TY - GEN
T1 - On recurrence of graph connectivity in Vicsek's model of motion coordination for mobile autonomous agents
AU - Tahbaz-Salehi, Alireza
AU - Jadbabaie, Ali
PY - 2007
Y1 - 2007
N2 - In this paper we complete the analysis of Vicsek's model of distributed coordination among kinematic planar agents. The model is a simple discrete time heading update rule for a set of kinematic agents (or self-propelled particles as referred to by Vicsek) moving in a finite plane with periodic boundary conditions. Contrary to existing results in the literature, we do not make any assumptions on connectivity but instead prove that under the update scheme, the network of agents stays jointly connected infinitely often for almost all initial conditions, resulting in global heading alignment. Our main result is derived using a famous theorem of Hermann Weyl on equidistribution of fractional parts of sequences. We also show that the Vicsek update scheme is closely related to the Kuramoto model of coupled nonlinear oscillators.
AB - In this paper we complete the analysis of Vicsek's model of distributed coordination among kinematic planar agents. The model is a simple discrete time heading update rule for a set of kinematic agents (or self-propelled particles as referred to by Vicsek) moving in a finite plane with periodic boundary conditions. Contrary to existing results in the literature, we do not make any assumptions on connectivity but instead prove that under the update scheme, the network of agents stays jointly connected infinitely often for almost all initial conditions, resulting in global heading alignment. Our main result is derived using a famous theorem of Hermann Weyl on equidistribution of fractional parts of sequences. We also show that the Vicsek update scheme is closely related to the Kuramoto model of coupled nonlinear oscillators.
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U2 - 10.1109/ACC.2007.4282958
DO - 10.1109/ACC.2007.4282958
M3 - Conference contribution
AN - SCOPUS:46449111512
SN - 1424409888
SN - 9781424409884
T3 - Proceedings of the American Control Conference
SP - 699
EP - 704
BT - Proceedings of the 2007 American Control Conference, ACC
T2 - 2007 American Control Conference, ACC
Y2 - 9 July 2007 through 13 July 2007
ER -