Displacement-Based Formation Control with Phase Synchronization in a Time-Invariant Flow Field

This paper discusses phase synchronization and circular formation control for multiple unicycle-type agents with fixed constant speeds in a time-invariant flow field. We describe the Lyapunov-based design of displacement formation control approach that stabilizes collective motion in a known flow field including uniform flow and non-uniform flow. The communication topology in displacement-based control utilizes all-to-all interactions. Moreover, we provide a combination of formation shape and steering control to stabilize formation and orientation simultaneously. The validity of the proposed algorithms above is confirmed by theoretical derivation and numerical simulation.