# Flying Quadrotors in Tight Formations using Learning-based Model Predictive Control

arXiv: https://arxiv.org/abs/2410.09727 · HTML: https://mlsanity.com/paper/2410.09727/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 31 references that are in the map.
- First posted on arXiv 13 Oct 2024.

## Builds on (most cited first, 15 of 15)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [acados: a modular open-source framework for fast embedded optimal control](https://mlsanity.com/paper/1910.13753/) (2019)
- [OmniDrones: An Efficient and Flexible Platform for Reinforcement Learning in Drone Control](https://mlsanity.com/paper/2309.12825/) (2023)
- [KNODE-MPC: A Knowledge-based Data-driven Predictive Control Framework for Aerial Robots](https://mlsanity.com/paper/2109.04821/) (2021)
- [Neural-Swarm: Decentralized Close-Proximity Multirotor Control Using Learned Interactions](https://mlsanity.com/paper/2003.02992/) (2020)
- [Neural-Swarm2: Planning and Control of Heterogeneous Multirotor Swarms using Learned Interactions](https://mlsanity.com/paper/2012.05457/) (2020)
- [Online Dynamics Learning for Predictive Control with an Application to Aerial Robots](https://mlsanity.com/paper/2207.09344/) (2022)
- [Knowledge-Based Learning of Nonlinear Dynamics and Chaos](https://mlsanity.com/paper/2010.03415/) (2020)
- [SO(2)-Equivariant Downwash Models for Close Proximity Flight](https://mlsanity.com/paper/2305.18983/) (2023)
- [Nonlinear MPC for Quadrotors in Close-Proximity Flight with Neural Network Downwash Prediction](https://mlsanity.com/paper/2304.07794/) (2023)
- [Nonlinear Model Predictive Control for Cooperative Transportation and Manipulation of Cable Suspended Payloads with Multiple Quadrotors](https://mlsanity.com/paper/2303.06165/) (2023)
- [Enhancing Sample Efficiency and Uncertainty Compensation in Learning-based Model Predictive Control for Aerial Robots](https://mlsanity.com/paper/2308.00570/) (2023)
- [Modeling Aggregate Downwash Forces for Dense Multirotor Flight](https://mlsanity.com/paper/2312.03488/) (2023)
- [Docking Multirotors in Close Proximity using Learnt Downwash Models](https://mlsanity.com/paper/2311.13988/) (2023)

## Built on by (most cited first, 2 of 2)

- [Online Adaptation for Flying Quadrotors in Tight Formations](https://mlsanity.com/paper/2506.17488/) (2025)
- [Wake Up to the Past: Using Memory to Model Fluid Wake Effects on Robots](https://mlsanity.com/paper/2603.22472/) (2026)

## Abstract (arXiv)

Flying quadrotors in tight formations is a challenging problem. It is known that in the near-field airflow of a quadrotor, the aerodynamic effects induced by the propellers are complex and difficult to characterize. Although machine learning tools can potentially be used to derive models that capture these effects, these data-driven approaches can be sample inefficient and the resulting models often do not generalize as well as their first-principles counterparts. In this work, we propose a framework that combines the benefits of first-principles modeling and data-driven approaches to construct an accurate and sample efficient representation of the complex aerodynamic effects resulting from quadrotors flying in formation. The data-driven component within our model is lightweight, making it amenable for optimization-based control design. Through simulations and physical experiments, we show that incorporating the model into a novel learning-based nonlinear model predictive control (MPC) framework results in substantial performance improvements in terms of trajectory tracking and disturbance rejection. In particular, our framework significantly outperforms nominal MPC in physical experiments, achieving a 40.1% improvement in the average trajectory tracking errors and a 57.5% reduction in the maximum vertical separation errors. Our framework also achieves exceptional sample efficiency, using only a total of 46 seconds of flight data for training across both simulations and physical experiments. Furthermore, with our proposed framework, the quadrotors achieve an exceptionally tight formation, flying with an average separation of less than 1.5 body lengths throughout the flight. A video illustrating our framework and physical experiments is given here: https://youtu.be/Hv-0JiVoJGo