[08cv-0039] a new fuzzy based stability index using predictive vehicle modeling and gps data

8/14/2019 [08CV-0039] A New Fuzzy Based Stability Index Using Predictive Vehicle Modeling and GPS Data

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08CV-0039

A New Fuzzy Based Stability Index Using Predictive VehicleModeling and GPS Data

Ben Duprey, Graduate StudentSeyed Hossein Tamaddoni, Ph.D. Student

Saied Taheri, Associate ProfessorDepartment of Mechanical Engineering

Virginia Polytechnic Institute and State UniversityBlacksburg, VA USA

Copyright 2008 SAE International

ABSTRACT

The use of global positioning systems, or GPS, as a means

of logistical organization for fleet vehicles has become morewidespread in recent years. The system has the ability totrack vehicle location, report on diagnostic trouble codes,and keep tabs on maintenance schedules thus helping toimprove the safety and productivity of the vehicles and theiroperators. In addition, the increasing use andimplementation of yaw and roll stability control in heavytrucks has contributed to an increased level of safety fortruck drivers and other motorists. However, these systemsrequire the vehicle to begin a yaw or roll event before theyassist in maintaining control. The aim of this paper is topresent a new method for utilizing the GPS signal inconjunction with the fuzzy based stability index to create atruly active safety system.

1. INTRODUCTION

There have been many notable research publicationsdescribing the efforts to incorporate GPS map tracking andfuzzy logic based lateral control. For example, the workdone by Jose Naranjo, et al [1] on lateral vehicle controlinvolving fuzzy logic techniques centered around the use ofGPS tracking as a means to control the vehicle steering,with autonomous vehicles being the ultimate goal. The workby Hessburg and Tomizuka [2] also used a fuzzy rule-based controller as a means for lateral control but there theintent was for use in an automated highway system. Thegoal here is to develop a fuzzy based stability index topredict the overall vehicle stability condition and take actionprior to initialization of vehicle instability. This system worksby taking the GPS signal and providing the data to thePredictive Dynamics Model which finds Lateral Velocity,Yaw Rate, Roll Angle, and Roll Angle Rate. The LateralAcceleration is then calculated. The maximum values ofLateral Acceleration, Lateral Velocity, Yaw Rate, and RollAngle are then found and processed by the Fuzzifier atwhich point the safety margins for Lateral Acceleration,Lateral Velocity, Yaw Rate, and Roll Angle are found.

These margins are collectively used to determine the TotaSafety Margin (TSM).

2. GPS OVERVIEW

The development of the Global Positioning System (GPSwas initiated in the early 1960s by several U.S. Governmenorganizations including the Department of Defense (DOD)NASA and the Department of Transportation (DOT) forthree-dimensional position determination. In 1969 the Officeof the Secretary of Defense (OSD) established the DefenseNavigation Satellite System (DNSS) program and from thiseffort, the system concept for NAVSTAR GPS was formedPresently, GPS is fully operational and meets the criteriaestablished in the 1960s for an optimum positioningsystem. The system provides accurate, continuous, worldwide, three-dimensional position and velocity information tousers with the appropriate receiving equipment [4-5]. Thesatellites are launched into 10,898 nautical mile orbits in 6orbital planes, each tipped 55 degrees with respect to theequator. The complete constellation consists of 21NAVSTAR satellites plus 3 active on-orbit spares [6]. GPSutilizes the concept of one-way time-of-arrival (TOA)ranging enabling the receiver to determine the satellite-touser range. At least four satellites are required to determinethe user latitude, longitude, height, and receiver clock offsetfor internal system time [4-5]. This is accomplished by thesimple resection process using the distances measured tosatellites [7]. The NAVSTAR GPS uses pseudorangingtechniques rather than Doppler shift measurements to fix

the users position. This means that a NAVSTAR receivermeasures the signal travel times from several satellitessimultaneously, instead of frequency variations from onlyone satellite at a time [6].

2.1. DIFFERENTIAL GPS (DGPS)

Differential GPS (DGPS) is a method to improve thepositioning or timing performance of GPS using one ormore ground-based reference stations at known (i.e. fixed)locations, each equipped with at least one GPS receiver [4]


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The stations broadcast the difference between the positionsindicated by the satellite systems (i.e. the measuredsatellite pseudoranges) and their known fixed positions.Since a reference station calculates differential correctionsfor its specific location and time, users can incorporatethese corrections to improve the accuracy of their positionsolution. Satellite ephemeris errors, as well as errorsintroduced via ionospheric and tropospheric distortions, cancause positioning errors to be spatially correlated, meaningthat position solutions for users further away from thereference receiver will be less accurate than those closer tothe reference station [5].

