Oscillator Models and Collective Motion: Splay State Stabilization of Self-Propelled Particles
Derek Paley, Naomi Ehrich Leonard and Rodolphe Sepulchre
Proc. 44th IEEE Conf. Decision and Control and European Control Conference,
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.