Multi-Robot Systems From Swarms to Intelligent Automata - Parker et al (Eds) Part 2 ppsx

I
SSUES IN MULTI-ROBOT COALITION
FORMATION
Love
k
es
h
V
ig
El
ectrica
l
Engineering an
d
Computer Science Departmen
t
Vanderbilt University, Nashville TN 3721
2
l
ovekesh.vi
g@
vanderbilt.ed
u
J
u
li
eA.A
d
am
s
El

ectrica
l
Engineering an
d
Computer Science Departmen
t
Vanderbilt University, Nashville TN 3721
2
j
ulie.a.adams
@
vanderbilt.ed
u
Abs
tr
act
N
umerous coa
li
t
i
on
f
ormat
i
on a
l
gor
i
t

h
ms ex
i
st
i
nt
h
eD
i
str
ib
ute
d
Art
ifi
c
i
a
l
In
-
t
elligence literature. Algorithms exist that form agent coalitions in both supe
r
additive and non-super additive environments. The employed techniques var
y
f
rom negotiation-based protocols in Multi-Agent System (MAS) environment
s
t

o those based on computation in Distributed Problem Solving (DPS) environ
-
m
ents. Coalition formation behaviors have also been discussed in the game the
-
o
ry literature.
D
espite the plethora of multi-agent coalition formation literature, to the bes
t
o
f our knowledge none of these algorithms have been demonstrated with a
n
actual multiple-robot system. There exists a discrepancy between the multi
-
agent algorithms and their applicability to the multiple-robot domain. This wor
k
aims to correct that discrepanc
y
b
y
unearthin
g
issues that arise while attemptin
g
t
o tailor these al
g
orithms to the multiple-robot domain. A well-known multiple
-

a
g
ent coalition formation al
g
orithm has been studied in order to identif
y
th
e
n
ecessar
y
modifications to facilitate its application to the multiple-robot domain
.
K
e
y
words:
C
oalition formation
,
fault-tolerance
,
multi-robot
,
task allocation
.
1. Introduction
Mu
l
t

i
-agent systems o
f
ten encounter s
i
tuat
i
ons t
h
at requ
i
re agents to co
-
o
perate an
d
per
f
orm a tas
k
. In suc
h
s
i
tuat
i
ons
i
t
i

so
f
ten
b
ene
fi
c
i
a
l
to ass
i
gn a
group o
f
agents to a tas
k
, suc
h
as w
h
en a s
i
ng
l
e agent cannot per
f
orm t
h
e tas

k
s
.
T
hi
s paper
i
nvest
i
gates a
ll
ocat
i
ng tas
k
sto
di
s
j
o
i
nt ro
b
ot teams, re
f
erre
d
to a
s
1

5
L
.E. Par
k
er et a
l
.(e
d
s.)
,
M
u
l
ti-Ro
b
ot S
y
stems. From Swarms to Inte
ll
i
g
ent Automata. Vo
l
ume III
,
1
5–26.

c
2

005
S
prin
g
er. Printe
d
in t
h
e Net
h
er
l
an
d
s
.
16
V
i
g
and Adams
c
oa
li
t
i
ons. C
h
oos
i

ng t
h
e opt
i
ma
l
coa
li
t
i
on
f
rom a
ll
poss
ibl
e coa
li
t
i
ons
i
san
i
n
-
tracta
bl
e
p

ro
bl
em
d
ue to t
h
es
i
ze o
f
coa
li
t
i
on structure s
p
ace (San
dh
o
l
meta
l
.
,
1999). A
l
gor
i
t
h

ms ex
i
st t
h
at y
i
e
ld
so
l
ut
i
ons w
i
t
hi
na
b
oun
df
rom t
h
e opt
i
ma
l
a
n
d
are tracta

bl
e. However t
h
ese a
l
gor
i
t
h
ms ma
k
eun
d
er
l
y
i
ng assumpt
i
on
s
t
h
at are not app
li
ca
bl
etot
h
emu

l
t
i
p
l
e-ro
b
ot
d
oma
i
n,
h
ence t
h
eex
i
stence o
f
adi
screpancy
b
etween t
h
emu
l
t
i
-agent an
d

mu
l
t
i
p
l
e-ro
b
ot coa
li
t
i
on
f
ormat
i
o
n
li
terature. T
hi
s paper
id
ent
ifi
es t
h
ese assumpt
i
ons an

d
prov
id
es mo
difi
cat
i
on
s
to t
h
emu
l
t
i
-agent coa
li
t
i
on
f
ormat
i
on a
l
gor
i
t
h
ms to

f
ac
ili
tate t
h
e
i
r app
li
cat
i
o
n
i
nt
h
emu
l
t
i
p
l
e-ro
b
ot
d
oma
i
n. Ger
k

ey an
d
Matar
i
c (Ger
k
ey an
d
Matar
i
c, 2004
)
i
n
di
cate t
h
at
d
esp
i
te t
h
eex
i
stence o
f
var
i
ous mu

l
t
i
-agent coa
li
t
i
on
f
ormat
i
o
n
al
gor
i
t
h
ms, none o
f
t
h
ese a
l
gor
i
t
h
ms
h

ave
b
een
d
emonstrate
di
nt
h
emu
l
t
i
p
l
e
-
r
o
b
ot
d
oma
i
n
.
Var
i
ous tas
k
a

ll
ocat
i
on sc
h
emes ex
i
st. T
h
e ALLIANCE
(
Par
k
er, 1998
)
ar
-
chi
tecture uses mot
i
vat
i
ona
lb
e
h
av
i
ors to mon
i

tor tas
k
pro
g
ress an
ddy
nam
i-
c
a
lly
rea
ll
ocate tas
k
s. T
h
e MURDOCH (Ger
k
e
y
an
d
Matar
i
c, 2002) an
d
BL
E
(

Wer
g
er and Mataric, 2000) s
y
stems use a Publish/ Subscribe method to al
-
l
ocate tasks that are hierarchicall
y
distributed. However, most current tas
k
a
llocation schemes assume that all of the s
y
stem robots are available for tas
k
e
xecution. These s
y
stems also assume that communication between robots i
s
a
lwa
y
s possible or that the s
y
stem can provide motivational feedback. Thes
e
a
ssumptions need not alwa

y
s hold, a set of tasks ma
y
be located at consider
-
a
ble distances from one another so that the best solution is to dis
p
atch a robo
t
team to each desi
g
nated task area and hope that the team can autonomousl
y
c
om
p
lete the task. The robots must then coalesce into teams res
p
onsible fo
r
e
ach task. The focus of this work is to investi
g
ate the various issues that aris
e
while attemptin
g
to form multiple-robot coalitions usin
g

existin
g
multi-a
g
en
t
c
oalition formation al
g
orithms. Some solutions are su
gg
ested and Shehor
y
an
d
K
rauss’ (Shehor
y
and Krauss, 1998) multi-a
g
ent task allocation scheme al
g
o-
r
ithm is modified to operate in the multiple-robot domain. This algorithm wa
s
c
hosen because it is designed for DPS Environments, has an excellent real-tim
e
r

es
p
onse and has been shown to
p
rovide results within a bound from o
p
timal.
T
hi
s paper
i
sorgan
i
ze
d
as
f
o
ll
ows. Sect
i
on 2 prov
id
es t
h
ere
l
ate
d
wor

k.
S
ect
i
on 3 presents an overv
i
ew o
f
S
h
e
h
ory an
d
Krauss’ a
l
gor
i
t
h
m. Sect
i
o
n
4
id
ent
ifi
es
i

ssues t
h
at enta
il
mo
difi
cat
i
on o
f
current coa
li
t
i
on
f
ormat
i
on a
l-
g
orithms. Experimental results are provided in Section
5
. Finally, Section
6
di
scusses t
h
e conc
l

us
i
ons an
df
uture
w
or
k
.
2. Related
W
ork
Sh
e
h
ory an
d
Krauss propose
d
avar
i
ety o
f
a
l
gor
i
t
h
ms

f
or agent coa
li
t
i
on
f
or
-
mat
i
on t
h
at e
ffi
c
i
ent
l
yy
i
e
ld
so
l
ut
i
ons c
l
ose to opt

i
ma
l
.T
h
ey
d
escr
ib
eaKer
-
ne
l
or
i
ente
d
mo
d
e
lf
or coa
li
t
i
on
f
ormat
i
on

i
n genera
l
env
i
ronments (S
h
e
h
or
y
I
ssues in Multi-Robot
C
oalition Formatio
n
17
and Krauss, 1996) and non-super additive environments (Shehory and Krauss,
1999). T
h
ey a
l
so prov
id
e
d
a computat
i
on
b

ase
d
a
l
gor
i
t
h
m
f
or non-super a
d-
di
t
i
ve env
i
ronments (S
h
e
h
ory an
d
Krauss, 1998). Broo
k
san
d
Dur
f
ee (Broo

k
s
an
d
Dur
f
ee, 2003) prov
id
eanove
l
a
l
gor
i
t
h
m
i
nw
hi
c
h
se
lfi
s
h
agents
l
earn t
o

f
orm congregat
i
ons. An
d
erson et a
l
. (An
d
erson et a
l
., 2004)
di
scuss t
h
e
f
or-
m
at
i
on o
fd
ynam
i
c coa
li
t
i
ons

i
nro
b
ot
i
c soccer env
i
ronments
b
y agents t
h
a
t
c
an
l
earn eac
h
ot
h
er’s capa
bili
t
i
es. Fass (Fass, 2004) prov
id
es resu
l
ts
f

or an
A
utomata-t
h
eoret
i
cv
i
ew o
f
agent coa
li
t
i
ons t
h
at can a
d
apt to se
l
ect
i
ng group
s
of
agents. L
i
an
d
So

h
(L
i
an
d
So
h
, 2004)
di
scuss t
h
e use o
f
are
i
n
f
orcement
l
earn
i
ng approac
h
w
h
ere agents
l
earn to
f
orm

b
etter coa
li
t
i
ons. Sor
b
e
ll
aeta
l.
(
Sor
b
e
ll
aeta
l
., 2004
)d
escr
ib
e a mec
h
an
i
sm
f
or coa
li

t
i
on
f
ormat
i
on
b
ase
d
o
n
apo
li
t
i
ca
l
soc
i
et
y.
3
.
S
hehory and Krauss’ Algorithm
S
h
e
h

ory an
d
Krauss (S
h
e
h
ory an
d
Krauss, 1998)
d
eve
l
ope
d
amu
l
t
i
-agent
a
l
gor
i
t
h
mt
h
at
i
s

d
es
i
gne
df
or tas
k
a
ll
ocat
i
on v
i
a agent coa
li
t
i
on
f
ormat
i
on
in
D
P
S
en
vi
ronments.
3

.1 Assum
p
tions
T
h
ea
l
gor
i
t
h
m
i
nc
l
u
d
es var
i
ous assumpt
i
ons. Assume a set o
f
n
agen
t
s,
N
=
A

1
,
A
2
,
A
n
.T
h
e agents commun
i
cate w
i
t
h
eac
h
ot
h
er an
d
are aware o
f
a
ll
tas
k
sto
b
e per

f
orme
d
. Eac
h
agent
h
as a vector o
f
rea
l
non-negat
i
ve capa
bil-
i
t
i
e
s
B
i
=
<
b
i
1
,
b
i

