基于几何代数的欠驱动无人机全局渐近稳定轨迹跟踪
Globally Asymptotically Stable Trajectory Tracking of Underactuated UAVs using Geometric Algebra
AI总结：
本文利用几何代数建立欠驱动无人机级联动力学模型，提出一种无需记忆和迭代搜索的简单控制策略，实现无奇异表示，并通过输入到状态稳定性证明和四倾转旋翼机有风环境仿真验证了全局渐近稳定的轨迹跟踪性能。
摘要：
本文采用几何代数（GA）工具对三维空间中物体的动力学进行建模，作为概念验证，以促进欠驱动系统轨迹跟踪的控制设计。出于控制目的，该模型被构造为级联系统，其中旋转子系统驱动平移子系统。旋转子系统是线性的，而平移子系统遵循线性加扰动形式，从而降低了控制设计的复杂性。本文提出了一种仅需简单运算、无需记忆且无需迭代搜索循环的控制策略，以展示GA模型的主要特征。通过使用GA对平移和旋转进行建模，可以利用几何积实现无奇异且几何直观的表示。利用输入到状态稳定性方法严格建立了闭环稳定性。四倾转旋翼机在有风环境中执行轨迹跟踪的数值仿真验证了控制器的稳定性和性能。
英文摘要：
This paper employs Geometric Algebra (GA) tools to model the dynamics of objects in 3-dimensional space, serving as a proof of concept to facilitate control design for trajectory tracking in underactuated systems. For control purposes, the model is structured as a cascade system, where a rotational subsystem drives a translational one. The rotational subsystem is linear, while the translational subsystem follows a linear-plus-perturbation form, thereby reducing the complexity of control design. A control strategy requiring only simple operations, no memory, and no iterative search loops is presented to illustrate the main features of the GA model. By employing GA to model both translations and rotations, a singularity-free and geometrically intuitive representation can be achieved through the use of the geometric product. Closed-loop stability is rigorously established using input-to-state stability methods. Numerical simulations of a quad tilt-rotorcraft performing trajectory tracking in a windy environment validate the controller's stability and performance.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
