  This paper presents a novel quaternion-based nonsingular control system for
underactuated vertical-take-off and landing (VTOL) Unmanned Aerial Vehicles
(UAVs). Position and attitude tracking is challenging regarding singularity and
accuracy. Quaternion-based Adaptive Backstepping Control (QABC) is developed to
tackle the underactuated issues of UAV control systems in a cascaded way.
Leveraging the virtual control (auxiliary control) developed in the QABC,
desired attitude components and required thrust are produced. Afterwards, we
propose Quaternion-based Sliding Mode Control (QASMC) to enhance the stability
and mitigate chattering issues. The sliding surface is modified to avoid
singularity compared to conventional SMC. To improve the robustness of
controllers, the control parameters are updated using adaptation laws.
Furthermore, the asymptotic stability of translational and rotational dynamics
is guaranteed by utilizing Lyapunov stability and Barbalet Lemma. Finally, the
comprehensive comparison results are provided to verify the effectiveness of
the proposed controllers in the presence of unknown time-varying parameter
uncertainties and significant initial errors. Keywords: Non-singular Sliding
Mode Control, Adaptive Backstepping Control, Unit-quaternion, Drones, Unmanned
Aerial Vehicles, Asymptotic Stability, Position and Orientation Control
