Hendrickx, Julien MYu, Changbin (Brad)Fidan, BarisAnderson, Brian2015-12-071561-8625http://hdl.handle.net/1885/23069This paper treats the problem of merging formations, where the underlying model of a formation is graphical. We first analyze the rigidity and persistence of meta-formations, which are formations obtained by connecting several rigid or persistent formations. Persistence is a generalization to directed graphs of the undirected notion of rigidity. In the context of moving autonomous agent formations, persistence characterizes the efficacy of a directed structure of unilateral distance constraints seeking to preserve a formation shape. We derive then, for agents evolving in a two- or three-dimensional space, the conditions under which a set of persistent formations can be merged into a persistent meta-formation, and give the minimal number of interconnections needed for such a merging. We also give conditions for a meta-formation obtained by merging several persistent formations to be persistent.Keywords: Agents; Autonomous agents; Canning; Graph theory; Rigidity; Three dimensional; Directed graphs; Distance constraints; Multi agents; Three-dimensional (3D) space; Merging Autonomous agents; Formations; Meta-formations; Persistence; Rigidity200810.1002/asjc.142015-12-07