Latency Analysis of Coalescence for Robot Groups

Coalescence is the problem of isolated mobile robots independently searching for peers with the goal of forming a single connected network. This is important because communication is a necessary requirement for several collaborative robot tasks. In this paper, we consider a scenario where the robots do not have any information about the environment or positions of other robots and perform a random walk search. We show through probabilistic analysis that as the number of isolated robots N increases, the expected coalescence time decreases as 1/radicN. Simulations results are presented to validate this analysis.