Systematic Design of Optimal Low-Thrust Transfers for the Three-Body Problem

TL;DR

This paper presents a computational method for designing optimal low-thrust transfers in the planar circular restricted three-body problem, extending invariant manifold techniques with continuous propulsion and using variational integrators for efficiency.

Contribution

It introduces a novel approach combining invariant manifolds with continuous low-thrust propulsion and variational integrators for efficient transfer trajectory design.

Findings

Successfully designed a transfer from Earth-Moon L1 orbit to lunar orbit.

Demonstrated the method's geometric accuracy and computational efficiency.

Validated the approach with a numerical simulation in the Earth-Moon system.

Abstract

A computational approach is developed for the design of continuous low thrust transfers in the planar circular restricted three-body problem. The transfer design method of invariant manifolds is extended with the addition of continuous low thrust propulsion. A reachable region is generated and it is used to determine transfer opportunities, analogous to the intersection of invariant manifolds. The reachable set is developed on a lower dimensional Poincare section and used to design transfer trajectories. This is solved numerically as a discrete optimal control problem using a variational integrator. This provides for a geometrically exact and numerically efficient method for the motion in the three-body problem. A numerical simulation is provided developing a transfer from a $L_1$ periodic orbit in the Earth-Moon system to a target orbit about the Moon.