mlsanityData to 14 Oct 2026

SO(2)-Equivariant Downwash Models for Close Proximity Flight

arXiv 2305.18983 ↗First posted 30 May 2023cs.RO cs.AI cs.LGcited by 7

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Abstract (arXiv)

Multirotors flying in close proximity induce aerodynamic wake effects on each other through propeller downwash. Conventional methods have fallen short of providing adequate 3D force-based models that can be incorporated into robust control paradigms for deploying dense formations. Thus, learning a model for these downwash patterns presents an attractive solution. In this paper, we present a novel learning-based approach for modelling the downwash forces that exploits the latent geometries (i.e. symmetries) present in the problem. We demonstrate that when trained with only 5 minutes of real-world flight data, our geometry-aware model outperforms state-of-the-art baseline models trained with more than 15 minutes of data. In dense real-world flights with two vehicles, deploying our model online improves 3D trajectory tracking by nearly 36% on average (and vertical tracking by 56%).

Key facts. Cited by 7 papers in the map (data through 14 Oct 2026). Builds on 28 of its 49 references that are in the map. First posted on arXiv 30 May 2023.

Builds on

28 of 49 references.

References · 28

  1. 2018Neural Ordinary Differential Equationscited by 3,779
  2. 2021Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gaugescited by 1,167
  3. 2016Group Equivariant Convolutional Networkscited by 1,165
  4. 2016Geometric deep learning: going beyond Euclidean datacited by 1,048
  5. 2021E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentialscited by 708
  6. 2020Directional Message Passing for Molecular Graphscited by 561
  7. 2022MACE: Higher Order Equivariant Message Passing Neural Networks for Fast and Accurate Force Fieldscited by 474
  8. 2018Spherical CNNscited by 456
  9. 2019General E(2)-Equivariant Steerable CNNscited by 446
  10. 2016Steerable CNNscited by 305
  11. 2017Learning SO(3) Equivariant Representations with Spherical CNNscited by 248
  12. 2018A General Theory of Equivariant CNNs on Homogeneous Spacescited by 228
16 more
  1. 2021Geometric and Physical Quantities Improve E(3) Equivariant Message Passingcited by 228
  2. 2018Clebsch-Gordan Nets: a Fully Fourier Space Spherical Convolutional Neural Networkcited by 171
  3. 2018Neural Lander: Stable Drone Landing Control using Learned Dynamicscited by 85
  4. 2022SO(2)-Equivariant Reinforcement Learningcited by 84
  5. 2021Equivariant Q Learning in Spatial Action Spacescited by 62
  6. 2022Sample Efficient Grasp Learning Using Equivariant Modelscited by 53
  7. 2022On-Robot Learning With Equivariant Modelscited by 42
  8. 2017Safe Learning of Quadrotor Dynamics Using Barrier Certificatescited by 35
  9. 2022The Surprising Effectiveness of Equivariant Models in Domains with Latent Symmetrycited by 33
  10. 2021KNODE-MPC: A Knowledge-based Data-driven Predictive Control Framework for Aerial Robotscited by 26
  11. 2020Theoretical Aspects of Group Equivariant Neural Networkscited by 25
  12. 2020Neural-Swarm: Decentralized Close-Proximity Multirotor Control Using Learned Interactionscited by 20
  13. 2020Neural-Swarm2: Planning and Control of Heterogeneous Multirotor Swarms using Learned Interactionscited by 20
  14. 2020EGO-Swarm: A Fully Autonomous and Decentralized Quadrotor Swarm System in Cluttered Environmentscited by 15
  15. 2022Equivariant Reinforcement Learning for Quadrotor UAVcited by 6
  16. 2023Nonlinear MPC for Quadrotors in Close-Proximity Flight with Neural Network Downwash Predictioncited by 6

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 1; 2024: 3; 2025: 1; 2026: 2.

7 papers.

  1. 2024Morphological-Symmetry-Equivariant Heterogeneous Graph Neural Network for Robotic Dynamics Learningcited by 5
  2. 2024ProxFly: Robust Control for Close Proximity Quadcopter Flight via Residual Reinforcement Learningcited by 4
  3. 2023Docking Multirotors in Close Proximity using Learnt Downwash Modelscited by 2
  4. 2024Flying Quadrotors in Tight Formations using Learning-based Model Predictive Controlcited by 2
  5. 2025Symmetries-enhanced Multi-Agent Reinforcement Learningcited by 1
  6. 2026Multi-Task Reinforcement Learning of Drone Aerobatics by Exploiting Geometric Symmetriescited by 0
  7. 2026Wake Up to the Past: Using Memory to Model Fluid Wake Effects on Robotscited by 0