The reference stations provide information to the end uservia a data link that may include:

Corrections to the raw end users pseudorangemeasurements, corrections to GPS satellite-provided clock and ephemeris data, or data toreplace the broadcast clock and ephemerisinformation

Raw reference station measurements (e.g.,pseudorange and carrier phase)

Integrity data (e.g., use or dont use indicationsfor each visible satellite, or statistical indicators ofthe accuracy of provided corrections)

DGPS techniques may be categorized in different ways:absolute or relative differential positioning; as local,regional, or widearea; and as codeor carrierbased [4].

Absolute differential positioning is the determination of theusers position with respect to an Earth-Centered Earth-Fixed (ECEF) coordinate system. This is the most common

goal of DGPS systems. For absolute differential positioning,each reference stations position must be accurately knownwith respect to the same ECEF coordinate system in whichthe user position is desired. In contrast, relative differentialpositioning is the determination of the users position withrespect to a coordinate system attached to the referencestations, whose absolute ECEF positions may not beperfectly known [4].

DGPS systems may also be categorized in terms of thegeographic area that is to be served. The simplest DGPSsystems are designed to function only over a very smallgeographic area, with the user separated by less than 10-

100 km from a single reference station. Multiple referencestations and different algorithms are typically involved toeffectively cover larger geographic areas. The termsregional areaand wide areaare frequently used to describeDGPS systems covering larger geographic regions, withregional-area systems generally covering up to around1,000 km and wide-area systems covering larger regions(i.e. larger than 1,000 km) [4].

When wide-area augmentation is used in conjunction withcode-based differential GPS, just a couple of referencereceivers could cover an area as large as the United

States. Its principle is based on estimating the errors ofeach component for the entire region, rather than only atthe station positions [5].

One final categorization of DGPS systems is between so-called code-based and carrier-based techniques. Codebased DGPS systems rely primarily on GPS code, opseudorange, measurements and can provide decimeterlevel position accuracies. Carrier-based DGPS systems, onthe other hand, rely primarily on carrier-phasemeasurements. They require more base stations thancode-based differential techniques [5] but are much moreprecise than pseudorange measurements and can providemillimeter-level performance [4].

2.2. INERTIAL NAVIGATION SYSTEMS (INS)

GPS receivers can be thought of as discrete-timeposition/velocity sensors with sampling intervals oapproximately 1 second. The need to provide continuousnavigation between the update periods of the GPS receiverduring periods of shading of the GPS receivers antennaand through periods of interference is the impetus fo

integrating GPS with various additional sensors. The mospopular are inertial sensors typically measuring yaw rateand acceleration, but altimeters, speedometers, andodometers can be used. The most widely used method forthis integration is the Kalman filter. One of the key attributesof the Kalman filter is that it provides a means of inferringinformation by the use of indirect measurements, the GPSmeasurements. It does not have to read control variablesdirectly, but it can read an indirect measurement andestimate the control variables which in GPS applicationsare position, velocity, and possible attitude errors [4-5].

Employing GPS and inertial sensors for navigation is a

complimentary relationship: the GPS sensor providesbounded accuracy and can calibrate the INS sensor whenits own accuracy degrades over time, and the INS cansupport GPS receiver performance issues such asinterference from external sources, time to first fix (i.e., firstposition solution), interruption of the satellite signal due toblockage by terrain or manmade structures such asbuildings and tunnels, as well as signal integrity andreacquisition capability. Thus the integration of these twotypes of sensors not only overcomes performance issuesfound in each individual sensor, but also produces a systemwhose performance exceeds that of the individual sensors[4-5].

The discrete-time nature of the GPS solution is of concernin real-time applications such as vehicle control. When onlythree usable satellite signals are available, most receiversrevert to a two-dimensional navigation mode by utilizingeither the last known height or a height obtained from anexternal source. If the number of usable satellites is lessthan three, some receivers have the option of not producinga solution at all or extrapolating the last position andvelocity forward, a process called dead-reckoning (DRnavigation. If a vehicles path changes between GPS signaupdates, this extrapolation of the last GPS measuremen


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produces an error in the estimated and true position. Theinertial navigation systems can therefore be used as aflywheel to provide navigation during shading outages [4-5].

When an INS is calibrated using a Kalman filter it can beused to improve GPS receiver performance in twoadditional ways. First, the information maintained by theintegration filter can be used to reduce the time to reacquireGPS signals that have been lost through interference orobstruction; second, the integration filter can be used to aidthe receivers tracking loops, extending the thresholds forsignal tracking [4].

The quality of INS very much depends on the quality of theinertial sensor used. With automotive-quality yaw ratesensors in combination with the wheel speed signals usedby the ABS system, the position of a vehicle can bepropagated up to 30 sec. with an error of less than 1m. Themost significant factor related to the quality of an inertialsystem is the drift of a yaw rate sensor [5].

