In order to have collaboration in multi-robot systems, exchange of information among the nodes needs to be always allowed. This can be achieved guaranteeing preservation of the connectivity of the communication graph, as the system evolves. Being this a crucial requirement in multi-robot systems, this problem has been extensively addressed in the literature. Multi-robot systems are often claimed to be more robust than single robot solutions, due to their inherent redundancy. However, guaranteeing connectivity preservation does not imply avoidance of single points of failure: central nodes often exist, whose failure has the potential to completely destroy the connectivity of the overall network.
In this talk I will briefly summarize some common approaches to connectivity maintenance, and I will give some examples that show the fact that high connectivity does not necessarily imply high robustness.
I will then discuss some concepts of robustness that has been defined in the last few years, with respect to multi-robot systems. I will then focus on robustness in terms of connectivity preservation, describing an exact method for enforcing bi-connectivity, that is the presence of at least two independent paths between each pair of nodes in a network. This method is based on controlling the value of the third smallest eigenvalue of the Laplacian matrix: for this purpose, I will describe a strategy for achieving decentralized estimation of eigenvalues and eigenvectors of the Laplacian matrix. Finally, I will describe a heuristic approach that has been recently developed, that aims at improving the robustness in a multi-robot network, without requiring eigenvalue and eigenvector computation.