Fo mal Speci ica ion
o
Holonic Con ol Sys em ADACOR
P oduc Holon, using High-Le el Pe i Ne s
Paul0
Lei b
’,
A mando
W.
Colombo
’,
F ancisco Res i o
3,
Ronald Schoop
Poly echnic Ins i u e o B aganqa
Quin a
S’”
Apolonia, Apa ado 134,5301-857 B aganp, Po ugal
E-mail: [email p o ec ed]
*
Schneide Elec ic GmbH
S einheime S . 117,63500 Seligens ad , Ge many
E-mail:
[email p o ec ed]
Facul y o Enginee ing, Uni e si y o Po o
Rua D . Robe o F ias, P-4200-465
Po o,
Po ugal
E-mail: [email p o ec ed]
Schneide Au oma ion SA
245 ou e des Lucioles BP147, Sophia An ipolis, F ance
E-mail:
[email p o ec ed]
Abs ac
-
Holonic manu ac u ing and mul i-agen pa adigms
a e sui able o suppo be ac ual challenges
o
lexible
manu ac u ing sys ems, due o hei decen alisa ion, modula i y
and au onomy ea u es. The o mal speci ica ion assumes a
c i ical ole in o de o unde s and and syn hesise hose complex
sys ems. The Pe i Ne s o malism
is
adequa e o model and
alida e he dynamic beha iou , bu p esen weak poin s when
he sys em con ains many ins ances
o
he same componen , since
he model g ows (s uc u e and componen s)
in
a
non-
con ollable manne . The use o High-Le el Pe i Ne s,
allows
o
educe his complexi y, by comp essing he ep esen a ion o
s a es, ac ions and e en s, o o e come he iden i ied limi a ions
and o suppo mo e complex and bigge coo dina ion scena ios.
This pape p esen s a o mal speci ica ion o he ADACOR
p oduc
holons
using High-Le el Pe i Ne s and he associa ed
o mal alida ion o he model.
Keywo cls:
Flexible Manu ac u ing Sys ems, Holonic
Manu ac u ing Sys ems, Colou ed Pe i Ne s, Fo mal
Speci ica ion, Modelling.
I.
INTRODUCTION
The lexible manu ac u ing sys ems a e complex and
s ochas ic en i onmen s equi ing he de elopmen
o
lexible, agile and in elligen managemen and con ol
a chi ec u es ha suppo small ba ches, p oduc di e si y,
high quali y and low cos s, imposed by global ma ke s.
Holonic and mul i-agen app oaches seems o be sui able o
ace hese equi emen s due o hei decen alisa ion,
modula i y, au onomy and e-use con ol so wa e ea u es.
In he las yea s, se e al a chi ec u es and de elopmen s in
holonic manu ac u ing we e epo ed, co e ing di e en
applica ion domains, such as manu ac u ing scheduling and
con ol, ma e ials handling, machine con olle s and assembly
sys ems,
as
e e ed in
[l-51,
and o he s compiled in [6].
One o hese holonic a chi ec u es, p oposed du ing he las
wo
yea s, is he ADACOR (Adap i e Holonic Con ol
A chi ec u e o Dis ibu ed Manu ac u ing Sys ems)
a chi ec u e [7], which aims o imp o e he pe o mance o
con ol sys em in indus ial s ochas ic
scena ios,
cha ac e ised
by he ?equen occu ence o unexpec ed dis u bances.
ADACOR is based
in
a se o au onomous, coope a i e, sel -
o ganised and in elligen holons, g ouped in o ou main
holon classes, Fig. 1: p oduc , ask, ope a ional and supe iso
holons
[7].
Each a ailable p oduc is ep esen ed by a p oduc holon ha
con ains all knowledge ela ed o he p oduc and p ocess.
P oduc ion o de s o be execu ed in he ac o y plan a e
ep esen ed by ask holons, which a e esponsible o he
con ol and supe ision o hei execu ion. The ope a ional
holons ep esen he manu ac u ing esou ces, such
as
ope a o s and obo s, managing i s beha iou and agenda
acco ding he esou ce goals, cons ain s and skills. The
p oduc , ask and ope a ional holons a e qui e simila o he
p oduc , o de and esou ce holons, p esen ed a he PROSA
e e ence a chi ec u e
[
11. The supe ision holon, p esen s
di e en cha ac e is ics han he s a holons de ined
in
PROSA, in oducing coo dina ion and global op imisa ion
in
decen alised con ol app oaches, coo dina ing se e al
ope a ional and supe iso holons.
In
no mal ope a ion, he
supe iso holon supe ises and egula es he ac i i y o he
holons unde i s domain, while when a dis u bance occu s,
hese holons may ha e o ind hei way wi hou he help o
0-7803-8200-5/03/$17.00 02003 IEEE
263
he supe iso holon. The supe iso holon is
also
esponsible
o he g oup o ma ion, based in p e-de ined clus e s o
holons, combining syne gies, agg ega ing skills and o e ing
he combined se ices o ex e nal en i ies in he
manu ac u ing sys em. These g oups can be o med o build a
shop loo , a manu ac u ing cell, o a machine equipped wi h
a se o ools, assuming he supe iso holon he con ol ole
o each g oup.
p acess
planning
lwel
supe ision
le el
coo dina ion
le el
(only
In
s able
-+-------- +-
E
Fig.
1
In e dependency be ween
ADACOR
Holon
Classes
In
o de o o malize he s uc u e and he beha iou o he
holonic manu ac u ing con ol sys ems, and o alida e i s
beha iou s and pa icula i y o analyse he co-ope a ion and
in e ac ion be ween he dis ibu ed holons, aiming o
unde s and and syn hesize he s uc u e and beha iou o he
sys em, i is impo an o coun wi h a o mal modelling
me hodology.
