基座与臂杆全弹性空间机器人的有限时间控制

探讨了基座、臂杆全弹性影响下,基于有限时间的漂浮基空间机器人系统轨迹跟踪以及柔性抑振问题.由于弹性基座与两柔性杆之间存在多重动力学耦合关系,此系统为高度非线性系统.将弹性基座与臂杆间的连接视为线性弹簧,利用拉格朗日第二类方程并结合假设模态法,推导出该系统的动力学模型;应用奇异摄动理论的两种时间尺度假设,将系统分解为表示刚性运动的慢变子系统和表示基座弹性、双柔杆振动的快变子系统.针对慢变子系统,设计了一种基于名义模型的有限时间控制器,保证完成刚性期望轨迹跟踪.设计的积分式滑模面具有有限时间收敛特性,比传统渐近收敛控制方法具有更快的收敛速度和更强的鲁棒性;对于快变子系统,采用线性二次型最优控制同时抑制弹性基座与两柔性杆的振动.Lyapunov理论证明了所提控制算法能使跟踪误差在有限时间内收敛到原点.仿真验证了控制方法的有效性.

Finite Time Control of Space Robot with Elastic Base and Flexible Arms

Based on the finite time control, the trajectory tracking and flexible vibration suppression of a free-floating space robot system with two flexible arms and elastic base are discussed. Because of the multiple dynamic coupling relationship between the elastic base and the two flexible arms, the system is a highly nonlinear system. Firstly, the connection between the elastic base and the first arm is regarded as a linear spring, and the dynamic model of the system is derived from the Lagrange equation of the second kind and the assumed mode method. Secondly, by applying the two time-scale assumptions of singular perturbation theory, the system is decomposed into a slow subsystem which represents the rigid motion and a fast subsystem which represents the elastic base and two arms vibration. For the slow subsystem, a finite-time controller based on the nominal model is designed to realize the rigid desired trajectory tracking. Due to the finite time convergence property of the integral sliding mode surface, it has faster convergence speed and stronger robustness than the traditional asymptotic convergence control method. For the fast subsystem, the linear quadratic optimal control method is adopted to suppress the vibration of the elastic base and the two flexible arms simultaneously. Lyapunov theory is used to prove that the proposed control algorithm can enable the tracking error converging to the origin within a finite time. Finally, the simulations verify the effectiveness of the control method.