Robustness to agent loss in vehicle formations & sensor networks

A primary motivation for using large-scale vehicle formations and sensor networks is potential robustness to loss of a single agent or a small number of agents. In this paper, we address the problem of agent loss by introducing redundancy into the information architecture such that limited agent loss does not destroy desirable properties. We model the information architecture as a graph G(V,E), where V is a set of vertices representing the agents and E is a set of edges representing information flow amongst the agents. We focus on two properties of the graph called rigidity and global rigidity, which are required for formation shape maintenance and sensor network self-localization, respectively. In particular, our objective in this paper is to investigate the structure of graphs in the plane with the property that rigidity or global rigidity is preserved after removing any single vertex (we call the property 2-vertex-rigidity or 2-vertex-global-rigidity, respectively). Information architectures with such properties would allow critical tasks, such as formation shape maintenance or self-localization, to be performed even in the event of agent failure. We review a characterization of a particular class of 2-vertex-rigidity and develop a separate class, making significant strides toward a complete characterization. We also present for the first time a characterization of a particular class of 2-vertex-global-rigidity. Finally, we list several related open problems and suggest directions for further research.