Generative and Regressive Approaches for Periodic Orbit-Based Spacecraft Mission Design in the Circular Restricted Three Body Problem

Abstract

The circular restricted three-body problem is a canonical example of chaotic dynamics and forms the basis of many advanced spacecraft trajectory designs. This thesis investigates whether emerging artificial intelligence based generative and regression methods can reduce computational costs and enable new tools for exploring families of periodic orbits in mission design.

Generative models are evaluated for their ability to reconstruct, sample, and represent multiple periodic-orbit families and their bifurcation structure, while regression-based surrogates are assessed for unstable manifold propagation. A loss formulation that explicitly incorporates the Jacobi constant is introduced, encouraging approximate conservation of energy within the system, and penalizing in-sequence variations in Jacobi.Generative models (variational autoencoders, transformer-based diffusion models) successfully capture orbital structure and orbital family bifurcationary relationships and support efficient exploration, though differential correction is typically required to enforce physical validity. Regression-based surrogates (Kolmogorov-Arnold and deep neural networks) reproduce qualitative behaviour but remain insufficiently accurate for mission design.