2
,
b
i
r
>
. Eac
h
capa
bili
ty quant
ifi
es t
h
ea
bili
ty to per
f
orm a
n
act
i
on. In or
d
er to assess coa
li
t
i
ons an
d

tas
k
execut
i
on
,
an eva
l
uat
i
on
f
unct
i
o
n
i
s attac
h
e
d
to eac
h
capa
bili
ty type t
h
at trans
f
orms capa

bili
ty un
i
ts
i
nto mone
-
tary un
i
ts. It
i
s assume
d
t
h
at t
h
ere
i
s a set o
f
m
i
n
d
epen
d
ent tas
ks
T

=
t
1
,
t
2
,
t
m
t
.
A
capa
bili
ty vecto
r
B
l
=
<
b
l
1
, ,
b
l
r
>
i
s necessary

f
or t
h
e sat
i
s
f
act
i
on o
f
eac
h
tas
k
t
l
.T
h
eut
ili
ty ga
i
ne
df
rom per
f
orm
i
ng t

h
e tas
kd
epen
d
sont
h
e capa
bili
t
i
e
s
r
equ
i
re
df
or
i
ts execut
i
on. A coa
li
t
i
on
i
s a group o
f

agents t
h
at
d
ec
id
e to coop
-
e
rate
i
nor
d
er to ac
hi
eve a common tas
k
. Eac
h
coa
li
t
i
on wor
k
sonas
i
ng
l
e tas

k.
A
coa
li
t
i
o
n
C
h
as a capa
bili
ty vector B
c
r
epresent
i
ng t
h
e sum o
f
t
h
e capa
bili
t
i
e
s
t

h
at t
h
e coa
li
t
i
on mem
b
ers contr
ib
ute to t
hi
ss
p
ec
ifi
c coa
li
t
i
on. A coa
li
t
i
o
n
C
c
an per

f
orm a tas
k
t
o
n
l
y
if
t
h
e capa
bili
ty vector necessary
f
or tas
kf
u
lfill
men
t
B
t
sat
i
s
fi
es
∀
0

≤
i
≤
r
,
r
r
b
t
i
<
b
c
i
.
3
.2 The algorithm
T
h
ea
l
gor
i
t
h
m cons
i
sts o
f
two pr

i
mary stages. T
h
e
fi
rst ca
l
cu
l
ates coa
li
t
i
ona
l
v
a
l
ues to ena
bl
e compar
i
son o
f
coa
li
t
i
ons. T
h

e secon
d
stage enta
il
san
i
tera
-
t
i
ve gree
d
y process t
h
roug
h
w
hi
c
h
t
h
e agents
d
eterm
i
ne t
h
e pre
f

erre
d
coa
li-
t
i
ons an
df
orm t
h
em. Stage one
i
st
h
e more re
l
evant to t
hi
swor
k
. Dur
i
ng t
his
stage t
h
e eva
l
uat
i

on o
f
coa
li
t
i
ons
i
s
di
str
ib
ute
d
amongst t
h
e agents v
i
a exten
-
18
V
i
g
and Adams
s
i
ve message pass
i
ng, requ

i
r
i
ng cons
id
era
bl
e commun
i
cat
i
on
b
etween agents
.
Af
ter t
hi
s stage, eac
h
agent
h
as a
li
st o
f
coa
li
t
i

ons
f
or w
hi
c
hi
tca
l
cu
l
ate
d
coa
li-
t
i
on va
l
ues. Eac
h
agent a
l
so
h
as a
ll
necessary
i
n
f

ormat
i
on regar
di
ng t
h
e coa
li-
t
i
on mem
b
ers
hi
ps’ capa
bili
t
i
es. In or
d
er to ca
l
cu
l
ate t
h
e coa
li
t
i

on va
l
ues, eac
h
a
gent t
h
en
:
1 Determ
i
nes t
h
ee
li
g
ibl
e coa
li
t
i
ons
f
or eac
h
tas
k
execut
i
o

n
t
i
b
y compar
-
i
ng t
h
e requ
i
re
d
capa
bili
t
i
es to t
h
e coa
li
t
i
on capa
bili
t
i
es
.
2

Ca
l
cu
l
ates t
h
e
b
est-ex
p
ecte
d
tas
k
outcome o
f
eac
h
coa
li
t
i
on (coa
li
t
i
o
n
we
i

g
h
t) an
d
c
h
ooses t
h
e coa
li
t
i
on y
i
e
ldi
ng t
h
e
b
est outcome
.
4. Issues in Multi
p
le-Robot
Sy
stems
T
h
ea

l
gor
i
t
h
m
d
escr
ib
e
di
n Sect
i
on 3 y
i
e
ld
s resu
l
ts t
h
at are c
l
ose to opt
i
ma
l.
T
h
e current a

l
gor
i
t
h
m cannot
b
e
di
rect
l
y app
li
e
d
to mu
l
t
i
p
l
e-ro
b
ot coa
li
t
i
o
n
f

ormat
i
on. T
hi
s sect
i
on
id
ent
ifi
es
i
ssues t
h
at must
b
ea
dd
resse
df
or mu
l
t
i
p
l
e
-
r
o

b
ot
d
oma
i
ns.
4.1 Com
p
utation vs. Communication
Sh
e
h
ory an
d
Krauss’s a
l
gor
i
t
h
m(S
h
e
h
ory an
d
Krauss, 1998) requ
i
res ex-
tens

i
ve commun
i
cat
i
on an
d
sync
h
ron
i
zat
i
on
d
ur
i
ng t
h
e computat
i
on o
f
coa
li-
t
i
on va
l
ues. W

hil
et
hi
s may
b
e
i
nexpens
i
ve
f
or
di
sem
b
o
di
e
d
agents,
i
t
i
so
f
te
n
d
es
i

ra
bl
etom
i
n
i
m
i
ze commun
i
cat
i
on
i
nmu
l
t
i
p
l
e-ro
b
ot
d
oma
i
ns even at t
he
e
xpense o

f
extra computat
i
on. T
hi
swor
ki
nvest
i
gates eac
h
agent assum
i
ng re
-
spons
ibili
ty
f
or a
ll
coa
li
t
i
ons
i
nw
hi
c

hi
t
i
s a mem
b
er an
d
t
h
ere
b
ye
li
m
i
nat
i
n
g
t
h
e nee
df
or commun
i
cat
i
on. It
i
s necessary to ana

l
yze
h
ow t
hi
swou
ld
a
ff
ec
t
e
ac
h
ro
b
ots computat
i
ona
ll
oa
d
.Ana
dd
e
d
assumpt
i
on
i

st
h
ataro
b
ot
h
as
a
p
r
i
or
ik
now
l
e
d
ge o
f
a
ll
ro
b
ots an
d
t
h
e
i
r capa

bili
t
i
es. Ro
b
ot capa
bili
t
i
es
d
ono
t
typ
i
ca
ll
yc
h
ange; t
h
ere
f
ore t
hi
s
i
s not a pro
bl
em un

l
ess a part
i
a
l
or tota
l
ro
b
o
t
f
a
il
ure
i
s encountere
d
(U
l
am an
d
Ar
ki
n, 2004). Suppose t
h
ere ar
e
N
id

ent
i
ca
l
r
o
b
ots an
d
w
i
t
h
a per
f
ect computat
i
ona
ll
oa
ddi
str
ib
ut
i
on, t
h
en t
h
e num

b
er o
f
c
oa
li
t
i
ons eac
h
ro
b
ot must eva
l
uate w
i
t
h
commun
i
cat
i
on
i
s
:
η
w
it
h

=
k
∑
r
=
0
(
n
r
)
/
n
(1
)
T
h
ea
l
gor
i
t
h
m
di
str
ib
utes coa
li
t
i

ons
b
etween agents as a rat
i
oo
f
t
h
e
i
r compu
-
tat
i
ona
l
capa
bili
t
i
es, a
ddi
ng unwante
d
comp
l
ex
i
ty. It
i

sun
lik
e
l
yt
h
at t
h
e
l
oa
d
w
ill b
e per
f
ect
l
y
di
str
ib
ute
d
, rat
h
er some agents w
ill
comp
l

ete t
h
e
i
r computa
-
t
i
ons
b
e
f
ore ot
h
ers an
d
rema
i
n
idl
e unt
il
a
ll
computat
i
ons are comp
l
ete
d

.T
he
worst case commun
i
cat
i
ona
ll
oa
d
per agent
i
sO
(
n
k
−
1
)d
ur
i
ng t
h
eca
l
cu
l
at
i
on-

di
str
ib
ut
i
on stage. I
f
eac
h
agent
i
s respons
ibl
e
f
or on
l
y computat
i
on o
f
coa
li-
t
i
ons
i
nw
hi
c

hi
t
i
s a mem
b
er
,
t
h
en t
h
e num
b
er o
f
coa
li
t
i
ons eva
l
uate
d
w
i
t
h
n
o
I

ssues in Multi-Robot
C
oalition Formatio
n
19
c
ommun
i
cat
i
on
b
ecomes:
η
w
it
h
out
=
k
−
1
∑
r
=
0
(
n
−
1

r
)
(
2)
Eq
uat
i
on 1 re
q
u
i
res
f
ewer com
p
utat
i
ons to eva
l
uate
b
ut t
hi
s
i
s not an or
d
e
r
of

magn
i
tu
d
e
diff
erence. In
b
ot
h
cases, t
h
e agent’s computat
i
ona
ll
oa
dis
O(
n
k
)p
er tas
k
.T
h
e commun
i
cat
i

ona
ll
oa
dp
er ro
b
ot
i
s O(1)
i
nt
h
eca
l
cu
l
at
i
on
-
di
str
ib
ut
i
on stage. T
h
ea
ddi
t

i
ona
l
computat
i
on may
b
e compensate
df
or
by
r
educed communication time. The Section
5
experiments demonstrate thi
s
p
o
i
nt. A
d
es
i
ra
bl
es
id
ee
ff
ect

i
sa
ddi
t
i
ona
lf
au
l
tto
l
erance. I
f
Ro
b
ot A
f
a
ils
d
ur
i
ng coa
li
t
i
on
li
st eva
l

uat
i
on, va
l
ues
f
or coa
li
t
i
ons conta
i
n
i
ng Ro
b
ot A ar
e
l
ost an
d
t
h
ose coa
li
t
i
ons are no
l
onger cons

id
ere
d
.T
h
us a ro
b
ot
f
a
il
ure
d
oe
s
n
ot requ
i
re
i
n
f
ormat
i
on retr
i
eva
lf
rom t
h

at ro
b
ot. However, t
h
eot
h
er ro
b
ot
s
m
ust
b
e aware o
f
t
h
e
f
a
il
ure so t
h
at t
h
ey can
d
e
l
ete a

ll
coa
li
t
i
ons conta
i
n
i
ng t
he
f
a
il
e
d
ro
b
ot
.
4
.2 Task Format
Current mu
l
t
i
-agent coa
li
t
i

on
f
ormat
i
on a
l
gor
i
t
h
ms assume t
h
at t
h
e agent
s
h
ave a capa
bili
ty vector,
<
b
i
1
, ,
b
i
r
>
.Mu

l
t
ipl
e-ro
b
ot ca
p
a
bili
t
i
es
i
nc
l
u
de
sensors (camera,
l
aser, sonar, or
b
umper) an
d
actuators (w
h
ee
l
sorgr
i
pper)

