三自由度串联机械臂的主从同步控制研究
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摘要
同步是指两个或多个具有同时性的相互关系的行为。同步现象广泛存在于自然界、生命、工程技术、甚至经济社会人类活动等许多领域。针对具有相同或不同机械结构的多机器人系统,可以采用外同步、互同步等策略完成同一工作目标。研究机器人机械动力学系统的广义同步问题在现代制造装配和空间工程应用中起着非常重要的作用,对深入研究机器人系统同步理论,服务工程实际都具有重要的理论价值和现实意义。
本文主要研究机械臂动力学系统的广义同步控制问题,以主从机械臂系统的外部同步为目标,主要应用机器人学理论、现代控制理论、系统稳定性理论,对实验室现有的AS-MRobot三自由度刚性机械臂进行动力学建模、外部同步控制器设计、控制系统稳定性判别和数值仿真,为进一步的实验与理论对比奠定基础。具体成果如下：
以AS-MRobot三自由度刚性机械臂为研究对象,分别进行运动学和动力学分析,建立动力学模型。针对机械臂系统本身的物理特征,论述构造满足机器人闭环系统全局渐近稳定的李雅普诺夫函数方法。
为实现机械臂系统外部同步控制,本文设计一种基于全状态可观测的主从外部同步控制器。随后,选取迟滞非线性系统为主系统,Duffing系统为从系统,应用李亚普诺夫稳定性判别方法推导出控制器,并通过数值仿真的方法证明了其有效性。
在末端轨迹同步跟踪方面,利用前面的方法设计了一种主从机械臂末端轨迹同步控制器,并通过仿真证明了其有效性。在关节同步方面,通过研究PD控制方法,提出了一种可调增益系数的方法,通过仿真可以看出该控制方法能有效的减小初始力矩的大小。针对机械臂动力学系统存在模型误差,本文提出机械臂鲁棒同步轨迹跟踪控制方法,设计了鲁棒同步轨迹跟踪控制器。最后,针对机械臂实际控制中利用多项式函数来“内插”或“逼近”期望轨迹的情况,进行了同步控制的仿真模拟,表明了该控制器可以快速实现对AS-MRobot的三个关节运动的同步轨迹跟踪控制。
本文研究了动力学系统的几种广义外部同步控制方法,从机械臂动力学系统建模、控制器设计方法、稳定性判别和数值仿真等角度对机械臂同步控制器的设计过程进行了深入研究。本文将为今后的主从机械臂系统内、外部同步,多机械臂系统同步等研究提供有力的理论帮助,同时也为实验与理论相对照奠定坚实基础。
Generally, the concept of synchronization means the correlated or corresponding in-time behaviors of two or more processes. The synchronized phenomena vastly exist in nature, sciences, and engineering technology, even as well as social and economical activities. Concerning a multi-robot system, which may include the identical or non-identical mechanical structures, many different synchronization patterns, such as external synchronization and mutually synchronization, are adopted to achieve their work task. In order to meet the requirement of trajectory tracking control of a parallel robot, the controlled synchronization method is used to enhance the accuracy of the track follower. The research on synchronization of robot dynamic system plays a key role in manufacturing and space engineering, whilst it expands the application of robotic synchronization and deepens the understanding of synchronized theory.
In this paper, based on robotics, modern control theory, system stability theory, the research focuses on the external synchronization of master-slave system. Dynamic model, external synchronization controller and stability of control system are studied repectively for AS-MRobot system, which pave the road to achieve comparison between experiments and simulation with synchronized control. The main content of this paper is following:
Considering the rigid AS-MRobot with 3 freedoms, the dynamic equation is built according to robotic kinematics and dynamics. The Lyapunov function is constructed in order to demonstrate the asymptotical stability of robotic closed-loop control system.
In order to realize the synchronized control goal, a controller based on all states observed is designed. Then the referred simulation is done on a master-slave system, where a nonlinear hysteretic system is chosen as master, and a Duffing system is taken as slave. The simulation indicates that the controller is applicable.
Then a controller on the track synchronization of the Mater-Slave end-manipulators is designed follow the above method, and the simulation indicates that the controller is applicable. Through the research on the PD control method, a method on variable gain is designed which can reduce the initial torque effectively. With the respect of model error of dynamic mathematic model, a kind of robust synchronized track control method is involved in this paper. Finally, considered the polynomial function is often used to approach the desired trajectory, AS-MRobot is simulated using the adaptive method in order to validate its application.
In this paper, some generalized methods about robotic external synchronized control are studied. From the aspects of building robot dynamic model, designing synchronized controller, establishing system stability and simulating validation, the whole process of synchronization of robot dynamic system is investigated deeply, which will promote the future work of master-slave robots' internal/external synthronization and multi-robots system synchronization research, meanwhile establish a strong background for the following robot synchronized experiment.
