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

TL;DR

This paper proves that quadrotor dynamics with rotor drag are differentially flat, enabling precise feed-forward control for high-speed trajectory tracking and reducing errors compared to existing methods.

Contribution

It introduces the first differential flatness property for quadrotors with rotor drag, facilitating improved control and trajectory tracking accuracy.

Findings

Significantly reduced trajectory tracking error with the proposed control method.

Validated the differential flatness property through extensive experiments.

Developed a gradient-free optimization method to identify rotor drag coefficients.

Abstract

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.