Page 56 - Innovations in Intelligent Machines

Team, Game, and Negotiation based UAV Task Allocation 45
every x ij = ζ such that 0 <ζ < 1, there exits a solution ˆx ij =0 or 1 that will
give a better or equal performance. Since we assume decentralized control of
the UAVs, each UAV solves the optimization problem individually to decide
on its action.

3.3 Team Theoretic Solution

The problem defined in Section 3.1 assumes that the optimization problem
is solved globally. However, in the scenario that we consider, the UAVs do
not have global information. Each UAV solves the optimization problem with
only local information available to it. Moreover, the value of the target status
is a random variable. Hence, we use concepts from team theory to solve this
optimization problem.
Before reformulating this problem, we define the benefit C ij that the i th
UAV gets by performing the task j. If it is a search task then

time left in the mission
C is = (9)
total flight time
If it is the task of attacking the target j then,

(10)
C ij = V j w r − S ij
where, V j = value of target j, w r = the weightage given to the search task
over the task of attacking a target, and

time to reach the target j by UAV i
S ij = (11)
total flight time
However, the i th UAV knows the values of the target j with some proba-
bility. The probability distribution is assumed to be linear and is shown in
Figure 1(a). Let p r (d ij ) define the probability of target j to have a value r
at a distance d ij . Here, r = {0, 0.5, 1} where, when r = 1, the target has not
been attacked and is intact, when r =0.5 the target is partially destroyed,
and when r = 0 the target is fully destroyed. Thus, C ij ’s are random variables
with probability distribution p(d ij )=[p 1 (d ij ),p 0.5 (d ij ),p 0 (d ij )].
Speculation/BDA: Since speculation on the target is done at every time step,
and is reflected on the value of targets, we will not attach any separate benefit
to the speculative task.
Each UAV also has to estimate the benefits that its neighbouring UAV
(say the k th UAV) will get from the different tasks that it can perform. It
calculates the benefits as follows:

Search task: The search task is similar to that defined above, hence the search
value is the same for all UAVs.