Eq. (2) breaks down as
d decreases to 0, since communication rates are limited by on-board processing
capabilities. We use a di?®erent capacity model:
C = ??±????????????
co( 1
d?® ??’ 1
r?®
zone
), rmin < d < rzone
co( 1
r?®
min
??’ 1
r?® ), d ?‰¤ rzone
0, d > rzone
???????????????
(3)
with a profile shown in Figure (2-a). Because the data rate varies with distance
between nodes, the optimal utility function value will also vary with
node location, as the solution of an unconstrained optimization problem using
Lagrange multipliers:
U??—(ri=1,N) = minpl>0maxxi>0(
N
Xi=1
wiU(xi) +
L
Xl=1
l l i l .
In a classical network formulation, the utility functions of each node are
i (to main-
3.1 Example: Capacity in a four-node network
Consider the four node network shown in Figure (2-b). The flow optimization
mal flow vector x??— = (x??—1
, x??—2
, x??—3
)T , solution of a 3D constrained optimization
problem. If the location of the nodes can vary, the maximum capacities will
also vary similarly with the graph in Figure 2. Assuming that the location
of nodes 1, 3, and 4 is fixed, but the second node is allowed to move in a
and is shown in Figure 3.
We describe the problem of adaptive sampling, e.g., the problem of reconstructing
a parametrized field model from observations taken using mobile
robot nodes. If the parametric form of a measurement field is known, as might
40
equally weighed.
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