Multi-Robot Systems From Swarms to Intelligent Automata - Parker et al (Eds) Part 7 pptx

1
2
0
P
arker
,
et al.
c
a
p
a
bili
t
i
es nee
d
e
d
to accom
pli
s
h
eac
h
ro
l
eorsu
b
tas
k
.T

h
ero
b
ot team mem
-
b
ers can t
h
en autonomous
l
yse
l
ect act
i
ons us
i
ng any o
f
a num
b
er o
f
commo
n
a
pproac
h
es to mu
l
t

i
-ro
b
ot tas
k
a
ll
ocat
i
on (see (Ger
k
ey an
d
Matar
i
c, 2004)
f
o
r
a
compar
i
son o
f
var
i
ous tas
k
a
ll

ocat
i
on approac
h
es),
b
ase
d
upon t
h
e
i
rsu
i
t
-
abili
ty
f
or t
h
ero
l
eorsu
b
tas
k
,aswe
ll
as t

h
e current state o
f
t
h
emu
l
t
i
-ro
b
o
t
system. T
h
es
h
ortcom
i
ng o
f
t
hi
s approac
hi
st
h
at t
h
e

d
es
i
gner
h
as to cons
id
e
r
i
na
d
vance a
ll
o
f
t
h
e poss
ibl
e com
bi
nat
i
ons o
f
ro
b
ot capa
bili

t
i
es t
h
at m
i
g
h
t
be
p
resent on a mu
l
t
i
-ro
b
ot team per
f
orm
i
ngag
i
ven tas
k
,an
d
to
d
es

i
gn coopera
-
t
i
ve
b
e
h
av
i
ors
i
n
li
g
h
to
f
t
hi
sa
d
vance
k
now
l
e
d
ge

.
H
owever,as
d
escr
ib
e
di
n(Par
k
er,2003), t
h
e spec
ifi
cro
b
ot capa
bili
t
i
espresen
t
o
n a team can
h
ave a s
i
gn
ifi
cant

i
mpact on t
h
e approac
h
a
h
uman
d
es
i
gne
r
wou
ld
c
h
oose
f
or t
h
e team so
l
ut
i
on. T
h
e examp
l
eg

i
ven
i
n(Par
k
er, 2003)
is
t
h
at o
fd
ep
l
o
yi
n
g
amo
bil
e sensor networ
k
,
i
nw
hi
c
h
cooperat
i
ve so

l
ut
i
ons
f
o
r
t
h
e same tas
k
cou
ld i
nvo
l
ve potent
i
a
l
-
fi
e
ld
-
b
ase
ddi
spers
i
on, marsup

i
a
ld
e
li
v
-
e
r
y
, or ass
i
st
i
ve nav
ig
at
i
on,
d
epen
di
n
g
on t
h
e capa
bili
t
i

es o
f
t
h
e team mem
b
ers
.
O
ur research is aimed at overcomin
g
these challen
g
es b
y
desi
g
nin
g
flexi
-
ble sensor-sharin
g
mechanisms within robot behavior code that do not requir
e
task-specific, pre-defined cooperative control solutions, and that translate di
-
r
ectl
y

into executable code on the robot team members. Some related wor
k
in sensor-sharin
g
has led to the development of application-specific solution
s
that allo
w
a robot team member to ser
v
e as a remote
v
ie
w
er of the actions o
f
o
ther teammates, providin
g
feedback on the task status to its teammates. I
n
p
articular, this has been illustrated b
y
several researchers in the multi-robo
t
box pushin
g
and material handlin
g

domain (Gerke
y
and Mataric, 2002, Adam
s
e
t al., 1995, S
p
letzer et al., 2001, Donald et al., 1997), in which one or mor
e
r
obots push an ob
j
ect while a remote robot or camera provides a perspectiv
e
o
f the task status from a stand-off position. Our work is aimed at
g
eneratin
g
these t
y
pes of solutions automaticall
y
, to enable robot teams to coalesce int
o
sensor-sharin
g
strate
g
ies that are not pre-defined in advance.

Our approach, which we call ASyMTRe (A
utomate
d
S
y
n
t
h
es
i
so
f
M
ul
t
i-
r
o
b
ot T
ask solutions through software Re
c
on
fi
gurat
i
on, pronounce
d
“Asym
-

metry”),
i
s
b
ase
d
on a com
bi
nat
i
on o
f
sc
h
ema t
h
eory (Ar
ki
neta
l
., 1993) an
d
i
nsp
i
rat
i
on
f
rom t

h
et
h
eory o
fi
n
f
ormat
i
on
i
nvar
i
ants (Dona
ld
et a
l
., 1993). T
he
b
as
i
c
b
u
ildi
ng
bl
oc
k

so
f
our approac
h
are co
ll
ect
i
ons o
f
p
erce
p
tua
l
sc
h
emas
,
motor
s
c
h
ema
s
,
an
d
as
i

mp
l
e new component we
i
ntro
d
uce, ca
ll
e
d
c
ommun
i-
c
ation
s
c
h
ema
s
.T
h
ese sc
h
emas are assume
d
to
b
e supp
li

e
d
to t
h
ero
b
ots w
h
en
t
h
ey are
b
roug
h
t toget
h
er to
f
orm a team, an
d
represent
b
ase
li
ne capa
bili
t
i
es o

f
r
o
b
ot team mem
b
ers. T
h
e ASyMTRe system con
fi
gures a so
l
ut
i
on
b
yc
h
oos
i
n
g
f
rom
diff
erent ways o
f
com
bi
n

i
ng t
h
ese
b
u
ildi
ng
bl
oc
k
s
i
nto a team
i
ng so
l
u
-
t
i
on, pre
f
err
i
ng t
h
eso
l
ut

i
on w
i
t
h
t
h
e
hi
g
h
est ut
ili
ty. D
iff
erent com
bi
nat
i
ons o
f
b
u
ildi
n
gbl
oc
k
s can
yi

e
ld
ver
y diff
erent t
y
pes o
f
cooperat
i
ve so
l
ut
i
ons to t
he
same tas
k.
Enablin
g
Autonomous Sensor-Sharin
g
121
In a companion paper (Tang and Parker, 200
5
), we have described an auto
-
m
ate
d

reason
i
ng system
f
or generat
i
ng so
l
ut
i
ons
b
ase
d
on t
h
esc
h
ema
b
u
ild-
i
ng
bl
oc
k
s. In t
hi
s paper, we

f
ocus on
ill
ustrat
i
ng a proo
f
-o
f
-pr
i
nc
i
p
l
e tas
k
t
h
at s
h
ows
h
ow
diff
erent
i
nterconnect
i
ons o

f
t
h
ese sc
h
ema
b
u
ildi
ng
bl
oc
k
sca
n
yi
e
ld f
un
d
amenta
ll
y
diff
erent so
l
ut
i
on strateg
i

es
f
or sensor-s
h
ar
i
ng
i
nt
i
g
h
t
l
y
-
c
oup
l
e
d
tas
k
s. Sect
i
on 2 out
li
nes our
b
as

i
c approac
h
. Sect
i
on 3
d
e
fi
nes
a
s
i
mp
l
e proo
f
o
f
pr
i
nc
i
p
l
e tas
k
t
h
at

ill
ustrates t
h
ea
bili
ty to
f
ormu
l
ate s
i
gn
ifi-
c
ant
l
y
diff
erent team
i
ng so
l
ut
i
ons
b
ase
d
on t
h

esc
h
ema representat
i
on. Sec
-
t
i
on 4 presents t
h
ep
h
ys
i
ca
l
ro
b
ot resu
l
ts o
f
t
hi
s proo
f
-o
f
-pr
i

nc
i
p
l
e tas
k
.W
e
p
resent concluding remarks and future work in Section
5.
2.
App
roach
O
ur ASyMTRe approac
h
to sensor-s
h
ar
i
ng
i
nt
i
g
h
t
l
y-coup

l
e
d
cooperat
i
v
e
tas
k
s
i
nc
l
u
d
es a
f
orma
li
sm t
h
at ma
p
senv
i
ronmenta
l
,
p
erce

p
tua
l
,an
d
moto
r
c
ontro
l
sc
h
emas to t
h
e requ
i
re
dfl
ow o
fi
n
f
ormat
i
on t
h
roug
h
t
h

emu
l
t
i
-ro
b
o
t
system, as we
ll
as an automate
d
reason
i
ng system t
h
at
d
er
i
ves t
h
e
hi
g
h
est
-
ut
ili

ty so
l
ut
i
on o
f
sc
h
ema con
fi
gurat
i
ons across ro
b
ots. T
hi
s approac
h
ena
bl
e
s
r
o
b
ots to reason a
b
out
h
ow to so

l
ve a tas
kb
ase
d
upon t
h
e
f
un
d
amenta
li
n
f
orma
-
t
i
on nee
d
e
d
to accomp
li
s
h
t
h
eo

bj
ect
i
ves. T
h
e
f
un
d
amenta
li
n
f
ormat
i
on w
ill be
t
h
e same regar
dl
ess o
f
t
h
e way t
h
at
h
eterogeneous team mem

b
ers may o
b
ta
in
o
r generate
i
t. T
h
us, ro
b
ots can co
ll
a
b
orate to
d
e
fi
ne
diff
erent tas
k
strateg
i
es
in
terms o
f

t
h
e requ
i
re
dfl
ow o
fi
n
f
ormat
i
on
i
nt
h
e system. Eac
h
ro
b
ot can
k
no
w
a
b
out
i
ts own sens
i

ng, e
ff
ector, an
db
e
h
av
i
or capa
bili
t
i
es an
d
can co
ll
a
b
orat
e
w
i
t
h
ot
h
ers to
fi
n
d

t
h
er
i
g
h
t com
bi
nat
i
on o
f
act
i
ons t
h
at generate t
h
e requ
i
re
d
fl
ow o
fi
n
f
ormat
i
on to so

l
ve t
h
e tas
k
.T
h
ee
ff
ect
i
st
h
at t
h
ero
b
ot team mem
b
er
s
i
nterconnect t
h
e appropr
i
ate sc
h
emas on eac
h

ro
b
ot, an
d
across ro
b
ots, to
f
or
m
c
oa
li
t
i
ons (S
h
e
h
or
y
, 1998) to so
l
ve a
gi
ven tas
k.
2.1 Formalism of A
pp
roach

W
e
f
orma
li
ze t
h
e representat
i
on o
f
t
h
e
b
as
i
c
b
u
ildi
ng
bl
oc
k
s
i
nt
h
emu

l
t
i-
r
o
b
ot system as
f
o
ll
ows:
A
c
l
ass o
f
In
f
ormation
,d
enote
d
F
=
{
F
1
FF
,
F

2
FF
,
}
.
En
v
ironmenta
lS
ensor
s
,d
enote
d
ES
=
{
ES
1
,
E
S
2
,
}
.T
h
e
i
n

p
ut t
o
ES
i
i
s a spec
ifi
cp
h
ys
i
ca
l
sensor s
i
gna
l
.T
h
e output
i
s
d
enote
d
a
s
O
ES

i
∈
F
.
P
erceptua
l
Sc
h
ema
s
,d
enote
d
P
S
=
{
P
S
1
,
PS
2
,
}
.In
p
uts to
PS

i
are
d
e-
n
ote
d
I
PS
i
k
I
∈
F
.T
h
e
p
erce
p
tua
l
sc
h
ema
i
n
p
uts can come
f

rom e
i
t
h
er t
he
o
ut
p
uts o
f
commun
i
cat
i
on sc
h
emas or env
i
ronmenta
l
sensors. T
h
e out
-
p
ut
i
s
d

enote
d
O
PS
i
∈
F
.
122
P
arker
,
et al.
C
ommunication
S
c
h
emas
,d
enote
d
CS
=
{
CS
1
,
CS
2

