Multi-Robot Systems. From Swarms to Intelligent Automata Volume III pdf

Multi-Robot S
y
stems. From Swarms to Intelli
g
ent Automata
V
olume III
Volume III
Proceedings from the 2005 International Workshop
on Multi-Robot Systems
Edited b
y
LYNNE E. PARKER
T
h
e University o
f
Tennessee
,
Knoxvi
ll
e, TN, U.S.A
.
an
d
FRANK E. SCHNEIDER
Multi-Robot Systems.
From
Swarms to
Intelligent
Automata

ALAN C. SCHULTZ
N
av
y
Center
f
or Applied Research in A.I.
,
N
ava
l
Researc
h
La
b
oratory
,
Was
h
ington, DC, U.S.A
.
F
GAN, Wac
h
t
b
erg, Germany
A
C.I.P. Catalogue record for this book is available from the Library of Congress.
Published by Springer,

P.O. Box 17
,
3300 AA Dordrecht
,
The Netherlands.
Printed on acid-
f
ree pape
r
All Rights Reserved
©
2005 Sprin
g
e
r
No part of this work may be reproduced, stored in a retrieval system, or transmitted
i
n any form or by any means, electronic, mechanical, photocopying, microfilming,
r
ecording or otherwise, without written permission from the Publisher, with the
exception of an
y
material supplied specificall
y
for the purpose of bein
g
entered
and executed on a computer system, for exclusive use by the purchaser of the work.
Print
ed

in th
e
N
e
th
e
rlan
ds.
ISBN-13 978-1-4020-3388-9 (HB) Springer Dordrecht, Berlin, Heidelberg, New York
ISBN-10 1-4020-3388-5 (HB) Sprin
g
er Dordrecht, Berlin, Heidelber
g
, New York
ISBN-10 1-4020-3389-3 (e-book) Springer Dordrecht, Berlin, Heidelberg, New York
I
SBN-13 978-1-4020-3389-6 (e-book) Springer Dordrecht, Berlin, Heidelberg, New York
C
ontents
Pr
e
f
ace
ix
Part I Task Allocatio
n
The Generation of Bidding Rules for Auction-Based Robot Coordination
3
C
rai

g
Tove
y
, Michail G. La
g
oudaki
s
,
Sonal Jain, and Sven Koeni
g
Issues in Multi-Robot Coalition Formatio
n
15
L
ovekesh Vi
g
and Julie A. Adam
s
Sensor Network-Mediated Multi-Robot Task Allocatio
n
27
M
axim A. Batalin and
G
aura
vS
.
S
ukhatm
e

Part II Coordination in Dynamic Environment
s
M
ulti-Ob
j
ective Cooperative Control of D
y
namical S
y
stem
s
41
Z
hihua Q
u
,
Jin
g
Wan
g
,
a
nd Richard A. Hul
l
L
evels of Multi-Robot Coordination for D
y
namic Environment
s
53

C
olin P. McMillen, Paul E. R
y
bski, and Manuela M. Velos
o
Parallel Stochastic Hill-Climbin
g
with Small Team
s
6
5
B
rian P. Gerke
y
, Sebastian Thru
n
,
Geo
ff
Gordo
n
T
owar
d
Versat
ili
t
y
o
f

Mu
l
t
i
-Ro
b
ot S
y
stem
s
79
C
o
l
in C
h
err
y
an
d
Hon
g
Z
h
an
g
Part III In
f
ormat
i

on / Sensor S
h
ar
i
n
g
an
d
Fus
i
o
n
Decentra
li
ze
d
Commun
i
cat
i
on Strate
gi
es
f
or Coor
di
nate
d
Mu
l

t
i
-A
g
ent Po
li
c
i
es 9
3
M
aayan Rot
h
, Rei
d
Simmons, an
d
Manue
l
aVe
l
os
o
Improving Multirobot Multitarget Tracking by Communicating
Ne
g
at
i
ve In
f

ormat
i
o
n
pgg
107
M
att
h
ew Powers, Ramprasa
d
Ravic
h
an
d
ran, Fran
k
De
ll
aert, an
d
Tuc
k
er Ba
l
c
h
vi
MU
LTI-R

O
B
O
T
S
Y
S
TEM
S
Enabling Autonomous Sensor-Sharing for Tightly-Coupled
C
ooperat
i
ve Tas
k
s
g
119
Ly
nne E. Parker, Maureen Chandra, and Fan
g
Tan
g
Part IV Distributed Mapping and Coverag
e
Merging Partial Maps without Using Odometr
y
1
3
3

Distributed Coverage of Unknown/Unstructured Environments
b
yMo
bil
e Sensor Networ
ks
g
14
5
P
art V Motion Planning and Contro
l
1
59
J
ames Bruce and Manuela
V
elos
o
A Multi-Robot Testbed for Biologically-Inspired
C
ooperat
i
ve Contro
l
171
Rafael Fierro, Justin Clark
,
k
k

Dean Hou
g
en, and Sesh Commuri
P
art VI Human-Robot Interactio
n
T
ask Switching and Multi-Robot Team
s
1
8
5
Michael A.
G
oodric
h
,
Mor
g
an Qui
g
le
y
,
a
nd Ker
y
l Cosenz
o
User Modelling for Principled Sliding Autonomy in Human-Robot Teams 19

7
Brennan Sellner, Reid Simmons, and San
j
iv Sing
h
P
art VII A
pp
lication
s
Multi-Robot Chemical Plume Tracin
g
211
Diana Spears, Dimitri Zarzhitsk
y
,
a
nd David Tha
y
er
Deploying Air-Ground Multi-Robot Teams
i
nUr
b
an Env
i
ronment
s
pyg
pyg

223
L. Chaimowicz, A. Cowle
y
, D. Gomez-Ibanez, B. Grocholsk
y
, M. A. Hsieh
,
H. Hsu, J
.
F. Keller, V. Kumar, R. Swaminathan, and C. J. Ta
y
lo
r
P
art VIII Poster S
h
ort Paper
s
A
Robust Monte-Carlo Algorithm for Multi-Robot Localizatio
n
251
A
Dialogue-Based Approach to Multi-Robot Team Contro
l
2
5
7
N
athanael Chambers, James Allen, Lucian Galescu, and Hyuckchul Jun

g
F
r
F
F
ancesco
rr
A
mi
g
oni
,
S
imon
e
G
as
p
arini, and Maria Gin
i
I
oanni
s
Rekleiti
s
,
Ai
P
eng
PP

N
ew
,
and Howie Choset
R
eal-Time Multi-Robot Motion Planning with Safe Dynamic
s
Va
z
ha Amiranashvil
i
and Gerhard Lakeme
y
e
r
Prec
i
s
i
on Man
ip
u
l
at
i
on w
i
t
h
Coo

p
erat
i
ve Ro
b
ot
s
2
35
A
s
h
l
e
y
e
S
t
r
o
r
r
u
p
u
e
,
T
e
T

T
r
r
y
r
r
H
u
HH
n
t
s
tt
b
e
r
g
rr
e
r
,
r
r
A
v
i
O
k
o
n

, and Hrand Aghazarian
C
ontent
s
vii
for Mobile Robot Teams
263
J
ason Derenick, Christo
p
her Thorne, and John S
p
letze
r
T
h
e
G
NATs – Lo
w
-
C
ost Em
b
e
dd
e
d
Net
w

or
ks
f
or Support
i
n
g
Mo
bil
eRo
b
ot
s
277
Keit
h
J. O’Hara, Danie
l
B. Wa
lk
er, an
d
Tuc
k
er R. Ba
l
c
h
2
9

1
2
9
9
S
warm
i
n
g
UAVS Be
h
av
i
or H
i
erarc
hy
269
K
uo-
C
hi Li
n
Ro
l
eBase
d
Operat
i
on

s
283
B
rian Satterˇ eld
,
Heeten Choxi
,
and Drew Housten
Hybrid
f
Free-Space Optics/Radio Frequency (FSO/RF) Networks
bil b
b
Er
godic Dynamics by Design: A Route to Predictable Multi-Robot System
s
A
ut
h
or
In
de
x
Dy
la
n
A.
S
hell
,

