Fast Design of Fuel-Optimal Maneuver Trajectories for Satellite Constellations via a Hybrid Binary Classification and Physics-Regularized Neural Network

Abstract

To address the requirement for the fast design of fuel-optimal maneuver trajectories in on-orbit servicing of satellite constellations, traditional numerical methods for solving the Lambert problem suffer from high computational complexity and numerous iterations, making them inefficient for scenarios involving multiple satellites and time windows. To overcome this, this article proposes a hybrid intelligent solving framework that integrates a binary classification neural network (BCNN) and a physics-regularized neural network (PRNN). By incorporating structural improvements and embedding physical constraints, the framework fundamentally overcomes the computational bottlenecks of traditional methods. Within this framework, the BCNN adopts a three-layer architecture—“feature extraction–attention weighting–classification”—to extract complex orbital-mechanics’ features and rapidly identify regions with no solution. The PRNN introduces a composite orbital-dynamics loss function, injecting strong nonlinear physical priors during training to achieve precise mapping of velocity increments for solvable cases. The two networks work in synergy, jointly enabling the efficient solution of the Lambert problem from the two perspectives of “solution existence judgment” and “high-precision solution estimation.” Based on this, the method can rapidly output fuel-optimal satellite assignments, flight times, and maneuver strategies. Simulations show that the proposed method achieves a significant speedup over conventional iterative solvers while maintaining a relative error below 2%. The method is validated through ablation studies and extensive experiments under J2-perturbed dynamics across diverse scenarios, confirming its robustness and efficiency for constellation-level trajectory design.