Position Control of a Planar Three-link Underactuated Mechanical System Based on Model Reduction
-
摘要: 针对第一关节为被动的平面三连杆欠驱动机械系统,提出一种基于模型降阶的位置控制方法. 首先,建立平面三连杆欠驱动系统数学模型,并分析其积分特性;其次,将部分可积的三连杆系统分段降阶为两个完全可积的两连杆子系统,并基于两子系统获得系统驱动杆与欠驱动杆之间的状态约束关系;然后,利用粒子群优化算法,根据系统末端点目标位置计算驱动杆目标角度;最后,分别设计两连杆子系统控制器,实现系统从任意初始位置到任意目标位置的控制目标. 仿真结果验证所提控制策略的有效性.
-
关键词:
- 平面欠驱动机械系统 /
- 模型降阶 /
- 位置控制 /
- 粒子群优化算法 /
- Lyapunov函数
Abstract: This paper presents a position control method based on model reduction for a planar three-link passive-active-active (PAA) under-actuated mechanical system with a passive first joint. Firstly, a mathematical model of the system is built, and its integral characteristic is analyzed. Next, the partially integrable three-link system is reduced to two completely integrable two-link systems by the method of piecewise degree reduction, and the state constraint relationships of the system between the active link and the passive link can be obtained based on the two subsystems. Then, the target angles of the active links are calculated by particle swarm optimization (PSO) algorithm according to the target position of the end of the system. Finally, the controllers of the two link subsystems are designed respectively to achieve the system control objective from any initial position to any target position. Simulation results demonstrate the validity of the proposed control method. -
[1] Lai X Z, Pan C Z, Wu M, Yang S X. Unified control of n-link underactuated manipulator with single passive joint: a reduced order approach. Mechanism and Machine Theory, 2012, 56(12): 170-185 [2] Huang Jing, Li Chuan-Jiang, Ma Guang-Fu, Liu Gang. Generalised inversion based maneuver attitude control for underactuated spacecraft. Acta Automatica Sinica, 2013, 39(3): 285-292(黄静, 李传江, 马广富, 刘刚. 基于广义逆的欠驱动航天器姿态机动控制. 自动化学报, 2013, 39(3): 285-292) [3] Xin X, She J H, Yamasaki T, Liu YN. Swing-up control based on virtual composite links for n-link underactuated robot with passive first joint. Automatica, 2009, 45(9): 1986-1994 [4] Zhang An-Cai, Lai Xu-Zhi, She Jin-Hua, Wu Min. Stabilization control of underactuated acrobot based on inverse method. Acta Automatica Sinica, 2012, 38(8): 1263-1269(张安彩, 赖旭芝, 佘锦华, 吴敏. 基于倒转方法的欠驱动Acrobot系统稳定控制. 自动化学报, 2012, 38(8): 1263-1269) [5] Chen Wei, Yu Yue-Qing, Zhang Xu-Ping, Su Li-Ying. Vibration controllability of underactuated flexible manipulator. Acta Automatica Sinica, 2007, 33(4): 391-398(陈炜, 余跃庆, 张绪平, 苏丽颖. 欠驱动柔性机器人的振动可控性分析. 自动化学报, 2007, 33(4): 391-398) [6] Luca A D, Mattone R, Oriolo G. Stabilization of an underactuated planar 2R manipulator. International Journal of Robust and Nonlinear Control, 2000, 10(4): 181-198 [7] Akbarimajd A, Kia S. NARMA-L2 controller for 2-DOF underactuated planar manipulator. In: Proceedings of the 11th International Conference on Control Automation Robotics and Vision. Singapore: IEEE, 2010. 195-200 [8] Alfredo J R F, Jaime A G, Rafael C L. Trajectory planning and control of an underactuated planar 2R manipulator. In: Proceedings of the 2001 IEEE International Conference on Control Applications. Mexico City, Mexico: IEEE, 2011. 548-552 [9] Mahindrakar A D, Banavar R N, Reyhanoglu M. Controllability and point-to-point control of 3-DOF planar horizontal underactuated manipulators. International Journal of Control, 2005, 78(1): 1-13 [10] Mahindrakar A D, Banavar R N. Controllability properties of a planar 3R underactuated manipulator. In: Proceedings of the 2002 IEEE International Conference on Control Applications. Glasgow, Scotland, UK: IEEE, 2002. 489-494 [11] Luca A D, Iannitti S, Mattone R, Oriolo G. Underactuated manipulators: control properties and techniques. Machine Intelligence and Robotic Control, 2002, 4(3): 113-125 [12] Oriolo G, Nakamura Y. Control of mechanical systems with second-order nonholonomic constraints: underactuated manipulators. In: Proceedings of the 30m th Conference on Decision and Control. Brighton, England: IEEE, 1991. 2398-2403 [13] Cao S Q, Lai X Z, Wu M. Motion control method of planar acrobot based on trajectory characteristics. In: Proceedings of the 31m st Chinese Control Conference. Hefei, China: IEEE, 2012. 4910-4915 [14] Shi Y H, Eberhart R. A modified particle swarm optimizer. In: Proceedings of the 1998 IEEE World Congress on Computational Intelligence. Anchorage, AK: IEEE, 1998. 69-73
点击查看大图
计量
- 文章访问数: 1731
- HTML全文浏览量: 80
- PDF下载量: 794
- 被引次数: 0