2.3. GPS ACCURACY AND SOURCES OF ERROR

The standard GPS currently available for civil applicationsenables positioning with an accuracy of at least 33 m, or a

1 horizontal, vertical, or three-dimensional position erroras a function of satellite geometry and the 1 range error[4-5]. More accurate precision navigation can be obtainedby Differential GPS based on error removal using thedifference between a reference receivers surveyed positionand its precisely-known geographic location. As mentionedabove, code-based differential techniques can providedecimeter-level position accuracy whereas carrier-basedtechniques, using the GPS satellite signal carrier frequency,can provide millimeter-level positioning.

Common sources for inaccuracies are: satellite clock error ephemeris prediction error atmospheric effects ionospheric effects tropospheric delays interference from external sources time to first fix (i.e., first position solution) interruption of the satellite signal due to blockage

by terrain or manmade structures such as buildingsand tunnels

signal integrity and reacquisition capability

reflected signals from buildingsNote that prior to the year 2000 a significant source of errorfor civilian-use GPS was Selective Availability, anintentional error induced by the U.S. DOD that degradedthe users navigation solution. An executive order byPresident Bill Clinton turned off Selective Availabilitypermanently in the year 2000 [4-5].

2.4. GPS MAP DATABASES

Besides the determination of the vehicle position usingGPS, the second key component in ground vehicle satellite-aided navigation is the digital road map, commonlyprovided on a CD-ROM. Two primary companies, Navteqand TeleAtlas, are developing digital road map databasesfor vehicle navigation and have extensive databasescovering most of the United States, Canada, Europe, some

countries in Asia and the Middle East, and other emergingmarkets worldwide. The accuracy of these databases, asdetermined by comparing road centerline vectors to groundtruth, ranges from under 12 meters in urban areas to 50meters or more in rural areas. New initiatives are underwayto map road centerlines to better than 5 meter accuraciesand to include vertical information for use in advanceddriving systems. For more information on the use of verticainformation in the GPS mapping, see below [4]. Someprimary factors that influence the accuracy of the mapsinclude the base map and photo material from which thedigital map is produced [5].

Venhovens, et al [5] refer to this digital cartography / GPS

combination as an electronic horizon of the vehicle andthey advocate that this is needed for the driver, and in thecase of this paper a predictive vehicle control system, toinform or react in advance to events which are eitheoutside of the drivers visual range or whose continuousmonitoring would pose an unnecessary burden on thedriver.

As pointed out by Kaplan, et al [4] the process of correlatingthe vehicle path with a drivable path in the digital road mapis called map matching. A basic assumption made is thathe vehicle is on the road network so that the dead-reckoning (DR) position is constrained to one of the road

segments in the map. The DR sensors, which provide apath of the vehicle, are combined with a robust mapmatching implementation that uses confidence measures todetermine all possible road segments in the map on whichthe vehicle could be traveling. As the vehicle travelsdistance traveled and changes in direction are used tocontinuously determine the shape of the route traveled; thisshape is used to match the road network in the mapthrough shape correlation. When an accurate heading isknown, the list of roads is reduced to those that have abearing within a tolerance of the vehicle heading. Throughthis process, the list of possible vehicle positions iseventually reduced to a unique segment and the confidence

in the positioning solution increases accordingly. Thisprocess continues until there is only one possible vehicleposition, at which point the map-matched position solutionwill have a small confidence region and can thus beconsidered highly reliable.

What if a driver drives on a road that is not in the mapdatabase? In order to support map matching, the map datashould have high position accuracy, ideally better than 15meters, to minimize incorrect road selections. The mapdata should be topologically correct, reflecting the realworld road network, so that the algorithm does not ge


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confused if the user drives on a road that is not in thedatabase. The expected accuracy of the road centerlinedata should be used in the map-matching process todetermine the overall confidence region of the map-matched position solution.Once a match is determined, the vehicle position is thendisplayed on the matched road segment. In traditional in-vehicle navigation systems this information would be usedfor the route guidance instructions, but in the case of thesafety system presented in this paper this data would befed into the Predictive Dynamics Model. In this instance themap would be used as a sensor itself to provide usefulinformation to the positioning subsystem or to calibrateinertial and other DR sensors. These capabilities arebroadly referred to as map aidingand map calibration[4].

Map aiding is most useful when map matching hasdetermined that the vehicle has just turned a corner, inwhich case its position is in close proximity to theintersection of two streets of a known location in the mapdatabase. This reference position may be treated as asingle position fix by the integration filter, which serves tocorrect or improve the accuracy of the absolute position

determined by GPS. Further, if map matching hasdetermined that the vehicle is traveling on a specific road inthe database and that the road is straight, then a headingfix may be generated for the integration filter based on thebearing of that road segment according to the mapdatabase. One low cost navigation solution, proposed byKaplan, et al is map feedback. In this case a constraint isimposed on the model to force the heading of the vehicle tomatch the bearing of the road. This utilization of headinginformation could be used instead of DR sensors [4]. Inorder to be reliable, however, this system would have toassume that the digital maps being used were alwayscorrect and up-to-date.

