Discrete-Time Sliding Mode Control for Deployment of Tethered Space Robot with only Length and Angle Measurement

This paper proposes a nonlinear discrete-time sliding mode based tension control for deployment of tethered space robot with only length and angle measurements. The discrete-time dynamics of deployment is uncovered based on discretization of Hamilton's principle. Taking into account the underactuated dynamics, the proposed discrete-time sliding surface can generate a specified reduced-order system, which can be regarded as an uncertain discrete-time system with multiple time delays, which is caused by a considerable sample interval, and the stability of a reduced-order system is well analyzed by combining a linear matrix inequation technique based on robust control theory and nonlinear discrete-time Lyapunov method. A novel input structure with the auxiliary variable sequence is presented to deal with the tension saturation, and the states can converge to the specified reduced-order system although the input saturation occurs. The proposed discrete-time method makes no appeal to velocity terms. It is cost-effective to use the proposed method for the information of length and angle are easily measured rather than that of velocity, and it conduces to low requirements for the measurement ability of sensors. Simulation results verify the stability analyses, and are coincident with the stability analyses.