The multi-agent rendezvous problem - the asynchronous case

This paper is concerned with the collective behavior of a group of n > 1 mobile autonomous agents, labelled 1 through n, which can all move in the plane. Each agent is able to continuously track the positions of all other agents currently within its "sensing region" where by an agent's sensing region is meant a closed disk of positive radius r centered at the agent's current position. The multi-agent rendezvous problem is to devise "local" control strategies, one for each agent, which without any active communication between agents, cause all members of the group to eventually rendezvous at single unspecified location. This paper describes a family of asynchronously functioning strategies for solving the problem. Correctness is established appealing to the concept of "analytic synchronization".