一种3R机械臂最短路径规划方法

为求解机械臂最短路径问题, 导出了机械臂末端路径长度的表示式, 并将最短路径问题归结为一个泛函极值问题。为简化求解过程, 将泛函极值问题转化成另一个同解的泛函极值问题, 并利用变分法求出了表示后一问题解的微分方程组。利用上三角矩阵逆矩阵的表示式, 将该微分方程组转化成了标准状态方程组, 与微分几何方法相比, 避免了逆矩阵计算, 使转化过程更加简单。利用 Matlab进行仿真, 求出了 3R机械臂最短路径所对应的三个关节角度的位移函数。

Abstract

In order to search out the shortest path of the 3R manipulator, a path length expression of manipulator’s end-effectors is given first, and then the problem is modeled as a functional extreme problem. For the purpose of simplifying the solving process, the functional extreme problem is translated into a new one with the same solution, and the solution of the latter expressed by a system of differential equations is derived by using variational method. By means of the inverse matrix expression of the upper triangular matrix, the system of differential equations is translated into a new one consisted of normal state equations. The method can avoid complex inverse matrix computing, and make the computation of the transition process simpler when compared with differential geometry method. By using Matlab simulation method, 3 joint angle functions corresponding to the shortest path of the 3R manipulator’s end-effectors is obtained.

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安凯, 马佳光. 一种3R机械臂最短路径规划方法[J]. 光电工程, 2014, 41(12): 1. AN Kai, MA Jiaguang. A Shortest-path Planning Algorithm of the 3R Manipulator[J]. Opto-Electronic Engineering, 2014, 41(12): 1.

一种3R机械臂最短路径规划方法

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