C
hri
s
V
V
V
J
ones, and Maja J. Matari
JJ
c
´
Prefac
e
T
h
eT
hi
r
d
Internat
i
ona
l
Wor
k
s
h
op on Mu
l
t

i
-Ro
b
ot Systems was
h
e
ld in
March 200
5
at the Naval Research Laboratory in Washington, D.C., USA
.
Br
i
ng
i
ng toget
h
er
l
ea
di
ng researc
h
ers an
d
government sponsors
f
or t
h
ree

d
ay
s
of
tec
h
n
i
ca
li
nterc
h
ange on mu
l
t
i
-ro
b
ot systems, t
h
ewor
k
s
h
op
f
o
ll
ows tw
o

p
rev
i
ous
hi
g
hl
y success
f
u
l
gat
h
er
i
ngs
i
n 2002 an
d
2003.L
ik
et
h
e prev
i
ous tw
o
wor
k
s

h
ops, t
h
e meet
i
ng
b
egan w
i
t
h
presentat
i
ons
b
yvar
i
ous government pro
-
gram managers
d
escr
ibi
ng app
li
cat
i
on areas an
d
programs w

i
t
h
an
i
nterest
in
m
u
l
t
i
-ro
b
ot systems. U.S. Government representat
i
ves were on
h
an
df
rom
t
h
eO
ffi
ce o
f
Nava
l
Researc

h
an
d
severa
l
ot
h
er governmenta
l
o
ffi
ces.Top re
-
searc
h
ers
i
nt
h
e
fi
e
ld
t
h
en presente
d
t
h
e

i
r current act
i
v
i
t
i
es
i
n many areas o
f
m
u
l
t
i
-ro
b
ot s
y
stems. Presentat
i
ons spanne
d
aw
id
e ran
g
eo
f

top
i
cs,
i
nc
l
u
d
-
i
n
g
tas
k
a
ll
ocat
i
on, coor
di
nat
i
on
i
n
dy
nam
i
cenv
i

ronments,
i
n
f
ormat
i
on/senso
r
s
h
ar
i
n
g
an
df
us
i
on,
di
str
ib
ute
d
mapp
i
n
g
an
d

covera
g
e, mot
i
on p
l
ann
i
n
g
an
d
c
ontro
l
,
h
uman-ro
b
ot
i
nteract
i
on, an
d
app
li
cat
i
ons o

f
mu
l
t
i
-ro
b
ot s
y
stems. A
ll
p
resentations were
g
iven in a sin
g
le-track workshop format. This proceed
-
i
n
g
s documents the work presented at the workshop.The research presenta
-
tions were followed b
y
panel discussions, in which all participants interacte
d
to hi
g
hli

g
ht the challen
g
es of this field and to develop possible solutions. I
n
addition to the invited research talks, researchers and students were
g
iven a
n
o
pportunit
y
to present their work at poster sessions.We would like to thank th
e
Naval Research Laborator
y
for sponsorin
g
this workshop and providin
g
the fa-
c
ilities for these meetin
g
s to take place.We are extremel
yg
rateful to Ma
g
dalen
a

Bu
g
a
j
ska, Paul Wie
g
and, and Mitchell A. Potter, for their vital help (and lon
g
hours) in editin
g
these proceedin
g
s and to Michelle Caccivio for providin
g
th
e
administrative su
pp
ort to the worksho
p
.
L
YNNE
E
.
P
ARKER
,
A
L

AN
C
.
S
C
H
U
LT
Z
,
A
ND
F
R
A
N
K
E
.
S
C
HNEIDER
ix
I
T
A
S
K ALL
OC
ATI

ON
THE GENERATION OF BIDDING RULES FOR
AUCTION-BASED ROBOT COORDINATION
∗
C
ra
i
g Tovey, M
i
c
h
a
il
G. Lagou
d
a
kis
Sc
h
oo
l
of In
d
ustria
l
an
d
Systems Engineering, Georgia Institute of Tec
h
no

l
og
y
{
ctovey, m
i
c
h
a
il
.
l
a
g
ou
d
a
kis
}
@
isye.
g
atech.ed
u
S
ona
l
Ja
i
n, Sven Koen

i
g
Computer Science Department, University of Sout
h
ern Ca
l
iforni
a
{
s
ona
lj
a
i
,s
k
oen
ig
}
@
usc.ed
u
Abs
tr
act
R
o
b
ot
i

cs researc
h
ers
h
ave use
d
auct
i
on-
b
ase
d
coor
di
nat
i
on systems
f
or ro
b
o
t
t
eams because of their robustness and efficiency. However, there is no researc
h
i
nto systematic methods for deriving appropriate bidding rules for given tea
m
o
bjectives. In this paper, we propose the first such method and demonstrate it b

y
d
eriving bidding rules for three possible team objectives of a multi-robot explo
-
r
ation task. We demonstrate experimentally that the resulting bidding rules in
-
d
eed exhibit good performance for their respective team objectives and compar
e
f
avorably to the optimal performance. Our research thus allows the designer
s
o
f auction-based coordination systems to focus on developing appropriate tea
m
o
bjectives, for which good bidding rules can then be derived automatically
.
K
eywords:
A
uctions, Bidding Rules, Multi-Robot Coordination, Exploration
.
1. Introduction
T
h
et
i
me requ

i
re
d
to reac
h
ot
h
er p
l
anets ma
k
es p
l
anetary sur
f
ace exp
l
orat
i
o
n
mi
ss
i
ons pr
i
me targets
f
or automat
i

on. Sen
di
ng rovers to ot
h
er p
l
anets e
i
t
h
e
r
i
nstea
d
o
f
or toget
h
er w
i
t
h
peop
l
e can a
l
so s
i
gn

ifi
cant
l
yre
d
uce t
h
e
d
anger an
d
c
ost
i
nvo
l
ve
d
. Teams o
f
rovers are
b
ot
h
more
f
au
l
tto
l

erant (t
h
roug
h
re
d
un
-
d
ancy) an
d
more e
ffi
c
i
ent (t
h
roug
h
para
ll
e
li
sm) t
h
an s
i
ng
l
e rovers

if
t
h
e rover
s
are coor
di
nate
d
we
ll
. However, rovers cannot
b
e eas
il
yte
l
e-operate
d
s
i
nce t
his
∗
W
et
h
an
k
Apurva Mu

dg
a
lf
or
hi
s
h
e
l
p. T
hi
s researc
h
was part
ly
supporte
dby
NSF awar
d
sun
d
er contract
s
I
TR/AP0113881
,
IIS-0098807
,
and IIS-0350584. The views and conclusions contained in this document
are t

h
ose o
f
t
h
e aut
h
ors an
d
s
h
ou
ld
not
b
e
i
nterprete
d
as represent
i
n
g
t
h
eo
ffi
c
i
a

l
po
li
c
i
es, e
i
t
h
er expresse
d
or
i
mp
li
e
d
,o
f
t
h
e sponsor
i
n
g
or
g
an
i
zat

i
ons, a
g
enc
i
es, compan
i
es or t
h
e U.S.
g
overnment
.
3
L.E. Parker et al. (eds.)
,
M
ulti-Robot Systems. From Swarms to Intelligent Automata. Volume III
,
3
–
14
.

c
2005 Springer. Printed in the Netherlands
.
4
T
ove

y
, et al.
r
equ
i
res a
l
arge num
b
er o
fh
uman operators an
di
s commun
i
cat
i
on
i
ntens
i
ve
,
e
rror prone, an
d
s
l
ow. Ne
i

t
h
er can t
h
ey
b
e
f
u
ll
y preprogramme
d
s
i
nce t
h
e
ir
a
ct
i
v
i
t
i
es
d
epen
d
on t

h
e
i
r
di
scover
i
es. T
h
us, one nee
d
stoen
d
ow t
h
em w
i
t
h
t
he
c
apa
bili
ty to coor
di
nate autonomous
l
yw
i

t
h
eac
h
ot
h
er. Cons
id
er,
f
or exam
-
pl
e, a mu
l
t
i
-ro
b
ot exp
l
orat
i
on tas
k
w
h
ere a team o
fl
unar rovers

h
as to v
i
s
i
t
a
num
b
er o
f
g
i
ven target
l
ocat
i
ons to co
ll
ect roc
k
samp
l
es. Eac
h
target must
be
vi
s
i

te
db
yat
l
east one rover. T
h
e rovers
fi
rst a
ll
ocate t
h
e targets to t
h
emse
l
ves,
a
n
d
eac
h
rover t
h
en v
i
s
i
ts t
h

e targets t
h
at are a
ll
ocate
d
to
i
t. T
h
e rovers
k
no
w
t
h
e
i
r current
l
ocat
i
on at a
ll
t
i
mes
b
ut m
i

g
h
t
i
n
i
t
i
a
ll
y not
k
now w
h
ere o
b
stac
l
e
s
a
re
i
nt
h
e terra
i
n. It can t
h
ere

f
ore
b
e
b
ene
fi
c
i
a
lf
or t
h
e rovers to re-a
ll
ocate t
he
targets to t
h
emse
l
vesast
h
ey
di
scover more a
b
out t
h
e terra

i
n
d
ur
i
ng execut
i
on
,
f
or examp
l
e, w
h
enarover
di
scovers t
h
at
i
t
i
s separate
dby
a
big
crater
f
ro
m

i
ts next tar
g
et. S
i
m
il
ar mu
l
t
i
-ro
b
ot exp
l
orat
i
on tas
k
sar
i
se
f
or m
i
ne sweep
i
n
g,
searc

h
an
d
rescue operat
i
ons, po
li
ce operat
i
ons, an
dh
azar
d
ous mater
i
a
l
c
l
ean
-
i
n
g
, amon
g
ot
h
ers
.

