Page 57 - Innovations in Intelligent Machines

46 P.B. Sujit et al.

b
1 d ^
P
a
p UAV
i j sr
1 UAV i
3 _
p p
,
j k

sr distance
Fig. 1. (a) Probability distribution of the values of the targets as a function of
distance (b) Determination of virtual targets

Attacking target j: If target j is within the sensor radius of the k th UAV then
(12)
C kj = V j w r − S kj
If target j is not in the sensor range of the k th UAV then C kj = 0. Here,
we have assumed that all the UAVs have the same sensor range and hence the
i th UAV can estimate whether the j th target is within the sensor range of the
k th UAV.
Attacking virtual target: The concept of virtual target is used to estimate the
environment beyond the sensor range of the i th UAV (see Figure 1(b)). The
i th UAV cannot see the shaded region which the j th UAV can see. Depending
on the number of targets present in that shaded region, the behaviour of the
j th UAV will vary. To estimate the number of targets that might be there, we
assume that the targets are uniformly distributed. We take into consideration
the combined effect of all these target, which we assume to be placed at a point
p, equidistant from point (a, b). This combined target is called the virtual
target for the k th UAV. The benefit that the k th UAV gets for attacking this
ˆ
virtual target k is

C ˆ = (average value of target)n k w r − S ˆ (13)
kk kk
where, n k is the number of targets that can be present in the shaded
2
region. Therefore, n k = n i (area of shaded region)/(πs )and C ˆ =0, ∀ l =
r
lk
1,...,n i ,l = k,and s r is the sensor range. That is, for any other UAVs,
ˆ
the benefit of attacking the virtual target k of the k th UAV is zero. Let us
ˆ ˆ
ˆ
i
denote T = {k 1 , k 2 , ··· , k n i −1 } to be the set of virtual targets for the n i − 1
v
neighbours that the i th UAV has to take into account.
Since, C ij are random variables, the i th UAV will maximize the expected
payoff. The expectation is calculated on the basis of the joint probability
distribution P i (s) on the state. Here, we assume that the value of the targets
are independent, therefore
m i

P i (s)= p(d j ) (14)
j=1