Vex4冗余驱动并联机构的动力学建模、力优化及力位混合控制

doi:10.3901/JME.2022.23.065

机械工程学报 ›› 2022, Vol. 58 ›› Issue (23): 65-74.doi: 10.3901/JME.2022.23.065

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Vex4冗余驱动并联机构的动力学建模、力优化及力位混合控制

王耀军^1,2, 张海峰¹, 李秦川¹

1. 浙江理工大学机械与自动控制学院杭州 310018;
2. 浙江机电职业技术学院杭州 310053

收稿日期:2021-08-10 修回日期:2021-11-25 出版日期:2022-12-05 发布日期:2023-02-08
通讯作者: 李秦川(通信作者),男,1975年出生,博士,教授,博士研究生导师。主要研究方向为并联机器人机构学与应用技术。E-mail:lqchuan@zstu.edu.cn
作者简介:王耀军,男,1977年出生,博士研究生,副教授。主要研究方向为并联机器人建模与控制。E-mail:yaojunw@vip.163.com;张海峰,男,1996年出生,博士研究生。主要研究方向为并联机器人运动控制。E-mail:zhanghf5688@163.com
基金资助:
国家自然科学基金(51935010)和浙江省自然科学基金(LQ19E050015)资助项目。

Dynamics Modeling, Force Optimization and Force/Position Hybrid Control for a Vex4 Redundantly Actuated Parallel Robot

WANG Yaojun^1,2, ZHANG Haifeng¹, LI Qinchuan¹

1. Faculty of Mechanical Engineering and Automation, Zhejiang Sci-Tech University, Hangzhou 310018;
2. Zhejiang Institute of Mechanical and Electrical Engineering, Hangzhou 310053

Received:2021-08-10 Revised:2021-11-25 Online:2022-12-05 Published:2023-02-08

摘要/Abstract

摘要： 并联机构引入冗余驱动可消除机构奇异位型，提高刚度和负载能力。但冗余驱动造成驱动力求解不唯一，可能引起内力对抗，造成能量损耗甚至机构损坏。因此冗余驱动并联机构的动力学建模与控制必须考虑驱动力分配和优化。应用自然正交补(NOC)法对Vex4三自由度冗余驱动并联机构进行动力学建模，采用右Moore-Penrose广义逆矩阵通过QR分解转置系数矩阵得到最小驱动力优化解。为平衡驱动力并跟踪轨迹，在力位混合即非冗余支链位置控制、冗余支链力(矩)控制基础上，采用动力学差分提出一种位控、力控支链驱动力同步优化方法，设计同步优化力位混合控制器实现轨迹跟踪控制。搭建Vex4冗余驱动并联机构样机开展轨迹跟踪试验，验证了所提优化和控制方法的有效性。

关键词: 冗余驱动, 自然正交补, 并联机构, 同步优化, 力位混合控制

Abstract: Introducing actuation redundancy in parallel kinematic machines can avoid singularities, improve stiffness and load. Redundant actuation, however, poses challenges to dynamics modeling and controller designing regarding internal force distribution and optimization. In order to solve the above problems, taking a Vex4 3-DOF parallel robot as an example, dynamics model is established based on the natural orthogonal complement method. Then, by resorting to the right Moore-Penrose generalized inverse, the solution of the minimum-actuating-force is obtained based on QR decomposition of coefficient matrix. To balance actuator-force and track trajectory, a synchronous optimization method is first proposed and then integrated into a force-position hybrid controller with non-redundant branch controlled by position law and redundant branch by force law. Finally, a prototype of Vex4 is built to test and verify the proposed modeling and controller designing approach.

Key words: actuation redundancy, natural orthogonal complement, parallel manipulator, synchronous optimization, force-position hybrid control

中图分类号:

TH113

王耀军, 张海峰, 李秦川. Vex4冗余驱动并联机构的动力学建模、力优化及力位混合控制[J]. 机械工程学报, 2022, 58(23): 65-74.

WANG Yaojun, ZHANG Haifeng, LI Qinchuan. Dynamics Modeling, Force Optimization and Force/Position Hybrid Control for a Vex4 Redundantly Actuated Parallel Robot[J]. Journal of Mechanical Engineering, 2022, 58(23): 65-74.

