一种分析四元数及其在6R机械臂逆运动学中的应用

doi:10.3901/JME.2022.09.031

机械工程学报 ›› 2022, Vol. 58 ›› Issue (9): 31-40.doi: 10.3901/JME.2022.09.031

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一种分析四元数及其在6R机械臂逆运动学中的应用

陈菲菲¹, 居鹤华¹, 余萌¹, 康杰¹, 孙帅²

1. 南京航空航天大学航天学院南京 211106;
2. 北京控制工程研究所北京 100190

收稿日期:2021-05-19 修回日期:2021-07-23 出版日期:2022-05-05 发布日期:2022-06-23
通讯作者: 居鹤华(通信作者)，男，1969年出生，博士，教授，博士研究生导师。主要研究方向为自主机器人导航与控制，飞行器设计，空间探测器任务规划与控制
作者简介:陈菲菲，女，1996年出生，博士研究生。主要研究方向为机器人运动学与动力学。E-mail：chenfeifei@nuaa.edu.cn;余萌，男，1988年出生，博士，副教授，硕士研究生导师。主要研究方向为航天器自主导航、任务自主规划。E-mail：yuxy21@nuaa.edu.cn;康杰，男，1993年出生，博士，讲师。主要研究方向为飞行器设计、结构动力学与振动测试。E-mail：kangjie@nuaa.edu.cn;孙帅，男，1989年出生，博士，工程师。主要研究方向为运动控制及仿真技术。E-mail：sunshuai_hitsa@163.com
基金资助:
国家自然科学基金(61673010)和江苏省科研与实践创新计划(KYCX20_0221)资助项目

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

CHEN Feifei¹, JU Hehua¹, YU Meng¹, KANG Jie¹, SUN Shuai²

1. College of Astronautics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016;
2. Beijing Institute of Control Engineering, Beijing 100190

Received:2021-05-19 Revised:2021-07-23 Online:2022-05-05 Published:2022-06-23

摘要/Abstract

摘要： 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。

关键词: 6R机械臂, 逆运动学, 四元数, 方向余弦矩阵

Abstract: 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^-15 m, and the direction accuracy is better than 10^-8(°). This work is done to effectively deal with the complex configuration of spatial 6R manipulators and meet the requirements of high precision and efficiency.

Key words: 6R manipulator, inverse kinematics, quaternion, direction cosine matrix

中图分类号:

TP242

陈菲菲, 居鹤华, 余萌, 康杰, 孙帅. 一种分析四元数及其在6R机械臂逆运动学中的应用[J]. 机械工程学报, 2022, 58(9): 31-40.

CHEN Feifei, JU Hehua, YU Meng, KANG Jie, SUN Shuai. An Analytical Quaternion and its Applications to Inverse Kinematics of 6R Manipulators[J]. Journal of Mechanical Engineering, 2022, 58(9): 31-40.

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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

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