Decentralized estimation of the minimum strongly connected subdigraph for robotic networks with limited field of view

In this work we focus on the topology control problem for robotic networks. In particular, we assume agents to be equipped with limited field of view sensors. As a consequence, directed graphs are required to model the robot-to-robot interaction. This significantly limits the applicability of algorithms developed for undirected graphs. In that view, we propose an auction-based solution for the decentralized estimation of an approximated minimum (in terms of number of links and in terms of a global cost function) strongly connected directed graph. This represents the first step towards the development of a connectivity maintenance framework for directed graphs. A theoretical analysis along with numerical simulations are provided to show the effectiveness of the proposed approach.