An Energy-Based Saturated Controller for the Underactuated Tethered System

This article addresses the stabilization control issue for the postcapture tethered system by tethered space robot (TSR). Due to the physical characteristics of space tether by nature, there exists no control inputs on the in-plane/out-of-plane channels of the tether; therefore, the postcapture tethered system is a typical multiinput and multioutput underactuated system. In this article, we propose an energy-based controller for the underactuated system subject to input saturation and the nonnegativity constraint of the tether tension. First, we give the dynamic model of the postcapture tethered system, with consideration of the three attitude angles of the postcapture combination, the in-plane/out-of-plane angles, and the tether length. Second, we list the analysis process of the system's equilibrium points. Third, we give the detailed controller design process, and verify the stability of the system by invoking the Lyapunov techniques and the extended Barbalat's lemma. Finally, numerical simulations and comparison results with the hierarchical sliding mode controller are conducted to validate the performance improvement of the developed control strategy.