Stabilization of Collective Motion with Bounded Trajectories in an External Flowfield

This paper aims to stabilize agents (or vehicles) on a commonly desired circle with bounded trajectories in an external flow field. We consider the formation in a balanced or synchronized phase pattern. In a balanced phase pattern, all agents symmetrically move on a desired common circle. In contrast, in a synchronized phase pattern, all agents move together with the same phase angle on a desired common circle. We propose the control scheme using the concept of the Barrier Lyapunov Function (BLF), which helps in restricting the agents’ trajectories within a predefined boundary. Simulations are provided to support the theoretical developments.