For example, robot R2 in Figure 2 has
six neighbors, which form subgraph of the Delaunay triangulation. For a cooperation
task, the motion of robot R2 is only affected by its immediate one-hop neighbors.
The robot model considering its one-hop neighbors can be described as:
?™ qi = fi(qi, ui),
ui = hi(pi1, pi2, . . . , pik),
(2)
where pi1, pi2, . . . , pik are the positions of the one-hop neighbors R1,R2, . . . ,Rk ???
Ki ??† R in the coordinate frame of robot Ri, ?§i.
3 Self-deployment Algorithm
3.1 Autonomous Deployment
In a mobile sensor network, the robot can cooperate to perform spatially distributed
tasks such as distributed sensing or cooperative manipulation. One of the objectives
of robot cooperation in such a system is to maximize the coverage area of the network,
for example, an incremental approach and a potential field approach have been
introduced [22]. In the present paper, a distributed self-deployment algorithm is proposed
based on both the potential field method and the Delaunay triangulation.
i
Lyapunov function) is defined as follows:
Vi =
1
2
mi
X
j=1
ki(kpijk ??’ ci j)2 +
1
2
kivkvik2, (3)
where pij is a vector from robot Ri to robot Rj in the coordinate frame of Ri,
and kpijk = p(xi ??’ xj)2 + (yi ??’ yj)2 and ci j are the actual and desired distance
between the two robots respectively.mi is the total number of the one-hop neighbors
of Ri. ki and kiv are parameters for the virtual potential energy and kinetic energy
of the robot.
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