Particle Swarm Optimization-Based Co-State Initialization for Low-Thrust Minimum-Fuel Trajectory Optimization

TL;DR

This paper introduces a particle swarm optimization-based method with energy-to-fuel continuation to effectively initialize co-state variables for low-thrust minimum-fuel trajectory optimization in the circular restricted three-body problem, enhancing convergence and solution discovery.

Contribution

It presents a novel PSO-based approach combined with energy-to-fuel homotopy for initializing co-states in low-thrust trajectory optimization, eliminating the need for initial guesses.

Findings

Successfully generates initial guesses for co-states in two low-thrust transfer scenarios.

Demonstrates improved convergence rate with strategic particle swarm sizing.

Validates the resulting trajectories against existing literature.

Abstract

In this paper, Particle Swarm Optimization with energy-to-fuel continuation is proposed for initializing the co-state variables for low-thrust minimum-fuel trajectory optimization problems in the circular restricted three-body problem. Particle Swarm Optimization performs a search of the solution space by minimizing the weighted sum of squares of the two-point boundary-value problem final boundary condition residuals for the minimum-energy problem. Next, an energy-to-fuel homotopy is employed to transition the minimum-energy trajectory to a minimum-fuel trajectory, starting from the generated guess. The proposed methodology is applied to two low-thrust transfer problems in the Earth-Moon system: a transfer from a geostationary transfer orbit to an L1 halo orbit, and a transfer from an L2 halo orbit to an L1 halo orbit. The resulting minimum-fuel trajectories are validated with the literature. It is demonstrated that the methodology can successfully generate guesses for the initial co-state variables which converge to a solution for both scenarios. A strategically chosen particle swarm size is shown to improve the convergence rate of the methodology. The proposed approach is of simple implementation, can be easily extended to other trajectory optimization problems, facilitates the discovery of multiple candidate trajectories, and does not require a user-provided guess, all of which are advantageous features for the preliminary phase of mission design.