Anderson, BrianYu, Changbin (Brad)2015-12-10May 23-259781424487363http://hdl.handle.net/1885/62832This paper is concerned with two related problems using graph theoretic methods for their solution. The central contribution to formation control is to demonstrate that if each agent senses a modest number of additional distances beyond those which are actively being controlled, and with limited message passing between neighboring agents, each agent can infer the relative positions of its neighbors in its own coordinate basis. Additional effort to related this to the basis used for viewing its controls may be required. Each agent can thus apply the known algorithms for formation shape control based on distance preservation, without needing to actually sense bearings. The contribution to sensor network localization is to identify circumstances in which the complexity is effectively linear in the number of nodes.Keywords: Formation control; Graph Rigidity; Graph-theoretic methods; Relative positions; Sensor Network Localization; Shape control; Graph theory; Message passing; Sensor networks; Sensors; Sensor nodes Formation Control; Graph Rigidity; Sensor Network Localization201110.1109/CCDC.2011.59688292016-02-24