The modelling
o
he
dynamic beha iou
o
he sys em
equi es a o mal ool ha cap u es cha ac e is ics like
concu ency o pa allelism, asynch onous ope a ions,
deadlocks, con lic s solu ions and esou ce sha ing, which a e
inhe en o ADACOR. Addi ionally, i is c ucial ha he
o mal modelling ool has he capabili y o alida e he
beha iou al cha ac e is ics o hese e en -d i en sys ems,
as
also he analysis o o he impo an aspec s, such as he
deadlock de ec ion and he pe o mance analysis.
The me hodology p oposed in [8] o he o mal modelling o
holonic applica ions,
as
illus a ed in Fig.
2,
combines he
UML
(Uni ied Modelling Language) and he PN modelling
ools.
UML
is
an objec o ien ed based modelling ool ha is
adequa e o model he s uc u e and he s a ic aspec s o a
manu ac u ing sys em. In he p oposed o mal me hodology,
he s a ic aspec s a e modelled using mainly he class
diag ams, which show he classes o objec s in he sys em, he
a ibu es and me hods o each class, and he ela ionships
be ween he objec s.
manu ac u ing sys em
I
I
ix
Ol
in e g bn
hag ams
I
./-J
I
Fig.
2
Modelling
a
Manu ac u ing Con ol
Sys em
The UML modelling ool doesn’ suppo e icien ly he
modelling o he dynamic beha iou aspec s and he o mal
alida ion o hese speci ica ions.
On
he o he hand, he PNs
is
a o mal modelling ool, bo h g aphical and ma hema ical
ha seems adequa e o model and analyse he s uc u e and
he dynamic beha iou o complex e en -d i en sys ems wi h
high dis ibu ion deg ee.
In
compa ison wi h
UML,
he
PN
o malism allows designing he con ol sys em beha iou , bu
also o o mally alida e and e i y he beha iou o he
sys em, based in a s ong ma hema ical backg ound inhe en ly
embedded in he
PN
o malism.
In
his sense, he p oposed
me hodology uses he PN o malism o model he dynamic
beha iou
o
he holonic manu ac u ing con ol sys em. Mo e
de ails abou PN heo y and ma hema ical undamen als a e
ou o he scope o his wo k, bu can be ound in he
ollowing e e ences
[9,
101.
The o mal me hodology desc ibed in
[8]
o model he
beha iou o he ADACOR-holon classes in a bo om-up
app oach, uses a kind o Pe i ne ailo ed o p oduc ion
managemen and con ol modelling pu poses. The indi idual
model
o
each holon uses special empo ised ansi ions o
model ac i i ies execu ion, ha can be exploded in o
a
mo e
de ailed and e med le el. These sub-models, acco ding o he
deg ee o e inemen , a e he di e en so wa e con ol
modules o he ha dwa e, i.e., a o mal ep esen a ion o he
holons. The edi ion, simula ion, analysis and o mal
alida ion o he s uc u al and beha iou al speci ica ions o
he ADACOR-holons can
be
ound in
[l
I].
Howe e , in indus ial manu ac u ing applica ions, he
PN
models become highly complex and di icul o handle and
he de eloped models
o
he
holon
classes p esen some
limi a ions. The modelling o simul aneous execu ion o
di e en ins ances, such
as
he modelling o di e en
esou ces using he same ope a ional holon model o di e en
p oduc ins ances using he same p oduc holon model, is a
complex ask ha canno be co e ed by he PN- o malism
p oposed in [8].
The use
o
High-le el PN, such
as
hose p oposed in [12],
allows educing his complexi y, by comp essing he
ep esen a ion o s a es, ac ions and e en s, o o e come he
iden i ied limi a ions and o suppo mo e complex and bigge
264
coo dina ion scena ios. In his case, o example each p oduc
has a colou - one, allowing o ha e he same model as many
imes
as
he numbe o colou - ones.
This pape is o ganised as ollows: Fi s , Sec ion
2
p esen s
he o mal no a ion and Sec ion 3 he basic concep s and
o mal de ini ions associa ed o he Colou ed Pe i Ne s. In
Sec ion 4 i is desc ibed he CPN model o one ADACOR
holon, he p oduc holon, ha allows o model he
simul aneous execu ion o di e en ins ances, suppo ing
mo e complex and bigge coo dina ion scena ios. Sec ion 4
discusses he co ec ness o s uc u e and beha iou o he
model. Finally, Sec ion
5
ounds up he pape wi h
conclusions.
II.
NOTATION
The no a ion ha will be used in he o mal modelling using
High Le el Pe i Ne s, will be b ie ly p esen ed.
Conside
N
as
he se o non-nega i e in ege s and
Z
as
he se
o in ege s. Le R be a ini e se . The se o unc ions om
R
o
N
is deno ed Bag
(a).
An
i em a o Bag
(0)
is deno ed
xa,,.u
whe e he summa ion
is o e
U
E
R.
I is also called a mul i-se a.
A
pa ial o de on Bag
(R)
is de ined by:
aSbi andonlyi Vu
E
R,a,,Sb,
The sum o wo i ems
o
Bag
(R)
is de ined by:
[a+b=
x
(a,,+
b.).~],
V
U
E
R
The inne p oduc o wo i ems o Bag (R) is de med by:
[a.+
x
(au. bJ],
V
U
E
R
Then <u,>.<u,>=O i i; j and
<u,>.<u,>=I
i i=j
a,,=
a<u> show he mul iplici y o he elemen
U
E
R.