,
}
.
T
h
e
i
n
p
uts
to
CS
i
a
re
d
enote
d
I
CS
i
k
I
∈
F
.
T
h
e
i

nputs or
i
g
i
nate
f
rom t
h
e outputs o
f
p
erce
p
tua
l
sc
h
emas or commun
i
cat
i
on sc
h
emas. T
h
e out
p
ut
i
s

d
enote
d
O
CS
i
∈
F
.
M
otor
S
c
h
ema
s
,d
enote
d
M
S
=
{
M
S
1
,
MS
2
,

}
.
T
h
e
i
n
p
uts t
o
M
S
i
are
d
enote
d
I
MS
I
I
i
k
I
I
∈
F
,
an
d

come
f
rom t
h
e out
p
uts o
fp
erce
p
tua
l
sc
h
ema
s
o
r commun
i
cat
i
on sc
h
emas. T
h
e output
i
s
d
enote

d
O
MS
i
∈
F
,
an
di
s
c
onnecte
d
to t
h
ero
b
ot e
ff
ector contro
lp
rocess
.
A
set o
f
n
r
o
b

ots
,d
enote
d
R
=
{
R
1
,
R
2
, ,
R
n
}
.
Eac
h
ro
b
ot
i
s
d
escr
ib
e
d
b

yt
h
e set o
f
sc
h
emas ava
il
a
bl
etot
h
at ro
b
ot:
R
i
=
{
E
S
i
,
PS
i
,
CS
i
,
MS

i
}
,
wh
ere E
S
i
i
st
h
e set o
f
en
vi
ronmenta
l
sensors a
v
a
il
a
bl
eto
R
i
,
an
d
PS
i

,
CS
i
,
MS
i
a
re t
h
e sets o
fp
erce
p
tua
l
, commun
i
cat
i
on, an
d
motor sc
h
ema
s
a
v
a
il
a

bl
eto
R
i
,
respect
i
ve
l
y.
Ta
sk
=
{
MS
1
,
MS
2
,
}
,
w
hi
c
hi
st
h
e set o
f

motor sc
h
emas t
h
at must
be
a
ct
i
vate
d
to accom
pli
s
h
t
h
e tas
k.
A
va
lid
con
fi
gurat
i
on o
f
sc
h

emas
di
str
ib
ute
d
across t
h
ero
b
ot team
h
as a
ll
o
f
t
h
e
i
nputs an
d
outputs o
f
t
h
esc
h
emas
in

T
c
onnecte
d
to appropr
i
ate sources
,
suc
h
t
h
at t
h
e
f
o
ll
ow
i
ng
i
s true
:
∀
k
∃
i
CO
NNE

C
T
(
O
S
i
,
I
S
j
k
I
)
⇔
O
S
i
=
I
S
j
k
I
I
,
w
h
er
e
S

i
a
n
d
S
j
a
re types o
f
sc
h
emas. T
hi
s notat
i
on means t
h
at
f
or a
ll
t
h
e
i
nputs o
f
S
j
,

t
h
ere ex
i
sts some
S
i
w
h
ose out
p
ut
i
s connecte
d
to one o
f
t
h
ere
q
u
i
re
di
n
p
uts
.
In(Tang and Parker, 200

5
), we define quality metrics to enable the system t
o
c
ompare a
l
ternat
i
ve so
l
ut
i
ons an
d
se
l
ect t
h
e
hi
g
h
est-qua
li
ty so
l
ut
i
on. Once t
he

r
eason
i
ng system
h
as generate
d
t
h
e recommen
d
e
d
so
l
ut
i
on, eac
h
ro
b
ot act
i-
v
ates t
h
e requ
i
re
d

sc
h
ema
i
nterconnect
i
ons
i
nso
f
tware
.
3
. Proof-of-Princi
p
le Task Im
p
lementation
To s
h
ow t
h
at
i
t
i
s poss
ibl
eto
d

e
fi
ne
b
as
i
csc
h
ema
b
u
ildi
ng
bl
oc
k
s to ena
ble
di
str
ib
ute
d
sensor s
h
ar
i
ng an
dfl
ex

ibl
eso
l
ut
i
on approac
h
es to a t
i
g
h
t
l
y-coup
l
e
d
c
ooperat
i
ve tas
k
,we
ill
ustrate t
h
e approac
hi
n a very s
i

mp
l
e proo
f
o
f
pr
i
nc
i
p
le
tas
k
.T
hi
s tas
k,
w
hi
c
h
we ca
ll
t
he
trans
p
ortation tas
k

, requ
i
res eac
h
ro
b
o
t
o
nt
h
e team to nav
i
gate to
i
ts pre-ass
i
gne
d
,un
i
que goa
l
po
i
nt. In or
d
er
f
or

a
r
o
b
ot to reac
hi
ts ass
i
gne
d
goa
l
,
i
t nee
d
sto
k
now
i
ts current pos
i
t
i
on re
l
at
i
v
e

t
o
i
ts goa
l
pos
i
t
i
on so t
h
at
i
t can move
i
nt
h
e proper
di
rect
i
on. In some cases
,
a
ro
b
ot may
b
ea
bl

e to sense
i
ts current pos
i
t
i
on us
i
ng
i
ts own sensors. In
o
t
h
er cases, t
h
ero
b
ot may not
h
ave enoug
hi
n
f
ormat
i
on to
d
eterm
i

ne
i
ts curren
t
p
os
i
t
i
on. In t
h
e
l
atter case, ot
h
er more capa
bl
ero
b
ots can
h
e
l
p
b
ys
h
ar
i
n

g
s
ensor
i
n
f
ormat
i
on w
i
t
h
t
h
e
l
ess capa
bl
ero
b
ot
.
A
ss
h
own
i
nTa
bl
e1,t

h
eenv
i
ronmenta
l
sensors ava
il
a
bl
e
i
nt
hi
s case stu
dy
a
re a
l
aser scanner, a camera, an
d
D
iff
erent
i
a
l
GPS. A ro
b
ot can use a
l

ase
r
Enablin
g
Autonomous Sensor-Sharin
g
1
2
3
T
able
1
.
E
nvironmental Sensors (ES) and Robot Types for proof-of-principle task
.
E
n
vi
ronmenta
lS
ensor
s
R
o
b
ot Type
s
N
am

e
D
escr
i
pt
i
o
n
I
n
f
o. Typ
e
N
am
e
Av
a
il
a
bl
e
S
ensor
s
ES
1
Lase
r
l

a
s
er
s
canne
r
R
1
Lase
r
E
S
2
C
amer
a
c
c
d
R
2
C
amer
a
E
S
3
D
G
P

S
d
gp
s
R
3
D
G
P
S
R
4
L
aser an
dC
amer
a
R
5
L
aser an
d
D
G
P
S
R
6
C
amera an

d
D
G
P
S
R
7
L
aser an
dC
amera an
d
D
G
P
S
R
8
—
T
able
2
.
P
erceptua
l
an
d
Commun
i

cat
i
ons Sc
h
emas
f
or proo
f
-o
f
-pr
i
nc
i
p
l
e tas
k.
Perceptual Schema
s
N
am
e
I
nput Info. Type
O
utput Info. Type
PS
1
l

aserrange
OR
d
gps
OR
c
urr-g
l
o
b
a
l
-pos
(
self
)
f
f
curr-g
l
o
b
a
l
-pos
(
self
)
f
f

O
R
(
curr-re
l
-pos
(
other
k
r
)
AND
c
urr-g
l
o
b
a
l
-po
s
(
other
k
r
))
PS
2
—
curr-g

l
o
b
a
l
-goa
l
(
self
)
f
f
PS
3
(
curr-g
l
o
b
a
l
-po
s
(
self
)
AND
f
f
c

urr-re
l
-pos
(
other
k
r
))
curr-g
l
o
b
a
l
-po
s
(
other
k
r
)
P
S
4
l
aserrange
o
r
c
c

d
c
urr-re
l
-pos
(
other
k
r
)
PS
5
curr-g
l
o
b
a
l
-po
s
(
other
)
c
urr-g
l
o
b
a
l

-po
s
(
other
)
C
ommunication
S
chema
s
N
am
e
I
nput Info. Type
O
utput Info. Type
CS
1
curr-g
l
o
b
a
l
-po
s
(
self
)

f
f
c
urr-g
l
o
b
a
l
-po
s
(
other
k
r
)
CS
2
curr-g
l
o
b
a
l
-po
s
(
other
k
r

)
curr-g
l
o
b
a
l
-po
s
(
self
)
f
f
scanner w
i
t
h
an env
i
ronmenta
l
ma
p
to
l
oca
li
ze
i

tse
lf
an
d
ca
l
cu
l
ate
i
ts curren
t
g
l
o
b
a
l
pos
i
t
i
on. A ro
b
ot’s camera can
b
e use
d
to
d

etect t
h
e pos
i
t
i
on o
f
anot
h
e
r
r
o
b
ot re
l
at
iv
eto
i
tse
lf
.T
h
eD
G
P
S
sensor can

b
e use
d
out
d
oors
f
or
l
oca
li
zat
i
o
n
an
d
to
d
etect t
h
ero
b
ot’s current g
l
o
b
a
l
pos

i
t
i
on. Base
d
upon t
h
ese env
i
ron
-
m
enta
l
sensors, t
h
ere are e
i
g
h
t poss
ibl
e com
bi
nat
i
ons o
f
ro
b

ots, as s
h
own
in
Ta
bl
e1. Int
hi
s paper, we
f
ocus on t
h
ree types o
f
ro
b
ots
–
R
8
:
aro
b
ot t
h
a
t
possesses no sensors
;
R

2
:
ro
b
ot t
h
at possesses on
l
y a camera; an
d
R
4
:
aro
b
ot
t
h
at possesses a camera an
d
a
l
aser ranger scanner (
b
ut no DGPS)
.
For t
hi
s tas
k

,we
d
e
fi
ne
fi
ve perceptua
l
sc
h
emas, as s
h
own
i
nTa
bl
e2
.
P
S
1
c
a
l
cu
l
ates a ro
b
ot’s current g
l

o
b
a
l
pos
i
t
i
on. W
i
t
h
t
h
e sensors we
h
ave
d
e
fi
ne
d,
t
hi
s pos
i
t
i
on cou
ld b

e
d
eterm
i
ne
d
e
i
t
h
er
b
yus
i
ng
i
nput
d
ata
f
rom a
l
aser scan
-
n
er com
bi
ne
d
w

i
t
h
an env
i
ronmenta
l
map,
f
rom DGPS, or
f
rom commun
i
ca
-
t
i
on sc
h
emas supp
l
y
i
ng s
i
m
il
ar
d
ata. For an examp

l
eo
f
t
hi
s
l
atter case, a ro
b
o
t
124
P
arker
,
et al.
c
an ca
l
cu
l
ate
i
ts current g
l
o
b
a
l
pos

i
t
i
on
b
y
k
now
i
ng t
h
eg
l
o
b
a
l
pos
i
t
i
on o
f
an
-
o
t
h
er ro
b

ot, com
bi
ne
d
w
i
t
hi
ts own pos
i
t
i
on re
l
at
i
ve to t
h
eg
l
o
b
a
ll
y pos
i
t
i
one
d

r
o
b
ot.
PS
2
o
utputs a ro
b
ot’s goa
l
pos
i
t
i
on,
b
ase
d
on t
h
e tas
kd
e
fi
n
i
t
i
on prov

id
e
d
b
yt
h
e user.
PS
3
c
a
l
cu
l
ates t
h
e current g
l
o
b
a
l
pos
i
t
i
on o
f
a remote ro
b

ot
b
ase
d
o
ntwo
i
n
p
uts – t
h
e
p
os
i
t
i
on o
f
t
h
e remote ro
b
ot re
l
at
i
ve to
i
tse

lf
an
di
ts ow
n
c
urrent g
l
o
b
a
l
pos
i
t
i
on
.
PS
4
c
a
l
cu
l
ates t
h
e
p
os

i
t
i
on o
f
anot
h
er ro
b
ot re
l
at
i
v
e
to
i
tse
lf
. Base
d
on t
h
e
d
e
fi
ne
d
sensors

