一种分析四元数及其在6R机械臂逆运动学中的应用

An Analytical Quaternion and its Applications to Inverse Kinematics of 6R Manipulators

为解决现有6R串联机械臂实时高精度逆运动学问题,提出一种新的分析四元数,用于6R机械臂逆运动学建模与求解。通过建立6R机械臂的坐标系和轴矢量,提出一种与传统Euler四元数同构的分析四元数,及与方向余弦矩阵同构的类方向余弦矩阵,以推导无冗余、二阶的机械臂逆运动学模型。基于机械臂的结构矢量分解,提出一种6R通用解耦机械臂建模的方法,分析机械臂的解耦条件,用于求解三轴解耦、偏置及正交解耦的6R机械臂逆运动学解析解。仿真试验结果表明,对于三种腕型的机械臂,所提出的方法单次求解速度在5.7 ms以下,位置精度优于10^(‒15)m,方向精度优于10^(‒8)(°),可以有效保证机械臂在线精密操作的性能。

In order to solve the real-time and high-precision inverse kinematics problem of 6R manipulators,a new analytical quaternion is proposed,which is used for inverse kinematics modelling and solutions of 6R manipulators.The coordinate system and axis vectors of 6R manipulators are established.An analytical quaternion which is isomorphic to the traditional unit quaternion and a quasi-direction cosine matrix isomorphic to the direction cosine matrix are proposed to establish a non-redundant and second-order inverse kinematics model of 6R manipulators.Based on the structural vectors’decomposition,the general method for modelling 6R decoupling manipulators is proposed,and the decoupling conditions are analyzed,which can be used to derive the analytical inverse kinematics solution of 6R manipulators with three-axis decoupling,offset decoupling and orthogonal decoupling mechanisms.The simulation results show that the solution speed of the proposed method is less than 5.7 ms,the position accuracy is better than 10;m,and the direction accuracy is better than 10;(°).This work is done to effectively deal with the complex configuration of spatial 6R manipulators and meet the requirements of high precision and efficiency.