Le A and B wo ini e non-emp y se s, hen a unc ion
E
[A
+
Bag (B)], whe e a and Bag (B) a e non-emp y se s, can be
uniquely ex ended o a linea unc ion e i
E
[Bag (A)
-+
Bag
(B)] called he mul i-se ,
:
V c
E
Bag
(A):
kx (c)=
x
c(a). (a),
V
a
E
A
As
an example, conside he se s A={al, a2, a3) and B={bl, b2.
b3, b4). Then we ob ain:
1) mul i-se msl= al + 2.a2
+
a3 and mul i-se ms2
=
a2 +
2)
i
4.a3 a e bo h membe s o Bag
(A).
E
[A
-+
Bag (B)] is de ined by (al)= bl
+
2.b3;
(a2)= b2
+
b3
+
b4; (a3)= b3
+
2.b4
hen V
c
E
Bag
(A),
ex (c)
=
c(al).(bl
+
2.b3)
+
c(a2).(b2+b3+b4)
+
c(a&(b3+2.b4)
=
c(al).bl
+
c(a2).b2
+
[2.c(al) + c(a2)
+
c(a3)l.b3
+
c(a2)
+
2.c(a3)l.b4
Rema ks:
In
his wo k we use he e ms unc ion
,, '
and i s
linea ex ension unc ion ,, ex " in he same way.
111.
COLOURED
PETRI NETS
A.
In oduc ion
Colou ed Pe i Ne s (CPN) a e ma hema ical-g aphical
o ien ed o malisms o design, speci ica ion, alida ion and
e i ica ion o concu en sys ems [13,14]. A CPN is
pa icula ly well sui ed o sys ems whe e communica ion,
synch oniza ion, concu ency and compe i ion on sha ed
esou ces a e impo an ela ionships. Typical examples o
applica ion a eas a e communica ion p o ocols, dis ibu ed
sys ems, embedded sys ems, lexible manu ac u ing sys ems
and wo k low analysis. Wi hou
loss
o igo , he es o he
pape concen a es on hei applica ion in he holonic
manu ac u ing a ea.
CPN ha e go hei name because hey allow he use o okens
ha cany da a alues and can be dis inguished om each
o he , in con as o he okens o low-le el Pe i ne s, which
by con en ion a e d awn
as
black-do s.
B.
De ini ions
Le 's ecall he e, unde he de ini ions o a CPN, he i ing
ule o ansi ions, he incidence ma ix and he ne lows.
De ini ion
1:
A CPN is a 7- uple, [15],
CPN= <P, T, C,
I?,
I-,
G,
Md
sa is ying he ollowing equi emen s:
-
P=
{pl, p2,
...,
pm} is
a
ini e se o places.
-
T= { l, 2,
...,
n}
is a ini e se o ansi ions
C is he colou unc ion de med bom PUT in o R; R is a
ini e and no emp y se . C(s) is called he colou se o
,$',
and an i em o C(s) is called a colou o
$'.
C
a aches o each place a se o possible oken-colou s C@)
and o each ansi ion a se o possible occu ence-colou s
o ing modes C( ).
I
(
1.)
a e espec i ely he inpu unc ion and he ou pu
unc ion de med on PxT, such ha 1' (p, ) is a unc ion
bo n
C( )xC(p)
o N (i.e., a unc ion om C( ) o Bag
(C(P)),
V
(P4
E
PxT.
No a ion: I is no ed
I+,
I-(p, ,
c,),
whe e
c,
belongs o
C( ), he co esponding i em
o
Bag (C(p)). ' and ' a e
he backwa d (p e-condi ions) and he o wa d (pos -
condi ions) se o places o he ansi ion .
-
G
is he
gua d i nc ion,
de ined om T in o exp essions
o ype Boolean, (i.e., a p edica e), such ha
V~ET:
[Type(G( ))= Boolean
A
Type(Va iable(G( )))
s
C].
265
V
E
T
A
Vc,,,
c,,,
&
E
c( )
3
G&,( )=
(ql
A
q,
(-&)
A
.
.
.),
ii j+k.
Each G&,( ) is a Boolean unc ion o occu ence modes,
ela ed o he ansi ion , whe e
Q
is a Boolean a iable
+
(-Q)=
1
exac ly when
Q=
0.
Acco ding o his de ini ion, a s anda d o m o a Gua d
unc ion is desc ibed bellow:
G( )= G&l( )
G&2( )
G&,( )
...
-
MO
is he ini ial ma king o he ne . I is a unc ion
de ined
on
P, whe e MO@) is a unc ion om C(p) o N
(i.e., an i em o Bag (CQ)),
V
p
E
P.
The M(p) and Mo(p) ma kings gi e espec i ely he
numbe o colou ed okens in he place ,,p" o he
cu en and he ini ial ma king.
De ini ion
2:
The i ing ule o CPNs is de ined by:
-
A ansi ion is enabled o a ma king M and o a colou
mode
c,
E
C( ) i and only i V p
E
' ,
M(p)
L
I-(p, ,
q).
-
The ing o ansi ion o a ma king M and a colou
mode
c,
E
C( ) gi es a new ma king
M'
de ined
V
p
E
P
by,
M'@)=
M(P)
-
UP,
4
+
4
4
(1)
De ini ion
3:
The incidence ma ix
I
o a CPN is de ined by
IQ,
,
c,)=
I+(P,
,
c )
-UP,
,
c,)
Then
I
is
a unc ion om C(p)xC( ) o
Z.
