Current formations commonly rely on invariant hierarchical structures, such as predetermined leaders or enumerated formation shapes. These structures could be unidirectional and sluggish, constraining their adaptability and agility when encountering cluttered environments. To surmount these constraints, this work proposes an omnidirectional affine formation approach with hierarchical reorganizations. We first delineate the critical conditions requisite for facilitating hierarchical reorganizations within formations, which informs the development of the omnidirectional affine criterion. Central to our approach is the fluid leadership and authority redistribution, for which we develop a minimum time-driven leadership evaluation algorithm and a power transition control algorithm. These algorithms facilitate autonomous leader selection and ensure smooth power transitions, enabling the swarm to adapt hierarchically in alignment with the external environment. Furthermore, we deploy a power-centric topology switching mechanism tailored for the dynamic reorganization of in-team connections. Finally, simulations and experiments demonstrate the performance of the proposed method. The formation successfully performs several hierarchical reorganizations, with the longest reorganization taking only 0.047s. This swift adaptability allows five aerial robots to carry out complex tasks, including executing swerving movements and navigating through hoops at velocities up to 1.9m/s.

翻译：现有编队方法通常依赖于固定的层次结构，如预设领导者或枚举队形。这些结构往往是单向且响应迟缓的，限制了编队在复杂环境中的适应性与敏捷性。为克服这些局限，本文提出一种支持层次化重构的全向仿射编队方法。我们首先阐述了编队内实现层次化重构所需的关键条件，并以此为基础推导出全向仿射准则。该方法的核心在于实现流动式领导权与权限的再分配，为此我们开发了最小时间驱动的领导力评估算法与权力转移控制算法。这些算法支持自主领导者选择并确保权力平稳过渡，使集群能够根据外部环境进行层次化自适应。此外，我们设计了一种以权力为中心的拓扑切换机制，专门用于团队内部连接的动态重构。最后，仿真与实验验证了所提方法的性能。编队成功执行了多次层次化重构，最长重构时间仅需0.047秒。这种快速适应能力使得五架空中机器人能够以高达1.9米/秒的速度完成复杂任务，包括执行急转弯机动与穿越圆环。