Table Of ContentVehicle DynamicsEstimation using Kalman Filtering
Vehicle Dynamics Estimation
using Kalman Filtering
Experimental Validation
Moustapha Doumiati
Ali Charara
Alessandro Victorino
Daniel Lechner
Series Editor
Bernard Dubuisson
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AlbertEinstein
Table of Contents
Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvii
I.1.NeedsofADASsystems . . . . . . . . . . . . . . . . . . . . . . . . . . . xvii
I.2.LimitationofavailableADASsystems . . . . . . . . . . . . . . . . . . . xix
I.3.Thisbookversusexistingstudies . . . . . . . . . . . . . . . . . . . . . . xix
I.4.Laboratoryvehicle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xx
I.5.Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxi
Chapter1.ModelingofTireandVehicleDynamics . . . . . . . . . . . . . . 1
1.1.Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2.Tiredynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2.1.Tireforcesandmoments . . . . . . . . . . . . . . . . . . . . . . . 2
1.2.1.1.Vertical/normalforces . . . . . . . . . . . . . . . . . . . . . . 2
1.2.1.2.Longitudinalforcesandlongitudinalslipratio . . . . . . . . 3
1.2.1.3.Lateralforcesandsideslipangle . . . . . . . . . . . . . . . . 4
1.2.1.4.Aligningmoment . . . . . . . . . . . . . . . . . . . . . . . . 5
1.2.1.5.Couplingeffectsbetweenlongitudinalandlateral
tireforces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.2.2.Tire–roadfrictioncoefficient . . . . . . . . . . . . . . . . . . . . . 7
1.2.2.1.Normalizedlongitudinaltractionforce . . . . . . . . . . . . 9
1.2.2.2.Normalizedlateraltractionforce . . . . . . . . . . . . . . . . 9
1.2.3.Quasi-statictiremodel .. . . . . . . . . . . . . . . . . . . . . . . . 10
1.2.3.1.Pacejka’smagictiremodel . . . . . . . . . . . . . . . . . . . 11
1.2.3.2.Dugoff’stiremodel . . . . . . . . . . . . . . . . . . . . . . . 17
1.2.3.3.Linearmodel . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
1.2.4.Transienttiremodel . . . . . . . . . . . . . . . . . . . . . . . . . . 18
1.3.Wheelrotationaldynamics . . . . . . . . . . . . . . . . . . . . . . . . . 19
viii VehicleDynamicsEstimationusingKalmanFiltering
1.3.1.Statictireradius . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
1.3.2.Effectivetireradius . . . . . . . . . . . . . . . . . . . . . . . . . . 20
1.4.Vehiclebodydynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
1.4.1.Vehicle’sverticaldynamics . . . . . . . . . . . . . . . . . . . . . . 22
1.4.1.1.Suspensionfunctions . . . . . . . . . . . . . . . . . . . . . . 23
1.4.1.2.Quarter-carvehiclemodel. . . . . . . . . . . . . . . . . . . . 23
1.4.2.Vehicleplanardynamics. . . . . . . . . . . . . . . . . . . . . . . . 25
1.4.2.1.Four-wheelvehiclemodel. . . . . . . . . . . . . . . . . . . . 25
1.4.2.2.Wheel-groundverticalforcescalculation . . . . . . . . . . . 27
1.4.2.3.Bicyclemodel . . . . . . . . . . . . . . . . . . . . . . . . . . 30
1.4.3.Rolldynamicsandlateralloadtransferevaluation . . . . . . . . . 31
1.5.Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
Chapter2.EstimationMethodsBasedonKalmanFiltering . . . . . . . . . 37
2.1.Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
2.2.State-spacerepresentationandsystemobservability . . . . . . . . . . . 38
2.2.1.Linearsystem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
2.2.2.Nonlinearsystem . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
2.3.Estimationmethod:whystochasticmodels?. . . . . . . . . . . . . . . . 40
2.3.1.Closed-loopobserver . . . . . . . . . . . . . . . . . . . . . . . . . 41
2.3.2.Choiceoftheobservertype . . . . . . . . . . . . . . . . . . . . . . 42
2.4.ThelinearKalmanfilter .. .. . . . . . . . . . . . . . . . . . . . . . . . 43
2.5.Extensiontothenonlinearcase . . . . . . . . . . . . . . . . . . . . . . . 44
2.6.TheunscentedKalmanfilter.. . . . . . . . . . . . . . . . . . . . . . . . 46
2.6.1.Unscentedtransformation . . . . . . . . . . . . . . . . . . . . . . . 46
2.6.2.UKFalgorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
2.7.IllustrationofalinearKalmanfilterapplication:roadprofile
estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
2.7.1.Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
2.7.2.Observerdesign . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
2.7.3.Experimentalresults:observerevaluation . . . . . . . . . . . . . . 53
2.7.3.1.ComparisonwithLPAsignal . . . . . . . . . . . . . . . . . . 53
2.7.3.2.ComparisonwithGMPsignal . . . . . . . . . . . . . . . . . 56