I(p,
,
c,)
can also be
iewed like a ma ix o R(p, c)xR( , c') o in ege s, whe e he
i s union is o e p
E
P and c
E
C(p) and he second union is
o e
E
T and c'
E
C( ), by he simple ans o ma ion I((p, c),
( , c'))= I(P, Nc, CY),
De ini ion
4:
A posi i e weigh ed se o places
is
a unc ion
S
de med on P, such ha
The ope a o "." is he gene aliza ion o ma ix mul iplica ion,
by subs i u ing each p oduc o a unc ion composi ion.
De ini ion
5:
Le be he equa ions sys em
XT.I=O
VT.
M'= T.
M
because T.
I=
0
(2)
The se o place- lows (p- lows)
E
o a CPN is de ined by
E=
{ : ec o o colou ed places
/
T .
I=
0)
The equa ion
(2)
is called a linea in a ian o ma kings
(place-in a ian s).
De ini ion
6:
Le
be
he equa ions sys em
I.
xT=
0
I x=w is a solu ion and i equa ion
(1)
is mul iplied on he
igh by wT, o all eachable ma kings M and
M',
hen
M'
.
wT=
M.
wT+
I.
wT
whe e wT
is
a ec o o he posi i e weigh ed se o ansi ions
( i ing modes o ansi ions) wi h dimension Ca d(T).
(3)
The se o ansi ion- lows ( - lows)
F
o
a CPN is de ined by,
F=
{w: ec o o i ing modes o ansi ions
/
LwT=
0)
The equa ion
(3)
is called a linea in a ian o ings
( ansi ion-in a ian s).
In p ac ice, he e a e some kind o colou domains and colou
unc ions, which a e equen ly used. These
a e
called
s anda d colou domains and s anda d unc ions ( o mo e
in o ma ion, he eade should consul
[15]).
M'
.
wT
=
M . wT because
I.
wT= 0, and
M=
M
De ini ion
7:
A
se
R,
is called "basic (s anda d)
colou
domain" and i s elemen s "colou ones".
SZ,
can be ex ended
o
he ing
(R,
,
63,
O),
whe e he a i hme ic unc ions
@
and
'
a e execu ed module
s
(s
is he ca dinali y o
0,)
[15].
Fo example, a s anda d colou domain in his wo k can be
de ined
as
PH=
(ph,, ph2, ...,p h,).
PH
is he colou
p oduc -holon and each elemen is a p oduc holon (colou
one ph,).
U:
The basic colou domain
Cl,={<*>}
is he se , which
unique elemen
is
he discolou ed oken co esponding o he
classical de ini ion o ma king
[9].
De ini ion
8:
A complex colou domain is de ined
as
he
Ca esian p oduc o
wo
o
mo e basic colou domains.
De ini ion
9:
The Uni e sal colou domain
R*
o he ne will
be he Ca esian p oduc o all basic colou domains. Tha is
I x
=
is a solu ion and i equa ion
(1)
is mul iplied
on
he
le by
6,
o all eachable ma kings M and M', hen
T
. M=
T .
M
+
T
.
I
.
D, whe e D is a ec o o he posi i e
weigh ed se o ansi ions
( uing
modes o ansi ions) wi h
dimension Ca dinal Ca d(T).
Q*=
nj
E
<ol,
%,
...,
a, and
a*
E
Q*
a*=
<a1,
a2:
...,
a>=
De ini ion
10:
The colou unc ions associa ed wi h he a cs
o he ne
a e
he elemen s o he ma ix
1'
(I-).
They a e
266
de ined
V
o*
E
R*
and hey a e buil om he ollowing
basic (s anda d) unc ions o hei linea combina ion
[16,17]:
whe e
MO
[
a>
deno es ha he sequencea may be ed a
MO,
and
MO
[
a>
Mk
deno es ha he i ing o
CJ
yields Mk..
-
P ojec ion unc ion (P oj), which selec s a componen oj
D.
G aphic Rep esen a ion
(colou ) o an i em
o*;
-
Iden i y unc ion (Id), which selec s all he componen s o
AS
example, conside Fig.
3
ha depic s he g aphical and
da a s uc u e o a sample CPN ailo ed o holonic con ol
sys em speci ica ions.
an i em
a*
;
-
Successo (Succ)
I
P edecesso (P ed) unc ion, which
selec s some successo
o
p edecesso o a componen o
an i em. Fo example, he
3“
successo o he k* colou
o
an i em
o*
is de ined as ollows:
succk3:
R*
-$’
R*:
<dw],
02,
...,
%,
...,
w)
(o[,
~2,
...,
a693,
...,
%)>,
V
k
E
Q;
-
Decolou ed unc ion (Abs), which ans o ms a colou ed
Rema k I is possible o build a composi ion o s anda d
colou unc ions. Fo example, i SucckJ:
R*
-$’
R*
and P ol,:
ma king in he uncolou ed oken
<a>.
I=Nl-=~-
h=--nl=i ,
I,J
“(Pa,,,
J
u~~‘-colo n’=nlxm=(y~ ,p4>i
061
=[ ,npa,l
Gh2
=
I ,np2]
G63
=
[,,A
p.J
&s_Fu~s.uz,
< ,
p>
=
< ,
y.,>
ld
m.=
y
p ql
y
=
< ,>
a*
lk hen [email p o ec ed]:
a*
-$’
Rk.
m
WI
=
‘PV
C.
Dynamic Beha iou
The ne e olu ion, i.e., dynamic beha iou , is suppo ed by
he ~ng o he ansi ions, which is cha ac e ized by he
mo emen o okens be ween places. A leas
wo
aspec s a e
ep esen ed by he e olu ions (when a ansi ion i es and he
CPN e ol es om one s a e o ano he one): he i s one
exp esses se ial and concu ence e en s ha can be obse ed,
i.e., he in e ac ion s a es achie ed by he agen s. The second
aspec desc ibes he causally p ecedence ha exis s among
p oduc ion componen s, i.e., physical agen s, and in e ac ion
ac s occu ed du ing p oduc ion con ol and managemen .
