Laman graphs are generically bearing rigid in arbitrary dimensions

Shiyu Zhao, Zhiyong Sun, Daniel Zelazo, Minh Hoang Trinh, Hyo Sung Ahn

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

This paper addresses the problem of constructing bearing rigid networks in arbitrary dimensions. We first show that the bearing rigidity of a network is a generic property that is critically determined by the underlying graph of the network. A new notion termed generic bearing rigidity is defined for graphs. If the underlying graph of a network is generically bearing rigid, then the network is bearing rigid for almost all configurations; otherwise, the network is not bearing rigid for any configuration. As a result, the key to construct bearing rigid networks is to construct generically bearing rigid graphs. The main contribution of this paper is to prove that Laman graphs, which can be generated by the Henneberg construction, are generically bearing rigid in arbitrary dimensions. As a consequence, if the underlying graph of a network is Laman, the network is bearing rigid for almost all configurations in arbitrary dimensions.

Original languageEnglish
Title of host publication2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017
Pages3356-3361
Number of pages6
ISBN (Electronic)9781509028733
DOIs
StatePublished - 28 Jun 2017
Event56th IEEE Annual Conference on Decision and Control, CDC 2017 - Melbourne, Australia
Duration: 12 Dec 201715 Dec 2017

Publication series

Name2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017
Volume2018-January

Conference

Conference56th IEEE Annual Conference on Decision and Control, CDC 2017
Country/TerritoryAustralia
CityMelbourne
Period12/12/1715/12/17

All Science Journal Classification (ASJC) codes

  • Decision Sciences (miscellaneous)
  • Industrial and Manufacturing Engineering
  • Control and Optimization

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