Hybrid Optimization of High-Fidelity Low-Thrust Transfers to the Lunar Gateway

NASA’s Artemis program aims to establish a sustainable and long-term human presence on, and in orbit around, the Moon. Transportation of humans and supplies to and from the Lunar Gateway will be a critical element of a successful Artemis program. Solar electric propulsion will play a key role in the supply chain for sustainable cislunar space operations. Solar electric propulsion engines are more efficient than chemical engines, thus requiring less propellant mass which in turn leads to smaller/lighter spacecraft that are cheaper to launch. In this paper we present a hybrid optimization scheme for solving fuel-optimal, low-thrust, transfers from a Geosynchronous Equatorial Orbit to a Near Rectilinear Halo Orbit, including a terminal manifold coast, considering a spacecraft with a thrust acceleration less than 0.25 mm/s^2 . Such problems are extremely challenging to solve with single- or multiple-shooting, even when continuation and smoothing are applied to thruster on/off switches and eclipse entry/exit conditions. Our hybrid optimization scheme is formulated using particle swarm optimization to compute the optimal sequence of intermediate target orbits between the departure orbit and the desired manifold injection point, such that the total propellant mass for the transfer is minimized. An indirect optimization approach is then used to compute fuel-optimal trajectory legs between each pair of intermediate orbits. To quantify the performance of our hybrid algorithm, we compare it to optimal trajectories obtained using single- or multiple-shooting for problems with a larger thrust-to-mass ratio that can be more easily converged using shooting methods.