De ini ion 11(Fi ing Rule):
I
a ansi ion o i ing-mode is
e ec i ely enabled, hen i can be i ed.
De ini ion
12
(E olu ion Rule): The i ing o a ansi ion o
a i ing mode i issues a change o he s a e o he ne (change
o he ma king), which can be ep esen ed as ollows:
being
A40
and M he ini ial and inal ma kings (s a es).
The e olu ion o he ne is cha ac e ized by he oken-game,
i.e., low o ma ks be ween places.
De ini ion 13 (Sequence
o
i ing): A i ing
sequence
om a
ma king
MO
is a (possibly emp y) sequence o ansi ion se s
C=
i 2
...
k
SO
ha
MO
[
i
>
MI
[
2
>
M2
....
[
k
>
Mk
Fig.
3
A
Colou ed
Pe i
Ne
Model
The ci cles o he ne a e called places and ep esen he s a es
o he modelled p oduc ion esou ces, i.e., manu ac u ing
uni s plus mecha onics componen s. The ma king o each
place belong o a speci ic se o colou ed okens.
In
his case,
each place can con ain a se o ma ke s called okens ca ying
a da a alue, which belongs o a gi en ype o se o ypes. In
he example o Fig.
3,
he ma king o he place pl belongs o
he se
o
obo s ep esen ed by di e en obo s ypes, and he
ma king
o
he place p4 belongs o he se o p oduc s
ep esen ed by di e en ypes o palle s.
The ec angles a e called ansi ions and desc ibe he
manu ac u ing ac i i ies. In he example o Fig.
3,
he
ansi ion
b
is modelling an Assembly Task. Tha is, he
obo is placing a pa
in
he palle .
The a cs connec places wi h ansi ions and ansi ions wi h
places. They ha e an a ached a c unc ion (exp ession),
which desc ibes how he s a e o he
CPN
changes when he
ansi ions a e ued.
Gua ds a e associa ed
o
he ansi ions. They ep esen
es ic ions o he ype
o
da a alue, i.e., colou ed ma ks, ha
a ansi ion can mo e du ing i s i ing. They a e also called:
ansi ion ~ng-modes. To be i ed wi h espec o a ~ng-
mode, a ansi ion mus ha e su icien okens on i s inpu
places.
In
his case, he okens mus ake alues ha ma ch he
a c exp essions, and hey mus belong o a ype ha ma ch
also he gua ds associa ed wi h he ansi ion.
A
ansi ion is
said hen “e ec i ely enabled”.
267

IV.
MODELLING
THE
BEHAVIOUR
OF
THE
ADACOR
PRODUCT HOLONS USING
HIGH LEVEL
PETRI
NETS
In his sec ion, one o he ADACOR holon classes, namely
he p oduc holon, will be modelled using High-Le el Pe i
Ne s, illus a ed in Fig.
4,
wi h he o mal no a ion, p e iously
desc ibed. The numbe o p oduc holons p esen in he
holonic manu ac u ing con ol applica ion is dependen
o
he
manu ac u ing con ex ualiza ion, bu one and only one model
o
a p oduc
holon
is
needed.
This
complex model
is
capable
o ep esen all p oduc s and hei ins ances.
A. Colou s
De ini ion
The ini ial phase
in
he modelling o p oduc holon class,
using High-Le el PN, is he de ini ion o he
colou s
ela ed
o he p oduc beha iou . Du ing he holon li e-cycle, hese
colou s will be managed by he unc ions associa ed wi h he
s uc u e o he holons p esen in he holonic con ol sys em.
Acco ding he De ini ion
7,
he basic colou s de ined in
his
wo k o he p oduc holon model a e:
-PH
=
{phi,
ph2,
...,
ph.}, which a e all possible p oduc
holons in he sys em. In case
o
1000000
p oduc holons
p esen in he sys em, he n alue is ela ed o 1000000;
-O
=
{o l,
o 2,
...,
o ,,,},
which a e all possible p oduc ion
o de s in he sys em;
-WP
=
{wpl,
wpz,
..,
wpl),
which a e all possible wo k
plans in he sys em;
-RMP
=
{ mpl, mp2.
..,
mp,}, which a e all possible aw
-TH
=
{ h,, hz,
..,
&},
which a e
all
possible
ask
holons
Some complex colou s, acco ding De ini ion
8,
a e also
de ined om he p oduc o
wo
o
mo e basic
colou
domains:
ma e ials and pa s
in
he sys em;
in
he sys em.
-
ClI2
=
PH
x
O
=
<
ph,,
o ,
2,
which ep esen s
a
p oduc ion
o de
o ,
o he p oduc ep esen ed
by
he p oduc holon
ph, (since each p oduc holon
can
ha e se e al ins ances
unning a he ac o y plan ).
-nlZ3
=
PH x
O
x WP
=
(
mk=
<
ph,,
o J,
wp,
>},
-n12~=
PHx
O x
WP x
RMP=
<
ph,,
o ,,
Wp,,
mph
>,
-Q212M5
=
PH
xO
x
WP
xRMP
xTH
=
<
ph,,
o J,
wp,,
mph, h,
>,
which is he uni e sal colou in he model, i.e.
he Ca esian p oduc o all basic colou domains.
One possible colou
in
eal ime associa ed wi h a eal
so wa eha dwa e componen is p esen ed in Fig.
5.
B.
