Effect of Topological Dimension on Rigidity of Vehicle Formations: Fundamental Limitations of Local Feedback

被引：32

作者：

Bamieh, Bassam ^{[1
]}

Jovanovic, Mihailo ^{[2
]}

Mitra, Partha ^{[3
]}

Patterson, Stacy ^{[4
]}

机构：

[1] Univ Calif Santa Barbara, Dept Mech Engn, Santa Barbara, CA 93106 USA

[2] Univ Minnesota, Dept Elect & Comp Engn, Minneapolis, MN 55455 USA

[3] Cold Spring Harbor Lab, Cold Spring Harbor, NY 11724 USA

[4] Univ Calif Santa Barbara, Dept Comp Sci, Santa Barbara, CA 93106 USA

来源：

47TH IEEE CONFERENCE ON DECISION AND CONTROL, 2008 (CDC 2008) | 2008年

关键词：

D O I：

10.1109/CDC.2008.4739314

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

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.

引用

页码：369 / 374

页数：6

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