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Connectivity maintenance is an essential task in multi-robot systems and ithas received a considerable attention during the last years. A connected systemcan be broken into two or more subsets simply if a single robot fails. A morerobust communication can be achieved if the network connectivity is guaranteedin the case of one-robot failures. The resulting network is called biconnected.In \cite{Zareh2016biconnectivitycheck}, we presented a criterion forbiconnectivity check, which basically determines a lower bound on thethird-smallest eigenvalue of the Laplacian matrix. In this paper, we introducea decentralized gradient-based protocol to increase the value of thethird-smallest eigenvalue of the Laplacian matrix, when the biconnectivitycheck fails. We also introduce a decentralized algorithm to estimate theeigenvectors of the Laplacian matrix, which are used for defining the gradient.Simulations show the effectiveness of the theoretical findings.

Enforcing Biconnectivity in Multi-robot Systems