Addressing agent loss in vehicle formations and sensor networks

In this paper, we address the problem of agent loss in vehicle formations and sensor networks via two separate approaches: (1) perform a ‘self-repair’ operation in the event of agent loss to recover desirable information architecture properties or (2) introduce robustness into the information architecture a priori such that 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. For the self-repair approach, we show that while previous results permit local repair involving only neighbours of the lost agent, the repair cannot always be implemented using only local information. We present new results that can be applied to make the local repair using only local information. We describe implementation and illustrate with algorithms and examples. For the robustness approach, we investigate the structure of graphs with the property that rigidity or global rigidity is preserved after removing any single vertex (we call the property as 2-vertex-rigidity or 2-vertex-global-rigidity, respectively). Information architectures with such properties would allow formation shape maintenance or self-localization to be performed even in the event of agent failure. We review a characterization of a class of 2-vertex-rigidity and develop a separate class, making significant strides towards a complete characterization. We also present a characterization of a class of 2-vertex-global-rigidity. Copyright 2008 John Wiley & Sons, Ltd.