本文主要研究机械臂动力学系统的广义同步控制问题,以主从机械臂系统的外部同步为目标,主要应用机器人学理论、现代控制理论、系统稳定性理论,对实验室现有的AS-MRobot三自由度刚性机械臂进行动力学建模、外部同步控制器设计、控制系统稳定性判别和数值仿真,为进一步的实验与理论对比奠定基础。具体成果如下：
以AS-MRobot三自由度刚性机械臂为研究对象,分别进行运动学和动力学分析,建立动力学模型。针对机械臂系统本身的物理特征,论述构造满足机器人闭环系统全局渐近稳定的李雅普诺夫函数方法。
为实现机械臂系统外部同步控制,本文设计一种基于全状态可观测的主从外部同步控制器。随后,选取迟滞非线性系统为主系统,Duffing系统为从系统,应用李亚普诺夫稳定性判别方法推导出控制器,并通过数值仿真的方法证明了其有效性。
在末端轨迹同步跟踪方面,利用前面的方法设计了一种主从机械臂末端轨迹同步控制器,并通过仿真证明了其有效性。在关节同步方面,通过研究PD控制方法,提出了一种可调增益系数的方法,通过仿真可以看出该控制方法能有效的减小初始力矩的大小。针对机械臂动力学系统存在模型误差,本文提出机械臂鲁棒同步轨迹跟踪控制方法,设计了鲁棒同步轨迹跟踪控制器。最后,针对机械臂实际控制中利用多项式函数来“内插”或“逼近”期望轨迹的情况,进行了同步控制的仿真模拟,表明了该控制器可以快速实现对AS-MRobot的三个关节运动的同步轨迹跟踪控制。
本文研究了动力学系统的几种广义外部同步控制方法,从机械臂动力学系统建模、控制器设计方法、稳定性判别和数值仿真等角度对机械臂同步控制器的设计过程进行了深入研究。本文将为今后的主从机械臂系统内、外部同步,多机械臂系统同步等研究提供有力的理论帮助,同时也为实验与理论相对照奠定坚实基础。
Generally, the concept of synchronization means the correlated or corresponding in-time behaviors of two or more processes. The synchronized phenomena vastly exist in nature, sciences, and engineering technology, even as well as social and economical activities. Concerning a multi-robot system, which may include the identical or non-identical mechanical structures, many different synchronization patterns, such as external synchronization and mutually synchronization, are adopted to achieve their work task. In order to meet the requirement of trajectory tracking control of a parallel robot, the controlled synchronization method is used to enhance the accuracy of the track follower. The research on synchronization of robot dynamic system plays a key role in manufacturing and space engineering, whilst it expands the application of robotic synchronization and deepens the understanding of synchronized theory.
In this paper, based on robotics, modern control theory, system stability theory, the research focuses on the external synchronization of master-slave system. Dynamic model, external synchronization controller and stability of control system are studied repectively for AS-MRobot system, which pave the road to achieve comparison between experiments and simulation with synchronized control. The main content of this paper is following:
Considering the rigid AS-MRobot with 3 freedoms, the dynamic equation is built according to robotic kinematics and dynamics. The Lyapunov function is constructed in order to demonstrate the asymptotical stability of robotic closed-loop control system.
In order to realize the synchronized control goal, a controller based on all states observed is designed. Then the referred simulation is done on a master-slave system, where a nonlinear hysteretic system is chosen as master, and a Duffing system is taken as slave. The simulation indicates that the controller is applicable.
Then a controller on the track synchronization of the Mater-Slave end-manipulators is designed follow the above method, and the simulation indicates that the controller is applicable. Through the research on the PD control method, a method on variable gain is designed which can reduce the initial torque effectively. With the respect of model error of dynamic mathematic model, a kind of robust synchronized track control method is involved in this paper. Finally, considered the polynomial function is often used to approach the desired trajectory, AS-MRobot is simulated using the adaptive method in order to validate its application.
In this paper, some generalized methods about robotic external synchronized control are studied. From the aspects of building robot dynamic model, designing synchronized controller, establishing system stability and simulating validation, the whole process of synchronization of robot dynamic system is investigated deeply, which will promote the future work of master-slave robots' internal/external synthronization and multi-robots system synchronization research, meanwhile establish a strong background for the following robot synchronized experiment.
引文
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2. Winfree, A. T. The Geometry of Biological Time[J], New York:Springer,1980.
3. Steven H S. Spontaneous synchronization in nature[C], IEEE internation frequency control symposium,1997
4. Blekhman I I. Synchronization in Science and Technology[M], New York:ASME Press Translations, 1988.
5. Gray C. M. Synchronous oscillations in neuronal systems:mechanisms and functions[J], Journal of Computational Neuroscience,1994,1:11-38.
6. Mirollo R E, Strogatz S H. Synchronization of pulse-coupled biological oscillators[J], SLAM J. Appl. Math.1990,50:1645-1662.
7. 闻邦椿等.机械系统的振动同步与控制同步[M],北京：科学出版社,2003
8. 闻邦椿,赵春雨,宋占伟.机械系统的振动同步、控制同步、复合同步[J],工程设计,1999,3：1-5.
9. 闻邦椿,刘树英,何琼.振动机械的理论与动态设计方法[M],北京：机械工业出版社,2001
10. Alejandro Rodriguez Angeles. Synchronization of Mechanical Systems[D], Technische Universiteit Eindhoven,2002
11. Brunt, M. Coordination of Redundant Systems[D], The Netherlands:Technical University Delft,1998
12. Lu Ren. Synchronized trajectory tracking control for parallel manipulators [D]. University of Toronto, 2006
13. Sun D, Mills J K. Adaptive synchronized control for coordination of multirobot assembly tasks [J], IEEE Trans On Roboticsand Automation,2002,18:498-510.
14. Koichi Ozaki, et al. Synchronized Motion by Multiple Mobile Robots using Communication. Proceedings of the 1993 IEEE/RSJ International Conference on Intelligent Robots and Systems Yokohama, Japan 1993:1164-1170.
15. Dong Sun. Position synchronization of multiple motion axes with adaptive coupling control[J], Automatica,2003,39:997-1005.
16. Spall J. C, Cristion, J. A. Model-free control of nonlinear stochastic systems with discrete-time measurements[J], IEEE Trans On Automatic Control,1998,43(9):1198-1210.
17. Huygens. The Pendulum Clock [M], America Iowa State University Press,1986.
18. Rayleigh J. The Theory of Sound[M], New York:Dover Publ,1945.
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