Enforcing Biconnectivity in Multi-robot Systems
  Connectivity maintenance is an essential task in multi-robot systems and it has received a considerable attention during the last years. A connected system can be broken into two or more subsets simply if a single robot fails. 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 \cite{Zareh2016biconnectivitycheck}, 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. 
Mehran Zareh, Lorenzo Sabattini, and Cristian Secchi
cs.RO cs.MA cs.SY math.DS