机器人学基础-第7章-机器人轨迹规划-蔡自兴.ppt

机器人学基础-第7章-机器人轨迹规划-蔡自兴.ppt

《机器人学基础-第7章-机器人轨迹规划-蔡自兴.ppt》由会员分享，可在线阅读，更多相关《机器人学基础-第7章-机器人轨迹规划-蔡自兴.ppt（53页珍藏版）》请在冰豆网上搜索。

中南大学蔡自兴，谢斌zxcai,2010,机器人学基础第七章机器人轨迹规划,1,Ch.7TrajectoryPlanningofRobots,FundamentalsofRobotics,Ch.7TrajectoryPlanningofRobots,2,Ch.7TrajectoryPlanningofRobots,Ch.7TrajectoryPlanningofRobots,3,Ch.7TrajectoryPlanningofRobots,7.1GeneralConsiderationsinTrajectoryPlanning轨迹规划应考虑的问题,BasicProblem:

Movethemanipulatorarmfromsomeinitialpositiontosomedesiredfinalposition（Maybegoingthroughsomeviapoints）.,4,7.1Generalconsiderations,7.1GeneralConsiderationsinTrajectoryPlanning,Trajectory:

Timehistoryofposition,velocityandaccelerationforeachDOFPathpoints:

Initial,finalandviapointsConstraints:

Spatial,time,smoothness,5,7.1Generalconsiderations,JointspaceEasytogothroughviapoints（Solveinversekinematicsatallpathpoints）NoproblemswithsingularitiesLesscalculationsCannotfollowstraightlineCartesianspaceWecantrackashape（fororientation:

equivalentaxes,Eulerangles,）Moreexpensiveatruntime（afterthepathiscalculatedneedjointanglesinalotofpoints）Discontinuityproblems,6,GeneralConsiderations-SolutionSpace,7.1Generalconsiderations,Cartesianplanningdifficulties:

7,GeneralConsiderations-SolutionSpace,7.1Generalconsiderations,Initial（A）andGoal（B）Pointsarereachable,butintermediatepoints（C）unreachable.,Ch.7TrajectoryPlanningofRobots,8,Ch.7TrajectoryPlanningofRobots,Joint-SpaceSchemesEachpathpointisconvertedintoasetofdesiredjointanglesbyapplicationoftheinversekinematics.Asmoothfunctionisfoundforeachofthenjointswhichpassthroughtheviapointsandendatthegoalpoint.Timerequiredforeachsegmentisthesameforeachjoint.Thedeterminationofthedesiredjointanglefunctionforaparticularjointisindependentwithotherjoints.,9,7.2InterpolatedCalculationofJointTrajectories关节轨迹的插值计算,7.2JointSpaceSchemes,Choiceofinterpolationfunctionisnotunique!

10,Joint-SpaceSchemes,7.2JointSpaceSchemes,Severalpossiblepathshapesforasinglejoint.,Somepossibleinterpolationfunctions:

CubicpolynomialsCubicpolynomialsforapathwithviapointsHigher-orderpolynomialsLinearfunctionwithparabolicblendsLinearfunctionwithparabolicblendsforapathwithviapoints,11,Joint-SpaceSchemes,7.2JointSpaceSchemes,Inmakingasinglesmoothmotion,atleastfourconstraintsonareevident:

12,7.2.1CubicPolynomials三次多项式插值,7.2JointSpaceSchemes,Combiningthefourconstraintsyieldsfourequationswithfourunknowns:

13,7.2.1CubicPolynomials,7.2JointSpaceSchemes,Thesefourconstraintsuniquelyspecifyaparticularcubic:

14,7.2.1CubicPolynomials,Thejointvelocityandaccelerationalongthispathare:

7.2JointSpaceSchemes,Eg.7.1Asingle-linkrobotwitharotaryjointismotionlessat=15degrees.Itisdesiredtomovethejointinasmoothmannerto=75degreesin3seconds.Findthecoefficientsofacubicwhichaccomplishesthismotionandbringsthemanipulatortorestatthegoal.Plottheposition,velocity,andaccelerationofthejointasafunctionoftime.,15,7.2.1CubicPolynomials,7.2JointSpaceSchemes,Solution:

Plugging0=15，f=75，tf=3into（7.6）,wefind,16,7.2.1CubicPolynomials,7.2JointSpaceSchemes,Solution:

17,7.2.1CubicPolynomials,7.2JointSpaceSchemes,Startsat15degreesandendsat75degrees!

Solution:

18,7.2.1CubicPolynomials,7.2JointSpaceSchemes,Startsandendsatrest!

Solution:

19,7.2.1CubicPolynomials,7.2JointSpaceSchemes,Accelerationprofileislinear!

Ifwecometorestateachpointuseformulafrompreviousslideorcontinuousmotion（nostops）needvelocitiesatintermediatepoints:

InitialConditions:

20,7.2.2Cubicpolynomialswithviapoints过路径点的三次多项式插值,7.2JointSpaceSchemes,Solutions:

Howtospecifyvelocityattheviapoints:

TheuserspecifiesthedesiredvelocityateachviapointintermsofaCartesianlinearandangularvelocityofthetoolframeatthatinstant.ThesystemautomaticallychoosesthevelocitiesattheviapointsbyapplyingasuitableheuristicineitherCartesianspaceorjointspace（averageof2sidesetc.）.Thesystemautomaticallychoosesthevelocitiesattheviapointsinsuchawayastocausetheaccelerationattheviapointstobecontinuous.,21,7.2JointSpaceSchemes,7.2.2Cubicpolynomialswithviapoints,Higherorderpolynomialsaresometimesusedforpathsegments.Forexample,ifwewishtobeabletospecifytheposition,velocity,andaccelerationatthebeginningandendofapathsegment,aquinticpolynomialisrequired:

22,7.2.3Higher-orderpolynomials高阶多项式插值,7.2JointSpaceSchemes,Wheretheconstraintsaregivenas:

23,7.2.3Higher-orderpolynomials,7.2JointSpaceSchemes,Solutiontotheseequations:

24,7.2.3Higher-orderpolynomials,7.2JointSpaceSchemes,Linearinterpolation（Straightline）:

Note:

Althoughthemotionofeachjointinthisschemeislinear,theend-effectoringeneraldoesnotmoveinastraightlineinspace.,25,7.2.4Linearfunctionwithparabolicblends用抛物线过渡的线性插值,7.2JointSpace