.
S
h
e
h
ory an
d
Krauss’s a
l
gor
i
t
h
m assumes t
h
at t
h
e
i
n
di
v
id
ua
l
agents’ resources
are co
ll
ect
i

ve
l
yava
il
a
bl
e upon coa
li
t
i
on
f
ormat
i
on. T
h
e
f
orme
d
coa
li
t
i
on
f
ree
ly
r
e

di
str
ib
utes resources amongst t
h
e mem
b
ers. However, t
hi
s
i
s not poss
ibl
e
in
amu
l
t
i
p
l
e-ro
b
ot
d
oma
i
n. Ro
b
ots cannot autonomous

l
yexc
h
ange capa
bili
t
i
es
.
Correct resource
di
str
ib
ut
i
on
i
sa
l
so an
i
ssue. T
h
e
b
ox-pus
hi
ng tas
k
can

b
e
use
d
to
ill
ustrate t
hi
spo
i
nt (Ger
k
ey an
d
Matar
i
c, 2002). T
h
ree ro
b
ots cooperat
e
to per
f
orm t
h
e tas
k
, two pus
h

ers (one
b
umper, one camera) an
d
one watc
h
e
r
(
one
l
aser, one camera). T
h
e tota
l
resource requ
i
rements are: two
b
umpers
,
t
h
ree cameras, an
d
one
l
aser. However t
hi
s

i
n
f
ormat
i
on
i
s
i
ncomp
l
ete, as
it
d
oes not represent t
h
e constra
i
nts re
l
ate
d
to sensor
l
ocat
i
ons. Correct tas
k
ex
-

e
cut
i
on requ
i
res t
h
e
l
aser an
d
camera res
id
eonas
i
n
gl
ero
b
ot. S
i
m
il
ar
ly i
t
is
n
ecessar
y

t
h
at t
h
e
b
umper an
dl
aser res
id
eon
diff
erent ro
b
ots. T
hi
s
i
mp
li
e
s
t
h
at s
i
mp
ly
possess
i

n
g
t
h
ea
d
equate resources
d
oes not necessar
ily
create
a
m
ultiple-robot coalition that can perform a task, other locational constraint
s
have to be represented and met.
A
matrix-based constraint representation is proposed for the multiple-robot
domain in order to resolve the problem. The task is represented via a capabilit
y
m
atrix called a Task Allocation Matrix (TAM). Each matrix entr
y
corresponds
to a capabilit
y
pair (for example [sonar, laser]). A 1 in an entr
y
indicate
s

that the capabilit
y
pair must reside on the same robot while a 0 indicates tha
t
the pair must reside on separate robots. Finall
y
an X indicates a do not car
e
c
ondition and the pair ma
y
or ma
y
not reside on the same robot. Ever
y
coalitio
n
2
0
V
i
g
and Adams
T
able
1
.
B
ox-pus
hi

ng tas
k
TAM.
B
umper
1
B
umper
2
C
amera
1
C
amera
2
C
amera
3
Lase
r
1
B
umper
1
X
0
1
0
0
0

B
umper
2
0
X
0
1
0
0
C
amera
1
1
0
X
0
0
0
C
amera
2
0
1
0
X
0
0
C
amera
3

0
0
0
0
X
1
Lase
r
1
0
0
0
0
1
X
must
b
e cons
i
stent
wi
t
h
t
h
eTAM
if i
t
i
sto

b
ee
v
a
l
uate
d
as a can
did
ate coa
li
t
i
on
.
T
h
e
b
ox-pus
hi
ng TAM
i
s prov
id
e
di
nTa
bl
e1.T

h
e entry (Laser
1
,
Camera
3
)i
s
m
ar
k
e
d
1,
i
n
di
cat
i
ng t
h
at a
l
aser an
d
a camera must res
id
eont
h
e same ro

b
ot
.
S
i
m
il
ar
l
yt
h
e (Bumper
1
,
Laser
1
)
entry
i
s mar
k
e
d
0
i
n
di
cat
i
ng t

h
e two sensor
s
must res
id
eon
diff
erent ro
b
ots.
T
h
e TAM can
b
e represente
d
as a Constra
i
nt Sat
i
s
f
act
i
on Pro
bl
em (CSP)
.
T
h

e CSP var
i
a
bl
es are t
h
e requ
i
re
d
sensors an
d
actuators
f
or t
h
e tas
k
.T
h
e
d
o-
ma
i
nva
l
ues
f
or eac

h
var
i
a
bl
e are t
h
eava
il
a
bl
ero
b
ots possess
i
ng t
h
e requ
i
re
d
sensor an
d
actuator capa
bili
t
i
es. Two types o
f
constra

i
nts ex
i
st; t
h
e sensors an
d
actuators must res
id
eont
h
e same mac
hi
ne or
diff
erent mac
hi
nes. A constra
i
n
t
g
rap
h
can
b
e
d
rawn w
i

t
hl
ocat
i
ona
l
constra
i
nts represente
d
as arcs
l
a
b
e
l
e
d
s
(
same ro
b
ot
)
or
d
(diff
erent ro
b
ot

)
. Anot
h
er constra
i
nt
i
st
h
e resource con-
stra
i
nt represent
i
ng t
h
at a ro
b
ot on
l
y
h
ave as many
i
nstances o
f
a sensor an
d
actuator as
i

n
di
cate
db
yt
h
e assoc
i
ate
d
capa
bili
ty vector. A ro
b
ot w
i
t
h
on
e
c
amera can on
ly b
e ass
ig
ne
d
one camera no
d
e

i
nt
h
e constra
i
nt
g
rap
h
.T
h
us a
ll
sensors an
d
actuators o
f
t
h
e same t
y
pe
h
ave a resource constra
i
nt arc
l
a
b
e

ll
e
d
r
b
etween t
h
em
.
F
ig
ure 1 prov
id
es t
h
e
b
ox-pus
hi
n
g
tas
k
constra
i
nt
g
rap
h
.T

hi
s tas
k
’s re-
source constraints between Bumper
1
a
n
d
Bum
p
e
r
2
a
re
i
mp
li
e
db
yt
h
e
i
r
l
oca
-
t

i
ona
l
constra
i
nts. S
i
nce Bum
p
e
r
1
a
n
d
Bum
p
e
r
2
must
b
e ass
i
gne
d
to
diff
erent
r

o
b
ots, t
h
ere cannot
b
easo
l
ut
i
on w
h
ere a ro
b
ot w
i
t
h
one
b
umper
i
s ass
i
gne
d
to
b
ot
h

Bumpe
r
1
a
n
d
Bum
p
e
r
2
.
S
i
m
il
ar
l
yt
h
e resource constra
i
nts
b
etwee
n
C
amer
a
1

,
Camera
2
a
n
dC
amer
a
3
a
re
i
mp
li
e
db
yt
h
e
l
ocat
i
ona
l
constra
i
nts
b
e
-

tween t
h
em an
d
t
h
ere
i
snonee
d
to test t
h
em separate
l
y. Hence t
h
ea
b
sence o
f
ed
ges
l
a
b
e
l
e
d
r

.
T
h
e
d
oma
i
nva
l
ues
f
or eac
h
var
i
a
bl
e
i
nt
h
e CSP
f
ormu
l
at
i
on
i
nF

i
gure
1
are t
h
ero
b
ots t
h
at possess t
h
e capa
bili
ty represente
db
yt
h
evar
i
a
bl
e. A coa
li-
t
i
on can
b
ever
ifi
e

d
to sat
i
s
f
yt
h
e constra
i
nts
b
y app
l
y
i
ng arc-cons
i
stency. I
fa
sensor
i
s
l
e
f
tw
i
t
h
an empty

d
oma
i
nva
l
ue set t
h
en t
h
e current ass
i
gnment
h
a
s
f
a
il
e
d
an
d
t
h
e current coa
li
t
i
on
i

s
d
eeme
di
n
f
eas
ibl
e. A success
f
u
l
ass
i
gnmen
t
i
n
di
cates t
h
esu
b
-tas
k
to w
hi
c
h
eac

h
ro
b
ot was ass
i
gne
d.
I
ssues in Multi-Robot
C
oalition Formatio
n
21
F
igure
1.
B
ox-pus
hi
ng tas
k
constra
i
nt grap
h
U
s
i
ng t
h

e CSP
f
ormu
l
at
i
on eac
h
can
did
ate coa
li
t
i
on
i
sc
h
ec
k
e
d
to ver
ify
if i
ts coa
li
t
i
on

i
s
f
eas
ibl
e. A
f
ter constra
i
nt c
h
ec
ki
ng
f
ewer coa
li
t
i
ons rema
in
f
or
f
urt
h
er eva
l
uat
i

on. W
hil
ea
ddi
t
i
ona
l
over
h
ea
di
s
i
ncurre
dd
ur
i
ng constra
i
n
t
ch
ec
ki
ng, t
hi
s over
h
ea

di
s somew
h
at compensate
df
or
b
yt
h
ere
d
uce
d
num
b
e
r
o
f coalitions. This is verified by the experimental results in Section
5.
4
.3 Coalition Imbalance
Coa
li
t
i
on
i
m
b

a
l
ance or
l
ops
id
e
d
ness
i
s
d
e
fi
ne
d
as t
h
e
d
egree o
f
unevennes
s
of
resource contr
ib
ut
i
ons ma

d
e
b
y
i
n
di
v
id
ua
l
mem
b
ers to t
h
e coa
li
t
i
on, a c
h
ar
-
acter
i
st
i
c not cons
id
ere

di
not
h
er coa
li
t
i
on
f
ormat
i
on a
l
gor
i
t
h
ms. A coa
li
t
i
o
n
w
h
ere one or more agents
h
ave a pre
d
om

i
nant s
h
are o
f
t
h
e capa
bili
t
i
es ma
y
h
ave t
h
e same ut
ili
ty (coa
li
t
i
on we
i
g
h
t) as a coa
li
t
i

on w
i
t
h
even
l
y
di
str
ib
ute
d
c
apa
bili
t
i
es, s
i
nce ro
b
ots are una
bl
etore
di
str
ib
ute t
h
e

i
r resources. T
h
ere
f
ore
c
oa
li
t
i
ons w
i
t
h
one or more
d
om
i
nat
i
ng mem
b
ers (resource contr
ib
utors) ten
d
to
b
e

h
eav
il
y
d
epen
d
ent on t
h
ose mem
b
ers
f
or tas
k
execut
i
on. T
h
ese
d
om
i
nat
-
i
ng mem
b
ers t
h

en
b
ecome
i
n
di
spensa
bl
e. Suc
h
coa
li
t
i
ons s
h
ou
ld b
e avo
id
e
d
i
nor
d
er to
i
mprove
f
au

l
tto
l
erance. Over re
li
ance on
d
om
i
nat
i
ng mem
b
ers ca
n
c
ause tas
k
execut
i
on to
f
a
il
or cons
id
era
bly d
e
g

ra
d
e. I
f
aro
b
ot
i
s not a
d
om
i-
n
at
i
n
g
mem
b
er t
h
en
i
t
i
s more
lik
e
ly
t

h
at anot
h
er ro
b
ot w
i
t
h
s
i
m
il
ar capa
bili
t
i
e
s
c
an rep
l
ace
i
t
.
Re
j
ect
i

n
gl
ops
id
e
d
coa
li
t
i
ons
i
n
f
avor o
fb
a
l
ance
d
ones
i
s not stra
igh
t
f
or
-
ward. When comparin
g

coalitions of different sizes, there can arise a subtl
e
trade-off between lopsidedness and the coalition size. The ar
g
ument ma
y
b
e
m
ade both for fault tolerance and for smaller coalition size. It ma
y
be desir
-
able to have coalitions with as few robots as possible. Conversel
y
, there ma
y
be a lar
g
e number of robots thus placin
g
the priorit
y
on fault tolerance and bal
-
anced coalitions. The Balance Coefficient metric is introduced to quantif
y
th
e
c

oalition imbalance level. In
g
eneral, if a coalition has a resource distributio
n
(
r
1
,
r
2
r
r
, ,
r
n
r
)
,t
h
en t
h
e
b
a
l
ance coe
ffi
c
i
ent

f
or t
h
at coa
li
t
i
on w
i
t
h
res
p
ect to
a
p
art
i
cu
l
ar tas
k
can
b
eca
l
cu
l
ate
d

as
f
o
ll
ow
s
BC
=
r
1
×
r
2
rr
×

r
n
r
[
tas
kv
a
l
ue
n
]
n
(
3)

