Key Words Adaptive Cruise Control, String Stabilit

1/30StringStabilityAnalysisofAdaptiveCruiseControlledVehiclesChi-YingLIANGandHueiPENGKeyWords:AdaptiveCruiseControl,StringStability,StringStabilityMargin,OptimalACCDesign,TrafficSimulatorDepartmentofMechanicalEngineeringandAppliedMechanics,UniversityofMichigan2272G.G.Brown,AnnArbor,MI48109-2125,USA,E-mail:[e-mail]:[phone],FAX:[phone]ABSTRACTAframeworkforstring-stabilityanalysisisformulatedinthispaper.First,uniformstringwillbeanalyzed.Wewillthenpresentanalysisresultsonstringsofmixedvehicles.AString-StabilityMargin(SSM)indexisdefinedinthispapertogiveaquantitativemeasurementofanyACCdesign.SimulationresultsusingMATLABandamicroscopictrafficsimulatorwillalsobegiventodemonstratetheeffectivenessofACCsystemsontrafficsmoothness.3/301.INTRODUCTIONAdaptiveCruiseControl(ACC)systemhasbeenproposedasanenhancementoverexistingcruisecontrollersongroundvehicles.ACCsystemscontrolthevehiclespeedtofollowadriver’ssetspeedcloselywhennoleadvehicleisinsight.Whenaslowerleadingvehicleispresent,theACCcontrolledvehiclewillfollowtheleadvehicleatasafedistance.ACCresearchfirstbeganinthe1960’s[1],andhasreceivedever-growingattentioninthelastdecade.Theircommercialimplementationisnotpossibleuntilrecentlywithsignificantprogressesinsensors,actuators,andotherenablingtechnologies.Overthelast10years,manydifferentapproacheshavebeenproposedforthedesignofACCalgorithms.Intheearlierworks,thefocushasbeenontheperformanceofthehostvehicle.Theperformancewasusuallyevaluatedbasedon2-carplatoons.TheeffectofACConastringofvehicleshasnotreceivedmuchattention.Recently,a2-stepsynthesismethodwasproposedwhichcanbeusedtodesignACCalgorithmwithguaranteedstability[2].Attheupperlevel,desiredvehicleaccelerationiscomputedbasedonvehiclerangeandrangeratemeasurement.Atthelower(servo)level,anadaptivecontrolalgorithmisdesignedtoensurethevehiclefollowstheaccelerationcommandaccurately.Itisshownthatitispossibletoincludeservo-leveldynamicsintheoveralldesignandstringstabilitycanbeguaranteedifcertaininequalityconstraintsaresatisfied.Theso-called“stringstability”problemhasbeenstudiedasearlyas1977[4].Thestring-stabilityensuresthatrangeerrorsdecreaseastheypropagatealonghevehiclestream.Itiswidelyknownthatwhenthetransferfunctionfromtherangeerrorofavehicletothatofitsfollowingvehiclehasamagnitudelessthan1,string4/30stabilityisguaranteed[5].Toachievestringstabilitywithconstantinter-vehiclespacing,vehicle-to-vehiclecommunicationwasshowntobenecessary[6].YanakievandKanellakopoulos[7]usedasimplespring-mass-dampersystemtodemonstratetheideaofstringstabilityandshowthestring-stabilitycriterionforconstanttime-headwayandvariabletime-headwaypolicies.SwaroopandHedrick[8]proved,amongmanyotherinterestingthingsthatifthecouplingbetweentwovehiclesisweakenough,thecontrolledsystemisstringstable.Despitethestridesmadeintheresearchfield,manyoftheprototypeACCvehicleswerestilldesignedwithoutconsideringstringstability.Thisismainlyduetothefactthathumandriversandpassengersareusedtothelevelofsmoothnessproducedbyhumandrivers.TheearlyimplementationofACChardwareisusuallymarkedbyslowresponseofactuationandroughdistanceandspeedmeasurement.Inordertoproducesmoothacceleration/decelerationresponse,theACCcontrollersareusuallyheavilyfiltered.Slowerresponsefromindividualvehiclesthenresultsinunstablestringresponse.Inthispaper,weplantodemonstrateadetailedstabilityanalysisofastringofvehicles.First,uniformstringwillbeanalyzed.Necessaryandsufficientconditionsforstringstabilitywillbepresented.Wewillthenpresentanalysisresultsonstringsofmixedvehicles.ItwillbeshownthatifwemixACCvehiclesthataredesignedtobestringstablebythemselves,themixedACCstringswillalsobestringstable.Thestabilitydegradationwillbeshowninthecontextofthe“stringstabilitymargin”(SSM)whichisanindexdefinedtomeasurethestringstabilityofavehicle.Asimulationtool(UMACC)isdevelopedintheUniversityofMichigantoassisttheanalysisofACCsystem.Thissimulatorisdividedintofourparts:drivermodel,vehicle/sensormodel,ACCmodel,andtheinteractionmodel(seeFig.1).The5/30drivermodelconsistsofalanechangemodel(forallvehicles)andacar-followingmodel(onlyformanuallycontrolledvehicles).TheparametersofthedrivermodelareobtainedfromtheFOCASfieldtestdata[9].Detailsofthismodelcanbefoundin[3].AsimulationstudyusingACCSimulatorhasshownthatthevehiclestringsizeincreasesdramaticallywiththetrafficdensity(SeeFig.2,3).Becausemanualvehiclesareusuallynotstringstable,thelargeplatoonsizeinhightrafficdensitywillmagnifytheso-called“slinkyeffect”andcausedtrafficjammed.AstringstableACCdesignisabletoreducethisslinkyeffectandthusimprovehighwaytraffic.Inthispaper,theperformanceofACCvehicleswillbeevaluatedbymixingACCvehiclesandmanuallycontrolledvehiclesusingtheACCSimulator.SimulationresultsusingtheUMACCSimulatorwillbepresentedtohighlighttheeffectofACCvehiclesonthetrafficvolumeandsmoothness.Theremainderofthispaperisorganizedasfollows:theformulationofvehicle-stringanalysisispresentedinSection2.InSection3,bothuniformedandmixedvehiclestringswillbeanalyzed.ThedefinitionofSSMandtheSSMcalculationofanoptimalACCdesignwillb