Trajectory design in multi-body models via homotopic convex optimization

The Moon will play a central role in upcoming human space exploration efforts, with numerous missions planned in the near future. Designing trajectories for spacecraft in the cislunar region requires advanced methods that account for the dynamics of complex multi-body systems. This work presents a sequential convex programming (SCP) framework for optimizing both impulsive and continuous-thrust trajectories within the restricted three- and four-body models, with a subsequent transition to high-fidelity ephemeris models. We employ a pulsating–rotating frame, use a homotopic approach, and leverage the Sundman transformation to improve convergence. The proposed method is demonstrated through simulations in the Sun-perturbed Earth–Moon system and the Moon-perturbed Sun–Earth system. The high accuracy and robustness make SCP an excellent choice even for solving highly nonlinear problems.