Multi-robot coordination tasks are t
y
picall
y
solved with heuristic method
s
since optimizin
g
the performance is often computationall
y
intractable. The
y
a
re often solved with decentralized methods since centralized methods lack ro
-
bustness: if the central controller fails, so does the entire robot team. Marke
t
mechanisms, such as auctions, are
p
o
p
ular decentralized and heuristic multi
-
r
obot coordination methods (Rabideau et al., 2000). In this case, the robot
s
a
re the bidders and the tar
g
ets are the

g
oods up for auction. Ever
y
robot bid
s
o
n tar
g
ets and then visits all tar
g
ets that it wins. As the robots discover mor
e
a
bout the terrain durin
g
execution, the
y
run additional auctions to chan
g
eth
e
a
llocation of tar
g
ets to themselves. The resultin
g
auction-based coordinatio
n
s
y

stem is efficient in terms of communication (robots communicate onl
y
nu
-
meric bids) and com
p
utation (robots com
p
ute their bids in
p
arallel). It is there
-
f
ore not surprisin
g
that auctions have been shown to be effective multi-robot
c
oordination methods (Gerkey and Matar
i
´
c, 2002, Zlot et al., 2002, Thayer
´
e
t al., 2000, Goldberg et al., 2003). However, there are currently no systemati
c
methods for deriving appropriate bidding rules for given team objectives. I
n
t
hi
s paper, we propose t

h
e
fi
rst suc
h
met
h
o
d
an
dd
emonstrate
i
t
b
y
d
er
i
v
i
n
g
biddi
ng ru
l
es
f
or t
h

ree poss
ibl
e team o
bj
ect
i
ves o
f
t
h
emu
l
t
i
-ro
b
ot exp
l
orat
i
o
n
tas
k
.We
d
emonstrate exper
i
menta
ll

yt
h
at t
h
e resu
l
t
i
ng
biddi
ng ru
l
es
i
n
d
ee
d
e
x
hibi
t goo
d
per
f
ormance
f
or t
h
e

i
r respect
i
ve team o
bj
ect
i
ves an
d
compare
f
a
-
v
ora
bl
ytot
h
e opt
i
ma
l
per
f
ormance. Our researc
h
t
h
us a
ll

ows t
h
e
d
es
i
gners o
f
a
uct
i
on-
b
ase
d
coor
di
nat
i
on systems to
f
ocus on
d
eve
l
op
i
ng appropr
i
ate tea

m
obj
ect
i
ves,
f
or w
hi
c
h
goo
d biddi
ng ru
l
es can t
h
en
b
e
d
er
i
ve
d
automat
i
ca
ll
y
.

T
he Generation of Bidding Rules for Auction-Based Robot Coordinatio
n
5
2. The Auction-Based Coordination
Sy
stem
In
k
nown env
i
ronments, a
ll
targets are
i
n
i
t
i
a
ll
y una
ll
ocate
d
. Dur
i
ng eac
h
r

oun
d
o
f biddi
ng, a
ll
ro
b
ots
bid
sona
ll
una
ll
ocate
d
targets. T
h
ero
b
ot t
h
a
t
pl
aces t
h
e overa
ll l
owest

bid
on any target
i
sa
ll
ocate
d
t
h
at part
i
cu
l
ar target.
A
n
ew roun
d
o
f biddi
ng starts, an
d
a
ll
ro
b
ots
bid
aga
i

nona
ll
una
ll
ocate
d
targets
,
an
d
so on unt
il
a
ll
targets
h
ave
b
een a
ll
ocate
d
to ro
b
ots. (Note t
h
at eac
h
ro
b

o
t
n
ee
d
sto
bid
on
l
yonas
i
ng
l
e target
d
ur
i
ng eac
h
roun
d
, name
l
y on one o
f
t
he
targets
f
or w

hi
c
hi
ts
bid i
st
h
e
l
owest, s
i
nce a
ll
ot
h
er
bid
s
f
rom t
h
e same ro
b
o
t
h
avenoc
h
ance o
f

w
i
nn
i
ng.) Eac
h
ro
b
ot t
h
en ca
l
cu
l
ates t
h
e opt
i
ma
l
pat
hf
o
r
t
h
eg
i
ven team o
bj

ect
i
ve
f
or v
i
s
i
t
i
ng t
h
e targets a
ll
ocate
d
to
i
tan
d
t
h
en move
s
a
l
ong t
h
at pat
h

.Aro
b
ot
d
oes not move
if
no targets are a
ll
ocate
d
to
i
t
.
In un
k
nown env
i
ronments, t
h
ero
b
ots procee
di
nt
h
e same way
b
ut un
d

e
r
t
h
e opt
i
m
i
st
i
c
i
n
i
t
i
a
l
assumpt
i
on t
h
at t
h
ere are no o
b
stac
l
es. As t
h

ero
b
ot
s
m
ove a
l
on
g
t
h
e
i
r pat
h
san
d
aro
b
ot
di
scovers a new o
b
stac
l
e,
i
t
i
n

f
orms t
he
o
t
h
er ro
b
ots a
b
out
i
t. Eac
h
ro
b
ot t
h
en re-ca
l
cu
l
ates t
h
e opt
i
ma
l
pat
hf

or t
he
gi
ven team o
bj
ect
i
ve
f
or v
i
s
i
t
i
n
g
t
h
eunv
i
s
i
te
d
tar
g
ets a
ll
ocate

d
to
i
t, ta
ki
n
g
i
nto account all obstacles that it knows about. If the performance si
g
nificantl
y
de
g
rades for at least one robot (in our experiments, we use a threshold of 10
p
ercent difference), then the robots use auctions to re-allocate all unvisite
d
tar
g
ets amon
g
themselves. Each robot then calculates the optimal path for th
e
g
iven team ob
j
ective for visitin
g
the tar

g
ets allocated to it and then moves alon
g
that path, and so on until all tar
g
ets have been visited
.
This auction-based coordination s
y
stem is similar to multi-round auction
s
and sequential sin
g
le-item auctions. Its main advanta
g
e is its simplicit
y
an
d
the fact that it allows for a decentralized im
p
lementation on real robots. Eac
h
r
obot computes its one bid locall
y
and in parallel with the other robots, broad
-
c
asts the bid to the other robots

,
listens to the broadcasts of the other robots
,
and then locall
y
determines the winnin
g
bid. Thus, there is no need for
a
c
entral auctioneer and therefore no sin
g
le point of failure. A similar but mor
e
r
estricted auction scheme has been used in the
p
ast for robot coordination (Dia
s
and Stentz, 2000).
3
. Team Objectives for Multi-Robot Ex
p
loration
A
mu
l
t
i
-ro

b
ot ex
pl
orat
i
on tas
k
cons
i
sts o
f
t
h
e
l
ocat
i
ons o
f
n
ro
b
ots an
d
m
targets as we
ll
as a cost
f
unct

i
on t
h
at spec
ifi
es t
h
e cost o
f
mov
i
ng
b
etween
l
oca
-
t
i
ons. T
h
eo
bj
ect
i
ve o
f
t
h
emu

l
t
i
-ro
b
ot exp
l
orat
i
on tas
ki
sto
fi
n
d
an a
ll
ocat
i
o
n
of
targets to ro
b
ots an
d
a pat
hf
or eac
h

ro
b
ot t
h
at v
i
s
i
ts a
ll
targets a
ll
ocate
d
t
o
i
tsot
h
at t
h
e team o
bj
ect
i
ve
i
sac
hi
eve

d
. Note t
h
at t
h
ero
b
ots are not requ
i
re
d
to return to t
h
e
i
r
i
n
i
t
i
a
ll
ocat
i
ons. In t
hi
s paper, we stu
d
yt

h
ree team o
bj
ect
i
ves
:
M
INI
S
UM
:
M
i
n
i
m
i
ze t
h
e sum o
f
t
h
e
p
at
h
costs over a
ll

ro
b
ots
.
6
T
ove
y
, et al.
M
INI
M
AX
:
M
i
n
i
m
i
ze t
h
e max
i
mum
p
at
h
cost over a
ll

ro
b
ots
.
M
INI
A
VE
A
A
:
M
i
n
i
m
i
ze t
h
e average per target cost over a
ll
targets
.
T
h
e pat
h
cost o
f
aro

b
ot
i
st
h
e sum o
f
t
h
e costs a
l
ong
i
ts pat
h
,
f
rom
i
ts
i
n
i
t
i
a
l
l
ocat
i

on to t
h
e
fi
rst target on t
h
e pat
h
,an
d
so on, stopp
i
ng at t
h
e
l
ast target o
n
t
h
e pat
h
.T
h
e per target cost o
f
a target
i
st
h

e sum o
f
t
h
e costs a
l
ong t
h
e pat
h
of
t
h
ero
b
ot t
h
at v
i
s
i
ts t
h
e target
i
n quest
i
on,
f
rom

i
ts
i
n
i
t
i
a
ll
ocat
i
on to t
h
e
fi
rs
t
target on t
h
e pat
h
,an
d
so on, stopp
i
ng at t
h
e target
i
n quest

i
on
.
O
pt
i
m
i
z
i
ng t
h
e per
f
ormance
f
or t
h
et
h
ree team o
bj
ect
i
ves
i
s NP-
h
ar
d

an
d
t
h
us
lik
e
l
y computat
i
ona
ll
y
i
ntracta
bl
e, as t
h
ey resem
bl
et
h
eTrave
li
ng Sa
l
es
-
p
erson Pro

bl
em, t
h
eM
i
n-Max Ve
hi
c
l
e Rout
i
ng Pro
bl
em, an
d
t
h
eTrave
li
ng Re
-
p
a
i
rperson Pro
bl
em (or M
i
n
i

mum Latency Pro
bl
em), respect
i
ve
l
y, w
hi
c
h
ar
e
i
ntracta
bl
eevenont
h
e Euc
lid
ean p
l
ane. However, t
h
ese team o
bj
ect
i
ves cove
r
aw

id
e ran
g
eo
f
app
li
cat
i
ons. For examp
l
e,
if
t
h
e cost
i
s ener
gy
consumpt
i
on
,
t
h
en t
h
e
M
INI

