柔性基、柔性关节空间机械臂的动力学与改进奇异摄动控制

Dynamics and Improved Singular Perturbation Control of Flexible-base and Flexible-joint Space Manipulator

采用线性伸缩弹簧、线性扭转弹簧来分别描述基座及关节柔性,并在此基础上经由线动量守恒原理、拉格朗日第二类建模方法,建立了姿态受控柔性基、柔性关节空间机械臂的动力学模型。将柔性补偿思想与奇异摄动理论相融合,推导了可分别表示系统刚性运动、基座与关节柔性运动的慢、快变子系统,并提出一种由协调运动慢变控制和基于高阶快变状态观测器的最优控制所组成的改进奇异摄动控制方案。与传统奇异摄动控制方案相比,所提改进控制方案可有效避免对系统高阶快变状态量进行实时地测量和反馈,且可适于具有较大关节柔性的柔性基、柔性关节空间机械臂的控制。仿真实验结果表明了所提方案在轨迹跟踪控制、基座与关节柔性振动抑制上的有效性。

The flexibilities of base and joint are described by a linear extension-compression spring and a linear torsion spring, respectively. The dynamic model of flexible-base and flexible-joint space manipulator with an attitude-controlled base is established with the linear momentum conservation principle and the second Lagrange modeling method. The flexibility compensating concept is integrated into the singular perturbation technique, and then the slow subsystem which describes the rigid motion of the system and the fast subsystem which describes the base and the flexible motions of joints are derived. Moreover, an improved singular perturbation control scheme consisting of a slow control for coordinated motion and an optimal control based on a high-order fast state observer is presented. Comparing with the traditional singular perturbation scheme, the improved control scheme can avoid the real-time measurement and feedback of high-order fast states of the system effectively, and it is more suitable for controlling the flexible-base and flexible-joint space manipulator with strong joint flexibility. The simulation results indicate that the proposed improved control scheme can track the desired trajectory accurately and suppress the vibration of the base and joints effectively.