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CDC
2008
IEEE

Effect of topological dimension on rigidity of vehicle formations: Fundamental limitations of local feedback

11 years 3 months ago
Effect of topological dimension on rigidity of vehicle formations: Fundamental limitations of local feedback
We consider the role of topological dimension in problems of network consensus and vehicular formations where only local feedback is available. In particular, we consider the simple network topologies of regular lattices in 1, 2 and higher dimensions. Performance measures for consensus and formation problems are proposed that measure the deviation from average and rigidity or tightness of formations respectively. A common phenomenon appears where in dimensions 1 and 2, consensus is impossible in the presence of any amount of additive stochastic perturbations, and in the limit of large formations. In dimensions 3 and higher, consensus is indeed possible. We show that microscopic error measures that involve only neighboring sites do not suffer from this effect. This phenomenon reflects the fact that in dimensions 1 and 2, local stabilizing feedbacks can not suppress long spatial wavelength "meandering" motions. These effects are significantly more pronounced in vehicular proble...
Bassam Bamieh, Mihailo R. Jovanovic, Partha P. Mit
Added 12 Oct 2010
Updated 12 Oct 2010
Type Conference
Year 2008
Where CDC
Authors Bassam Bamieh, Mihailo R. Jovanovic, Partha P. Mitra, Stacy Patterson
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