Low-thrust resonance gravity assist trajectory design to the Moon

Abstract

The trajectory optimization problem of low-thrust resonance gravity assist to the Earth-Moon L1 periodic orbit in the Earth-Moon circular restricted three-body problem is presented. We introduce a threefold systematic optimization procedure to generate a mass-optimal solution from the initial to the final resonance orbit. The procedure consists of: i) gravity assist geometry determination, ii) two-point boundary-value-problem-based initial guess generation, and iii) multiple-point boundary-value-problem-based gravity assist linking. We present a new method of rotating the periapsis before the close approach to the Moon to break the symmetry of the resonance orbit, which produces gravity-assist-like trajectories to the next resonance orbit. The optimal control problem is divided into solving an easier two-point boundary value problem, which is used as an initial guess solution for the full optimal control problems. By the threefold optimization procedure, we minimize the optimal control problem to k-2 amount of optimal control problem, given k amount of resonance orbits. The low-thrust resonance gravity-assist trajectory is compared to the traditional pure-low-thrust trajectories. Utilizing Q-law guidance from GTO to the first resonance orbit, the low-thrust resonance gravity assist trajectories were found capable of saving up to 35% of fuel compared to the pure-low-thrust trajectories.