参考文献

[1] WANG Yaojun,BELZILE B,ANGELES J,et al. Kinematic analysis and optimum design of a novel 2PUR-2RPU parallel robot[J]. Mechanism and Machine Theory,2019,139:407-423.
[2] SICILIANO B,KHATIB O. Springer handbook of robotics[M]. Berlin:Springer,2016.
[3] CHENG Chen,XU Weiliang,SHANG Jianzhong. Optimal distribution of the actuating torques for a redundantly actuated masticatory robot with two higher kinematic pairs[J]. Nonlinear Dynamics,2015,79(2):1235-1255.
[4] SAGLIA J A,DAI J S,CALDWELL D G. Geometry and kinematic analysis of a redundantly actuated parallel mechanism that eliminates singularities and improves dexterity[J]. Journal of Mechanical Design,2008,130(12):124501.
[5] PHAM Q C,STASSE O. Time-optimal path parameterization for redundantly actuated robots:A numerical integration approach[J]. IEEE/ASME Transactions on Mechatronics,2015,20(6):3257-3263.
[6] MULLER A. Consequences of geometric imperfections for the control of redundantly actuated parallel manipulators[J]. IEEE Transactions on Robotics,2009,26(1):21-31.
[7] VALASEK M,BAUMA V,BELDA K,et al. Design-by-optimization and control of redundantly actuated parallel kinematics sliding star[J]. Multibody System Dynamics,2005,14(3):251-267.
[8] PARIKH P J,LAM S S. Solving the forward kinematics problem in parallel manipulators using an iterative artificial neural network strategy[J]. The International Journal of Advanced Manufacturing Technology,2009,40(5-6):595-606.
[9] KIM J,PARK F C,RYU S J,et al. Design and analysis of a redundantly actuated parallel mechanism for rapid machining[J]. IEEE Transactions on Robotics and Automation,2001,17(4):423-434.
[10] WANG Liping,WU Jun,WANG Jinsong,et al. An experimental study of a redundantly actuated parallel manipulator for a 5-DOF hybrid machine tool[J]. IEEE/ASME Transactions on Mechatronics,2009,14(1):72-81.
[11] WU Jun,WANG Jinsong,LI Tiemin,et al. Performance analysis and application of a redundantly actuated parallel manipulator for milling[J]. Journal of Intelligent and Robotic Systems,2007,50(2):163-180.
[12] WEN Shuhuan,YU Haiyang,ZHANG Baowei,et al. Fuzzy identification and delay compensation based on the force/position control scheme of the 5-DOF redundantly actuated parallel robot[J]. International Journal of Fuzzy Systems,2017,19(1):124-140.
[13] CHAI Xinxue,ZHANG Ningbin,HE Leiying,et al. Kinematic sensitivity analysis and dimensional synthesis of a redundantly actuated parallel robot for friction stir welding[J]. Chinese Journal of Mechanical Engineering,2020,33(1):1-10.
[14] CHENG H,LIU G F,YIU Y K,et al. Advantages and dynamics of parallel manipulators with redundant actuation[C]//Proceedings 2001 IEEE/RSJ International Conference on Intelligent Robots and Systems. Expanding the Societal Role of Robotics in the the Next Millennium,Maui,HI,USA,29 Oct.-3 Nov.,2001:171-176.
[15] LIU G F,WU Y L,WU X Z,et al. Analysis and control of redundant parallel manipulators[C]//Proceedings 2001 ICRA. IEEE International Conference on Robotics and Automation. Seoul,Korea,21-26 May,2001:3748-3754.
[16] GOSSELIN C,SCHREIBER L T. Redundancy in parallel mechanisms:A review[J]. Applied Mechanics Reviews,2018,70(1):010802.
[17] CHEN Genliang,YU Weidong,LI Qinchuan,et al. Dynamic modeling and performance analysis of the 3-P RRU 1T2R parallel manipulator without parasitic motion[J]. Nonlinear Dynamics,2017,90(1):339-353.
[18] KANE T R,LEVINSON D A. The use of Kane's dynamical equations in robotics[J]. The International Journal of Robotics Research,1983,2(3):3-21.
