Adaptive Control for Autonomous Spacecraft Rendezvous with Approaching Path Constraint

This paper investigates the translational control problem for autonomous spacecraft rendezvous with a freely tumbling target under approaching path constraints. Specifically and firstly, a dynamic model resolved in the target's body-fixed frame is established for relative translational motion of the pursuer with respect to the target, which allows to facilitate the closed-loop control design and stability analysis significantly. To ensure that the approaching path constraint is satisfied, the constrained zone is parameterized in terms of spatial geometrical feature, and then an artificial potential function (APF) is designed accordingly. Moreovre, by mathematical analysis, it is shown that the APF is free of local minima problem inherent in traditional APF-based control. Subsequently, an adaptive controller is synthesized within the backstepping control framework using the designed APF. The designed controller enables the pursuer to reach the desired position, while complying with the approaching path constraint. Following Lyapunov's direct method, the closed-loop stability is analyzed. Finally, simulation results are given to demonstrate key features and illustrate the effectiveness of the proposed control scheme.