence (URAIrsquo11) pp 363ndash365 Incheon Republic of Korea November 2011
[17] S Mika G Ratsch J Weston B Scholkopf and K MullerldquoFisher discriminant analysis with kernelsrdquoNeural Networks forSignal Processing vol 9 pp 41ndash48 1999
[18] S Mika G Ratsch and K R Muller ldquoA mathematical pro-gramming approach to the kernel fisher algorithmrdquo Advancesin Neural Information Processing vol 13 pp 591ndash597 2001
[19] G Camps-Valls and L Bruzzone Kernel Methods for RemoteSensing Data Analysis JohnWiley amp Sons New York NY USA2009
[20] R E Kalman ldquoA new approach to linear filtering and predictionproblemsrdquo Journal of Basic Engineering vol 82 no 1 pp 35ndash451960
[21] R E Kalman and R S Bucy ldquoNew results in linear filtering andprediction theoryrdquo Journal of Basic Engineering vol 83 no 3pp 95ndash108 1961
[22] J J Leonard and H F Durrant-Whyte Directed Sonar Sensingfor Mobile Robot Navigation Kluwer Academic DordrechtTheNetherlands 1992
[23] B W Parkinson and J J Spilker Global Positioning SystemTheory and ApplicationsThe American Institute of Aeronauticsand Astronautics Washington DC USA 1996
[24] K O Arras and R Y Siegwart ldquoFeature extraction and sceneinterpretation for map-based navigation and map buildingrdquo in12th Mobile Robots Conference vol 3210 of Proceedings of SPIEpp 42ndash53 Pittsburgh Pa USA January 1998
[25] S T Pfister S I Roumeliotis and J W Burdick ldquoWeighted linefitting algorithms for mobile robot map building and efficientdata representationrdquo in Proceedings of the IEEE InternationalConference on Robotics and Automation pp 1304ndash1311 Septem-ber 2003
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
8 Mathematical Problems in Engineering
(a)
0 1 2 3
0
1
2
3
4
5
6
7
Detected road surface
minus1minus2
minus1
minus2minus3minus4minus5minus6
y(m
)
x (m)
(b)
0 1 2 3
0
1
2
3
4
5
6
7
minus1minus2
minus1
minus2minus3minus4minus5minus6
y(m
)
x (m)
R2
L1 R1
L2
(c)
Extracted curbs
0 1 2 3
0
1
2
3
4
5
6
7
minus1minus2
minus1
minus2minus3minus4minus5minus6
y(m
)
x (m)
(d)
Figure 8 Curb extraction results (a) Road environment (b) Road surface detection (c) Curb feature candidates on both sides (d) Extractedcurb
0 50 100 150
0
50
100
150
y(m
)
x (m)
minus50
minus50minus100
Figure 9 Curb mapping result on experimental path
Mathematical Problems in Engineering 9
Reference pathDGPS measurements
SG
A
B
DE
C
F
(a)
0 5 10 15 20 25 300
2
4
6
8
Time (min)
Dist
ance
(m)
A B C D E F
120590DGPS
(b)
Figure 10 (a) DGPS measurement and (b) DGPS uncertainty measurement (1120590 bound)
CurbAdditional LRF
Figure 11 Additional LRF for ground truth of the curbs
The uncertainty measurements in areas B D and E werealmost infinite as shown in Figure 10(b) Furthermore largeDGPS errors occurred in areas A C and F due to thedegraded satellite signals In particular measurement errorswere 21m on average in area F The standard deviation thatwas measured in area F was 64m on average The resultimplies that the regional properties ofDGPSwere obtained bymeasuring the DGPS uncertainty in real time However theprecision of the localization only by DGPS can be decreasedwhen the robot navigates near the buildings
The curb estimation errors are considered in order todefine the error covariance The most accurate result forthe quantitative curb uncertainty is obtained by measuringthe estimation errors in experimental environments Theestimation errors were measured while the robot navigatesthrough the road with curbs Ground truth for the curb wasprovided by an additional LRF that is attached to the sideof the robot as shown in Figure 11 Ground truth of thecurb was provided by line feature from the additional LRFdata Experiments were conducted in order to measure theestimation errors prior to the localization experiment The
Table 3 Error covariance of extracted curb
Range std 120590119903
Angle std 120590120572
Correlation 120590119903120572
Right curb 01620m 00575 rad 00035msdotradLeft curb 01614m 00649 rad minus00034msdotrad
following results show the estimation errors for the range andangle of the extracted curb
Figure 12 shows the histogram of the curb estimationerrors for each sideThe number of the estimation error mea-surements is approximately 5000 The covariance matrix ofthe curb was computed from the distributions of estimationerrors The elements of error covariance for each side of thecurb are listed in Table 3
The covariance representation for the extracted curbs isshown in Figure 13 The extracted curbs are represented byblue lines and the error bounds for the curbs are representedby green dotted lines The resultant curbs exist within theerror bounds with 95 confidence
44 Outdoor Localization Results The localization results areshown in Figure 14 The proposed method was comparedwith the conventional framework for outdoor localizationthat combines DGPS measurement with odometry The bluedash-dot line represents the localization results correctedonly by the DGPS measurements The estimated paths showsome difference with respect to the reference path (yellowdotted line) in area AndashF due to theDGPS errorsThemagentaline represents the localization results corrected byDGPS andthe extracted curb When the curb information is appliedthe results show that the robot position well matches thereference path even if the DGPS errors are large or a blackoutoccurs (area AndashF) It is clear that the curb information plays adominant role The following part presents the localizationerrors in area AndashF as shown in Figure 14 The localizationerrors were compared with the conventional framework thatcombines DGPS measurement with odometry The ground
10 Mathematical Problems in Engineering
0
100
200
300Histogram of left curb range errors
Estimation error (m)
N(c
ount
)
040302010minus01minus02minus03minus04
0
100
200
300
400Histogram of left curb angle errors
Estimation error (rad)
N(c
ount
)
010050minus005minus01
(a)
Estimation error (m)
0
200
400
600
800Histogram of right curb range errors
N(c
ount
)
040302010minus01minus02minus03minus04
0
