一种任意起始位姿的连续曲率泊车路径在线规划方法

一种任意起始位姿的连续曲率泊车路径在线规划方

法

Introduction

Parallelparking,alsoknownascurbparkingorreverseparking,isacommontaskfordrivers.However,manydriversfinditdifficulttosuccessfullyexecutethismaneuverduetothecomplexityofthetaskandthelimitedspaceavailable.Toaddressthisissue,researchershaveproposedmethodsforautomatedparallelparking,whichcanassistdriversoreventakeoverthetaskcompletely.Inparticular,continuouscurvaturepathplanningisaneffectivetechniqueforgeneratingsmoothandsafedrivingtrajectories.Inthispaper,weproposeanovelonlinealgorithmforgeneratingcontinuouscurvatureparallelparkingpathsstartingfromarbitraryinitialposes.

RelatedWork

Variousmethodsforautomatedparkinghavebeenproposedintheliterature.Onecommonapproachismodel-basedpathplanning,wherethevehiclekinematicsandenvironmentconstraintsaremodeledusingmathematicalequations.Thisapproachisefficientandaccurate,butrequirespriorknowledgeoftheparkingspaceandvehiclecharacteristics.Anotherapproachissearch-basedplanning,whereapathisgeneratedbysearchingadiscretizedstatespace.Thismethodismoreflexibleandcanhandlecomplexenvironments,butcanbecomputationallyexpensiveandlessoptimal.

Continuouscurvaturepathplanningisapopularmethodforgeneratingsmoothandfeasibledrivingtrajectories.Thepathisrepresentedasasequenceof(x,y,θ,k)points,wherex,yarethevehicleposition,θistheheadingangle,andkisthecurvature.Acontinuouscurvaturepathsatisfiestheconstraintsoncurvature,velocity,andacceleration,andcanbeexecutedbyasuitablecontroller.Variousalgorithmshavebeenproposedforcontinuouscurvaturepathplanning,includingDubinspath,Reeds-Shepppath,andclothoidpath.

Methodology

Ourproposedalgorithmforgeneratingcontinuouscurvatureparallelparkingpathsstartswithagiveninitialpose(x,y,θ)andthe

dimensionsofthevehicle,parkingspace,andobstacles.Thealgorithmconsistsoftwomainsteps:(1)computingacandidatepathusingasearch-basedapproach,and(2)optimizingthecandidatepathusinganon-linearprogramming(NLP)solver.

Step1:CandidatePathGeneration

Inthisstep,wediscretizethestatespaceofthevehicleandperformasearchtofindasetofcandidatepathsthatsatisfytheconstraintsoncurvature,velocity,andclearancefromobstacles.Thestatespaceisdiscretizedalongthex-axis,andthevehicleisassumedtomoveonlyintheforwarddirection.ThesearchisperformedusingA*algorithm,wherethecostfunctionistheEuclideandistancefromthecurrentstatetothegoalstate.Ateachpointinthestatespace,wecheckthefeasibilityofapotentialpathbycomputingthecurvatureandcheckingifitsatisfiestheconstraints.Wealsocheckifthepathclearsanyobstacles,includingtheboundariesoftheparkingspace.Ifthepotentialpathisfeasible,weaddittoalistofcandidatepaths.

Step2:PathOptimization

Inthisstep,thecandidatepathsareoptimizedusinganon-linearprogramming(NLP)solver.Theobjectivefunctionistominimizethedeviationfromthedesiredparkingposeandthefinalangle.Theconstraintsonthepathincludethecurvature,velocity,andclearancefromobstacles.Thefinalposeoftheoptimizedpathmustbeparalleltothefinalorientationoftheparkingspace.TheNLPsolversolvestheoptimizationproblembyiterativelyrefiningthepathuntilconvergence.

ExperimentalResults

Wetestedouralgorithmonseveralsimulatedparkingscenariosusingdifferentinitialposesandparkingspacedimensions.Theresultsshowthatouralgorithmcansuccessfullygeneratecontinuouscurvaturepathsstartingfromarbitraryinitialposes.Thegeneratedpathsaresmoothandavoidcollisionwithobstacles.Thetotalexecutiontimeofthealgorithmisreasonableforreal-timeapplications.

Conclusion

Inthispaper,weproposedanovelonlinealgorithmforgeneratingcontinuouscurvatureparallelparkingpathsstartingfromarbitraryinitialposes.Ouralgorithmfirstgeneratesasetofcandidatepathsusingasearch-basedapproach.Then,thecandidatepathsareoptimizedusinganon-linearprogrammingsolver.Experimentalresultsshowthatouralgorithmgenerates