The paper presents an architecture for distributed control of multi-robot systems with an integrated fault detection, isolation, and recovery strategy. The proposed solution is based on a distributed observer-controller schema where each robot, by communicating only with its direct neighbors, is able to estimate the overall state of the system; such an estimate is then used by the controllers of each robot to achieve global missions as, for example, centroid and formation tracking. The information exchanged among the observers is also used to compute residual vectors that allow each robot to detect failures on anyone of the teammates, even if not in direct communication. The proposed strategy considers both recoverable and unrecoverable actuator faults as well as it properly manages the possible activation of reactive local control behaviors of the robots (e.g., the activation of obstacle avoidance strategy), which generate control inputs different from those required by the global mission control. In particular, when the robots are subject to recoverable faults, those are managed at a local level by computing a proper compensating control action. On the other side, when the robots are subject to unrecoverable faults, the faults are isolated from anyone of the teammates by means of a distributed fault detection and isolation strategy; then, the faulty robots are removed from the team and the mission is rearranged. The proposed strategy is validated via numerical simulations where the system properly identifies and manages the different cases of recoverable and unrecoverable actuator faults, as well as it manages the activation of local reactive control in an integrated case study.