Model predictive control for close-proximity maneuvering of spacecraft with adaptive convexification of collision avoidance constraints

This study investigated model predictive control (MPC) for close-proximity maneuvering of spacecraft. It is essential for a designed MPC to effectively handle collision avoidance between the servicer spacecraft and the client spacecraft, especially while the client is rotating. The rotating motion of the client leads to dynamic changes in the collision avoidance constraints, which increases the difficulty of optimizing the control input in the MPC framework. Therefore, this study presents a method to improve the performance and computational efficiency of MPC for rendezvous and docking with a nonrotating or rotating client. An ellipsoid is adopted to model the client’s keep-out zone (KOZ). Given the spherical KOZ of the servicer, an expanded ellipsoid is introduced to describe the KOZ for the center of mass of the servicer and modeled as a nonlinear constraint. The linearization method for reference points located at the expanded ellipsoid is adopted to convexify the nonlinear constraints. The reference points are adaptively determined according to the positions of the servicer, client, and expanded ellipsoidal KOZ. The resulting hyperplanes are then used to describe the collision avoidance constraints. By utilizing the aforementioned strategies, combined with the calculated reference points, an adaptive convex programming algorithm suitable for real-time implementation of MPC is derived. The performance of the proposed method is demonstrated through numerical simulations.