200
400
600
800Histogram of right curb angle errors
Estimation error (rad)
N(c
ount
)
010050minus005minus01
(b)
Figure 12 Distribution of estimation errors for (a) left and (b) right curbs
0 1 2 3
0
1
2
3
4
5
6
7
Range dataExtracted curbCovariance (95 confidence)
minus1minus2
minus1
minus2minus3minus4minus5minus6
y(m
)
x (m)
Figure 13 Extracted curbs and covariance representation
truth was computed using the additional LRF attached to theside of the robot
Figure 15 shows the lateral errors of the localizationresults The position errors when using the fusion of theodometry and DGPS are shown in Figure 15(a) The lateralerrors in each areawere usually greater than 1m In particularthe maximum error in area F was 5m In contrast thelocalization result which was corrected by odometry DGPSand curb information shows that the lateral errors werewithin 06m across the entire area as shown in Figure 15(b)
SG
A
B
DE
C
F
Reference pathEKF (odometry + DGPS)EKF (odometry + DGPS + curb)
Figure 14 Localization results in semistructured road environment
Therefore the proposed method shows robust performancein terms of lateral position estimation errors despite the largeDGPS errorsTheheading errors of the localization results arerepresented in Figure 16 The result that was corrected usingonly the DGPS data is shown in Figure 16(a) The headingerrors were greater than 1∘ on averageThe variancewas largerthan 2∘ However when the curb information is used forcorrection the heading errors were remarkably decreasedFurthermore the errors rarely exceed 3∘ in the entire areaIn experiments the proposed method showed precise androbust performance for the lateral and heading errors despitethe large DGPS errors and a temporal blackout
Mathematical Problems in Engineering 11
0
1
2
3
4
5
Late
ral e
rror
s (m
)
A B C D E FSection
EKF (odometry + DGPS)
minus1
minus2
minus3
minus4
(a)
A B C D E F
0
1
2
3
4
5
Late
ral e
rror
s (m
)Section
EKF (odometry + DGPS + curb)
minus1
minus2
minus3
minus4
(b)
Figure 15 Lateral errors (a) corrected by DGPS and (b) corrected by DGPS and extracted curb
A B C D E FSection
EKF (odometry + DGPS)
0
5
10
15
Ang
ular
erro
rs (d
eg)
minus5
minus10
(a)
A B C D E F
0
5
10
15
Ang
ular
erro
rs (d
eg)
Section
EKF (odometry + DGPS + curb)
minus5
minus10
(b)
Figure 16 Heading errors (a) corrected by DGPS and (b) corrected by DGPS and extracted curb
5 Conclusion
This paper presents a localization method for outdoor robotsusing curb features in semistructured road environmentsA reliable curb extraction scheme is proposed to classifythe curb candidates as curb and noncurb classes Mostof the curbs in an experimental path are extracted withhigh accuracy An EKF-based localization is also proposed
to combine the extracted curbs with odometry and DGPSmeasurements The uncertainty models of the sensors aredefined by experiments to provide a practical solution forlocalization From experimental results the robustness of theproposed method is demonstrated in real road experimentsThe curb features can correct significantly the lateral positionand heading errors in dense area where the DGPS signal getsdegraded by buildings
12 Mathematical Problems in Engineering
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This research was supported in part by the MKE (TheMinis-try of Knowledge Economy) Korea under the HumanResources Development Program for Convergence RobotSpecialists Support Program supervised by the NIPA(National IT Industry Promotion Agency) (NIPA-2013-H1502-13-1001) This work was also supported by theNational Research Foundation of Korea (NRF) Grant fundedby Korea Government (MEST) (2013-029812)
References
[1] S Thrun M Montemerlo H Dahlkamp et al ldquoStanley therobot that won the DARPA Grand Challengerdquo Journal of FieldRobotics vol 23 no 9 pp 661ndash692 2006
[2] M Buehler K Lagnemma and S Singh The DARPA UrbanChallenge Autonomous Vehicles in City Traffic Springer NewYork NY USA 2009
[3] A Soloviev ldquoTight coupling of GPS laser scanner and iner-tial measurements for navigation in urban environmentsrdquo inProceedings of the IEEEION Position Location and NavigationSymposium pp 511ndash525 Monterey Calif USA May 2008
[4] S Panzieri F Pascucci and G Ulivi ldquoAn outdoor navigationsystem using GPS and inertial platformrdquo IEEEASME Transac-tions on Mechatronics vol 7 no 2 pp 134ndash142 2002
[5] E-J Jung andD-J Yi ldquoTask-oriented navigation algorithms foran outdoor environment with colored borders and obstaclesrdquoIntelligent Service Robotics vol 6 no 2 pp 69ndash77 2013
[6] S Kim J Kang andM Jin Chung ldquoProbabilistic voxelmappingusing an adaptive confidence measure of stereo matchingrdquoIntelligent Service Robotics vol 6 no 2 pp 89ndash99 2013
[7] M Joerger and B Pervan ldquoRange-domain integration of GPSand laser-scanner measurements for outdoor navigationrdquo inProceedings of the 19th International Technical Meeting of theSatellite Division of The Institute of Navigation (ION GNSS rsquo06)pp 1115ndash1123 Fort Worth Tex USA September 2006
[8] M Hentschel O Wulf and B Wagner ldquoA GPS and laser-basedlocalization for urban and non-urban outdoor environmentsrdquoin Proceedings of the IEEERSJ International Conference on Intel-ligent Robots and Systems pp 149ndash154 Nice France September2008
[9] A Georgiev and P K Allen ldquoLocalizationmethods for amobilerobot in urban environmentsrdquo IEEE Transactions on Roboticsvol 20 no 5 pp 851ndash864 2004
[10] Y Morales T Tsubouchi and S Yuta ldquoVehicle localizationin outdoor mountainous forested paths and extension of two-dimensional road centerline maps to three-dimensional mapsrdquoAdvanced Robotics vol 24 no 4 pp 489ndash513 2010
[11] W SWijesoma K R S Kodagoda andA P Balasuriya ldquoRoad-boundary detection and tracking using ladar sensingrdquo IEEETransactions onRobotics andAutomation vol 20 no 3 pp 456ndash464 2004
[12] M Jabbour and P Bonnifait ldquoGlobal localization robust toGPS outages using a vertical ladarrdquo in Proceedings of the 9th