2.8.Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
Chapter3.EstimationoftheVerticalTireForces . . . . . . . . . . . . . . . 61
3.1.Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
3.1.1.Relatedworks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
3.2.Algorithmdescription . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
3.3.Techniquesforlateralloadtransfercalculationinanopen-loop
scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
TableofContents ix
3.3.1.Lateralaccelerationcalculation . . . . . . . . . . . . . . . . . . . . 65
3.3.2.Rollanglecalculation . . . . . . . . . . . . . . . . . . . . . . . . . 65
3.3.3.Limitationoftheopen-loopmodel . . . . . . . . . . . . . . . . . . 66
3.4.Observerdesignforverticalforcesestimation . . . . . . . . . . . . . . . 67
3.5.Verticalforcesestimation . . . . . . . . . . . . . . . . . . . . . . . . . . 69
3.5.1.ObserverO design . . . . . . . . . . . . . . . . . . . . . . . . . 70
FzE
3.5.2.ObserverO formulation . . . . . . . . . . . . . . . . . . . . . . 72
FzL
3.6.Analysisconcerningthetwo-partestimationstrategy. . . . . . . . . . . 73
3.7.Modelsobservabilityanalysis . . . . . . . . . . . . . . . . . . . . . . . . 74
3.8. Determiningthevehicle’smass . . . . . . . . . . . . . . . . . . . . . . 74
3.8.1.Experimentalvalidationofthevehicle’sweightidentification
method. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
3.9.Detectionofrolloveravoidance:LTRevaluation . . . . . . . . . . . . . 76
3.10.Experimentalvalidation . . . . . . . . . . . . . . . . . . . . . . . . . . 78
3.10.1.Regulationofobservers . . . . . . . . . . . . . . . . . . . . . . . 80
3.10.2.Evaluationofobservers . . . . . . . . . . . . . . . . . . . . . . . 81
3.10.3.Roadexperimentalresults . . . . . . . . . . . . . . . . . . . . . . 82
3.10.3.1.Starting-slalom-brakingtest . . . . . . . . . . . . . . . . . . 82
3.10.3.2.Circle-brakingtest . . . . . . . . . . . . . . . . . . . . . . . 86
3.10.3.3.Turntest . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
3.10.3.4.Concludingremarks .. . . . . . . . . . . . . . . . . . . . . 93
3.10.4.Comparisonbetweenlinearandnonlinearobservers:
O versusO . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
FzL FzE
3.10.5.Observabilityresults . . . . . . . . . . . . . . . . . . . . . . . . . 94
3.10.6.LTRevaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
3.10.7.Roadgeometryeffects . . . . . . . . . . . . . . . . . . . . . . . . 97
3.11.Summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
Chapter4.EstimationoftheLateralTireForces . . . . . . . . . . . . . . . 101
4.1.Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
4.2.Backgroundonlateralforceparameterscalculation . . . . . . . . . . . 102
4.2.1.Lateralforceparametersevaluation . . . . . . . . . . . . . . . . . 103
4.2.1.1.Sideslipangleestimation . . . . . . . . . . . . . . . . . . . . 104
4.2.1.2.Tire–roadfrictionestimation . . . . . . . . . . . . . . . . . . 105
4.2.1.3.Corneringstiffnessestimation . . . . . . . . . . . . . . . . . 106
4.2.1.4.Effectofcamberangle.. . . . . . . . . . . . . . . . . . . . . 106
4.3.Lateralforcereconstructioninanopen-loopscheme . . . . . . . . . . . 107
4.3.1.Testatlowlateralaccelerationlevel . . . . . . . . . . . . . . . . . 108
4.3.2.Testathighlateralaccelerationlevel . . . . . . . . . . . . . . . . . 112
4.4.Techniquesforlateraltireforceevaluation. . . . . . . . . . . . . . . . . 112
4.5.Estimationprocessforsideslipangleandindividuallateraltire
forceestimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
x VehicleDynamicsEstimationusingKalmanFiltering
4.5.1.Estimationalgorithm. . . . . . . . . . . . . . . . . . . . . . . . . . 116
4.5.2.Vehiclemodel.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
4.5.3.Dynamictiremodelrepresentation . . . . . . . . . . . . . . . . . . 118
4.5.4.Referencelateraltireforcemodel . . . . . . . . . . . . . . . . . . 119
4.5.5.FurtherconsiderationforthecorneringstiffnessC . . . . . . . . 120
α
4.5.6.Lateralforceobservers:state-spacerepresentation . . . . . . . . . 121
4.5.7.Observabilityanalysis . . . . . . . . . . . . . . . . . . . . . . . . . 124
4.5.8.Estimationmethodologies . . . . . . . . . . . . . . . . . . . . . . . 124
4.5.9.Sensitivityanalysisofthesideslipangleestimation . . . . . . . . 125
4.6.Experimentalvalidation . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
4.7.Pavementexperimentalresults . . . . . . . . . . . . . . . . . . . . . . . 128
4.7.1.Left–rightbendcombinationtest . . . . . . . . . . . . . . . . . . . 128
