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

翻译：本文提出了一种基于四元数的新型非奇异控制系统，用于欠驱动垂直起降无人机。位置与姿态跟踪在奇异性与精度方面具有挑战性。本文开发了基于四元数的自适应反步控制，以级联方式处理无人机控制系统的欠驱动问题。利用QABC中设计的虚拟控制（辅助控制），可生成期望的姿态分量与所需推力。随后，我们提出基于四元数的滑模控制以增强稳定性并抑制抖振现象。相较于传统滑模控制，改进的滑模面可避免奇异性。为提升控制器的鲁棒性，控制参数通过自适应律进行更新。此外，通过利用李雅普诺夫稳定性理论与Barbalet引理，保证了平移与旋转动力学的渐近稳定性。最后，提供了全面的对比结果，验证了所提控制器在存在未知时变参数不确定性与显著初始误差情况下的有效性。关键词：非奇异滑模控制，自适应反步控制，单位四元数，无人机，渐近稳定性，位置与姿态控制