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外文翻译--一种实用的办法--带拖车移动机器人的反馈控制 英文版.pdf

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外文翻译--一种实用的办法--带拖车移动机器人的反馈控制 英文版.pdf

1Proceedingsofthe1998IEEEInternationalConferenceonRoboticsAutomationLeuven,BelgiumMay1998ApracticalapproachtofeedbackcontrolforamobilerobotwithtrailerF.LamirauxandJ.P.LaumondLAASCNRSToulouse,France{florent,jpl}laas.frAbstractThispaperpresentsarobustmethodtocontrolamobilerobottowingatrailer.Bothproblemsoftrajectorytrackingandsteeringtoagivenconfigurationareaddressed.Thissecondissueissolvedbyaniterativetrajectorytracking.Perturbationsaretakenintoaccountalongthemotions.ExperimentalresultsonthemobilerobotHilareillustratethevalidityofourapproach.21IntroductionMotioncontrolfornonholonomicsystemshavegivenrisetoalotofworkforthepast8years.Brockettscondition2madestabilizationaboutagivenconfigurationachallengingtaskforsuchsystems,provingthatitcouldnotbeperformedbyasimplecontinuousstatefeedback.Alternativesolutionsastimevaryingfeedbackl0,4,11,13,14,15,18ordiscontinuousfeedback3havebeenthenproposed.See5forasurveyinmobilerobotmotioncontrol.Ontheotherhand,trackingatrajectoryforanonholonomicsystemdoesnotmeetBrockettsconditionandthusitisaneasiertask.Alotofworkhavealsoaddressedthisproblem6,7,8,12,16fortheparticularcaseofmobilerobots.Allthesecontrollawsworkunderthesameassumptiontheevolutionofthesystemisexactlyknownandnoperturbationmakesthesystemdeviatefromitstrajectory.Fewpapersdealingwithmobilerobotscontroltakeintoaccountperturbationsinthekinematicsequations.lhoweverproposedamethodtostabilizeacaraboutaconfiguration,robusttocontrolvectorfieldsperturbations,andbasedoniterativetrajectorytracking.Thepresenceofobstaclemakesthetaskofreachingaconfigurationevenmoredifficultandrequireapathplanningtaskbeforeexecutinganymotion.Inthispaper,weproposearobustschemebasedoniterativetrajectorytracking,toleadarobottowingatrailertoaconfiguration.Thetrajectoriesarecomputedbyamotionplannerdescribedin17andthusavoidobstaclesthataregivenininput.Inthefollowing.Wewontgiveanydevelopmentaboutthisplanner,werefertothisreferencefordetails.Moreover,weassumethattheexecutionofagiventrajectoryissubmittedtoperturbations.Themodelwechosefortheseperturbationsisverysimpleandverygeneral.Itpresentssomecommonpointswithl.Thepaperisorganizedasfollows.Section2describesourexperimentalsystemHilareanditstrailertwohookingsystemswillbeconsideredFigure1.Section3dealswiththecontrolschemeandtheanalysisofstabilityandrobustness.InSection4,wepresentexperimentalresults.32DescriptionofthesystemHilareisatwodrivingwheelmobilerobot.Atrailerishitchedonthisrobot,definingtwodifferentsystemsdependingonthehookingdeviceonsystemA,thetrailerishitchedabovethewheelaxisoftherobotFigure1,top,whereasonsystemB,itishitchedbehindthisaxisFigurel,bottom.AistheparticularcaseofB,forwhichrl0.Thissystemishoweversingularfromacontrolpointofviewandrequiresmorecomplexcomputations.Forthisreason,wedealseparatelywithbothhookingsystems.Twomotorsenabletocontrolthelinearandangularvelocities(vr,roftherobot.Thesevelocitiesaremoreovermeasuredbyodometricsensors,whereastheanglebetweentherobotandthetrailerisgivenbyanopticalencoder.Thepositionandorientation(xr,yr,r)oftherobotarecomputedbyintegratingtheformervelocities.Withthesenotations,thecontrolsystemofBiscossinsincosrrrrrrrrrrrrttxvyvvlll(1)Figure1Hilarewithitstrailer43Globalcontrolscheme3.1MotivationWhenconsideringrealsystems,onehastotakeintoaccountperturbationsduringmotionexecution.Thesemayhavemanyoriginsasimperfectionofthemotors,slippageofthewheels,inertiaeffects...Theseperturbationscanbemodeledbyaddingaterminthecontrolsysteml,leadingtoanewsystemoftheform,xfxuwheremaybeeitherdeterministicorarandomvariable.Inthefirstcase,theperturbationisonlyduetoabadknowledgeofthesystemevolution,whereasinthesecondcase,itcomesfromarandombehaviorofthesystem.Wewillseelaterthatthissecondmodelisabetterfitforourexperimentalsystem.Tosteerarobotfromastartconfigurationtoagoal,manyworksconsiderthattheperturbationisonlytheinitialdistancebetweentherobotandthegoal,butthattheevolutionofthesystemisperfectlyknown.Tosolvetheproblem,theydesignaninputasafunctionofthestateandtimethatmakesthegoalanasymptoticallystableequilibriumoftheclosedloopsystem.Now,ifweintroducethepreviouslydefinedterminthisclosedloopsystem,wedontknowwhatwillhappen.Wecanhoweverconjecturethatiftheperturbationissmallanddeterministic,theequilibriumpointifthereisstillonewillbeclosetothegoal,andiftheperturbationisarandomvariable,theequilibriumpointwillbecomeanequilibriumsubset.Butwedontknowanythingaboutthepositionofthesenewequilibriumpointorsubset.Moreover,timevaryingmethodsarenotconvenientwhendealingwithobstacles.Theycanonlybeusedintheneighborhoodofthegoalandthisneighborhoodhastobeproperlydefinedtoensurecollisionfreetrajectoriesoftheclosedloopsystem.Letusnoticethatdiscontinuousstatefeedbackcannotbeappliedinthecaseofrealrobots,becausediscontinuityinthevelocityleadstoinfiniteaccelerations.Themethodweproposetoreachagivenconfigurationtnthepresenceofobstaclesisthefollowing.Wefirstbuildacollisionfreepathbetweenthecurrentconfigurationandthe

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