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

arXiv: https://arxiv.org/abs/2608.00320 · HTML: https://mlsanity.com/paper/2608.00320/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 36 references that are in the map.
- First posted on arXiv 31 Jul 2026.

## Builds on (most cited first, 11 of 11)

- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets](https://mlsanity.com/paper/2103.10974/) (2021)
- [In-Context Operator Learning with Data Prompts for Differential Equation Problems](https://mlsanity.com/paper/2304.07993/) (2023)
- [A Machine Learning Framework for Solving High-Dimensional Mean Field Game and Mean Field Control Problems](https://mlsanity.com/paper/1912.01825/) (2019)
- [Learning in Mean Field Games: A Survey](https://mlsanity.com/paper/2205.12944/) (2022)
- [Back to Newton's Laws: Learning Vision-based Agile Flight via Differentiable Physics](https://mlsanity.com/paper/2407.10648/) (2024)
- [Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning](https://mlsanity.com/paper/2506.10973/) (2025)
- [In-Context Operator Learning on the Space of Probability Measures](https://mlsanity.com/paper/2601.09979/) (2026)
- [Markov Decision Processes for Satellite Maneuver Planning and Collision Avoidance](https://mlsanity.com/paper/2501.02667/) (2025)
- [Self-Supervised Amortized Neural Operators for Optimal Control: Scaling Laws and Applications](https://mlsanity.com/paper/2512.24897/) (2025)
- [Regional Constellation Reconfiguration Problem: Integer Linear Programming Formulation and Lagrangian Heuristic Method](https://mlsanity.com/paper/2206.02910/) (2022)

## Abstract (arXiv)

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.