Connectivity maintenance is an essential task in multi-robot systems and it has received a considerable attention during the last years. However, a connected system can be broken into two or more subsets simply if a single robot fails. Then, a more robust communication can be achieved if the network connectivity is guaranteed in the case of one-robot failures. The resulting network is called biconnected. In [1] we presented a criterion for biconnectivity check, which basically determines a lower bound on the third-smallest eigenvalue of the Laplacian matrix. In this paper we introduce a decentralized gradient-based protocol to increase the value of the third-smallest eigenvalue of the Laplacian matrix, when the biconnectivity check fails. We also introduce a decentralized algorithm to estimate the eigenvectors 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 / Zareh Eshghdoust, Mehran; Sabattini, Lorenzo; Secchi, Cristian. - (2016), pp. 1800-1805. ((Intervento presentato al convegno 55th IEEE Conference on Decision and Control, CDC 2016 tenutosi a ARIA Resort and Casino, usa nel 2016.

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