  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.
