<i>L</i> ₁Quad: <i>L</i> ₁ Adaptive Augmentation of Geometric Control for Agile Quadrotors With Performance Guarantees

Abstract

Quadrotors that can operate predictably in the presence of imperfect model knowledge and external disturbances are crucial in safety-critical applications. We present <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\boldsymbol}{\mathcal{L}}_1$</tex-math> </inline-formula> Quad, 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 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\boldsymbol}{\mathcal{L}}_1$</tex-math> </inline-formula> adaptive controller, the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\boldsymbol}{\mathcal{L}}_1$</tex-math> </inline-formula> Quad 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 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\boldsymbol}{\mathcal{L}}_1$</tex-math> </inline-formula> Quad architecture through extensive experiments for 11 types of uncertainties across various trajectories. The results demonstrate that the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\boldsymbol}{\mathcal{L}}_1$</tex-math> </inline-formula> Quad can achieve consistently small tracking errors despite the uncertainties and disturbances and significantly outperforms existing state-of-the-art controllers.