Page 54 - Innovations in Intelligent Machines

Team, Game, and Negotiation based UAV Task Allocation 43
decision maker can take. Then, the function δ i : Y i → X i is called the decision
function for the i th decision maker and we have
x i = δ i (y i ) (2)

Considering the decision function of all the decision makers, the vector
δ = {δ 1 ,δ 2 ,...,δ N } is called the team decision function. There can be some
constraints on the team decision functions. For example, for every s ∈ S,let
n
k(s) ∈ R be a close convex set. We will consider only those decision func-
tions for which δ(η(s)) ∈ k(s), ∀s.Let x = {x 1 ,x 2 ,...,x N } denote the team
decision.
The outcome of the decisions of the team members depends jointly on the
state s and the team decision x and it is determined according to some function
u(s, x) which is pre-specified. Hence, the payoff of the team is given by

ω = u(s, x) (3)
The team decision problem is concerned with finding the maximum expected
payoff with respect to the team decision function i.e.,

max E[ω(s, x)] = max γ(s)u(s, δ(η(s))) (4)
δ δ
x∈k(s)
If the payoff function is linear in the decision variables, the team is called a
linear team. As shown in [26], the solution of the linear team can be obtained
by solving a linear programming problem in the decision function space. Let
the payoff function be ω = C i x i , where C i is a function of the state and
i
so it is also a random variable. Then, the objective function is given as

max E C i x i , (5)
x∈k(s)
i
3.2 Problem Formulation

Let us consider a battlefield scenario where N UAVs are deployed to search
and destroy targets within a stipulated time. Thus the team T consists
of the N UAVs, which are the decision makers. The environment comp-
rises of the targets of different strengths scattered on a plain. Assume
that there are M targets, the location and the strength of which are not
known a priori to the UAVs. We define the state of the environment as
u N t M M u th t
s =({Z } i=1 , {Z } , {V j } j=1 ) where Z is the position of the i UAVs, Z j
j j=1
i
i
is the position of the j th target and V j is the strength/values of the j th target.
The UAVs can observe the environment within a given sensor radius. We
assume that there is no communication among the UAVs. Thus, the infor-
mation available to the UAVs about the state of the environment are the
number of targets, their values and the number of other UAVs present within