S
UM
team o
bj
ect
i
ve m
i
n
i
m
i
zes t
h
e tota
l
energy consume
dby
a
ll
ro
b
ots unt
il
a
ll
targets
h
ave
b

een v
i
s
i
te
d
.I
f
t
h
e cost
i
s trave
l
t
i
me, t
h
en t
he
M
I
N
IM
AX
team o
bj
ect
i
ve m

i
n
i
m
i
zes t
h
et
i
me unt
il
a
ll
targets
h
ave
b
een v
i
s
i
te
d
(
tas
k
-com
pl
et
i

on t
i
me) an
d
t
h
e
M
INI
A
VE
AA
t
eam o
bj
ect
i
ve m
i
n
i
m
i
zes
h
ow
l
ong
i
tta

k
es on average unt
il
a target
i
sv
i
s
i
te
d
(target-v
i
s
i
tt
i
me). T
h
e
M
INI
S
UM
a
n
dM
INI
M
AX

team o
bj
ect
i
ves
h
ave
b
een use
di
nt
h
e context o
f
mu
l
t
i
-ro
b
o
t
ex
pl
orat
i
on (D
i
as an
d

Stentz, 2000, D
i
as an
d
Stentz, 2002, Ber
h
au
l
teta
l
.
,
2003, Lagou
d
a
ki
seta
l
., 2004). T
h
e
M
INI
A
VE
A
A
t
eam o
bj

ect
i
ve, on t
h
eot
h
e
r
h
an
d
,
h
as not
b
een use
db
e
f
ore
i
nt
hi
s context a
l
t
h
oug
hi
t

i
s very appropr
i-
ate
f
or searc
h
-an
d
-rescue tas
k
s
,
w
h
ere t
h
e
h
ea
l
t
h
con
di
t
i
on o
f
severa

l
v
i
ct
i
ms
d
eter
i
orates unt
il
aro
b
ot v
i
s
i
ts t
h
em. Cons
id
er,
f
or examp
l
e, an eart
h
qua
ke
scenar

i
ow
h
ere an acc
id
ent s
i
te w
i
t
h
one v
i
ct
i
m
i
s
l
ocate
d
at a trave
l
t
i
me o
f
20 un
i
ts to t

h
e west o
f
aro
b
ot an
d
anot
h
er acc
id
ent s
i
te w
i
t
h
twenty v
i
ct
i
m
s
is located at a travel time of 2
5
units to its east. In this case, visiting the sit
e
to t
h
e west

fi
rst an
d
t
h
en t
h
es
i
te to t
h
e east ac
hi
eves
b
ot
h
t
h
e
M
INI
S
UM
an
d
t
h
e
M

INI
M
AX
team o
bj
ect
i
ves. However, t
h
e twenty v
i
ct
i
ms to t
h
e east ar
e
vi
s
i
te
d
very
l
ate an
d
t
h
e
i

r
h
ea
l
t
h
con
di
t
i
on t
h
us
i
s very
b
a
d
.Ont
h
eot
h
er
h
an
d,
vi
s
i
t

i
ng t
h
es
i
te to t
h
e east
fi
rst an
d
t
h
en t
h
es
i
te to t
h
e west ac
hi
eves t
h
e
M
INI
-
A
VE
A

A
team o
bj
ect
i
ve an
d
resu
l
ts
i
nanovera
ll b
etter average
h
ea
l
t
h
con
di
t
i
o
n
of
t
h
ev
i

ct
i
ms. T
hi
s examp
l
e
ill
ustrates t
h
e
i
mportance o
f
t
h
e
M
INI
A
VE
A
A
t
ea
m
obj
ect
i
ve

i
n cases w
h
ere t
h
e targets occur
i
nc
l
usters o
f diff
erent s
i
zes
.
4.
S
ystematic Generation of Bidding Rules
W
e see
k
to
d
er
i
ve an appropr
i
ate
biddi
ng ru

l
e
f
orag
i
ven team o
bj
ect
i
ve
.
T
hi
s
p
ro
bl
em
h
as not
b
een stu
di
e
db
e
f
ore
i
nt

h
ero
b
ot
i
cs
li
terature. Assum
e
t
h
at t
h
ere are
n
r
o
b
ots
r
1
, ,
r
n
r
a
n
d
m
current

l
y una
ll
ocate
d
target
s
t
1
, ,
t
m
t
.
A
ssume
f
urt
h
er t
h
at t
h
e team o
bj
ect
i
ve
h
as t

h
e structure to ass
i
gn a set o
f
tar
-
g
e
t
s
T
i
T
T
to ro
b
o
t
r
i
f
or a
ll
i
,
w
h
ere t
h

e sets
T
=
{
T
1
T
T
, ,
T
n
T
T
}
f
orm a
p
art
i
t
i
on o
f
T
he Generation of Bidding Rules for Auction-Based Robot Coordinatio
n
7
a
ll
targets t

h
at opt
i
m
i
zes t
h
e per
f
ormanc
e
f

g
(
r
1
,
T
1
TT
)
, ,
g
(
r
n
r
,
T

n
T
T
)

f
or g
i
ven
f
unct
i
on
s
f
a
n
d
g
.
Funct
i
on
g
d
eterm
i
nes t
h
e

p
er
f
ormance o
f
eac
h
ro
b
ot, an
d
f
unct
i
o
n
f
d
eterm
i
nes t
h
e per
f
ormance o
f
t
h
e team as a
f

unct
i
on o
f
t
h
e per
f
or
-
m
ance o
f
t
h
ero
b
ots. T
h
et
h
ree team o
bj
ect
i
ves
fi
tt
hi
s structure. For any ro

b
o
t
r
i
an
d
any set o
f
targets
T
i
T
T
,l
et
PC
(
r
i
,
T
i
T
T
)
d
enote t
h
em

i
n
i
mum
p
at
h
cost o
f
ro
b
o
t
r
i
an
d
S
T
C
(
r
i
,
T
i
T
T
)
d

enote t
h
em
i
n
i
mum sum o
f
per target costs over a
ll
target
s
in
T
i
T
T
if
ro
b
ot
r
i
vi
s
i
ts a
ll
targets
i

n
T
i
T
T
f
rom
i
ts current
l
ocat
i
on. T
h
en
,i
t
h
o
lds
t
h
at
M
INI
S
UM
:
m
in

T
∑
j
PC
(
r
j
r
,
T
j
T
)
,
M
INI
M
AX
:
m
in
T
max
j
PC
(
r
j
r
,

T
j
T
)
,
an
d
M
INI
A
VE
A
A
:
m
in
T
1
m
∑
j
S
T
C
(
r
j
r
,
T

j
T
)
.
A biddi
ng ru
l
e
d
eterm
i
nes
h
ow muc
h
aro
b
ot
bid
s on a target. We propos
e
t
h
e
f
o
ll
ow
i
ng

biddi
ng ru
l
e
f
or a g
i
ven team o
bj
ect
i
ve, w
hi
c
hi
s
di
rect
l
y
d
er
i
ve
d
f
rom t
h
e team o
bj

ect
i
ve
i
tse
lf.
Bi
dd
i
n
g
Rul
e
Ro
b
o
t
r
bid
s on target
t
th
e
diff
erence
i
n per
f
ormance
f

or t
he
gi
ven team o
bj
ect
i
ve
b
etween t
h
e current a
ll
ocat
i
on o
f
targets to ro
b
ot
s
a
n
d
t
h
ea
ll
ocat
i

on t
h
at resu
l
ts
f
rom t
h
e current one
if
ro
b
o
t
r
i
sa
ll
ocate
d
t
arge
t
t
.
(Una
ll
ocate
d
targets are

i
gnore
d
.
)
C
onsequent
l
y, ro
b
o
t
r
i
s
h
ou
ld bid
on targe
t
t
f

g
(
r
1
,
T


1
T
T
)
, ,
g
(
r
n
r
,
T

n
T
T
)