International Conference on Control Automation Robotics andVision pp 1ndash6 December 2006
[13] P Bonnifait M Jabbour and V Cherfaoui ldquoAutonomousnavigation in urban areas using GIS-managed informationrdquoInternational Journal of Vehicle Autonomous Systems vol 6 no5 pp 83ndash103 2008
[14] Y Shin D Kim H Lee J Park and W Chung ldquoAutonomousnavigation of a surveillance robot in harsh outdoor environ-mentsrdquo Advances in Mechanical Engineering vol 2013 ArticleID 837484 15 pages 2013
[15] Y Shin C Jung andWChung ldquoDrivable road region detectionusing a single laser range finder for outdoor patrol robotsrdquo inProceedings of the IEEE Intelligent Vehicles Symposium (IV rsquo10)pp 877ndash882 San Diego Calif USA June 2010
[16] D Kim and W Chung ldquoLocalization of outdoor mobile robotsusing road featuresrdquo in Proceedings of the 8th International Con-ference on Ubiquitous Robots and Ambient Intelligence (URAIrsquo11) pp 363ndash365 Incheon Republic of Korea November 2011
[17] S Mika G Ratsch J Weston B Scholkopf and K MullerldquoFisher discriminant analysis with kernelsrdquoNeural Networks forSignal Processing vol 9 pp 41ndash48 1999
[18] S Mika G Ratsch and K R Muller ldquoA mathematical pro-gramming approach to the kernel fisher algorithmrdquo Advancesin Neural Information Processing vol 13 pp 591ndash597 2001
[19] G Camps-Valls and L Bruzzone Kernel Methods for RemoteSensing Data Analysis JohnWiley amp Sons New York NY USA2009
[20] R E Kalman ldquoA new approach to linear filtering and predictionproblemsrdquo Journal of Basic Engineering vol 82 no 1 pp 35ndash451960
[21] R E Kalman and R S Bucy ldquoNew results in linear filtering andprediction theoryrdquo Journal of Basic Engineering vol 83 no 3pp 95ndash108 1961
[22] J J Leonard and H F Durrant-Whyte Directed Sonar Sensingfor Mobile Robot Navigation Kluwer Academic DordrechtTheNetherlands 1992
[23] B W Parkinson and J J Spilker Global Positioning SystemTheory and ApplicationsThe American Institute of Aeronauticsand Astronautics Washington DC USA 1996
[24] K O Arras and R Y Siegwart ldquoFeature extraction and sceneinterpretation for map-based navigation and map buildingrdquo in12th Mobile Robots Conference vol 3210 of Proceedings of SPIEpp 42ndash53 Pittsburgh Pa USA January 1998
[25] S T Pfister S I Roumeliotis and J W Burdick ldquoWeighted linefitting algorithms for mobile robot map building and efficientdata representationrdquo in Proceedings of the IEEE InternationalConference on Robotics and Automation pp 1304ndash1311 Septem-ber 2003
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
Mathematical Problems in Engineering 9
Reference pathDGPS measurements
SG
A
B
DE
C
F
(a)
0 5 10 15 20 25 300
2
4
6
8
Time (min)
Dist
ance
(m)
A B C D E F
120590DGPS
(b)
Figure 10 (a) DGPS measurement and (b) DGPS uncertainty measurement (1120590 bound)
CurbAdditional LRF
Figure 11 Additional LRF for ground truth of the curbs
The uncertainty measurements in areas B D and E werealmost infinite as shown in Figure 10(b) Furthermore largeDGPS errors occurred in areas A C and F due to thedegraded satellite signals In particular measurement errorswere 21m on average in area F The standard deviation thatwas measured in area F was 64m on average The resultimplies that the regional properties ofDGPSwere obtained bymeasuring the DGPS uncertainty in real time However theprecision of the localization only by DGPS can be decreasedwhen the robot navigates near the buildings
The curb estimation errors are considered in order todefine the error covariance The most accurate result forthe quantitative curb uncertainty is obtained by measuringthe estimation errors in experimental environments Theestimation errors were measured while the robot navigatesthrough the road with curbs Ground truth for the curb wasprovided by an additional LRF that is attached to the sideof the robot as shown in Figure 11 Ground truth of thecurb was provided by line feature from the additional LRFdata Experiments were conducted in order to measure theestimation errors prior to the localization experiment The
Table 3 Error covariance of extracted curb
Range std 120590119903
Angle std 120590120572
Correlation 120590119903120572
Right curb 01620m 00575 rad 00035msdotradLeft curb 01614m 00649 rad minus00034msdotrad
following results show the estimation errors for the range andangle of the extracted curb
Figure 12 shows the histogram of the curb estimationerrors for each sideThe number of the estimation error mea-surements is approximately 5000 The covariance matrix ofthe curb was computed from the distributions of estimationerrors The elements of error covariance for each side of thecurb are listed in Table 3
The covariance representation for the extracted curbs isshown in Figure 13 The extracted curbs are represented byblue lines and the error bounds for the curbs are representedby green dotted lines The resultant curbs exist within theerror bounds with 95 confidence
44 Outdoor Localization Results The localization results areshown in Figure 14 The proposed method was comparedwith the conventional framework for outdoor localizationthat combines DGPS measurement with odometry The bluedash-dot line represents the localization results correctedonly by the DGPS measurements The estimated paths showsome difference with respect to the reference path (yellowdotted line) in area AndashF due to theDGPS errorsThemagentaline represents the localization results corrected byDGPS andthe extracted curb When the curb information is appliedthe results show that the robot position well matches thereference path even if the DGPS errors are large or a blackoutoccurs (area AndashF) It is clear that the curb information plays adominant role The following part presents the localizationerrors in area AndashF as shown in Figure 14 The localizationerrors were compared with the conventional framework thatcombines DGPS measurement with odometry The ground
10 Mathematical Problems in Engineering
0
100
200
300Histogram of left curb range errors
Estimation error (m)
N(c
ount
)
