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, 2005.
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.

(6 pages pdf)
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