Formation control of the mobile sensor network is further
discussed. The formation control algorithms allow a mobile sensor network to
sweep larger areas along specified paths.
2 Distributed Graph Model
2.1 Mobile Robot Model
The mobile sensor network in this chapter is given by n mobile robots, as shown in
Figure 1. The mobile robots, denoted by R = {R1,R2, ?· ?· ?· ,Rn}, are deployed on
a planar space. The configuration of robot Ri is denoted by qi(t) = [xi, yi, ?µi] , i =
1, 2, . . . , n. where xi and yi are the coordinates of robot Ri and ?µi is the orientation
of the robot with respect to its local coordinate system. The dynamics of mobile robot
Ri can be described by ?™ qi = fi(qi, ui), where ui is the control input of subsystem
Ri.
In this chapter, the discussion is based on both the holonomic model and the
nonholonomic model of a mobile robot. The holonomic model of the robot can be
described as:
?™ xi = vix,
?™ yi = viy,
?™ vix = ui1,
?™ viy = ui2,
(1)
where vix and viy are the translational velocities along x and y direction in its local
coordinate system, respectively. In this model, the control input ui is defined as:
ui = {ui1, ui2}T .
2.2 Delaunay triangulation and network model
The configuration and control input of the entire system can then be denoted by
68 Jindong Tan
q = {q1, q2, . . . , qn}T
and
u = {u1, u2, . . . , un}T
interconnected system, the overall system can be denoted by ?™ q = f(q, u), where f
is the vector field of system dynamics [20].
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