This paper reviews a number of very recent results in rigid graph theory and their extension for directed graphs to persistence theory, with an application focus on the cooperative control of formations. Particular attention is paid to issues related to the merging of formations, where the internal structure of each of the individually merging formations is, to the maximum extent possible, downplayed in the calculation. The meta-formation framework is then introduced in light of merging process for its construction. The ideas also have application to sensor network localization, where there is potential to make great computational saving.
Anderson, B. D. O., Yu, C., Fidan, B., & Hendrickx, J. (2006). Use of meta-formations for cooperative control. Proceedings of the 17th International Symposium on Mathematical Theory of Networks and Systems, 2381-2387. https://hdl.handle.net/2078.5/219084