In addition to the horizontal position components of roadvectors, ground elevation data may be used to augment theperformance of GPS. A digital terrain model (DTM) is arepresentation of the Earths surface that can be used toextract elevation data. A digital elevation model (DEM) is atype of DTM with a regularly spaced grid of elevationscorresponding to the elevation of the Earths terrain at thatpoint. Modern DTMs are derived from airborne or satellite-based remote sensors, are georeferenced using GPScoordinates, and have vertical accuracies better than 10meters [4].

Terrain elevation can be used to improve the accuracyassociated with GPS fixes for land applications. To apply aheight constraint to a real-time Kalman filter, for example,an approximate or previous position can be used to extractthe corresponding elevation from a DTM or DEM. Using aDEM would involve a simple value lookup and interpolationbased on the coordinates and would therefore be easierfrom a computational perspective but would require a largeamount of storage. On the other hand, a DTM that has theelevation data organized into vectors would use lessstorage but would require more involved computations todetermine the elevation at a specific point. Another option

would be for the elevation data to be integrated into thedigital road maps as attribute data. This would simplifyelevation lookup and keep storage requirements lowerAccording to Kaplan, et al, the vertical axis is the weakespart of the GPS solution yet terrain elevation data has notyet been widely used to augment GPS. This will likelychange in navigation and driver safety systems once theelevation data is integrated into the digital road maps [4].

Map calibration is very similar to the process of using GPSdata to calibrate inertial and other DR sensors. Foexample, a constant road heading may be used to calibratea low-cost gyro or magnetic compass. In this case the gyroreading is then a direct measure of its bias. In the case of avehicle making a turn at an intersection, the change inheading between the inbound and outbound segments canbe used to calibrate a heading sensor. As Kaplan pointsout, however, with the current performance of GPS, mapcalibration of sensors is less common than it once was [4].

Since the GPS-aided navigation system relies on a digitamap stored on a database, a significant concern arisesregarding the accuracy of the map over time. In other

words, what happens if a road has changed significantlysince the map was made? Perhaps there is a new highwayon- or off-ramp, or maybe a bridge is out. Up-to-the-minutecartographic material is crucial in providing viable, efficiennavigation. According to the map compilers, 10 25% ofthe road segments will undergo changes every yearTherefore, map database updates for route guidance aremade available to the end user on a quarterly basis[5]. Buwhat if someone decides not to update their map when anew version becomes available? For the purpose of thispaper it is assumed that map databases are up to date, butone idea for future implementation could be if the mapdatabase is stored on a hard drive in the vehicle instead of

only on CDs then it might be possible to have automaticupdates via an internet connection similar to what isavailable now for anti-virus programs and Windows

TM

operating systems on personal computers.

Several additional questions are:

Rather than relying on map CDs, would it be possible touse a system like Google Earth

TMto provide the

cartographic information? It would seem that since GoogleEarth

TMis accessible through the internet this would require

internet access all of the time. Beyond that, further researchneeds to be done.

The CD-based navigation system described here wouldrequire an in-vehicle navigation processing system similato those in passenger cars with this feature. Further moreas pointed out above the digital maps need to be updatedperiodically, so how do these affect not only the initial costof the vehicle but also the long-term operating cost, both foupkeep of the navigation system and the map updates?Since the intent of this paper is to describe the technologyfusion of fuzzy logic and GPS-assisted guidance, cost is nota consideration. A future research step would be to


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Therefore, the Safe, Caution, and Danger regions werechosen based on the relative differences between theresults of the multiple mass cases simulated as well aswhat values seemed reasonable for the vehicle beingsimulated. The results of the multi mass study arepresented in Section 6.It should be noted that with respectto the 0.3 g Lateral Acceleration Safe/Caution region,this value is commonly considered the limit at which avehicle can corner at steady state while remaining withinthe linear region of the tire [9-11]. Since the linear tireassumption was used, this makes sense.

Based on the multi mass study the following fuzzy ruleswere used:

IF Lat_Acc < abs(0.3g), THEN in Safe Region (no controlnecessary)IF Lat_Acc >= abs(0.3g) and < abs(0.6g), THEN in CautionRegion (control may be necessary)IF Lat_Acc >= abs(0.6g), THEN in Danger Region (controlis necessary)

IF Lateral Velocity < abs(1 kph), THEN in Safe Region (no

control is necessary)IF Lateral Velocity >= abs(1 kph) and < abs(4 kph), THENin Caution Region (control may be necessary)IF Lateral Velocity >= abs(4 kph), THEN in Danger Region(control is necessary)

IF Yaw Rate < abs(1 deg/s), THEN in Safe Region (nocontrol is necessary)IF Yaw Rate >= abs(1 deg/s) and < abs(6 deg/s), THEN inCaution Region (control may be necessary)IF Yaw Rate >= abs(6 deg/s), THEN in Danger Region(control is necessary)

IF Roll Angle < abs(1 deg), THEN in Safe Region (nocontrol is necessary)IF Roll Angle >= abs(1 deg) and < abs(4 deg), THEN inCaution Region (control may be necessary)IF Roll Angle >= abs(4 deg), THEN in Danger Region(control is necessary)

Lateral Acceleration, Lateral Velocity, Yaw Rate, and RollAngle each have a set of three conditions: Safe, Caution,and Danger. A situation might exist where one condition isDanger, two are Caution, and one is Safe. Thus based onthe weighted safety margins for these parameters the TotalSafety Margin (TSM) would decide what the overall vehicle

safety margin was (See Figure 14).

