Oscillator Models and Collective Motion

This article describes PCOD, a cooperative control framework for stabilizing relative equilibria in a model of self-propelled, steered particles moving in the plane at unit speed. Relative equilibria correspond either to motion of all of the particles in the same direction or to motion of all of the particles around the same circle. Although the framework applies to time-varying and directed interaction between individuals, we focus here on time-invariant and undirected interaction, using the Laplacian matrix of the interaction graph to design a set of decentralized control laws applicable to mobile sensor networks. Since the direction of motion of each particle is represented in the framework by a point on the unit circle, the closed-loop model has coupled-phase oscillator dynamics.