A Speed Observer for Robot Based on Hamiltonian Theory and Immersion & Invariance
-
摘要: 近期, Astolfi和Stamnes等对一类机械系统设计了速度观测器. 采用了分步设计Lyapunov 函数的方法, 这导致观测误差系统结构复杂、 证明繁琐. 而且设计的偏微分方程(Partial differential equation, PDE) 不合理, 导致计算量大、不易求解. 本文在Astolfi和Stamnes等的基础上, 对一类机械(机器人) 系统设计了速度观测器. 通过对观测误差系统的Hamiltonian 实现, 克服了Astolfi和Stamnes等方法中的上述缺点. 并设计了一类偏微分方程, 避免了繁琐计算. 最后, 将所设计的速度观测器应用到一类关节机器人中, 仿真结果验证了设计方法的有效性.
-
关键词:
- 观测器 /
- 浸入与不变流形 /
- Hamiltonian /
- 机器人
Abstract: Recently, a speed observer for general Euler-Lagrange systems adopting the step by step design of the Lyapunov function was proposed, which makes the structure of the observer error systems complex and the proof complicated. Also, the computation is very intensive for the unreasonable design of the partial differential equation (PDE). In this paper, the speed observer for a mechanical system based on the aforementioned is designed. By the Hamiltonian realization of the observer error systems, we remove the obstacle the observer. What is more, the problem of the computational burden by designing the PDE is solved. At last, the designed observer is applied to estimation of the angular velocities in a robot.-
Key words:
- Observer /
- immersion and invariance (I & /
- I) /
- Hamiltonian
-
[1] Yin Feng, Wang Yao-Nan, Wei Shu-Ning. Inverse kinematic solution for robot manipulator based on electromagnetism-like and modified DFP algorithms. Acta Automatica Sinica, 2011, 37(1): 74-82(印峰, 王耀南, 魏书宁. 基于类电磁和改进DFP算法的机械手逆运动学计算. 自动化学报, 2011, 37(1): 74-82)[2] Zhao Dong-Ya, Li Shao-Yuan, Gao Feng. Decentralized robust nonlinear control for six-degrees-of-freedom parallel robots. Control Theory Applications, 2008, 25(5): 867-872 (赵东亚, 李少远, 高峰. 六自由度并联机器人分散鲁棒非线性控制. 控制理论与应用, 2008, 25(5): 867-872)[3] Astolfi A, Karagiannis D, Ortega R. Nonlinear and Adaptive Control with Applications. Berlin: Springer-Verlag, 2008. 91-114[4] Nicosia S, Tomei P. Robot control by using only joint position measurements. IEEE Transactions on Automatic Control, 1990, 35(9): 1058-1061[5] Venkatraman A, Ortega R, Sarras I, Van der Schaft A J. Speed observation and position feedback stabilization of partially linearizable mechanical systems. IEEE Transactions on Automatic Control, 2010, 55(5): 1059-1074[6] Venkatraman A, Van der Schaft A J. Full-order observer design for a class of port-Hamiltonian systems. Automatica, 2010, 46(3): 555-561[7] Yin Zheng-Nan, Su Jian-Bo, Liu Yan-Tao. Design of disturbance observer with robust performance based on H∞ norm optimization. Acta Automatica Sinica, 2011, 37(3): 331-341 (尹正男, 苏剑波, 刘艳涛. 基于H∞范数优化的干扰观测器的鲁棒设计. 自动化学报, 2011, 37(3): 331-341)[8] Wu Ai-Guo, Duan Guang-Ren. Dual Luenberger observer design for linear systems. Control Theory Applications, 2008, 25(3): 583-586(吴爱国, 段广仁. 线性系统对偶Luenberger 观测器设计. 