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  • An Experimental Platform for Motion Estimation andManeuver Characterization in High Speed Off-Road Driving

    Haomiao Huang, Lyle Chamberlain, and Richard M. MurrayControl and Dynamical Systems

    California Institute of Technology1200 E. California Blvd, Padadena, CA 91126

    haomiao, lyle, murray @its.caltech.edu

    Abstract This paper describes a low-cost experimentalplatform for investigating control of a vehicle performinghigh speed sliding turns in an off-road environment. Thehardware design and field performance of the vehicle arediscussed. State and control input data were recorded duringa series of human-controlled off-road driving maneuvers.Analysis performed on the data demonstrates the ability toslippage and measure sideslip angle. Preliminary classificationof human control inputs using pattern recognition techniquesshows the ability to predict safe and unsafe maneuvers. Thesetools and techniques will be used for the development of highspeed autonomous off-road driving.

    Index Terms maneuver classification, motion estimation,off-road vehicle control, autonomous vehicles, dynamic con-trol

    I. INTRODUCTION

    There has been much recent interest in off-road au-tonomous vehicles. Spurred on by a congressional mandateto make one-third of the ground vehicles in the armyautnomous by 2015, DARPA recently held the first DARPAGrand Challenge, a competition to race autonomous groundvehicles off-road 150 miles through the Mojave Desert.Many interesting research issues have arisen as a result ofthis competition. One such is the issue of controlling a racevehicle turning at high speeds on terrain such as dirt or adry lake bed. Though a fair amount of previous work hasbeen done in vehicle lateral stability and traction control[2] [4], much of this prior work has been conducted onhighways and paved road surfaces. Off-road control workhas tended to focus primarily on path generation assumingno slippage, and then controlling vehicles to minimizeslip [3]. Indeed, except under racing conditions, sideslipis something that is usually desirable to minimize. Like-wise, existing on-road traction control and lateral controltechniques and algorithms have also focused on reducingsideslip and spin rather than taking advantage of them [5][2]. However, in a situation such as a race, time is ofparamount importance.

    A sliding turn like those performed by professional race-car drivers allows a vehicle to enter a sharp turn withoutreducing speed. Such maneuvers in full-scale vehicles arehighly difficult and require a skilled, alert driver to besuccessfully performed. In order to successfully control anautonomous vehicle during such maneuvering the controlsystem must have a clear and accurate estimation of the

    Fig. 1. Peggy, our test vehicle, during an early test run

    vehicles degree of sideslip and spin and react very quickly.It was with these concerns in mind that we approached theproblem of designing a vehicle to perform such maneuversautonomously. The contributions of this paper are three-fold. First, we describe a low cost platform for controland characterization high-performance off-road driving.Second, we demonstrate the ability to accurately determinesideslip angle with noisy, low-cost sensors. Finally, wedemonstrate the ability to classify maneuvers for high-performance driving using pattern recognition techniques.

    II. DESCRIPTION OF EXPERIMENT

    A. Platform Requirements

    There were several main requirements for the design ofPeggy, our experimental platform. First, it was to be ca-pable of sustained high-speed/high-performance operationson rough terrain. Second, since we would be exploringsliding turns during which the vehicle would break traction,all platform hardware had to be capable of withstanding theshock of a rollover at speeds possibly up to 30 mph. Finally,the entire platform had to cost less than about $7000.These requirements drove the design for both the vehicleplatform and the computing hardware. The vehicle itselfhad to be physically capable of driving at high-speeds off-road, with appropriate suspension and an engine powerfulenough to break traction in order to enter sliding turns.The computing hardware would have to operate in a high

    Richard MurrayText BoxSubmitted, 2005 Int'l Conference on Robotics and Automationhttp://www.cds.caltech.edu/~murray/papers/2004v_hcm05-icra.html

  • shock/vibe environment and also be fast enough to controlthe vehicle during high speed maneuvers that require quickcontrol inputs. Finally, sensors had to be found that wouldgive us vehicle attitude and position.

    B. Peggy: Design & Construction

    Cost and ease of testing dictated that the vehicleplatform be something small rather than a full-scalevehicle. The platform chosen was an FG Marder 1/6-scaleradio controlled racecar. The Marder is designed for highspeed off-road RC races, so it possesses a 23cc two-strokegasoline engine and wheels designed for off-road surfaces.We chose a gas powered vehicle because the testbedwould have to carry a fairly hefty payload: laptop, sensors,embedded system, and roll protection.

