基于四元数矩阵与Groebner基的6R机器人运动学逆解算法

General 6Rrobot inverse solution algorithm based on a quaternion matrix and a Groebner base

为促进一般6R机器人运动学逆解的应用,提出了一种四元数矩阵和对偶四元数矩阵算法,该算法把四元数应用于平面旋转的特殊情况,把旋转角度的正弦、余弦改写为矩阵形式,可以导出平面四元数的2个矩阵形式的基,建立了四元数矩阵形式的串联6R机械手运动学方程,再通过线性消元和2次应用分次字典序Groebner基消去5个变元,最后采用Dixon结式进行消元,得到没有增根的一元16次方程。这种算法得出的结果通过与过去得出的6R机器人逆解算法进行对比,表明所提出的算法可行性和正确性。

An inverse solution algorithm was developed for general 6Rrobot kinematics using quaternion and dual quaternion matrices.The quaternion method is applied to the special circumstances of the plane of rotation where the rotation angles for the sine and cosine are rewritten in matrix form exported to a flat quaternion base of a second order matrix for the quaternion matrix form of the series 6R manipulator kinematic equations.Five variables are eliminated by the elimination of the linear and double application lexicographic Groebner base.Finally Dixon resultant elimination is used to develop a 16degree equation contained one variable.This equation does not have any roots.Comparison with the classic 6R robot inverse kinematics algorithm shows that the current algorithm is accurate.