控制理论与应用, 2008, 25(3): 583-586)[9] Aghannan N, Rouchon P. An intrinsic observer for a class of Lagrangian systems. IEEE Transactions on Automatic Control, 2003, 48(6): 936-945[10] Bonnabel S, Martin P, Rouchon P. Symmetry-preserving observers. IEEE Transactions on Automatic Control, 2008, 53(11): 2514-2526[11] Xian B, de Queiroz M S, Dawson D M, McIntyre M L. A discontinuous output feedback controller and velocity observer for nonlinear mechanical systems. Automatica, 2004, 40(4): 695-700[12] Su Y X, Muller P C, Zhang C H. A simple nonlinear observer for a class of uncertain mechanical systems. IEEE Transactions on Automatic Control, 2007, 52(7): 1340-1345[13] Karagiannis D, Carnevale D, Astolfi A. Invariant manifold based reduced-order observer design for nonlinear systems. IEEE Transactions on Automatic Control, 2008, 53(11): 2602-2614[14] Astolfi A, Ortega R. Immersion and invariance: a new tool for stabilization and adaptive control of nonlinear systems. IEEE Transactions on Automatic Control, 2003, 48(4): 590-606[15] Astolfi A, Ortega R, Venkatraman A. A globally exponentially convergent immersion and invariance speed observer for mechanical systems with non-holonomic constraints. Automatica, 2010, 46(1): 182-189[16] Stamnes N, Aamo O M, Kaasa G O. A constructive speed observer design for general Euler-Lagrange systems. Automatica, 2011, 47(10): 2233-2238[17] Astolfi A, Ortega R, Venkatraman A. A globally exponentially convergent immersion and invariance speed observer for n degrees of freedom mechanical systems. In: Proceedings of the 48th Conference on Decision and Control. Shanghai, China: IEEE, 2009. 6508-6513[18] Karagiannis D, Astolfi A. Observer design for a class of nonlinear systems using dynamic scaling with application to adaptive control. In: Proceedings of the 47th Conference on Decision and Control. Cancun, Mexico: IEEE, 2008. 2314-2319[19] Karagiannis D, Sassano M, Astolfi A. Dynamic scaling and observer design with application to adaptive control. Automatica, 2009, 45(12): 2883-2889[20] Sassano M, Carnevale D, Astolfi A. Observer design for range and orientation identification. Automatica, 2010, 46(8): 1369-1375[21] Wang Y Z, Li C W, Cheng D Z. Generalized Hamiltonian realization of time-invariant nonlinear systems. Automatica, 2003, 39(8): 1437-1443[22] Liu Yan-Hong, Li Chun-Wen, Wang Yu-Zhen. Decentralized excitation control of multi-machine multi-load power systems using Hamiltonian function method. Acta Automatica Sinica, 2009, 35(7): 919-925 (刘艳红, 李春文, 王玉振. 基于Hamilton函数方法的多机多负荷电力系统分散励磁控制. 自动化学报, 2009, 35(7): 919-925)[23] Wang Y Z, Cheng D Z, Ge S S. Approximate dissipative Hamiltonian realization and construction of local Lyapunov functions. Systems and Control Letters, 2007, 56(2): 141-149[24] Wang Y Z, Cheng D Z, Hu X M. Problems on time-varying port-controlled Hamiltonian systems: geometric structure and dissipative realization. Automatica, 2005, 41(4): 717-723[25] Xi Z R, Cheng D Z, Lu Q, Mei S W. Nonlinear decentralized controller design for multimachine power systems using Hamiltonian function method. Automatica, 2002, 38(3): 527-534[26] Van der Schaft A J. L2-Gain and Passivity Techniques in Nonlinear Control. Berlin: Springer, 2000[27] Wang Yu-Zhen. Generalized Hamiltonian Control System Theory—— Realization, Control and Application. Beijing: Science Press, 2007(王玉振. 广义Hamilton控制系统理论——实现, 控制与应用. 北京: 科学出版社, 2007)[28] Spong M W, Vidyasagar M. Robot Dynamics and Control. New York: Wiley, 1989
点击查看大图
计量
- 文章访问数: 1442
- HTML全文浏览量: 43
- PDF下载量: 840
- 被引次数: 0