Low-Thrust Resonance Gravity-Assist Trajectory Design for Lunar Missions

This paper introduces a procedure to optimize a low-thrust gravity-assist trajectory to the Earth–moon L1 periodic orbit utilizing the resonance-orbital structure as a guideline. The Earth–moon circular restricted three-body problem formulation is used to describe the problem. The proposed procedure determines the gravity-assist geometry and then finds the gravity-assist linking based on the multiple-point boundary value problem. The gravity-assist geometry determination step designs the periapsis rotation angle by solving a gradient descent optimization problem, yielding trajectories that break the symmetry of the resonance orbits. The multiple-point boundary-value problem seeks to solve a minimum-fuel problem linking two intermediate resonance-like orbits with rotated periapses. The first step of the optimal control problem establishes and solves a relatively easy two-point boundary problem approximating the original problem. The solution is used as the initial guess for the more complex multiple-point boundary value problem. The low-thrust resonance gravity-assist trajectory is compared to the trajectories designed based on traditional approaches involving low-thrust propulsion, demonstrating its validity and efficiency.