多切断点分离-重构技术推导非球型手腕6R机器人逆解公式  

Deriving the Inverse Solution Formula of 6R Robot with Non-spherical Wrist with Multi-cut Point Separation and Reconstruction Technique

作　　者：肖帆 曾克俭 XIAO Fan;ZENG Kejian(College of Mechanical Engineering,Hunan University of Technology,Zhuzhou 412007,Hu'nan,China;College of Science and Technology,Hunan University of Technology,Zhuzhou 412007,Hu'nan,China)

机构地区：[1]湖南工业大学机械工程学院,湖南株洲412007 [2]湖南工业大学科技学院,湖南株洲412007

出　　处：《机械科学与技术》2022年第4期559-565,共7页Mechanical Science and Technology for Aerospace Engineering

摘　　要：本文提出一种利用多切断点分解—重构技术求解非球型手腕机器人逆解新方法,简化了该类机器人逆运动学公式的推导过程。首先利用指数积公式的变形,说明了n自由度机器人的可分解性,以及重构连接的通用几何约束;然后以一款手腕前端偏置型机器人为例,给出了针对常见非球型手腕机器人的分解方法及重新连接的几何约束条件。以满足约束条件为目的,得到了只含θ6的非线性封闭方程,以及其它关节角关于θ6的求解公式,推导过程具有更直观的物理几何意义。最后使用二分法求解,算法约2 ms可得到目标位姿所有解,计算位姿误差在10^(−12)mm以内。To simplify the derivation of the inverse solution formula of the 6R robot,firstly,the decompositions of a n-degree-offreedom robot and the general geometric constraints of its reconstructed joints are explained with the deformation of the product of exponential formula based on the screw theory.Then,taking a wrist front offset robot as an example,the decomposition method and the geometric constraints for the reconnection of common non-spherical wrist robots are given.In order to satisfy the constraint conditions,the nonlinear closed equation with onlyθ6 and the solution formula of other joint angles withθ6 are obtained.The derivation process is of more intuitively physical and geometric significance.Finally,the dichotomy method is used to obtain the solution.The algorithm can obtain all the solutions of the target pose at about 2 ms,and the calculated pose error is within 10^(−12)mm.

关 键 词：非球型手腕 工业机器人 指数积公式 逆运动学 非线性封闭方程 

分 类 号：TP242.2[自动化与计算机技术—检测技术与自动化装置]