−
f

g
(
r
1
,
T
1
T
T

)
, ,
g
(
r
n
r
,
T
n
T
T
)

,
wh
ere
T

i
T
T
=
T
i
T
T
∪
{
t

}
an
d
T

j
T
=
T
j
T
f
or
i

=


j
.
T
h
e
biddi
ng ru
l
et
h
us per
f

orms
hill
cli
m
bi
ng to max
i
m
i
ze t
h
e per
f
ormance an
d
can t
h
us su
ff
er
f
rom
l
oca
l
opt
i
ma
.
H

owever, opt
i
m
i
z
i
ng t
h
e per
f
ormance
i
s NP-
h
ar
df
or t
h
et
h
ree team o
bj
ect
i
ves
.
O
ur auct
i
on-

b
ase
d
coor
di
nat
i
on system
i
st
h
ere
f
ore not
d
es
i
gne
d
to opt
i
m
i
z
e
t
h
e per
f
ormance

b
ut to
b
ee
ffi
c
i
ent an
d
resu
l
t
i
n a goo
d
per
f
ormance, an
d hill
cli
m
bi
ng
h
as t
h
ese propert
i
es. One potent
i

a
l
pro
bl
em w
i
t
h
t
h
e
biddi
ng ru
le
i
st
h
at t
h
ero
b
ots m
i
g
h
t not
h
ave a
ll
t

h
e
i
n
f
ormat
i
on nee
d
e
d
to compute t
he
bid
s. For examp
l
e, a ro
b
ot may not
k
now t
h
e
l
ocat
i
ons o
f
t
h

eot
h
er ro
b
ots
.
H
owever, we w
ill
now s
h
ow t
h
ataro
b
ot can ca
l
cu
l
ate
i
ts
bid
s
f
or t
h
et
h
re

e
team o
bj
ect
i
ves
k
now
i
ng on
l
y
i
ts current
l
ocat
i
on, t
h
e set o
f
targets a
ll
ocate
d
to
i
t, an
d
t

h
e cost
f
unct
i
on:
For t
h
eM
INI
S
UM
team o
bj
ect
i
ve, ro
b
o
t
r
i
s
h
ou
ld bid
on targe
t
t
∑

j
PC
(
r
j
r
,
T

j
T
)
−
∑
j
PC
(
r
j
r
,
T
j
T
)=
PC
(
r
i
,

T
i
T
T
∪
{
t
}
)
−
PC
(
r
i
,
T
i
T
T
)
.
8
T
ove
y
, et al.
For t
h
eM
INI

M
AX
team o
bj
ect
i
ve, ro
b
o
t
r
i
s
h
ou
ld bid
on targe
t
t
max
j
PC
(
r
j
r
,
T

j

T
)
−
max
j
PC
(
r
j
r
,
T
j
T
)
=
P
C
(
r
i
,
T
i
T
T
∪
{
t
}

)
−
max
j
PC
(
r
j
r
,
T
j
T
)
.
T
hi
s
d
er
iv
at
i
on uses t
h
e
f
act t
h
at ma

x
j
PC
(
r
j
r
,
T

j
T
)
=
PC
(
r
i
,
T

i
T
T
)
,
ot
h
er
-

w
i
se target
t
wou
ld h
ave a
l
rea
d
y
b
een a
ll
ocate
di
n a prev
i
ous roun
d
o
f
biddi
ng. T
h
e term max
j
PC
(
r

j
r
,
T
j
T
)
can
b
e
d
ro
pp
e
d
s
i
nce t
h
e outcomes
of
t
h
e auct
i
ons rema
i
n unc
h
ange

dif
a
ll bid
sc
h
ange
b
y a constant. T
h
us
,
r
o
b
ot
r
i
c
an
bid j
us
t
PC
(
r
i
,
T
i
T

T
∪{
t
}
)
o
n
t
arge
t
t
.
For t
h
eM
INI
A
VE
A
A
team o
bj
ect
i
ve, ro
b
ot
r
i
s

h
ou
ld bid
on targe
t
t
1
m
∑
j
S
T
C
(
r
j
r
,
T

j
T
)
−
1
m
∑
j
S
T

C
(
r
j
r
,
T
j
T
)
=
1
m

S
T
C
(
r
i
,
T
i
T
T
∪
{
t
}
)

−
S
T
C
(
r
i
,
T
i
TT
)

.
T
h
e
f
actor 1
/
m
can
b
e
d
ro
pp
e
d
s

i
nce t
h
e outcomes o
f
t
h
e auct
i
ons re
-
m
a
i
n unc
h
ange
dif
a
ll bid
s are mu
l
t
i
p
li
e
db
y a constant
f

actor. T
h
us
,
r
o
b
ot
r
i
c
an
bid j
us
t
S
T
C
(
r
i
,
T
i
TT
∪{
t
}
)
−

S
T
C
(
r
i
,
T
i
T
T
)
o
n
t
arge
t
t
.
T
h
us, t
h
e
biddi
ng ru
l
es
f
or t

h
et
h
ree team o
bj
ect
i
ves ar
e
B
ID
S
UM
:
PC
(
r
i
,
T
i
T
T
∪{
t
}
)
−
PC
(

r
i
,
T
i
T
T
)
,
B
ID
M
AX
:
PC
(
r
i
,
T
i
T
T
∪{
t
}
)
,
an
d

B
ID
A
VE
AA
:
S
T
C
(
r
i
,
T
i
T
T
∪{
t
}
)
−
S
T
C
(
r
i
,
T

i
T
T
)
.
T
h
ero
b
ots nee
d
to
b
ea
bl
etoca
l
cu
l
ate t
h
e
i
r
bid
se
ffi
c
i
ent

l
y
b
ut comput
i
n
g
PC
(
r
i
,
T
i
T
T
∪{
t
}
)
or
S
T
C
(
r
i
,
T
i

T
T
∪{
t
}
)
i
s NP-
h
ar
d
.Ro
b
ot
r
i
t
h
us uses a gree
dy
m
et
h
o
d
to approx
i
mate t
h
ese va

l
ues. In part
i
cu
l
ar,
i
t
fi
n
d
s a goo
d
pat
h
t
h
a
t
vi
s
i
ts t
h
e targets
i
n
T
i
TT

∪{
t
}
f
or a g
i
ven team o
bj
ect
i
ve as
f
o
ll
ows. It a
l
rea
dy
h
as a goo
d
pat
h
t
h
at v
i
s
i
ts t

h
e targets
in
T
i
T
T
.
F
i
rst,
i
t
i
nserts target
t
i
nto a
ll
p
os
i
t
i
ons on t
h
eex
i
st
i

ng pat
h
, one a
f
ter t
h
eot
h
er. T
h
en,
i
ttr
i
es to
i
mprov
e
e
ac
h
new pat
hb
y
fi
rst us
i
ng t
h
e 2-opt

i
mprovement ru
l
ean
d
t
h
en t
h
e 1-targe
t
3
-opt
i
mprovement ru
l
e. F
i
na
ll
y,
i
tp
i
c
k
st
h
e
b

est one o
f
t
h
e resu
l
t
i
ng pat
hs
f
or t
h
eg
i
ven team o
bj
ect
i
ve. T
h
e 2-opt
i
mprovement ru
l
eta
k
es a pat
h
an

d
i
nverts t
h
eor
d
er o
f
targets
i
n eac
h
one o
fi
ts cont
i
nuous su
b
pat
h
s
i
n turn, p
i
c
ks
t
h
e
b

est one o
f
t
h
e resu
l
t
i
ng pat
h
s
f
or t
h
eg
i
ven team o
bj
ect
i
ve, an
d
repeat
s
t
h
e proce
d
ure unt
il

t
h
e pat
h
can no
l
onger
b
e
i
mprove
d
.T
h
e 1-target 3-op
t
i
mprovement ru
l
e removes a target
f
rom t
h
e pat
h
an
di
nserts
i
t

i
nto a
ll
ot
h
e
r
p
oss
ibl
e pos
i
t
i
ons on t
h
e pat
h
,p
i
c
k
st
h
e
b
est one o
f
t
h

e resu
l
t
i
ng pat
h
s
f
or t
he
gi
ven team o
bj
ect
i
ve, an
d
repeats t
h
e proce
d
ure unt
il
t
h
e pat
h
can no
l
on

g
er
be
i
mprove
d
.
T
h
et
h
ree
biddi
n
g
ru
l
es are not
g
uarantee
d
to ac
hi
eve t
h
e
i
r respect
i
ve tea

m
obj
ect
i
ves even
if
t
h
eva
l
ue
s
P
C
(
r
i
,
T
i
T
T
∪{
t
}
)
a
n
d
S

T
C
(
r
i
,
T
i
TT
∪{
t
}
)
a
re com
p
ute
d
exact
l
y. Cons
id
er t
h
es
i
mp
l
emu
l

