Adaptive geodesic feedback controller design for the quadrotor

In this paper, a non-linear adaptive control method based on SO(3) for the quadrotor attitude tracking is proposed. Distinct from other control methods on Euclidean space, the controller proposed is developed on SO(3), which can avoid singularities and ambiguities. Besides, the geodesic on SO(3) is used to provide the shortest curve between the current attitude configuration and the desire attitude configuration. Then, a feedback controller based on geodesic is derived. To solve the problem that the inertial tensor of the quadrotor is unknown, an adaptive term is designed with the Lyapunov theory to estimate the inertial tensor. Thus, the almost global asymptotic stability of the quadrotor attitude tracking is achieved without the prior knowledge of the quadrotor inertia tensor. The numerical simulations are utilised to show better control performance of the adaptive geodesic feedback control method.