Robustness Of Communication Links For Teams Of Unmanned Aircraft By Sensitivity Analysis Of Minimum Spanning Trees

This paper addresses the problem of sensitivity analysis of minimum spanning trees on a weighted graph and its application to optimal communication topologies for teams of unmanned aerial vehicles. In particular, we analyze the robustness of a minimum spanning tree with respect to changing edge weights due to movement of the aircraft. Stability analysis is used to determine whether a previously computed minimum spanning tree remains optimal after the edge weights change. Building upon necessary and sufficient conditions for optimality of a spanning tree, we derive a polyhedral description of the stability region, that is, the set of all perturbations to the edge weights for which a given minimum spanning tree remains optimal, and analyze its properties and relevant subsets. The application of sensitivity analysis to robustness assessment of an optimal communication topology for teams of unmanned aircraft is demonstrated through numerical simulations.