574 research outputs found
Network Localization by Shadow Edges
Localization is a fundamental task for sensor networks. Traditional network
construction approaches allow to obtain localized networks requiring the nodes
to be at least tri-connected (in 2D), i.e., the communication graph needs to be
globally rigid. In this paper we exploit, besides the information on the
neighbors sensed by each robot/sensor, also the information about the lack of
communication among nodes. The result is a framework where the nodes are
required to be bi-connected and the communication graph has to be rigid. This
is possible considering a novel typology of link, namely Shadow Edges, that
account for the lack of communication among nodes and allow to reduce the
uncertainty associated to the position of the nodes.Comment: preprint submitted to 2013 European Control Conference, July 17-19
2013, Zurich, Switzerlan
Toward the Universal Rigidity of General Frameworks
Let (G,P) be a bar framework of n vertices in general position in R^d, d <=
n-1, where G is a (d+1)-lateration graph. In this paper, we present a
constructive proof that (G,P) admits a positive semi-definite stress matrix
with rank n-d-1. We also prove a similar result for a sensor network where the
graph consists of m(>= d+1) anchors.Comment: v2, a revised version of an earlier submission (v1
Bearing-Based Network Localization Under Gossip Protocol
This paper proposes a bearing-based network localization algorithm with a
randomized gossip protocol. Each sensor node is assumed to be able to obtain
the bearing vectors and communicate its position estimates with several
neighboring agents. Each update involves two agents, and the update sequence
follows a stochastic process. Under the assumption that the network is
infinitesimally bearing rigid and contains at least two beacon nodes, we show
that the proposed algorithm could successfully estimate the actual positions of
the network in probability. The randomized update protocol provides a simple,
distributed, and reduces the communication cost of the network. The theoretical
result is then supported by a simulation of a 1089-node sensor network.Comment: preprint, 7 pages, 2 figure
Graph invariants for unique localizability in cooperative localization of wireless sensor networks: rigidity index and redundancy index
Rigidity theory enables us to specify the conditions of unique localizability
in the cooperative localization problem of wireless sensor networks. This paper
presents a combinatorial rigidity approach to measure (i) generic rigidity and
(ii) generalized redundant rigidity properties of graph structures through
graph invariants for the localization problem in wireless sensor networks. We
define the rigidity index as a graph invariant based on independent set of
edges in the rigidity matroid. It has a value between 0 and 1, and it indicates
how close we are to rigidity. Redundant rigidity is required for global
rigidity, which is associated with unique realization of graphs. Moreover,
redundant rigidity also provides rigidity robustness in networked systems
against structural changes, such as link losses. Here, we give a broader
definition of redundant edge that we call the "generalized redundant edge."
This definition of redundancy is valid for both rigid and non-rigid graphs.
Next, we define the redundancy index as a graph invariant based on generalized
redundant edges in the rigidity matroid. It also has a value between 0 and 1,
and it indicates the percentage of redundancy in a graph. These two indices
allow us to explore the transition from non-rigidity to rigidity and the
transition from rigidity to redundant rigidity. Examples on graphs are provided
to demonstrate this approach. From a sensor network point of view, these two
indices enable us to evaluate the effects of sensing radii of sensors on the
rigidity properties of networks, which in turn, allow us to examine the
localizability of sensor networks. We evaluate the required changes in sensing
radii for localizability by means of the rigidity index and the redundancy
index using random geometric graphs in simulations.Comment: 13 pages, 7 figures, to be submitted for possible journal publicatio
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