Collective Motion of Self-Propelled Particles: Stabilizing Symmetric Formations on Closed Curves
Derek Paley, Naomi Ehrich Leonard and Rodolphe Sepulchre
Proceedings of the 45th IEEE Conference on Decision and Control, San Diego,
CA, December 2006, pp. 5067-5072.
We provide feedback control laws to stabilize formations of multiple, unit
speed particles on smooth, convex, and closed curves with definite curvature. As in previous
work we exploit an analogy with coupled phase oscillators to provide controls which isolate
symmetric particle formations that are invariant to rigid translation of all the particles.
In this work, we do not require all particles to be able to communicate; rather we assume
that inter-particle communication is limited and can be modeled by a fixed, connected and
undirected graph. Because of their unique spectral properties, the Laplacian matrices of circulant
graphs play a key role. The methodology is demonstrated using a superellipse,
which is a type of curve that includes circles, ellipses, and rounded
rectangles. These results can be used in applications involving multiple autonomous vehicles that
constant, arbitrary speed particles around fixed beacons.
(7.2 MB pdf)
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