Optimization of Low-Thrust Transfer Trajectories to L₁ and L₂ Halo Orbits in the Earth-Moon System

Abstract

This paper proposes a design method for low-thrust transfer trajectories from an Earth parking orbit to L₁ and L₂ halo orbits in the Earth-Moon system using stable manifold and backward feedback controller design. The transfer trajectory is divided into two phases: a trajectory from the Earth parking orbit to a stable manifold, and one to the halo orbit along the stable manifold. The stable manifold is discretized by two parameters to describe the injection point. A backward feedback controller for the thruster steering in the first phase is employed. By designing the controller backward in time, the target orbital elements can be treated as constants of the Earth parking orbit. Then, the feedback gains and the manifold injection point are optimized using Differential Evolution to minimize ΔV. In numerical simulations, transfer trajectories from an Earth parking orbit to L₁ and L₂ halo orbits are designed by the proposed method to demonstrate its validity.