shortest paths to obstacles for a polygonal car-like robotnew

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1、Shortestpathstoobstaclesforapolygonalcar-likerobotM.Vendittelli,Universit`adiRoma“LaSapienza”,Roma,ItalyJ.P.Laumond,LAAS-CNRS,Toulouse,FranceP.Sou`eres,LAAS-CNRS,Toulouse,FranceAbstractaxlemidpoint(referencepoint)ofthecar,whileθistheanglethattheunitdirectionvectorvformswithThispapershowshowtocompu

2、tethenonholonomicthepositivexaxis.Aconfigurationofthecarisgivenbyatriple(x,y,θ)∈C≡R2×S1,whereS1isthedistancebetweenacar-likerobotofpolygonalshape2andpolygonalobstacles.Adoptinganoptimalcontrolunitcircleintheplane.ThepointP(x,y)∈Rwillbepointofview,weusetransversalityconditionstogetreferredtoasthepos

3、itionofthecarintheplane.informationaboutthestructureofpathsthataread-missiblesolutions.Withthisinformation,theproblemLetusconsiderapolygonalobstacle.Thedomainofofminimizingthelengthofapaththatis,ingeneral,theconfigurationspacegatheringtheconfigurationsatfunctionofthreeparameters,isreducedtothatofmin

4、-whichtherobotcollidestheobstacleareboundedbyimizingafunctionofonevariable,namely,therobottwotypesofsurfacescorrespondingtotwotypesofcon-tact[2]:robot-vertexonobstacle-edgeorrobot-edgeonfinalorientation.Tosolvetheproblem,wedecomposeitintothreesubproblemsandfindsufficientfamiliesofobstacle-vertex.Suchc

5、ontactsgenerateruledsurfacesshortestpathssolvingeachofthesubproblems.whicharetheboundaryoftheobstacleintheconfig-urationspace.Theintersectionoftwosuchsurfacesarecurvescorrespondingtocontactsrobot-vertexonobstacle-vertex,androbot-edgeonobstacle-edge.For1Introductiontheproblemconsideredinthepaper,the

6、robotfinalconfigurationisconstrainedtobelongtosuchsurfaces.Distancecomputationplaysacrucialroleinrobotmo-tionplanning.NumerousmotionplanningalgorithmsControlmodelThemodelofthecartowhichwerelyonobstacledistancecomputation,e.g.,skeletoniza-willreferalongthepaperisdescribedbythecontroltionandpotentialfi

7、eldsmethods[11].Thedistancesystem:fromarobotconfigurationtoanobstacleisthelengthx˙(t)=cosθ(t)·u1(t)oftheshortestfeasiblepathbringingonepointonthey˙(t)=sinθ(t)·u1(t)(1)robotboundaryincontactwiththeobstacle.θ˙(t)