    Fig. 2. Peggy in her latest configuration. Note the placement of thelaptop beneath the clamshell and the spring rollbars to either side. Theedges of the clamshell are bent for extra strength.

    One of the more difficult design problems was mountingthe laptop and assorted equipment on to the vehicle ina way that would protect them from damage duringthe rollovers sure to occur during testing. The eventualsolution was to build a 3/8th inch aluminum clamshellover the top of the vehicle. At this scale, a one-piececlamshell provides as much or more strength as a cagestructure, with little weight penalty. It is also muchsimpler and cheaper than a welded or bolted cage andhas no joints to break, with the additional benefit thatit doubles as mounting structure. The clamshell is alsoeasily removable to allow access to the vehicle chasis. Thelaptop, embedded system box, and sensors were mountedon the underside of this clamshell. The two main sensors(IMU/GPS) needed to be shared with another vehicle, sothey were placed together on a small detachable mountwhich could be easily removed and replaced in the samelocation. The laptop is mounted under the sloped forwardpart of the clamshell, sandwhiched between layers of foamto protect it from shock and vibration. The sensor mountand the embedded box were mounted side by side in therear of the vehicle. The GPS antenna was magneticallymounted on top. A sort of rollbar was also attached,consisting of a piece of metal shaped like a large Cprojecting from each side. The ends were left unattached

    on the bottom, so there would be some spring force topush Peggy towards the upright position if it were justabout to roll over. Sealed lead-acid batteries were chosento supply power to sensors and the embedded system.Although they do not have the highest power density, theirlarge mass and low placement (on small outriggers toeither side of the vehicle) help lower the center of gravity.

    Fig. 3. Block diagram of Peggys systems

    A microcontroller-based embedded system handles low-level vehicle control and data acquisition. It monitorsbattery levels and power regulation for onboard systems(not including the laptop), engine temperature, wheel andengine velocities, and radio receiver commands. It alsosends postion commands to the two digital RC car servosthat actuate the vehicle (one for steering and one for throt-tle/brake). Hall-effect switches monitor magnets mountedon the wheels and engine for velocity measurement. Aserial link enables it to communicate with other computingdevices. The car can be driven manually through radiocontrol or autonomously through the serial port.

    The system sends updates of vehicle state and receivescommands over the serial port at 10Hz. Steering andthrottle positions are assumed to be consistent with thecommanded positions. The high speed servos and therelatively slow human control input allow us to assume thatsteering and throttle positions correspond closely to controlinputs. A hobby RC receiver enables human control. Theradio receiver sends commands as pulse-width modulatedsignals. The data aquisition monitors these signals witha small amount of noise (corresponding to 1-2 degreesof wheel deflection) that doesnt actually affect the servoposition.

    The computing hardware was designed to fill the re-quirements stated above, and to be easy to interface anddevelop on. We chose a laptop as the computing platformsince it has a self-contained power system and is alreadysomewhat hardened against vibration and shock. Linux waschosen as the operating system over a real-time system forease of use and hardware compatibility. Since the IBMR32 laptop we use does not have any physical serial ports,

  • USB-to-serial converters had to be used to connect to thesensor hardware and vehicle embedded system. These wereplugged into a USB hub, which was then plugged into thelaptop. This minimized the number of connections that hadto be made to the laptop, which made taking the laptop onand off of the vehicle very quick and simple. Unfortunately,due to time constraints a wireless networking solution hasnot yet been implemented. Instead, an ethernet cross-overcable was used during testing to start and stop data-logging.Although a standard laptop hard disk was used for codingdevelopment and initial testing, it was quickly discoveredthat hard drives are completely unsuitable for rough terraintesting. A 1 GB high-speed flash card was purchased, alongwith a 2.5 flash to IDE converter. Linux was installedonto the card, and during field tests and data-taking thehard drive was pulled out and replaced with the cardand adapter. The entire operation takes about 5 minutes(including shutting down and booting up the laptop), andthe flash card system has proved extremely reliable in fielduse.

    Fig. 4. The modular sensor mount for the GPS and IMU. The smallblack box on top is the Crista IMU, and the larger silver box below isthe AC12 GPS.

