# Differential Flatness of Quadrotor Dynamics Subject to Rotor Drag for Accurate Tracking of High-Speed Trajectories

arXiv: https://arxiv.org/abs/1712.02402 · HTML: https://mlsanity.com/paper/1712.02402/

## Key facts

- Cited by 32 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Dec 2017.

## Built on by (most cited first, 30 of 32)

- [Neural-Fly Enables Rapid Learning for Agile Flight in Strong Winds](https://mlsanity.com/paper/2205.06908/) (2022)
- [Real-time Neural-MPC: Deep Learning Model Predictive Control for Quadrotors and Agile Robotic Platforms](https://mlsanity.com/paper/2203.07747/) (2022)
- [Bootstrapping Reinforcement Learning with Imitation for Vision-Based Agile Flight](https://mlsanity.com/paper/2403.12203/) (2024)
- [Time-Optimal Planning for Quadrotor Waypoint Flight](https://mlsanity.com/paper/2108.04537/) (2021)
- [Learning Perception-Aware Agile Flight in Cluttered Environments](https://mlsanity.com/paper/2210.01841/) (2022)
- [Training Efficient Controllers via Analytic Policy Gradient](https://mlsanity.com/paper/2209.13052/) (2022)
- [Learning a Single Near-hover Position Controller for Vastly Different Quadcopters](https://mlsanity.com/paper/2209.09232/) (2022)
- [DATT: Deep Adaptive Trajectory Tracking for Quadrotor Control](https://mlsanity.com/paper/2310.09053/) (2023)
- [SOUS VIDE: Cooking Visual Drone Navigation Policies in a Gaussian Splatting Vacuum](https://mlsanity.com/paper/2412.16346/) (2024)
- [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)
- [Meta-Learning-Based Robust Adaptive Flight Control Under Uncertain Wind Conditions](https://mlsanity.com/paper/2103.01932/) (2021)
- [Feedback Favors the Generalization of Neural ODEs](https://mlsanity.com/paper/2410.10253/) (2024)
- [Dashing for the Golden Snitch: Multi-Drone Time-Optimal Motion Planning with Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2409.16720/) (2024)
- [Leveling the Playing Field: Carefully Comparing Classical and Learned Controllers for Quadrotor Trajectory Tracking](https://mlsanity.com/paper/2506.17832/) (2025)
- [Robust Navigation for Racing Drones based on Imitation Learning and Modularization](https://mlsanity.com/paper/2105.12923/) (2021)
- [Constrained Reinforcement Learning using Distributional Representation for Trustworthy Quadrotor UAV Tracking Control](https://mlsanity.com/paper/2302.11694/) (2023)
- [TACO: General Acrobatic Flight Control via Target-and-Command-Oriented Reinforcement Learning](https://mlsanity.com/paper/2503.01125/) (2025)
- [Learned Controllers for Agile Quadrotors in Pursuit-Evasion Games](https://mlsanity.com/paper/2506.02849/) (2025)
- [Mastering Diverse, Unknown, and Cluttered Tracks for Robust Vision-Based Drone Racing](https://mlsanity.com/paper/2512.09571/) (2025)
- [FLEX: an Adaptive Exploration Algorithm for Nonlinear Systems](https://mlsanity.com/paper/2304.13426/) (2023)
- [Automatic Generation of Aerobatic Flight in Complex Environments via Diffusion Models](https://mlsanity.com/paper/2504.15138/) (2025)
- [Interpretable Stochastic Model Predictive Control using Distributional Reinforced Estimation for Quadrotor Tracking Systems](https://mlsanity.com/paper/2205.07150/) (2022)
- [Why Change Your Controller When You Can Change Your Planner: Drag-Aware Trajectory Generation for Quadrotor Systems](https://mlsanity.com/paper/2401.04960/) (2024)
- [PI-WAN: A Physics-Informed Wind-Adaptive Network for Quadrotor Dynamics Prediction in Unknown Environments](https://mlsanity.com/paper/2507.00816/) (2025)
- [From Distances to Trajectories: Real-Time Signed Distance Function Mapping and Distance-Accelerated Motion Planning for UAVs](https://mlsanity.com/paper/2607.19306/) (2026)
- [Safe Online Dynamics Learning with Initially Unknown Models and Infeasible Safety Certificates](https://mlsanity.com/paper/2311.02133/) (2023)
- [Online parameter estimation for the Crazyflie quadcopter through an EM algorithm](https://mlsanity.com/paper/2601.17009/) (2026)
- [Learning over Forward-Invariant Policy Classes: Reinforcement Learning without Safety Concerns](https://mlsanity.com/paper/2604.07875/) (2026)
- [Fuzzy Logic Theory-based Adaptive Reward Shaping for Robust Reinforcement Learning (FARS)](https://mlsanity.com/paper/2604.15772/) (2026)
- [Don't Fool Me Twice: Adapting to Adversity in the Wild with Experience-Driven Reasoning](https://mlsanity.com/paper/2605.31119/) (2026)

## Abstract (arXiv)

In this paper, we prove that the dynamical model of a quadrotor subject to linear rotor drag effects is differentially flat in its position and heading. We use this property to compute feed-forward control terms directly from a reference trajectory to be tracked. The obtained feed-forward terms are then used in a cascaded, nonlinear feedback control law that enables accurate agile flight with quadrotors. Compared to state-of-the-art control methods, which treat the rotor drag as an unknown disturbance, our method reduces the trajectory tracking error significantly. Finally, we present a method based on a gradient-free optimization to identify the rotor drag coefficients, which are required to compute the feed-forward control terms. The new theoretical results are thoroughly validated trough extensive comparative experiments.