多自由度串联机器人的高效率反向动力学建模方法

摘要/Abstract

摘要：

针对多自由度串联机器人的反向动力学建模问题，通过引入解耦的自然正交补的概念和方法，消除了牛顿-欧拉动力学方程中的约束力项，得到了一种基于解耦的自然正交补的高效反向动力学递推建模方法。编制程序对七自由度串联机器人进行了仿真验证，并将其与牛顿-欧拉递推建模方法进行了对比。结果表明，基于解耦的自然正交补的反向动力学递推建模方法可节省约2/3的CPU计算时间，仿真结果正确、合理，从而验证了该方法的可靠性和高效性。

关键词: 自然正交补, 递推算法, 动力学建模, 串联机器人

Abstract:

To deal with the problem of inverse dynamics modelling for multi-DOF serial robot, a recursive inverse dynamics modelling method was presented based on decoupled natural orthogonal complement. In this model, the concepts and methods of decoupled natural orthogonal complement(DeNOC) matrices were used to eliminate the constraint forces in the Newton-Euler kinematic equations. Finally, a 7-DOF serial robot was simulated by, and the results were compared with those of the recursive Newton-Euler kinematic equations. Simulation results show that the proposed method based on decoupled natural orthogonal complement can save 2/3 amount of CPU time that is spent in computing compared with the traditional approach, and the results is correct and reasonable, which can verify the reliability and efficiency of the method.

Key words: natural orthogonal complement, recursive algorithm, dynamics modeling, serial robot

中图分类号:

TP242

申浩宇, 吴洪涛, 陈柏. 多自由度串联机器人的高效率反向动力学建模方法[J]. 中国机械工程, 2016, 27(01): 20-24.

参考文献

[1]熊有伦. 机器人技术基础[M]. 武汉:华中科技大学出版社, 1996.
[2]吴洪涛，熊有伦. 机械工程中的多体系统动力学问题[J]. 中国机械工程，2000，11(6)：608-611.
Wu Hongtao，Xiong Youlun. The Problem of Multibody Systems Dynamics in Mechanical Engineering[J]. China Mechanical Engineering，2000，11(6)：608-611.
[3]刘树青，王兴松. 基于零空间法的柔性多体系统动力学计算及仿真[J]. 东南大学学报(自然科学版)，2010，40(6)：1348-1352.
Liu Shuqing，Wang Xingsong. Dynamics Calculation and Simulation of Flexible Multi-body System Based on Null-space Method[J]. Journal of Southeast University(Natural Science Edition)，2010，40(6)：1348-1352.
[4]陆震，何广平. 冗余自由度机器人原理及应用[M]. 北京：机械工业出版社，2007.
[5]孙立宁，赵建文，杜志江. 单冗余度机器人避障能力指标的建立及在7自由度冗余手臂上的实践[J].机械工程学报，2007，43(5)：223-229.
Sun Lining，Zhao Jianwen，Du Zhijiang. Concept and Application on 7-DOF Redundant Manipulator of Index to Measure Capability of Collision-avoidance for Single Redundant Manipulator[J]. Chinese Journal of Mechanical Engineering，2007，43(5)：223-229.
[6]孙奎，金明河，谢宗武，等. 一种稳定的冗余度机器人动力学解法[J]. 哈尔滨工业大学学报，2009，41(9)：38-41.
Sun Kui，Jing Minghe，Xie Zongwu，et al. A Stabilized Dynamics Resolution for Redundant Manipulators[J]. Journal of Harbin Institute of Technology，2009，41(9)：38-41.
[7]陈伟海，游贤强，崔翔，等. 绳驱动拟人臂机器人的动力学建模及张力分析[J]. 北京航空航天大学学报，2013，39(3)：335-339.
Chen Weihai，You Xianqiang，Cui Xiang，et al. Dynamics Modeling and Tension Analysis for a Cable-driven Humanoid-arm Robot[J]. Journal of Beijing University of Aeronautics and Astronautics，2013，39(3)：335-339.
[8]Agarwal A，Shah S V，Bandyopadhyay S，et al. Dynamics of Serial Kinematic Chains with Large Number of Degrees-of-freedom[J]. Multibody System Dynamics，2014, 32(3): 273-298.
[9]方喜峰，吴洪涛，刘云平，等. 基于空间算子代数理论计算多体系统动力学建模[J]. 机械工程学报，2009，45(1)：228-234.
Fang Xifeng，Wu Hongtao，Liu Yunping，et al. Computational Dynamics of Multi-body System Modeling Based on Spatial Operator Algebra Theory[J]. Journal of Mechanical Engineering，2009，45(1)：228-234.
[10]Mohan A，Saha S K. A Recursive, Numerically Stable, and Efficient Simulation Algorithm for Serial Robots with Flexible Links[J]. Multibody System Dynamics，2009，21(1)：1-35.
[11]邵兵，吴洪涛，程世利，等. 基于李群李代数的主被动关节机器人动力学及控制[J]. 中国机械工程，2010，21(3)：253-257.
Shao Bing，Wu Hongtao，Cheng Shili，et al. Dynamics and Control of Robot with Active and Passive Joints Using Lie Groups and Lie Algebras[J]. China Mechanical Engineering，2010，21(3)：253-257.
[12]黄玉钏，曲道奎，徐方. 基于自然正交补的真空机器人动力学建模[J]. 机器人，2012，34(6)：730-736.
Huang Yuchuan，Qu Daokui，Xu Fang. Dynamic Modeling of Vacuum Robots Based on Natural Orthogonal Complement[J]. Robot，2012，34(6)：730-736.
[13]Angeles J，Lee S K. The Formulation of Dynamical Equations of Holonomic Mechanical Systems Using a Natural Orthogonal Complement[J]. Journal of Applied Mechanics，1988，55(1)：243-244.
[14]Angeles J. 机器人机械系统原理: 理论、方法和算法[M]. 宋伟刚，译. 北京：机械工业出版社，2004.
[15]Saha S K. Dynamics of Serial Multibody Systems Using the Decoupled Natural Orthogonal Complement Matrices[J]. Journal of Applied Mechanics，1999，66(4)：986-996.
[16]Saha S K. Recursive Dynamics Algorithms for Serial, Parallel, and Closed-chain Multibody Systems[C]//Indo-US Workshop on Protein Kinematics & Protein Conformations. Bangalore，2007：10-11.
[17]Shah S V，Saha S K，Dutt J K. Dynamics of Tree-type Robotic Systems[M]. Dordrecht: Springer, 2013.