,
t
hi
sca
l
cu
l
at
i
on cou
ld b
e
d
er
i
ve
df
ro
m
ei
t
h
er a
l
aser scanner or a camera
.
P
S
5
r

ece
i
ves
i
n
p
ut
f
rom anot
h
er ro
b
ot’
s
c
ommun
i
cat
i
on sc
h
ema
,
CS
1
,
w
hi
c
h

commun
i
cates t
h
e current
p
os
i
t
i
on o
f
t
h
a
t
o
t
h
er ro
b
ot.
C
ommun
i
cat
i
on sc
h
emas commun

i
cate
d
ata to anot
h
er ro
b
ot’s perceptua
l
sc
h
emas. As s
h
own
i
nTa
bl
e2
,
CS
1
c
ommun
i
cates a ro
b
ot’s current g
l
o
b

a
l
p
os
i
t
i
on to anot
h
er ro
b
ot, w
hil
e
CS
2
c
ommun
i
cates t
h
e current g
l
o
b
a
l
pos
i
t

i
o
n
of
a remote ro
b
ot t
h
at remote ro
b
ot. Motor sc
h
emas sen
d
contro
l
s
i
gna
l
stot
he
r
o
b
ot’s e
ff
ectors to ena
bl
et

h
ero
b
ot to accomp
li
s
h
t
h
e ass
i
gne
d
tas
k
.Int
his
c
ase stu
d
y, we
d
e
fi
ne on
l
y one motor sc
h
ema
,

M
S
,
w
hi
c
h
enco
d
es
a
g
o-to-
g
oa
l
b
e
h
av
i
or
.
T
h
e
i
nput
i
n

f
ormat
i
on requ
i
rements o
f
M
S
are
c
urr-
gl
o
b
a
l
-pos
(
self
) and
f
f
c
urr-
gl
o
b
a
l

-
g
oa
l
(
s
e
lf
). In this case, the motor schema’s output is derived based
f
f
o
nt
h
ero
b
ot’s current pos
i
t
i
on rece
i
ve
df
rom P
S
1
a
n
di

ts goa
l
pos
i
t
i
on rece
i
ve
d
f
rom
PS
2
.
F
i
gure 1 s
h
ows a
ll
t
h
eava
il
a
bl
esc
h
emas

f
or t
hi
s tas
k
an
dh
ow t
h
ey can
be
c
onnecte
d
to eac
h
ot
h
er,
b
ase
d
on t
h
e
i
n
f
ormat
i

on
l
a
b
e
li
ng. T
h
eso
lid
-
li
ne ar
-
r
ows go
i
ng
i
nto a sc
h
ema represent an “OR” con
di
t
i
on –
i
t
i
ssu

ffi
c
i
ent
f
or t
he
sc
h
ema to on
l
y
h
ave one o
f
t
h
e spec
ifi
e
di
nputs to pro
d
uce output. T
h
e
d
as
h
e

d-
li
ne arrows represent an “AND” con
di
t
i
on, mean
i
ng t
h
at t
h
esc
h
ema requ
i
re
s
a
ll
o
f
t
h
e
i
n
di
cate
di

nputs
f
or
i
ttoca
l
cu
l
ate an output. For examp
l
e
,
PS
1
can
p
ro
d
uce output w
i
t
hi
nput(s)
f
rom e
i
t
h
er E
S

1
(
com
bi
ne
d
w
i
t
h
t
h
eenv
i
ronmen
-
ta
l
Ma
p
),
ES
3
,
CS
j
2
(
R
j

’
s
CS
2
)
,or
(
PS
4
a
n
d
PS
5
).
4. Ph
y
sical Robot Ex
p
eriments
T
h
ese sc
h
ema were
i
m
pl
emente
d

on two P
i
oneer ro
b
ots e
q
u
ipp
e
d
w
i
t
ha
S
ICK
l
aser range scanner an
d
a Sony pan-t
il
t-zoom camera. Bot
h
ro
b
ots a
l
s
o
p

ossesse
d
aw
i
re
l
ess a
dh
oc networ
ki
ng capa
bili
ty, ena
bli
ng t
h
em to commu
-
n
i
cate w
i
t
h
eac
h
ot
h
er. Exper
i

ments were con
d
ucte
di
na
k
nown
i
n
d
oor en
-
vi
ronment us
i
ng a map generate
d
us
i
ng an autonomous
l
aser range mapp
i
n
g
al
gor
i
t
h

m. Laser-
b
ase
dl
oca
li
zat
i
on use
d
a stan
d
ar
d
Monte-Car
l
o Loca
li
zat
i
o
n
tec
h
n
i
que. T
h
eco
d

e
f
or t
h
e
i
mp
l
ementat
i
on o
f
P
S
4
ma
k
es use o
fp
r
i
or wor
k
b
y(Par
k
er et a
l
., 2004)
f

or per
f
orm
i
ng v
i
s
i
on-
b
ase
d
sens
i
ng o
f
t
h
ere
l
at
i
ve
p
os
i
t
i
on o
f

anot
h
er ro
b
ot. T
hi
s approac
h
ma
k
es use o
f
acy
li
n
d
r
i
ca
l
mar
k
e
r
d
es
i
gne
d
to prov

id
eaun
i
que ro
b
ot ID, as we
ll
as re
l
at
i
ve pos
i
t
i
on an
d
or
i
enta
-
Enablin
g
Autonomous Sensor-Sharin
g
1
2
5
F
igure

1.
Ill
ustrat
i
on o
f
connect
i
ons
b
et
w
een a
ll
a
v
a
il
a
bl
esc
h
emas
.
t
i
on
i
n
f

ormat
i
on su
i
ta
bl
e
f
orav
i
s
i
on-
b
ase
d
ana
l
ys
i
s. Us
i
ng t
h
ese two ro
b
ots,
t
h
ree var

i
at
i
ons on sensor ava
il
a
bili
ty were teste
d
to
ill
ustrate t
h
ea
bili
ty o
f
t
h
ese
b
u
ildi
ng
bl
oc
k
s to generate
f
un

d
amenta
ll
y
diff
erent cooperat
i
ve
b
e
h
av
-
i
ors o
f
t
h
e same tas
k
t
h
roug
h
sensor s
h
ar
i
ng. In t
h

ese exper
i
ments, t
h
e
d
es
i
re
d
i
nterconnect
i
ons o
f
sc
h
emas were
d
eve
l
ope
db
y
h
an
d
;
i
nsu

b
sequent wor
k,
we can now generate t
h
e requ
i
re
di
nterconnect
i
ons automat
i
ca
ll
yt
h
roug
h
ou
r
A
SyMTRe reasoning process (Tang and Parker, 200
5
)
.
V
ariation 1.
T
h

e
fi
rst
v
ar
i
at
i
on
i
sa
b
ase
li
ne case
i
n
whi
c
hb
ot
h
ro
b
ots are o
f
t
ype
R
4

, mean
i
ng t
h
at t
h
ey
h
ave
f
u
ll
use o
fb
ot
h
t
h
e
i
r
l
aser scanner an
d
a cam
-
e
ra. Eac
h
ro

b
ot
l
oca
li
zes
i
tse
lf
us
i
ng
i
ts
l
aser scanner an
d
map an
d
reac
h
e
s
i
ts own un
i
que goa
l
s
i

n
d
epen
d
ent
l
y. T
hi
s case
i
st
h
e most
id
ea
l
so
l
ut
i
on
b
u
t
o
n
l
ywor
k
s

if
t
h
e
b
ot
h
ro
b
ots possess
l
aser scanners an
d
maps. I
f
one o
f
t
h
e
r
o
b
ots
l
oses
i
ts
l
aser scanner, t

hi
sso
l
ut
i
on no
l
onger wor
k
s. F
i
gure 2 s
h
ow
s
t
h
esc
h
ema
i
nstant
i
ate
d
on t
h
ero
b
ots

f
or t
hi
svar
i
at
i
on
.
P
S
1
an
d
PS
2
are con-
n
ecte
d
t
o
MS
to supp
l
yt
h
e requ
i
re

di
nputs to t
he
g
o-to-
g
oa
l
b
e
h
a
vi
or. A
l
s
o
s
h
own
i
nF
i
gure 2 are snaps
h
ots o
f
t
h
ero

b
ots per
f
orm
i
ng t
hi
s
i
nstant
i
at
i
on o
f
t
h
esc
h
ema. In t
hi
s case, s
i
nce
b
ot
h
ro
b
ots are

f
u
ll
y capa
bl
e, t
h
ey move to
-
w
ar
d
st
h
e
i
r goa
l
s
i
n
d
epen
d
ent
l
yw
i
t
h

out t
h
e nee
df
or any sensor s
h
ar
i
ng o
r
c
ommun
i
cat
i
on.
1
2
6
P
arker
,
et al.
F
igure
2.
R
esu
l
ts o

f
Va r
i
at
i
on 1: Two ro
b
ots o
f
typ
e
R
4
p
er
f
orm
i
ng t
h
e tas
k
w
i
t
h
out nee
df
o
r

sensor-sharing or communication. Goals are black squares on the floor. Graphic shows schem
a
i
nterconnections (only white boxes activated)
.
V
ariation 2. T
h
e secon
d
var
i
at
i
on
i
nvo
l
ves a
f
u
ll
y capa
bl
ero
b
ot o
f
typ
e

R
4
,as
we
ll
as a ro
b
ot o
f
type
R
2
w
h
ose
l
aser scanner
i
s not ava
il
a
bl
e
,b
ut st
ill h
as us
e
of i
ts camera. As

ill
ustrate
di
nF
i
gure 3, Ro
b
o
t
R
4
h
e
lp
s
R
2
b
y commun
i
cat
i
n
g
(
v
ia
CS
1
)i

ts own current pos
i
t
i
on, ca
l
cu
l
ate
dby
P
S
1
u
s
i
ng
i
ts
l
aser scanner
(
E
S
1
)
an
d
env
i

ronmenta
l
ma
p
.Ro
b
o
t
R
2
r
ece
iv
es t
hi
s commun
i
cat
i
on
via
P
S
5
a
n
d
t
h
en uses

i
ts camera
(
E
S
2
)
to
d
etec
t
R
4
’s
p
os
i
t
i
on re
l
at
i
ve to
i
tse
lf
(v
ia
P

