$\mathcal{L}_1$Quad: $\mathcal{L}_1$ Adaptive Augmentation of Geometric Control for Agile Quadrotors with Performance Guarantees

Quadrotors that can operate predictably in the presence of imperfect model knowledge and external disturbances are crucial in safety-critical applications. We present L1Quad, a control architecture that ensures uniformly bounded transient response of the quadrotor's uncertain dynamics on the special Euclidean group SE(3). By leveraging the geometric controller and the L1 adaptive controller, the L1Quad architecture provides a theoretically justified framework for the design and analysis of quadrotor's tracking controller in the presence of nonlinear (time- and state-dependent) uncertainties on both the translational and rotational dynamics. In addition, we validate the performance of the L1Quad architecture through extensive experiments for eleven types of uncertainties across various trajectories. The results demonstrate that the L1Quad can achieve consistently small tracking errors despite the uncertainties and disturbances and significantly outperforms existing state-of-the-art controllers.