TY - GEN
T1 - Laman graphs are generically bearing rigid in arbitrary dimensions
AU - Zhao, Shiyu
AU - Sun, Zhiyong
AU - Zelazo, Daniel
AU - Trinh, Minh Hoang
AU - Ahn, Hyo Sung
N1 - Publisher Copyright:
© 2017 IEEE.
PY - 2017/6/28
Y1 - 2017/6/28
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85046160278&partnerID=8YFLogxK
U2 - 10.1109/CDC.2017.8264151
DO - 10.1109/CDC.2017.8264151
M3 - Conference contribution
T3 - 2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017
SP - 3356
EP - 3361
BT - 2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 56th IEEE Annual Conference on Decision and Control, CDC 2017
Y2 - 12 December 2017 through 15 December 2017
ER -