TY - GEN
T1 - Effect of topological dimension on rigidity of vehicle formations
T2 - 47th IEEE Conference on Decision and Control, CDC 2008
AU - Bamieh, Bassam
AU - Jovanovic, Mihailo
AU - Mitra, Partha
AU - Patterson, Stacy
PY - 2008
Y1 - 2008
N2 - 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.
AB - 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.
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U2 - 10.1109/CDC.2008.4739314
DO - 10.1109/CDC.2008.4739314
M3 - Conference contribution
AN - SCOPUS:62949108506
SN - 9781424431243
T3 - Proceedings of the IEEE Conference on Decision and Control
SP - 369
EP - 374
BT - Proceedings of the 47th IEEE Conference on Decision and Control, CDC 2008
PB - Institute of Electrical and Electronics Engineers Inc.
Y2 - 9 December 2008 through 11 December 2008
ER -