Directed graphs for the analysis of rigidity and persistence in autonomous agent systems

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Distributed Formation Control of Multi-Agent Systems Using Complex Laplacian (2014, background): “The former mainly concentrates on defining a formation using graph-theoretic rigidity [4], [16], [17], [22], [33], [40], while the latter concerns stabilization to a formation [7], [8], [10], [24], [32], [38], [39] and control of formation shape in moving [3], [5], [12]–[14], [20].”
Closing ranks in rigid multi‐agent formations using edge contraction (2010, background): “Some discussions on the need for using the qualifiers ‘generic’ and ‘almost all’ can be found in [15, 19].”
Stabilisation of infinitesimally rigid formations of multi-robot networks (2009, methodology): “The precise definition of constraint consistence from Hendrickx et al. (2006a) is complex and beyond what is needed for the implementation proposed in this work.”
Rigid graph control architectures for autonomous formations (2008, background): “We note the following key facts about constraint consistence and persistence; see [19] and [28] for precise definitions.”