This paper proposes a novel quaternion-based approach for tracking the translation (position and linear velocity) and rotation (attitude and angular velocity) trajectories of underactuated Unmanned Aerial Vehicles (UAVs). Quadrotor UAVs are challenging regarding accuracy, singularity, and uncertainties issues. Controllers designed based on unit-quaternion are singularity-free for attitude representation compared to other methods (e.g., Euler angles), which fail to represent the vehicle's attitude at multiple orientations. Quaternion-based Adaptive Backstepping Control (ABC) and Adaptive Fast Terminal Sliding Mode Control (AFTSMC) are proposed to address a set of challenging problems. A quaternion-based ABC, a superior recursive approach, is proposed to generate the necessary thrust handling unknown uncertainties and UAV translation trajectory tracking. Next, a quaternion-based AFTSMC is developed to overcome parametric uncertainties, avoid singularity, and ensure fast convergence in a finite time. Moreover, the proposed AFTSMC is able to significantly minimize control signal chattering, which is the main reason for actuator failure and provide smooth and accurate rotational control input. To ensure the robustness of the proposed approach, the designed control algorithms have been validated considering unknown time-variant parametric uncertainties and significant initialization errors. The proposed techniques has been compared to state-of-the-art control technique. Keywords: Adaptive Backstepping Control (ABC), Adaptive Fast Terminal Sliding Mode Control (AFTSMC), Unit-quaternion, Unmanned Aerial Vehicles, Singularity Free, Pose Control

翻译：本文提出了一种新颖的基于四元数的方法，用于跟踪欠驱动无人机（UAV）的平移（位置与线速度）与旋转（姿态与角速度）轨迹。四旋翼无人机在精度、奇异性和不确定性方面存在挑战。与其他方法（如欧拉角）相比，基于单位四元数设计的控制器在姿态表示上无奇异性，而欧拉角等方法无法表示飞行器在多个方向上的姿态。为应对一系列具有挑战性的问题，本文提出了基于四元数的自适应反步控制（ABC）与自适应快速终端滑模控制（AFTSMC）。首先，提出了一种基于四元数的ABC，这是一种优越的递归方法，用于生成必要的推力以处理未知的不确定性并实现无人机平移轨迹跟踪。其次，开发了一种基于四元数的AFTSMC，以克服参数不确定性、避免奇异性，并确保在有限时间内快速收敛。此外，所提出的AFTSMC能够显著最小化控制信号抖振（这是导致执行器故障的主要原因），并提供平滑且精确的旋转控制输入。为确保所提方法的鲁棒性，所设计的控制算法已在考虑未知时变参数不确定性和显著初始化误差的情况下得到验证。所提出的技术已与最先进的控制技术进行了比较。关键词：自适应反步控制（ABC），自适应快速终端滑模控制（AFTSMC），单位四元数，无人机，无奇异性，位姿控制