Every vehicle has a lateral acceleration limit for a givenradius of turn. In the case of a sports sedan the tires wouldlikely saturate well before the vehicle reached its rolloverlimits and would therefore either understeer or oversteer. Inthe case of a high CG heavy truck the vehicle might rolloveron a high mu surface before it could saturate its tires andtherefore might not understeer or oversteer. As describedabove in the assumptions of Section 4. Fuzzy Logic-BasedGPS Controller, the job of the GPS-assist is to detect thecurve in advance and provide the road characteristics data

to the on-board GPS Controller (See Figure 14) whichwould then decide if a rollover could occur.

0 200 400 600 800 1000 1200 1400 1600 1800 2000

5

10

15

20

25

30

35

40

Radius of Curvature, m

La

tera

lAcce

lera

tion=

U2/R

,m

/s2

Lateral Acceleration vs. Radius of Curvature

U1

= 40 kph

U2

= 60 kph

U3

= 80 kph

U4

= 100 kph

U5

= 120 kph

U6

= 140 kph

Figure 1: Lateral Acceleration vs. Radius of Curvature

assuming uniform circular motion

Figure 1 shows the steady state lateral acceleration as afunction of road radius. When the vehicle is traveling on astraight, level road the radius of curvature is very large andso the lateral acceleration, lateral velocity, yaw rate, and rolangle would be zero or nearly zero. Therefore all of thesafety margins would be zero and the TSM would decidethe vehicle condition was Safe. Alternatively the radii ofcurvature could decrease to a point such that theaforementioned safety margins resulted in a TSM of onewhich would indicate a Danger condition.

5. GPS CONTROLLER DESIGN

As described previously, this system works by taking theGPS signal (i.e. radius of curvature and other roadwayproperties) and providing the data to the PredictiveDynamics Model which finds Lateral Velocity, Yaw RateRoll Angle, and Roll Rate (See Figure 14). The LateraAcceleration is then calculated. The maximum values ofLateral Acceleration, Lateral Velocity, Yaw Rate, and RolAngle are then found and processed by the Fuzzifier atwhich point the safety margins for Lateral AccelerationLateral Velocity, Yaw Rate, and Roll Angle are foundThese margins are used in conjunction with the weightingfactors shown in Table 1 to determine the Total SafetyMargin (TSM), defined as:

( )* * * *lm vm rm pm

lm vm rm pm

lm W vm W rm W pm W TSM

W W W W

+ + +=

+ + +(5)

For the time being the Safety Margin Weighting Factorswere determined arbitrarily based on the vehicle type beingconsidered. For example, since the vehicle being simulatedis a large truck the roll margin, pm, is given a largeweighting factor than the lateral acceleration and yaw rate

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margins (lm and rm, respectively) since it was assumedthat the truck would roll more than it would yaw. Asresearch progresses and the TruckSim data is used inconjunction with the Matlab code, a more scientificapproach can be used to justify the Weighting Factors.

Table 1: Safety Margin Weighting Factors

i W

lm 5vm 7

rm 5

pm 10

8

Although not presented in this paper, the ongoing researchwill make use of the Total Safety Margin as an input into aDecision Making block which would determine the requiredvehicle stabilizing actions based on the overall vehiclesafety condition. This overall vehicle safety condition wouldbe used along with the onboard EBS sensors as inputs tothe EBS controller which would send the necessary signalsto the actuators. These would command and then apply the

necessary vehicle stabilizing brake pressures and if needbe, reduce engine torque to keep the vehicle within thespecified safety regions, thus remaining under control.

This information would be run through an Actual PlantDynamics block which would contain all of the vehiclesensor information and as such would have collectedinformation on the stabilized vehicle, i.e., has the vehiclestabilized or not. This information would feed back into thePredictive Dynamics Model as the new Initial Conditionsalong with updated GPS data and the cycle would repeat.

6. SIMULATION AND RESULTS

A simulation was performed for an arbitrary situation withthe following initial conditions:

80u kph

138R m=

( )

( )

=

( ) 0

0

0 0

_ max 52

SWA

SWA

=

=

0 0

0 0

v k

radr

s

=

=

ph

( )

( )

0 0

0 0

rad

rad

s

=

=

( )_ 0 g= 0 Lat AccThe results are plotted in Figures 2-9.

