基于倍四元数和Groebner基的6R机械手的位置反解

Qeneral 6R Robot Inverse Solution Based on Double Quaternion and Groebner Base

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。

A new algorithm for the position inverse solution of the introduced general 6R robot was introduced. It is the homogeneous transformation matrix that translated to the double quaternions form, and on this basis, the series 6R robot kinematics equation with double quaternions form was established. And five variables were eliminated by the elimination of linear and two-time applications lexicographic Groebner base, a 16th degree equation contained a variable has been obtained. This method did not have any roots, it is a new algorithm that solves and presents the space of arbitrary size 6R robot modeling. Groebner base which used computer algebra system rational calculation was requested, and the current solution is not yet a high speed, it needs further improvement.