Geometric L1 Adaptive Attitude Control for a Quadrotor Unmanned Aerial Vehicle

Abstract

In this paper, we study the quadrotor unmanned aerial vehicle (UAV) attitude control on special orthogonal group (SO(3)) in the presence of unknown disturbances and model uncertainties. L1 adaptive control for UAVs using Euler angles/quaternions is shown to exhibit robustness and precise attitude tracking in the presence of disturbances and uncertainties. However, it is well known that dynamical models and controllers that use Euler angle representations are prone to singularities and typically have smaller regions of attraction while quaternion representations are subject to the unwinding phenomenon. To avoid such complexities, we present a geometric L1 adaptation control law to estimate the uncertainties. A model reference adaptive control approach is implemented, with the attitude errors between the quadrotor model and the reference model defined on the manifold. Control laws for the quadrotor and reference models are developed directly on SO(3) to track the desired trajectory while rejecting the uncertainties. Control Lyapunov function-based analysis is used to show the exponential input-to-state stability of the attitude errors. The proposed L1 adaptive controller is validated using numerical simulations. Preliminary experimental results are shown comparing a geometric proportional-derivative controller to the geometric L1 adaptive controller. Experimental validation of the proposed controller is carried out on an Autel X-star quadrotor.