Time-Optimal Rendezvous Trajectory Planning for Micro/Nano Satellites with Waypoint Constraints

The time-optimal rendezvous problem is crucial for efficiently executing on-orbit servicing (OOS) missions in the future. To fulfill the detection requirement during rendezvous process, it is an essential issue that the maneuvering spacecraft flies over the designated waypoint. This paper presents an innovative methodology for planning the time-optimal spacecraft rendezvous trajectory, involving the constraints related to a flyover waypoint and being forced by a constant thrust. The method is specifically designed to handle the optimal problems with the shortest and unspecified flyover time and terminal rendezvous time. First, this article outlines the scenarios for a time-optimal rendezvous that incorporates the constraints of a flyover waypoint. Second, a time-normalized relative dynamic model for maneuvering spacecraft is derived using the Clohessy–Wiltshire (CW) equation. Third, the time-optimal control output under the constant thrust is provided leveraging Pontryagin’s minimum principle (PMP). Meanwhile, an indirect solution equation is established with the constraints of relative position and velocity for the flyover waypoint during the rendezvous process. Finally, a computational methodology for solving this time-optimal problem is proposed, integrating the initial guess for the unspecified time, multi-objective particle swarm optimization using multiple search strategies (MMOPSO) and Newton–Raphson method (NRM). Simulation results demonstrate that the method can effectively and practically solve the time-optimal rendezvous trajectory planning under a constant thrust, while satisfying the constraints of the flyover waypoint. Moreover, Monte Carlo simulations are performed, the results of which indicate that the proposed methodology exhibits strong robustness and fidelity.