    The need for low-latency, high frequency updates ofvehicle state including attitude led us to choose a systembased on GPS-aided INS. The GPS used was a ThalesNavigation AC12, a small OEM board packaged into aruggedized casing. During testing it was found that theunit had a time-lag of about 1.25 sec which had to becorrected for. The IMU chosen was a Cloudcap CristaIMU, which gave full 6-DOF accelerometer and gyromeasurements through RS232 serial. The Crista unit is verysmall, measuring about 3 cm x 2 cm x 2 cm, and has lowpower draw, which made it ideal for our application. Gyrobias and drift were also very low; over periods of up to 2minutes simple numerical integration of the yaw rate gyroyielded errors of less than 10 degrees when driving on adry lakebed.

    C. Field Testing

    Peggy was taken to El Mirage Dry Lake Bed, whereextensive driving and data-logging runs were conducted.A human operator maneuvered Peggy around a test area,conducting multiple sliding turns, doughnuts, and other off-road racing-style maneuvers whild GPS and IMU data were

    logged. The system has proven to be extremely reliableunder very harsh conditions. Peggy was rolled severaltimes at high speed, including a few cases where it wastipped over its nose and flipped end to end. The laptopand all sensors continued functioning, and no action wasrequired on our part beyond flipping the vehicle upright andcontinuing testing. The rollbars also functioned well, andon several occasions we were saved from a roll-over whenPeggy tipped but not without enough force to go over therollbars. However, sometimes during tests the laptop wouldstop recording data from the sensors. The excecutableswould still be running but no data would be logged from theserial ports. It is unclear to us whether this was caused byhardware (such as vibration issues) or software. The samesetup, running on a different laptop on a larger vehicledid not experience this problem, so it is possible that thehigher vibration environment on Peggy was responsible.The problem was intermittent, and as noted above thesensors and logging functioned through rollover impacts,so the software may have been at fault. Surprisingly, dustwas not a major issue for us. Masking tape over most ofthe laptops openings (except the air vents for the fan) keptmost of the dust out, and spraying the air vents with thefan has so far kept dust buildup from being a problem.

    III. MOTION ESTIMATION

    A. Motivation & Setup

    In order to successfully control the vehicle during highspeed driving, it is necessary to determine in real-time thecurrent state of the vehicle. However, the standard methodof fusing GPS and IMU data using a Kalman filter mustbe slightly modified to take into account the differences invehicle dynamics between turning without wheel slip andturning during a slide. When the vehicle is turning withoutsliding, the velocity vector and heading vectors are in linewith each other, so GPS velocity updates can be used toobserve the error in gyro heading estimates. It was notedobservationaly that the scale-factor errors of our gyro wasnegligible over the time periods we were concerned with,so the gyro readings can be modeled simply as in [1]:

    rgyro = + gbias + wgyro (1)

    Where wgyro is a white sensor noise, is the heading, andgbias is the gyro bias. A simple Kalman filter can be usedto correct the drift error using GPS updates [1]:

    [

    gbias

    ]

    =

    [

    0 10 0

    ] [

    gbias

    ]

    +

    [

    rgyro0

    ]

    +

    [

    wgyro0

    ]

    (2)

    with measurement update:

    gps =[

    1 0]

    [

    gbias

    ]

    + vgps (3)

    The key factor is determining whether the vehicle iscurrently sliding during its turn. During a sliding turn,the velocity vector and the actual heading of the vehicle(by which we mean the direction the front of the vehicleis pointed at) do not coincide. In such a maneuver the

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    42

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    Heading and Position Plot

    Easting

    Nor

    thin

    g

    PositionHeadingSlip

    Fig. 5. A plot of the position of the vehicle, with heading superimposedas arrow vectors. Note how the heading comes around before the positiondoes. The parts where the vehicle is determined to be sliding are plottedas circles.

    actual heading leads the velocity vector until friction stopsthe vehicle from sliding, at which point the heading andvelocities once again coincide. During such turns, the GPScannot be used to update the bias error on the gyro, so it isnecessary for the gyro bias errors to be small over the timeperiod of the maneuver. The state estimation system mustautomatically recognize when it is in such a maneuver andwhen it is not in order to determine when to use GPS toupdate the headings. This is done by continously comparingthe gyro-derived heading to the vehicle velocity vector toobtain an estimate of the current sideslip angle, defined as:

    = gyro velocity (4)

    Since GPS updates are slow, the velocity vector should bederived by integrating onboard accelerometer data. Whenthe estimated sideslip angle is above a certain threshold, thesystem recognizes that the vehicle is sliding and does notuse GPS updates. The duration of our turning maneuversis short enough ( 30 seconds in most cases) that gyro driftdoes not become a major source of error. Wheel-speedsensors (which in our case were not completely operative)can also be used to give a sense of how much the vehicleis sliding, helping to make the determination of whether ornot to use GPS updates.