22
V
i
g
and Adams
A
per
f
ect
l
y
b
a
l
ance
d
coa
li
t
i
on
h
as a coe
ffi
c
i
ent o
f
1. T
h

e quest
i
on
i
s
h
ow t
o
i
ncorporate t
h
e
b
a
l
ance coe
ffi
c
i
ent
i
nto t
h
ea
l
gor
i
t
h
m

i
nor
d
er to se
l
ect
b
ette
r
c
oa
li
t
i
ons. As prev
i
ous
l
y
di
scusse
d
two cases ar
i
se:
1
Su
ffi
cient num
b

er o
f
ro
b
ots an
dh
ig
hf
au
l
tto
l
erance
:
In
i
t
i
a
ll
yt
h
ea
l
-
g
or
i
t
h

m procee
d
sas
i
n Sect
i
on 3,
d
eterm
i
n
i
ng t
h
e
b
est-va
l
ue
d
coa
li
t
i
o
n
w
i
t
h

out cons
id
er
i
ng
l
ops
id
e
d
ness. As a mo
difi
cat
i
on, a
li
st o
f
a
ll
coa
li-
tions is maintained whose values are within a certain range (
5
%) of th
e
b
est coa
li
t

i
on va
l
ue. T
h
emo
difi
e
d
a
l
gor
i
t
h
mt
h
en ca
l
cu
l
ates t
h
e
b
a
l-
a
nce coe
ffi

c
i
ent
f
or a
ll
t
h
ese coa
li
t
i
ons an
d
c
h
ooses t
h
e most
b
a
l
ance
d
coa
li
t
i
on. T
hi

s ensures t
h
at t
h
ea
l
gor
i
t
h
ma
l
ways
f
avors t
h
e
b
a
l
ance
d
coa
li
t
i
on
.
2
E

conomize on t
h
e num
b
er of ro
b
ots
:
M
a
i
nta
i
na
li
st o
f
a
ll
coa
li
t
i
ons w
i
t
h
v
a
l

ues w
i
t
hi
na
b
oun
d
o
f
t
h
e
b
est coa
li
t
i
on va
l
ue. Remove a
ll
coa
li
t
i
on
s
l
ar

g
er t
h
an t
h
e
b
est coa
li
t
i
on
f
rom t
h
e
li
st. Se
l
ect t
h
e coa
li
t
i
on w
i
t
h
t

he
high
est
b
a
l
ance coe
ffi
c
i
ent
.
5. Ex
p
eriment
s
T
h
ree exper
i
ments test
i
ng t
h
eva
lidi
ty o
f
t
h

ea
l
gor
i
t
h
mmo
difi
cat
i
ons wer
e
c
on
d
ucte
d
, eac
hhi
g
hli
g
h
t
i
ng a suggeste
d
mo
difi
cat

i
on. T
h
e
fi
rst exper
i
men
t
measure
d
t
h
evar
i
at
i
on o
f
t
i
me requ
i
re
d
to eva
l
uate coa
li
t

i
ons w
i
t
h
an
d
w
i
t
h-
o
ut commun
i
cat
i
on. T
h
e num
b
er o
f
agents an
d
max
i
mum coa
li
t
i

on s
i
ze wer
e
b
ot
hfi
xe
d
at
fiv
e.
C
ommun
i
cat
i
on occurre
dvi
aT
C
P
/
IP soc
k
ets o
v
er a
wi
re

l
es
s
LAN (see F
i
gure 2). T
h
et
i
me
f
or coa
li
t
i
on eva
l
uat
i
on w
i
t
h
out commun
i
cat
i
o
n
i

ss
i
gn
ifi
cant
l
y
l
ess t
h
an t
h
et
i
me requ
i
re
df
or eva
l
uat
i
on w
i
t
h
commun
i
cat
i

on
.
T
h
et
i
me w
i
t
h
out commun
i
cat
i
on
i
ncreases at a
f
aster rate as t
h
e num
b
er o
f
tas
k
s
i
ncreases. T
hi

s resu
l
t occurs
b
ecause t
h
e agent must eva
l
uate a
l
arge
r
num
b
er o
f
coa
li
t
i
ons w
h
en
i
t
f
orgoes commun
i
cat
i

on. Presuma
bl
y, t
h
etw
o
c
on
di
t
i
ons w
ill
eventua
ll
y meet an
d
t
h
erea
f
ter t
h
et
i
me requ
i
re
d
w

i
t
h
commu
-
n
i
cat
i
on w
ill b
e
l
ess t
h
an t
h
at requ
i
re
d
w
i
t
h
out commun
i
cat
i
on. For an

y
pract
i-
c
a
l
A
g
ent/Tas
k
rat
i
ot
h
et
i
me save
dby
m
i
n
i
m
i
z
i
n
g
commun
i

cat
i
on outwe
ighs
t
h
e extra computat
i
on
i
ncurre
d.
T
h
e secon
d
set o
f
exper
i
ments measure
d
t
h
ee
ff
ect o
f
t
h

e CSP
f
ormu
l
at
i
o
n
o
n the al
g
orithm’s execution time. This experiment demonstrates the al
g
o
-
r
ithm’s scalabilit
y
.Fi
g
ure 3 measures the variation of execution time a
g
ains
t
the number of a
g
ents both with and without constraint checkin
g
in the con
-

straint satisfaction
g
raph. Fi
g
ure 4 shows the variation of execution time com
-
p
ared to the number of tasks. The task complexit
y
in these experiments wa
s
similar to the box-pushin
g
task. It can be seen from Fi
g
ures 3 and 4 that th
e
C
SP formulation does not add a
g
reat deal to the al
g
orithm’s execution or run
-
nin
g
time. This implies that this formulation can be used to test the validit
y
o
f

a
multiple-robot coalition without incurrin
g
much overhead
.
I
ssues in Multi-Robot
C
oalition Formatio
n
2
3
F
igure
2.
E
xecut
i
on t
i
me
wi
t
h
an
dwi
t
h
out commun
i

cat
i
o
n
F
igure
3.
E
xecut
i
on t
i
me vs. Num
b
er o
f
Agent
s
T
h
et
hi
r
d
set o
f
exper
i
ments
d

emonstrates t
h
ee
ff
ect o
f
ut
ili
z
i
ng t
h
eBa
l
anc
e
Coe
ffi
c
i
ent to
f
avor t
h
e creat
i
on o
fb
a
l

ance
d
coa
li
t
i
ons. T
h
eP
l
ayer/Stage s
i
m
-
u
l
at
i
on env
i
ronment(Ger
k
ey et a
l
., 2003) was emp
l
oye
df
or t
hi

s exper
i
ment
.
T
h
es
i
mp
l
e tas
k
s requ
i
re
db
rea
ki
ng up a
f
ormat
i
on o
f
res
i
ze
dh
oc
k

ey puc
ks
b
y
b
ump
i
ng
i
nto t
h
e
f
ormat
i
on. T
h
e
d
egree o
f
tas
k diffi
cu
l
ty was a
dj
uste
dby
v

ary
i
ng t
h
e
h
oc
k
ey puc
k
s’ coe
ffi
c
i
ent o
ff
r
i
ct
i
on w
i
t
h
t
h
e
fl
oor. A
dj

ust
i
ng t
he
f
orces t
h
ey cou
ld
exert var
i
e
d
t
h
ero
b
ots’ capa
bili
t
i
es. T
h
ere are no
l
ocat
i
ona
l
c

onstra
i
nts on t
h
e tas
k
capa
bili
ty requ
i
rements. Ten s
i
mu
l
ate
d
ro
b
ots wer
e
used for the experiment, as shown in Figure
5
. The robots were numbered 1 t
o
10
f
rom t
h
e top o
f

t
h
e
fi
gure a
l
ong
l
e
f
ts
id
e. Eac
h
ro
b
ot
h
a
d
a spec
ifi
c capa
-
bili
ty type: sma
ll
ro
b
ots

h
a
d
10 un
i
ts o
ff
orce (ro
b
ots 1, 2, 8, 9, 10), me
di
u
m
sized robots had 1
5
units of force (robots
5
, 6, 7) and lar
g
e robots had 20 unit
s
of f
orce (ro
b
ots 3, 4). S
i
mu
l
at
i

on snaps
h
ots are prov
id
e
df
or a tas
k
requ
i
r
i
n
g
24
V
i
g
and Adams
F
igure
4.
E
xecut
i
on t
i
me
v
s. Num

b
er o
f
Tas
ks
F
igure
5.
T
wo
l
arge ro
b
ots an
d
one sma
ll
ro
b
ot
f
orm a coa
li
t
i
o
n
5
0 units of force. Figure
5

shows the formed coalition without balancing. Th
e
c
oa
li
t
i
on
i
s compr
i
se
d
o
f
two
l
arge ro
b
ots an
d
one sma
ll
ro
b
ot
.
Figure 6 shows the same task incorporating the balance coefficient into th
e
c

oa
li
t
i
on
f
ormat
i
on. T
hi
sc
h
o
i
ce p
l
aces a
l
ow pr
i
or
i
ty on
f
au
l
tto
l
erance an
d

ahi
g
h
pr
i
or
i
ty on econom
i
z
i
ng t
h
e num
b
er o
f
ro
b
ots (Case 1
f
rom Sect
i
o
n
4.3). T
h
e
f
orme

d
coa
li
t
i
on
i
s compr
i
se
d
o
f
two me
di
um s
i
ze
d
ro
b
ots an
d
on
e
l
arge ro
b
ot. T
h

e resu
l
t
i
ng coa
li
t
i
on
i
s more
b
a
l
ance
d
an
dh
as a
hi
g
h
er
b
a
l
anc
e
c
oefficient (0.972 as opposed to 0.8