S
4
)
an
d
ca
l
cu
l
ate
i
ts own current g
l
o
b
a
l
pos
i
t
i
on (us
i
n
g
P
S
1
)b
ase

d
on
R
4
’s re
l
at
ive
p
os
i
t
i
on an
d
R
4
’s commun
i
cate
d
g
l
o
b
a
l
pos
i
t

i
on. Once
b
ot
h
ro
b
ots
k
now t
h
e
ir
o
wn current pos
i
t
i
ons an
d
goa
l
pos
i
t
i
ons, t
h
e
i

r motor sc
h
emas can ca
l
cu
l
ate t
he
motor contro
l
requ
i
re
d
to nav
i
gat
i
on to t
h
e
i
r goa
l
po
i
nts. F
i
gure 3 a
l

so s
h
ow
s
s
naps
h
ots o
f
t
h
ero
b
ots per
f
orm
i
ng t
h
eVar
i
at
i
on 2
i
nstant
i
at
i
on o

f
t
h
esc
h
ema
.
In t
hi
s case
,
R
2
b
eg
i
ns
b
y searc
hi
ng
f
or
R
4
u
s
i
ng
i

ts camera. At present, w
e
h
ave not yet
i
mp
l
emente
d
t
h
e constra
i
nts
f
or automat
i
ca
ll
y ensur
i
ng t
h
at t
he
c
orrect
li
ne o
f

s
i
g
h
t
i
sma
i
nta
i
ne
d
, so we use commun
i
cat
i
on to sync
h
ron
i
z
e
t
h
ero
b
ots. T
h
us
,

w
h
en R
2
l
ocate
s
R
4
,i
t commun
i
cates t
hi
s
f
act to
R
4
.
R
4
t
h
en
i
s
f
ree to move towar
d

s
i
ts goa
l
.I
f
R
2
were to
l
ose s
i
g
h
to
f
R
4
,i
twou
ld
c
ommun
i
cate a message t
o
R
4
to re-sync
h

ron
i
ze t
h
ere
l
at
i
ve s
i
g
h
t
i
ng o
f
R
4
by
Enablin
g
Autonomous Sensor-Sharin
g
1
2
7
F
igure
3.
V

ar
i
at
i
on 2: A ro
b
ot o
f
type
R
4
an
d
o
f
typ
e
R
2
s
h
are sensory
i
n
f
ormat
i
on to ac-
complish their task. Here
,

R
2
(on t
h
e
l
e
f
t) turns towar
d
R
4
to locali
z
e
R
4
r
e
l
at
iv
eto
i
tse
lf.
R
4
commun
i

cates
i
ts current g
l
o
b
a
l
pos
i
t
i
on t
o
R
2
, ena
bli
ng
i
tto
d
eterm
i
ne
i
ts own g
l
o
b

a
l
pos
i
t
i
on
,
and thus move successfully to its goal position
.
R
2
.W
i
t
h
t
hi
sso
l
ut
i
on, t
h
ero
b
ots automat
i
ca
ll

yac
hi
eve nav
i
gat
i
on ass
i
stanc
e
of
a
l
ess capa
bl
ero
b
ot
b
y a more capa
bl
ero
b
ot
.
V
ariation 3.
T
h
et

hi
r
d
var
i
at
i
on
i
nvo
l
ves a sensor
l
ess ro
b
ot o
f
typ
e
R
8
,
w
hi
c
h
h
as access to ne
i
t

h
er
i
ts
l
aser scanner nor camera. As
ill
ustrate
di
nF
i
gure 4
,
t
h
e
f
u
ll
y-capa
bl
ero
b
ot o
f
typ
e
R
4
h

e
lp
s
R
8
b
y commun
i
cat
i
ng
R
8
’s current
g
l
o
b
a
l
pos
i
t
i
on.
R
4
c
a
l

cu
l
ate
s
R
8
’s current g
l
o
b
a
l
pos
i
t
i
on
b
y
fi
rst us
i
ng
i
ts
o
wn
l
aser
(

ES
1
)
an
d
map to ca
l
cu
l
ate
i
ts own current g
l
o
b
a
l
pos
i
t
i
on
(
P
S
1
)
.
R
4

a
l
so uses
i
ts own camera (
ES
2
)
to
d
etec
t
R
8
’s pos
i
t
i
on re
l
at
i
ve to
i
tse
lf
(us
i
n
g

P
S
4
)
.T
h
en,
b
ase
d
on t
hi
sre
l
at
i
ve pos
i
t
i
on an
di
ts own current g
l
o
b
a
l
pos
i

t
i
on
,
R
4
c
a
l
cu
l
ate
s
R
8
’s current g
l
o
b
a
l
pos
i
t
i
on (us
i
ng P
S
3

)
an
d
commun
i
cates t
his
to
R
8
(
v
ia
CS
2
)
.Ro
b
ot
R
8
f
ee
d
s
i
ts own g
l
o
b

a
l
pos
i
t
i
on
i
n
f
ormat
i
on
f
ro
m
R
4
di
rect
l
yto
i
ts motor sc
h
ema. S
i
nce
b
ot

h
o
f
t
h
ero
b
ots
k
now t
h
e
i
r own cur
-
r
ent an
d
goa
l
pos
i
t
i
ons, eac
h
ro
b
ot can ca
l

cu
l
ate
i
ts motor contro
l
s
f
or go
i
n
g
to t
h
e
i
r goa
l
pos
i
t
i
ons. F
i
gure 4 a
l
so s
h
ows snaps
h

ots o
f
t
h
ero
b
ots per
f
orm
i
ng
t
h
eVar
i
at
i
on 3
i
nstant
i
at
i
on o
f
t
h
esc
h
ema. W

i
t
h
t
hi
sso
l
ut
i
on
,
t
h
ero
b
ots auto
-
m
at
i
ca
ll
yac
hi
eve nav
i
gat
i
on ass
i

stance o
f
a sensor
l
ess ro
b
ot
b
y a more capa
ble
r
o
b
ot.
A
na
ly
sis.
I
n extens
i
ve ex
p
er
i
mentat
i
on,
d
ata on t

h
et
i
me
f
or tas
k
com
pl
et
i
on
,
c
ommun
i
cat
i
on cost, sens
i
ng cost, an
d
success rate was co
ll
ecte
d
as an averag
e
1
2

8
P
arker
,
et al.
F
igure
4.
V
ar
i
at
i
on 3: A ro
b
ot o
f
typ
e
R
4
h
e
l
ps a ro
b
ot w
i
t
h

no sensors (typ
e
R
8
)b
ys
h
ar
i
n
g
sensory information so that both robots accomplish the objective. Note ho
w
R
4
(on t
h
er
i
g
h
t)
t
urns to
w
ar
d
R
8
t

oo
b
ta
i
n
vi
s
i
on-
b
ase
d
re
l
at
iv
e
l
oca
li
zat
i
on o
f
R
8
.
R
4
th

en gu
id
e
s
R
8
t
o
i
ts goa
l
p
osition. Onc
e
R
8
i
sat
i
ts goa
ll
ocat
i
on
,
R
4
th
en moves to
i

ts own goa
l
pos
i
t
i
on
.
of
10 tr
i
a
l
so
f
eac
h
var
i
at
i
on. Fu
ll d
eta
il
s are ava
il
a
bl
e

i
n(C
h
an
d
ra, 2004). W
e
b
r
i
e
fl
y
d
escr
ib
e
h
ere t
h
e success rate o
f
eac
h
var
i
at
i
on. In a
ll

t
h
ree var
i
at
i
ons
,
r
o
b
ot
R
4
was 100% success
f
u
li
n reac
hi
ng
i
ts goa
l
pos
i
t
i
on. T
h

us,
f
or Var
i
at
i
o
n
1, s
i
nce t
h
ero
b
ots are
f
u
ll
y capa
bl
ean
dd
o not re
l
yoneac
h
ot
h
er, t
h

ero
b
ot
s
a
l
ways succee
d
e
di
n reac
hi
ng t
h
e
i
r goa
l
pos
i
t
i
ons. In Var
i
at
i
on 2, ro
b
o
t

R
2
succeeded in reaching its goal 6 times out of 10, and in Variation 3, robo
t
R
8
success
f
u
ll
y reac
h
e
di
ts goa
l
9t
i
mes out o
f
10 tr
i
es. T
h
e
f
a
il
ures o
f

ro
b
ot
s
R
4
a
n
d
R
8
i
nVar
i
at
i
ons2an
d
3 were cause
db
yvar
i
a
bl
e
li
g
h
t
i

ng con
di
t
i
ons t
h
a
t
l
e
d
to a
f
a
l
se ca
l
cu
l
at
i
on o
f
t
h
ere
l
at
i
ve ro

b
ot pos
i
t
i
ons us
i
ng t
h
ev
i
s
i
on-
b
ase
d
r
o
b
ot mar
k
er
d
etect
i
on. However
,
even w
i

t
h
t
h
ese
f
a
il
ures
,
t
h
ese overa
ll
resu
l
t
s
are
b
etter t
h
an w
h
at wou
ld b
e poss
ibl
ew
i

t
h
out sensor s
h
ar
i
ng. In Var
i
at
i
on
s
2
an
d
3,
if
t
h
ero
b
ots
did
not s
h
are t
h
e
i
r sensory resources, one o

f
t
h
ero
b
ots
wou
ld
never reac
hi
ts goa
l
pos
i
t
i
on, s
i
nce
i
twou
ld
not
h
ave enoug
hi
n
f
ormat
i

o
n
to
d
eterm
i
ne
i
ts current pos
i
t
i
on. T
h
us, our sensor s
h
ar
i
ng mec
h
an
i
sm exten
ds
t
h
ea
bili
ty o
f

t
h
ero
b
ot team to accomp
li
s
h
tas
k
st
h
at ot
h
erw
i
se cou
ld
not
h
av
e
b
een ac
hi
eve
d.
Enablin
g
Autonomous Sensor-Sharin

g
1
2
9
5. Conclusions and Future Work
In t
hi
s paper, we
h
ave s
h
own t
h
e
f
eas
ibili
ty o
f
t
h
e ASyMTRe mec
h
an
i
s
m
to ac
hi
eve autonomous sensor-s

h
ar
i
ng o
f
ro
b
ot team mem
b
ers per
f
orm
i
ng
a
t
i
g
h
t
l
y-coup
l
e
d
tas
k
.T
hi
s approac

hi
s
b
ase
d
on an extens
i
on to sc
h
ema t
h
eory
,
w
hi
c
h
a
ll
ows sc
h
emas
di
str
ib
ute
d
across mu
l
t

i
p
l
ero
b
ots to
b
e autonomous
ly
c
onnecte
d
an
d
execute
d
at run-t
i
me to ena
bl
e
di
str
ib
ute
d
sensor s
h
ar
i

ng. T
he
i
nputs an
d
outputs to sc
h
emas are
l
a
b
e
l
e
d
w
i
t
h
un
i
que
i
n
f
ormat
i
on types,
i
n

