基于力矩变换的PAA型欠驱动机器人鲁棒镇定控制

doi:10.3969/j.issn.0255-8297.2016.06.014

应用科学学报 ›› 2016, Vol. 34 ›› Issue (6): 789-798.doi: 10.3969/j.issn.0255-8297.2016.06.014

• 控制与系统 • 上一篇

基于力矩变换的PAA型欠驱动机器人鲁棒镇定控制

潘昌忠, 周兰, 周少武, 肖小石

湖南科技大学信息与电气工程学院, 湖南湘潭 411201

收稿日期:2016-03-21 修回日期:2016-07-30 出版日期:2016-11-30 发布日期:2016-11-30
作者简介:潘昌忠,博士,讲师,研究方向:机器人控制、非线性系统控制,E-mail:cpan@hnust.edu.cn
基金资助:
国家自然科学基金（No.61403135，No.51577057，No.61403134）；湖南省教育厅资助项目基金（No.14C0440）资助

Robust Stabilization Control of Underactuated PAA Robot Based on Torque Transformation

PAN Chang-zhong, ZHOU Lan, ZHOU Shao-wu, XIAO Xiao-shi

School of Information and Electrical Engineering, Hunan University of Science and Technology, Xiangtan 411201, Hunan Province, China

Received:2016-03-21 Revised:2016-07-30 Online:2016-11-30 Published:2016-11-30

摘要/Abstract

摘要：

针对在第2 关节和第3 关节仅有两个驱动器的PAA（passive-active-active）型欠驱动三连杆机器人，提出一种基于力矩变换的鲁棒镇定控制方法. 首先对第3 关节的控制输入引入一种与第2 关节控制输入和机器人状态相关的力矩变换，以消除第3 关节控制输入对系统的影响，将机器人动力学方程化为更简单的形式，然后基于能量进行摇起控制设计. 在平衡区，将机器人第1 连杆和第2 连杆的角速度看成一种不确定性，得到机器人在不稳定平衡点附近的不确定模型；然后基于线性矩阵不等式推导鲁棒镇定状态反馈控制律，达到较大范围的平衡控制. 仿真结果表明，该控制方法具有稳定时间短和控制力矩小等优点.

关键词: 欠驱动机器人, 鲁棒控制, 摇起控制, 线性矩阵不等式

Abstract:

Robust stabilization control based on torque transform is proposed for an underactuated three-link manipulator, named a passive-active-active (PAA) robot. It is equipped with only two actuators on the second and third joints. A torque transform,as a function of control input of the second joint and state of the robot,is used for the control input of the third joint. The robot dynamics is transformed to a simpler form,where the influence of control input of the third joint is explicitly eliminated. An energy-based swingup control law is then designed. In the balancing area,an uncertain model is obtained by treating velocities of the first and second links around the unstable equilibrium as uncertainties. A robust stabilizing state feedback control law is derived to reach a large balancing region based on a technique of linear matrix inequality (LMI). Simulation results show that the proposed approach has advantages of short settling time and small control torques.

Key words: swing-up control, linear matrix inequality (LMI), underactuated manipulator, robust control

中图分类号:

TP24

潘昌忠, 周兰, 周少武, 肖小石. 基于力矩变换的PAA型欠驱动机器人鲁棒镇定控制[J]. 应用科学学报, 2016, 34(6): 789-798.

PAN Chang-zhong, ZHOU Lan, ZHOU Shao-wu, XIAO Xiao-shi. Robust Stabilization Control of Underactuated PAA Robot Based on Torque Transformation[J]. Journal of Applied Sciences, 2016, 34(6): 789-798.

参考文献

[1] 赖旭芝,佘锦华,吴敏. 欠驱动机械系统控制[M]. 北京:科学出版社,2013.
[2] Choukchou-Braham A,Cherki B,Djemaï M,Busawon K. Analysis and control of underactuated mechanical systems [M]. Berlin: Springer,2014.
[3] Sun N,Fang Y. New energy analytical results for the regulation of underactuated overhead cranes: an end-effector motion-based approach [J]. IEEE Transactions on Industrial Electronics, 2012,59(12): 4723-4734.
[4] Zhang A,She J,Lai X. Motion planning and tracking control for an acrobot based on a rewinding approach [J]. Automatica,2013,49(1): 278-284.
[5] 徐亚鹏,苏成利,孙小平. 四旋翼无人机飞行姿态的自适应反演滑模控制[J]. 应用科学学报, 2016,34(3): 339-351. Xu Y P,Su C L,Sun X P. Adaptive ackstepping sliding mode approach to flight attitude of quadrotor UAVs [J]. Journal of Applied Sciences,2016,34(3): 339-351. (in Chinese)
[6] 刘海涛,田雪虹,王贵. 高性能欠驱动水面机器人的有限时间跟踪控制[J]. 应用科学学报, 2016,34(2): 203-214. Liu H T,Tian X H,Wang G. Finite-time tracking control of high-performance underactuated USV [J]. Journal of Applied Sciences,2016,34(2): 203-214. (in Chinese)
[7] Spong W. The control of underactuated mechanical system [C]//Proceedings of the 1st International Conference on Mechatronics,Mexico City,Mexico,1994: 1-21.
[8] Mettin U,Hera P L,Freidovich L,Shiriaev A. Generating human-like motions for an underactuated three-link robot based on the virtual constraints approach [C]//Proceedings of the 46th IEEE Conference on Decision and Control,New Orleans,2007: 5138-5143.
[9] 张华,李祖枢,古建功,陈桂强,谭智. 三连杆单杠体操机器人的仿人智能运动控制[J]. 重庆大学学报:自然科学版,2007,32(3): 74-78. Zhang H,Li Z S,Gu J G,Chen G Q,Tan Z. Human simulated intelligence motion control for three-link acrobot on horizontal bar [J]. Journal of Chongqing University: Natural Science,2007,32(3): 74-78. (in Chinese)
[10] Xin X,Kaneda M. Swing-up control for a 3-DOF gymnastic robot with passive first joint: design and analysis [J]. IEEE Transactions on Robotics,2007,23(6): 1277–1285.
[11] Lai X,She J,Yang S,Wu M. Comprehensive unified control strategy for underactuated twolink manipulators [J]. IEEE Transactions on Systems,Man and Cybernetics,Part B,2009,39(2): 389-398.
[12] Lai X,Zhang A,She J,Wu M. Motion control of underactuated three-link gymnast robot based on combination of energy and posture [J]. IET Control Theory and Applications,2011,5(13): 1484-1493.
[13] Lai X,Zhang A,Wu M. Singularity-avoiding swing-up control for underactuated three-link gymnast robot using virtual coupling between control torques [J]. International Journal of Robust and Nonlinear Control,2015,25(2): 207-221.
[14] Lai X Z,Pan C Z,Wu M,Yang S,Cao W H. Control of an underactuated three-link passive– active–active manipulator based on three stages and stability analysis [J]. ASME Journal of Dynamic Systems,Measurement and Control,2015,137(2): 021007(1-9).
[15] 申铁龙. H_∞控制理论与应用[M]. 北京:清华大学出版社,1996.
[16] 赖旭芝,潘昌忠,吴敏. 一类欠驱动机械系统的全局鲁棒控制[J]. 控制与决策,2009,24(7): 1023-1027. Lai X Z,Pan C Z,Wu M. Global robust control of a class of underactuated mechanical systems [J]. Control and Decision,2009,24(7): 1023-1027. (in Chinese)

基于力矩变换的PAA型欠驱动机器人鲁棒镇定控制

Robust Stabilization Control of Underactuated PAA Robot Based on Torque Transformation

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