6
4 for the coalition in Figure
6
). Figur
e
7d
ep
i
cts t
h
e exper
i
ment con
d
ucte
d
w
i
t
h
no restr
i
ct
i
ons on t
h
e coa
li
t
i

on s
i
z
e
(
Case 2
f
rom Sect
i
on 4.3). T
h
e resu
l
t
i
ng coa
li
t
i
on cons
i
sts o
ffi
ve sma
ll
ro
b
ots
.
T

h
us a per
f
ect
l
y
b
a
l
ance
d
coa
li
t
i
on (
b
a
l
ance coe
ffi
c
i
ent=1)
i
so
b
ta
i
ne

d
w
h
e
n
t
h
e coa
li
t
i
on s
i
ze
i
s unconstra
i
ne
d
.T
h
ea
d
vanta
g
e
i
st
h
at a

l
ar
g
er num
b
er o
f
sma
ll
(
l
ess capa
bl
e) ro
b
ots s
h
ou
ld h
ave
high
er
f
au
l
tto
l
erance. I
f
one ro

b
o
t
f
a
il
s,
i
ts
h
ou
ld b
e eas
i
er to
fi
n
d
a rep
l
acement as oppose
d
to rep
l
ac
i
n
g
a
l

ar
g
e
r
(
more capa
bl
e) ro
b
ot
.
I
ssues in Multi-Robot
C
oalition Formatio
n
2
5
F
igure
6.
O
ne
l
arge an
d
two me
di
u
m

s
iz
ed
r
obots
f
o
rm
a coa
li
t
i
on
F
igure
7.
Fiv
e sma
ll
ro
b
ots
f
orm a coa
li-
t
i
o
n
6

. Conclusion and Future Work
F
i
n
di
ng t
h
e opt
i
ma
l
mu
l
t
i
p
l
e-ro
b
ot coa
li
t
i
on
f
or a tas
ki
san
i
ntracta

bl
e pro
b-
l
em. T
hi
swor
k
s
h
ows t
h
at
,
w
i
t
h
certa
i
nmo
difi
cat
i
ons
,
coa
li
t
i

on
f
ormat
i
o
n
a
l
gor
i
t
h
ms prov
id
e
di
nt
h
emu
l
t
i
-agent
d
oma
i
n can
b
e app
li

e
d
to t
h
emu
l
t
i
p
l
e
-
r
o
b
ot
d
oma
i
n. T
hi
s paper
id
ent
ifi
es mo
difi
cat
i
ons an

di
ncorporates t
h
em
i
nt
o
an ex
i
st
i
ng mu
l
t
i
-agent coa
li
t
i
on
f
ormat
i
on a
l
gor
i
t
h
m. T

h
e
i
mpact o
f
extens
i
v
e
c
ommun
i
cat
i
on
b
etween ro
b
ots was s
h
own to
b
e severe enoug
h
to en
d
orse re
-
li
nqu

i
s
hi
ng commun
i
cat
i
on
i
n
f
avor o
f
a
ddi
t
i
ona
l
computat
i
on w
h
en poss
ibl
e
.
T
h
e tas

kf
ormat
i
nmu
l
t
i
-ro
b
ot coa
li
t
i
ons was mo
difi
e
d
to a
d
equate
l
y represen
t
a
ddi
t
i
ona
l
constra

i
nts
i
mpose
db
yt
h
emu
l
t
i
p
l
e-ro
b
ot
d
oma
i
n. T
h
e concept o
f
c
oa
li
t
i
on
i

m
b
a
l
ance was
i
ntro
d
uce
d
an
di
ts
i
mpact on t
h
e coa
li
t
i
on’s
f
au
l
tto
l-
e
rance was
d
emonstrate

d.
Furt
h
er a
lg
or
i
t
h
mmo
difi
cat
i
ons w
ill
perm
i
t more comp
l
ex tas
k
execut
i
o
n
by
ut
ili
z
i

n
g
a MURDOCH (Ger
k
e
y
an
d
Matar
i
c, 2002) st
yl
e tas
k
a
ll
ocat
i
o
n
sc
h
eme w
i
t
hi
n coa
li
t
i

ons. A
f
uture
g
oa
li
sto
i
nvest
ig
ate met
h
o
d
so
ff
orm
i
n
g
c
oa
li
t
i
ons w
i
t
hi
na

dy
nam
i
c rea
l
-t
i
me env
i
ronment. T
h
e
l
on
g
-term
g
oa
li
st
o
develop a hi
g
hl
y
adaptive, fault tolerant s
y
stem that would be able to flexibl
y
handle different tasks and task environments

.
R
eferences
An
d
erson, J. E., Tanner, B., an
d
Ba
l
tes, J. (2004). Dynam
i
c coa
li
t
i
on
f
ormat
i
on
i
nro
b
ot
i
c soccer
.
T
echnical Report WS-04-06, AAAI workshop
.

Brooks, C. H. and Durfee, E. H. (2003). Congregation formation in multiagent systems
.
Au
-
tonomous Agents and Multi-Agent System
s
,
79:145–170
.
F
ass, L. (2004). An automatic-theoretic view of agent coalitions. Technical Report WS-04-06
,
A
AAI workshop
.
Gerkey, B. and Mataric, M. (2002). Sold! auction methods for multirobot coordination
.
I
EE
E
Transactions on Robotics and Automatio
n
,
18:758–68
.
Gerkey, B. and Mataric, M. (2004). A framework for studying multi-robot task allocation
.
I
n-
ternational Journal of Robotics Researc

h
.t
o appear
.
2
6
V
i
g
and Adams
G
erkey, B., Vaughan, R. T., and Howard, A. (2003). The player/stage project: Tools for multi
-
r
obot and distributed sensor systems. In 11th Intr. Conf. on Advanced Robotic
s
, pages 317
–
3
2
3.
L
i, X. and Soh, L K. (2004). Investigating reinforcement learning in multiagent coalition for
-
m
ation. Technical Report WS-04-06, AAAI workshop
.
P
arker, L. (1998). Alliance: An architecture for fault tolerant multi-robot cooperation
.

I
EE
E
Transactions on Robotics and Automatio
n
,
14:220–240
.
Sandholm, T., Larson, K., Andersson, M., Shehory, O., and Tomhe, F. (1999). Coalition struc
-
t
ure generation with worst case guarantees
.
Artificial Intelligence
,
111:209–238
.
Shehory, O. and Krauss, S. (1996). A kernel oriented model for coalition-formation in genera
l
e
nvironments: Implementation and results. I
n
AAAI, pages 134–140
.
Shehory, O. and Krauss, S. (1998). Methods for task allocation via agent coalition formation
.
A
rti
fi
cial Intelligence Journa

l
,
101:165–200
.
S
hehor
y
, O. and Krauss, S. (1999). Feasible formation of coalitions amon
g
autonomous a
g
ent
s
i
n non-su
p
er-additive environments
.
Computational Intelli
g
enc
e
,
15:218–251
.
S
orbella, R., Chella, A., and Arkin, R. (2004). Meta
p
hor of
p

olitics: A mechanism of coalitio
n
f
ormation. Technical Re
p
ort WS-04-0
6
, AAAI worksho
p.
Ul
am, P. an
d
Ar
ki
n, R. (2004). W
h
en
g
oo
d
comms
g
o
b
a
d
: Communcat
i
ons recover
yf

or mu
l
t
i-
r
o
b
ot teams. In
2
004 IEEE Intr. Con
f
.onRo
b
otics an
d
Automatio
n
,pa
g
es
3
7
2
7–
3
7
34.
W
er
g

er, B. an
d
Matar
i
c, M. (2000). Broa
d
cast o
fl
oca
l
e
ligibili
t
y
:Be
h
av
i
or-
b
ase
d
contro
lf
o
r
s
tron
gly
-cooperat

i
ve ro
b
ot teams. I
n
A
utonomous
Ag
ent
s
,pa
g
es 347–3
5
6
.
S
ENSOR NETWORK-MEDIATED
M
ULTI-ROBOT TASK ALLOCATION
Max
i
m A. Bata
li
nan
dG
aura
vS
.
S

u
kh
atm
e
R
o
b
otic Em
b
e
dd
e
d
Systems La
b
orator
y
Center for Robotics and Embedded System
s
Computer Science Departmen
t
University of Southern Californi
a
L
os Angeles, CA 90089, US
A
maxim
@
robotics.usc.edu,
g

aurav
@
usc.ed
u
Abs
tr
act
W
ea
dd
ress t
he
O
n
l
ine Mu
l
ti-Ro
b
ot Tas
k
A
ll
ocation (OMRTA
)
p
ro
bl
em. Ou
r

approach relies on a computational and sensing fabric of networked sensors em
-
b
edded into the en
v
ironment. This sensor net
w
ork acts as a distributed senso
r
and computational platform which computes a solution to OMRTA and direct
s
r
obots to the vicinity of tasks. We term this Distributed In-Network Task Allo
-
c
ation (DINTA). We describe DINTA, and show its application to multi-robo
t
t
ask allocation in simulation, laboratory, and field settings. We establish tha
t
such network-mediated task allocation scales well, and is especially amendabl
e
t
o simple, heterogeneous robots
.
K
eywords:
M
obile robots
,

sensor networks
,
task allocation
,
distribute
d
1. Introduction
W
e
f
ocus on t
h
e
i
ntent
i
ona
l
cooperat
i
on o
f
ro
b
ots towar
d
a goa
l
((Par
k

er
,
1998)). W
i
t
hi
n suc
h
a sett
i
ng, a natura
l
quest
i
on
i
st
h
e ass
i
gnment o
f
ro
b
ots t
o
su
b
-goa
l

s suc
h
t
h
at t
h
e ensem
bl
eo
f
ro
b
ots ac
hi
eves t
h
e overa
ll
o
bj
ect
i
ve. Fo
l-
l
ow
i
ng ((Ger
k
ey an

d
Matar
i
ct’, 2004)) we ca
ll
suc
h
su
b
-goa
l
s, ta
sks
,
an
d
t
h
e
ir
ass
i
gnment to ro
b
ots, t
h
e Mu
l
ti-Ro
b

ot Tas
k
A
ll
ocation (MRTA)
p
ro
bl
em. S
i
m
-
pl
y state
d
,MRTA
i
s a pro
bl
em o
f
ass
i
gn
i
ng or a
ll
ocat
i
ng tas

k
sto(
i
ntent
i
ona
lly
c
ooperat
i
ng) ro
b
ots over t
i
me suc
h
t
h
at some measure o
f
overa
ll
per
f
ormanc
e
i
s max
i
m

i
ze
d.
W
e
f
ocus on t
h
eon
li
ne vers
i
on o
f
t
h
e pro
bl
em (OMRTA), w
h
ere 1. tas
k
s
are geograp
hi
ca
ll
yan
d
tempora

ll
y sprea
d
, 2. a tas
k
sc
h
e
d
u
l
e
i
s not ava
il
a
ble
i
na
d
vance, an
d
3. ro
b
ots nee
d
to p
hy
s
i

ca
lly
v
i
s
i
t tas
kl
ocat
i
ons to accomp
li
s
h
tas
k
comp
l
et
i
on
(
e
.
g
.,
t
o pus
h
an o

bj
ect). Our approac
h
to OMRTA re
li
es o
n
a computat
i
ona
l
an
d
sens
i
n
gf
a
b
r
i
co
f
networ
k
e
d
sensors em
b
e

dd
e
di
nto t
he
27
L.E. Parker et al.
(
eds.)
,
Multi-Robot Systems. From Swarms to Intelligent Automata. Volume III
,
2
7–38.