-
sp
i
re
db
yt
h
et
h
eory o
fi
n
f
ormat
i
on
i
nvar
i
ants, ena
bli
ng any sc
h
ema connec
-
t
i
ons w
i
t

h
matc
hi
ng
i
n
f
ormat
i
on types to
b
e con
fi
gure
d
,regar
dl
ess o
f
t
h
e
l
o
-
c
at
i
on o
f

t
h
ose sc
h
ema or t
h
e manner
i
nw
hi
c
h
t
h
esc
h
ema accomp
li
s
h
es
i
t
s
j
o
b
.We
h
ave

d
emonstrate
d
,t
h
roug
h
as
i
mp
l
e transportat
i
on tas
ki
mp
l
emente
d
o
ntwop
h
ys
i
ca
l
ro
b
ots, t
h

ea
bili
ty o
f
t
h
esc
h
ema-
b
ase
d
met
h
o
d
o
l
ogy to gener
-
ate ver
y diff
erent cooperat
i
ve contro
l
tec
h
n
i

ques
f
or t
h
e same tas
kb
ase
d
upo
n
t
h
eava
il
a
bl
e sensor
y
capa
bili
t
i
es o
f
t
h
ero
b
ot team mem
b

ers. I
f
ro
b
ots
d
ono
t
h
ave t
h
ea
bili
t
y
to accomp
li
s
h
t
h
e
i
ro
bj
ect
i
ve, ot
h
er team mem

b
ers can s
h
ar
e
t
h
e
i
r sensor
yi
n
f
ormat
i
on, trans
l
ate
d
appropr
i
ate
ly
to anot
h
er ro
b
ot’s
f
rame o

f
r
eference. This approach provides a framework within which robots can
g
ener
-
ate the hi
g
hest-qualit
y
team solution for a ti
g
htl
y
-coupled task, and eliminate
s
the need of the human desi
g
ner to pre-desi
g
n all alternative solution strate
g
ies
.
In continuin
g
work, we are extendin
g
the formalism to impose motion con-
straints (such as line-of-si

g
ht) needed to ensure that robots can successfull
y
share sensor
y
data while the
y
are in motion,
g
eneralizin
g
the information label
-
i
n
g
technique, and implementin
g
this approach in more complex applications
.
In addition, we are developin
g
a distributed reasonin
g
approach that enable
s
team members to autonomousl
yg
enerate the hi
g

hest-qualit
y
confi
g
uration o
f
schemas for solvin
g
the
g
iven task
.
R
eferences
A
d
ams, J. A., Ba
j
csy, R., Kosec
k
a, J., Kumar, V., Man
d
e
lb
aum, R., M
i
ntz, M., Pau
l
, R., Wang
,

C., Yamamoto, Y., and Yun, X. (1995). Cooperative material handling by human and ro
-
b
otic agents: Module development and system synthesis. I
n
Proc. of IEEE/RSJ Internationa
l
Conference on Intelligent Robots and System
s
.
Arkin, R. C., Balch, T., and Nitz, E. (1993). Communication of behavioral state in multi-agen
t
r
etrieval tasks. In
P
roceedings of the 1993 International Conference on Robotics and Au
-
tomatio
n
, pages 588–594
.
Chandra, M. (2004). Software reconfigurability for heterogeneous robot cooperation. Master’
s
t
hesis, Department of Computer Science, University of Tennessee
.
Donald, B. R., Jennings, J., and Rus, D. (1993). Towards a theory of information invariants fo
r
cooperating autonomous mobile robots. I
n

Proceedings of the International Symposium o
f
R
obotics Researc
h
,
Hidden Valley, PA
.
D
onald, B. R., Jennings, J., and Rus, D. (1997). Information invariants for distributed manipu
-
l
ation
.
I
nternational Journal o
f
Robotics Researc
h
,16
(
5
)
:673–702.
130
P
arker
,
et al.
G

erkey, B. and Mataric, M. (2002). Pusher-watcher: An approach to fault-tolerant tightly
-
c
oupled robot cooperation. I
n
Proc. of IEEE International Conference on Robotics and Au
-
to
m
ation
, pages 464–469
.
G
erkey, B. and Mataric, M. J. (2004). A formal analysis and taxonomy of task allocation i
n
m
ulti-robot systems.
I
nt. J. of Robotics Researc
h
, 23(9):939–954.
P
arker, L. E. (2003). The effect of heterogeneity in teams of 100+ mobile robots. In Schultz
,
A
.
,
Parker
,
L. E.

,
and Schneider
,
F.
,
editors
,
Multi-Robot Systems Volume II: From Swarm
s
t
o Intelligent Automat
a
.
Kluwer
.
P
arker, L. E., Kannan, B., Tang, F., and Bailey, M. (2004). Tightly-coupled navigation assistanc
e
i
n heterogeneous multi-robot teams. I
n
Proceedings of IEEE International Conference o
n
I
ntelligent Robots and System
s
.
S
hehory, O. (1998). Methods for task allocation via agent coalition formation
.

A
rti
fi
cial Intelli
-
g
enc
e
,
101
(
1-2
)
:165–200
.
S
pletzer, J., Das, A., Fierro, R., Ta
y
ler, C., Kumar, V., and Ostrowski, J. (2001). Cooperativ
e
l
ocalization and control for multi-robot mani
p
ulation. I
n
Proc. o
f
the IEEE/RSJ Internationa
l
Con

f
erence on Intelligent Robots and System
s
,
Hawaii
.
T
an
g
, F. and Parker, L. E. (200
5
). AS
y
MTRe: Automated s
y
nthesis of multi-robot task solution
s
th
rou
gh
so
f
tware recon
fig
urat
i
on
.
Su
b

mitte
d
.
I
V
D
I
S
TRIB
U
TED MAPPIN
G
AND
CO
VERA
G
E
M
ERGING PARTIAL MAPS
WITHOUT USING ODOMETRY
Francesco Am
i
gon
i
∗
,
S
i
mone Gaspar
i

n
i
D
ipartimento
d
iE
l
ettronica e Informazion
e
P
olitecnico di Milano, 20133 Milano, Ital
y
ami
g
oni
@
elet.polimi.it,
g
asparin
@
elet.polimi.i
t
Mar
i
a
Gi
n
i
D
ept of Computer Science an

d
Engineerin
g
University of Minnesota, Minneapo
l
is, US
A
†
g
ini
@
cs.umn.ed
u
Abs
tr
act
M
ost map
b
u
ildi
ng met
h
o
d
s emp
l
oye
db
ymo

bil
ero
b
ots are
b
ase
d
on t
h
eas
-
sumption that an estimate of the position of the robots can be obtained fro
m
o
dometry readings. In this paper we propose methods to build a global geomet
-
r
ical map by integrating partial maps without using any odometry information
.
T
his approach increases the flexibility in data collection. Robots do not nee
d
t
o see each other during mapping, and data can be collected by a single robo
t
o
r multiple robots in one or multiple sessions. Experimental results show th
e
e
ffectiveness of our approach in different types of indoor environments

.
K
eywords:
s
can matching, map merging, distributed mapping
.
1. Introduction
In t
hi
s paper we s
h
ow
h
ow to
b
u
ild
ag
l
o
b
a
l
map o
f
an env
i
ronment
by
m

erg
i
ng part
i
a
l
maps w
i
t
h
out us
i
ng any re
l
at
i
ve pos
i
t
i
on
i
n
f
ormat
i
on
b
ut re
-

l
y
i
ng on
l
y on geometr
i
ca
li
n
f
ormat
i
on. T
h
e maps we cons
id
er are co
ll
ect
i
on
s
of
segments o
b
ta
i
ne
df

rom 2D
l
aser range
d
ata. T
h
ey prov
id
e a compact an
d
e
asy-to-use (
f
or examp
l
e, to p
l
an a pat
h
) representat
i
on o
f
t
h
eenv
i
ronment
.
No

h
ypot
h
es
i
s
i
sma
d
ea
b
out t
h
eenv
i
ronment to
b
e mappe
d
: exper
i
ment
s
d
emonstrate t
h
at our met
h
o
d

swor
k
we
ll b
ot
hi
nregu
l
ar an
di
n scattere
d
en
-
vi
ronments. We re
d
uce t
h
e merg
i
ng o
f
a sequence o
f
part
i
a
l
maps to t

h
e
i
t
-
∗
P
art
i
a
lf
un
di
n
g
prov
id
e
dby
aFu
lb
r
igh
t
f
e
ll
ows
hi
pan

dby
“Pro
g
etto G
i
ovan
i
R
i
cercator
i
” 1999.
†
P
artial fundin
g
provided b
y
NSF under
g
rants EIA-02243
6
3 and EIA-03248
6
4.
133
L.E. Parker et al.
(
eds.)
,

Multi-Robot S
y
stems. From Swarms to Intelli
g
ent Automata. Volume III
,
1
33
–144.

c
2005
Sprin
g
er. Printed in the Netherlands
.
134
Ami
g
oni, et al
.
e
rate
di
ntegrat
i
on o
f
two part
i

a
l
maps. T
h
e met
h
o
d
s we propose are ro
b
ust
to
di
sp
l
acements
b
etween t
h
e part
i
a
l
maps, prov
id
e
d
t
h
at t

h
ey
h
ave at
l
east
a
c
ommon geometr
i
ca
lf
eature
.
Map merg
i
ng w
i
t
h
out o
d
ometry
i
n
f
ormat
i
on
h

as t
h
ea
d
vantage o
fb
e
i
ng
i
n
-
d
epen
d
ent
f
rom
h
ow t
h
e
d
ata
h
ave
b
een co
ll
ecte

d
.It
i
s
i
n
diff
erent
if
t
h
e part
i
a
l
maps are co
ll
ecte
dd
ur
i
ngas
i
ng
l
e sess
i
on or mu
l
t

i
p
l
e sess
i
ons,
b
yas
i
ng
l
e ro-
b
ot or mu
l
t
i
p
l
ero
b
ots. Ro
b
ots can
b
ea
dd
e
d
or remove

d
at any t
i
me, an
d
t
h
e
y
d
o not nee
d
to
k
now t
h
e
i
r own pos
i
t
i
on. For t
h
e exper
i
ments
i
nt
hi

s paper w
e
u
se
d
as
i
ng
l
ero
b
ot
b
ut a
ll
t
h
e resu
l
ts are app
li
ca
bl
etomu
l
t
i
ro
b
ots

.
T
hi
s paper
i
s structure
d
as
f
o
ll
ows. T
h
e next sect
i
on
di
scusses t
h
ema
in
a
pproac
h
es to scan matc
hi
ng an
d
map merg
i

ng. Sect
i
on 3
d
escr
ib
es our sca
n
matc
hi
ng a
l
gor
i
t
h
m, an
d
Sect
i
on 4 our map merg
i
ng met
h
o
d
s. Exper
i
menta
l

r
esults are in Section
5.
2. Previous
W
ork
Scan matc
h
in
g
i
st
h
e process o
f
ca
l
cu
l
at
i
ng t
h
e trans
l
at
i
on an
d
rotat

i
on o
fa
scan to max
i
m
i
ze
i
ts over
l
a
p
w
i
t
h
are
f
erence scan. A num
b
er o
f
scan matc
h-
i
ng a
l
gor
i

t
h
ms
h
ave
b
een presente
di
nt
h
e
l
ast two
d
eca
d
es; t
h
ey
diff
er
f
or t
he
ki
n
d
o
f
env

i
ronments
i
nw
hi
c
h
t
h
ey per
f
orm we
ll
, e.g., w
i
t
h
stra
i
g
h
t perpen
-
di
cu
l
ar wa
ll
s(We
i

ss et a
l
., 1994),
f
or t
h
e computat
i
ona
l
e
ff
ort,
f
or t
h
ec
h
o
i
c
e
of
operat
i
ng
di
rect
l
yont

h
e scan
d
ata (Lu an
d
M
ili
os, 1997) or on segment
s
a
pprox
i
mat
i
ng t
h
e
d
ata (Z
h
ang an
d
G
h
os
h
, 2000). A
ll
t
h

ese met
h
o
d
s requ
i
r
e
a
n
i
n
i
t
i
a
l
pos
i
t
i
on est
i
mate to avo
id
erroneous a
li
gnments o
f
t

h
e two scans
.
T
h
e most use
d
a
l
gor
i
t
h
m (Lu an
d
M
ili
os, 1997)
i
terat
i
ve
l
ym
i
n
i
m
i
zes an er

