Three and higher dimensional autonomous formations: Rigidity, persistence and structural persistence

In this paper, we generalize the notion of persistence, which has been originally introduced for two-dimensional formations, to Rd for d 3, seeking to provide a theoretical framework for real world applications, which often are in three-dimensional space as opposed to the plane. Persistence captures the desirable property that a formation moves as a cohesive whole when certain agents maintain their distances from certain other agents. We verify that many of the properties of rigid and/or persistent formations established in R2 are also valid for higher dimensions. Analysing the closed subgraphs and directed paths in persistent graphs, we derive some further properties of persistent formations. We also provide an easily checkable necessary condition for persistence. We then turn our attention to consider some practical issues raised in multi-agent formation control in three-dimensional space. We display a new phenomenon, not present in R2, whereby subsets of agents can behave in a prob...

• Type: Journal
• Year: 2007
• Where: AUTOMATICA
• Authors: Changbin Yu, Julien M. Hendrickx, Baris Fidan, Brian D. O. Anderson, Vincent D. Blondel
• Keywords: AUTOMATICA 2007, Persistent Formations, Persistent Graphs, Three-dimensional Space