    B. Experimental Results

    A set of experiments were conducted by driving Peggyunder human control on a dry lakebed where IMU, GPS,and command input data were recorded. This data was thenpost-processed by feeding it into a state estimator designedaccording to the above specifications. Accelerometer data

    18 16 14 12 10 8 6 4 2 0

    50

    48

    46

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    Heading and Position Plot

    Easting

    Nor

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    PositionHeadingSlip

    Fig. 6. Another plot of a turn. Note the sharp corner at the end of thisturn as the vehicle slams to a stop sideways because the turn occurredtoo sharply

    110 111 112 113 114 115 116 117 118 1190

    1

    2

    3

    4

    5

    Headings from GPS & IMU

    Time (s)

    Hea

    ding

    (ra

    d fr

    om n

    orth

    )

    IMUGPS

    Fig. 7. The actual heading of the vehicle as compared to the velocityvector derived from GPS plotted for figure 6.

    was available, but there was insufficient time to write an ac-curate Kalman filter to convert the raw accelerometer datainto velocities, so a cubic spline interpolation was fit to therecorded GPS position and velocity data. Accelerometer-derived velocity is to be implemented in the very nearfuture, so that sideslip can be determined in real-time onthe platform. A time delay of about 1.25 seconds on theGPS readings was also corrected for in the updates. Theseinterpolated points were then used in lieu of accelerometerdata to estimate the sideslip angles during a turn sequence.Gyro yaw rate was integrated using numerical trapezoidalintegration to get actual heading, where:

    n+1 = n + t(n+1 + n)

    2(5)

    corrected by GPS updates when not slipping. The orienta-tion of the velocity vector was derived from the north/east

  • velocities, so sideslip became:

    = gyro atan2(veast, vnorth) (6)

    Figures 5 and 6 show sliding turn maneuvers as pro-cessed by the state estimator. The sliding entry into the turncan be clearly seen, as the nose of the vehicle (indicatedby the heading arrows) pulls around while the vehiclecontinues on its earlier path until friction grabs hold and thevehicle once again drives without slipping. An interestingpoint to note is the very distinct difference in curvatureof the two turns. The turn shown in figure 5 is a muchsmoother, better controlled turn. Figure 6 shows a skilledturn which was too sharp. The vehicle skid sideways for arelatively short while before friction caught it, tipped thewheels up, and then slammed back down. The differencesbetween these two turns will be explored in more detailedin the section on maneuver characterization.

    IV. MANEUVER CHARACTERIZATION

    One of the advantages of Peggy is that a human drivercan guide it through repeated high-risk maneuvers that aretoo risky for a larger more expensive vehicle. The humancontrol inputs have the potential of providing valuableinsight into control techniques for technical driving. Thissection discusses analysis of human driving inputs topredict vehicle behavior during a maneuver.

    The open differential that drives the rear wheels intro-duces unexpected vehicle behavior. First, left turns are verydifferent dynamically from right turns. A right turn requiresa constant right steering input, even during sliding. A leftturn is much different. The differential is imbalanced infavor of left turns, so a small left steering input at highspeed can quickly spin the car out of control. A controlledleft sliding turn requires a small kick to the left, thenimmediate counter-steering to the right. This unexpectedbehavior can make the control inputs for controlled leftand right turns look quite similar.

    Second, if one of the rear wheels lifts from the groundduring a sliding turn all of the engines power is transferredto the lifted wheel, stealing nearly all torque from theremaining drive wheel. The remaining wheel can no longerapply the force necessary to spin out and continue slidingwith kinetic friction. Static friction quickly overcomes thatwheel and the turn abruptly stops as if the vehicle has hit awall. We refer to these maneuvers as jerk turns(see figure6). A smooth turn keeps both drive wheels in contact withthe ground at all times (see figure 5).

    Peggy logged telemetry during human driving on anoval-shaped dry lake bed course. Driving consisted of manyright and left turns that show the properties discussedabove. Afterwards, the telemetry was manually segmentedinto vectors that contain the steering commands used toexecute a maneuver. The maneuvers were also manuallyclassified as a left or right turn, and as a smooth or a jerkturn. The vectors were all rescaled to the same size, thenassigned to relevant training test sets.