Func ions
De ini ion
In
a CPN model, each inpu and ou pu a c ha e associa ed a
unc ion ha manipula es he colou s componen s, by
emo ing app op ia ed componen s om he inpu elemen s
and pu ing app op ia ed componen s in he ou pu elemen s.
268
In
he p oduc holon model, he ollowing unc ions we e
de ined:
-p ojl.q
=
<
ph,
>
,
is he p ojec ion unc ion ha il e s
he ph, colou .
-p oj2.~
=
<
o J
>
,
is he p ojec ion unc ion ha il e s
he o J colou , c ea ing a new ins ance o a p oduc ion
o de .
-p oj3.q
=
<
wp,
>
,
is he p ojec ion unc ion ha il e s
he
wp,
colou .
-
p oj4.q
=
<
mph
>
,
is he p ojec ion unc ion ha il e s
he mpb colou .
-
p oj5.W
=
<
h
>
,
is he p ojec ion unc ion ha il e s
he h, colou .
-p ojl2.y,
=
<
ph,, o J
>
,
il e s composed sub- uples in
o de o ge e ined in o ma ion, in his case he pai
p oduc holon (i) and p oduc ion o de
0).
-p oj123.@
=
<
ph,, o J
,
wp,
>
,
il e s
W,
e u ning he
pai p oduc holon (i), p oduc ion o de
6)
and wo k plan
(2).
-p oj1235.q
=
<
ph,, o J
,
wp,,
h,
,
il e s
q,
e u ning
he pai p oduc holon (i), p oduc ion o de
G),
wo k plan
(z) and ask holon ( ).
-
succ3,.wak=
<
ph,, o J
,
wp,,,
>
,
wp,
being one possible
Wo k Plan o he se
W,
he unc ion
SUCC~~
selec s he
"y" successo o he
wp,,
acco ding p ojl, p oj2 and p oj3
unc ions, i.e. ha
wp
ha ma ches wi h he cu en
p oduc holon-p oduc ion o de pai .
-succ4..~
mn
>
=
<
m~h+~
>
,
e u ns he x successo o
he mp componen , i.e. he nex mp componen in he
p oduc s uc u e.
-
id.%
=
q,
which
is
he iden i y unc ion, i.e. his unc ion
applied o a speci ic colou gi es as esul he same colou .
A ansi ion ha ep esen s he selec ion o wo dis inc
ac ions o he esul o a decision o an componen has so
many i ing modes as holons o hese ypes we e de ined.
Only by il e ing i will be possible o know which ac ion will
be pe o med o which componen is aking he ac ion.
As
example,
in
he model o know i all aw ma e ial and pa s,
necessa y o execu e he p oduc , a e a ailable, i is used a
gua d unc ion ha selec s he low
o
he okens. The gua d
G=[ I mp,=l] has he T ue Boolean alue i all ins ances
o
RMP
colou domain a e T ue, i.e. all aw ma e ial o pa s a e
a ailable o p oduce a p oduc . O he wise, his gua d unc ion
is alse, bu he gua d G=[n mp,=O] has he T ue Boolean
alue, e-di ec ing he
low
o he okens o he need o
eques he missing aw ma e ials o pa s.
Analysing in mo e de ail he p oduc holon model, i is
possible o e i y ha i con ains ecu si i y. In he case ha a
P10
P11
sub-p oduc is eques ed h ough he
" eques
o
missing
aw
ma e ial
and
pa s"
ac i i y, his model is ecu si ely
in oked, implying
a
p oduc ion o de (belongs o O ), and he
sub-p oduc will be conside ed by a p oduc holon (belongs o
PH).
{<ph3.
o j,
WPS,
hp>)
.
FORMAL
VALIDATION
OF
THE
MODEL
Taking in o conside a ion he exempla y ma king p esen ed
in
Fig.
5,
which ep esen s a s a e
o
he ne depic ed in Fig.
4,
he ollowing a e some o he speci ica ions ha can be
alida ed
-The e
a e
wo
p oduc s wi h hei co esponding
p oduc ion o de s ha a e being cu en ly p ocessed:
The p oduc holon ph,, which is in cha ge o he
p oduc ion o de o 2, has al eady assignedelabo a ed a
wo k plan
(wpk)
o
he p oduc and is eady o
s a
he
e i ica ion
o
he a ailabili y o pa s and aw ma e ial
ha a e necessa y o he p oduc ion p ocess.
The p oduc holon ph3, which is in cha ge o he
p oduc ion o de o ,, has al eady inished he
e i ica ion o a ailable pa s and aw ma e ial and i
has also synch onised i s ac ions wi h a ask holon
( hp). The las is eady
o
s a wi h he con ol o he
execu ion o he p oduc ion o de using he wo k plan
wps
-The sys em is eady o ini ia e he p ocess o
(n-2)
new
p oduc s, o p ocess
(m-2)
new o de s, o assign
(1-2)
wo k
plans, and o synch onize he ac i i ies wi h
(q-1)
ask
holons.
Example
o
Ma king
I
p1
I
{<P~I>, <ph2>, ,<ph4>, <ph(i-l)>, <ph(i+l)>,
,
<phn>)
I
{(X[i:
1-11
wpi)
-
Wpk-wps)
I
p4
I
269
PI
P3
P3
I
p ojl
I
0
P4
I
0
I
0
Place- low 1
I
Place- low
2
1
0
n
I
n
p oj
1
P7
P8
p oil
17
,
I
PI0
I
p ojl
I
p oj5
P11
I
omi
1
I
O oi5
Fig
7
Place- lows
o
Incidence Ma ix
As an example,
wo
place- lows o he Incidence ma ix a e
shown in Fig. 7. These se s o place- lows gene a e a se o
place-in a ian s (PI). Fo example:
PIl:
M(Pl)+<P oJ
I>
[M(P~)+M(P~)+M(P~)+M(P~)+M(P~O)+M(P~
1
)I=
Mo(p
1
)+<p OJ
I>
[Mo(~~)+Mo(~~)+M~(P~)+M~(P~)+Mo(P
IO)+Mo(p
1
1
)I=
I-“]
<ph?