t
i
-ro
b
ot exp
l
orat
i
on tas
ki
nF
i
gure 1 w
i
t
h
2ro
-
b
ots an
d
2 targets an
d
un
i
t costs
b
etween a
dj
acent

l
ocat
i
ons. A
ll biddi
ng ru
l
e
s
T
he Generation of Bidding Rules for Auction-Based Robot Coordinatio
n
9
F
igure
1.
A
s
i
mp
l
emu
l
t
i
-ro
b
ot exp
l
orat

i
on tas
k
.
c
an resu
l
t
i
nt
h
ero
b
ots
f
o
ll
ow
i
ng t
h
eso
lid li
nes, resu
l
t
i
ng
i
n a per

f
ormance o
f
3f
or t
h
e
M
INI
S
UM
team o
bj
ect
i
ve, a per
f
ormance o
f
3
f
or t
h
e
M
INI
M
AX
t
ea

m
obj
ect
i
ve, an
d
a per
f
ormance o
f
2
f
or t
h
e
M
INI
A
VE
A
A
t
eam o
bj
ect
i
ve. However
,
t
h

ero
b
ots s
h
ou
ld f
o
ll
ow t
h
e
d
as
h
e
dli
nes to max
i
m
i
ze t
h
e
p
er
f
ormance
f
or a
ll

t
h
ree team o
bj
ect
i
ves, resu
l
t
i
ng
i
n a per
f
ormance o
f
2
f
or t
h
e
M
INI
S
UM
t
ea
m
obj
ect

i
ve, a per
f
ormance o
f
1
f
or t
h
eM
INI
M
AX
t
eam o
bj
ect
i
ve, an
d
a per
f
or
-
m
ance o
f
1
f
or t

h
e
M
INI
A
VE
AA
team o
bj
ect
i
ve. (We re
l
y on a part
i
cu
l
ar wa
y
of b
rea
ki
ng t
i
es
i
nt
hi
smu
l

t
i
-ro
b
ot exp
l
orat
i
on examp
l
e
b
ut can eas
il
yc
h
ang
e
t
h
ee
d
ge costs
b
y sma
ll
amounts to guarantee t
h
at t
h

e
biddi
ng ru
l
es resu
l
t
in
t
h
ero
b
ots
f
o
ll
ow
i
ng t
h
eso
lid li
nes
i
n
d
epen
d
ent
l

yo
fh
ow t
i
es are
b
ro
k
en.) I
n
a
f
ort
h
com
i
ng paper, we ana
l
yze t
h
e per
f
ormance o
f
t
h
et
h
ree
biddi

ng ru
l
e
s
t
h
eoret
i
ca
ll
yan
d
s
h
ow t
h
at t
h
e per
f
ormance o
f
t
h
e
B
ID
S
UM
biddi

ng ru
l
e
i
n
t
h
e Euc
lid
ean case
i
s at most a
f
actor o
f
two away
f
rom opt
i
mum, w
h
ereas n
o
c
onstant-
f
actor
b
oun
d

ex
i
sts
f
or t
h
e per
f
ormance o
f
t
h
e
B
ID
M
AX
an
dB
ID
A
VE
AA
biddi
ng ru
l
es even
i
nt
h

e Euc
lid
ean case
.
5. Ex
p
erimental Evaluation
To
d
emonstrate t
h
at t
h
e per
f
ormance o
f
t
h
et
h
ree
biddi
ng ru
l
es
i
s
i
n

d
ee
d
goo
df
or t
h
e
i
r respect
i
ve team o
bj
ect
i
ves, we
i
mp
l
emente
d
t
h
em an
d
t
h
en teste
d
t

h
em
i
no
ffi
ce-
lik
eenv
i
ronments w
i
t
h
rooms
,d
oors
,
an
d
corr
id
ors
,
as s
h
own
i
nF
i
gure 2. We per

f
orme
d
exper
i
ments w
i
t
hb
ot
h
unc
l
ustere
d
an
d
c
l
ustere
d
targets. T
h
e
l
ocat
i
ons o
f
t

h
ero
b
ots an
d
targets
f
or eac
h
mu
l
t
i
-ro
b
ot exp
l
orat
i
o
n
tas
k
were c
h
osen ran
d
om
l
y

i
nt
h
e unc
l
ustere
d
target case. T
h
e
l
ocat
i
ons o
f
t
he
r
o
b
ots an
d
targets were a
l
so c
h
osen ran
d
om
l

y
i
nt
h
ec
l
ustere
d
target case,
b
u
t
with the restriction that
5
0 percent of the targets were placed in clusters of
5
targets eac
h
.T
h
e num
b
ers
i
nt
h
eta
bl
es
b

e
l
ow are averages over 10
diff
eren
t
m
u
l
t
i
-ro
b
ot exp
l
orat
i
on tas
k
sw
i
t
h
t
h
e same sett
i
ngs. T
h
e per

f
ormance o
f
t
he
b
est
biddi
ng ru
l
e
f
or a g
i
ven team o
bj
ect
i
ve
i
ss
h
own
i
n
b
o
ld.
5.1 Known Environments
W

e mappe
d
our env
i
ronments onto e
i
g
h
t-connecte
d
un
if
orm gr
id
so
f
s
i
z
e
51
×
5
1 and com
p
uted all costs between locations as the shortest distances o
n
t
h
egr

id
. Our auct
i
on-
b
ase
d
coor
di
nat
i
on system use
d
t
h
ese costs to
fi
n
d
a
n
10
T
ove
y
, et al.
all
ocat
i
on o

f
targets to ro
b
ots an
d
a pat
hf
or eac
h
ro
b
ot t
h
at v
i
s
i
ts a
ll
target
s
all
ocate
d
to
i
t. We
i
nter
f

ace
di
ttot
h
e popu
l
ar P
l
ayer/Stage ro
b
ot s
i
mu
l
ato
r
(
Ger
k
ey et a
l
., 2003) to execute t
h
e pat
h
san
d
v
i
sua

li
ze t
h
e resu
l
t
i
ng ro
b
o
t
tra
il
s. F
i
gure 2 s
h
ows t
h
e
i
n
i
t
i
a
ll
ocat
i
ons o

f
t
h
ero
b
ots (squares) an
d
target
s
(
c
i
rc
l
es) as we
ll
as t
h
e resu
l
t
i
ng ro
b
ot tra
il
s(
d
ots)
f

or eac
h
one o
f
t
h
et
h
re
e
biddi
ng ru
l
es
f
or a samp
l
emu
l
t
i
-ro
b
ot exp
l
orat
i
on tas
k
w

i
t
h
3ro
b
ots an
d
2
0
u
nc
l
ustere
d
targets
i
n a comp
l
ete
l
y
k
nown env
i
ronment.
S
UM
,M
AX
and A

VE
A
A
i
nt
h
e capt
i
on o
f
t
h
e
fi
gure
d
enote t
h
e per
f
ormance
f
or t
h
e
M
INI
S
UM
,M

INI
-
M
AX
an
dM
INI
A
VE
A
A
team o
bj
ect
i
ves, respect
i
ve
l
y. Eac
h biddi
ng ru
l
e resu
l
ts
in
a
b
etter per

f
ormance
f
or
i
ts team o
bj
ect
i
ve t
h
an t
h
eot
h
er two
biddi
ng ru
l
es. Fo
r
e
xamp
l
e, t
h
e
B
ID
S

UM
biddi
ng ru
l
e resu
l
ts
i
n pat
h
so
f
very
diff
erent
l
engt
h
s
,
wh
ereas t
h
eB
ID
M
AX
biddi
ng ru
l

e resu
l
ts
i
n pat
h
so
f
s
i
m
il
ar
l
engt
h
s. T
h
ere
-
f
ore, t
h
e
p
er
f
ormance o
f
t

h
eB
ID
M
AX
biddi
ng ru
l
e
i
s
b
etter
f
or t
h
e
M
INI
M
AX
team o
bj
ect
i
ve t
h
an t
h
e one o

f
t
h
e
B
ID
S
UM
biddi
ng ru
l
e.
W
e compare
d
t
h
e per
f
ormance o
f
t
h
et
h
ree
biddi
ng ru
l
es aga

i
nst t
h
eop
-
t
i
ma
l
per
f
ormance
f
or mu
l
t
i
-ro
b
ot exp
l
orat
i
on tas
k
sw
i
t
h
one or two ro

b
ot
s
an
d
ten targets. T
h
e opt
i
ma
l
per
f
ormance was ca
l
cu
l
ate
db
y
f
ormu
l
at
i
ng t
he
m
u
l

t
i
-ro
b
ot exp
l
orat
i
on tas
k
sas
i
nteger programs an
d
so
l
v
i
ng t
h
em w
i
t
h
t
he
c
ommerc
i
a

l
m
i
xe
di
nteger program so
l
ver CPLEX. T
h
e NP-
h
ar
d
ness o
f
opt
i-
mi
z
i
ng t
h
e per
f
ormance
did
not a
ll
ow us to so
l

ve
l
arger mu
l
t
i
-ro
b
ot exp
l
orat
i
o
n
tas
k
s. Ta
bl
e1s
h
ows t
h
e per
f
ormance o
f
eac
h biddi
ng ru
l

ean
d
t
h
e opt
i
ma
l
per
-
f
ormance
f
or eac
h
team o
bj
ect
i
ve. Aga
i
n, eac
h biddi
ng ru
l
e resu
l
ts
i
na

b
ette
r
p
er
f
ormance
f
or
i
ts team o
bj
ect
i
ve t
h
an t
h
eot
h
er two
biddi
ng ru
l
es, w
i
t
h
t
he

e
xcept
i
on o
f
t
i
es
b
etween t
h
e
B
ID
S
UM
a
n
dB
ID
M
AX
biddi
ng ru
l
es
f
or mu
l
t

i-
r
o
b
ot ex
pl
orat
i
on tas
k
sw
i
t
h
one ro
b
ot. T
h
ese t
i
es are unavo
id
a
bl
e
b
ecause t
he
M
INI

