Neural Operator Learning for Collision-Aware Trajectory Planning of Spacecraft Swarms

Satellite constellations require orbital transfers that are both fuel efficient and collision avoidant. Yet, the computational cost of optimization methods traditionally used to plan their trajectories scales poorly with both the number of satellites as well as the number of obstacles to avoid, due to the pairwise safety constraints. In this work, we introduce a permutation-equivariant neural operator for trajectory planning of spacecraft swarms. This neural operator maps distributions of spacecraft initial states, target states, and obstacle initial states to trajectories which avoid collision and conserve fuel. This neural operator output is then paired with a batched Gauss-Newton finish to enforce exact orbital dynamics, and further reduce fuel use. The operator is self-supervised, trained without optimal trajectory labels. When trained on ten spacecraft, the proposed method generalized zero-shot to swarms of 1,000 spacecraft and 11,000 obstacles. The generated trajectories matched a per-agent optimal control solver's accuracy while retaining collision avoidance. Operator learning grounded in physics may offer a fast, scalable alternative to trajectory optimization in the increasingly crowded orbits of the future.