In a recent Physical Rewiew Letters article, Vicsek et al. propose a simple but compelling discrete-time model of 7~ autonomous agents {i.e., points or particles) all moving in the plane with the same speed but with different headings. Each agent's heading is updated using a local rule based on the average of its own heading plus the headings of its "neighbors." In their paper, Vicsek et al. provide simulation results which demonstrate that the nearest neighbor rule they are studying can c a w all agents to eventually move in the same direction despite the absence of centralized coordination and despite the fact that each agent's set of nearest neighbors change with time as the system evolves. This paper provides a theoretical explanation for this observed behavior. In addition, convergence reults are derived for several other similarly inspired models. The Vicsek model proves t o be a graphic example of a switched linear system which is stable, but for which there do= not exist a common quadratic Lyapunov function.
In 2003, Jadbabaie et al. REF analyzed a simplified Vicsek model without noise effects and provided a theoretical explanation for the nearest neighbor rule that can cause all agents to eventually move in the same direction.
Coordination of groups of mobile autonomous agents using nearest neighbor rules
Proceedings of the 41st IEEE Conference on Decision and Control, 2002.
Proceedings of the 41st IEEE Conference on Decision and Control, 2002.
Computer Science