S
UM
an
dM
INI
M
AX
team o
bj
ect
i
ves are
id
ent
i
ca
lf
or one-ro
b
ot exp
l
o
-
r
at
i
on tas
k
s. T
h

e per
f
ormance o
f
t
h
e
b
est
biddi
ng ru
l
e
f
or eac
h
team o
bj
ect
i
v
e
i
sa
l
ways c
l
ose to t
h
e opt

i
ma
l
per
f
ormance. In part
i
cu
l
ar, t
h
e per
f
ormance o
f
t
h
e
B
ID
S
UM
biddi
ng ru
l
e
f
or t
h
e

M
INI
S
UM
t
eam o
bj
ect
i
ve
i
sw
i
t
hi
na
f
actor o
f
1
.
10 o
f
o
p
t
i
ma
l
,t

h
e
p
er
f
ormance o
f
t
h
e
B
ID
M
AX
biddi
ng ru
l
e
f
or t
h
e
M
INI
-
M
AX
team o
bj
ect

i
ve
i
sw
i
t
hi
na
f
actor o
f1
.
4
4o
f
o
p
t
i
ma
l
,an
d
t
h
e
p
er
f
ormanc

e
of
t
h
eB
ID
A
VE
A
A
biddi
ng ru
l
e
f
or t
h
e
M
INI
A
VE
A
A
t
eam o
bj
ect
i
ve

i
sw
i
t
hi
na
f
acto
r
of
1
.
2
8o
f
o
p
t
i
ma
l.
W
ea
l
so compare
d
t
h
e per
f

ormance o
f
t
h
et
h
ree
biddi
ng ru
l
es aga
i
nst eac
h
o
t
h
er
f
or
l
arge mu
l
t
i
-ro
b
ot exp
l
orat

i
on tas
k
sw
i
t
h
one,
fi
ve or ten ro
b
ots an
d
100 targets. Ta
bl
e2s
h
ows t
h
e per
f
ormance o
f
eac
h biddi
ng ru
l
e. Aga
i
n, eac

h
biddi
ng ru
l
e resu
l
ts
i
na
b
etter per
f
ormance
f
or
i
ts team o
bj
ect
i
ve t
h
an t
h
eot
h
e
r
two
biddi

ng ru
l
es, w
i
t
h
t
h
e except
i
on o
f
t
h
e unavo
id
a
bl
et
i
es
.
T
he Generation of Bidding Rules for Auction-Based Robot Coordinatio
n
11
F
igure
2.
Pl

ayer/Stage screens
h
ots:
i
n
i
t
i
a
ll
ocat
i
ons (top
l
e
f
t) an
d
ro
b
ot tra
il
sw
i
t
h
t
he
B
ID

S
UM
(top r
i
g
h
t) [
S
UM
=
182.50,
M
AX
=113.36 , A
VE
A
A
=
48.
6
1], B
ID
M
AX
(
b
ottom
l
e
f

t
)
[S
UM
=
218
.
12
,
M
AX
=93.87 , A
VE
A
A
=
4
6
.01], and
B
ID
A
VE
A
A
(b
ottom r
i
g
h

t) [
S
UM
=2
6
9.27
,
M
AX
=109.39 , A
VE
A
A
=
45.15] bidding rules.
5.2 Unknown Environments
W
e compare
d
t
h
e per
f
ormance o
f
t
h
et
h
ree

biddi
ng ru
l
es aga
i
nst eac
h
ot
h
e
r
f
or t
h
e same
l
arge mu
l
t
i
-ro
b
ot exp
l
orat
i
on tas
k
sas
i

nt
h
e prev
i
ous sect
i
on
b
ut
in
i
n
i
t
i
a
ll
y comp
l
ete
l
yun
k
nown env
i
ronments. In t
hi
s case, we mappe
d
our env

i-
r
onments onto four-connected uniform grids of size
51
×
5
1 and computed all
c
osts
b
etween
l
ocat
i
ons as t
h
es
h
ortest
di
stances on t
h
egr
id
.T
h
ese gr
id
s wer
e

al
so use
d
to s
i
mu
l
ate t
h
e movement o
f
t
h
ero
b
ots
i
n a coarse an
d
no
i
se-
f
ree
s
i
mu
l
at
i

on. (We cou
ld
not use e
i
g
h
t-connecte
d
gr
id
s
b
ecause
di
agona
l
move
-
ments are
l
onger t
h
an
h
or
i
zonta
l
an
d

vert
i
ca
l
ones, an
d
t
h
es
i
mu
l
at
i
on step
s
t
h
us wou
ld
nee
d
to
b
e muc
h
sma
ll
er t
h

an mov
i
ng
f
rom ce
ll
to ce
ll
.) T
h
ero
b
ot
s
sense a
ll bl
oc
k
ages
i
nt
h
e
i
r
i
mme
di
ate
f

our-ce
ll
ne
i
g
hb
or
h
oo
d
.Ta
bl
e3s
h
ow
s
12
T
ove
y
, et al.
T
able
1
.
P
er
f
ormance o
f biddi

ng ru
l
es aga
i
nst opt
i
ma
li
n
k
nown env
i
ronments
.
R
o
b
ots B
iddi
ng
U
nc
l
ustere
d
Cl
ustere
d
Ru
l

e
S
UM
M
AX
A
VE
AA
S
UM
M
AX
A
VE
AA
1B
ID
S
UM
1
99.9
51
99.95
103
.
08
1
4
3
.69 14

3
.6
9
7
8
.
65
1B
ID
M
AX
199.9
51
99.95
103
.
08
1
4
3
.69 14
3
.6
9
7
8
.
65
1B
ID

A
VE
A
A
214
.
93 214
.
93
98.66
155
.
50
1
55
.
50
6
3
.1
2
1
O
PTIMAL
1
99
.
9
51
99

.
9
5
9
8.3
7
1
43.
69
143.
69 6
3.1
2
2B
ID
S
UM
19
3
.5
0
168.50 7
9
.2
1
13
4.1
8
9
7.17

6
2.4
7
2B
ID
M
AX
2
1
9
.1
5
1
25
.84
6
1.3
9
144
.
84
90.
1
0
5
7.
38
2B
ID
A

VE
A
A
2
1
9
.16 128.4
5
59.
1
2
1
57.2
9
100.5
6
4
9.
15
2O
PTIMAL
18
9
.15 10
9
.34 55.4
5
13
2.
06 85

.
86
47.
63
T
able
2
.
P
er
f
ormance o
f biddi
ng ru
l
es aga
i
nst eac
h
ot
h
er
i
n
k
nown env
i
ronments
.
R

o
b
ots B
iddi
n
g
U
nc
l
ustere
d
Cl
ustere
d
Ru
l
e
S
UM
M
AX
A
VE
AA
S
UM
M
AX
A
VE

A
A
1B
ID
S
UM
5
54
.
4
0
554
.
4
0
281
.
11
43
7.25 4
3
7.2
5
212
.
81
1B
ID
M
AX

5
54
.
4
0
554
.
4
0
281
.
11
43
7.25 4
3
7.2
5
212
.
81
1B
ID
A
VE
AA
6
11.
50 6
11.
50

2
4
3
.
30
53
2.4
653
2.4
6
169.
2
0
5B
ID
S
UM
4
8
3
.8
9
210
.
30 80
.7
4
3
74.
33

1
86.50 66.
94
5B
ID
M
AX
5
4
8
.4
0
13
0.4
1
58
.7
0
450
.7
2
1
12
.
1
8
50
.
50
5B

ID
A
VE
AA
60
1.2
8
14
6
.1
8
5
5
.
1
9
5
00.05 132.
98
42
.
4
1
10
B
ID
S
UM
43
5.

