6R Robot Inverse Solution Algorithm Based on Quaternion Matrix and Groebner Base

This article proposes a new algorithm of quaternion and dual quaternion in matrix form. It applies quaternion in special cases of rotated plane, transforming the sine and cosine of the rotation angle into matrix form, then exporting flat quaternions base in two matrix form. It establishes serial 6R manipulator kinematic equations in the form of quaternion matrix. Then five variables are eliminated through linear elimination and application of lexicographic Groebner base. Thus, upper bound of the degree of the equation is determined, which is 16. In this way, a 16-degree equation with single variable is obtained without any extraneous root. This is the first time that quaternion matrix modeling has been used in 6R robot inverse kinematics analysis.

基于倍四元数和Groebner基的6R机械手的位置反解

提出了一般6R机械手的位置反解的新算法,该算法是把齐次变换矩阵转以倍四元数形式表示,建立了倍四元数形式的串联6R机械手运动学方程,再通过线性消元和两次应用分次字典序Groebner基消去5个变元,得到一个一元16次方程。此方法没有增根,是一种对空间任意尺寸6R机械手进行建模和求解的新算法。其中求解Groebner基采用了计算机代数系统进行有理数运算,目前的求解速度尚不是很高,需进一步改进。