Aggregation and rendezvous in an unbounded domain without a shared coordinate system

Many swarm robotics problems focus on the details of robotic dynamics, while ignoring certain other practical issues such as the boundedness of the exploration space, the probability of unsuccessful communication or sensing between agents, knowledge of a common coordinate system, or the initial distribution of robots. A two-phase control is devised which, under appropriate individual bounds, almost surely leads to successful rendezvous. We examine a likely and practical initial distribution, which leads to an exploration protocol wherein an agent is obligated to stay within a certain range of its initial position. Furthermore, the rate of convergence is primarily limited to the velocity limitations of the agents. We solve the aggregation and rendezvous problem with random initial conditions in an arbitrary, unbounded 2D domain without an a priori share coordinate system. We examine rates of successful aggregation under certain initial distributions, and rates of convergence under uncertain communication.