We focus on creating a robot/sensor architecture that combines navigation
and communication. Specifically, we would like to control individual robot
location (ri), and its sensor data rate (xi) over time in order to maximize
a combined network utility function, subject to a set of capacity constraints
that vary with distance:
maxx?‰?0
N
Xi=1
Ui(xi) subject to Rx ?‰¤ c(ri) (1)
where Ui is a strictly concave utility function, R is the routing matrix for the
network, and c(r) is a position dependent link capacity function. The concave/
convex requirement for Ui, combined with a full row rank condition of
the routing matrix R are su?±cient (but not necessary) conditions to ensure
that there exists a unique minimum solution to the associated constrained optimization
problem (1). Various utility functions are used for di?®erent network
models, for example arctan(xi) for TCP Reno and log(xi) for TCP Vegas [35].
As a reflection of the network mobility, however, we assume that the link
capacity constraints can vary with the distance between network nodes. This is
consistent with Shannon??™s theorem that predicts that the maximum achievable
data rate between two nodes is given by:
39
Solutions to both the routing and congestion control problems are di?®er-
3 Communication Models
Dan O. Popa and Frank L. Lewis
C = Wlog2 ?µ1 +
K
WNo
Pt
d?®?¶ (2)
where P is the power, d is the distance between nodes, W is the bandwidth,
?® is the path loss coe?±cient, F is the fading margin, K??? is the propagation
constant dependent on the medium, and K = K???F [42].
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