Hierarchical adaptive backstepping sliding mode control for underactuated space robot

In this paper, the position control problem of the underactuated space robot with the effect of unknown external disturbance is addressed, and a new sliding mode control scheme is proposed. The underactuated system was divided into active subsystem and passive subsystem, and the Lyapunov functions and adaptive laws were designed for both subsystems by the adaptive backstepping algorithm which backstepping to the entire subsystem until the control law was finished. Combining with the subsystems' sliding planes a global sliding plane was constructed, then using the Lyapunov function and the exponential approach law with saturation function the control law for the entire system was derived. The control system is designed and simulated by proposed algorithm for two degrees of freedom underactuated space robot, and the simulation results have shown that the proposed algorithm not only can effectively and quickly implement the position control of the active and passive joints, but also can reduce the chattering caused by characteristic of the sliding mode control, and has robustness to the disturbance.