Gaussian Process Regression for Efficiently Approximating the Flow of the Circular Restricted Three-Body Problem

Abstract

Efficient trajectory mapping and global trajectory optimization are important areas of research within the field of astronautics. Performing numerical integration near a gravitational body for the purpose of trajectory mapping can be numerically stiff, resulting in high computational energy requirements. One method of reducing computationally energy requirements is to apply machine learning principles to trajectory mapping, avoiding the need to perform stiff numerical integration.

The overall goal of this thesis was to determine whether Gaussian process regression could be used as a method to learn the dynamical flow of the CR3BP and perform trajectory mapping. This thesis has two main components: a CR3BP model that was designed to produce trajectory data and an algorithm that utilized Gaussian process regression to perform the trajectory mapping.

The results showed that Gaussian process regression did indeed perform trajectory mapping for the points with varying error. As the trajectories approached the Earth - Moon L1 point, points within the lobe that corresponded to the invariant manifold to the Lyapunov orbit around the L1 had little error, while nearby points that diverged had a greater level of error. This validates the theory that machine learning principles can be used for efficient trajectory mapping, but emphasizes the need for continued research in order to reduce error.

Although this thesis focuses on Gaussian process regression in the planar CR3BP case, future areas of research include refining the regression analysis and performing trajectory optimization.