-
r
or measure
b
y
fi
rst
fi
n
di
ng a correspon
d
ence
b
etween po
i
nts
i
nt
h
e two scans
,
a
n
d
t
h
en
d
o

i
ng a
l
east square m
i
n
i
m
i
zat
i
on o
f
a
ll
po
i
nt-to-po
i
nt
di
stances t
o
d
eterm
i
ne t
h
e
b

est trans
f
ormat
i
on. W
h
en t
h
eenv
i
ronment cons
i
sts o
f
stra
ight
p
erpen
di
cu
l
ar wa
ll
s matc
hi
n
gi
ss
i
mp

l
er. Cross-corre
l
at
i
on o
f
t
h
e
hi
sto
g
ram
s
of
an
gl
es
b
etween t
h
e actua
l
an
d
prev
i
ous scans prov
id

es t
h
eor
i
entat
i
on o
f
t
he
two maps, w
hil
et
h
e trans
l
at
i
on
i
so
b
ta
i
ne
d
e
i
t
h

er
by
cross-corre
l
at
i
on o
f
t
he
distance histo
g
ram (Weiss et al., 1994) or b
y
least square minimization (Mar
-
ti
g
noni III and Smart, 2002). These methods are sensitive to lar
g
e displace
-
ments between the maps and to chan
g
es in the environment
.
M
ap merging, namel
y
the problem of buildin

g
a
g
lobal map from data col
-
l
ected b
y
several robots, is usuall
y
solved b
y
extendin
g
SLAM techniques (Bur
-
g
ard et al., 2002, Ko et al., 2003, Fenwick et al., 2002), or usin
g
EM (Simmon
s
e
t al., 2000, Thrun et al., 2000).
Most map mer
g
in
g
techniques rel
y
on the assumption that the robot posi

-
tions are known. For example, in (Simmons et al., 2000, Bur
g
ard et al., 2002
)
the
p
ositions of the robots are assumed to be known at all times; in (Thrun et al.
,
2000) the robots don’t know their relative start
p
osition but each robot has t
o
M
er
g
in
g
Partial Maps without Usin
g
Odometr
y
135
start w
i
t
hi
ns
i
g

h
to
f
t
h
e team
l
ea
d
er. An except
i
on
i
st
h
ewor
ki
n (Kono
li
g
e
e
ta
l
., 2003) w
h
ere map merg
i
ng
i

s
d
one us
i
ng a
d
ec
i
s
i
on t
h
eoret
i
c approac
h.
T
h
ero
b
ots
d
o not nee
d
to
k
now t
h
e
i

r own pos
i
t
i
on,
b
ut to
f
ac
ili
tate t
h
e matc
h
t
h
e maps
h
ave to
b
e annotate
d
manua
ll
yw
i
t
hdi
st
i

nct
i
ve
f
eatures. In (Ko et a
l
.
,
2
003), part
i
c
l
e
fil
ters are use
df
or part
i
a
l
map
l
oca
li
zat
i
on an
d
t

h
ero
b
ots
h
av
e
to act
i
ve
l
yver
if
yt
h
e
i
rre
l
at
i
ve
l
ocat
i
ons
b
e
f
ore t

h
e maps are merge
d.
3
. Method for
S
can Matchin
g
W
e
p
ro
p
ose a MAT
CH
f
unct
i
on
f
or matc
hi
ng two part
i
a
l
maps compose
d
o
f

segments. Our met
h
o
di
sexc
l
us
i
ve
l
y
b
ase
d
on t
h
e geometr
i
ca
li
n
f
ormat
i
o
n
an
d
constra
i

nts (Gr
i
mson, 1990) conta
i
ne
di
nt
h
e part
i
a
l
maps. In part
i
cu
l
ar
,
we cons
id
er ang
l
es
b
etween pa
i
rs o
f
segments
i

nt
h
e part
i
a
l
maps as a sort o
f
“
geometr
i
ca
ll
an
d
mar
k
s” on w
hi
c
h
t
h
e matc
hi
ng process
i
s
b
ase

d
.T
hi
s use o
f
“l
oca
l
” geometr
i
ca
lf
eatures
i
ss
i
gn
ifi
cant
l
y
diff
erent
f
rom ot
h
er re
l
ate
d

wor
ks
i
n map
b
u
ildi
ng t
h
at use “g
l
o
b
a
l
” geometr
i
ca
lf
eatures (e.g., t
h
ose represente
d
b
yan
hi
stogram o
f
ang
l

e
diff
erences)
.
M
AT
CH
i
ntegrates two part
i
a
l
maps
i
nt
o
at
hi
r
d
one. Let’s ca
ll
S
1
an
d
S
2
t
h

etwo
p
art
i
a
l
ma
p
san
d
S
1
,
2
t
h
e resu
l
t
i
ng map
.
MAT
C
H
o
perates
i
nt
h

ree ma
j
or steps
:
1. Determ
i
ne poss
i
ble trans
f
ormat
i
ons.
Thi
s step
fi
rst
fi
n
d
st
h
e ang
l
es
b
e-
tween t
h
e segments

in
S
1
an
db
etween t
h
e segments
in
S
2
an
d
t
h
en
fi
n
d
st
he
poss
ibl
e trans
f
ormat
i
ons (name
l
y, t

h
e rotat
i
ons an
d
trans
l
at
i
ons) t
h
at super
i
m
-
pose at
l
east one ang
l
e
α
2
of
S
2
to an (approx
i
mate
l
y) equa

l
ang
le
α
1
of
S
1
.
Reca
ll
t
h
at ang
l
es
b
etween pa
i
rs o
f
segments
i
n a part
i
a
l
map are t
h
e geomet

-
ri
ca
ll
an
d
mar
k
swea
d
opt
.
In pr
i
nc
i
p
l
e, w
i
t
h
out any
i
n
f
ormat
i
on a
b

out t
h
ere
l
at
i
ve pos
i
t
i
ons o
f
t
h
etw
o
scans
,
t
h
ere are
O
(
n
2
1
n
2
2
)

p
oss
ibl
e trans
f
ormat
i
ons, w
h
ere
n
1
an
d
n
2
are t
h
e
n
um
b
er o
f
segments
i
n
S
1
an

d
S
2
, respect
i
ve
l
y. We
h
ave
d
ev
i
se
d
t
h
ree
h
eur
i
s
-
t
i
cs to s
p
ee
d
u

p
t
h
e com
p
utat
i
on
:
a
C
onsi
d
er An
gl
es
b
etween Consecutive Se
g
ments
.
In eac
h
scan
,
we con-
s
id
er on
l

yt
h
e ang
l
es
b
etween two consecut
i
ve segments;
l
e
t
A
s
1
an
d
A
s
2
b
et
h
e sets o
f
suc
h
ang
l
es

f
o
r
S
1
an
d
S
2
, respect
i
ve
l
y. T
h
e num
b
er o
f
p
oss
ibl
e trans
f
ormat
i
ons
d
ro
p

sto
O
(
n
1
n
2
)
.
F
i
n
di
ng t
h
e sets
A
s
1
an
d
A
s
2
is
e
asy w
h
en t
h

e segments
i
n
S
1
an
din
S
2
are or
d
ere
d
,w
hi
c
hi
s usua
ll
yt
he
c
ase w
i
t
hl
aser range scanners.
b
Consi
d

er An
gl
es
b
etween Ran
d
om
ly
Se
l
ecte
d
Se
g
ments
.
In eac
h
scan
,
w
e exam
i
ne t
h
e ang
l
es
b
etween pa

i
rs o
f
segments se
l
ecte
d
ran
d
om
l
y
.
W
e ass
i
gn a
hi
g
h
er pro
b
a
bili
ty to
b
ese
l
ecte
d

to
l
onger segments, s
i
nc
e
t
h
ey prov
id
e more prec
i
se
i
n
f
ormat
i
on a
b
out t
h
eenv
i
ronment. Le
t
A
r
1
an

d
A
r
2
b
et
h
e sets o
f
t
h
ese
l
ecte
d
ang
l
es
f
o
r
S
1
an
d
S
2
, respect
i
ve

l
y. T
he
n
um
b
er o
f
trans
f
ormat
i
ons generate
db
yt
hi
s met
h
o
dis
O
(
a
1
a
2
)
,
w
h

ere
136
Ami
g
oni, et al
.
a
1
=
|
A
r
1
|
a
n
d
a
2
=
|
A
r
2
|
a
re t
h
e num
b

er o
f
se
l
ecte
d
ang
l
es
in
A
r
1
a
n
d
A
r
2
,
r
espect
i
ve
l
y.
c
C
onsi
d

er An
gl
es
b
etween Perpen
d
icu
l
ar Se
g
ments
.
In eac
h
scan
,
w
e
se
l
ect on
l
y ang
l
es
b
etween perpen
di
cu
l

ar segments. T
hi
s
h
eur
i
st
i
c
is
p
art
i
cu
l
ar
l
y conven
i
ent
f
or
i
n
d
oor env
i
ronments, w
h
ere wa

ll
s are o
f
te
n
n
orma
l
to eac
h
ot
h
er. T
h
e
h
eur
i
st
i
c
i
s compute
df
rom t
h
e
hi
stogram o
f

segments groupe
db
yor
i
entat
i
on. T
h
e
di
rect
i
on w
h
ere t
h
e sum o
f
t
he
l
engt
h
so
f
t
h
e segments
i
s max

i
ma
li
st
he
p
rinci
p
a
ld
irectio
n
.
In F
i
g. 1
,
t
h
e
hi
stogram o
f
a scan ta
k
en
i
nan
i
n

d
oor env
i
ronment
i
ss
h
own. T
he
p
r
i
nc
i
pa
ldi
rect
i
on
i
st
h
ee
l
emen
t
L
9
a
n

d
t
h
e norma
ldi
rect
i
on
i
st
h
ee
l
-
e
men
t
L
0
.
Le
t
A
h
1
a
n
d
A
h

2
b
et
h
e sets o
f
ang
l
es
f
orme
db
y a segment
i
n
t
h
epr
i
nc
i
pa
ldi
rect
i
on an
d
a segment
i
nt

h
e norma
ldi
rect
i
on o
f
t
h
e
hi
s
-
tograms o
f
S
1
a
n
d
S
2
,
respect
i
ve
l
y. T
h
e set o

f
poss
ibl
e trans
f
ormat
i
ons
i
s
f
oun
d
compar
i
ng t
h
e ang
l
es
in
A
h
1
a
n
d
A
h
2

.
T
h
e num
b
er o
fp
oss
ibl
e trans-
f
ormat
i
ons
is
O
(
p
1
n
1
p
2
n
2
)
,
w
h
er

e
p
i
a
n
d
n
i
a
re respect
i
ve
l
yt
h
e num
b
e
r
of
segments
i
nt
h
epr
i
nc
i
pa
l

an
di
nt
h
e norma
ldi
rect
i
ons o
f
t
h
e
hi
stogra
m
of
sca
n
S
i
.
F
igure
1.
Th
e
hi
stogram o
f

asca
n
2. E
va
l
ua
t
e
th
e
tr
a
n
s
f
o
rm
a
ti
o
n
s.
To measure t
h
e goo
d
ness o
f
a trans
f

or-
m
at
i
on
t
w
e trans
f
orm
S
2
on
S
1
(i
nt
h
ere
f
erence
f
rame o
f
S
1
)
accor
di
ng t

o
t
(
o
b
ta
i
n
i
n
g
S
t
2
)
,t
h
en we ca
l
cu
l
ate t
h
e approx
i
mate
l
engt
h
o

f
t
h
e segments o
f
S
1
t
h
at correspon
d
to (name
l
y, matc
h
w
i
t
h
) segments o
f
S
t
2
.
T
h
us
,
t

h
e measure o
f
a trans
f
ormat
i
on
i
st
h
e sum o
f
t
h
e
l
engt
h
so
f
t
h
e correspon
di
ng segments t
h
a
t
t

h
e trans
f
ormat
i
on pro
d
uces. More prec
i
se
l
y,
f
or every pa
i
ro
f
segment
s
s
1
∈
S
1
a
n
d
s
t
2

