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

Bassam Bamieh, Mihailo Jovanovic, Partha Mitra, Stacy Patterson

Research output: Chapter in Book/Report/Conference proceedingConference contribution

30 Scopus citations

Abstract

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 problems than in consensus, and yet they are unrelated to string stability issues.

Original languageEnglish (US)
Title of host publicationProceedings of the 47th IEEE Conference on Decision and Control, CDC 2008
Pages369-374
Number of pages6
DOIs
StatePublished - 2008
Event47th IEEE Conference on Decision and Control, CDC 2008 - Cancun, Mexico
Duration: Dec 9 2008Dec 11 2008

Publication series

NameProceedings of the IEEE Conference on Decision and Control
ISSN (Print)0191-2216

Other

Other47th IEEE Conference on Decision and Control, CDC 2008
CountryMexico
CityCancun
Period12/9/0812/11/08

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