空间6R串联机器人机构位置逆解新算法

黄昔光; 廖启征

空间6R串联机器人机构位置逆解新算法

黄昔光¹,
廖启征²

1.
北方工业大学机电工程学院, 北京 100041
2. 北京邮电大学自动化学院, 北京

基金项目: 国家自然科学基金资助项目(50775012); 北京市属院校人才强教计划资助项目; 北京市特色专业建设资助项目; 北方工业大学校科研基金资助项目

详细信息

作者简介:
黄昔光(1979-),男,湖南岳阳人,讲师,huangxiguang@gmail.com.

中图分类号: TH 112
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出版历程
- 收稿日期: 2009-03-05
- 网络出版日期: 2010-03-31

New algorithm for inverse kinematics of 6R serial robot mechanism

Huang Xiguang¹,
Liao Qizheng²

1.
School of Mechanical and Electrical Engineering, North China University of Technology, Beijing 100041, China
2. School of Automation, Beijing University of Posts and Telecommunications, Beijing 100876, China

摘要

摘要: 将倍四元数的复指数形式应用于串联机构位置逆解分析中,提出了空间6R(R代表转动副)串联机构位置逆解新算法.基于倍四元数建立了空间6R串联机构位置逆解的数学模型;然后,使用线性消元和Dixon结式消元法,得到了6×6的结式;由于采用未知转角的复指数形式,不需要提取任何公因式,可直接获得该机构位置逆解的一元16次输入输出方程和全部16组封闭解.最后通过数字实例证明了该方法无增根无漏根.算例表明算法简洁,易于程序实现,为串联机构位置逆解分析提供了新的理论基础.
- 串联机构 /
- 倍四元数 /
- 位置逆解
Abstract: The theory of double quaternions and its application in the inverse kinematics of serial mechanisms was introduced. A new algorithm for the inverse kinematics of 6R mechanisms was presented based on the complex exponent form of double quaternions. Based on double quaternions, a mathematical model of 6R mechanisms was created. Then, a 6×6 resultant matrix was obtained directly by using linear elimination and Dixon resultant method, without factoring out or deriving the greatest common divisor, due to the proposed algorithm used the complex exponent form of double quaternions. A 16th degree univariate equation was achieved from the determinant of the matrix and all 16 closed-form solutions were also obtained. The proposed algorithm is comparably easy and simple to program. It was verified by a numerical example that the obtained roots satisfy the original equations. The research result provides a new method for the inverse kinematics of serial mechanisms.
- serial mechanism /
- double quaternions /
- inverse kinematics

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参考文献(1)

[1] Duffy J.Analysis of mechanisms and robot manipulators[M]．London:Edwart Arnold Ltd,1980 [2] 廖启征,梁崇高,张启先．空间7R机构位移分析的新研究[J]．机械工程学报,1986,22(3):1-5 Liao Qizheng,Liang Chonggao,Zhang Qixian．New research of displacement analysis of spatial 7R mechanism[J]．Chinese Journal of Mechanical Engineering,1986,22(3):1-5(in Chinese) [3] 赵杰,王卫忠,蔡鹤皋．可重构机器人封闭形式的运动学逆解计算[J]．机械工程学报,2006,42(8):210-214 Zhao Jie,Wang Weizhong,Cai Hegao．Generation of closed-form inverse kinematics for reconfigurable robots[J]．Chinese Journal of Mechanical Engineering,2006,42(8):210-214(in Chinese) [4] Etzel K R, McCarthy J M．A metric for spatial displacement using biquaternions on SO(4) //Proceedings of IEEE International Conference on Robotics and Automation．Piscataway,NJ:IEEE,1996:3185-3190 [5] Geng Q J, Varshney A, Menon J P,et al．Double quaternions for motion interpolation //Proceedings of the ASME DETC’98．Atlanta:ASME,1998:13-16 [6] McCarthy J M．Mechanisms synthesis theory and the design of robots //Proceedings of IEEE International Conference on Robotics and Automation．San Francisco,CA:IEEE,2000:24-28 [7] 乔曙光．6自由度串联机械手位置逆解新方法．北京:北京邮电大学自动化学院,2008 Qiao Shuguang．New algorithm for inverse kinematics of 6 DOF serial manipulator ．Beijing:School of Automation,Beijing University of Posts and Telecommunications,2008(in Chinese) [8] Clifford W K.A preliminary sketch of biquaternions //Tucker R.Mathematical Papers．London:London Mathematical Society,1882:658 [9] 于艳秋,王品,廖启征．一般6R机器人位置反解与运动仿真[J]．中国机械工程,2003,14(24):2130-2132 Yu Yanqiu,Wang Pin,Liao Qizheng．Forward kinematics analysis of general 6R robot and its simulation[J]．China Mechanical Engineering,2003,14(24):2130-2132(in Chinese)

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