In the context of robot navigation, the potential field method creates a vector
field representing a navigational path based on a potential function. These
vectors then act as artificial forces upon the nodes resulting in motion through
a dynamic equation of motion. Given a scalar potential field function U(r) that
depends on the robot position, one can calculate forces governing the robot
motion based on the gradient of the scalar potential field F = ??’??‡U(??’?†’r
).
Similar approaches for MWSN deployment have been described by others in
[21, 31, 58], but in their case the potential field forces are not based on actual
measures of communication or information. For a MWSN, we consider the
following actuation forces:
53
the following infinity norm is maximized over the search space ??–:
6 Potential Fields
Dan O. Popa and Frank L. Lewis
Fig. 6. The convergence of slope and intercept in a combined KF field estimation and
localization problem for the default (a,c) and optimal (b,d) 1D sampling sequence.
54
(a) (b)
(c)
(d)
Chapter 2 Algorithms for Robotic Deployment of WSN
??? Attractive forces towards goals, which are defined as locations in space
where the sensor nodes need to sample next, based on adaptive sampling
criteria: Fgoal = ??’wg(r ??’ rgoal).
??? Repulsive forces given by obstacles and other robots, in particular rolling
down a potential ???hill??? around the object:
Fobs = (??( 1
D(r) ??’ 1
Q)??‡D(r)
D2(r) , D(r) ?‰¤ Q
0, D(r) > 0
where Q is area of influence of the obstacle and D(r) is the Euclidean
distance from the obstacle to the robot.
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