Nonlinear Analysis of Discrete-Time Sliding Mode Prediction Deployment of Tethered Space Robot

This article proposes a discrete-time sliding mode prediction controller for deploying tethered space robot, and tension control strategy in deployment carries a limited input nature for the underactuated system. A linear component involving swinging angle and a fractional power component involving length combine to establish a novel discrete-time quasi-terminal sliding surface for underactuated dynamics. The corresponding reduced-order system is decoupled by using a hierarchical constrictive analysis methodology to generate an equivalent relationship between length and swinging angle, and the stability of the entire system is governed by multidelay system of length. The D-decomposition technique is employed to deduce that the steady-state error of length is ultimately uniformly bounded. The optimal reaching law is designed based on the sliding mode prediction algorithm, which can guarantee that the prediction correction converge to zero, and the sliding surface with a small boundary layer can hence be established in finite steps under the limited tension control with a modified input compensation sequence. Simulation results verify the correction of stability analyses on dynamics and the steady-state behavior of the sliding mode, and from the numerical results, the proposed method can save \text{15}{\%} time for deploying tethered space robot by only using tension than normal discrete-time sliding mode control.