Global Optimization for Trajectory Design via Invariant Manifolds in the Earth-Moon Circular Restricted Three-Body Problem

TL;DR

This paper introduces a global optimization method combining basin hopping and quadratic programming to efficiently find minimum delta-V trajectories in the Earth-Moon CR3BP, including heteroclinic connections and low propellant solutions.

Contribution

It presents a novel global optimization framework for trajectory design in the CR3BP, capable of systematically identifying minimum delta-V transfers and heteroclinic connections.

Findings

Successfully reproduces known connections from literature.

Identifies very low delta-V solutions across different scenarios.

Demonstrates the efficiency of the method in exploring periodic orbits.

Abstract

This study addresses optimal impulsive trajectory design within the Circular Restricted Three-Body Problem (CR3BP), presenting a global optimization-based approach to identify minimum $\Delta V$ transfers between periodic orbits, including heteroclinic connections. By combining a Monotonic Basin Hopping (MBH) algorithm with a sequential quadratic solver in a parallel optimization framework, a wide range of minimum $\Delta V$ transfers are efficiently found. To validate this approach, known connections from the literature are reproduced. Consequently, three-dimensional periodic orbits are explored and a systematic search for minimum propellant trajectories is conducted within a selected interval of Jacobi constants and a maximum time of flight. Analysis of the results reveals the presence of very low $\Delta V$ solutions and showcases the algorithm's effectiveness across various mission scenarios.