4.7.2.Singleleftbendtest . . . . . . . . . . . . . . . . . . . . . . . . . . 132
4.7.3.Slalomtest . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
4.7.4.Circletest . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
4.7.5.Longitudinalforcesestimation . . . . . . . . . . . . . . . . . . . . 143
4.7.6.Concludingremarksonexperimentalresults . . . . . . . . . . . . 152
4.7.7.O versusO . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
FyE FyU
4.7.8.Tuningofobservers . .. . . . . . . . . . . . . . . . . . . . . . . . 153
4.8.Analysisandobservations . .. . . . . . . . . . . . . . . . . . . . . . . . 154
4.8.1.Robustnesswithrespecttoroadfrictionvariation . . . . . . . . . 156
4.9.Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
Chapter5.EmbeddedReal-TimeSystemforVehicleStateEstimation:
ExperimentalResults . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
5.1.Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
5.2.Laboratoryvehicle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
5.2.1.Embeddedsensors . . . . . . . . . . . . . . . . . . . . . . . . . . . 160
5.2.2.Softwaremodules . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
5.2.3.DLLconfiguration . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
5.3.Estimationprocess:VSOsystem .. . . . . . . . . . . . . . . . . . . . . 165
5.4.Testtracks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
5.5.Testresults . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168
5.5.1.Bourbriactest .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
5.5.2.Callactest . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
5.5.3.Rostrenentest.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
5.5.4.Concludingremarks . . . . . . . . . . . . . . . . . . . . . . . . . . 199
5.6.Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200
APPENDICES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201
Appendix1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203
TableofContents xi
Appendix2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207
Appendix3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209
Appendix4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217
Appendix5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221
Appendix6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237
Preface
Vehicle dynamics and stability have been of considerable interest to automotive
engineers, automobile manufacturers, government, public safety groups and the
generalpublic for a number of years. The obviousdilemma is that people naturally
desire to drive faster and faster on the roads and highways, yet they expect their
vehiclestobeinfinitelystableandsafeduringallnormalandemergencymaneuvers.
Forthemostpart,peoplepaylittleattentiontothelimitedhandlingpotentialoftheir
vehicles until some unusual behavior is observed that often results in accidents and
evenfatalities.
Over the past few decades, vehicle control systems have been developed to
enhance vehicle handling and passenger safety. These systems seek to prevent
unintended vehicle behavior through active vehicle control assisting drivers in
maintaining control of their vehicles. Unfortunately, these systems are limited by
lackofknowledgeofthevehiclestatesandoperatingconditions.Whilesomevehicle
states such as yaw rate, wheel speeds and longitudinal and lateral accelerations
are currently available from existing reasonably-price sensors, other fundamental
parameters are unmeasurable for both technical and economical reasons, and thus
need to be estimated/reconstructed. For example, although the vehicle is governed
by the forces generated between the tires and the road, the knowledgeof individual
tire/roadforcesislargelyunavailableforcurrentsafetysystems.Besides,thevehicle
sideslip angle, which relates its lateral velocity to its longitudinal velocity, is an
importantstability factor that is also missed for vehicle controlsystems. If onboard
control systems have accurate knowledge of body sideslip angle and individual tire
forces in each direction(vertical, lateral and longitudinal),they could offer stability
while maximizing the vehicle’s handling capability in a given maneuver. This book
tacklestheproblemofverticalandlateralvehicledynamicsestimationbydiscussing
severalobserversexistingintheliteratureandproposingoriginal/practicalones.The
efficiency of the proposed methods is confirmed by onboard implementation on a
laboratoryvehiclewhiledriveninrealconditions.
