空间一般6R机械手位置反解的新方法

New Algorithm for Inverse Kinematics Analysis of General 6R Serial Robot

将共形几何代数(CGA)和迪克逊(Dixon)结式引入串联机构逆运动分析中,对一般6R机器人的位置进行了反解.先把齐次变换矩阵转以共形几何代数形式表示,在此基础上建立了共形几何代数形式的串联6R机械手运动学方程,再通过线性消元和Dixon结式消元消去5个变元,然后对Dixon结式进一步处理,最后得到1个一元16次方程.这种算法也适用于其他具有16解的7R、1P5R和4R1C等串联机械手位置反解问题,具有一定的通用性.

Conformal geometric algebra （CGA） and Dixon resultant are introduced to the inverse kine- matics analysis of the serial mechanisms and to the inverse solution of the general 6R robot. First, it shows that homogeneous transforms matrix in terms of CGA will lead to CGA form kinematics equations of 6R robot; Second, the resultant is obtained by using linear elimination and Dixon elimination to eliminate 5 variables; Finally, a 16th degree equation containing a variable is properly derived from the resultant. This algorithm also can be applicable to the inverse kinematics analysis of the robots with 16 roots such as 7R, 1P5R and 4R1C, so it has universal usage.