Detecting Separation in Robotic and Sensor Networks

In this paper we consider the problem of monitoring detecting separation of agents from a base station in robotic and sensor networks. Such separation can be caused by mobility and/or failure of the agents. While separation/cut detection may be performed by passing messages between a node and the base in static networks, such a solution is impractical for networks with high mobility, since routes are constantly changing. We propose a distributed algorithm to detect separation from the base station. The algorithm consists of an averaging scheme in which every node updates a scalar state by communicating with its current neighbors. We prove that if a node is permanently disconnected from the base station, its state converges to $0$. If a node is connected to the base station in an average sense, even if not connected in any instant, then we show that the expected value of its state converges to a positive number. Therefore, a node can detect if it has been separated from the base station by monitoring its state. The effectiveness of the proposed algorithm is demonstrated through simulations, a real system implementation and experiments involving both static as well as mobile networks.