$mathcal{L}_1$ Adaptive Augmentation for Geometric Tracking Control of Quadrotors

This paper introduces an $mathcal{L}_1$ adaptive control augmentation for geometric tracking control of quadrotors. In the proposed design, the $mathcal{L}_1$ augmentation handles nonlinear (time- and state-dependent) uncertainties in the quadrotor dynamics without assuming/enforcing parametric structures, while the baseline geometric controller achieves stabilization of the known nonlinear model of the system dynamics. The $mathcal{L}_1$ augmentation applies to both the rotational and the translational dynamics. Experimental results demonstrate that the augmented geometric controller shows consistent and (on average five times) smaller trajectory tracking errors compared with the geometric controller alone when tested for different trajectories and under various types of uncertainties/disturbances.