A Comparison of Data-Driven Learning Algorithms to Predict Trajectories in the DRO Family

Generating precise, accurate, and efficient trajectories in the Earth-Moon circular restricted three-body problem (CR3BP) is crucial for long-term lunar missions, yet it remains challenging. A primary reason for this is that the CR3BP is an extremely nonlinear and chaotic system. Fortunately, neural networks present a promising approach for addressing such complex nonlinear challenges. Thus, this work addresses the challenge of solving a nonlinear system within the CR3BP framework to determine the trajectories of spacecraft within the Distant Retrograde Orbit (DRO) family using neural networks (NNs). For a comprehensive comparison analysis of trajectory generation, we present numerical simulations using four NNs trained, learned, and updated on the DRO family, specifically using ODE45, ODE78, ODE113, and the low-complexity algorithm (LCA) developed by the authors. Once the NNs are trained, learned, and updated, the proposed networks are utilized to predict the state trajectory of the spacecraft without using conventional trajectory generation in the CR3BP framework. Numerical results have shown that the adaptation of neural networks to the CR3BP framework determines spacecraft trajectory within the DRO family with higher accuracy compared to conventional trajectory generation algorithms.