# NeuroBEM: Hybrid Aerodynamic Quadrotor Model

arXiv: https://arxiv.org/abs/2106.08015 · HTML: https://mlsanity.com/paper/2106.08015/

## Key facts

- Cited by 37 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Jun 2021.

## Built on by (most cited first, 30 of 37)

- [Reaching the Limit in Autonomous Racing: Optimal Control versus Reinforcement Learning](https://mlsanity.com/paper/2310.10943/) (2023)
- [Real-time Neural-MPC: Deep Learning Model Predictive Control for Quadrotors and Agile Robotic Platforms](https://mlsanity.com/paper/2203.07747/) (2022)
- [Demonstrating Agile Flight from Pixels without State Estimation](https://mlsanity.com/paper/2406.12505/) (2024)
- [KNODE-MPC: A Knowledge-based Data-driven Predictive Control Framework for Aerial Robots](https://mlsanity.com/paper/2109.04821/) (2021)
- [The Reality Gap in Robotics: Challenges, Solutions, and Best Practices](https://mlsanity.com/paper/2510.20808/) (2025)
- [Physics-Inspired Temporal Learning of Quadrotor Dynamics for Accurate Model Predictive Trajectory Tracking](https://mlsanity.com/paper/2206.03305/) (2022)
- [Contrastive Learning for Enhancing Robust Scene Transfer in Vision-based Agile Flight](https://mlsanity.com/paper/2309.09865/) (2023)
- [Active Learning of Discrete-Time Dynamics for Uncertainty-Aware Model Predictive Control](https://mlsanity.com/paper/2210.12583/) (2022)
- [Vision-based Learning for Drones: A Survey](https://mlsanity.com/paper/2312.05019/) (2023)
- [What Matters in Learning A Zero-Shot Sim-to-Real RL Policy for Quadrotor Control? A Comprehensive Study](https://mlsanity.com/paper/2412.11764/) (2024)
- [SkyJEPA: Learning Long-Horizon World Models for Zero-Shot Sim-to-Real Control of Quadrotors](https://mlsanity.com/paper/2606.23444/) (2026)
- [Residual Physics Learning and System Identification for Sim-to-real Transfer of Policies on Buoyancy Assisted Legged Robots](https://mlsanity.com/paper/2303.09597/) (2023)
- [DroneDiffusion: Robust Quadrotor Dynamics Learning with Diffusion Models](https://mlsanity.com/paper/2409.11292/) (2024)
- [Environment as Policy: Learning to Race in Unseen Tracks](https://mlsanity.com/paper/2410.22308/) (2024)
- [Leveling the Playing Field: Carefully Comparing Classical and Learned Controllers for Quadrotor Trajectory Tracking](https://mlsanity.com/paper/2506.17832/) (2025)
- [Neural Moving Horizon Estimation for Robust Flight Control](https://mlsanity.com/paper/2206.10397/) (2022)
- [Reasoning in visual navigation of end-to-end trained agents: a dynamical systems approach](https://mlsanity.com/paper/2503.08306/) (2025)
- [Temporal Convolutions for Multi-Step Quadrotor Motion Prediction](https://mlsanity.com/paper/2110.04182/) (2021)
- [TACO: General Acrobatic Flight Control via Target-and-Command-Oriented Reinforcement Learning](https://mlsanity.com/paper/2503.01125/) (2025)
- [Low-Latency Event-Based Velocimetry for Quadrotor Control in a Narrow Pipe](https://mlsanity.com/paper/2507.15444/) (2025)
- [Learning Physics-Guided Residual Dynamics for Deformable Object Simulation](https://mlsanity.com/paper/2607.13451/) (2026)
- [Learning Reduced Nonlinear State-Space Models: an Output-Error Based Canonical Approach](https://mlsanity.com/paper/2206.04791/) (2022)
- [Safety Filter Design for Neural Network Systems via Convex Optimization](https://mlsanity.com/paper/2308.08086/) (2023)
- [Learning Long-Horizon Predictions for Quadrotor Dynamics](https://mlsanity.com/paper/2407.12964/) (2024)
- [On learning racing policies with reinforcement learning](https://mlsanity.com/paper/2504.02420/) (2025)
- [Towards Task-Oriented Flying: Framework, Infrastructure, and Principles](https://mlsanity.com/paper/2504.15129/) (2025)
- [NOVA: Navigation via Object-Centric Visual Autonomy for High-Speed Target Tracking in Unstructured GPS-Denied Environments](https://mlsanity.com/paper/2506.18689/) (2025)
- [PI-WAN: A Physics-Informed Wind-Adaptive Network for Quadrotor Dynamics Prediction in Unknown Environments](https://mlsanity.com/paper/2507.00816/) (2025)
- [Superhuman Safe and Agile Racing through Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2605.22748/) (2026)
- [Wind-Aware Reinforcement Learning Control of a Small Quadrotor Using Learned Onboard Wind Estimation in Simulated Atmospheric Turbulence](https://mlsanity.com/paper/2607.01528/) (2026)

## Abstract (arXiv)

Quadrotors are extremely agile, so much in fact, that classic first-principle-models come to their limits. Aerodynamic effects, while insignificant at low speeds, become the dominant model defect during high speeds or agile maneuvers. Accurate modeling is needed to design robust high-performance control systems and enable flying close to the platform's physical limits. We propose a hybrid approach fusing first principles and learning to model quadrotors and their aerodynamic effects with unprecedented accuracy. First principles fail to capture such aerodynamic effects, rendering traditional approaches inaccurate when used for simulation or controller tuning. Data-driven approaches try to capture aerodynamic effects with blackbox modeling, such as neural networks; however, they struggle to robustly generalize to arbitrary flight conditions. Our hybrid approach unifies and outperforms both first-principles blade-element theory and learned residual dynamics. It is evaluated in one of the world's largest motion-capture systems, using autonomous-quadrotor-flight data at speeds up to 65km/h. The resulting model captures the aerodynamic thrust, torques, and parasitic effects with astonishing accuracy, outperforming existing models with 50% reduced prediction errors, and shows strong generalization capabilities beyond the training set.