Time-Optimal Guidance Laws Using a Frequency Domain Approach for Spacecraft Rendezvous

Abstract This paper proposes a novel approach to solving the time-optimal rendezvous problem for spacecraft in orbit. Initially, the characteristics of the time-optimal rendezvous solution in the in-plane motion of the relative equations of motion are analyzed using the direct collocation method. A time-delay filter is designed in the frequency domain using the analysis results. And then, it transforms the time-optimal control problem into a parameter optimization problem. By solving this optimization problem, the switching times of the bang–bang control profile can be determined. The effectiveness of the proposed method is examined through various simulations, demonstrating its ability to resolve the discontinuities caused by the bang–bang control profile while also being effectively applicable under various boundary conditions. Additionally, the proposed method turns out to be robust against disturbances through real-time application.