c
2
00
5
Springer. Printed in the Netherlands
.
2
8
B
atalin and
S
ukhatm
e
e
nv

i
ronment. T
hi
s sensor networ
k
acts as a
di
str
ib
ute
d
sensor an
d
com
p
uta
-
t
i
ona
lpl
at
f
orm w
hi
c
h
com
p
utes a so

l
ut
i
on to OMRTA an
ddi
rects ro
b
ots to t
he
vi
c
i
n
i
ty o
f
tas
k
s. To ma
k
ea
l
oose ana
l
ogy, ro
b
ots are route
df
rom source t
o

d
est
i
nat
i
on
l
ocat
i
ons
i
n muc
h
t
h
e same way pac
k
ets are route
di
n convent
i
ona
l
networ
k
s. We term t
hi
s, D
i
str

ib
ute
d
In-networ
k
Tas
k
A
ll
ocat
i
on
(
DINTA
)
.
T
h
ere are
fi
ve a
d
vantages to
d
o
i
ng t
h
e tas
k

a
ll
ocat
i
on
i
nt
hi
s manner
:
1
S
im
p
licit
y
:
Si
nce t
h
e tas
k
-a
ll
ocat
i
on
i
s
d

one
i
nt
h
e networ
k,
ro
b
ot
s
may
b
e very s
i
mp
l
e,
d
es
i
gne
d
spec
ifi
ca
ll
y
f
or opt
i

ma
l
tas
k
execut
i
on
(
e
.
g
.,
s
pec
i
a
li
ze
d
en
d
e
ff
ectors) rat
h
er t
h
an computat
i
ona

l
sop
hi
st
i
cat
i
on
.
Furt
h
er, ro
b
ots
d
o not nee
d
convent
i
ona
ll
oca
li
zat
i
on or mapp
i
ng sup
-
p

or
t
.
2
Communication:
R
o
b
ots are not requ
i
re
d
to
b
ew
i
t
hi
n commun
i
cat
i
o
n
r
ange o
f
eac
h
ot

h
er. T
h
e networ
ki
s use
df
or propagat
i
ng messages
b
e
-
tween t
h
ero
b
ots
.
3
S
calin
g:
T
h
ere
i
s no computat
i
on or commun

i
cat
i
on over
h
ea
d
assoc
i-
ate
d
w
i
t
hi
ncreas
i
n
g
t
h
e num
b
er o
f
ro
b
ots
.
4

I
dentit
y
: Ro
b
ots are not requ
i
re
d
to reco
g
n
i
ze eac
h
ot
h
er
.
5
Heterogeneity
:
R
o
b
ots ma
yb
eo
f diff
erent t

y
pes, an
d
nee
d
on
ly
a com
-
mon
i
nter
f
ace to t
h
e sensor networ
k.
In t
hi
s paper we ma
k
et
h
e
f
o
ll
ow
i
n

g
contr
ib
ut
i
ons. We
b
r
i
e
fly
rev
i
ew t
he
d
eta
il
so
f
DI
N
T
A
1
,
an
dd
emonstrate
i

ts app
li
cat
i
on to a system
f
or spat
i
otem
-
p
ora
l
mon
i
tor
i
ng o
f
env
i
ronmenta
l
var
i
a
bl
es
i
n nature. We note t

h
at w
hile
we stu
d
yt
h
e tas
k
a
ll
ocat
i
on pro
bl
em
i
nt
h
e context o
f
mo
bil
ero
b
ots, senso
r
n
etwor
k

-me
di
ate
d
tas
k
a
ll
ocat
i
on can a
l
so
b
e use
di
not
h
er sett
i
ngs
(
e
.
g
.
,
i
na
n

e
mergency peop
l
e try
i
ng to
l
eave a
b
u
ildi
ng wou
ld b
egu
id
e
d
(tas
k
e
d
)tot
he
cl
osest ex
i
ts
b
yt
h

e networ
k
)
.
2. Related
W
ork
T
h
e
p
ro
bl
em o
f
mu
l
t
i
-ro
b
ot tas
k
a
ll
ocat
i
on (MRTA)
h
as rece

i
ve
d
cons
id
er
-
abl
e attent
i
on. For an overv
i
ew an
d
compar
i
son o
f
t
h
e
k
ey MRTA arc
hi
tecture
s
see ((Ger
k
ey an
d

Matar
i
ct’, 2004)), w
hi
c
h
su
bdi
v
id
es MRTA arc
hi
tectures
i
nt
o
b
e
h
av
i
or-
b
ase
d
an
d
auct
i
on-

b
ase
d
. For examp
l
e, ALLIANCE ((Par
k
er, 1998)
)
i
sa
b
e
h
av
i
or-
b
ase
d
arc
hi
tecture t
h
at cons
id
ers a
ll
tas
k

s
f
or (re)ass
i
gnment at
e
very
i
terat
i
on
b
ase
d
on ro
b
ots’ ut
ili
ty. Ut
ili
ty
i
s compute
db
y measures o
f
a
cqu
i
escence an

di
mpat
i
ence. Broa
d
cast o
f
Loca
l
E
li
g
ibili
ty ((Werger an
d
Matar
i
t’c, 2000))
i
sa
l
so a
b
e
h
av
i
or-
b
ase

d
approac
h
,w
i
t
hfi
xe
d
-pr
i
or
i
ty tas
k
s.
For every tas
k
t
h
ere ex
i
sts a
b
e
h
av
i
or capa
bl

eo
f
execut
i
ng t
h
e tas
k
an
d
est
i
-
mat
i
ng t
h
eut
ili
ty o
f
ro
b
ot execut
i
ng t
h
e tas
k
. Auct

i
on-
b
ase
d
approac
h
es
i
n
-
cl
u
d
et
h
e M+ system ((Bote
lh
oan
d
A
l
am
i
, 2000)) an
d
Mur
d
oc
h

((Ger
k
ey an
d
S
ensor Net
w
ork-Mediated Multi-Robot Task Allocatio
n
2
9
Matar
i
ct’, 2004)). Bot
h
systems re
l
yont
h
e Contract Net Protoco
l
(CNP) t
h
a
t
m
a
k
es tas
k

sava
il
a
bl
e
f
or auct
i
on
,
an
d
can
did
ate ro
b
ots ma
k
e‘
bid
s’ t
h
at ar
e
t
h
e
i
r tas
k

-spec
ifi
cut
ili
ty est
i
mates. T
h
e
hi
g
h
est
bidd
er (
i
.e., t
h
e
b
est-
fi
tro
b
ot
)
w
i
ns a contract
f

or t
h
e tas
k
an
d
procee
d
s to execute
i
t. A
ll
prev
i
ous MRT
A
approac
h
es
i
nt
h
ero
b
ot
i
cs commun
i
ty
h

ave
f
ocuse
d
on per
f
orm
i
ng t
h
e tas
k
a
ll
ocat
i
on computat
i
on on t
h
ero
b
ots, or at some centra
li
ze
dl
ocat
i
on externa
l

to t
h
ero
b
ots. A
ll
t
h
e sens
i
ng assoc
i
ate
d
w
i
t
h
tas
k
s, an
d
ro
b
ot
l
oca
li
zat
i

on,
is
typ
i
ca
ll
y per
f
orme
d
on t
h
ero
b
ots t
h
emse
l
ves. Our approac
h
re
li
es on a sen
-
sor networ
k
,w
hi
c
h

per
f
orms event
d
etect
i
on an
d
tas
k
-a
ll
ocat
i
on computat
i
on
,
a
ll
ow
i
ng ro
b
ots to
b
es
i
mp
l

ean
dh
eterogeneous
.
3
. Distributed In-
N
etwork Task Allocation: DI
N
TA
A
s an exper
i
menta
l
su
b
strate, we use a part
i
cu
l
ar sty
li
ze
d
mon
i
tor
i
ng sce

-
n
ar
i
o
i
nw
hi
c
h
ro
b
ots are tas
k
e
d
w
i
t
h
‘atten
di
ng’ to t
h
eenv
i
ronment suc
h
t
h

a
t
areas o
f
t
h
eenv
i
ronment
i
nw
hi
c
h
somet
hi
ng s
i
gn
ifi
cant
h
appens,
d
o not sta
y
unatten
d
e
df

or
l
ong. We mo
d
e
l
t
hi
sus
i
ng t
h
e not
i
on o
f
a
l
arms. An a
l
arm
is
spat
i
a
ll
y
f
ocuse
d

,
b
ut
h
as tempora
l
extent
(
i
.e.,
i
t rema
i
ns on unt
il i
t
i
s turne
d
off b
yaro
b
ot). A
l
arms are
d
etecte
db
y sensor no
d

es em
b
e
dd
e
di
nt
h
eenv
i
ron
-
m
ent. For examp
l
e
i
n a natura
l
sett
i
ng, an a
l
arm m
i
g
h
t
b
e generate

di
n cas
e
an a
b
rupt c
h
ange
i
n temperature
i
s
d
etecte
d
requ
i
r
i
ng
i
nspect
i
on o
f
t
h
e area
by
t

h
ero
b
ot. T
h
e tas
k
o
f
t
h
e team o
f
ro
b
ots
i
s to turn o
ff
t
h
ea
l
arms
b
y respon
d-
i
ng to eac
h

a
l
arm. T
hi
s
i
s
d
one
b
yaro
b
ot nav
i
gat
i
ng to t
h
e
l
ocat
i
on o
f
t
he
a
l
arm. Once t
h

ero
b
ot arr
i
ves
i
nt
h
ev
i
c
i
n
i
ty o
f
t
h
ea
l
arm, t
h
ea
l
arm
i
s
d
eac
-

t
i
vate
d
.T
h
us t
h
ero
b
ot response
i
s pure
ly
not
i
ona
li
nt
h
at t
h
e tas
k
t
h
ero
b
o
t

p
er
f
orms
i
stoarr
i
ve at t
h
e appropr
i
ate
l
ocat
i
on on
ly
.T
h
e
g
oa
li
stom
i
n
i
m
i
z

e
t
h
e cumu
l
at
i
ve a
l
ar
m
O
nTim
e
a
cross a
ll
a
l
arms, over t
h
e
d
urat
i
on o
f
t
h
een

-
t
i
re exper
i
menta
l
tr
i
a
l
. Eac
h
a
l
arm’
s
O
n Time
i
s compute
d
as t
h
e
diff
erence
between the time the alarm was deactivated b
y
a robot and the time the alar

m
was detected b
y
one of the nodes of the network
.
The basic idea of DINTA is that
g
iven a set of alarms (each correspondin
g
to a task) detected b
y
the network
(
e
.g.,
n
odes detect motion,
p
resence of dan
-
g
erous chemicals, etc.), ever
y
node in the network computes a su
gg
ested ‘best
’
motion direction for all robots in its vicinit
y
. The ensemble of su

gg
ested di
-
r
ections computed over all nodes is called a navi
g
ation field. In case multipl
e
tasks arrive at the same time, multiple navi
g
ation fields (one for ever
y
task) ar
e
maintained in the network and explicitl
y
assi
g
ned to robots. Navi
g
ation field
s
a
re assi
g
ned to robots usin
g
a
g
reed

y
polic
y
.
3
.1 Computing Navigation Field
W
e assume t
h
at t
h
e networ
ki
s
d
ep
l
oye
d
an
d
every no
d
e stores a
di
scret
e
p
ro
b

a
bili
ty
di
str
ib
ut
i
on o
f
t
h
e trans
i
t
i
on pro
b
a
bili
t
y
P
(
s

|
s
C
,

a
)
(
pro
b
a
bili
ty o
f
30
B
atalin and
S
ukhatm
e
A
lgorithm 1
.
Ad
apt
i
ve D
i
str
ib
ute
d
Nav
i
gat

i
on F
i
e
ld
Computat
i
on A
l
gor
i
t
h
m (runn
i
n
g
o
n every node).
s
-cu
rr
e
n
t
n
ode
S
-
set of all node

s
A
(
s
)
-
set of all actions possible from nod
e
s
C
(
s
,
a
)
-
cost of taking an actio
n
a from nod
e
s
P
(
s

|
s
,
a
)

