Adaptive Hierarchical Sliding Mode Control with Input Saturation for Attitude Regulation of Multi-satellite Tethered System

This paper proposes a novel adaptive hierarchical sliding mode control for the attitude regulation of the multi-satellite inline tethered system, where the input saturation is taken into account. The governing equations for the attitude dynamics of the three-satellite inline tethered system are derived firstly by utilizing Lagrangian mechanics theory. Considering the fact that the attitude of the central satellite can be adjusted by using the simple exponential stabilization scheme, the decoupling of the central satellite and the terminal ones is presented, and in addition, the new adaptive sliding mode control law is applied to stabilize the attitude dynamics of the two terminal satellites based on the synchronization and partial contraction theory. In the adaptive hierarchical sliding mode control design, the input is modeled as saturated input due to the fact that the flywheel torque is bounded, and meanwhile, an adaptive update rate is introduced to eliminate the effect of the saturated input and the external perturbation. The proposed control scheme can be applied on the two-satellite system to achieve fixed-point rotation. Numerical results validate the effectiveness of the proposed method.