Hybrid Control Strategy for Low-Thrust Earth-to-Moon Transfers: Integrating Ballistic Lunar Transfer with Q-Law Guidance

Abstract

This project develops and evaluates a hybrid control strategy for a fuel-efficient, low-thrust Earth-to-Moon transfer by combining a Ballistic Lunar Transfer (BLT) - derived from the CAPSTONE spacecraft trajectory - with Q-Law guidance. Motivated by a revival of interest around lunar exploration efforts, the objective of this project was to design an autonomous trajectory that uses natural multi-body dynamics to venture beyond the Earth–Moon system and then transition to a controlled, continuous low-thrust phase under a two-body approximation. This was implemented by introducing a varying “effective central mass” to enable the preservation of a Keplerian structure - which is required by Q-Law - while approximating the gradual shift from Earth- to Moon-dominated gravity. The impact of Q-Law weighting parameters and discretization levels on trajectory stability was evaluated and analyzed. While the Q-Law guidance control demonstrated numerical robustness and convergence across initial segments, this research identified that such numerical convergence did not imply physical validity. In higher-discretization trials (e.g. 10 and 15 segments), the simultaneous decrease of the semi-major axis and the gravitational parameter μ led to positive specific energies and unbound trajectories (a<0). These findings characterized the trade-offs between transfer time, fuel efficiency, and dynamical robustness. Fundamentally, this study provides a foundational road-map that demonstrates that energy-informed constraints are essential for the autonomous guidance of low-thrust spacecraft in multi-body environments for future sustainable lunar exploration.