040302010minus01minus02minus03minus04
0
100
200
300
400Histogram of left curb angle errors
Estimation error (rad)
N(c
ount
)
010050minus005minus01
(a)
Estimation error (m)
0
200
400
600
800Histogram of right curb range errors
N(c
ount
)
040302010minus01minus02minus03minus04
0
200
400
600
800Histogram of right curb angle errors
Estimation error (rad)
N(c
ount
)
010050minus005minus01
(b)
Figure 12 Distribution of estimation errors for (a) left and (b) right curbs
0 1 2 3
0
1
2
3
4
5
6
7
Range dataExtracted curbCovariance (95 confidence)
minus1minus2
minus1
minus2minus3minus4minus5minus6
y(m
)
x (m)
Figure 13 Extracted curbs and covariance representation
truth was computed using the additional LRF attached to theside of the robot
Figure 15 shows the lateral errors of the localizationresults The position errors when using the fusion of theodometry and DGPS are shown in Figure 15(a) The lateralerrors in each areawere usually greater than 1m In particularthe maximum error in area F was 5m In contrast thelocalization result which was corrected by odometry DGPSand curb information shows that the lateral errors werewithin 06m across the entire area as shown in Figure 15(b)
SG
A
B
DE
C
F
Reference pathEKF (odometry + DGPS)EKF (odometry + DGPS + curb)
Figure 14 Localization results in semistructured road environment
Therefore the proposed method shows robust performancein terms of lateral position estimation errors despite the largeDGPS errorsTheheading errors of the localization results arerepresented in Figure 16 The result that was corrected usingonly the DGPS data is shown in Figure 16(a) The headingerrors were greater than 1∘ on averageThe variancewas largerthan 2∘ However when the curb information is used forcorrection the heading errors were remarkably decreasedFurthermore the errors rarely exceed 3∘ in the entire areaIn experiments the proposed method showed precise androbust performance for the lateral and heading errors despitethe large DGPS errors and a temporal blackout
Mathematical Problems in Engineering 11
0
1
2
3
4
5
Late
ral e
rror
s (m
)
A B C D E FSection
EKF (odometry + DGPS)
minus1
minus2
minus3
minus4
(a)
A B C D E F
0
1
2
3
4
5
Late
ral e
rror
s (m
)Section
EKF (odometry + DGPS + curb)
minus1
minus2
minus3
minus4
(b)
Figure 15 Lateral errors (a) corrected by DGPS and (b) corrected by DGPS and extracted curb
A B C D E FSection
EKF (odometry + DGPS)
0
5
10
15
Ang
ular
erro
rs (d
eg)
minus5
minus10
(a)
A B C D E F
0
5
10
15
Ang
ular
erro
rs (d
eg)
Section
EKF (odometry + DGPS + curb)
minus5
minus10
(b)
Figure 16 Heading errors (a) corrected by DGPS and (b) corrected by DGPS and extracted curb
5 Conclusion
This paper presents a localization method for outdoor robotsusing curb features in semistructured road environmentsA reliable curb extraction scheme is proposed to classifythe curb candidates as curb and noncurb classes Mostof the curbs in an experimental path are extracted withhigh accuracy An EKF-based localization is also proposed
to combine the extracted curbs with odometry and DGPSmeasurements The uncertainty models of the sensors aredefined by experiments to provide a practical solution forlocalization From experimental results the robustness of theproposed method is demonstrated in real road experimentsThe curb features can correct significantly the lateral positionand heading errors in dense area where the DGPS signal getsdegraded by buildings
12 Mathematical Problems in Engineering
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This research was supported in part by the MKE (TheMinis-try of Knowledge Economy) Korea under the HumanResources Development Program for Convergence RobotSpecialists Support Program supervised by the NIPA(National IT Industry Promotion Agency) (NIPA-2013-H1502-13-1001) This work was also supported by theNational Research Foundation of Korea (NRF) Grant fundedby Korea Government (MEST) (2013-029812)
References
[1] S Thrun M Montemerlo H Dahlkamp et al ldquoStanley therobot that won the DARPA Grand Challengerdquo Journal of FieldRobotics vol 23 no 9 pp 661ndash692 2006
[2] M Buehler K Lagnemma and S Singh The DARPA UrbanChallenge Autonomous Vehicles in City Traffic Springer NewYork NY USA 2009
[3] A Soloviev ldquoTight coupling of GPS laser scanner and iner-tial measurements for navigation in urban environmentsrdquo inProceedings of the IEEEION Position Location and NavigationSymposium pp 511ndash525 Monterey Calif USA May 2008
[4] S Panzieri F Pascucci and G Ulivi ldquoAn outdoor navigationsystem using GPS and inertial platformrdquo IEEEASME Transac-tions on Mechatronics vol 7 no 2 pp 134ndash142 2002
[5] E-J Jung andD-J Yi ldquoTask-oriented navigation algorithms foran outdoor environment with colored borders and obstaclesrdquoIntelligent Service Robotics vol 6 no 2 pp 69ndash77 2013
[6] S Kim J Kang andM Jin Chung ldquoProbabilistic voxelmappingusing an adaptive confidence measure of stereo matchingrdquoIntelligent Service Robotics vol 6 no 2 pp 89ndash99 2013
[7] M Joerger and B Pervan ldquoRange-domain integration of GPSand laser-scanner measurements for outdoor navigationrdquo inProceedings of the 19th International Technical Meeting of theSatellite Division of The Institute of Navigation (ION GNSS rsquo06)pp 1115ndash1123 Fort Worth Tex USA September 2006
[8] M Hentschel O Wulf and B Wagner ldquoA GPS and laser-basedlocalization for urban and non-urban outdoor environmentsrdquoin Proceedings of the IEEERSJ International Conference on Intel-ligent Robots and Systems pp 149ndash154 Nice France September2008
[9] A Georgiev and P K Allen ldquoLocalizationmethods for amobilerobot in urban environmentsrdquo IEEE Transactions on Roboticsvol 20 no 5 pp 851ndash864 2004
[10] Y Morales T Tsubouchi and S Yuta ldquoVehicle localizationin outdoor mountainous forested paths and extension of two-dimensional road centerline maps to three-dimensional mapsrdquoAdvanced Robotics vol 24 no 4 pp 489ndash513 2010
[11] W SWijesoma K R S Kodagoda andA P Balasuriya ldquoRoad-boundary detection and tracking using ladar sensingrdquo IEEETransactions onRobotics andAutomation vol 20 no 3 pp 456ndash464 2004
