Page 38 - Innovations in Intelligent Machines

26 M.L. Cummings et al.
C=cost of fuel total UAV distance
∗
+cost per missed target # of missed targets
∗
∗
+ operation cost per time total time (5)
In order to maximize performance, the cost function should be minimized
by finding the optimal values for the variables in the cost equation. However,
the variables in the cost equation are themselves dependent on the number of
UAVs and the specific paths planned for those UAVs. One way to minimize the
cost function is to hold the number of UAVs variable constant at some initial
value and to vary the mission routes (individual routes for all the UAVs) until
a mission plan with minimum cost is found. We then select a new setting for
the number of UAVs variable and repeat the process of varying the mission
plan in order to minimize the cost. After iterating through all the possible
values for the number of UAVs, the number of UAVs with the least cost and
the corresponding optimized mission plan are then the settings that minimize
the cost equation. As the number of UAVs is increased, new routing will be
required to minimize the cost function. Thus, the paths, which determine time
of flight, are a function of number of UAVs.
Moreover, if a target is missed, then there is an additional, more significant
cost. When the number of UAVs planned is too low, the number of missed
targets increases and hence the cost is high. When the number of UAVs is
excessive, more UAVs are used than required and thus additional, unnecessary
costs are incurred. We therefore expect the lowest cost to be somewhere in
between those two extremities, and that the shape of the cost curve is therefore
1
concave upwards (Figure 8). The profile in Figure 8 does not include the effect
of wait times, and it does not take into account the interaction between the
vehicles and the human operator.

Too many
missed targets

Mission Plan Cost # of UAVs with UAVs
Too many

minimum cost

# of UAVs
Fig. 8. Mission Plan Costs as a Function of Number of UAVs

1
Note that this claim is dependent on the assumption that the UAVs indepen-
dently perform tasks.