Low thrust resonance-orbit-based multiple gravity-assist trajectory

Abstract

This paper presents a methodology for optimizing a low-thrust gravity assist trajectory to achieve the Earth-Moon L1 periodic orbit, leveraging the resonance-orbital structure as a guiding framework. The formulation employed in this study utilizes the Earth-Moon circular restricted three-body problem to describe the system’s dynamics. The proposed optimization procedure involves the determination of the gravity-assist geometry and the subsequent identification of the gravity-assist linking through the solution of a multiple-point boundary value problem. The periapsis rotation angle is designed by solving a gradient descent optimization problem in the gravity-assist geometry determination step. This process results in trajectories that intentionally deviate from the symmetry observed in resonance orbits. The multiple-point boundary value problem focuses on resolving a minimum-fuel challenge by connecting two intermediate resonance-like orbits characterized by rotated periapses. The optimal control problem unfolds in two steps. Firstly, a relatively straightforward two-point boundary problem, serving as an approximation to the original problem, is established and solved. The solution obtained from this step serves as the initial guess for the subsequent and more intricate multiple-point boundary value problem. To assess the efficacy of the proposed methodology, the low-thrust resonance gravity-assist trajectory is compared against trajectories designed using conventional approaches involving low-thrust propulsion. This comparative analysis aims to validate and highlight the efficiency of the proposed method in optimizing trajectories for space missions within the Earth-Moon system. The proposed methodology converged to a fuel-optimal solution that is 40% more efficient than the previous research. In addition to the LTRGA trajectory, possible extended missions to the Low-Lunar Orbit (LLO), and hyperbolic escape trajectory from Earth is discussed.