用代数方法高效求解6轴机械臂逆运动学问题
Inverse Kinematics for a 6-Degree-of-Freedom Robot Manipulator Using Comprehensive Gröbner Systems
- 基于综合格罗布纳系解决含参数的逆运动学方程
- 适用于旋转轴两两相交的更广类机械臂，提升适用范围
- 避免重复计算，适合工业机械臂快速规划场景
本文提出一种利用计算机代数求解特定6自由度机械臂逆运动学问题的有效方法。已知当三个连续旋转关节的转轴共点时，逆运动学可分解为位置与姿态求解。本文将该方法扩展至旋转轴两两相交的更一般情况，扩大了可解机械臂的种类，并有望实现更高效的求解。采用综合格罗布纳系统（CGS），将机械臂关节参数作为系数中的参数，避免重复计算格罗布纳基。实验验证了所提方法的有效性。
原文摘要 · Abstract (English)
We propose an effective method for solving the inverse kinematic problem of a specific model of 6-degree-of-freedom (6-DOF) robot manipulator using computer algebra. It is known that when the rotation axes of three consecutive rotational joints of a manipulator intersect at a single point, the inverse kinematics problem can be divided into determining position and orientation. We extend this method to more general manipulators in which the rotational axes of two consecutive joints intersect. This extension broadens the class of 6-DOF manipulators for which the inverse kinematics problem can be solved, and is expected to enable more efficient solutions. The inverse kinematic problem is solved using the Comprehensive Gröbner System (CGS) with joint parameters of the robot appearing as parameters in the coefficients to prevent repetitive calculations of the Gröbner bases. The effectiveness of the proposed method is shown by experiments.
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