Modeling and Analysis of Multi-agent Coordination Using Nearest Neighbor Rules

In a recent IEEE Transactions on Automatic Control article, Jadbabaie et al. provides a theoretical explanation of the discrete-time model of groups of mobile autonomous agents raised by Vicsek et al. in 1995. In their paper, Jadbabaie et al. established conditions given in terms of neighbor graphs for coordination of agents and 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. The theorems in this paper show that convergence will be attained if these neighbor graphs are finally linked together. This condition is also strictly weaker than the one Jadbabaie et al. desired. An example is provided that illustrates the soundness of the theorem.