非球型手腕6R机器人实时高精度逆运动学算法

Real-time and high-precision algorithm for inverse kinematics of the 6R robots with non-spherical wrist

针对非球型手腕结构的6R机器人逆运动学不存在封闭解,以及现有算法存在实时性差、精度低、稳定性差等问题,提出了一种基于符号运算和矩阵变换的实时高精度逆运动学算法.该算法首先利用代数变换得到逆运动学方程的系数矩阵,然后通过矩阵拆分和符号运算消去系数矩阵中的未知变量,采用矩阵特征值的分解和特征向量的选取,得到了逆运动学的至多16组解.最后以自主研发的非球型手腕的6R喷涂机器人为实例,求解结果表明:该算法的平均求解时间约为1.87ms,计算位姿误差在10-10范围内,满足实时高精度及稳定性的要求.

In terms of no closed-form solution for inverse kinematics(IK)of the 6Rrobots with nonspherical wrist and the existing algorithms owning the problems of the lack of real-time,precision and stability,a real-time and high-precision algorithm for IK based on symbolic operation and matrix transformation was proposed.This algorithm firstly used algebraic transformation to obtain the coefficient matrices of IK equations,and then eliminated unknown variables in the coefficient matrices with matrix splitting and symbolic operation,adopted matrix eigenvalue decomposition and eigenvector selection further,got 16set of solutions at most.Finally,a spray painting robot with non-spherical wrist,which was researched and developed independently,was used as an example,the results show that this algorithm,in which the average running time is about 1.87ms and the computation accuracy is in the range of 10-10,meets the requirements of real-time,high-precision and stability,and provides a better solution for inverse kinematics of other general serial mechanisms.