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基于解析几何实现Dubins避障路径.docx

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基于解析几何实现Dubins避障路径 Abstract: Dubinspathistheshortestpathbetweentwopointswithfixedinitialandfinalheadings,whileavoidingobstacles.ThispaperproposesasolutiontotheDubinspathproblemusinganalyticalgeometry.ThismethodinvolvesfindingtheintersectionpointsbetweentheobstacleboundaryandtheDubinspath,andadjustingthepathaccordingly.Theproposedmethodistestedondifferentobstacleconfigurationsandcomparedtoexistingalgorithms. Introduction: Dubinspathisacrucialconceptinmotionplanningandcontrol,especiallyinapplicationssuchasrobotics,aviationandnavigation.Itisdefinedastheshortestpathbetweentwopointswithfixedinitialandfinalheadings,whilerespectingcertainconstraints.Theconstraintsincludeavoidingobstaclesandsatisfyingthekinematicanddynamiclimitationsofthevehicle.ThesimplicityoftheDubinspath,alongwithitsoptimality,makesitattractiveforreal-timeapplications. TheDubinspathproblemcanbesolvedusingdifferenttechniques,suchasnumericaloptimization,graph-basedmethods,andanalyticalgeometry.Inthispaper,wewillfocusontheanalyticalgeometryapproach.ThismethodinvolvesfindingtheintersectionpointsbetweentheDubinspathandtheobstacles,andmodifyingthepathaccordingly. Methodology: ThemethodologyforsolvingtheDubinspathproblemusinganalyticalgeometryisasfollows: 1.Determinetheinitialandfinalpositionsandheadingsofthevehicle. 2.ComputethelengthoftheDubinspathbasedontheinitialandfinalheadings. 3.GeneratetheDubinspath,whichconsistsofthreesegments:acirclesegment,astraightsegment,andanothercirclesegment. 4.FindtheintersectionpointsbetweentheDubinspathandtheobstacleboundaries. 5.AdjusttheDubinspathtoavoidtheobstaclesandsatisfytheconstraints. 6.Repeatsteps4and5untilafeasiblepathisfound. Findingtheintersectionpoints: Tofindtheintersectionpoints,weneedtorepresenttheDubinspathandtheobstacleboundariesinparametricequations.TheDubinspathcanberepresentedasfollows: x=x1+R1cosθ1+Lsin(θ1+α)+R2cos(θ1+α+θ2) y=y1+R1sinθ1-Lcos(θ1+α)+R2sin(θ1+α+θ2) Wherex1andy1arethecoordinatesoftheinitialposition,R1andR2aretheradiiofthetwocirclesegments,Li