Over the past few decades, continuous quaternion-based attitude control has been proven highly effective for driving rotational systems that can be modeled as rigid bodies, such as satellites and drones. However, methods rooted in this approach do not enforce the existence of a unique closed-loop (CL) equilibrium attitude-error quaternion (AEQ); and, for rotational errors about the attitude-error Euler axis larger than {\pi}rad, their proportional-control effect diminishes as the system state moves away from the stable equilibrium of the CL rotational dynamics. In this paper, we introduce a new type of attitude control law that more effectively leverages the attitude-error Euler axis-angle information to guarantee a unique CL equilibrium AEQ and to provide greater flexibility in the use of proportional-control efforts. Furthermore, using two different control laws as examples-through the construction of a strict Lyapunov function for the CL dynamics-we demonstrate that the resulting unique equilibrium of the CL rotational system can be enforced to be uniformly asymptotically stable. To assess and demonstrate the functionality and performance of the proposed approach, we performed numerical simulations and executed dozens of real-time tumble-recovery maneuvers using a small quadrotor. These simulations and flight tests compellingly demonstrate that the proposed axis-angle-based method achieves superior flight performance-compared with that obtained using a high-performance quaternion-based controller-in terms of stabilization time.

翻译：过去几十年来，基于连续四元数的姿态控制已被证明对驱动可建模为刚体的旋转系统（如卫星和无人机）极为有效。然而，基于此方法的技术并不强制要求存在唯一的闭环（CL）平衡姿态误差四元数（AEQ）；并且，当绕姿态误差欧拉轴的旋转误差超过{\pi}弧度时，其比例控制效果会随着系统状态远离闭环旋转动力学的稳定平衡点而减弱。本文提出一种新型姿态控制律，能更有效地利用姿态误差欧拉轴角信息，以保证唯一的闭环平衡AEQ，并为比例控制力的运用提供更大灵活性。此外，通过构建闭环动力学的严格李雅普诺夫函数，我们以两种不同控制律为例，证明闭环旋转系统的唯一平衡点可被强制实现为一致渐近稳定。为评估并验证所提方法的功能与性能，我们进行了数值仿真，并利用小型四旋翼飞行器执行了数十次实时翻滚恢复机动。这些仿真与飞行测试充分表明：在稳定时间指标上，所提出的基于轴角的方法相较于采用高性能四元数控制器获得了更优越的飞行性能。