    0 10 20 30 400.4

    0.2

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    0.41

    0 10 20 30 400.4

    0.2

    0

    0.2

    0.42

    0 10 20 30 400.4

    0.3

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    0.33

    0 10 20 30 400.4

    0.3

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    0

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    0.34

    Fig. 8. PCA-Derived Steering Input Eigenvectors

    A. Interpretation of turns with counter-steer:

    As discussed above, controlled turns require very littleto no left steering input, and significant right countersteer. This may confuse pattern recognition for automatedsegmentation as well as pose problems for controller de-sign. To understand the difference between the maneuvers,Principle Component Analysis (PCA) is performed on theset of steering control vectors to reduce dimensionality.Using a set of n training vectors i, we calculate the meanvector :

    =1

    n

    n

    i=1

    i (7)

    And the covariance matrix M as;

    M =1

    n 1

    n

    i=1

    (i )(i )T (8)

    The unit eigenvectors p1, p2, ..., pd of the covariance matrixM are then computed and arranged in order of descend-ing eigenvalues. These eigenvectors encode the principlecomponents, a set of linearly independent features orprimitives. Projection of a vector i onto the basis set{p1, p2, ..., pk} gives the k-dimensional vector space thatpreserves the most information.

    It is informative to view the first vectors of the PCAspace, as they show recurring trends in the data. Figure 8shows these principle components.

    The projection of right vs. left turns onto the firsttwo eigenvectors results in the clustering shown in Figure9. These clusters strongly suggest that eigenvector 1 isinvolved primarily in right turns, and eigenvector 2 is re-sponsible for left turns. Examination of these vectors showsthe expected control inputs for the associated maneuver.

    Assuming the characteristics of these clusters are known,characterization of test points is performed by computing

  • 200 100 0 100 200300

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    300Test Data

    200 100 0 100 200

    300

    200

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    0

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    300

    Training Data

    o = right+ = left

    Fig. 9. PCA Right vs. Left Turn Detection Clustering

    the likelihood ratio R:

    R =P (T = 1|x)

    P (T = 2|x)=

    P (x|T = 1)

    P (x|T = 2)P (T = 1)

    P (T = 2)(9)

    The likelihood ratio is computed as the likelihood of eventT = 1 over the likelihood of event T = 2, given a controlvector x. Bayes Rule allows us to use the equivalenceshown on the right hand side, which is easily computedas:

    R =e

    1

    2(x1)

    1

    1(x1)

    e1

    2(x2)

    1

    2(x2)

    1 (10)

    Where i is the mean vector of cluster i, and i is thecovariance matrix of the training vectors in that cluster. Therelative likelihood of the two events P (T = 1)/P (T = 2)is assumed to be 1. If R > 1, then T = 1 is more likely.If R < 1, T = 2 is favored.

    The performance of the classifier is shown in the Re-ceiver Operating Characteristic (ROC) curve in Figure 10as the detection rate of left turns vs. false alarms as thethreshold of R is varied. Here, 80% of the data set of318 vectors was used for training, and the remaining 20%for testing. Only the first two PCA eigenvectors wereused for this classification. This curve shows predictionof turn direction despite similarities of control inputs dueto counter-steer required by the drive wheels differential.

    B. Detection of dangerous turns:

    The prediction of jerk turns as described in the in-troduction to this section proves to be a more difficultproblem. The sequence of control inputs that causes oneside of the vehicle to dangerously lift is less straightforwardthan the simple counter-steering identified above. The mainproblem with the current analysis is a lack of training data.The beginning analysis is done on a set of 51 left turnswith jerk vs. a set of 95 smooth left turns. This is notquite enough to be statistically significant with PCA and

    0 0.2 0.4 0.6 0.8 10

    0.1

    0.2

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    0.7

    0.8

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    1

    Percent False Alarms

    Per

    cent

    Det

    ecte

    d

    Fig. 10. PCA Right vs. Left Turn Detection Receiver OperatingCharacteristic

    200 100 0 100 200200

    150

    100

    50

    0

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    200Test Data

    200 100 0 100 200200

    150

    100

    50

    0

    50

    100

    150

    200Training Data+ = Jerk

    o = smooth

    Fig. 11. PCA Jerk Detection Clustering

    the other techniques used, but pending our second set offield trials, the preliminary results are promising.

