Connectivity management in mobile robot teams

We develop a framework for controlling a team of robots to maintain and improve a communication bridge between a stationary robot and an independently exploring robot in a walled environment. We make use of two metrics for characterizing the communication: the Fiedler value of the weighted Laplacian describing the communication interactions of all the robots in the system, and the k-connectivity matrix that expresses which robots can interact through k or less intermediary robots. At each step, we move in such a way as to improve the Fiedler value as much as possible while keeping the number of intermediary robots between the two robots of interest below a desired value. We demonstrate the use of this framework in a scenario where the hop-count constraint cannot be satisfied, but show that communication quality is maintained anyways.