∈
S
t
2
we pro
j
ec
t
s
t
2
o
nt
h
e
li
ne support
i
ng
s
1
a
n
d
compute t
h
e
l
engt
h

l
1
of
t
h
e common
p
art o
f
s
1an
d
t
h
e pro
j
ecte
d
segment. We repeat t
h
e proces
s
b
y pro
j
ect
i
n
g
s

1
on
s
t
2
,
o
b
ta
i
n
i
n
g
l
2
.
T
h
e average o
f
l
1
a
n
d
l
2
i
s a measure o

f
h
ow t
h
epa
i
ro
f
segments matc
h
.T
hi
s step eva
l
uates a s
i
ng
l
e trans
f
ormat
i
on
by
c
ons
id
er
i
ng a

ll
t
h
epa
i
rs o
f
segments o
f
t
h
e two scans t
h
at ar
e
O
(
n
1
n
2
)
.
M
er
g
in
g
Partial Maps without Usin
g

Odometr
y
137
3. Apply the best transformation and fuse the se
g
ments
.
O
nce t
h
e
b
es
t
trans
f
ormat
i
on
¯
t
h
as
b
een
f
oun
d
,t
hi

s ste
p
trans
f
orms t
h
e secon
dp
art
i
a
l
ma
p
S
2
i
nt
h
ere
f
erence
f
rame o
f
S
1
accor
di
ng t

o
¯
t
ob
ta
i
n
i
ng
S
¯
t
2
.T
h
ema
p
t
h
at const
i
-
tutes t
h
e out
p
ut o
f
MAT
CH

i
st
h
en o
b
ta
i
ne
db
y
f
us
i
ng t
h
e segments o
f
S
1
wi
t
h
t
h
e segments o
f
S
¯
t
2

.T
h
ema
i
n
id
ea
b
e
hi
n
d
t
h
e
f
us
i
on o
f
segments
i
st
h
at a set o
f
m
atc
hi
ng segments

i
ssu
b
st
i
tute
di
nt
h
e
fi
na
l
map
b
yas
i
ng
l
epo
l
y
li
ne. We
i
t
-
e
rat
i

ve
l
y
b
u
ild
a sequence o
f
approx
i
mat
i
ng po
l
y
li
ne
s
P
0
P
P
,
P
1
P
P
,
t
h

at converge
s
to t
h
epo
l
y
li
n
e
P
th
at a
d
equate
l
y approx
i
mates (an
d
su
b
st
i
tutes
i
nt
h
e resu
l

t
i
n
g
m
ap) a set o
f
matc
hi
ng segments. T
h
epo
l
y
li
n
e
P
0
P
P
i
s compose
d
o
f
as
i
ng
l

eseg-
m
ent connect
i
ng t
h
epa
i
ro
ff
art
h
est po
i
nts o
f
t
h
e matc
hi
ng segments. G
i
ve
n
t
h
epo
l
y
li

n
e
P
n
P
P
−
1
,
ca
ll
s
t
h
e (matc
hi
ng) segment at max
i
mum
di
stance
f
rom
i
t
s
corresponding (closest) segment ¯
in
P
n

PP
−
1
.I
f
t
h
e
di
stance
b
et
w
ee
n
s
and ¯
s
i
s
l
ess t
h
an t
h
e acce
p
ta
bl
e error, t

h
e
n
P
n
PP
−
1
i
st
h
e
fi
na
l
a
pp
rox
i
mat
i
on
P
.
O
t
h
er
-
wi

se
,
s
substitutes ¯
s
in
P
n
P
P
−
1
an
d
s
i
s connecte
d
to t
h
etwoc
l
osest segments
in
P
n
P
P
−
1

to o
b
ta
i
nt
h
enewpo
l
y
li
n
e
P
n
P
P
.
4
. Methods for Map Mergin
g
W
enow
d
escr
ib
e met
h
o
d
s

f
or
i
ntegrat
i
ng a sequenc
e
S
1
,
S
2
,
S
n
of
n
p
art
i
a
l
m
aps
b
y repeate
dl
yca
lli
n

g
M
AT
CH
.
S
e
q
uential Method
.
T
hi
s
i
st
h
es
i
m
pl
est met
h
o
d
,w
hi
c
h
o
p

erates as
f
o
ll
ows
.
T
h
e
fi
rst two part
i
a
l
maps are
i
ntegrate
d
,t
h
eo
b
ta
i
ne
d
map t
h
en
i

s grown
by
sequent
i
a
ll
y
i
ntegrat
i
ng t
h
et
hi
r
d
part
i
a
l
map, t
h
e
f
ourt
h
part
i
a
l

map, an
d
so on
.
Eventua
ll
y, t
h
e
fi
na
l
map
S
1
,
2
, ,
n
i
s constructe
d
.Inor
d
er to
i
ntegrate
n
p
art

i
a
l
m
a
p
s, t
h
ese
q
uent
i
a
l
met
h
o
d
re
q
u
i
re
s
n
−
1
ca
ll
sto

M
AT
C
H
.
A
p
ro
bl
em w
i
t
h
t
hi
s met
h
o
di
st
h
at, as t
h
e process goes on
,
M
AT
CH
i
sa

ppli
e
d
to a
p
art
i
a
l
ma
p
t
h
at grows
l
arger an
dl
arger (
i
t conta
i
ns more an
d
more segments). T
hi
sw
ill
c
ause
diffi

cu
l
t
i
es
i
nt
h
e
i
ntegrat
i
on o
f
S
i
w
i
t
hl
arg
e
i
,
s
i
nc
e
S
i

c
ou
ld
matc
hwi
t
h
diff
erent parts o
f
t
h
e
l
arger map
.
Tr
ee
M
e
th
od.
To overcome t
h
ea
b
ove pro
bl
em, t
h

e
i
ntegrat
i
on o
f
a sma
ll
p
art
i
a
l
map w
i
t
h
a
l
arge part
i
a
l
map s
h
ou
ld b
e avo
id
e

d
.T
hi
s
i
st
h
e
id
ea un
-
d
er
l
y
i
ng t
he
t
ree met
h
o
d
,w
hi
c
h
wor
k
sas

f
o
ll
ows. Eac
h
part
i
a
l
map o
f
t
he
i
n
i
t
i
a
l
sequence
i
s
i
ntegrate
d
w
i
t
h

t
h
e success
i
ve part
i
a
l
map o
f
t
h
e sequenc
e
to o
b
ta
i
n a new sequenc
e
S
1
,
2
,
S
2
,
3
,

,
S
n
−
1
,
n
of
n
− 1
p
art
i
a
l
ma
p
s. T
h
en,
e
ac
h
part
i
a
l
map o
f

t
hi
s new sequence
i
s
i
ntegrate
d
w
i
t
h
t
h
e success
i
ve one t
o
ob
ta
i
n a new sequenc
e
S
1
,
2
,
3
,

S
2
,
3
,
4
,

,
S
n
−
2
,
n
−
1
,
n
of
n
− 2
p
art
i
a
l
ma
p
s. T

h
e
p
rocess cont
i
nues unt
il
as
i
ng
l
e
fi
na
l
ma
p
S
1
,
2
, ,
n
i
s
p
ro
d
uce
d

.T
h
e tree met
h
o
d
a
l
ways
i
ntegrates part
i
a
l
maps o
f
t
h
e same s
i
ze, s
i
nce t
h
ey approx
i
mate
l
y con
-

ta
i
nt
h
e same num
b
er o
f
segments. T
h
e num
b
er o
f
ca
ll
st
o
M
AT
C
H requ
i
re
dby
t
h
e tree met
h
o

d
to
i
ntegrate a sequence o
f
n
p
art
i
a
l
ma
p
s
is
n
(
n
−
1
)
/
2. Not
e
a
l
so t
h
at, w
hil

et
h
e sequent
i
a
l
met
h
o
d
can
b
e app
li
e
di
nanon-
li
ne
f
as
hi
on (
i
.e.
,
138
Ami
g
oni, et al

.
w
hil
et
h
ero
b
ot
i
smov
i
ng), t
h
e most natura
li
mp
l
ementat
i
on o
f
t
h
e tree met
h
o
d
i
so
ff

-
li
ne. To spee
d
up t
h
e tree met
h
o
d
we
h
ave
d
eve
l
ope
d
an
h
eur
i
st
i
ct
h
at
,
gi
ven a sequence o

f
part
i
a
l
maps at any
l
eve
l
o
f
t
h
e tree (
l
et us suppose at
l
eve
l
0f
or s
i
mp
li
c
i
ty), attempts to
i
ntegrate t
h

e part
i
a
l
map
s
S
i
a
n
d
S
i
+
2
;if
t
h
e
i
n-
tegrat
i
on succee
d
s, t
h
e
fi
na

l
resu
lt
S
i
,
i
+
2
r
e
p
resents t
h
e same ma
p
t
h
at wou
ld
h
ave
b
een o
b
ta
i
ne
d
w

i
t
h
t
h
ree
i
ntegrat
i
ons
:
S
i
wi
t
h
S
i
+
1
to o
b
ta
in
S
i
,
i
+
1

,
S
i
+
1
wi
t
h
S
i
+
2
to o
b
ta
in
S
i
+
1
,
i
+
2
,
an
d
S
i
,

i
+
1
wi
t
h
S
i
+
1
,
i
+
2
to o
b
ta
in
S
i
,
i
+
1
,
i
+
2
.
More-

o
ver, t
h
e num
b
er o
f
part
i
a
l
maps
i
nt
h
e new sequence
i
sre
d
uce
db
y one un
i
t
,
b
ecause
S
i
,

i
+
2
su
b
st
i
tutes
b
ot
h
S
i
,
i
+
1
a
n
d
S
i
+
1
,
i
+
2
.
T

hi
s
h
eur
i
st
i
c
i
s
b
est use
d
w
h
en t
h
e part
i
a
l
map
s
S
i
a
n
d
S
i

+
2
a
re a
l
rea
d
yt
h
e resu
l
to
f
a num
b
er o
fi
ntegra
-
t
i
ons per
f
orme
db
yt
h
e tree met
h
o

d
an
d
t
h
e
i
r common part
i
ss
i
gn
ifi
cant. Fo
r
e
xamp
l
e,
i
nt
h
e sequence pro
d
uce
d
at t
h
e
l

eve
l
3o
f
t
h
e tree tec
h
n
i
que t
h
e
fi
rs
t
(
S
1
,
2
,
3
,
4
)
an
d
t
h

et
hi
r
d(
S
3
,
4
,
5
,
6
)
part
i
a
l
maps
h
aveas
i
gn
ifi
cant common part
,
s
i
nce approx
i
mate

l
y
h
a
lf
o
f
t
h
e two part
i
a
l
maps over
l
aps
.
A
pro
bl
em w
i
t
h
t
h
e tree met
h
o
di

s
d
ue to t
h
e presence o
f
“spur
i
ous” seg
-
ments
i
nt
h
e
i
ntegrate
d
maps, name
l
y segments t
h
at correspon
d
to t
h
e sam
e
p
art o

f
t
h
e rea
l
env
i
ronment
b
ut t
h
at are not
f
use
d
toget
h
er. T
hi
s pro
bl
em
is
e
xacer
b
ate
di
nt
h

e tree met
h
o
d
s
i
nce t
h
e same parts o
f
t
h
e part
i
a
l
maps ar
e
r
epeate
dl
y
f
use
d
toget
h
er
.
Pi

vo
tM
e
th
od.
T
h
e
pi
vot met
h
o
d
com
bi
nes t
h
e
b
est
f
eatures o
f
t
h
et
wo
p
rev
i

ous met
h
o
d
s. T
hi
s met
h
o
d
starts as t
h
e tree met
h
o
d
an
d
constructs a se
-
q
u
ence
S
1
,
2
,
S
2

