L₁Adaptive Augmentation for Geometric Tracking Control of Quadrotors

Abstract

This paper introduces an <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$L$</tex> <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf> adaptive control aug-mentation for geometric tracking control of quadrotors. In the proposed design, the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$L$</tex> <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf> augmentation handles nonlinear (time-and state-dependent) uncertainties in the quadrotor dynamics without assuming or enforcing parametric structures, while the baseline geometric controller achieves stabilization of the known nonlinear model of the system dynamics. The <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$L$</tex> <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf> augmentation applies to both the rotational and the translational dynamics. Experimental results demonstrate that the augmented geomet-ric 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.