Symmetries in the Coordinated Consensus Problem

Abstract

In this paper we consider a widely studied problem in the robotics and control communities, called consensus problem. The aim of the paper is to characterize the relationship between the amount of information exchanged by the vehicles and the speed of convergence to the consensus. Time-invariant communication graphs that exhibit particular symmetries are shown to yield slow convergence if the amount of information exchanged does not scale with the number of vehicles. On the other hand, we show that retaining symmetries in time-varying communication networks allows to increase the speed of convergence even in the presence of limited information exchange.