[12] M Jabbour and P Bonnifait ldquoGlobal localization robust toGPS outages using a vertical ladarrdquo in Proceedings of the 9th
International Conference on Control Automation Robotics andVision pp 1ndash6 December 2006
[13] P Bonnifait M Jabbour and V Cherfaoui ldquoAutonomousnavigation in urban areas using GIS-managed informationrdquoInternational Journal of Vehicle Autonomous Systems vol 6 no5 pp 83ndash103 2008
[14] Y Shin D Kim H Lee J Park and W Chung ldquoAutonomousnavigation of a surveillance robot in harsh outdoor environ-mentsrdquo Advances in Mechanical Engineering vol 2013 ArticleID 837484 15 pages 2013
[15] Y Shin C Jung andWChung ldquoDrivable road region detectionusing a single laser range finder for outdoor patrol robotsrdquo inProceedings of the IEEE Intelligent Vehicles Symposium (IV rsquo10)pp 877ndash882 San Diego Calif USA June 2010
[16] D Kim and W Chung ldquoLocalization of outdoor mobile robotsusing road featuresrdquo in Proceedings of the 8th International Con-ference on Ubiquitous Robots and Ambient Intelligence (URAIrsquo11) pp 363ndash365 Incheon Republic of Korea November 2011
[17] S Mika G Ratsch J Weston B Scholkopf and K MullerldquoFisher discriminant analysis with kernelsrdquoNeural Networks forSignal Processing vol 9 pp 41ndash48 1999
[18] S Mika G Ratsch and K R Muller ldquoA mathematical pro-gramming approach to the kernel fisher algorithmrdquo Advancesin Neural Information Processing vol 13 pp 591ndash597 2001
[19] G Camps-Valls and L Bruzzone Kernel Methods for RemoteSensing Data Analysis JohnWiley amp Sons New York NY USA2009
[20] R E Kalman ldquoA new approach to linear filtering and predictionproblemsrdquo Journal of Basic Engineering vol 82 no 1 pp 35ndash451960
[21] R E Kalman and R S Bucy ldquoNew results in linear filtering andprediction theoryrdquo Journal of Basic Engineering vol 83 no 3pp 95ndash108 1961
[22] J J Leonard and H F Durrant-Whyte Directed Sonar Sensingfor Mobile Robot Navigation Kluwer Academic DordrechtTheNetherlands 1992
[23] B W Parkinson and J J Spilker Global Positioning SystemTheory and ApplicationsThe American Institute of Aeronauticsand Astronautics Washington DC USA 1996
[24] K O Arras and R Y Siegwart ldquoFeature extraction and sceneinterpretation for map-based navigation and map buildingrdquo in12th Mobile Robots Conference vol 3210 of Proceedings of SPIEpp 42ndash53 Pittsburgh Pa USA January 1998
[25] S T Pfister S I Roumeliotis and J W Burdick ldquoWeighted linefitting algorithms for mobile robot map building and efficientdata representationrdquo in Proceedings of the IEEE InternationalConference on Robotics and Automation pp 1304ndash1311 Septem-ber 2003
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
10 Mathematical Problems in Engineering
0
100
200
300Histogram of left curb range errors
Estimation error (m)
N(c
ount
)
040302010minus01minus02minus03minus04
0
100
200
300
400Histogram of left curb angle errors
Estimation error (rad)
N(c
ount
)
010050minus005minus01
(a)
Estimation error (m)
0
200
400
600
800Histogram of right curb range errors
N(c
ount
)
040302010minus01minus02minus03minus04
0
200
400
600
800Histogram of right curb angle errors
Estimation error (rad)
N(c
ount
)
010050minus005minus01
(b)
Figure 12 Distribution of estimation errors for (a) left and (b) right curbs
0 1 2 3
0
1
2
3
4
5
6
7
Range dataExtracted curbCovariance (95 confidence)
minus1minus2
minus1
minus2minus3minus4minus5minus6
y(m
)
x (m)
Figure 13 Extracted curbs and covariance representation
truth was computed using the additional LRF attached to theside of the robot
Figure 15 shows the lateral errors of the localizationresults The position errors when using the fusion of theodometry and DGPS are shown in Figure 15(a) The lateralerrors in each areawere usually greater than 1m In particularthe maximum error in area F was 5m In contrast thelocalization result which was corrected by odometry DGPSand curb information shows that the lateral errors werewithin 06m across the entire area as shown in Figure 15(b)
SG
A
B
DE
C
F
Reference pathEKF (odometry + DGPS)EKF (odometry + DGPS + curb)
Figure 14 Localization results in semistructured road environment
Therefore the proposed method shows robust performancein terms of lateral position estimation errors despite the largeDGPS errorsTheheading errors of the localization results arerepresented in Figure 16 The result that was corrected usingonly the DGPS data is shown in Figure 16(a) The headingerrors were greater than 1∘ on averageThe variancewas largerthan 2∘ However when the curb information is used forcorrection the heading errors were remarkably decreasedFurthermore the errors rarely exceed 3∘ in the entire areaIn experiments the proposed method showed precise androbust performance for the lateral and heading errors despitethe large DGPS errors and a temporal blackout
Mathematical Problems in Engineering 11
0
1
2
3
4
5
Late
ral e
rror
s (m
)
A B C D E FSection
EKF (odometry + DGPS)
minus1
minus2
minus3
minus4
(a)
A B C D E F
0
1
2
3
4
5
Late
ral e
rror
s (m
)Section
EKF (odometry + DGPS + curb)
minus1
minus2
minus3
minus4
(b)
Figure 15 Lateral errors (a) corrected by DGPS and (b) corrected by DGPS and extracted curb
A B C D E FSection
EKF (odometry + DGPS)
0
5
10
15
Ang
ular
erro
rs (d
eg)
minus5
minus10
(a)
A B C D E F
0
5
10
15
Ang
ular
erro
rs (d
eg)
Section
EKF (odometry + DGPS + curb)
minus5
minus10
(b)
Figure 16 Heading errors (a) corrected by DGPS and (b) corrected by DGPS and extracted curb
5 Conclusion
This paper presents a localization method for outdoor robotsusing curb features in semistructured road environmentsA reliable curb extraction scheme is proposed to classifythe curb candidates as curb and noncurb classes Mostof the curbs in an experimental path are extracted withhigh accuracy An EKF-based localization is also proposed
