空间6R机器人位置反解的对偶四元数法

Dual Four Element Method for Inverse Kinematics Analysis of Spatial 6R Manipulator

将对偶四元数的复指数形式引入到串联机械手位置逆解分析中,提出一种空间6R串联机械手位置逆解的新算法。采用复指数形式的四元数以及对偶四元数建立空间6R串联机械手位置逆解的封闭方程。通过对获得的四个位置约束方程构造Dixon结式,得到一个6×6的行列式等于零的矩阵,去掉其中相关的公因式,导出既无增根也无漏根的一元16次方程。通过实际计算,得出该机器人位置反解一元高次方程的次数为16且最多只有16组解的结论。通过一种串联机械手逆运动学分析为例进行求解验证,数字实例证明了该方法既无增根也无漏根。这种方法可达到在消元过程中自动消除机构结构参数变化或者轨迹规划过程中某些奇异位置造成的方程相关性,避免增根的产生。

Complex exponential form of dual four elements is introduced into the inverse kinematics analysis of serial mechanisms. A new algorithm is proposed for the inverse solution of space 6R serial mechanism. The mathematical model is established for the space 6R serial mechanism by adopting complex exponential form and dual four elements. A 6×6 matrix is obtained from the Dixon resultant constructed with the obtained four position constraint equations. By deleting the interrelated rows of the matrix and taking t...