Oscillator Models and Collective Motion: Splay State Stabilization of Self-Propelled Particles

This paper presents a Lyapunov design for the
stabilization of collective motion in a planar kinematic model
of N particles moving at constant speed. We derive a control law
that achieves asymptotic stability of the splay state formation,
characterized by uniform rotation of N evenly spaced particles
on a circle. In designing the control law, the particle headings
are treated as a system of coupled phase oscillators. The
coupling function which exponentially stabilizes the splay state
of particle phases is combined with a decentralized beacon
control law that stabilizes circular motion of the particles in the
splay state formation around the center of mass of the group.