Abstract: The trajectory tracking and flexible vibration suppression of a two-flexible-link free-floating space robot system were discussed based on finite time with the joint torque output dead-zone. Using singular perturbation theory, the dynamics equations of the system were decomposed into a slow subsystem for rigid motions and a fast subsystem for flexible vibrations. For the slow subsystem with unknown model parameters and dead-zone parameters, a dead-zone pre-compensator and a finite-time controller were designed based on nominal model. An integral sliding mode surface with finite time convergence property was introduced, which had faster convergence speed, better robustness and anti-interference performance than the traditional asymptotic convergence control method. For the fast subsystem, the linear quadratic optimal control method was adopted to suppress the vibrations actively to ensure good stability of the system. Combined with the finite-time stability lemma, the Lyapunov theory was used to prove that the proposed control algorithm may make the tracking errors converge to the origin within a finite time. The simulation examples confirm the effectiveness of the proposed method.

Key words: two-flexible-link space robot, finite-time control, singular perturbation, joint torque output dead zone, flexible vibration suppression

摘要： 探讨了存在关节力矩输出死区情况下，基于有限时间的漂浮基双柔杆空间机器人系统的轨迹跟踪与柔性抑振问题。采用奇异摄动理论，将系统的动力学方程分解为慢变与快变子系统，分别表示刚性运动与柔性振动。针对模型存在不确定性和死区参数未知的慢变子系统，设计了死区预补偿器和一种基于名义模型的有限时间控制器。引入了具有有限时间收敛特性的积分式滑模面，它与传统渐近收敛控制方法相比，具有更快的收敛速度、更好的鲁棒性和抗干扰特性。对于快变子系统，采用线性二次最优控制方法主动抑制其振动，以保证系统良好的稳定性。结合有限时间稳定性引理，采用李雅普诺夫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。仿真算例验证了所提方法的有效性。

关键词: 双柔杆空间机器人, 有限时间控制, 奇异摄动, 关节力矩输出死区, 柔性抑振