A-nested-PID-steering-control-for-lane-keeping-in-

ANestedPIDSteeringControlforLaneKeepinginVisionBasedAutonomousVehiclesRiccardoMarino*,StefanoScalzi*,GiuseppeOrlando*,MarianaNetto**Abstract—InthispaperanestedPIDsteeringcontrolforlanekeepinginvisionbasedautonomousvehiclesisdesignedtoperformpathfollowinginthecaseofroadswithanuncertaincurvature.Thecontrolinputisthesteeringwheelangle:itisdesignedonthebasisoftheyawrate,measuredbyagyroscope,andthelateraloffset,measuredbythevisionsystemasthedistancebetweentheroadcenterlineandavirtualpointatafixeddistancefromthevehicle.Nolateralaccelerationandnolateralspeedmeasurementsarerequired.APIactivefrontsteeringcontrolontheyawratetrackingerrorisusedtorejectconstantdisturbancesandtheoveralleffectofparametervariationswhileimprovingvehiclesteeringdynamics.Theyawratereferenceisviewedasthecontrolinputinanexternalcontrolloop:itisdesignedusingaPIDcontrolonthelateraloffsettorejectthedisturbancesonthecurvaturewhichincreaselinearlywithrespecttotime.Therobustnessisinvestigatedwithrespecttospeedvariationsanduncertainvehiclephysicalparameters:itisshownthatthecontrolledsystemisasymptoticallystableforallperturbationsintherangeofinterest.SeveralsimulationsarecarriedoutonastandardbigsedanCarSimvehiclemodeltoexploretherobustnesswithrespecttounmodelledeffectssuchascombinedlateralandlongitudinaltireforces,pitchandroll.Thesimulationsshowreducedlateraloffsetandnewstableμ-splitbrakingmanoeuvresincomparisonwiththeCarSimmodelpredictivesteeringcontrollerimplementedbyCarSim.I.INTRODUCTIONIntelligentvehiclesandautomatedhighwaysystemshaveattractedagrowingattentioninthelastyearswiththeaimofincreasingsafetyandcomfort:seeforinstance[1],[2],[3],[4],[5],[6],[7],[8],[9],[10],[11],[12],[13],[14],[15]and[16].In[1],[2]afeedbackfromlateralandlongitudinalvehiclespeed,yawangleerrorandyawrateisusedtohelpthedrivertosteerthevehiclebacktothelaneduringdiminisheddrivingcapabilityduetoinattention.ThecontrolstrategyisbasedontheLyapunovtheoryandLMIoptimizationbydefiningpolytopicandhypercubicstatespaceregions,whereifthedriverstaysin,thedrivingtaskisconsideredsafe;themainideaistoapproximatetheseregionsbystandardandcompositeLyapunovlevelcurves.In[3]aH∞controllerisdesignedtominimizetheeffectofthedisturbancesonthemeasuredlateraloffsetandthedesiredyawangle.In[4]asteeringcontroller,whichusesfinitepreviewoptimalcontrolmethods,isproposedtocontrolthe*UniversityofRomeTorVergata,ElectronicEngineeringDepartment-ViadelPolitecnico1,00133Roma-Italy,Tel.[phone].email:{marino,scalzi}@ing.uniroma2.it**LCPC/INRETS-LIVICVehicle-Infrastructure-DriverInteractionsRe-searchUnit,14Routedelaminiére,78000Versailles,France.measuredlateraloffset,theyawangleandtheirderivatives.In[5]aclosedloopcontrolstrategywhichfeedsbackthelateraloffsetisproposed:anautomaticlanekeepingiscombinedwiththedriver’ssteeringwithnoneedofswitchingstrategiesbetweenthedriverandthelanekeepingcontrol.In[6]acontrolsystembasedontheloopshapingtechniqueistestedbyexperimentsusingafeedbackfromthelateraloffset.In[7]anonlinearobserverbasedcontrolstrategyisinvestigatedbymeasuringthelateraloffset,itsderivative,theyawangleandtheyawrate.In[8]amodelpredictivesteeringcontrollerisusedtoemulatethedriverbehaviourintheCarSimenvironment:itisdesignedonthebasisofasimplifiedlinearmodelandonlongitudinalandlateralspeed,yawangleandyawratemeasurementstopredicttheerrorwithrespecttoagiventargetpath.Alsoin[9]amodelpredictivecontrolapproachisfollowed:thecontrolledoutputsarethelateraloffset,theyawrateandtheyawangle;thecontrollerisdesignedbothonanonlinearandalinearvehiclemodelusinglateralandlongitudinalvehiclespeed,yawangleandyawratemeasurements.In[10]afeedforwardandafeedbackactiononthelateraloffsetandtheyawangleerrorisexperimented.In[11]againschedulingbasedproportionalfeedbackfromthelateraloffsetisexperimented.In[12]afeedforwardtermfromroadcurvatureandaPIDonaweightedsumoftheheadingerrorandthelateraloffsetareusedassteeringcontrollerintheDARPAGrandChallenge.Inthesamecompetitiontheyawangleandanonlineartermproportionaltothelateraloffsetareusedin[13]asmeasurementstodesignthesteeringcontroller.Furthermore,toimprovesafety,drivercomfortandvehicleperformance,severaldriverassistancesystemsareinvestigatedintheliterature.In[14]asteeringassistancecontrolsystemwithafeedbackfromthelateraloffsetandlateralspeedisdesignedtofollowthedesiredpathwhileanassistancetorqueisappliedinordertoimprovethevehiclehandlingandsteeringfeel.In[15]and[16]theactivefrontsteeringisproposedandimplementedonBMW5Seriesvehicle.In[15]aPIactivefrontsteeringcontrolontheyawratetrackingerrorwithdifferentgainsforbrakedandunbrakeddrivingconditionisusedwhilein[16]apatentedmethodisproposedtoensuresafetyduringactivesteeringsystemfailurecomputingthesteeringwheelangleasthesumoftheproposedcontrollawsteeringangleandthedriversteeringangle.Mostcontrolalgorithmsemployedinlanekeepingmakeuseofpoleplacement,modelpredictiveandobserverbasedtechniquesorrequiredifficultmeasurements2009AmericanControlConferenceHyattRegencyRiverfront,St.Louis,MO,USAJune10-12,2009ThB08.6978-1-4244-4524-0/09/$25.00©2009AACC2885oflateralspeed,vehic