Prescribed performance-based time-varying sliding mode control for target approaching and hovering

The on-orbit servicing of target spacecraft, such as approaching and hovering to inspect defunct payloads, demands precise and robust control under stringent constraints. This paper proposes a time-varying sliding mode control scheme integrated with prescribed performance functions for a 6-DOF approaching and hovering mission. First, a reverse model predictive control planner is developed to generate feasible state trajectories that rigorously satisfy collision avoidance, time-varying hovering corridors, and attitude-pointing constraints. Second, a novel sliding mode manifold is designed using the prescribed performance function, eliminating the reaching phase inherent in conventional sliding mode control, preventing excessive control gains, and making the maximum control magnitude predictable. Third, a quantitative framework is established to explore the relationship between initial errors, convergence time, and control magnitude, which has rarely been studied in previous work. It enables the synthesis of either finite-thrust or finite-time convergence controllers tailored to specific missions. Simulations demonstrate the control scheme's robustness for various targets (including maneuvering and tumbling ones) and its superiority in both mission safety and fuel economy.