机器人学基础-第7章-机器人轨迹规划-蔡自兴PPT文件格式下载.ppt
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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!
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
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