Multi-agent coordination using nearest neighbor rules: revisiting the Vicsek model

Recently, Jadbabaie, Lin, and Morse (IEEE TAC, 48(6)2003:988-1001) offered a mathematical analysis of the discrete time model of groups of mobile autonomous agents raised by Vicsek et al. in 1995. In their paper, Jadbabaie et al. showed that all agents shall move in the same heading, provided that these agents are periodically linked together. This paper sharpens this result by showing that coordination will be reached under a very weak condition that requires all agents are finally linked together. This condition is also strictly weaker than the one Jadbabaie et al. desired.