Low-thrust transfers to halo orbits in different systems: Hybrid optimization and free-coast design

To address the low-thrust transfer problem from Earth parking orbits to halo orbits, this study proposes a segment-matching design method in the Circular Restricted Three-Body Problem (CRTBP) with variable specific impulse engines. The trajectory designed by the proposed method consists of multiple thrust arcs, free-coast arcs, and invariant manifold arcs. However, optimizing low-thrust trajectories remains challenging due to the sensitivity of initial guesses and convergence issues. To tackle this, a hybrid optimization strategy is developed to cope with the optimal control problem under multiple constraints. Specifically, a global method is employed to determine the matching points, followed by an indirect optimization method using constrained gradients to determine the required thrust magnitude and direction. Additionally, a comprehensive analysis is conducted on the feasible ranges of variables involved in the optimization process. The investigation including transfer trajectories from Earth parking orbits to sample halo orbits around the L1 and L2 libration points in both the Earth–Moon and Sun–Earth/Moon systems is discussed in detail. Numerical results verify that this strategy performs significant improvements in fuel efficiency in certain scenarios, even for transfers in different systems. Given the promising application of variable specific impulse low-thrust propulsion in future deep space missions, the obtained results can provide valuable references for selecting parking orbits, determining flight time, and identifying capture locations along the transfer path.