基于旋量理论和Paden-Kahan子问题的机器人反解算法

Inverse-Solution Algorithm of Robot Based on Screw Theory and Paden-Kahan Sub-Problem

摘要: 对工业机器人进行运动学分析包括正向运动学分析和反向运动学分析，运动学反解问题是当前研究的热点和难点。本文以旋量理论和几何法为基础，结合Paden-Kahan子问题解法，给出一种机器人运动学反解算法。以某六轴串联工业机器人为例，给定一组关节角度，求解出其运动学正解，以此为基础得到若干组运动学反解作为理论值，然后利用上述基于旋量理论的反解算法验证其有效性。典型应用结果表明：该机器人运动学反解算法，可避免D-H参数法中因为关节轴平行引起的奇异性问题，不仅满足对工业机器人重复定位精度的要求，并能够使机器人运动更加平稳。

Abstract: The kinematics analysis of industrial robots includes forward kinematics analysis and reverse kinematics analysis. The problem of inverse kinematics solution is a hot and difficult point. Based on the screw theory and geometry method, and combined with Paden-Kahan sub-problem solution, this paper presents a kinematic inverse solution algorithm for robots. Taking a six-axis series industrial robot as an example, given a set of joint angles, the kinematic positive solution is solved. And then several sets of kinematic inverse solutions are obtained as theoretical values. Then, the above inverse solution algorithm based on the screw theory is used to verify its effectiveness. The typical application results show that the inverse kinematics solution algorithm can avoid the sin-gularity problem caused by the parallel joint axis in the D-H parameter method, which not only meets the requirement of repeated positioning accuracy of industrial robot, but also can make the robot move more stable.