-
pro
b
a
bili
ty o
f
arr
i
v
i
ng at no
d
e
s

gi
ve
n
t
h
at t
h
e
r
obot sta
r
ted at
n
ode

s
a
n
dco
mm
a
n
ded a
n
act
i
on
a
,
sto
r
ed o
nn
ode
s
π
(
s
)
-
optimal direction that robot should take at nod
e
s
C
ompute Direction(goa

l
n
ode
)
if
s
=
= goa
l
node
V
0
VV
=
some
bi
g num
b
e
r
e
l
se
V
0
V
V
=0
w
hil

e
V
t
VV
−
V
t
VV
−
1
>
ε
do
Q
uery neighbor nodes for their new value
s
V
t
V
V
if
r
ece
iv
e
d
ne
wv
a
l

ue
s
V
t
V
V
f
rom a
ll
ne
i
g
hb
or no
d
e
s
s

V
t
VV
+
1
(
s
)=
C
(
s

,
a
)
+
max
a
∈
A
(
s
)
∑
s

∈
S
−
s
P
(
s

|
s
,
a
)
×
V
t

VV
(
s

)
U
pdate neighbor nodes with new valu
e
V
t
V
V
+
1
(
s
)
Q
uery neighbor nodes for their final value
s
V
(
s

)
π
(
s
)=
a

rgma
x
a
∈
A
(
s
)
∑
s

∈
S
−
s
P
(
s

|
s
,
a
)
×
V
(
s

)

t
h
ero
b
ot arr
i
v
i
ng at no
de
s

gi
ven t
h
at
i
t starte
d
at no
de
s
C
a
n
dw
as to
ld
to
e

xecute act
i
o
n
a
)
.T
h
e rea
d
er
i
sre
f
erre
d
to
((
Bata
li
nan
d
Su
kh
atme, 2004a
))
f
or a
d
eta

il
e
ddi
scuss
i
on on
h
o
w
suc
hdi
str
ib
ut
i
ons can
b
eo
b
ta
i
ne
d.
Al
gor
i
t
h
m1s
h

ows t
h
e pseu
d
oco
d
eo
f
t
h
ea
d
apt
i
ve
di
str
ib
ute
d
nav
i
gat
i
o
n
fi
e
ld
computat

i
on a
l
gor
i
t
h
m, w
hi
c
h
runs on every networ
k
no
d
e. We use va
l
u
e
i
terat
i
on ((Koen
i
gan
d
S
i
mmons, 1992)) to compute t
h

e
b
est act
i
on at a g
i
ve
n
no
d
e. T
h
e genera
lid
ea
b
e
hi
n
d
va
l
ue
i
terat
i
on
i
s to compute t
h

eva
l
ues (o
r
u
t
ili
t
i
es)
f
or every no
d
ean
d
t
h
en p
i
c
k
t
h
e act
i
ons t
h
at y
i
e

ld
a pat
h
towar
ds
t
h
e goa
l
w
i
t
h
max
i
mum expecte
d
va
l
ue. Expecte
d
va
l
ues are
i
n
i
t
i
a

li
ze
d
to 0
.
Si
nce
C
(
s
,
a
)
i
st
h
e cost assoc
i
ate
d
w
i
t
h
mov
i
ng to t
h
enextno
d

e,
i
t
i
sc
h
ose
n
to
b
eane
g
at
i
ve num
b
er w
hi
c
hi
s sma
ll
er t
h
a
n
−
(m
i
n

i
m
al
re
w
ar
d
)
k
,
w
h
ere
ki
st
h
e
n
um
b
er o
f
no
d
es. T
h
e rat
i
ona
l

e
i
st
h
at t
h
ero
b
ot s
h
ou
ld
pay
f
or ta
ki
ng an act
i
o
n
(
ot
h
erw
i
se any pat
h
t
h
ero

b
ot m
i
g
h
tta
k
ewou
ld h
ave t
h
e same va
l
ue),
h
owever
,
t
h
e cost s
h
ou
ld
not
b
e too
l
arge (ot
h
erw

i
se t
h
ero
b
ot m
i
g
h
t pre
f
er to stay at t
he
same no
d
e
)
.
Next, as s
h
own
i
nA
l
gor
i
t
h
m1,ano
d

e quer
i
es
i
ts ne
i
g
hb
ors
f
or t
h
e
l
ates
t
ut
ili
ty va
l
ues
V
.
Once t
h
eva
l
ues are o
b
ta

i
ne
df
rom a
ll
ne
i
g
hb
ors, a no
d
eup
-
d
ates
i
ts own ut
ili
ty. T
hi
s process cont
i
nues unt
il
t
h
eva
l
ues
d

o not c
h
ang
e
b
eyon
d
a
n
ε
(
set to 10
−
3
i
n our ex
p
er
i
ments). A
f
ter t
h
e
l
atest va
l
ues
f
rom

S
ensor Net
w
ork-Mediated Multi-Robot Task Allocatio
n
3
1
a
ll
ne
i
g
hb
ors are co
ll
ecte
d
,ano
d
e can compute an act
i
on po
li
c
y
π
(
o
p
t

i
ma
l
di
rect
i
on) t
h
ataro
b
ot s
h
ou
ld
ta
k
e
if i
t
i
s
i
nt
h
eno
d
e’s v
i
c
i

n
i
ty
.
In com
bi
nat
i
on, t
h
e opt
i
ma
ldi
rect
i
ons compute
db
y
i
n
di
v
id
ua
l
networ
k
no
d

es
,
c
onst
i
tute a g
l
o
b
a
l
nav
i
gat
i
on
fi
e
ld
. Pract
i
ca
l
cons
id
erat
i
ons
f
or ro

b
ot nav
i
ga
-
t
i
on us
i
ng t
hi
s approac
h
are
di
scusse
di
n ((Bata
li
neta
l
., 2004
b
))
.
3
.2 Task Allocation
D
INTA ass
i

gns tas
k
s
i
n
d
ecision epoc
hs
-s
h
ort
i
nterva
l
so
f
t
i
me
d
ur
i
n
g
w
hi
c
h
on
l

yt
h
e tas
k
st
h
at
h
ave arr
i
ve
d
s
i
nce t
h
een
d
o
f
t
h
e prev
i
ous epoc
h
ar
e
c
ons

id
ere
df
or ass
i
gnment. T
h
e
f
o
ll
ow
i
ng
d
escr
ib
es t
h
e
b
e
h
av
i
or o
f
DINTA
in
a part

i
cu
l
ar epoc
h
e
.
Let t
h
e net
w
or
kd
etect t
w
oa
l
arm
s
A
1
an
d
A
2
(
F
i
gure 1a)
b

yno
d
e
s
a
1
an
d
a
2
r
espect
i
ve
l
y
i
nanepoc
h
e
.
Bot
h
no
d
e
s
a
1
an

d
a
2
n
ot
if
yt
h
e
e
nt
i
re networ
k
a
b
out t
h
enewa
l
arms an
d
start two nav
i
gat
i
on
fi
e
ld

computa
-
t
i
ons (us
i
ng A
l
gor
i
t
h
m 1) - one
f
or eac
h
goa
l
no
d
e. Next cons
id
er no
d
e
s
r
1
an
d

r
2
r
t
h
at
h
ave unass
i
gne
d
ro
b
ot
s
R
1
an
d
R
2
(
F
i
gure 1
b
)
i
nt
h

e
i
rv
i
c
i
n
i
ty.
r
1
an
d
r
2
r
r
p
ropagate t
h
e
di
stances
b
etween t
h
e unass
i
gne
d

ro
b
ots an
d
t
h
ea
l
arm
s
A
1
an
d
A
2
. Four suc
hdi
stances are compute
d
an
ddi
str
ib
ute
d
t
h
roug
h

out t
h
e networ
k.
In t
h
e
fi
na
l
stage, every no
d
e
i
nt
h
e networ
kh
as t
h
e same
i
n
f
ormat
i
on a
b
ou
t

t
h
e
l
ocat
i
on o
f
a
l
arms an
d
ava
il
a
bl
ero
b
ots
,
an
ddi
stances
b
etween t
h
ero
b
ot
s

an
d
eac
h
a
l
arm. Eac
h
no
d
e
i
nt
h
e networ
k
can now
d
ec
id
eun
i
que
l
yw
hi
c
h
nav
-

i
gat
i
on
fi
e
ld
to ass
i
gn to w
hi
c
h
ro
b
ot. F
i
gure 1c s
h
ows two nav
i
gat
i
on
fi
e
lds
(
one
f

or eac
h
ro
b
ot) generate
d
an
d
ass
i
gne
d
to t
h
ero
b
ots. A ro
b
ot t
h
en s
i
mp
ly
f
o
ll
ows t
h
e

di
rect
i
ons suggeste
db
y networ
k
no
d
es
.
4
.MRTAEx
p
eriments in
S
imulation
In t
h
e
fi
rst set o
f
exper
i
ments
d
escr
ib
e

dh
ere we use
d
t
h
eP
l
ayer/Stage (
(
Ger
k
ey et a
l
., 2003)) s
i
mu
l
at
i
on eng
i
ne popu
l
ate
d
w
i
t
h
s

i
mu
l
ate
d
P
i
onee
r
2
DX mobile robots. A network of 2
5
network nodes
(
simulated motes
((
Piste
r
e
t al., 1999))) was pre-deployed in a test environment of size
5
7
6
m
2
.T
h
e com-
m
un

i
cat
i
on range o
f
t
h
eno
d
es an
d
ro
b
ots was set to approx
i
mate
l
y 4 meters
.
Ro
b
ots were requ
i
re
d
to nav
i
gate to t
h
epo

i
nt o
f
eac
h
a
l
arm an
d
m
i
n
i
m
i
ze t
he
c
umu
l
at
iv
ea
l
ar
m
O
nTim
e
.

