机械臂三次样条路径规划系数递推算法

针对机械臂三次样条路径规划涉及高阶矩阵求逆,因而算法复杂、响应速度慢的问题,提出一种不需要求逆矩阵运算的三次样条系数的递推算法,递推算法的初始值由递推公式表示的边界条件获得.按照三次样条的3种不同的边界条件,分别给出了递推算法初始值的确定方法和递推公式.仿真结果表明,改进的算法不仅运算简单,而且可以获得理想的三次样条系数.

Coefficient Recursive Algorithm for Manipulator Trajectory Planning Based on Cubic Splines

The algorithm for manipulator trajectory planning based on cubic splines relates to the inversion of the matrix with higher order, and hence, the operation becomes very complex. As a result, the response rate of the manipulator was reduced certainly. In view of this situation, a recursive algorithm to obtain the coefficients of cubic splines was put forward. The recursive algorithm did not require any matrix inversion, and the initial values of recursion came from the boundary conditions expressed by recursive formula. The methods to determine initial values and the recursive formula were presented according to three different boundary conditions. Simulation result showed that the improved algorithm not only can simplify the computes, but also can obtain desired coefficients of cubic splines.