pdf-A-stable-tracking-control-method-for-an-autono

YutakaKanayamaAStableTrackingControlMethodforanAutonomousMobileRobotYoshihikoKimuraFumioMiyazakiTetsuoNoguchiDeptofComputerScienceCenterforRoboticSystemsOsakaUniversityCenterforroboticSystemsNavalPostgraduateSchoolMonterey,CA93943CORIDeptofComputerScienceUniversityofCaliforniaTokyo,JapanSantaBarbara,CA93106DeptofMechanicalEngineeringToyonaka,JapanUniversityofCaliforniaSantaBarbara,CA93106UniversityofCaliforniaSantaBarbara,CA93106MitsubishiMetalCorp.ABSTRACTThispaperproposesastabletrackingcontrolrulefornon-bolonomicvehicles.StabilityoftheruleisprovedthroughtheuseofaLiapunovfunction.Inputtothevehiclearearefer-enceposture(x,,y,,8,)'andreferencevelocities(v,,ar)'.Themajorobjectiveofthispaperistoproposeacontrolruletofindareasonabletargetlinearandrotationalvelocities(v,a)'.Linearizingthesystem'sdifferentialequationisusefultodecideparametersforcriticaldumpingforasmalldisturbance.Inordertoavoidanyslippage,avelocity/accelerationlimita-tionschemewasintroduced.Severalsiniulationresultsarepresentedwithorwithoutthevelocity/accelerationlimiter.Thecontrolruleandlimitingmethodproposedinthispaperarerobot-independentandhencecanbeappliedtovariouskindofmobilerobotswithadeadreckoningability.ThismethodwasimplementedontheautonomousmobilerobotYamabico-11.Experimentalresultsobtainedareclosetotheresultswiththevelocity/accelerationlimiter.1.IntroductionThepurposeofthispaperistoproposeastabletrackingcontrolmethodforanon-holonomicvehiclewithabundantsimulationresults.RealexperimentalresultsontheautonomousmobilerobotYamabico-1Iarealsopresented.Tsumuraproposedamethodinwhichthereferencepointsequenceisstoredinmemory.Ineachcycleofthelocomotioncontrol,thereferencepointandthefuturepositionoftherobotiscomparedfordeterminingthenextsteering[2].Kanayamaproposedamethodusingstraightlinerefer-encefortherobot'slocomotioninsteadofasequenceofpoints131.Itsvelocityandsteeringcontrolniethodhassomesimilaritiestotheonepro-posedinthispaper.Crowleydevelopedalocomotioncontrolsystemwhoseorganizationha$athreelayeredstructure[4].Hedefilestheconceptofvirtualvehiclewhichisusefulforconstructingasystemwluchisrobotindependent.Initscommandsystem,independentcontroloflinearandrotationalmotionispossible,thusenabhgsnioothclothoidcurves[SI.Sin&usedaninversekinematicandaquinticpolynomialmetbodforcom-pensatingerrorsinvehicletracking[6].Inthesecondmethod,heinterpo-latesthecurrentpointandafuturereferencepointwithasmoothcurve.Kanayamaproposedtheuseofareferenceandcurrentposturesforvehiclecontrol,theuseofalocalerrorcoordinatesystem,andaPIcontrolalgorithmforlineadrotationalvelocityrulesinanearlierlocomotioncontrolmethodontheYamabico-11robot[7].Nelsonproposedalocomotioncon-trolmethodforacartwithafrontsteeringwheel,inwhichtheyalsousedtheerrorcoordinatesystem[8].Theyadoptedalinearfunctionincontrolrulesforsteeringandlinearvelocity.Thesetwopapersareregardedaspioneersofthispaper.Inthispaper,anewcontrolrulefordeterminingvehicle'slinearandrotationalvelocitiesaregiven,whicharedifferentfrombothof[7]and[8].ThestabilityofthecontrolruleisprovenusingaLiapunovfunction[91[101[11].Theuseofthetracefunction(I-cose)oforientation0issuc-cessfulinfindinganappropriateLiapunovfunction[Ill.Oneofthedifficultiesofthisproblemliesinthefactthatordinaryvehiclespossessonlytwodegreesoffreedom(linearvelocityvandrotationalvelocityCO)forlocomotioncontrol,althoughvehicleshavethreedegreesoffreedom,x,y.and8initspositioning.Anotherdifficultyisinthenon-linearityofthekinematicrelationbetween(v,CO)'and(i,i,6)'.TheuseofaLiapunovfunctionresolvesthesedifficulties.Bylinearizingthesystem'sdifferentialequation,wefindaconditionforcriticaldumping,whichgivesappropriateparametersforspeciliccon-trolrules.Theneedofvelocity/accelerationlimitationisalsodiscussed.Aftertheseanalysesanddiscussions,abundantsimulationresultsarepresented.Themethoddescribedsofarishardwareindependentandappli-cabletoordinary(notomni-directional)vehicles.Thismethodisusefultotheclassofautonomousvehiclesinwhich(a)adeadreckoningcapabilityisprovided,(b)referencepathspecificationandcurrentpositionestimation(throughdeadreckoning)aregivenseparately,and(c)highprecisioninpositionalcontrolismandatory.ThismethodwasimplementedontheautonomousmobilerobotYamabico-11whichhasbeendevelopedattheUniversityofTsukuba,theUniversityofCalifomiaatSantaBarbara,andNavalPostgraduateSchool.Itwasdemon-stratedthatthesealgorithmsaresoundandprovidedprecisetrackingcon-trol.Anextensivesetoftheexperimentalresultsareshown.2.ProblemStatementsBeforestatingtheproblem,wewillgiveafewpreliminarydefinitions.2.1.PathRepresentationandVehicleKinematicsThereisamobilerobotwhichislocatedona2DplaneinwhichaglobalCartesiancoordinatesystemisdefined.TherobotintheworldcH2876-1/90/oooO/0384$01.0001990IEEE384possessesthreedegreesoffreedominitspositioningwhicharerepresentedbyaposture,PI](1)wheretheheadingdirection0istakencounterclockwisefromthex-axis.Let0denoteanullposture(0,0,2nx)',wherenisaninteger.Sincetherobothasalocomotioncapab~tyintheplane,theposturepisinfactafunctionoftimer.Theentirelocusofthepoint(x(I),y(I))iscalleda