Distributed Average Consensus with Beep Communication

Motivated by the hostile working environments that lack a robust communication infrastructure, such as in the case of precision agriculture settings, we propose a novel bandwidth-saving average consensus procedure that exploits the beep communication model. Specifically, we allow the agents to alternatively perform traditional average consensus steps and steps where the agents only inform their neighbors about the fact that their state has increased or decreased with respect to the previous time step. All the information is transmitted among the agents via beeps, which represent a weak communications model with bandwidth preservation. We theoretically characterized the practical convergence property of the proposed algorithm towards the network average, i.e., the consensus error can be made arbitrarily small by acting on the parameters of the protocol. Additionally, we also numerically demonstrate that, for a proper choice of such parameters, the protocol exhibits an interesting trade-off between convergence rate and achievable accuracy.