Statistical Analysis and Neural Network Approximation of Mass-Optimal, Free-Final-Time Trajectories Using Kolmogorov–Arnold Networks for Multi-Target Rendezvous Planning

This paper addresses the statistical analysis and prediction of characteristics for mass-optimal, free-final-time (MOFFT) transfer trajectories of spacecraft equipped with electric propulsion systems. Transitioning from single-target flybys to multi-target asteroid missions requires evaluating numerous orbital transfer options. Classical indirect methods for solving MOFFT trajectory problems suffer from severe sensitivity of the boundary value problem to the initial guess of costate variables. To overcome this, a two-level parameter homotopy continuation scheme is proposed. This approach enabled the generation of a large-scale dataset and, through subsequent statistical analysis, the determination of an optimal empirical coefficient k to achieve an efficient balance between propellant consumption and flight time. To resolve the absence of an a priori initial guess when solving boundary value problems, a proxy model based on Fast Kolmogorov–Arnold Networks (FastKAN) was developed. It is demonstrated that incorporating FastKAN significantly enhances the convergence probability of the numerical shooting method without requiring a priori approximations. The trained FastKAN model is integrated into a beam search algorithm to plan multi-target rendezvous sequences. This approach is shown to nearly double the number of visited asteroids, given identical resource constraints, compared to planning based on time-optimal trajectories, thereby ensuring high ballistic efficiency and increasing the potential scientific value of the designed missions.