Preserving Strong Connectivity in Directed Proximity Graphs

This paper proposes a method to maintain the strong connectivity property of a mobile robot ad hoc network in the presence of disturbances or additional control goals. Each robot has a communication range modeled by an $n$-dimensional sphere centered at the robot. The spheres for different robots may have different radii, resulting in a directed communication network. This paper is based on two concepts. The first is the structure of the Perron vector for reducible stochastic matrices. The second is the design of nonlinear controllers that ensure that two robots remain within a certain distance of each other despite disturbances. The results are supported by analysis and simulations.