PI2
M(p9) cp ojS> [M(p
1
O)+M(p
1
1
)]=Mo(p9)+<p Oj5> [&(p
1
O)+Mo
(PI
1
)I=
1-11
<W
The p ocessing o hese in a ian s allows he alida ion o
di e en speci ica ions, o example:
P oposi ion 1:
A any one ime, he maximum numbe o
p oduc holons ha can be se in o ope a ion by ADACOR is
limi ed o
n,
i.e., he ini ial ma king o place pl, o he ne
depic ed
in
Fig.
4.
-
P oo
F om PI1, i his is mul iplied by <phi>, hen
Vw‘=<phj,o ,,wpl, mp~, h,>
E
Cl’
<phi>. {M(pl)+<p oj
12.
[M(p3)+M(p5)+M(p7)+M(p8)+M(pI
O)+M(
pll)l)=
=<Phi>. {MO(pl Fp oj
I>.
[M~(P~)+M~(P~)+M~(P~)+M~(P~)+M~(P
1
O)+Mo(pl
I)])
=
<phi>.Zl, I.ll.<phi>
=
n
Wi h his equali y i is possible
o
conclude ha ,
<ph,>.<p oj
1
>.
[M(p3)+M(p5)+M(p7)+M(pS)+M(p
1
O)+M(p
1 1
)]
i
n,
i.e he numbe
o
p oduc holons in ac i i y,
and
<ph,>.M(pl)
5
n
,
i.e. he numbe o p oduc holons idle.
The p oo is s aigh o wa dly ob ained hm bo h un-
equali ies.
Co olla yl:
Fo he exempla y s a e o he model p esen ed
in
Fig.
3,
he applica ion o he esul s o p oposi ion
1,
when
he p oduc holon <ph3> is assigned, ende s he ollowing
main conclusion:
<ph3>.~p oj1>.[M(p3)+M(p5)+M(p7)+M(p8)+M(plO)+M(pl1)]
=
=
<ph3>.<p ojI>.[O~phi,
o 2,
wpkz+ .
{(XL,:
1-11
mp,))+O+O+{(Z,i,
=
<ph3>.[0+0+0+0+<ph3z+0]=
1
and
<phn>)
=
0
This means, ha a any one ime, a p oduc holon can only be
assigned o he p ocess
o
a p oduc .
Co olla y
2:
I is possible o o mal alida e ha a p oduc
holon can be assigned o p oduce a any ime di e en
o de s). Since he colou se s de ined
in
Sec ion IV-A a e
Bags, a colou one can be p esen wi h a gi en mul iplici y,
i.e., u.<phi>. This means ha addi ionally, a p oduc holon
can a any ime handle he execu ion o se e al di e en
o de s, in he maximum o
n
(ca dinali y o he se
O ).
Fo
example, an o de
o (2)
o p oduce he p oduc A wi h due
da e D1,
...,
and an o de
0412)
o p oduce he p oduc A wi h
due da e D4.
Rema ks: The ADACOR a chi ec u e (see [7]) was de eloped
ollowing he speci ica ion ha a ask holon needs o he
ollowing in o ma iodelemen s o supe ise he execu ion
o
a p oduc ion o de : in o ma ion abou he p oduc ion o de
(quan i y, due da e,...), he physical a ailabili y o aw
ma e ial
o
pa s ha belongs o he p oduc
BOM,
and a se
o p ocess plans ha indica es how o p oduce he p oduc . A
he end o execu ion, he ask holon p o ides o he p oduc
holon some in o ma ion ela ed o how he p oduc ion o de
was eally execu ed, such
as
s a and end da es o each
1-11
W-
hql+{<ph3,
O j,
WP~.
hp>)l
=
<P~~>.M(P~F
<ph>.{<phl>, <phz>.
.
..
,ph4, <Ph(i-il>> <Ph(i+i,>,..
,
,
270
ope a ion, he indica ion abou he esou ces ha execu ed he
ope a ions, e c.
P oposi ion
2:
A any one ime, he maximum numbe o ask
holons ha can be se in o ope a ion by ADACOR is limi ed
o
p,
i.e., he ini ial ma king o place p9, o he ne depic ed in
Fig. 4. This alue is equal o he sum o all p oduc ion o de s
launched o he shop loo o be execu ed ( hose
in
places p10
and pl
l),
plus he se o
ask
holons ha a e al eady idle.
-
P oo
Immedia e om he s uc u e o place-in a ian
ela ionship
P12.
Co olla y: The ansi ion 4 models ac i i ies ela ed o he
decision i all aw ma e ials and pa s
a e
physically a ailable
o p oduce a p oduc . The ansi ion 7 models he p oduc ion
o de execu ion.
This
ansi ion ini ially launches he ask
holon
(o
s a s
o gi es he indica ion o he ask holon),
passing he p oduc ion o de in o ma ion and a se
o
p ocess
plans. A e ha , he con ol is passed o he ask holon ( i ing
colou o he ansi ion 7), which is esponsible o he
execu ion o he p oduc ion o de . When he p oduc ion o de
is inished, he ask holon e u ns he con ol o he p oduc
holon passing back in o ma ion abou he o de execu ion, by
means o he i ing o ansi ion 8. The mu ual exclusion
ela ionship be ween he ma kings o p9, p10 and pll, is
closed ela ed o he i ing sequence associa ed o he se
o
ansi ions add essed abo e.
