J. Graver, B. Servatius, and H. Servatius. Combinatorial Rigidity. American Mathematical Society, 1993. Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
Cooperative Control of Multi-Vehicle Systems Using.. - Olfati-Saber, Dunbar, .. (2003) (Correct)
....with linear (i.e. double integrator) dynamics. Later, in [11] we formalized the notion of formations of multiple agents vehicles and minimal requirements, in terms of the number of edges, for uniquely specifying a formation. This is done based on the tools from combinatorial graph rigidity [12, 13, 14, 15]. Here, we add specification of foldability [10] to the definition of a formation graph. In addition, we explicitly specify the required cost for navigation and tracking in formation for a group of vehicles. In [16] for the special case of three vehicles, the problem of formation stabilization is ....
J. Graver and H. Servatius, B. Servatius, Combinatorial Rigidity, vol. 2 of Graduate Studies in Mathematics, American Mathematical Society, 1993.
Straightening Polygonal Arcs and Convexifying Polygonal Cycles - Connelly, Demaine, Rote (2000) (6 citations) (Correct)
.... blowing up of the linkage. This notion was formalized by third author with the idea that perhaps an arc could be straightened via an expansive motion. The new tools that are applied here come from the theory of mechanisms and rigid frameworks. Arcs and cycles can be regarded as frameworks. See [1, 2, 9, 10, 11, 12, 13, 18, 27, 37, 38, 39, 40, 41] for relevant information about this theory. Our approach is to prove that for any configuration there is an infinitesimal motion that increases all distances. Because of the nature of the arc and cycle set, this implies that there is a motion that works at least for a small expansive ....
J. Graver, B. Servatius, and H. Servatius. Combinatorial rigidity. American Mathematical Society, 1993.
Oriented Matroid Pairs, Theory and an Electric Application - Chaiken (Correct)
....problem for digraphs [22] These problems have been recognized as deep, unsolved combinatorial problems for which it is unknown whether they lie in complexity classes P, NP complete or in between [22, 39] Rigidity and Elasticity. It would be interesting to know electrical analogs of rigidity [17] properties, or if some rigidity properties are equivalent to no common covectors. We mention the basic analogies. Stress (a signed scalar for each bar) in 1 The distinguished edge represents the emitter and collector terminal pair. ORIENTED MATROID PAIRS 7 a multidimensional bar framework is ....
J. Graver, B. Servatius, and H. Servatius, Combinatorial Rigitity, Graduate Studies in Mathematics, 2, American Mathematical Society, Providence, RI, (1993).
Graph Rigidity and Distributed Formation Stabilization of.. - Olfati-Saber, Murray (2002) Self-citation (Rigidity) (Correct)
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J. Graver and H. Servatius, B. Servatius, Combinatorial Rigidity, vol. 2 of Graduate Studies in Mathematics, American Mathematical Society, 1993.
Planar Embeddings of Graphs with Specified Edge Lengths - Cabello, Demaine, Rote (Correct)
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J. Graver, B. Servatius, and H. Servatius. Combinatorial Rigidity. American Mathematical Society, 1993.
Distributed Structural Stabilization and Tracking for.. - Olfati-Saber, Murray (2002) (Correct)
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J. Graver and H. Servatius, B. Servatius, Combinatorial Rigidity, vol. 2 of Graduate Studies in Mathematics, American Mathematical Society, 1993.
Anchor-Free Distributed Localization in Sensor Networks - Hari (2003) (10 citations) (Correct)
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GRAVER, J., SERVATIUS, B., AND SERVATIUS, H. Combinatorial Rigidity. American Mathematical Society, 1993.
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