# Nonlinear MPC for Quadrotors in Close-Proximity Flight with Neural Network Downwash Prediction

arXiv: https://arxiv.org/abs/2304.07794 · HTML: https://mlsanity.com/paper/2304.07794/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Apr 2023.

## Built on by (most cited first, 6 of 6)

- [SO(2)-Equivariant Downwash Models for Close Proximity Flight](https://mlsanity.com/paper/2305.18983/) (2023)
- [ProxFly: Robust Control for Close Proximity Quadcopter Flight via Residual Reinforcement Learning](https://mlsanity.com/paper/2409.13193/) (2024)
- [Docking Multirotors in Close Proximity using Learnt Downwash Models](https://mlsanity.com/paper/2311.13988/) (2023)
- [Flying Quadrotors in Tight Formations using Learning-based Model Predictive Control](https://mlsanity.com/paper/2410.09727/) (2024)
- [Wake Up to the Past: Using Memory to Model Fluid Wake Effects on Robots](https://mlsanity.com/paper/2603.22472/) (2026)
- [Temporal Learning for End-Effector Position Estimation under Aerodynamic Disturbances in Aerial Continuum Manipulation](https://mlsanity.com/paper/2609.28716/) (2026)

## Abstract (arXiv)

Swarm aerial robots are required to maintain close proximity to successfully traverse narrow areas in cluttered environments. However, this movement is affected by the downwash effect generated from other quadrotors in the swarm. This aerodynamic effect is highly nonlinear and hard to describe through mathematical modeling. Additionally, the existence of the downwash disturbance can be predicted based on the states of neighboring quadrotors. If this prediction is considered, the control loop can proactively handle the disturbance, resulting in improved performance. To address these challenges, we propose an approach that integrates a Neural network Downwash Predictor with Nonlinear Model Predictive Control (NDP-NMPC). The neural network is trained with spectral normalization to ensure robustness and safety in uncollected cases. The predicted disturbances are then incorporated into the optimization scheme in NMPC, which enforces constraints to ensure that states and inputs remain within safe limits. We also design a quadrotor system, identify its parameters, and implement the proposed method on board. Finally, we conduct a prediction experiment to validate the safety and effectiveness of the network. In addition, a real-time trajectory tracking experiment is performed with the entire system, demonstrating a 75.37% reduction in tracking error in height under the downwash effect.