to combine the extracted curbs with odometry and DGPSmeasurements The uncertainty models of the sensors aredefined by experiments to provide a practical solution forlocalization From experimental results the robustness of theproposed method is demonstrated in real road experimentsThe curb features can correct significantly the lateral positionand heading errors in dense area where the DGPS signal getsdegraded by buildings
12 Mathematical Problems in Engineering
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This research was supported in part by the MKE (TheMinis-try of Knowledge Economy) Korea under the HumanResources Development Program for Convergence RobotSpecialists Support Program supervised by the NIPA(National IT Industry Promotion Agency) (NIPA-2013-H1502-13-1001) This work was also supported by theNational Research Foundation of Korea (NRF) Grant fundedby Korea Government (MEST) (2013-029812)
References
[1] S Thrun M Montemerlo H Dahlkamp et al ldquoStanley therobot that won the DARPA Grand Challengerdquo Journal of FieldRobotics vol 23 no 9 pp 661ndash692 2006
[2] M Buehler K Lagnemma and S Singh The DARPA UrbanChallenge Autonomous Vehicles in City Traffic Springer NewYork NY USA 2009
[3] A Soloviev ldquoTight coupling of GPS laser scanner and iner-tial measurements for navigation in urban environmentsrdquo inProceedings of the IEEEION Position Location and NavigationSymposium pp 511ndash525 Monterey Calif USA May 2008
[4] S Panzieri F Pascucci and G Ulivi ldquoAn outdoor navigationsystem using GPS and inertial platformrdquo IEEEASME Transac-tions on Mechatronics vol 7 no 2 pp 134ndash142 2002
[5] E-J Jung andD-J Yi ldquoTask-oriented navigation algorithms foran outdoor environment with colored borders and obstaclesrdquoIntelligent Service Robotics vol 6 no 2 pp 69ndash77 2013
[6] S Kim J Kang andM Jin Chung ldquoProbabilistic voxelmappingusing an adaptive confidence measure of stereo matchingrdquoIntelligent Service Robotics vol 6 no 2 pp 89ndash99 2013
[7] M Joerger and B Pervan ldquoRange-domain integration of GPSand laser-scanner measurements for outdoor navigationrdquo inProceedings of the 19th International Technical Meeting of theSatellite Division of The Institute of Navigation (ION GNSS rsquo06)pp 1115ndash1123 Fort Worth Tex USA September 2006
[8] M Hentschel O Wulf and B Wagner ldquoA GPS and laser-basedlocalization for urban and non-urban outdoor environmentsrdquoin Proceedings of the IEEERSJ International Conference on Intel-ligent Robots and Systems pp 149ndash154 Nice France September2008
[9] A Georgiev and P K Allen ldquoLocalizationmethods for amobilerobot in urban environmentsrdquo IEEE Transactions on Roboticsvol 20 no 5 pp 851ndash864 2004
[10] Y Morales T Tsubouchi and S Yuta ldquoVehicle localizationin outdoor mountainous forested paths and extension of two-dimensional road centerline maps to three-dimensional mapsrdquoAdvanced Robotics vol 24 no 4 pp 489ndash513 2010
[11] W SWijesoma K R S Kodagoda andA P Balasuriya ldquoRoad-boundary detection and tracking using ladar sensingrdquo IEEETransactions onRobotics andAutomation vol 20 no 3 pp 456ndash464 2004
[12] M Jabbour and P Bonnifait ldquoGlobal localization robust toGPS outages using a vertical ladarrdquo in Proceedings of the 9th
International Conference on Control Automation Robotics andVision pp 1ndash6 December 2006
[13] P Bonnifait M Jabbour and V Cherfaoui ldquoAutonomousnavigation in urban areas using GIS-managed informationrdquoInternational Journal of Vehicle Autonomous Systems vol 6 no5 pp 83ndash103 2008
[14] Y Shin D Kim H Lee J Park and W Chung ldquoAutonomousnavigation of a surveillance robot in harsh outdoor environ-mentsrdquo Advances in Mechanical Engineering vol 2013 ArticleID 837484 15 pages 2013
[15] Y Shin C Jung andWChung ldquoDrivable road region detectionusing a single laser range finder for outdoor patrol robotsrdquo inProceedings of the IEEE Intelligent Vehicles Symposium (IV rsquo10)pp 877ndash882 San Diego Calif USA June 2010
[16] D Kim and W Chung ldquoLocalization of outdoor mobile robotsusing road featuresrdquo in Proceedings of the 8th International Con-ference on Ubiquitous Robots and Ambient Intelligence (URAIrsquo11) pp 363ndash365 Incheon Republic of Korea November 2011
[17] S Mika G Ratsch J Weston B Scholkopf and K MullerldquoFisher discriminant analysis with kernelsrdquoNeural Networks forSignal Processing vol 9 pp 41ndash48 1999
[18] S Mika G Ratsch and K R Muller ldquoA mathematical pro-gramming approach to the kernel fisher algorithmrdquo Advancesin Neural Information Processing vol 13 pp 591ndash597 2001
[19] G Camps-Valls and L Bruzzone Kernel Methods for RemoteSensing Data Analysis JohnWiley amp Sons New York NY USA2009
[20] R E Kalman ldquoA new approach to linear filtering and predictionproblemsrdquo Journal of Basic Engineering vol 82 no 1 pp 35ndash451960
[21] R E Kalman and R S Bucy ldquoNew results in linear filtering andprediction theoryrdquo Journal of Basic Engineering vol 83 no 3pp 95ndash108 1961
[22] J J Leonard and H F Durrant-Whyte Directed Sonar Sensingfor Mobile Robot Navigation Kluwer Academic DordrechtTheNetherlands 1992
[23] B W Parkinson and J J Spilker Global Positioning SystemTheory and ApplicationsThe American Institute of Aeronauticsand Astronautics Washington DC USA 1996
[24] K O Arras and R Y Siegwart ldquoFeature extraction and sceneinterpretation for map-based navigation and map buildingrdquo in12th Mobile Robots Conference vol 3210 of Proceedings of SPIEpp 42ndash53 Pittsburgh Pa USA January 1998
[25] S T Pfister S I Roumeliotis and J W Burdick ldquoWeighted linefitting algorithms for mobile robot map building and efficientdata representationrdquo in Proceedings of the IEEE InternationalConference on Robotics and Automation pp 1304ndash1311 Septem-ber 2003
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
Mathematical Problems in Engineering 11
0
1
2
3
4
5
Late
ral e
rror
s (m
)
A B C D E FSection
EKF (odometry + DGPS)
minus1
minus2
minus3
minus4
(a)
A B C D E F
0
1
2
3
4
5
Late
ral e
rror
s (m
)Section
EKF (odometry + DGPS + curb)
minus1
minus2
minus3
