Coordination of an asynchronous multi-agent system via averaging

This paper is concerned with the coordination of a group of n > 1 mobile autonomous agents which all move in the plane with the same speed but with different headings. Each agent updates its heading from time to time to a new value equal to the average of its present heading and the headings of its current \neighbors". Although all agents use the same rule, individual updates are executed asynchronously. By appealing to the concept of "analytic synchronization", it is shown that under mild connectivity assumptions of the underlying directed graph characterizing neighbor relationships, the local update rules under consideration can cause 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 neighbors change with time as the system evolves.