# Neural-Swarm2: Planning and Control of Heterogeneous Multirotor Swarms using Learned Interactions

arXiv: https://arxiv.org/abs/2012.05457 · HTML: https://mlsanity.com/paper/2012.05457/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Dec 2020.

## Built on by (most cited first, 20 of 20)

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- [SO(2)-Equivariant Downwash Models for Close Proximity Flight](https://mlsanity.com/paper/2305.18983/) (2023)
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- [Tiny-PULP-Dronets: Squeezing Neural Networks for Faster and Lighter Inference on Multi-Tasking Autonomous Nano-Drones](https://mlsanity.com/paper/2407.02405/) (2024)
- [Flying Quadrotors in Tight Formations using Learning-based Model Predictive Control](https://mlsanity.com/paper/2410.09727/) (2024)
- [Automatic Optimisation of Normalised Neural Networks](https://mlsanity.com/paper/2312.10672/) (2023)
- [Online Adaptation for Flying Quadrotors in Tight Formations](https://mlsanity.com/paper/2506.17488/) (2025)
- [Learning to Initialize Trajectory Optimization for Vision-Based Autonomous Flight in Unknown Environments](https://mlsanity.com/paper/2309.10683/) (2023)
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- [Wake Up to the Past: Using Memory to Model Fluid Wake Effects on Robots](https://mlsanity.com/paper/2603.22472/) (2026)

## Abstract (arXiv)

We present Neural-Swarm2, a learning-based method for motion planning and control that allows heterogeneous multirotors in a swarm to safely fly in close proximity. Such operation for drones is challenging due to complex aerodynamic interaction forces, such as downwash generated by nearby drones and ground effect. Conventional planning and control methods neglect capturing these interaction forces, resulting in sparse swarm configuration during flight. Our approach combines a physics-based nominal dynamics model with learned Deep Neural Networks (DNNs) with strong Lipschitz properties. We make use of two techniques to accurately predict the aerodynamic interactions between heterogeneous multirotors: i) spectral normalization for stability and generalization guarantees of unseen data and ii) heterogeneous deep sets for supporting any number of heterogeneous neighbors in a permutation-invariant manner without reducing expressiveness. The learned residual dynamics benefit both the proposed interaction-aware multi-robot motion planning and the nonlinear tracking control design because the learned interaction forces reduce the modelling errors. Experimental results demonstrate that Neural-Swarm2 is able to generalize to larger swarms beyond training cases and significantly outperforms a baseline nonlinear tracking controller with up to three times reduction in worst-case tracking errors.