minus4
(b)
Figure 15 Lateral errors (a) corrected by DGPS and (b) corrected by DGPS and extracted curb
A B C D E FSection
EKF (odometry + DGPS)
0
5
10
15
Ang
ular
erro
rs (d
eg)
minus5
minus10
(a)
A B C D E F
0
5
10
15
Ang
ular
erro
rs (d
eg)
Section
EKF (odometry + DGPS + curb)
minus5
minus10
(b)
Figure 16 Heading errors (a) corrected by DGPS and (b) corrected by DGPS and extracted curb
5 Conclusion
This paper presents a localization method for outdoor robotsusing curb features in semistructured road environmentsA reliable curb extraction scheme is proposed to classifythe curb candidates as curb and noncurb classes Mostof the curbs in an experimental path are extracted withhigh accuracy An EKF-based localization is also proposed
to combine the extracted curbs with odometry and DGPSmeasurements The uncertainty models of the sensors aredefined by experiments to provide a practical solution forlocalization From experimental results the robustness of theproposed method is demonstrated in real road experimentsThe curb features can correct significantly the lateral positionand heading errors in dense area where the DGPS signal getsdegraded by buildings
12 Mathematical Problems in Engineering
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This research was supported in part by the MKE (TheMinis-try of Knowledge Economy) Korea under the HumanResources Development Program for Convergence RobotSpecialists Support Program supervised by the NIPA(National IT Industry Promotion Agency) (NIPA-2013-H1502-13-1001) This work was also supported by theNational Research Foundation of Korea (NRF) Grant fundedby Korea Government (MEST) (2013-029812)
References
[1] S Thrun M Montemerlo H Dahlkamp et al ldquoStanley therobot that won the DARPA Grand Challengerdquo Journal of FieldRobotics vol 23 no 9 pp 661ndash692 2006
[2] M Buehler K Lagnemma and S Singh The DARPA UrbanChallenge Autonomous Vehicles in City Traffic Springer NewYork NY USA 2009
[3] A Soloviev ldquoTight coupling of GPS laser scanner and iner-tial measurements for navigation in urban environmentsrdquo inProceedings of the IEEEION Position Location and NavigationSymposium pp 511ndash525 Monterey Calif USA May 2008
[4] S Panzieri F Pascucci and G Ulivi ldquoAn outdoor navigationsystem using GPS and inertial platformrdquo IEEEASME Transac-tions on Mechatronics vol 7 no 2 pp 134ndash142 2002
[5] E-J Jung andD-J Yi ldquoTask-oriented navigation algorithms foran outdoor environment with colored borders and obstaclesrdquoIntelligent Service Robotics vol 6 no 2 pp 69ndash77 2013
[6] S Kim J Kang andM Jin Chung ldquoProbabilistic voxelmappingusing an adaptive confidence measure of stereo matchingrdquoIntelligent Service Robotics vol 6 no 2 pp 89ndash99 2013
[7] M Joerger and B Pervan ldquoRange-domain integration of GPSand laser-scanner measurements for outdoor navigationrdquo inProceedings of the 19th International Technical Meeting of theSatellite Division of The Institute of Navigation (ION GNSS rsquo06)pp 1115ndash1123 Fort Worth Tex USA September 2006
[8] M Hentschel O Wulf and B Wagner ldquoA GPS and laser-basedlocalization for urban and non-urban outdoor environmentsrdquoin Proceedings of the IEEERSJ International Conference on Intel-ligent Robots and Systems pp 149ndash154 Nice France September2008
[9] A Georgiev and P K Allen ldquoLocalizationmethods for amobilerobot in urban environmentsrdquo IEEE Transactions on Roboticsvol 20 no 5 pp 851ndash864 2004
[10] Y Morales T Tsubouchi and S Yuta ldquoVehicle localizationin outdoor mountainous forested paths and extension of two-dimensional road centerline maps to three-dimensional mapsrdquoAdvanced Robotics vol 24 no 4 pp 489ndash513 2010
[11] W SWijesoma K R S Kodagoda andA P Balasuriya ldquoRoad-boundary detection and tracking using ladar sensingrdquo IEEETransactions onRobotics andAutomation vol 20 no 3 pp 456ndash464 2004
[12] M Jabbour and P Bonnifait ldquoGlobal localization robust toGPS outages using a vertical ladarrdquo in Proceedings of the 9th
International Conference on Control Automation Robotics andVision pp 1ndash6 December 2006
[13] P Bonnifait M Jabbour and V Cherfaoui ldquoAutonomousnavigation in urban areas using GIS-managed informationrdquoInternational Journal of Vehicle Autonomous Systems vol 6 no5 pp 83ndash103 2008
[14] Y Shin D Kim H Lee J Park and W Chung ldquoAutonomousnavigation of a surveillance robot in harsh outdoor environ-mentsrdquo Advances in Mechanical Engineering vol 2013 ArticleID 837484 15 pages 2013
[15] Y Shin C Jung andWChung ldquoDrivable road region detectionusing a single laser range finder for outdoor patrol robotsrdquo inProceedings of the IEEE Intelligent Vehicles Symposium (IV rsquo10)pp 877ndash882 San Diego Calif USA June 2010
[16] D Kim and W Chung ldquoLocalization of outdoor mobile robotsusing road featuresrdquo in Proceedings of the 8th International Con-ference on Ubiquitous Robots and Ambient Intelligence (URAIrsquo11) pp 363ndash365 Incheon Republic of Korea November 2011
[17] S Mika G Ratsch J Weston B Scholkopf and K MullerldquoFisher discriminant analysis with kernelsrdquoNeural Networks forSignal Processing vol 9 pp 41ndash48 1999
[18] S Mika G Ratsch and K R Muller ldquoA mathematical pro-gramming approach to the kernel fisher algorithmrdquo Advancesin Neural Information Processing vol 13 pp 591ndash597 2001
[19] G Camps-Valls and L Bruzzone Kernel Methods for RemoteSensing Data Analysis JohnWiley amp Sons New York NY USA2009
[20] R E Kalman ldquoA new approach to linear filtering and predictionproblemsrdquo Journal of Basic Engineering vol 82 no 1 pp 35ndash451960
[21] R E Kalman and R S Bucy ldquoNew results in linear filtering andprediction theoryrdquo Journal of Basic Engineering vol 83 no 3pp 95ndash108 1961
[22] J J Leonard and H F Durrant-Whyte Directed Sonar Sensingfor Mobile Robot Navigation Kluwer Academic DordrechtTheNetherlands 1992
[23] B W Parkinson and J J Spilker Global Positioning SystemTheory and ApplicationsThe American Institute of Aeronauticsand Astronautics Washington DC USA 1996