30
136.70 45.8
9
3
18.5
2
10
2.1
535
.1
4
10 B
ID
M
AX
5
36.
90
7
7
.95
31
.
39
402
.
30
6
3
.8

9
2
5
.
88
10 B
ID
A
VE
A
A
56
4.7
388
.2
3
3
0.0
4
43
7.2
3
71.
52
22
.02
t
h
e per
f

ormance o
f
eac
h biddi
ng ru
l
e. Aga
i
n, eac
h biddi
ng ru
l
e resu
l
ts
i
n
a
b
etter per
f
ormance
f
or
i
ts team o
bj
ect
i
ve t

h
an t
h
eot
h
er two
biddi
ng ru
l
es, w
i
t
h
t
h
e except
i
on o
f
t
h
e unavo
id
a
bl
et
i
es an
d
two ot

h
er except
i
ons. T
h
e averag
e
num
b
er o
f
auct
i
ons
i
s2
8
.
3
7
wi
t
h
a max
i
mum o
f8
2 auct
i
ons

i
n one case. I
n
g
enera
l
,t
h
e num
b
er o
f
auct
i
ons
i
ncreases w
i
t
h
t
h
e num
b
er o
f
ro
b
ots. Note t
h

a
t
t
h
e
diff
erence
i
n per
f
ormance
b
etween
k
nown an
d
un
k
nown env
i
ronments
is
a
t most a
f
actor o
f
t
h
ree. It

i
s remar
k
a
bl
et
h
at our auct
i
on-
b
ase
d
coor
di
nat
i
o
n
system manages to ac
hi
eve suc
h
a goo
d
per
f
ormance
f
or a

ll
team o
bj
ect
i
ve
s
s
i
nce t
h
ere
h
as to
b
e some per
f
ormance
d
egra
d
at
i
on g
i
ven t
h
at we sw
i
tc

h
e
d
b
ot
hf
rom
k
nown to un
k
nown env
i
ronments an
df
rom e
i
g
h
t-connecte
d
to
f
our
-
c
onnecte
dg
r
id
s

.
6
. Conclusions and Future Work
In t
hi
s paper, we
d
escr
ib
e
d
an auct
i
on-
b
ase
d
coor
di
nat
i
on system an
d
t
h
e
n
p
ropose
d

a systemat
i
c met
h
o
df
or
d
er
i
v
i
ng appropr
i
ate
biddi
ng ru
l
es
f
or g
i
ve
n
T
he Generation of Bidding Rules for Auction-Based Robot Coordinatio
n
1
3
T

able
3
.
P
er
f
ormance o
f biddi
ng ru
l
es aga
i
nst eac
h
ot
h
er
i
nun
k
nown env
i
ronments
.
Ro
b
ots B
iddi
n
g

U
nc
l
ustere
d
Cl
ustere
d
R
u
l
e
S
UM
M
AX
A
VE
AA
S
UM
M
AX
A
VE
AA
1B
ID
S
UM

1459.90 1459.90 81
3
.4
0
1
1
3
9.20 11
3
9.2
0
6
72.1
4
1B
ID
M
AX
1459.90 1459.90 81
3
.4
0
1
1
3
9.20 11
3
9.2
0
6

72.1
4
1B
ID
A
VE
A
A
1
588
.
50
1
588
.
50 8
2
6
.
82
1
1
6
4.4
0
11
6
4.4
0
46

3
.1
4
5B
ID
S
UM
9
4
3
.6
0
5
86.
9
0 223.4
7
7
71
.
4
0
4
32.
9
01
66
.
60
5B

ID
M
AX
9
7
9
.
00
23
8.1
0
98
.
48
8
11.30 216.
9
0 86.5
8
5B
ID
A
VE
A
A
992
.
10 240
.
10

90.
5
4
838
.
30
2
14.10 79.
36
10
B
ID
S
UM
799.
5
0
3
12.20
9
3.
69
596.10
2
23.20 63.
95
1
0
B
ID

M
AX
885
.4
0
12
3
.6
0
48
.
43
6
77.
80
1
1
0.60
3
7.
92
1
0B
ID
A
VE
A
A
8
7

1
.
80 133
.
00
4
5
.
1
9
69
7.80 121.5
0
3
5.4
3
team o
bj
ect
i
ves. We t
h
en
d
emonstrate
di
t
b
y
d

er
i
v
i
ng
biddi
ng ru
l
es
f
or t
h
re
e
p
oss
ibl
e team o
bj
ect
i
ves o
f
amu
l
t
i
-ro
b
ot exp

l
orat
i
on tas
k
,t
h
at re
l
ate to m
i
n
i-
mi
z
i
ng t
h
e tota
l
energy consumpt
i
on, tas
k
-comp
l
et
i
on t
i

me, an
d
average target
-
vi
s
i
tt
i
me. (T
h
e
l
ast team o
bj
ect
i
ve
h
a
d
not
b
een use
db
e
f
ore
b
ut we s

h
owe
dit
to
b
e appropr
i
ate
f
or searc
h
-an
d
-rescue tas
k
s.) F
i
na
ll
y, we
d
emonstrate
d
exper
-
i
menta
ll
yt
h

at t
h
e
d
er
i
ve
d biddi
ng ru
l
es
i
n
d
ee
d
ex
hibi
t goo
d
per
f
ormance
f
o
r
t
h
e
i

r respect
i
ve team o
bj
ect
i
ves an
d
compare
f
avora
bl
ytot
h
e opt
i
ma
l
per
f
or
-
m
ance. In t
h
e
f
uture, we
i
nten

d
to a
d
apt our met
h
o
d
o
l
ogy to ot
h
er mu
l
t
i
-ro
b
o
t
c
oor
di
nat
i
on tas
k
s. For examp
l
e, we
i

nten
d
to stu
d
ymu
l
t
i
-ro
b
ot coor
di
nat
i
o
n
w
i
t
h
auct
i
on-
b
ase
d
coor
di
nat
i

on systems
i
nt
h
e presence o
f
a
ddi
t
i
ona
l
con
-
stra
i
nts, suc
h
as compat
ibili
ty constra
i
nts w
hi
c
hdi
ctate t
h
at certa
i

n targets ca
n
o
n
ly b
ev
i
s
i
te
dby
certa
i
nro
b
ots
.
R
eferences
Ber
h
au
l
t, M., Huang, H., Kes
ki
noca
k
, P., Koen
i
g, S., E

l
mag
h
ra
b
y, W., Gr
iffi
n, P., an
d
K
l
eywegt
,
A
. (2003). Robot exploration with combinatorial auctions. I
n
Proceedings of the Interna
-
tional Conference on Intelligent Robots and System
s
, pages 1957–1962
.
Dias, M. and Stentz, A. (2000). A free market architecture for distributed control of a multirobo
t
system. In
P
roceedings of the International Conference on Intelligent Autonomous System
s
,
p

ages 115–122
.
Dias, M. and Stentz, A. (2002). Enhanced negotiation and opportunistic optimization for market
-
b
ased multirobot coordination. Technical Report CMU-RI-TR-02-18, Robotics Institute
,
Carnegie Mellon University, Pittsburgh (Pennsylvania)
.
Gerkey, B. and Matari
´
c, M. (2002). Sold!: Auction methods for multi-robot coordination.
´
I
EE
E
Transactions on Robotics and Automatio
n
,
18
(
5
)
:758–768
.
Gerkey, B., Vaughan, R., Stoy, K., Howard, A., Sukhatme, G., and Matar
i
´
c, M. (2003). Most
´

v
aluable player: A robot device server for distributed control. I
n
Proceedings o
f
the Interna
-
tional Con
f
erence on Intelligent Robots and System
s
,pa
g
es 1226–1231
.
14
T
ove
y
, et al.
G
oldberg, D., Circirello, V., Dias, M., Simmons, R., Smith, S., and Stentz, A. (2003). Market
-
b
ased multi-robot planning in a distributed layered architecture. I
n
P
roceedings from th
e
I

nternational Workshop on Multi-Robot System
s
, pages 27–38
.
L
agoudakis, M., Berhault, M., Keskinocak, P., Koenig, S., and Kleywegt, A. (2004). Simpl
e
a
uctions with performance guarantees for multi-robot task allocation. I
n
P
roceedings of th
e
I
nternational Conference on Intelligent Robots and System
s
.
R
abideau, G., Estlin, T., Chien, S., and Barrett, A. (2000). A comparison of coordinated plan
-
n
ing methods for cooperating rovers. I
n
Proceedings of the International Conference o
n
A
utonomous Agent
s
,
pages 100–101

.
T
hayer, S., Digney, B., Dias, M., Stentz, A., Nabbe, B., and Hebert, M. (2000). Distribute
d
r
obotic mapping of extreme environments. In Proceedings o
f
SPIE: Mobile Robots XV an
d
Telemanipulator and Telepresence Technolo
g
ies VI
I
, volume 4195, pa
g
es 84–95
.
Z
lot, R., Stentz, A., Dias, M., and Tha
y
er, S. (2002). Multi-robot exploration controlled b
ya
m
arket econom
y
.I
n
Proceedings o
f
the International Con

f
erence on Robotics and Automa
-
t
io
n
,
pa
g
es 3016–3023
.
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