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4 Formal Description of the Problem. Experimental
Scenario
4.1 Formal Description of the Problem
The optimal multi-tasks allocation problem in multi-robot systems can be for-
mally defined as follows: ”Given a robot team formed by
N
heterogeneous robots,
and given
K
different types of heterogeneous specialized tasks to be executed,
obtain an optimal distribution of the existing tasks among the available robots”.
The load or number of each task can be constant (i.e, the stationary case) or can
be variable and time-dependent (i.e, the dynamic case). Most of the proposed
solutions in the technical literature are of a centralized nature, in the sense that
an external controller is in charge of distributing the tasks among the robots
by means of conventional optimization methods and based on global informa-
tion about the system state [19]. However, we are mainly interested on truly
decentralized solutions in which the robots themselves, autonomously and in an
individual and local manner, select a particular task so that all the tasks are
optimally distributed and executed. In this regard, we have experimented with
bio-inspired threshold models to tackle this hard self-coordination problem as
described in the sequel.
4.2 Experimental Scenario
In this area of research, we propose the following experimental scenario, with
the objective of analyzing a concrete strategy or solution for the coordination
of multi-robot systems as regards the optimal distribution of the existing task.
Given a set of
N
heterogeneous mobile robots distributed within a single region
or at different regions in which case they form sub-teams in each region that
will perform a set of tasks
T
that may be divided into j sub-tasks. The sub-
teams are dynamic over time, i.e. the same robots will not be always part of the
same sub-team, but the components of each sub-team can vary depending on
the situation.
Let
H
=
be the set of regions to be explored. Let
T
denote the
task, which divided into
j
sub-tasks
{
h
1
,h
2
, ..., h
N
}
{
t
1
,t
2
, ..., t
J
}
.Let
R
=
{
r
1
,r
2
, ..., r
K
}
be the
set of
K
heterogeneous mobile robots (
K
≥
J
). Let
S
=
{
s
1
,s
2
, ..., s
M
}
be the set
of
M
sub-teams by region, where
s
M
⊆
R
, i.e. the sum of
s
1
+
s
2
, ...,
+
s
M
=
K
.
Using the mathematical model of response threshold, to obtain the optimal
solution to the problems raised here:
1. To perform the distribution of a set of
K
heterogeneous mobile robots in
N
regions for all
K
=1to
K
.
2. To perform the task allocation for each robot
r
k
belonging to the sub-team
s
M
.
To solve the problem, we make the following assumption: that each region has
the same number of
J
tasks; that all members
R
=
{
r
1
,r
2
, ...r
K
}
areableto
participate in any sub-task
t
j,m
.
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