    The ROC curve for jerk turn detection in figure 12 wasgenerated using 15 PCA vectors and the gausian clusteringdiscussed above. 60% of the data set was used as training,and the remaining 40% for testing. The reason for the poorperformance is seen in the 2-D slice of PCA space shownin figure 11. The cluster means are very close, and the onlyway to recognize the jerk cluster is by its higher variance.

    We used Fisher Linear Discriminants (FLD) to furtherreduce the dimensionality of the data. FLD uses class in-formation in order to generate basis vectors that maximizethe distance between the means of different clusters.

    A full description of linear discriminant analysis isbeyond the scope of this paper, however we will providea simplified example. Discriminant analysis is a methodof solving for a projection of a data set X of dimen-sionality N of known grouping onto some subspace Yof dimensionality M < N such that the projections ofthe groupings are maximally separated [6]. For example,in a two dimensional dataset with 2 groups, we wouldattempt find a projection which maximizes the Fisher lineardiscriminant criterion function [6]:

    J() =|1 2|

    2

    21 + 22

    (11)

    where n is the mean of the projection of group n, 2nis the variance of group n, and is the projection onto

  • 0 0.2 0.4 0.6 0.8 10

    0.1

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    1

    Percent False Alarms

    Per

    cent

    Det

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    d

    Fig. 12. PCA Jerk Detection Receiver Operating Characteristic

    a lower dimension space. The maximum of this functionwould ensure that the means of the two groups are as farapart as possible while minimizing the variances withineach group, thus making the the projection of the twogroups as distinct as possible. This is generalized to higherdimensionality problems.

    0 0.2 0.4 0.6 0.8 10

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    Percent False Alarms

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    cent

    Det

    ecte

    d

    Fig. 13. PCA to FLD Receiver Operating Characteristic for JerkDetection

    For this experiment, the same test data was projectedonto 10 PCA vectors. These vectors in PCA space werethen projected onto 3 FLD vectors. The same gaussianclustering was used to classify these points in 3 space.The resulting ROC curve is shown in figure 13. 95% ofall dangerous jerk turns were predicted with a 60% falsepositive rate. While not spectacular, the high false positiverate could be acceptible in safety applications, especiallyin autonomous driving.

    The clusters in FLD 3 space do not appear gaussian.Use of another clustering technique such as k-means couldprobably increase the performance markedly. More tech-niques will be applied after enough field data is collected

    to produce statistically significant results.

    V. SUMMARY & FUTURE WORK

    The results outlined in this paper have demonstratedan ability to characterize different types of sliding turnmaneuvers as well as to detect the state variables necessaryfor their control. We are able to detect when the vehicle issliding, when it is not sliding and the degree of sideslip.We have preliminary results using pattern recognition thatpredict the control inputs which put the vehicle into safeand unsafe sliding turns. The next logical step (after real-time slide-detection is implemented) is to utilize thesefindings in autonomous control of the vehicle. A controlsystem employing human driving patterns observed bythe pattern recognition software or hybrid control/gain-scheduling can be designed which will kick the vehicleinto a sliding turn, with another controller bringing thevehicle back out of the slide in a controlled fashion. Thefinal step is trajectory generation and path planning toutilize these maneuvers in a real-world situation.

    ACKNOWLEDGMENTS

    We would like to thank Dmitry Kogan, Pierre Moreels,John van Deusen, Tully Foote, and Lihi Domitilla for theirassistance with this project.

    REFERENCES

    [1] David M. Bevly, Christian Gerdes, and Christopher Wilson. The useof gps based velocity measurements for measurement of sideslip andwheel slip. Vehicle System Dynamics, 2002.

    [2] S. Brennan and A. Alleyne. Driver assisted yaw rate control. Proc.of the American Controls Conference, San Diego, CA, 1999.

    [3] D. Coombs, K. Murphy, A. Lacaze, and S. Legowik. Drivingautonomously offroad at 35 km/h.

    [4] Zhou Doyle, S. Brennan, and A. Alleyne. Using a scale testbed:Controller design and evaluation. IEEE Control Systems Magazine,2001.

    [5] Jay A. Farrell, Han Shue Tan, and Yunchun Tang. Carrier phase gps-aided ins-based vehicle lateral control. Journal of Dynamic Systems,Measurement, and Control, 2003.

    [6] Pietro Perona. Note on fisher linear discriminants.

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