HandlingStudiesofDriver-VehicleSystemsM.Lin,A.A.PopovandS.McWilliamSchoolofMechanical,Materials,ManufacturingEngineeringandManagement,UniversityofNottingham,UniversityPark,NottinghamNG72RD,U.K.Email:eaxmlnottingham.ac.ukThedriver-vehiclesystemapproachprovidesafirmbasisforanalysingvehicleanddriverdynamicsinvehiclehandlingdesign.Thepaperaimstoprovideananalysisofdriverssteeringandspeedcontrolduringdriver-vehicleinteraction.Genericmathematicalmodelsofvehicleanddriverareimplemented,andthehandlingcharacteristicsintypicalmanoeuvresarestudiedthroughnumericalsimulations.Asinformationtechnologyandelectronicsystemsarewidelyintroducedforvehiclechassiscontrolnowadays,newhumanfactorproblemshavebeenposedinthesimulationforvehiclehandlingstudies.Theproposedmodelshereprovidetoolsforexploringtheeffectsofactivechassisinterventionsystemsonthedriver-vehicle.Keywords/driver-vehiclesystems,vehicledynamics,driverbehaviour,chassisenhancementsystems1.INTRODUCTIONRecently,asvirtualprototypinghasbeenincreasinglyappliedinvehicledevelopment,vehiclehandlingdesigninavirtualenvironmenthasalsobeenwidelyusedinbothacademicresearchandthemanufacturingarea.Forvehiclehandlingsimulations,vehicledynamicssimulationmodels(VDSMs)arenecessitiesforthedevelopers.Since1960s35611,VDSMshavebeendevelopedforavarietyofapplications,includingdynamicanalysis,interactivedrivingsimulation,andvehicletesting.Themodelcomplexityandsolutionproceduresaredefinedaccordingtoagivenapplication.Itcanbeseenthatthevehicleanddriverformacloselycoupledman-machinesystem.Theinteractionbetweenthedynamicsofthevehicleandthedriverbehaviourplaysaparamountrolethroughoutthewholeprocessofthesimulation.Atthesametime,duetothedesireforpersonalmobility,automotivechassisenhancementsystemsareintroducedintovehicles.Theyaretargetingonprovidingsafety,stabilityandcomfort,andminimisingtheenvironmentalimpacts.However,itisarguedthatinsomecasesthesechassisenhancementsystemscancausemoreharmthangood.In9,Sharppointedoutthattheassessmentofdriver-vehicledynamicsqualitiesinthecontextofelectronicenhancedvehiclescontainsmanyseparatequalityissuesandmanydesignconflicts.Thisinvolvesdriver-vehiclespeedcontrolanditsrelationshipwithdirectional/steeringcontrol,whichhasonlyrecentlyreceivedattention.Adetailedreviewonautomotivechassisenhancementsystemsinheavyvehicles,providedbyPalkovicsandFries8,includessystemssuchasanti-lockbrakingsystem(ABS),tractioncontrolsystem(TCS),rearaxlesteeringsystemanddynamicstabilitycontrolsystem.Itissuggestedthatthedriveriskeptinthecontrolloopasdriversintentionisnecessarytoactivatethesystems.Bymakingavehicleeasiertocontrol,driversmaybeencouragedtodriveclosertothevehiclelimits,thereforeaffectingtheintendedsafetybenefits.Inthefollowingsections,abasic4-DOF(longitudinal,lateral,yaw,roll)vehiclemodelandadrivercontrolmodelarepresented.Thedrivermodelisdirectionallystructuredtocontrolvehicleheading/yawangleandlateralposition,andlongitudinallyperceivingthelongitudinalaccelerationerror.InSection4,driver-vehicleinteractionisreviewed.ThesimulationisthenemployedinSection5toanalysemanoeuvresinvolvingdoublelanechangeandbrakinginturn.2.VEHICLEMODELThevehicleisrepresentedbyafourdegreesoffreedommodel4,forthelongitudinal,lateral,yawandrollmotion.AsshowninFig.1,althoughthesuspensionsarenotincludedinthemodelling,themodelusesasimplifieddescriptionofbodyrollassumingafixedrollaxisdefinedbytheheightsoftherollcentresofthefrontandrearaxlesofthevehicle.VehiclemodelparametersarereportedintheAppendix.Theequationsofmotionusingaxesfixedtothevehiclebodyaregivenby,sincos)(yfFxfFxrFrvum+=+G26sincos)(xfFyfFyrFruvm+=+G26)sincos(sin)sincos(yfFxfFxrFhyrFbxfFyfFapxzIrzI+=G26G26)sincos(cos)(sin)()(xfyfyrzrzfrfrfxzxFFFhFFhpcckkrIpI+=+G26G26(1)mgzyC.G.hrfruVvLC.G.C.G.abFzrFyrFxfFxrFzfFxrFxfFyf,rhgxzyxFzf,rFyfrollaxisFig.1VehicleModelwhereFxf,Fxr,Fyf,Fyr,andFzf,Fzrarevehicleaxlelongitudinal,lateralandverticalforces,respectively.ristheyawrateandpandaretherollrateandrollangle.Thesideslipanglesandstaticcamberanglesofthefrontandrearwheelsf,randf,rcanbedefinedintermsofvehiclemotionvariables,rrffrhuhprbvarhuhpravaGf7Gf7Gf8Gf6Ge7Ge7Ge8Ge6+=Gf7Gf7Gf8Gf6Ge7Ge7Ge8Ge6+=sincostansincostan(2)rrff=(3)Whenthevehicleisrunningatconstantspeed,thelongitudinalmotioncanbeuncoupledfromtheequationsofmotion.Thedynamicsofthenon-linearvehiclemodelincludestheinfluenceofthenon-lineartyrecharacteristics,whicharemodelledbythemagicformula7.Theeffectsoflateralandlongitudinalloadtransfershavebeenevaluatedthroughasteadystateapproximation10.Assumingafixedrollaxisposition,theexpressionofthelateralloadtransferforthefrontandtherearaxlesare,)()(_hdLhhatmruFhdLhhbtmruFrgrlatrzfgflatfz+=+=(4)Thelongitudinalloadtransfer,occurringwhilethevariedvehicleforwardvelocityistakenintoaccount,iscalculatedasfollows,LhFFFgFrfxlongz/)(_+=(5)3.DRIVERBEHAVIOURTHROUGHPATHPREVIEWObviously,onlythevehicleitselfcannotmaintainadesiredpath.Thisdemandsacombinationwithdrivermodel.Thedriverhasvisualandmotionfeedbacksfordevelopingsteeringcontrolactions.Driverbehaviourthroughpathpreviewinvolvesactionsbasedonperceptionofcommands.Fordirectional/steeringcontrol,driverscanusepreviewbehaviourtofollowcurvedpaths.Avehiclewillfollowacurvedpathforagivensteeringangle,sothedrivercanmatchhorizontalroadcurvaturewithappropriatesteerangle,andtheremaininglanedisplacementcanbehandledwithcompensatorycontrolactions.Forspeedcontrol,thedrivertriestomatchroadgradewithathrottleangle,althoughthecorrectperceptionofroadgradeismuchmoredifficultandimprecisethantheperceptionforhorizontalcurvature.3.1Directional/SteeringControlFordriversvisualfeedback,atwo-level(previewandcompensatory)driversteeringmodelbasedonthecontrolstrategyproposedbyDonges3ispresentedhere.Thedriverexertssteeringcontroltomaintainlanepositionthroughpreviewcontrol,andtomanoeuvrethevehicleduringcurvenegotiation,lanechangeorobstacleavoidance.Unpredictableroaddisturbancescanrandomlymovethevehiclewithinthelane,andthedrivermustcounteractthesedisturbanceswithcompensatorycontrol.Forpreviewcontrol,WeirandMcRuer12suggestedthat,systemsstructuredtocontrolvehicleheading/yawangleandlateralpositionorpathangleandlateralpositionoffergoodclosed-loopcharacteristics.Therefore,itisassumedherethatthedriverdevelopssteeringcorrectionsbasedonperceivedheading/yawandlanepositionerrors.BysettingapreviewpointPonthevehicle-fixedxaxis,asortofpredictivebehaviourisincorporatedintothesystem.Fig.2illustratesdriversbehaviourthroughpathpreview.Acompositeheadingerrorofthepreviewpointrelativetothedesiredpathatthepreviewpointisgivenby,)(/PPecLy+=(6)whereyeisthelanepositionerror,LPisthepreviewdistance,istheheadingangleandPistheheadinganglebetweenxaxisandAPline.Insteadofseparatelyperceivingbothheadingandlanepositionerrors,thedriverneedsonlytoperceivetheangularerrorctothepreviewpointdowntheroad.ThepreviewdistanceLPhereistheproductofvehicleforwardspeedandpreviewtimeconstantTP.Thisisconsistentwithoureverydayexperiencethatdriverseesnearerdistanceatlowerspeedsandfurtherdistanceathigherspeeds.FollowingMcRuerscrossovermodel6,driverscompensatoryfeedbackcontrolcanbedefinedbythetransferfunctionofthesteeringangletothecompositeheadingerror,sILcesTsTGss+=)11()()(7)Itincludesthreecomponents:againGwhichsetsthemagnitudeofroadsteeringanglecorrectionsforgivenheadingerrorc；aleadterm)1(+sTLthatthedriveradoptstocounteractvehicletyredelay；alagterm)1(+sTIcorrespondingtotheneuromusculardelay；and,atimedelayseapproximatingdriversreactiontimedelay.Fordriversmotionfeedback,itprovidesinformationonmotionperformedbyhumanorgansandonorientationwithrespecttothegravitationaldirection.In1,Allennotedthattheyawrateinformationcanbeusedasamotionfeedbackelement.ThemotionfeedbackgainKmprovidesaleadthatthedrivercanusetocompensateforthevehicleyawratelag.3.2SpeedControlSpeedcontrolisimportantinavarietyofscenarios,includingmaintainingsafelateralaccelerationlevelswhilefollowingcurvedpaths,respondingtospeedlimits,andslowingdownduringemergencyavoidance.Duringstraightrunningthedrivercontinuesatspecifiedspeed.Whenthedriverdetectscurvature,speedisthenreducedaccordinglyinordertomaintaindesiredlateralacceleration.ThedriverspeedcontrollawcanthenbedescribedasFig.3(a).Thedrivercommandsdecelerationconsistentwithadesiredspeedchange,andperceivesdecelerationerrors.Especially,whenelectronicchassiscontrols,suchasABS,TCS,etc.,areinvolved,speedcontrolwillbeessential.Aswecanseefromtheoperatingprinciplesofthesecontrolsystems,mostofthemareactivatedunderemergencysituations.Speedchangingisthereforeinevitable.Forexample,byaddinganeffectiveABS,therelationshipbetweenthebrakepedalforceandvehicledecelerationisillustratedinFig.3(b).Withtheapplicationofthisrelationshipandthespeedcontrollawdescribedabove,theassessmentofeffectsoftheseelectroniccontrolsisfeasible.AcPreviewpointPPLPyxXYye/LPDesiredpathPFig.2DriverModelthroughPathPreviewFig.3(b)DriverSpeedControlLaw(a)ABSSystemCharacteristic4.DRIVER-VEHICLEINTERACTION4.1Driver-VehicleDynamicswithoutSpeedControlGiventheabovedynamiccharacteristicsforthevehicleanddriver,ablockdiagramoftheoveralldriver-vehiclesystemmodelwithoutspeedcontrolcanbestructuredasshowninFig.4.Itisassumedthatthevehicleistravellingatconstantforwardspeed.Vehiclelateralvelocityv,yawraterandrollrateparegeneratedbysteeringinputstothevehicleequationsofmotion.Vehiclelateralvelocityvandyawraterarethenunderdirectcontrolofthedriver.Althoughtherollmotionisnotcontrolledbythedriverdirectly,italsoinfluencesdriverbehaviour,especiallywhenthevariationofvehicleforwardvelocityistakenintoaccount.Kinematicalequationsthenprovidevehicleheadingangleandlaterallanepositionfromlateralvelocityandyawrate.Finally,steeringcorrectionswillbemadebythedriverbasedonthecompositeheadingerror.Fortheclosed-loopanalysis,therearetwosysteminputs,oneisthepathcommandyc,andtheotheristheinitialheadinganglecommandP.Thevehiclewillbesteeredtofollowpathcommands,andPwillhel