Robust adaptive control for aggressive quadrotor maneuvers via SO(3) and backstepping techniques

Abstract

For decades, a number of nonlinear control methodologies such as backstepping control and model predictive control have been studied to guarantee the stability and performance of systems under control. Most of these designs were based on local coordinates like Euler angles or quaternions, coming with inherent limitations such as singularities and unwinding phenomena, thereby hindering practical applications where large angle rotational maneuvers are commanded. In this paper, we propose a novel adaptive geometric tracking controller based on the logarithmic map of $\mathrm{SO}\left(3\right)$, the special orthogonal group, for aggressive maneuvers of a quadrotor subject to uncertain mass and inertia matrix. By directly synthesizing control laws on $\mathrm{SO}\left(3\right)$, issues raised by local coordinates can be circumvented. Furthermore, we provide theoretical proofs establishing asymptotic tracking and the boundedness of all signals in the closed-loop system. We enhance robustness by applying projection operators to adaptive laws, addressing nonparametric uncertainties like sensor noise. Through simulation, our proposed controller outperforms prior geometric controllers in tracking aggressive trajectories, particularly excelling in the face of uncertainties.