TY - GEN
T1 - Collective motion of self-propelled particles
T2 - 45th IEEE Conference on Decision and Control 2006, CDC
AU - Paley, Derek A.
AU - Leonard, Naomi Ehrich
AU - Sepulchre, Rodolphe J.
PY - 2006
Y1 - 2006
N2 - 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 travel at constant speed around fixed beacons.
AB - 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 travel at constant speed around fixed beacons.
UR - http://www.scopus.com/inward/record.url?scp=34547781025&partnerID=8YFLogxK
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U2 - 10.1109/cdc.2006.377462
DO - 10.1109/cdc.2006.377462
M3 - Conference contribution
AN - SCOPUS:34547781025
SN - 1424401712
SN - 9781424401710
T3 - Proceedings of the IEEE Conference on Decision and Control
SP - 5067
EP - 5072
BT - Proceedings of the 45th IEEE Conference on Decision and Control 2006, CDC
PB - Institute of Electrical and Electronics Engineers Inc.
Y2 - 13 December 2006 through 15 December 2006
ER -