In the chapter, a distributed model for
the mobile sensor network is introduced. The distributed model has two parts: the
dynamical model of each subsystem, and the relationship between a subsystem and
its neighboring robots.
To facilitate the definition of a global objective of the mobile sensor network,
??pi = {??xi(t), ??yi(t)}T is defined as the position of the robot Ri in a unified inertial
coordinate system, and ??p = {??p1, ??p2, . . . , ??pn}T is the position of the mobile
sensor network in a unified inertial coordinate system. We further define that
pi = {xi(t), yi(t)}T is the coordinate frame of robot Ri in its local coordinate
frame.
R2
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y 1
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Voronoi diagram
Region V1
Delaunay tessellation
Fig. 2. Delaunay triangulation and Voronoi diagram.
The neighborhood relationship between robot nodes is defined by two graphs, a
Delaunay tessellation and a Voronoi diagram [16], as shown in Figure 2. Given an
open set ? ??† IRn, the Delaunay tessellation is a triangulation of the space based
on a set of points ??p = {??p1, ??p2, . . . , ??pn}T [14], [29]. The Delaunay triangulation
with a set of nodes ??p is defined such that any additional edge between any two nodes
intersects one of the existing edges. The robot Ri is also called a generator. The
Voronoi diagram and the Delaunay triangulation are dual to each other in a planar
space.
In the graph, the nodes that are directly connected to node Ri are called the
one-hop neighbors of Ri.
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