Transfer between the planar Lyapunov orbits around the Earth–Moon L2 point using low-thrust engine

Abstract

We present a study of the low-thrust transfer problem near the secondary body in the Earth–Moon circular restricted three-body problem (CRTBP). Based on the Pontryagin maximum principle, the time-optimal, energy-optimal and fuel-optimal transfers between the planar Lyapunov orbits around the L2 point of the Earth–Moon system are constructed as a two-point boundary value problem (TPBVP). A criterion for identifying the best trajectory is also described. The Lyapunov orbit structure is used to deal with the potential difficulties of initial guess. As a result, the final transfer trajectory follows a multi-revolution structure, which takes a long time of flight. The homoclinic connection configuration is investigated by introducing the relevant invariant manifolds, allowing for faster transfer and less fuel consumption in the same case. It is designed a linear time-varying model predictive control (MPC) algorithm to perform trajectory tracking in the presence of initial orbit error and deviations in engine operation. Numerical simulations show the efficiency and practicability of the optimal transfer trajectory design strategy and trajectory tracking controller proposed in this paper for future lunar exploration missions.