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

• 作者: Ruikun Wu Zhensong Ni
• 来源期刊: 线性代数与矩阵理论研究进展(英文)
• 学科: 数学
• 关键词: 6R ROBOT QUATERNION MATRIX Groebner BASE INVERSE KINEMATICS Analysis
• 年，卷（期）: 2018,（1）
• 页码范围: 33-40
• 页数: 8页
• 分类号: O1

摘要

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.