0 1 2 3 4 5 6 70

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Time (sec)

LateralAcceleration(g)

Lateral Acceleration vs Time

vehicle mass1

= 13172.6 lb

vehicle mass2

= 17000 lb

vehicle mass3

= 20000 lb

vehicle mass4

= 23000 lb

vehicle mass5

= 26000 lb

Figure 2: Lateral Acceleration vs. Time

0 1 2 3 4 5 6-5

-4

-3

-2

-1

0

1Lateral Velocity v vs Time

Time (sec)

LateralVelocity(kph)

vehicle mass1

= 13172.6 lb

vehicle mass2

= 17000 lb

vehicle mass3

= 20000 lb

vehicle mass4

= 23000 lb

vehicle mass5

= 26000 lb

Figure 3: Lateral Velocity vs. Time

0 1 2 3 4 5 6 70

1

2

3

4

5

6

7Yaw Rate r vs Time

Time (sec)

Yaw

Ra

te

(deg

/s)

vehicle mass1

= 13172.6 lb

vehicle mass2

= 17000 lb

vehicle mass3

= 20000 lb

vehicle mass4

= 23000 lb

vehicle mass5

= 26000 lb

Figure 4: Yaw Rate vs. Time


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0 1 2 3 4 5 6 7-5

-4

-3

-2

-1

0

1Roll Angle vs Time

Time (sec)

RollAn

gle(deg)

vehicle mass1

= 13172.6 lb

vehicle mass2

= 17000 lb

vehicle mass3

= 20000 lb

vehicle mass4

= 23000 lb

vehicle mass5

= 26000 lb

Figure 5: Roll Angle vs. Time

Now for the single vehicle case using the baseline truckgiven in Appendix A.

0 1 2 3 4 5 6 70

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Time (sec)

La

tera

lAcce

lera

tion

(g)

Lateral Acceleration vs Time

Caution Region: 0.3 => 0.6

Danger Region: Beyond 0.6

Safe Region: 0 => 0.3

Figure 6: Lateral Acceleration vs. Time

0 1 2 3 4 5 6 7-5

-4

-3

-2

-1

0

1Lateral Velocity v vs Time

Time (sec)

LateralVelocity(kph)

Danger Region: Beyond -4

Caution Region: -1 => -4

Safe Region: 0 => -1

9

Figure 7: Lateral Velocity vs. Time

0 1 2 3 4 5 60

1

2

3

4

5

6

7Yaw Rate r vs Time

Time (sec)

Yaw

Rate

(deg

/s)

Caution Region: 1 => 6

Safe Region: 0 => 1

Danger Region: Beyond 6

Figure 8: Yaw Rate vs. Time

0 1 2 3 4 5 6-5

-4.5

-4

-3.5

-3

-2.5

-2

-1.5

-1

-0.5

0Roll Angle vs Time

Time (sec)

RollAngle(deg)

Caution Region: -1 => -4

Danger Region: Beyond -4

Safe Region: 0 => -1

Figure 9: Roll Angle vs. Time

Figure 6 shows the lateral acceleration vs. time. In this casethe region bounded by 0 and 0.3 is the Safe Region, theregion between 0.3 and 0.6 is the Caution Region, andanything beyond 0.6 is the Danger Region. The plotteddata has a peak value of 0.228g and is still in the SafeRegion.

Figure 7 shows the lateral velocity vvs. time. In this casethe region bounded by 0 and -1 is the Safe Region, theregion between -1 and -4 is the Caution Region, andanything beyond -4 is the Danger Region. The plotteddata has a peak value of -2.6 kph which falls in the middleof the Caution Region.

Figure 8 shows the yaw rate r vs. time. In this case theregion bounded by 0 and 1 is the Safe Region, the regionbetween 1 and 6 is the Caution Region, and anythingbeyond 6 is the Danger Region. The plotted data has a


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peak value of 5.954 deg/s, settles at 5.729 deg/s and is justbelow the Caution/Danger Region threshold.

Figure 9 shows the roll angle vs. time. In this case theregion bounded by 0 and -1 is the Safe Region, the regionbetween -1 and -4 is the Caution Region, and anythingbeyond -4 is the Danger Region. The plotted data has apeak value of -0.714 deg and is about 70% to theSafe/Caution threshold.

The resulting margins are shown in Table 2. The SafetyMargin Weighting Factors of Table 1 were used in equation5 to calculate the Total Safety Margin.

