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

TL;DR

The paper confronts the problem of accurate trajectory tracking for agile quadrotors by directly comparing nonlinear-model-predictive control (NMPC) with an improved differential-flatness-based controller (DFBC), both augmented with Incremental Nonlinear Dynamic Inversion (INDI) as a robust inner-loop and evaluated with an aerodynamic drag model. It demonstrates that NMPC delivers superior performance on dynamically infeasible trajectories at the cost of higher computation and potential convergence issues, while DFBC achieves competitive tracking on feasible trajectories with far lower computational load. The study emphasizes the critical role of the inner-loop controller and shows that incorporating INDI substantially reduces tracking errors in real-world flights for both controllers, with real experiments indicating over a 78% position-tracking error reduction when using these enhancements. Collectively, the results offer a practical baseline and actionable guidance for deploying agile quadrotor controllers, and they motivate future work on hybrid NMPC-DFBC schemes to combine robustness and efficiency in real-time operations.

Abstract

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.

Figures (17)

• Figure 1: Top: Our quadrotor tracking a race trajectory. Bottom: Box plot comparing the position tracking root-mean-square-error (RMSE) of NMPC, DFBC, and their variations with INDI inner-loop, with or without considering aerodynamic drag effects. For each method, data are collected from real-world flights tracking different reference trajectories with speeds up to 20 m/s (i.e., 72 km/h) and accelerations up to 5g.
• Figure 2: Coordinate definitions and propeller numbering convention.
• Figure 3: The control diagram of the model predictive controller with an INDI inner-loop controller.
• Figure 4: The control diagram of the differential-flatness-based controller, combined with an INDI inner-loop controller.
• Figure 5: Boxplot of tracking error (RMSE) in tracking different dynamically feasible trajectories (76 in total) categorized by maximum accelerations.