Deep Neural Networks-Based Efficient Mapping of Three-Dimensional Lunar Gravity Assist in the Circular Restricted Three-Body Problem

Lunar gravity assists (LGAs) are widely utilized in mission designs to potentially reduce transfer costs, particularly in non-coplanar cases requiring inclination adjustments. The commonly used patched-conic model and Keplerian map have low accuracy in designing close LGAs within the Earth-Moon system. Propagating LGA trajectories in the circular restricted three-body problem (CR3BP) offers higher fidelity but requires numerical integration. Therefore, a fast and accurate approach to estimate the state variation of the spacecraft after an LGA is significant. In this work, a three-dimensional LGA mapping in the CR3BP is studied, where deep neural networks (DNNs) are utilized to predict the state variation, gravity assist radius, and gravity assist type within a single orbital period. The LGA mapping is formulated with specific input and output parameters. The dynamical characteristics and data features resulting from the large mass ratio of the Earth-Moon CR3BP are analyzed. In particular, a small gravity assist radius causes significant perturbations to the Keplerian orbit, leading to abrupt local variations in the mapping outputs and challenges in sampling and fitting. To address this, a sampling approach based on the physical interpretation of the mapping inputs is proposed to improve the dataset, and a prediction framework combining classification and regression DNNs is employed. Test results demonstrate the efficiency and accuracy of the proposed DNNs-based LGA mapping, with average relative errors of 1.17% for state variation and 0.45% for gravity assist radius, and a 99.90% classification accuracy. Additionally, the error distribution and extrapolation capability are evaluated and analyzed.