基于倒转方法的欠驱动 Acrobot 系统稳定控制

张安彩; 赖旭芝; 佘锦华; 吴敏

doi:10.3724/SP.J.1004.2012.01263

基于倒转方法的欠驱动 Acrobot 系统稳定控制

doi: 10.3724/SP.J.1004.2012.01263

张安彩^1,2,
赖旭芝^1,2,,
佘锦华³,
吴敏^1,2

1.
中南大学信息科学与工程学院长沙 410083, 中国;
2.
先进控制与智能自动化湖南省工程实验室长沙 410083, 中国;
3.
东京工科大学计算机科学学部东京 192-0982, 日本

详细信息

通讯作者:
赖旭芝

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- 被引次数: 0
出版历程
- 收稿日期: 2011-12-02
- 修回日期: 2012-03-21
- 刊出日期: 2012-08-20

Stabilization Control of Underactuated Acrobot Based on Inverse Method

ZHANG An-Cai^1,2,
LAI Xu-Zhi^{1,2
,},
SHE Jin-Hua³,
WU Min^1,2

1.
School of Information Science and Engineering, Central South University, Changsha 410083, P.R.China;
2.
Hunan Engineering Laboratory for Advanced Control and Intelligent Automation, Changsha 410083, P.R.China;
3.
School of Computer Science, Tokyo University of Technology, Tokyo 192-0982, Japan

摘要

摘要: 针对欠驱动两杆体操机器人Acrobot, 提出一种新的稳定控制方法.首先,通过利用一个虚拟摩擦力矩为Acrobot 构造一条下摆轨迹;然后,运用倒转的思想为它设计出一条由垂直向下位置到垂直向上位置的期望运动轨迹, 并以此将系统的稳定控制问题转化为跟踪控制问题;最后, 基于最优控制理论来设计跟踪控制器,使Acrobot 能够沿期望轨迹渐近稳定在垂直向上位置处. 仿真结果验证了所提方法的有效性.
- 欠驱动Acrobot /
- 稳定控制 /
- 李雅普诺夫函数 /
- 倒转 /
- 黎卡提方程
Abstract: This paper presents a new method of stabilizing an underactuated two-link gymnast robot, Acrobot. First, an artificial friction torque is used to construct a falling-down motion trajectory. Next, we design a reference motion trajectory for the Acrobot from the straight-down position to the straight-up position based on an inverse idea. This transforms the problem of stabilizing the Acrobot into a tracking control problem. Finally, we use the knowledge of optimal control to design a tracking controller, which enables the Acrobot to be asymptotically stabilized at the straight-up position along the desired trajectory. Simulation results demonstrate the validity of our method.
- Underactuated Acrobot /
- stabilization control /
- Lyapunov function /
- inverse /
- Riccati equation

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参考文献(1)

[1]

Grizzle J W, Moog C H, Chevallereau C. Nonlinear control of mechanical systems with an unactuated cyclic variable. IEEE Transactions on Automatic Control, 2005, 50(5): 559 -576[2] Jia He-Ming, Zhang Li-Jun, Cheng Xiang-Qin, Bian Xin-Qian, Yan Zhe-Ping, Zhou Jia-Jia. Three-dimensional path following control for an underactuated UUV based on nonlinear iterative sliding mode. Acta Automatica Sinica, 2012, 38(2): 308-314 (贾鹤鸣, 张利军, 程相勤, 边信黔, 严浙平, 周佳加. 基于非线性迭代滑模的欠驱动 UUV 三维航迹跟踪控制. 自动化学报, 2012, 38(2): 308-314)[3] Kotyczka P. Local linear dynamics assignment in IDA-PBC for underactuated mechanical systems. In: Proceedings of the 50th IEEE Conference on Decision and Control and European Control Conference. Orlando, FL, USA: IEEE, 2011. 6534-6539[4] Cheng Hong-Tai, Zhao Yi-Ni, Zhang Xiao-Hua. Dynamical servo control and symmetrical virtual constraints method for the Acrobot. Acta Automatica Sinica, 2010, 36(11): 1594-1600 (程红太, 赵旖旎, 张晓华. Acrobot 动态伺服控制及其对称虚约束方法研究. 自动化学报, 2010, 36(11): 1594-1600)[5] Oriolo G, Nakamura Y. Control of mechanical systems with second-order nonholonomic constraints: underactuated manipulators. In: Proceedings of the 30th IEEE Conference on Decision and Control. Brighton, UK: IEEE, 1991. 2398-2403[6] Spong M W. The swing up control problem for the Acrobot. IEEE Control Systems Magazine, 1995, 15(1): 49-55[7] Lai X Z, She J H, Yang S X, Wu M. Comprehensive unified control strategy for underactuated two-link manipulators. IEEE Transactions on Systems, Man, and Cybernetics —Part B: Cybernetics, 2009, 39(2): 389-398[8] Lai X Z, She J H, Ohyama Y, Cai Z. Fuzzy control strategy for Acrobots combining model-free and model-based control. IEE Proceedings —Control Theory and Applications, 1999, 146(6): 505-510[9] Lai Xu-Zhi, Wu Min, She Jin-Hua, Yang Simon X. Controller design and global stability analysis of Acrobot. Acta Automatica Sinica, 2007, 33(7): 719-725 (赖旭芝, 吴敏, 佘锦华, Yang Simon X. Acrobot 控制器设计与全局稳定性分析. 自动化学报, 2007, 33(7): 719-725)[10] Willson S S, Mullhaupt P, Bonvin D. Quotient method for controlling the Acrobot. In: Proceedings of the 48th IEEE Conference on Decision and Control. Shanghai, China: IEEE, CDC/CCC 2009. 1770-1775[11] Olfati-Saber R. Control of underactuated mechanical systems with two degrees of freedom and symmetry. In: Proceedings of the 2000 American Control Conference. Chicago, USA: IEEE, 2000. 4092-4096[12] Khalil H K. Nonlinear Systems (Third edition). New Jersey, USA: Prentice Hall, 2002. 191-195

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