全柔性空间机器人基于虚拟力的输出反馈有限维重复学习控制及振动抑制

探讨了基座、关节、臂均存在柔性情况下，空间机器人关节轨迹运动及多重柔性振动的主动控制和主动抑制问题.结合线性弹簧、扭转弹簧、简支梁及假设模态法，利用拉格朗日方程建立了基座、关节、臂全柔性影响下的空间机器人系统动力学模型，利用奇异摄动法，将模型分解为关节运动慢变子系统与关节柔性振动快变子系统.为控制慢变子系统中载体姿态、关节刚性运动并且抑制臂的柔性振动，依据虚拟控制力的概念，设计了基于有限维傅里叶级数解析周期信号的输出反馈重复学习算法.李雅普诺夫直接法证实了上述控制器的稳定性.为了抑制快变子系统中基座和关节的柔性振动，分别采用线性二次最优控制方法以及引入关节柔性补偿器间接增大关节等效刚度的方式，使控制算法不局限于求解弱非线性问题.系统数值仿真结果表明，所提出的控制器能够有效抑制机器人多重柔性构件的振动，实现对期望信号的高品质追踪. 

Output Feedback Finite-dimensional Repetitive Learning Control on Virtual Force for Flexible-base Flexible-link and Flexible-joint Space Robot

Motion control and flexible vibration synchronous suppression of base, links and joints for flexible space robot are studied. By combining linear spring, torsion spring, simply supported beam and hypothetical modal method, and using Lagrange equation, the dynamic model of flexible-base, flexible-link and flexible-joint space robot is established. Then, by using singular perturbation method, the model is decomposed into a joint motion slow subsystem and joint flexible vibration fast subsystem. In order to control the rigid motion of the base and joints in the slow subsystem and suppress flexible vibration of links, according to the concept of virtual control force, an output feedback repetitive learning algorithm based on the finite-dimensional Fourier series analytical periodic signal is proposed. The algorithm uses virtual force to suppress the flexible vibration of the robotic links. The output feedback method is designed so that the controller can be implemented based on position measurement only. It is proposed that the repetitive learning algorithm can effectively compensate for repeated errors in periodic tasks and improve the control quality of the system. The Lyapunov direct method confirms the stability of the above controller. In addition, in order to suppress the flexible vibration of the base and joint in the fast subsystem, the linear quadratic optimal control method and the joint flexible compensator are used to indirectly increase the joint equivalent stiffness, so that the control algorithm cannot be limited to solving the weak nonlinear problem. Simulation results show that the proposed controller can effectively suppress the vibration of multiple flexible components of the system, and achieve high-quality tracking of the desired signal.