In this paper, the stability problem of formation of multi-agents subject to failures in their communication links is addressed. The objective of the formation control problem is to maintain the inter-agent distances to be constants over time using a distributed control algorithm implemented in each agent. Previous research results showed that a distributed gradient-based control can locally asymptotically stabilize an undirected formation. However, in the case of failures in the inter-agent communication network, the degrees of freedom for some nodes might become uncontrollable and, consequently, the formation starts deviating from the desired conditions due to uncertainties and noise. In this paper, it is proved that in a faulty formation system, if there still exists a path between the agents on the both sides of the failed link, the gradient-based control signal can recover the formation without adding any new link to the network. Based on this feature, an algorithm for recovering the formation from the fault is developed. Simulation results show that the proposed recovery algorithm can tolerate small values of delays in data communications.
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