# A Comparative Study of Nonlinear MPC and Differential-Flatness-Based Control for Quadrotor Agile Flight

arXiv: https://arxiv.org/abs/2109.01365 · HTML: https://mlsanity.com/paper/2109.01365/

## Key facts

- Cited by 24 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Sep 2021.

## Built on by (most cited first, 24 of 24)

- [Learning Perception-Aware Agile Flight in Cluttered Environments](https://mlsanity.com/paper/2210.01841/) (2022)
- [Learning Quadrotor Control From Visual Features Using Differentiable Simulation](https://mlsanity.com/paper/2410.15979/) (2024)
- [DATT: Deep Adaptive Trajectory Tracking for Quadrotor Control](https://mlsanity.com/paper/2310.09053/) (2023)
- [Learning Speed Adaptation for Flight in Clutter](https://mlsanity.com/paper/2403.04586/) (2024)
- [Active Learning of Discrete-Time Dynamics for Uncertainty-Aware Model Predictive Control](https://mlsanity.com/paper/2210.12583/) (2022)
- [Deep Model Predictive Optimization](https://mlsanity.com/paper/2310.04590/) (2023)
- [Data-Driven Control with Inherent Lyapunov Stability](https://mlsanity.com/paper/2303.03157/) (2023)
- [Leveling the Playing Field: Carefully Comparing Classical and Learned Controllers for Quadrotor Trajectory Tracking](https://mlsanity.com/paper/2506.17832/) (2025)
- [Constrained Reinforcement Learning using Distributional Representation for Trustworthy Quadrotor UAV Tracking Control](https://mlsanity.com/paper/2302.11694/) (2023)
- [Decentralized Aerial Manipulation of a Cable-Suspended Load using Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2508.01522/) (2025)
- [TACO: General Acrobatic Flight Control via Target-and-Command-Oriented Reinforcement Learning](https://mlsanity.com/paper/2503.01125/) (2025)
- [Perception-Aware Perching on Powerlines with Multirotors](https://mlsanity.com/paper/2202.06434/) (2022)
- [PI-WAN: A Physics-Informed Wind-Adaptive Network for Quadrotor Dynamics Prediction in Unknown Environments](https://mlsanity.com/paper/2507.00816/) (2025)
- [Decentralized Real-Time Planning for Multi-UAV Cooperative Manipulation via Imitation Learning](https://mlsanity.com/paper/2510.17143/) (2025)
- [Crazyflow: An Accurate, GPU-Accelerated, Differentiable Drone Simulator in JAX](https://mlsanity.com/paper/2606.01478/) (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)
- [Autonomous Navigation of Micro Air Vehicles in Warehouses Using Vision-based Line Following](https://mlsanity.com/paper/2310.00950/) (2023)
- [Hovering Flight of Soft-Actuated Insect-Scale Micro Aerial Vehicles using Deep Reinforcement Learning](https://mlsanity.com/paper/2502.12355/) (2025)
- [Multi-Task Reinforcement Learning of Drone Aerobatics by Exploiting Geometric Symmetries](https://mlsanity.com/paper/2602.10997/) (2026)
- [Drag-Aware Aerodynamic Manipulability for Torque-Limited Redundant Multirotors: Aerodynamic Promptness based on the Symmetric Acceleration Capacity](https://mlsanity.com/paper/2603.07998/) (2026)
- [MAVEN: A Meta-Reinforcement Learning Framework for Varying-Dynamics Expertise in Agile Quadrotor Maneuvers](https://mlsanity.com/paper/2603.10714/) (2026)
- [Online Reinforcement Learning for Safe Gain Scheduling in Nonlinear Quadrotor Control](https://mlsanity.com/paper/2604.16819/) (2026)
- [Exploiting Differential Flatness for Efficient Learning-based Model Predictive Control of Constrained Multi-Input Control Affine Systems](https://mlsanity.com/paper/2604.24706/) (2026)
- [Self-Adaptive Learning and Model Predictive Control for Tracking Unknown Dynamics with No Regret](https://mlsanity.com/paper/2607.26370/) (2026)

## Abstract (arXiv)

Accurate trajectory tracking control for quadrotors is essential for safe navigation in cluttered environments. However, this is challenging in agile flights due to nonlinear dynamics, complex aerodynamic effects, and actuation constraints. In this article, we empirically compare two state-of-the-art control frameworks: the nonlinear-model-predictive controller (NMPC) and the differential-flatness-based controller (DFBC), by tracking a wide variety of agile trajectories at speeds up to 20 m/s (i.e.,72 km/h). The comparisons are performed in both simulation and real-world environments to systematically evaluate both methods from the aspect of tracking accuracy, robustness, and computational efficiency. We show the superiority of NMPC in tracking dynamically infeasible trajectories, at the cost of higher computation time and risk of numerical convergence issues. For both methods, we also quantitatively study the effect of adding an inner-loop controller using the incremental nonlinear dynamic inversion (INDI) method, and the effect of adding an aerodynamic drag model. Our real-world experiments, performed in one of the world's largest motion capture systems, demonstrate more than 78% tracking error reduction of both NMPC and DFBC, indicating the necessity of using an inner-loop controller and aerodynamic drag model for agile trajectory tracking.