,
3
,

,
S
n
−
1
,
n
of
n
− 1
p
art
i
a
l
ma
p
s. At t
hi
s
p
o
i
nt, we note t
h
a

t
S
2
i
s
p
art o
fb
ot
h
S
1
,
2
a
n
d
S
2
,
3
a
n
d
t
h
at t
h
e trans
f

ormat
i
o
n
¯
t
1
,
2
u
se
d
to
i
ntegrat
e
S
1
a
n
d
S
2
p
rov
id
es t
h
e
p

os
i
t
i
on an
d
or
i
entat
i
on o
f
t
h
ere
f
erence
f
rame o
f
S
2
in
t
h
ere
f
erence
f
rame o

f
S
1
,
2
.
It
i
st
h
ere
f
ore
p
oss
ibl
e to trans
f
orm
S
2
,
3
a
ccor
di
ng
to
¯
t

1
,
2
a
n
df
use t
h
e segments o
f
t
h
e part
i
a
l
map
s
S
1
,
2
a
n
d
S
¯
t
1
,

2
2
,
3
to o
b
ta
in
S
1
,
2
,
3
.
In a s
i
m
il
ar way
,
S
1
,
2
,
3
,
4
c

an
b
eo
b
ta
i
ne
df
rom
S
1
,
2
,
3
a
n
d
S
3
,
4
b
y app
l
y
i
ng to t
he
l

atter t
h
e trans
f
ormat
i
o
n
¯
t
2
,
3
a
n
df
us
i
ng t
h
e segments o
f
S
1
,
2
,
3
a
n

d
S
¯
t
2
,
3
3
,
4
.
Iterat
-
i
ng t
hi
s process,
f
rom t
h
e sequence
S
1
,
2
,
S
2
,
3

,

,
S
n
−
1
,
n
t
h
e
fi
na
l
ma
p
S
1
,
2
, ,
n
i
so
b
ta
i
ne
d

.T
h
ep
i
vot met
h
o
di
ntegrates part
i
a
l
maps o
f
t
h
e same s
i
ze,
lik
et
he
tree met
h
o
d
,an
d
re
q

u
i
re
s
n
−
1
ca
ll
sto
M
AT
CH
, lik
et
h
ese
q
uent
i
a
l
met
h
o
d
.(I
n
a
ddi

t
i
on
i
tre
q
u
i
re
s
n
−
2 execut
i
ons o
f
t
h
e not-so-ex
p
ens
i
ve ste
p
3o
f
MAT
C
H.)
T

h
ep
i
vot met
h
o
di
s natura
ll
y
i
mp
l
ementa
bl
e
i
nanon-
li
ne system. T
h
e pro
b-
l
em o
f
spur
i
ous segments
i

sre
d
uce
db
ut not comp
l
ete
l
ye
li
m
i
nate
d
;awayt
o
f
urt
h
er re
d
uce t
hi
s pro
bl
em
i
sto
f
use no

t
S
1
,
2
a
n
d
S
¯
t
1
,
2
2
,
3
,b
ut
S
1
,
2
a
n
d
S
¯
t
1

,
3
3
,
w
h
er
e
¯
t
1
,
3
i
st
h
e com
p
os
i
t
i
on o
f
¯
t
1
,
2
a

n
d
¯
t
2
,
3
.
5. Ex
p
erimental Result
s
T
h
e
d
escr
ib
e
d
met
h
o
d
s
h
ave
b
een va
lid

ate
d
us
i
ng a Ro
b
uter mo
bil
ep
l
at
f
or
m
e
qu
i
ppe
d
w
i
t
h
a SICK LMS 200
l
aser range scanner mounte
di
nt
h
e

f
ront o
f
t
he
M
er
g
in
g
Partial Maps without Usin
g
Odometr
y
1
3
9
r
obot at a height of approximately
5
0cm. For these experiments we acquire
d
3
2 scans w
i
t
h
angu
l
ar reso

l
ut
i
on o
f1
◦
an
d
w
i
t
h
angu
l
ar range o
f
18
0
◦
. Eac
h
scan
h
as
b
een processe
d
to approx
i
mate t

h
epo
i
nts returne
db
yt
h
e sensor w
i
t
h
segments, accor
di
ng to t
h
ea
l
gor
i
t
h
m
i
n (Gonzá
l
es-Baños an
d
Latom
b
e, 2002)

.
T
h
e programs
h
ave
b
een co
d
e
di
n ANSI C++ emp
l
oy
i
ng t
h
e LEDA
lib
rar
i
e
s
4
.
2
an
d
t
h

ey
h
ave
b
een run on a 1GHz Pent
i
um III processor w
i
t
h
L
i
nux SuS
e
8
.
0
.
T
h
e scans
h
ave
b
een acqu
i
re
di
n
diff

erent env
i
ronments (
f
orm
i
ng a
l
oo
p
a
b
out 40m
l
ong)
b
y
d
r
i
v
i
ng t
h
ero
b
ot manua
ll
yan
d

w
i
t
h
out recor
di
ng an
y
od
ometr
i
c
i
n
f
ormat
i
on. We starte
df
rom a
l
a
b
oratory, a very scattere
d
env
i-
r
onment, t
h

en we crosse
d
a narrow
h
a
ll
way w
i
t
h
rect
ili
near wa
ll
s to enter
a
d
epartment
h
a
ll
,a
l
arge open space w
i
t
hl
ong perpen
di
cu

l
ar wa
ll
s, an
dfi
na
lly
w
e closed the loop re-enterin
g
the laborator
y
(see the dashed path in Fi
g
.
6
)
.
T
h
e correctness o
fi
nte
g
rat
i
ons
h
as
b

een
d
eterm
i
ne
dby
v
i
sua
lly
eva
l
uat
i
n
g
t
he
start
i
n
g
part
i
a
l
maps an
d
t
h

e
fi
na
l
map w
i
t
h
respect to t
h
e rea
l
env
i
ronment
.
5.1
S
can Matching Experiments
1
m
1m
1m
1m
1m
1m
1m
1m
1m
F

igure
2.
T
op,
l
e
f
ttor
i
g
h
t: scan
s
S
4
,
S
5
,
S
18
,
S
19
,
S
25
,an
d
S

26
;
b
ottom,
l
e
f
ttor
i
g
h
t:
fi
na
l
map
s
S
4
,
5
,
S
18
,
19
,an
d
S
25

,
26
Ta
bl
e1s
h
ows t
h
e resu
l
ts o
b
ta
i
ne
db
y matc
hi
ng t
h
ree
i
nterest
i
ng pa
i
rs o
f
scans (see a
l

so F
i
g. 2).
S
4
an
d
S
5
were ta
k
en
i
ns
id
et
h
e
l
a
b
oratory: t
h
ey conta
in
a
l
arge num
b
er o

f
s
h
ort segments s
i
nce t
h
eenv
i
ronment
i
s
hi
g
hl
y scattere
d.
S
18
an
d
S
19
were ta
k
en a
l
ong t
h
e

h
a
ll
way: t
h
ey conta
i
n
f
ewer segments t
h
an t
he
p
rev
i
ous scans an
d
are c
h
aracter
i
ze
db
y
l
ong rect
ili
near segments
.

S
2
5
an
d
S
2
6
were ta
k
en
i
nt
h
e
h
a
ll
:t
h
ey conta
i
non
l
y
f
ew segments s
i
nce t
h

eenv
i
ronmen
t
i
sc
h
aracter
i
ze
db
y
l
ong rect
ili
near an
d
perpen
di
cu
l
ar wa
ll
s
.
In genera
l
, our exper
i
menta

l
resu
l
ts
d
emonstrate t
h
at scan matc
hi
ng per
-
f
orms we
ll
(Ta
bl
e 2),
b
ut not a
ll
t
h
epa
i
rs can
b
e matc
h
e
d

.28pa
i
rs o
f
scan
s
1
4
0
Ami
g
oni, et al
.
T
able
1
.
E
xperimental results on matching pairs of scan
s
S
cans
S
4
S
5
S
18
S
19

S
2
5
S
2
6
#
of segments 47 36 24 24 10 1
2
T
i
me # tr
i
e
d
T
i
me # tr
i
e
d
T
i
me # tr
i
e
d
A
ll transformations 936 41
,

260 32 3
,
096 0.38 23
1
C
onsecutive segments 1.2
5
2 0.73 27 0.13
4
Random segments 7.69 20,000 2.
5
1 20,000 0.78 20,00
0
Hi
stogram 3.2
9
73 1.
9
71
9
2 0.1
5
3
2
1
m
1m
1m
F
igure

3.
S
can
s
S
1
(
l
e
f
t),
S
2
(center), an
d
S
3
(r
i
g
h
t) ta
k
en
i
nt
h
e
l
a

b
entranc
e
1m
1m
F
igure
4.
S
can
s
S
2
7
(
l
e
f
t) an
d
S
28
(r
i
g
h
t) ta
k
en
i

nt
h
e
h
a
ll
o
ut o
f
31
h
ave
b
een correct
l
y matc
h
e
d
. Unsurpr
i
s
i
ng
l
y, t
h
e
hi
stogram-

b
ase
d
h
eur
i
st
i
cwor
k
e
d
we
ll
w
i
t
h
scans conta
i
n
i
ng
l
ong an
d
perpen
di
cu
l

ar segments
,
a
st
h
ose ta
k
en
i
nt
h
e
h
a
ll
way an
di
nt
h
e
h
a
ll
.T
h
e
h
eur
i
st

i
c
b
ase
d
on consec
-
u
t
i
ve segments seems to wor
k
we
ll i
na
ll
t
h
ree
ki
n
d
so
f
env
i
ronment, even
if
somet
i

mes
i
t nee
d
s some parameter a
dj
ustments
.
For scan pa
i
r
s
S
1
−
S
2
a
n
d
S
2
−
S
3
o
ur met
h
o
dw

as not a
bl
eto
fi
n
d
t
h
e correc
t
trans
f
ormat
i
on. As s
h
own
i
nF
i
g. 3, t
h
e scans are extreme
l
yr
i
c
h
o
f

s
h
ort seg-
ments represent
i
ng scattere
d
sma
ll
o
bj
ects (c
h
a
i
rs, ta
bl
es, ro
b
ots, an
db
oxes).
It
i
sa
l
most
i
mposs
ibl

e, even
f
or a
h
uman
b
e
i
ng, to
fi
n
d
t
h
e correct matc
hb
e
-
tween t
h
ese scans w
i
t
h
out any pr
i
or
i
n
f

ormat
i
on a
b
out t
h
e
i
rre
l
at
i
ve pos
i
t
i
ons
.
Si
m
il
ar pro
bl
ems emerge
di
nt
h
e
h
a

ll
.F
i
g.4s
h
ows scan
s
S
27
a
n
d
S
28
,
w
h
ere
t
h
e secon
d
one
h
as
b
een ta
k
en a
f

ter rotat
i
ng t
h
ero
b
ot o
f
a
b
out 100
d
egrees
.
Si
nce t
h
eenv
i
ronment
i
s
l
arge an
dh
as on
l
y
f
ew o

bj
ects t
h
at can
b
e use
d
as re
f-