Affine transformation-based no-beacon circular formation of agents

This paper proposes a circular formation control algorithm for a group of agents to form a circular motion behaviour without the guidance of a global beacon. The control law consists of two parts which correspond to two systems (original system and reference exosystem) based on affine transformation. First, a displacement-based decentralised control law is used to form a regular polygon formation for the reference exosystem. Second, let the original system track a rotating motion of reference exosystem by affine transformation. Combining the above two steps, the proposed strategy ensures exponential convergence of a group of single-integrator modelled agents to the desired circular formation. Then, the authors generalise the approach to double-integrator and unicycle type. Both theoretical analysis and numerical simulations are given to show the effectiveness of the proposed strategies.