舵叶固定式球形关节动力学建模及控制
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摘要
针对球面运动机构驱动方式问题,提出一种新型的二自由度液压驱动球形关节运动机构,该机构利用超全周转动马达及舵叶摆动马达作为驱动,可以实现球面的全方位输出。对该球形机构的动力学及轨迹跟踪控制进行研究,首先考虑机构惯性力及重力的影响,运用拉格朗日方程和欧拉方程建立了球形关节的动力学模型。在此基础上,采用一种鲁棒自适应分散控制策略对关节运动轨迹进行跟踪,该控制器由一个线性PD反馈加补偿不确定动力学的非线性自适应反馈构成,能够有效克服难于建模的摩擦力及外部扰动的影响,而仅需要了解该球形关节的输出位置及速度状态,最后能够保证全局的渐进稳定。仿真结果表明,利用该控制策略可以使球形关节具有良好的轨迹跟踪能力。
Following the driving mode problem for the spherical motion mechanism, a new type of hydraulic drive spherical joint with two degrees of freedom was proposed. The full cycle rotating motor and a rudder blade swing motor were used as drive in the joint mechanism, and a spherical surface output in all directions could be achieved. The dynamics and trajectory tracking control of the spherical mechanism was researched. Firstly, considering the effects of the inertial force and gravity, the Lagrange equation and Euler equation were adopted and the dynamic model of the spherical joint was established. On this basis, a decentralized robust adaptive control strategy was utilized for the joint trajectory tracking. The controller was made up of a linear PD feedback and a nonlinear adaptive-feedback of compensating uncertainty dynamics, the effects such as frictions and external disturbance could be overcome effectively, and the only information required in setting up the strategy was the output position and speed states of the joint. Finally the global asymptotic stability could be warranted. It is shown by the simulations that the spherical joint has a good capability of trajectory tracking to use the control strategy.
Following the driving mode problem for the spherical motion mechanism, a new type of hydraulic drive spherical joint with two degrees of freedom was proposed. The full cycle rotating motor and a rudder blade swing motor were used as drive in the joint mechanism, and a spherical surface output in all directions could be achieved. The dynamics and trajectory tracking control of the spherical mechanism was researched. Firstly, considering the effects of the inertial force and gravity, the Lagrange equation and Euler equation were adopted and the dynamic model of the spherical joint was established. On this basis, a decentralized robust adaptive control strategy was utilized for the joint trajectory tracking. The controller was made up of a linear PD feedback and a nonlinear adaptive-feedback of compensating uncertainty dynamics, the effects such as frictions and external disturbance could be overcome effectively, and the only information required in setting up the strategy was the output position and speed states of the joint. Finally the global asymptotic stability could be warranted. It is shown by the simulations that the spherical joint has a good capability of trajectory tracking to use the control strategy.
引文
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[10]SHANG W W,CONG S.Nonlinear Adaptive Task Space Control for a 2-DOF Redundantly Actuated Parallel Manipulator[J].Nonlinear Dynamics,2010,59(1/2):61-72.
[2]UMASHANKAR N,ANISH M,GEORGE K.State Transition,Balancing,Station Keeping and Yaw Control for a Dynamically Stable Single Spherical Wheel Mobile Robot[C]//Proceedings of IEEE International Conference on Robotics and Automation.Kobe,Japan:IEEE,2009:998-1003.
[3]CARRELLA A,BRENNAN M J,WATERS T P.Static Analysis of a Passive Vibration Isolator with Quasi-zero-stiffness Characteristic[J].Journal of Sound and Vibration,2007,301(3/4/5):678-689.
[4]YUE M,DENG Z Q.Dynamic Modeling and Optimal Controller Design of a Spherical Robot in Climbing State[J].Journal of Mechanical Engineering,2009,45(11):46-51.
[5]王群京,陈丽霞,吴立建.基于加权无向图的永磁球形步进电机运动控制[J].中国电机工程学报,2005,25(9):130-134.WANG Q J,CHEN L X,WU L J.The Control of a Permanent Magnet Spherical Stepper Motor Based on Weighted Graph[J].Proceedings of the Chinese Society for Electrical Engineering,2005,25(9):130-134.
[6]王亮,胡永杨,方守龙.轴向串联式超全周转动液压马达:CN101858369A[P].2010-10-13.
[7]CRITCHLOW A J.机器人学导论[M].贠超,译.3版.北京:机械工业出版社,2006:33-36,138-140,145-147.
[8]周衍柏.理论力学教程[M].3版.北京:高等教育出版社,2009:155-165.
[9]代颖,郑南宁,李春来.机器人鲁棒自适应分散控制[J].机器人,1998,20(3):187-191.DAI Y,ZHENG N N,LI C L.Decentralized Robust Adaptive Tracking Control of Robot Manipulators[J].Robot,1998,20(3):187-191.
[10]SHANG W W,CONG S.Nonlinear Adaptive Task Space Control for a 2-DOF Redundantly Actuated Parallel Manipulator[J].Nonlinear Dynamics,2010,59(1/2):61-72.