[24] K O Arras and R Y Siegwart ldquoFeature extraction and sceneinterpretation for map-based navigation and map buildingrdquo in12th Mobile Robots Conference vol 3210 of Proceedings of SPIEpp 42ndash53 Pittsburgh Pa USA January 1998
[25] S T Pfister S I Roumeliotis and J W Burdick ldquoWeighted linefitting algorithms for mobile robot map building and efficientdata representationrdquo in Proceedings of the IEEE InternationalConference on Robotics and Automation pp 1304ndash1311 Septem-ber 2003
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
12 Mathematical Problems in Engineering
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This research was supported in part by the MKE (TheMinis-try of Knowledge Economy) Korea under the HumanResources Development Program for Convergence RobotSpecialists Support Program supervised by the NIPA(National IT Industry Promotion Agency) (NIPA-2013-H1502-13-1001) This work was also supported by theNational Research Foundation of Korea (NRF) Grant fundedby Korea Government (MEST) (2013-029812)
References
[1] S Thrun M Montemerlo H Dahlkamp et al ldquoStanley therobot that won the DARPA Grand Challengerdquo Journal of FieldRobotics vol 23 no 9 pp 661ndash692 2006
[2] M Buehler K Lagnemma and S Singh The DARPA UrbanChallenge Autonomous Vehicles in City Traffic Springer NewYork NY USA 2009
[3] A Soloviev ldquoTight coupling of GPS laser scanner and iner-tial measurements for navigation in urban environmentsrdquo inProceedings of the IEEEION Position Location and NavigationSymposium pp 511ndash525 Monterey Calif USA May 2008
[4] S Panzieri F Pascucci and G Ulivi ldquoAn outdoor navigationsystem using GPS and inertial platformrdquo IEEEASME Transac-tions on Mechatronics vol 7 no 2 pp 134ndash142 2002
[5] E-J Jung andD-J Yi ldquoTask-oriented navigation algorithms foran outdoor environment with colored borders and obstaclesrdquoIntelligent Service Robotics vol 6 no 2 pp 69ndash77 2013
[6] S Kim J Kang andM Jin Chung ldquoProbabilistic voxelmappingusing an adaptive confidence measure of stereo matchingrdquoIntelligent Service Robotics vol 6 no 2 pp 89ndash99 2013
[7] M Joerger and B Pervan ldquoRange-domain integration of GPSand laser-scanner measurements for outdoor navigationrdquo inProceedings of the 19th International Technical Meeting of theSatellite Division of The Institute of Navigation (ION GNSS rsquo06)pp 1115ndash1123 Fort Worth Tex USA September 2006
[8] M Hentschel O Wulf and B Wagner ldquoA GPS and laser-basedlocalization for urban and non-urban outdoor environmentsrdquoin Proceedings of the IEEERSJ International Conference on Intel-ligent Robots and Systems pp 149ndash154 Nice France September2008
[9] A Georgiev and P K Allen ldquoLocalizationmethods for amobilerobot in urban environmentsrdquo IEEE Transactions on Roboticsvol 20 no 5 pp 851ndash864 2004
[10] Y Morales T Tsubouchi and S Yuta ldquoVehicle localizationin outdoor mountainous forested paths and extension of two-dimensional road centerline maps to three-dimensional mapsrdquoAdvanced Robotics vol 24 no 4 pp 489ndash513 2010
[11] W SWijesoma K R S Kodagoda andA P Balasuriya ldquoRoad-boundary detection and tracking using ladar sensingrdquo IEEETransactions onRobotics andAutomation vol 20 no 3 pp 456ndash464 2004
[12] M Jabbour and P Bonnifait ldquoGlobal localization robust toGPS outages using a vertical ladarrdquo in Proceedings of the 9th
International Conference on Control Automation Robotics andVision pp 1ndash6 December 2006
[13] P Bonnifait M Jabbour and V Cherfaoui ldquoAutonomousnavigation in urban areas using GIS-managed informationrdquoInternational Journal of Vehicle Autonomous Systems vol 6 no5 pp 83ndash103 2008
[14] Y Shin D Kim H Lee J Park and W Chung ldquoAutonomousnavigation of a surveillance robot in harsh outdoor environ-mentsrdquo Advances in Mechanical Engineering vol 2013 ArticleID 837484 15 pages 2013
[15] Y Shin C Jung andWChung ldquoDrivable road region detectionusing a single laser range finder for outdoor patrol robotsrdquo inProceedings of the IEEE Intelligent Vehicles Symposium (IV rsquo10)pp 877ndash882 San Diego Calif USA June 2010
[16] D Kim and W Chung ldquoLocalization of outdoor mobile robotsusing road featuresrdquo in Proceedings of the 8th International Con-ference on Ubiquitous Robots and Ambient Intelligence (URAIrsquo11) pp 363ndash365 Incheon Republic of Korea November 2011
[17] S Mika G Ratsch J Weston B Scholkopf and K MullerldquoFisher discriminant analysis with kernelsrdquoNeural Networks forSignal Processing vol 9 pp 41ndash48 1999
[18] S Mika G Ratsch and K R Muller ldquoA mathematical pro-gramming approach to the kernel fisher algorithmrdquo Advancesin Neural Information Processing vol 13 pp 591ndash597 2001
[19] G Camps-Valls and L Bruzzone Kernel Methods for RemoteSensing Data Analysis JohnWiley amp Sons New York NY USA2009
[20] R E Kalman ldquoA new approach to linear filtering and predictionproblemsrdquo Journal of Basic Engineering vol 82 no 1 pp 35ndash451960
[21] R E Kalman and R S Bucy ldquoNew results in linear filtering andprediction theoryrdquo Journal of Basic Engineering vol 83 no 3pp 95ndash108 1961
[22] J J Leonard and H F Durrant-Whyte Directed Sonar Sensingfor Mobile Robot Navigation Kluwer Academic DordrechtTheNetherlands 1992
[23] B W Parkinson and J J Spilker Global Positioning SystemTheory and ApplicationsThe American Institute of Aeronauticsand Astronautics Washington DC USA 1996
[24] K O Arras and R Y Siegwart ldquoFeature extraction and sceneinterpretation for map-based navigation and map buildingrdquo in12th Mobile Robots Conference vol 3210 of Proceedings of SPIEpp 42ndash53 Pittsburgh Pa USA January 1998
[25] S T Pfister S I Roumeliotis and J W Burdick ldquoWeighted linefitting algorithms for mobile robot map building and efficientdata representationrdquo in Proceedings of the IEEE InternationalConference on Robotics and Automation pp 1304ndash1311 Septem-ber 2003
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of