提出新型轴角姿态控制法,提升旋转系统稳定速度与精度。
A New Type of Axis-Angle Attitude Control Law for Rotational Systems: Synthesis, Analysis, and Experiments
- 基于姿态误差轴角信息设计新控制律,确保唯一稳定平衡点。
- 实测表明,恢复时间比高性能四元数控制器快30%以上。
- 适合对响应速度要求高的无人机、卫星等旋转系统应用。
过去几十年,基于四元数的姿态控制在卫星、无人机等刚体旋转系统中被证明极为有效。然而,这类方法无法保证闭环(CL)姿态误差四元数(AEQ)存在唯一平衡点;当绕姿态误差欧拉轴的旋转误差超过π弧度时,比例控制效果会随状态远离稳定平衡而减弱。本文提出一种新型姿态控制律,更有效地利用姿态误差欧拉轴角信息,确保唯一闭环平衡AEQ,并增强比例控制灵活性。通过构建严格李雅普诺夫函数,以两种不同控制律为例,证明所获闭环系统的唯一平衡点可实现一致渐近稳定。为验证该方法的功能与性能,我们进行了数值仿真,并在小型四旋翼上执行了数十次实时翻滚恢复操作。仿真与飞行测试均表明,相比高性能四元数控制器,所提轴角方法在稳定性时间上表现更优,显著提升了飞行性能。
原文摘要 · Abstract (English)
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 πrad, 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.
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