Eac
h
a
l
arm’
s
O
nTim
e
i
s compute
d
as t
h
e
diff
er
-
e
nce
b
etween t
h
et
i
me t
h
ea
l
arm was serve

db
yaro
b
ot an
d
t
h
et
i
me t
h
ea
l
ar
m
w
as
d
etecte
db
y one o
f
t
h
eno
d
es o
f
t
h

e sensor networ
k
. Every exper
i
ment wa
s
c
on
d
ucte
di
nt
h
e same env
i
ronment w
i
t
h
ro
b
ot group s
i
zes vary
i
ng
f
rom1t
o
4

,10tr
i
a
l
s per group. T
h
esc
h
e
d
u
l
eo
f
10 a
l
arms was
d
rawn
f
romaPo
i
sson
di
str
ib
ut
i
on
(

λ
=
1
6
0
, roug
hl
y one a
l
arm per m
i
nute), w
i
t
h
un
if
orm
l
y
di
str
ib
ute
d
n
o
d
es t
h

at
d
etecte
d
a
l
arms.
W
e measure
d
cumu
l
at
iv
ea
l
ar
m
O
nTim
e
f
or net
w
or
k
-me
di
ate
d

tas
k
a
ll
o
-
c
at
i
on
(
i
.e., DINTA). As a
b
ase case we compare
d
t
h
e resu
l
ts to t
h
es
i
tuat
i
o
n
w
h

ere t
h
ero
b
ots are programme
d
to exp
l
ore t
h
eenv
i
ronment us
i
ng
di
rect
i
ve
s
3
2
B
atalin and
S
ukhatm
e
A
1
A

2
(
a
)
P
h
ase 1
.
R
1
R
2
(b)
P
h
ase 2
.
A
1
A
2
(
c
)
P
h
ase 3
.
F
igure

1.
Th
et
h
ree stages o
f
DINTA
i
na
d
ec
i
s
i
on epoc
h
.a)T
h
e sensor networ
kd
etect
s
e
vents (marked
A
1
a
n
d
A

2
)
an
d
propagates event
d
ata t
h
roug
h
out t
h
e networ
k
.
b
) Next, no
d
e
s
t
hat have unassigned robots in their vicinity propagate distances (in hop counts) from robots t
o
e
ach of the alarms. c) In the final stage, every node in the network has the same informatio
n
a
bout the location of events and available robots
,
and distances between robots and each event

.
H
ence, a unique assignment of direction suggestion at every node can occur
.
f
rom t
h
e sensor networ
kd
es
i
gne
d
on
l
ytoopt
i
m
i
ze t
h
e
i
renv
i
ronmenta
l
cov
-
e

rage ((Bata
li
nan
d
Su
kh
atme, 2004a)). T
h
e compar
i
son
hi
g
hli
g
h
ts t
h
e
b
en
-
efi
ts o
f
purpose
f
u
l
tas

k
a
ll
ocat
i
on. F
i
gure 2 s
h
ows t
h
e
O
nTim
e
c
ompar
i
son
f
or DINTA an
d
t
h
eexp
l
orat
i
on-on
l

y case. C
l
ear
l
y, DINTA outper
f
orms t
he
e
xp
l
orat
i
on-on
l
ya
l
gor
i
t
h
mevent
h
oug
h
as t
h
eenv
i
ronment

b
ecomes saturate
d
w
i
t
h
ro
b
ots, t
h
e
diff
erence
b
ecomes sma
ll
er. T
h
e
diff
erence
i
s stat
i
st
i
ca
ll
ys

i
g
-
n
ifi
cant (t
h
e T-test p-va
l
ue
i
s
l
ess t
h
an 10
−
4
f
or every pa
i
r
i
nt
h
e
d
ata set).
Furt
h

er, t
h
e
p
er
f
ormance o
f
DINTA
i
s sta
bl
e (sma
ll
an
d
constant var
i
ance
)
w
h
ereas var
i
ances pro
d
uce
db
yt
h

eexp
l
orat
i
on-on
l
ymo
d
ec
h
ange
d
rast
i
ca
lly
a
n
d
re
d
uce as t
h
een
vi
ronment
b
ecomes saturate
dwi
t

h
ro
b
ots
.
5. Laborator
y
Ex
p
eriments with NIM
S
T
h
e secon
d
set o
f
exper
i
ments we
di
scuss use a new test
b
e
d
, current
l
yun
d
e

r
d
eve
l
opment - Networ
k
e
d
In
f
o-Mec
h
an
i
ca
l
System ((NIMS, 2004)). F
i
gure 3
s
h
ows NIMS
d
ep
l
oye
di
na
f
orest reserve

f
or cont
i
nuous operat
i
on. T
h
e system
i
nc
l
u
d
es support
i
ng ca
bl
e
i
n
f
rastructure, a
h
or
i
zonta
ll
ymov
i
ng mo

bil
ero
b
o
t
(
t
h
e NIMS no
d
e) equ
i
ppe
d
w
i
t
h
a camera, an
d
a vert
i
ca
ll
ymo
bil
e meteoro
l
og
-

i
ca
l
sensor system carry
i
ng water vapor, temperature, an
d
p
h
otosynt
h
et
i
ca
lly
a
ct
i
ve ra
di
at
i
on (PAR) sens
i
ng capa
bili
ty. T
h
e purpose o
f

NIMS
i
s to ena
ble
t
h
e stu
d
yo
f
spat
i
otempora
l
p
h
enomena
(
e.
g
.
,
h
um
idi
ty, car
b
on
fl
ux, e

t
c
.
)in
n
atura
l
env
i
ronments. F
i
gure 3a sc
h
emat
i
ca
ll
ys
h
ows NIMS w
i
t
hd
ep
l
oye
d
sta
-
t

i
c sensor no
d
es (assem
bl
e
di
n stran
d
s)
i
nt
h
evo
l
ume surroun
di
ng t
h
e sens
i
ng
S
ensor Net
w
ork-Mediated Multi-Robot Task Allocatio
n
33
1
2

3
4
0
1
000
2000
3000
4
000
5
000
6000
7000
8000
9000
N
umber o
f
Robot
s
O
nTim
e
Ex
p
lorat
i
on
DINT
A

F
igure
2.
C
ompar
i
son
b
etween
i
mp
l
ementat
i
on o
f
DINTA an
d
exp
l
orat
i
on-on
l
y
.
C
ell
1
C

ell
2
C
ell
3
C
ell
5
C
ell
4
C
ell
6
S
trand 1
S
trand 2
S
trand 3
NIMS HN
VN
(
a
)
NIMS
h
or
i
zonta

l(
HN
)
an
d
vert
i
ca
l(
VN
)
n
o
d
es an
d
stat
i
c sensors (sc
h
emat
i
ca
lly)
(
b
) NIMS
d
ep
l

o
y
e
di
na
f
orest reserv
e
F
igure
3.
N
IMS system
d
ep
l
oye
di
nt
h
e
f
orest reserve
f
or cont
i
nuous operat
i
on
.

transect. W
i
re
l
ess networ
ki
ng
i
s
i
ncorporate
d
to
li
n
k
t
h
e stat
i
c sensor no
d
e
s
w
i
t
h
t
h

e NIMS no
d
e. T
h
e NIMS system
i
s
d
ep
l
oye
di
n a transect o
fl
engt
h
7
0m and average height of 1
5
m with a total area of over 1,00
0
m
2
.
T
h
e exper
i
menta
l

NIMS system operates w
i
t
h
a
li
near spee
d
range
f
or no
de
m
ot
i
on o
f
0.1 to 1 m/secon
d
.T
h
us, t
h
et
i
me requ
i
re
d
to map an ent

i
re 1,00
0
m
2
transect
wi
t
h0
.
1
m
2
r
eso
l
ut
i
on
will
excee
d
1
0
4
to 1
0
5
secon
d

s. P
h
enom
-
34
B
atalin and
S
ukhatm
e
2
4
6 8 1
0
12
14
16
18
2
0
0
5000
10000
1
5000
2
0000
25000
30000
Number of Event

s
O
nTime
(
in seconds
)
TA
Raster
S
can
(
a
)
Event OnT
i
me
.
2
4
6
8
10
12
14
16
1
8
2
0
0

500
1000
1500
2000
2500
3000
350
0
400
0
450
0
500
0
C
onsumed Energy (in t.i.m.
)
TA
Raster
S
can
Number o
f
Event
s
(
b
) Ener
gy
consumpt

i
on.
F
igure
4.
N
IMS
l
a
b
exper
i
ments: tas
k
a
ll
ocat
i
on vs. a raster scan.
e
na t
h
at vary at a c
h
aracter
i
st
i
c rate excee
di

ng t
hi
s scann
i
ng rate may not
be
a
ccurate
l
y represente
d
. Hence tas
k
a
ll
ocat
i
on
i
s requ
i
re
d
to
f
ocus samp
li
ng
in
spec

ifi
c areas
d
epen
di
ng on t
h
e
i
rsc
i
ent
ifi
cva
l
ue. T
h
e pre
li
m
i
nary exper
i
ment
s
u
s
i
ng our
i

n-networ
k
tas
k
a
ll
ocat
i
on met
h
o
d
o
l
ogy s
h
ow an or
d
er o
f
magn
i
tu
de
i
mprovement
i
nt
h
et

i
me
i
tta
k
es to comp
l
ete samp
li
ng
.
W
e con
d
ucte
d
exper
i
ments on a sma
ll
er vers
i
on o
f
NIMS
i
nsta
ll
e
di

nt
he
l
a
b
2
.
A network of 6 Mica2 motes was pre-deployed in the volume surroundin
g
t
h
e NIMS transect (s
i
m
il
ar to F
i
gure 3a)
i
n a test env
i
ronment. Exper
i
ments
were con
d
ucte
d
compar
i

ng a vers
i
on o
f
DINTA w
i
t
h
a Raster Scan (RS) as
a
b
ase case. RS
i
sana
l
gor
i
t
h
mo
f
c
h
o
i
ce w
h
en t
h
ere

i
sno
i
n
f
ormat
i
on a
b
ou
t
t
h
ep
h
enomenon
l
ocat
i
on (w
h
ere t
h
ea
l
arms are). RS scans every po
i
nt o
f
t

he
transect w
i
t
h
a spec
ifi
e
d
reso
l
ut
i
on. W
h
en t
h
e Raster Scan reac
h
es t
h
e
l
ocat
i
o
n
of
an a
l

arm, t
h
ea
l
arm
i
s cons
id
ere
d
to
b
e turne
d
o
ff.
In our experiment, schedules of 3,
5
, 7, 10 and 20 alarms (henceforth
,
e
vents
)
were
d
rawn
f
rom a un
if
orm

di
str
ib
ut
i
on to arr
i
ve w
i
t
hi
n10m
i
nutes,
w
i
t
h
un
if
orm
l
y
di
str
ib
ute
d
no
d

es t
h
at
d
etecte
d
t
h
e event. Note t
h
at
f
or actua
l
app
li
cat
i
ons we
d
o not expect to rece
i
ve/process more t
h
an1-10events
i
n1
0
m
i

nutes on avera
g
e. Hence t
h
e case o
f
20 events s
h
ows t
h
e
b
e
h
av
i
or o
f
t
he
s
y
stem at t
h
e
li
m
i
t.
F

ig
ure4s
h
ows exper
i
menta
l
resu
l
ts compar
i
n
g
O
nTim
e
p
er
f
ormance o
f
DINTA and RS. The number of events varies between 3 and 20. Both al
g
o
-
r
ithms were evaluated from 3 different startin
g
positions of the mobile node o
n

the transect (drawn from a uniform distribution). The results were avera
g
ed.
A
s can be seen from the
g
raph, DINTA performs 9-22 times better on the entir
e
interval of 3-20 events. Note also that DINTA is stable, as indicated b
y
erro
r