VI.
CONCLUSIONS AND FUTURE
WORK
The o mal speci ica ion o holonic con ol sys ems assumes a
c ucial ole o unde s and and syn hesize he beha iou
o
complex and concu en sys ems, such
as
he
lexible
manu ac u ing sys ems.
A b ie o e iew o he la es wo ks published in he a ea (see
e.g. [19, 201 and ou las epo s
[SI
and [ll]) allowed us o
iden i y a se o weak poin s in using he PN- o malism and
o he simila ex ensions o his ool. This is pa icula ly ue i
he sys em p esen s many ins ances o he same componen
(e.g.,
n
esou ces need
n
ope a ional holons). In his case, he
model will g ow (s uc u e and componen s)
in
a non-
con ollable manne . In ou opinion, he use o High-Le el
PN, allows o educe his complexi y, by comp essing he
ep esen a ion o s a es, ac ions and e en s, o o e come he
iden i ied limi a ions and o suppo mo e complex and bigge
coo dina ion scena ios, like hese p esen ed he e.
In
his pape a High-Le el
PN
o malism, i.e. Colou ed Pe i
Ne s, is used o model he dynamic beha iou o ADACOR
p oduc holons and o mally alida ed his model allowing o
e i y and op imise he hnc ioning o he sys em.
Applying he same me hodology, he se o speci ica ions o
he beha iou o each ADACOR-holon and o he whole
ADACOR-con ol sys em can be alida ed, and o cou se
op imised.
ACKNOWLEDGEMENTS
The us au ho would like o acknowledge he PRODEP
p og am o he inancial suppo g an ed (PRODEP
III-
5.3/2000).
REFERENCES
[I] H. Van B ussel,
J.
Wyns, P. Valckenae s, L. Bongae s and P.
Pee e s, “Re e ence A chi ec u e o Holonic Manu ac u ing
Sys ems: PROSA”,
Compu e s In Indus y,
ol. 37, 1998,
pp.
[2]
K.
Fishe , “Agen -Based Design
o
Holonic Manu ac u ing
Sys ems”,
Jou nal
o
Robo ics and Au onomous Sys ems,
Else ie Science
B.V.,
o1.27,
pp 3-13.
[3] M. Fle che ,
V.
Ma ik and P. V ba, “Design
Issues
in
Holonic
In en oly Managemen and Ma e ial Handling Sys ems”,
in
Knowledge and Technology In eg a ion in P oduc ion and
Se ices: Balancing Knowledge and Technology in P oduc ion
and Se ice Li e Cycle,
V.
Ma ik,
L.
M
Cama inha-Ma os
and
H.
A sa maneh (eds.),
Kluwe Academic Publise s, 2002, pp.
[4] L.
Gou,
P. B.
Luh
and
Y.
Kyoya, “Holonic manu ac u ing
scheduling: a chi ec u e, coope a ion mechanism, and
implemen a ion”,
compu e s in Indus y,
ol.
37, 1998, pp.
[5]
A.
W. Colombo, R. Neube and
R.
Schoop,
“
A
Solu ion o
Holonic Con ol Sys ems”,
in P oceedings
o
he
gh
IEEE
In e na ional Con e ence
on
Eme ging Technologies and
Fac o y Au oma ion,
SophiaiNice, F ance, 2001, pp 489-498.
[6] Jou nal o Applied Sys ems S udies, Special
Issue
on Indus ial
Applica ions o Mul i-Agen and Holonic Sys ems, 2(
I),
2001.
[7]
P. Lei Sio
and
F. Res i o, “Adap i e P oduc ion Con ol
Sys ems”,
in P oceedings
o
special session
on
Agen -based
In elligen Au oma ion and Holonic Con ol Sys ems
o
he 28 h
Annual Con e ence
o
he IEEE Indus ial Elec onics Socie y,
Se illa, Spain,
5-8
No embe , 2002, pp 2968-2973.
[8] P. Lei b, A.W. Colombo and
F.
Res i o, “An App oach o he
Fo mal Speci ica ion o Holonic Con ol Sys ems”,
o
appea in
he
1’‘
In e na ional Con e ence
on
Applica ions
o
Holonic and
Mul i-Agen Sys ems
(HoloMAS),
Sep embe 1-3, 2003, P ague,
Republic Czech.
[9]
T.
Mu a a, “Pe i Ne s: P ope ies, Analysis and Applica ions”,
P oceedings
o
he IEEE,
77(4), 1989, pp 541-580.
[IO] A.W. Colombo and R. Ca elli, “Pe i Ne s o Designing
Manu ac u ing Sys ems”,
Compu e -Assis ed Managemen and
Con ol
o
Manu ac u ing Sys ems,
S.G.
Tza es as
(ed.), cap.
11,
Sp inge -Ve lag 1997.
[I
I] P. Lei lo, A.W. Colombo and F. Res i o, “A Fo mal Valida ion
App oach
o
Holonic Con ol Sys em Speci ica ions”,
submi ed
o he
Yh
IEEE In e na ional Con e ence
on
Eme ging
Technologies and Fac o y Au oma ion,
Sep embe 16- 19, 2003,
Lisboa, Po ugal.
[12] A. W. Colombo, R. Neube and B. Sussmann, “A Colo ed Pe i
Ne based App oach Towa ds a Fo mal Speci ica ion o Agen -
Con olled P oduc ion Sys ems”,
in P oceedings o he IEEE
In e na ional Con e ence
on
Sys ems, Man and Cybe ne ics,
Tunisia, 2002.
255-274.
271-280.
213-231.
271