Distributed estimation of articulation node importance for robustness of multi-robot systems

This paper shows a definition of importance of an articulation node in a multi-robot network, and proposes a distributed algorithm to estimate the importance value. Articulation nodes are weak spots of a network, since the network will be disconnected when any of them is failed. However, an amount of the damage to the system is depend on the position of the failure node, that is to say, a centrality of the node. Therefore we define an importance of the articulation node to explain such centrality. Since a calculation of the importance requires the network structure, we propose a distributed algorithm to estimate the importance using a Fiedler vector of the network. Theoretical properties of the Fiedler vector are analyzed to design the estimation algorithm. Numerical examples illustrates the theoretically derived properties, and validity of the proposed method.