Koopman Expectation-Based Optimization for Offline Spacecraft Rendezvous Guidance Under Parametric Uncertainties

Precise and robust trajectory optimization is critical for autonomous spacecraft rendezvous, proximity operations and docking (RPOD), especially in the presence of uncertainties such as mass variability. Traditional methods, particularly Monte Carlo simulations, are computationally intensive and often impractical for real-time implementation. This thesis introduces a novel approach that leverages Koopman operator theory—specifically, the Koopman Expectation (KE)—to efficiently propagate and optimize trajectories under uncertainty without extensive numerical sampling. A key contribution of this research is the development of a Koopman Expectation framework for spacecraft guidance optimization. By transforming nonlinear spacecraft dynamics into a linear operator-theoretic representation, the proposed approach efficiently computes expectation values of critical mission observables, significantly outperforming standard Monte Carlo methods in both speed and robustness. To further enhance computational efficiency and enable real-time capabilities, this work integrates physics-informed deep learning methods with the Koopman Expectation framework, resulting in the Koopman Expectation Deep Learning (KEDL) guidance strategy. KEDL utilizes neural network surrogates trained on datasets generated via KE optimization, enabling rapid prediction of optimal initial conditions across uncertain spacecraft mass scenarios. Comparative numerical studies show that KEDL substantially reduces computational overhead while maintaining or surpassing the accuracy and reliability of classical optimization approaches. Comprehensive numerical simulations validate the proposed methods, demonstrating their superior balance between accuracy, computational efficiency, and robustness under realistic mass uncertainties. The developed guidance strategies are poised to significantly enhance autonomous operations capability for future rendezvous and servicing missions, enabling efficient onboard decision-making even in highly uncertain operational environments.