漂浮基柔性关节-柔性臂空间机器人运动非线性滑模控制及双重弹性振动主动抑制

讨论了漂浮基柔性关节-柔性臂空间机器人系统的动力学建模过程、运动控制律设计及关节和臂双重弹性振动的抑制问题。利用动量、动量矩守恒关系和拉格朗日-假设模态法对系统进行动力学分析，并建立系统动力学方程。基于奇异摄动法，将系统分解为三个相互独立的子系统：仅表示系统刚性运动的“刚性关节-刚性臂”慢变子系统、仅表示柔性关节引起的系统弹性振动的“柔性关节-刚性臂”快变子系统和仅表示柔性臂引起的系统弹性振动的“刚性关节-柔性臂”快变子系统。分别针对三个子系统设计适当的控制律，其中非线性滑模控制方法用来实现空间机器人期望运动轨迹的渐近跟踪，速度差值反馈控制器用来抑制柔性关节引起的系统弹性振动，线性二次型最优控制器用来抑制柔性臂引起的系统弹性振动。因此，系统的总控制律为三个子系统的控制律组成的混合控制律。仿真实验证明所提出的混合控制律能够保证系统的控制精度，且能够有效地抑制柔性关节和柔性臂引起的系统弹性振动。

Nonlinear Sliding Mode Motion Control and Double Elastic Vibration Active Suppression of Free-floating Flexible-joint and Flexible-link Space Robot

A dynamics modeling, motion controller design and joint-link double flexible vibration suppression problem of free-floating flexible-link and flexible-joint space robot were discussed. The dynamic equations of the system were established according to system's momentum conservation, angular momentum conservation and Lagrange-assumed mode method. Based on singular perturbation method, the system was decomposed into three mutual independent subsystems: a “rigid-joint and rigid-link” slow subsystem represented the rigid-joint and rigid-link system's rigid motion, a “flexible-joint and rigid-link” fast subsystem represented the system's elastic vibration caused by flexible-joint and a “rigid-joint and flexible-link” fast subsystem represented the system's elastic vibration caused by flexible-link. Then three controllers were designed for the three subsystems respectively. A nonlinear sliding mode controller was designed to realize the asymptotic tracking of the system's motion trajectory. A feedback controller was used to suppress the flexible vibration caused by flexible-joint based on the velocity difference between the link and the motor. A linear quadric regulator was used to suppress the flexible vibration caused by flexible-link. Therefore, the system's total controller was a composite of the three controllers. The simulation proves the proposed compound controller can guarantee the control system's accuracy and suppress the elastic vibration caused by flexible-joint and flexible-link effectively.