[19] THOMAS M J,JOY M L,SUDHEER A P. Kinematic and dynamic analysis of a 3-PR US spatial parallel manipulator[J]. Chinese Journal of Mechanical Engineering,2020,33(1):1-17.
[20] TSAI L W. Solving the inverse dynamics of a Stewart-Gough manipulator by the principle of virtual work[J]. Journal of Mechanical Design,2000,122(1):3-9.
[21] 柴馨雪,杨泳,徐灵敏,等. 2-UPR-RPU并联机器人的动力学建模与性能分析[J]. 机械工程学报,2020,56(13):110-119. CHAI Xinxue,YANG Yong,XU Lingmin,et al. Dynamic modeling and performance analysis of a 2-UPR-RPU parallel manipulator[J]. Journal of Mechanical Engineering,2020,56(13):110-119.
[22] CHENG Hui,YIU Y K,LI Zexiang. Dynamics and control of redundantly actuated parallel manipulators[J]. IEEE/ASME Transactions on Mechatronics,2003,8(4):483-491.
[23] MILLER K. Optimal design and modeling of spatial parallel manipulators[J]. The International Journal of Robotics Research,2004,23(2):127-140.
[24] WANG Yaojun,BELZILE B,ANGELES J,et al. The modeling of redundantly actuated mechanical systems[J]. Journal of Mechanisms and Robotics,2019,11(6):061005.
[25] MULLER A. Internal preload control of redundantly actuated parallel manipulators-its application to backlash avoiding control[J]. IEEE Transactions on Robotics,2005,21(4):668-677.
[26] MULLER A,HUFNAGEL T. Model-based control of redundantly actuated parallel manipulators in redundant coordinates[J]. Robotics and Autonomous Systems,2012,60(4):563-571.
[27] WEN Shuhuan,HU Xueheng,ZHANG Baowei,et al. Fractional-order internal model control algorithm based on the force/position control structure of redundant actuation parallel robot[J]. International Journal of Advanced Robotic Systems,2020,17(1):1729881419892143.
[28] SHANG Weiwei,CONG Shuang. Robust nonlinear control of a planar 2-DOF parallel manipulator with redundant actuation[J]. Robotics and Computer Integrated Manufacturing,2014,30(6):597-604.
[29] HARANDI M R J,KHALIL P S,TAGHIRAD H D,et al. Adaptive control of parallel robots with uncertain kinematics and dynamics[J]. Mechanical Systems and Signal Processing,2021,157:107693.
[30] SHANG Weiwei,ZHANG Bin,CONG Shuang,et al. Dual-space adaptive synchronization control of redundantly-actuated cable-driven parallel robots[J]. Mechanism and Machine Theory,2020,152:103954.
[31] LIU Shiwei,PENG Gaoliang,GAO Huijun. Dynamic modeling and terminal sliding mode control of a 3-DOF redundantly actuated parallel platform[J]. Mechatronics,2019,60:26-33.
[32] LIU Xiaofei,YAO Jiantao,LI Qi,et al. Coordination dynamics and model-based neural network synchronous controls for redundantly full-actuated parallel manipulator[J]. Mechanism and Machine Theory,2021,160:104284.
[33] GOLUB G H,CHARLES F,VAN L. Matrix computations[M]. Baltimore:JHU Press,2012.
[34] MERLET J P. Parallel robots[M]. Dordrecht,The Netherlands:Springer Science & Business Media,2005.
[35] ANGELES J. Fundamentals of robotic mechanical systems:Theory,methods,and algorithms[M]. Cham,Switzerland:Spinger,2014.
[36] 卿建喜,李剑锋,方斌. 冗余驱动Tricept并联机构的驱动优化[J]. 机械工程学报,2010,46(5):8-14. QING Jianxi,LI Jianfeng,FANG Bin. Drive optimization of Tricept parallel mechanism with redundant actuation[J]. Journal of Mechanical Engineering,2010,46(5):8-14.
[37] 吴军,李铁民,王立平. 驱动冗余并联机床的性能分析与控制[M]. 北京:科学出版社,2019. WU Jun,LI Tiemin,WANG Liping. Performance analysis and control of redundantly actuated parallel kinematic machines[M]. Beijing:Science Press,2019.

Vex4冗余驱动并联机构的动力学建模、力优化及力位混合控制

Dynamics Modeling, Force Optimization and Force/Position Hybrid Control for a Vex4 Redundantly Actuated Parallel Robot

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