Table 2: Safety Margin Results on a scale of 0 to 1

margin value

lm 0.3151

vm 0.7264

rm 0.9998

pm 0.0843

TSM 0.4631

10

Interpreting this table the value of lm is 0.3151 or 31.51% ofthe total lateral acceleration margin range. The value of vmis 0.7264 or 72.64% of the total lateral velocity marginrange. The value of rm is 0.9998 or 99.98% of the total yawrate margin range, and the value of pm is 0.0843 or 8.43%of the total roll angle margin range. The total safety margin,or TSM, is 0.4631 or 46.31% of the total TSM range. If avalue of TSM = 1 indicates a completely unstable vehiclethen in this case the vehicles instability level 46.31%.

As vehicle parameters such as forward speed, radius ofcurvature, and CG height deviate from the assumed valuesthe safety margins will change accordingly thus updatingthe TSM to reflect the new total.

7. CONCLUSION

A new Fuzzy based predictive control was developed whichis capable of predicting the vehicle instability level throughuse of GPS data and predictive vehicle modeling. Thesimulation results for two case scenarios, a multi masscase as well as the baseline vehicle case, showed theapplicability of the methodology for heavy trucks where theoutput of the fuzzy controller would be used as an input intoa Decision Making block which in turn would command theEBS to take the necessary actions to keep the vehiclewithin the specified safety regions, thus remaining undercontrol.

8. REFERENCES

[1] Naranjo, Jose E et al, Fuzzy Logic Based LateralControl for GPS Map Tracking, Madrid, Spain: SpanishMinistry of Fomento, Spanish Ministry of Science andTechnology, Citroen Spain S.A., 2003.

[2] Hessburg, Thomas, and Masayoshi Tomizuka, A FuzzyRule-based Controller for Automotive Vehicle Guidance,Berkeley, University of California, 1991.

[3] Dahlberg, E., Commercial Vehicle Stability - Focusing onRollover, ISRN: KTH/FKT/D-01/09-SE, 2001.

[4] Kaplan, Elliot D., Hegarty, Christopher J.Understanding GPS Principles and Applications, 2

nded.

Artech House Publishers, 2006.

[5] Venhovens, P.J. Th., Bernasch, J.H., Lowenau, J.P.Rieker, H.G., Schraut, M., The Application of AdvancedVehicle Navigation with BMW Driver Assistance SystemsSAE technical paper 1999-01-0490, 1999.

[6] Logsdon, Tom, Understanding the NAVSTAR GPSGIS, and IVHS, 2

nded., Van Nostrand Reinhold, 1995.

[7] Hofmann-Wellenhof, B., Lichtenegger, H., Collins, J.GPS Theory and Practice, 5

thed., Springer-Verlag Wien

New York, 2001.

[8] Beiker, Sven A., Gaubatz, Karl Heinz, Gerdes, JChristian, Rock, Kirsten L., GPS Augmented VehicleDynamics Control, SAE technical paper 2006-01-12752006.

[9] Gillespie, Thomas D, Fundamentals of VehicleDynamics, Warrendale, PA, Society of AutomotiveEngineers, 1992.

[10] Pacejka, Hans B, Tire and Vehicle Dynamics 2nd

ed.,Warrendale, PA, Society of Automotive Engineers, 2006.

[11] Wong, J.Y, Theory of Ground Vehicles 3rd

ed., NewYork, John Wiley and Sons, Inc., 2001.

9. DEFINITION OF TERMS

a : horizontal distance between front axle and vehiclecenter of gravity (m)

b : horizontal distance between rear axle and vehiclecenter of gravity (m)

Bicycle Model: single track model

CG : vehicle center of gravity

C: tire cornering stiffness (N/rad)

C : total roll damping (Nms/rad)

DOF : degrees of freedom

EBS : electronic braking system


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EBS Sensors : This block represents the onboard vehicleelectronic braking system sensors.

, yf rF : tire lateral force (N)

xrF : tire tractive force. Rear tractive force here since the

vehicle is rear wheel drive. (N)

Fuzzifier : This block of code uses a third order polynomialto fit an S-shaped curve between upper and lower limits onthe x and y axis of a fuzzy logic graph. The upper and lowerlimits are chosen based on the output from the PredictiveDynamics Model.

h : CG height with respect to the sprung mass origin (m)

xI : roll moment of inertia (kg-m2)

zI : yaw moment of inertia (kg-m2)

IC: initial conditions

K : total roll stiffness (Nm/rad)

usK : understeer coefficient

L = (a + b) : wheelbase (m)

lm : lateral acceleration margin

max_values : This takes the maximum calculated values oflateral acceleration (Lat_Acc), lateral velocity (v), yaw rate

(r), and roll angle ()and runs them through the fuzzifier.

pm : roll angle () margin

Predictive Dynamics Model : This block of code containsEqn. 2 from above in matrix form. The ode45 command inMATLAB is used to integrate the equation to solve for theLateral Velocity, Yaw Rate, Roll Angle, and Roll Angle Ratebased on vehicle and other input parameters. Thereforethis block serves as an initial guess of the vehicle androadway conditions.

