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1、TrajectoryGenerationUsingCubicCurvaturePolynomialsYuliangLi2017-4ClemsonUniversityIndex•TrajectoryGenerationProblem•Methodfortrajectorygeneration•Experiments&Examples•Futurework•ReferencesBeforewestartHistoryofthisalgorithm•2001,IntroducedbyNagy,Bryan,andAlonz
2、oKelly.•2007,Bosstheautonomousvehicle,CMU(winnerofDARPA’07)•2011,McNaughton’sPhDThesis,CMU•2015,Open-SourceprojectCPFL-AutowareTrajectoryGenerationProblem•Configuration(C)SpaceofAisthespaceofallpossibleconfigurationsofA.•MotionPlanning:Howtomovearobotfromanini
3、tialconfigurationtoagoalconfigurationinitsCSpace.Pic:[5]ChosetTrajectoryGenerationProblem•InverseKinematicsProblem:–determiningthecontrolinputwhichcausesthevehicletoachieveagoalposture(x,y,θ,κ).•WhyCurvatureκ:–steeringmechanismhasmassandissubjecttorestoringfor
4、cesthatdependonvehiclestateandterrain.•TheTask:–Solveanunderdetermineddifferentialequationforavectortrajectorywhichachievessomeunknownstatetrajectorythatendsatthegoalposture.•Difficults:–twoinput:LinearVelocity&SteerAngleVelocityV.S4outputs(x,y,θ,κ).–steeringa
5、ctuatormovescontinuouslyV.Scontrollerswhichaskittomovediscontinuously[4]Nagy&KellyTrajectoryGenerationProblem•PolynomialSpirals:–ThecurveisageneralizationoftheEuler’sspiral,forwhichthecurvatureislinearlyrelatedtothearclengths.•CubicSolution:–Considerthesolutio
6、ntothestateequationsforacurvatureinputwhichisathirdorderpolynomialinarclengthPic:GoogleImageSearchTrajectoryGenerationProblem•Benefits:T–Variability:4params[a,b,c,s]todetermine4state(x,y,θ,κ),soithassufficientκ:curvatures:arclengthdegreesoffreedom–Feasibility:
7、SuchinputsarecontinuousinRecallthevehicleposture(x,y,θ,κ).thethirdderivativeofsteeringangleandhencearesmoothinthetorqueappliedtothesteeringactuator.–FeasibleControls:Cubicscoverthesetofallcurve.Itthereforeapproximatetheoptimalcontrolsignalverywell.[4]Nagy&Kell
8、yTrajectoryGenerationProblem•Solution:–Usingcubiccurvaturetoconnecttheinitialvehicleconfigandgoalconfig.Pic:[3]McNaughtonWhat’sNext•Steps:1.Definemodelsforvehicle,pathandtrajectory
