As a result the node can remain useful as
a network node.
56
Chapter 2 Algorithms for Robotic Deployment of WSN
Fig. 7. 2D force fields indicating communication forces on the end-node for a simple
plots were obtained for ?® = 2, rmin = 2, rzone = 8 in equation (3) by numerically
We can also tie the cost of node movement with the information measures
while sampling by noting that the covariance measure Pk behaves like an
according to a spring constant such as F = W?–?x. Then more energy is used
as (xk+1??’xk) increases. Therefore, define predicted work needed to go to the
next predicted state as:
?†M
k+1 = ( ?†X
??’k+1 ??’ Xk)TW( ?†X
??’k+1 ??’ Xk) (16)
where sti?®ness weighting matrix W can be used to select only the vehicle
states xk and not the parameters ak, which do not contribute to motion
energy needed. We can then move to the state that minimizes the weighed
cost
Ek+1 = ?® ?†M
k+1 + (1 ??’ ?®)tr(PT
k+1Pk+1)
57
energy. Suppose that battery usage is proportional to the distance moved
solving the capacity optimization problem and di?®erentiating to obtain the force.
3-node network (a), and on the ???middle??? node for a simple 4-node network. The
Dan O. Popa and Frank L. Lewis
with ?® a weighting tradeo?® parameter. Note that if the SVD of P is P =
U PV T , then
tr(PTP) = tr(V X 2V T ) = tr(V V TX 2) = tr(X 2),
which is the sum of the singular values.
6.2 EXAMPLE: Using potential fields for navigation and
communication
Simulations of navigation based on the potential fields were run using Zone
Routing Protocol (ZRP) routing [19], optimal data rates, and attractive 2D
goals.
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