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HandlingStudiesofDriverVehicleSystemsM.Lin,A.A.PopovandS.McWilliamSchoolofMechanical,Materials,ManufacturingEngineeringandManagement,UniversityofNottingham,UniversityPark,NottinghamNG72RD,U.K.Emaileaxmlnottingham.ac.ukThedrivervehiclesystemapproachprovidesafirmbasisforanalysingvehicleanddriverdynamicsinvehiclehandlingdesign.Thepaperaimstoprovideananalysisofdriver’ssteeringandspeedcontrolduringdrivervehicleinteraction.Genericmathematicalmodelsofvehicleanddriverareimplemented,andthehandlingcharacteristicsintypicalmanoeuvresarestudiedthroughnumericalsimulations.Asinformationtechnologyandelectronicsystemsarewidelyintroducedforvehiclechassiscontrolnowadays,newhumanfactorproblemshavebeenposedinthesimulationforvehiclehandlingstudies.Theproposedmodelshereprovidetoolsforexploringtheeffectsofactivechassisinterventionsystemsonthedrivervehicle.Keywords/drivervehiclesystems,vehicledynamics,driverbehaviour,chassisenhancementsystems1.INTRODUCTIONRecently,asvirtualprototypinghasbeenincreasinglyappliedinvehicledevelopment,vehiclehandlingdesigninavirtualenvironmenthasalsobeenwidelyusedinbothacademicresearchandthemanufacturingarea.Forvehiclehandlingsimulations,vehicledynamicssimulationmodelsVDSMsarenecessitiesforthedevelopers.Since1960’s35611,VDSMshavebeendevelopedforavarietyofapplications,includingdynamicanalysis,interactivedrivingsimulation,andvehicletesting.Themodelcomplexityandsolutionproceduresaredefinedaccordingtoagivenapplication.Itcanbeseenthatthevehicleanddriverformacloselycoupledmanmachinesystem.Theinteractionbetweenthedynamicsofthevehicleandthedriverbehaviourplaysaparamountrolethroughoutthewholeprocessofthesimulation.Atthesametime,duetothedesireforpersonalmobility,automotivechassisenhancementsystemsareintroducedintovehicles.Theyaretargetingonprovidingsafety,stabilityandcomfort,andminimisingtheenvironmentalimpacts.However,itisarguedthatinsomecasesthesechassisenhancementsystemscancausemoreharmthangood.In9,Sharppointedoutthattheassessmentofdrivervehicledynamicsqualitiesinthecontextofelectronicenhancedvehiclescontainsmanyseparatequalityissuesandmanydesignconflicts.Thisinvolvesdrivervehiclespeedcontrolanditsrelationshipwithdirectional/steeringcontrol,whichhasonlyrecentlyreceivedattention.Adetailedreviewonautomotivechassisenhancementsystemsinheavyvehicles,providedbyPalkovicsandFries8,includessystemssuchasantilockbrakingsystemABS,tractioncontrolsystemTCS,rearaxlesteeringsystemanddynamicstabilitycontrolsystem.Itissuggestedthatthedriveriskeptinthecontrolloopasdriver’sintentionisnecessarytoactivatethesystems.Bymakingavehicleeasiertocontrol,driversmaybeencouragedtodriveclosertothevehiclelimits,thereforeaffectingtheintendedsafetybenefits.Inthefollowingsections,abasic4DOFlongitudinal,lateral,yaw,rollvehiclemodelandadrivercontrolmodelarepresented.Thedrivermodelisdirectionallystructuredtocontrolvehicleheading/yawangleandlateralposition,andlongitudinallyperceivingthelongitudinalaccelerationerror.InSection4,drivervehicleinteractionisreviewed.ThesimulationisthenemployedinSection5toanalysemanoeuvresinvolvingdoublelanechangeandbrakinginturn.2.VEHICLEMODELThevehicleisrepresentedbyafourdegreesoffreedommodel4,forthelongitudinal,lateral,yawandrollmotion.AsshowninFig.1,althoughthesuspensionsarenotincludedinthemodelling,themodelusesasimplifieddescriptionofbodyrollassumingafixedrollaxisdefinedbytheheightsoftherollcentresofthefrontandrearaxlesofthevehicle.VehiclemodelparametersarereportedintheAppendix.Theequationsofmotionusingaxesfixedtothevehiclebodyaregivenby,δδsincosyfFxfFxrFrvum−G26δδsincosxfFyfFyrFruvmG26sincossinsincosδδφδδyfFxfFxrFhyrFbxfFyfFapxzIrzI−−⋅−⋅⋅−⋅G26G26sincoscossinδδφφφφφφφxfyfyrzrzfrfrfxzxFFFhFFhpcckkrIpI−⋅−⋅G26G261mgφβzyC.G.hrαfαruVvLC.G.C.G.abFzrFyrFxfFxrFzfFxrFxfFyf,rhgxzyxδFzf,rFyfrollaxisFig.1VehicleModelwhereFxf,Fxr,Fyf,Fyr,andFzf,Fzrarevehicleaxlelongitudinal,lateralandverticalforces,respectively.ristheyawrateandpandφaretherollrateandrollangle.Thesideslipanglesandstaticcamberanglesofthefrontandrearwheelsfα,rαandfγ,rγcanbedefinedintermsofvehiclemotionvariables,φεφφαδφεφφαrrffrhuhprbvarhuhprava−Gf7Gf7Gf8Gf6Ge7Ge7Ge8Ge6−⋅−−−Gf7Gf7Gf8Gf6Ge7Ge7Ge8Ge6−⋅sincostansincostan2φξγφξγrrff3Whenthevehicleisrunningatconstantspeed,thelongitudinalmotioncanbeuncoupledfromtheequationsofmotion.Thedynamicsofthenonlinearvehiclemodelincludestheinfluenceofthenonlineartyrecharacteristics,whicharemodelledbythe‘magicformula’7.Theeffectsoflateralandlongitudinalloadtransfershavebeenevaluatedthroughasteadystateapproximation10.Assumingafixedrollaxisposition,theexpressionofthelateralloadtransferforthefrontandtherearaxlesare,__hdLhhatmruFhdLhhbtmruFrgrlatrzfgflatfzφφ−∆−∆4Thelongitudinalloadtransfer,occurringwhilethevariedvehicleforwardvelocityistakenintoaccount,iscalculatedasfollows,LhFFFgFrfxlongz/_⋅∆53.DRIVERBEHAVIOURTHROUGHPATHPREVIEWObviously,onlythevehicleitselfcannotmaintainadesiredpath.Thisdemandsacombinationwithdrivermodel.Thedriverhasvisualandmotionfeedbacksfordevelopingsteeringcontrolactions.Driverbehaviourthroughpathpreviewinvolvesactionsbasedonperceptionofcommands.Fordirectional/steeringcontrol,driverscanusepreviewbehaviourtofollowcurvedpaths.Avehiclewillfollowacurvedpathforagivensteeringangle,sothedrivercanmatchhorizontalroadcurvaturewithappropriatesteerangle,andtheremaininglanedisplacementcanbehandledwithcompensatorycontrolactions.Forspeedcontrol,thedrivertriestomatchroadgradewithathrottleangle,althoughthecorrectperceptionofroadgradeismuchmoredifficultandimprecisethantheperceptionforhorizontalcurvature.3.1Directional/SteeringControlFordriver’svisualfeedback,atwolevelpreviewandcompensatorydriversteeringmodelbasedonthecontrolstrategyproposedbyDonges3ispresentedhere.Thedriverexertssteeringcontroltomaintainlanepositionthroughpreviewcontrol,andtomanoeuvrethevehicleduringcurvenegotiation,lanechangeorobstacleavoidance.Unpredictableroaddisturbancescanrandomlymovethevehiclewithinthelane,andthedrivermustcounteractthesedisturbanceswithcompensatorycontrol.Forpreviewcontrol,WeirandMcRuer12suggestedthat,systemsstructuredtocontrolvehicleheading/yawangleandlateralpositionorpathangleandlateralpositionoffergoodclosedloopcharacteristics.Therefore,itisassumedherethatthedriverdevelopssteeringcorrectionsbasedonperceivedheading/yawandlanepositionerrors.BysettingapreviewpointPonthevehiclefixedxaxis,asortofpredictivebehaviourisincorporatedintothesystem.Fig.2illustratesdriver’sbehaviourthroughpathpreview.Acompositeheadingerrorofthepreviewpointrelativetothedesiredpathatthepreviewpointisgivenby,/PPecLyψψψ−6whereyeisthelanepositionerror,LPisthepreviewdistance,ψistheheadingangleandPψistheheadinganglebetweenxaxisandAPline.Insteadofseparatelyperceivingbothheadingandlanepositionerrors,thedriverneedsonlytoperceivetheangularerrorcψtothepreviewpointdowntheroad.ThepreviewdistanceLPhereistheproductofvehicleforwardspeedandpreviewtimeconstantTP.Thisisconsistentwithoureverydayexperiencethatdriverseesnearerdistanceatlowerspeedsandfurtherdistanceathigherspeeds.FollowingMcRuer’scrossovermodel6,driver’scompensatoryfeedbackcontrolcanbedefinedbythetransferfunctionofthesteeringangletothecompositeheadingerror,sILcesTsTGssτψδ−117ItincludesthreecomponentsagainGwhichsetsthemagnitudeofroadsteeringangleδcorrectionsforgivenheadingerrorcψaleadterm1sTLthatthedriveradoptstocounteractvehicletyredelayalagterm1sTIcorrespondingtotheneuromusculardelayand,atimedelayseτ−approximatingdriver’sreactiontimedelay.Fordriver’smotionfeedback,itprovidesinformationonmotionperformedbyhumanorgansandonorientationwithrespecttothegravitationaldirection.In1,Allennotedthattheyawrateinformationcanbeusedasamotionfeedbackelement.ThemotionfeedbackgainKmprovidesaleadthatthedrivercanusetocompensateforthevehicleyawratelag.3.2SpeedControlSpeedcontrolisimportantinavarietyofscenarios,includingmaintainingsafelateralaccelerationlevelswhilefollowingcurvedpaths,respondingtospeedlimits,andslowingdownduringemergencyavoidance.Duringstraightrunningthedrivercontinuesatspecifiedspeed.Whenthedriverdetectscurvature,speedisthenreducedaccordinglyinordertomaintaindesiredlateralacceleration.ThedriverspeedcontrollawcanthenbedescribedasFig.3a.Thedrivercommandsdecelerationconsistentwithadesiredspeedchange,andperceivesdecelerationerrors.Especially,whenelectronicchassiscontrols,suchasABS,TCS,etc.,areinvolved,speedcontrolwillbeessential.Aswecanseefromtheoperatingprinciplesofthesecontrolsystems,mostofthemareactivatedunderemergencysituations.Speedchangingisthereforeinevitable.Forexample,byaddinganeffectiveABS,therelationshipbetweenthebrakepedalforceandvehicledecelerationisillustratedinFig.3b.Withtheapplicationofthisrelationshipandthespeedcontrollawdescribedabove,theassessmentofeffectsoftheseelectroniccontrolsisfeasible.AcψPreviewpointPPψψ−ψLPyxXYye/LPDesiredpathPψFig.2DriverModelthroughPathPreviewFig.3bDriverSpeedControlLawaABSSystemCharacteristic4.DRIVERVEHICLEINTERACTION4.1DriverVehicleDynamicswithoutSpeedControlGiventheabovedynamiccharacteristicsforthevehicleanddriver,ablockdiagramoftheoveralldrivervehiclesystemmodelwithoutspeedcontrolcanbestructuredasshowninFig.4.Itisassumedthatthevehicleistravellingatconstantforwardspeed.Vehiclelateralvelocityv,yawraterandrollrateparegeneratedbysteeringinputstothevehicleequationsofmotion.Vehiclelateralvelocityvandyawraterarethenunderdirectcontrolofthedriver.Althoughtherollmotionisnotcontrolledbythedriverdirectly,italsoinfluencesdriverbehaviour,especiallywhenthevariationofvehicleforwardvelocityistakenintoaccount.Kinematicalequationsthenprovidevehicleheadingangleandlaterallanepositionfromlateralvelocityandyawrate.Finally,steeringcorrectionswillbemadebythedriverbasedonthecompositeheadingerror.Fortheclosedloopanalysis,therearetwosysteminputs,oneisthepathcommandyc,andtheotheristheinitialheadinganglecommandPψ.Thevehiclewillbesteeredtofollowpathcommands,andPψwillhelpimplementthecorrectionofvisualerror.However,withtheapplicationofthe‘crossovermodel’merely,alateraldeviationcanbefoundinthesimulationFig.5a.Itisassumedthatthedrivercontinuestosteeruntilthevehicle’sattitudeintersectsthepreviewpointdowntheroad.Thisstrategyfinallyeliminatesvehicleattitudeerrorsbutdoesnotcorrectlanepositionerrors.Therefore,anadditionalfeedbackisneededthataccumulateserrorwhenevervehicleisnotcorrectlypositionedlaterallyinthelane.Byaddingaparallelintegratorinthesystem,thisoffseterrorcanbeeliminatedFig.5b.Thefunctionofthisintegratoristocompensateforthecompositeheadingerror,whichaccumulatesboththevehicleheadingerrorandthelanepositionerrorFig.4.Itdevelopsmuchquickercompensationthanhavingtheintegratorcompensateforlanepositionerroronly.Thetransferfunctionofthesteeringangletothecompositeheadingerrorcanthenbedefinedas,111sKesTsTGsssILcψτψδ⋅−7Fig.4DriverVehicleSystemDirectionalControlModelBrakePedalForce_decelerationerrorWithoutABSWithABSVehicledecelerationSpeedControlVehicleLongitudinalDynamicsbrakePedalforceactualdecelerationdecelerationcommandba
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