Robust connectivity of networked vehicles

We present a simple geometric analysis of wireless connectivity in vehicle networks. We introduce a localized notion of connectedness, and construct a function that measures the robustness of this local connectedness to variations in position. Under a mild feasibility hypothesis, this function provides a sufficient condition for global connectedness of the network. Further, it is distributed, in the sense that both the function and its gradients can be calculated using only neighbor-to-neighbor communications. It can thus form the basis for distributed motion-control algorithms which respect connectivity constraints. We conclude with two simple examples of target applications.