  In this paper, we study the quadrotor UAV attitude control on 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 PD controller to the geometric L1 adaptive
controller. Experimental validation of the proposed controller is carried out
on an Autel X-star quadrotor.
