This paper addresses the problem of topology control for dealing with node failures in networks of multiple robots. While connectivity maintenance has been widely addressed in the literature, issues related to failures are typically not considered in such networks. However, physical robots can fail (i.e. stop working) due to several reasons. It is then mandatory to consider this aspect, as connectivity maintenance is usually critical. In fact, failures of a small fraction of robots - in particular on those that play a crucial role in routing information through the network - can lead to connectivity loss. In this paper, we present a decentralized estimation procedure for letting each robot (a) assess its degree of robustness w.r.t. to connectivity maintenance under the occurrence of failures in its neighborhood, and (b) take actions to improve it when needed. This estimation is combined with a connectivity maintenance control law, thus providing a mechanism that ensures, in the absence of failures, both the network connectivity and an improvement in the overall robustness to failures. In addition, for failures scenarios, the mechanism is able to postpone, or even avoid network fragmentation, as verified through a set of validation experiments.
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