Pseudorange - GPS receivers typically use an inexpensivecrystal clock which is set approximately to GPS time. Thus,

the clock of the ground receiver is offset from true GPStime, and because of this offset, the distance measured tothe satellite differs from the true range. These distancesare called pseudoranges since they are the true range plusa range correction resulting from the receiver clock error[7].

R : radius of curvature (m)

Refresh Rate : In the simplified controller presented hereseveral variables such as longitudinal velocity and radius of

curvature were assumed to be constant. However if thedriver changes his throttle position and/or adjusts thesteering wheel angle the radius of curvature will change, soit is necessary for the controller to be continuouslyrechecking the input signals for changes. It is alsonecessary for the GPS to have a refresh rate so it can keeptrack of global changes such as abrupt changes in theactual radius of curvature of the roadway. A value of 1 secis common [4-5]. See Figures 10 and 11.

rm : yaw rate margin

r : yaw velocity (i.e., yaw rate) (rad/s)

r : yaw acceleration (rad/s2)

SWA : steering wheel angle

TSM - Total Safety Margin - This calculation takes thecalculated margins and multiplies each by a weightingfactor, adds each of these up, and divides the total by thesum of the weighting factors. This new value is the TotaSafety Margin and in future work would be used by the

Decision Maker block to determine the overall vehiclesafety condition.

The weighting factors were determined arbitrarily and assuch were scaled to give priority to the factors that wouldbe most likely to cause a given vehicle instability. Forexample, for a low CG, stiffly sprung vehicle an understeer-or oversteer condition might be more likely than anuntripped rollover and so the yaw rate margin is scaledhigher than the roll angle margin. Conversely, in a high CGsoftly sprung vehicle an untripped rollover might be morelikely to occur than an understeer- or oversteer event andthus the roll angle margin would carry more weight.

u : longitudinal velocity (m/s)

v : lateral velocity (m/s)

v : lateral acceleration (m/s2)

vm : lateral velocity margin

fW : total front axle normal load (N)

Wi: weighting factors for the longitudinal velocity, yaw rate,and roll angle

rW : total rear axle normal load (N)

,f r : tire slip angle (rad)

f : front steer angle (rad)

: roll angle (rad)

11


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: roll velocity (rad/s)

: roll acceleration (rad/s2)

Subscripts

f:front

i : lm, vm, rm, pm

inst: instantaneous, as in the instantaneous time. SeeFigures 10 and 11.

r:rear

10. APPENDIX A: VEHICLE PARAMETERS

Truck Parameters from TruckSim 7

Vehicle is baseline 2 axle van, 4 rear tires, unladen

Parameter Value Unit Description

GR = 25 - Nominal Steering Gear Ratio

a = 1.113 mLongitudinal distance from CG tofront axle

b = 3.887 mLongitudinal distance from CG torear axle

l = 5 m Wheelbase

h = 1.173 m CG height

Tf = 2.022 m Track Width, Front

Tr = 1.829 m Track Width, Rear

Ix = 8419.5 kg-m2

Roll Moment of Inertia

Iz = 40344 kg-m2

Yaw Moment of Inertia

ms = 4457 kg Sprung Mass

mus,f = 527 kg Unsprung Mass, Front

mus,r = 1004 kg Unsprung Mass, Rear

m = 5988 kg Total Vehicle Mass

Cf = 203629 N/radFront Tire Cornering Stiffness, pertire*

Cf, total = 407258 N/rad Total Front Tire Cornering Stiffness*

Cr = 37245 N/radRear Tire Cornering Stiffness, pertire*

Cr, total = 148980 N/rad Total Rear Tire Cornering Stiffness*

K= 1333665 Nm/rad Total Roll Stiffness*

C= 80842 Nms/rad Total Roll Damping*

* Calculated values

12


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11. APPENDIX B: FIGURES

13

Figure 10: Vehicle executing a constant radius turn from straight ahead driving

Figure 11: Vehicle traveling on roadway with constantly changing radii

Actual

Roadway

Vehicle attime = tinst.

Radius attime = tinst

Travel Direction =>

Radius attime = tinst

Vehicle prior to

entering turn

Vehicle at time = tinst

Vehicle afterexiting turn


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Figure 12: Simple car model with side force characteristics for front and rear (driven) axle, Yaw Plane [10]

Y

Xab

l

y

x

FyFFyR

r

f

V

u

Fxr

m, Iz @ CG

r

-v

Figure 13: Simple Car Model for Roll. View is from the rear.

Max_values

Figure 14: GPS State-flow Diagram

Turn Radius, RGPS Predictive DynamicsModel

Fuzzifier

Weighted Total

Safety Margin

Decision MakerEBS

ControllerActuators

Actual PlantDynamics

EBSSensors

lmvmrmpm

Initial Conditions, IC

The dashed portions shown in the state flow diagram represent future work to be done on this controller design.

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[08cv-0039] a new fuzzy based stability index using predictive vehicle modeling and gps data

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