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Formation control of rigid graphs with flex edges
Author(s) -
Pham Viet Hoang,
Trinh Minh Hoang,
Ahn HyoSung
Publication year - 2018
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.4037
Subject(s) - tetrahedron , mathematics , space (punctuation) , group (periodic table) , series (stratigraphy) , combinatorics , graph , stability theory , node (physics) , rigid body , topology (electrical circuits) , computer science , geometry , physics , nonlinear system , classical mechanics , paleontology , quantum mechanics , biology , operating system
Summary This paper studies a distance‐based formation control problem of multiagent systems, in which each agent uses only relative positions of its neighbors with respect to its own coordinate system. First, we provide an analysis for the properties of the undesired equilibria‐corresponding 2 specific formations, ie, a triangle group in 2‐dimensional space and a tetrahedron group in 3‐dimensional space. Then, we consider the formation of multiagent systems whose interaction graph consists of a rigid group and an extra node. Although the extra node may have an additional control input, the desired formation where all interagent distance constraints are satisfied is asymptotically stable. If the rigid group is a triangle in 2‐dimensional space or a tetrahedron in 3‐dimensional space, any undesired equilibrium is unstable. In these cases, the desired formations are almost globally asymptotically stable. Finally, we extend these results to a more general formation, which is a series of rigid groups connecting via flex edges.