冗余度机械臂的自运动流形计算及关节轨迹规划

Self-motion Manifolds Calculation and Joint Trajectory Planning of Redundant Manipulators

为了求解冗余度机械臂的全部逆运动学解,以计算包含全部逆运动学解的自运动流形为目标,提出了一种新的自运动流形计算方法。该方法基于人工蜂群算法完成自运动流形各分支初值的搜索,解决了分支初值难以确定的问题,并提出了分支搜索策略,实现了完整流形分支的搜索。在此基础上,为提高自运动流形的计算效率,定义了自运动流形的全等性与渐变性并建立了流形库,通过索引流形库内的自运动流形能够快速计算工作空间任意位置的自运动流形。利用流形库对机械臂进行全局性能分析,得到了各流形分支的局部最优位形;以每条分支的局部最优位形作为初始位形进行关节轨迹规划,实现了给定末端轨迹的全局最优关节轨迹规划,并通过4R机械臂和7R机械臂验证了方法的有效性。该方法还可用于超冗余度机械臂自运动流形的计算,具有较好的通用性。

To solve all the inverse kinematics solutions of the redundant manipulators,a new self-motion manifolds calculation method is proposed to calculate the self-motion manifolds including all inverse kinematics solutions.This method is based on the artificial bee colony algorithm to complete the initial value search of each branch of self-motion manifolds,which solves the problem that the initial value of the branch is difficult to determine.Furthermore,a branch search strategy is proposed to realize the search of complete manifolds branches.On this basis,to improve the calculation efficiency of self-motion manifolds,the congruence and gradient of self-motion manifolds are defined,and the manifolds library is established.By indexing the self-motion manifolds in the manifolds library,the self-motion manifolds at any position in the workspace can be quickly calculated.The manifolds library is used to analyze the global performance of the manipulators,and the local optimal configurations on each branch are obtained.The local optimal configurations of each branch are used as the initial configuration for joint trajectory planning,and the global optimal joint trajectory planning for a given end trajectory is realized.The 4R manipulator and 7R manipulator verify the method's effectiveness.This method can also be used to calculate the self-motion manifolds of hyper-redundant manipulators,and it has good universality.