基于遗传算法的机械臂时间最优轨迹规划

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1、硕士学位论文points(datapoints)onagiventrajectoryinterpolation．Theseobtaineddatapointsaretransformedintojointanglevalueswithinversekinematics．TherestrainsthatareinCartesiantrajectoryspacearetransformedintothejointspace．Then，weuseB—splinetofiteachjointtrajectory．While，thedatawasintroducedintoADAM

2、Stosimulatethetrajectoryplanning．Wegainangledisplacementcurve，angularvelocitycurveandangularaccelerationcurveofeachjoint．Formthecurve，wecanseethatthespeedchangesgently，buttheangularaccelerationcurvehasdistinctmutations．Andtheentirerunningtimeofthetrackis1ls，thetimeisnotthebest．Sothetrajec

3、toryalsocannotcometobeoptimized．Finally，settingtheoptimizationobjectiveisthetime，weselectethegeneticalgorithmstooptimizetheentiremanipulatortrajectory．Webrieflyintroducetheprinciplesofgeneticalgorithm．Consideringtheangularvelocityconstraint，theangularaccelerationconstraint，angularaccelera

4、tionconstraintsandtorquevariationconstraints，weusegeneticalgorithmstooptimizetheobtainedB-splinetrajectory．Wesettimeastheoptimizationobjectives．Wegivethespecificoptimizationsteps．Ultimately，wegotB—splinetimeoptimaltrajectorymeetingthekinematicconstraintsanddynariaicconstraints．Keywords：Di

5、rectdriverotarytable；Staticpressuresupport；Dynamicandstaticchrematistics；Multi·objectiveoptimizationIll基于遗传算法的机械臂时间最优轨迹规划插图索引图2．1位置矢量的表示⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯8图2．2旋转矩阵的表示⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯9图2．3纯平移变换⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯．10图2．4绕轴纯旋转变换⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯．．10图2．5复合变换⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯

6、⋯⋯⋯⋯⋯⋯⋯．11图2．6PUMA560的实体模型⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯．．13图2．7PUMA560机械臂各关节坐标系⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯．13图2．8仿真前各连杆之间位置关系⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯．．16图2．9仿真后各连杆之间位置关系⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯．．16图2．10末端的角位移曲线⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯．．16图4．1轨迹规划原理⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯．．39图4．2关节变量空间轨迹设定算法⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯42图4．3笛卡尔空问轨迹设定点算法⋯⋯⋯⋯⋯⋯

7、⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯．．56图4．4三点确定圆弧⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯．．57图4．5空间转化为平面形成的新坐标系与三维坐标系关系⋯⋯⋯⋯⋯⋯⋯⋯58图4．6B．样条函数轨迹规划各关节角位移图⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯62图4．7B．样条函数轨迹规划各关节角速度图⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯．62图4．8B一样条函数轨迹规划各关节角加速度图⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯63图4．9机械臂末端轨迹空间状态⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯．．63图5．1遗传算法流程图⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