Discrete Event Decision & Control - UTA talks/Xian PN 08.pdf · r J2 J5 J6 R1 R2 R3 Two 1’s in...

F.L. LewisAutomation & Robotics Research Institute (ARRI)

The University of Texas at Arlington

Discrete Event Decision & Control

Petri Nets in Agile AutomationMengchu Zhou & Zhiwu Li

Automation & Robotics Research Institute (ARRI)The University of Texas at Arlington

F.L. Lewis, Fellow IEEE, Fellow IFACMoncrief-O’Donnell Endowed ChairHead, Controls and Sensors Group

http://ARRI.uta.edu/acs

Discrete Event Decision & Control

Springer-Verlag 2006

ARRI Intelligent Material Handling (IMH) Cell3 robots, 3 conveyors, two part paths

EXAMPLE

Layout of the IMH Cell

X5

X2X8

X4

X6

X7

X3

X9X1

R1

R3 R2

M2 M1

B3

B2

B1 A B A B

IBM robot

PUMA robotADEPT robot

Conveyorbidirectional Conveyorunidirectional

conveyor

machinemachine

Reentrant Flow Line PART B OUT PART A OUT PART A PART B

CRS

ROBOT 1

ROBOT 2

ROBOT 3

Machine 1

Machine 2

A(1)R1

A(2)R1 B(1)R1

B(2)R1

A(1)R2

A(2)R2

B(1)R2

B(1)R3

B(2)R3 A(1)R3

PUMA

ADEPT

Routing and Dispatching Decisions are Needed

Wireless Sensor NetworksARRI Distributed Intelligence & Autonomy Lab- DIAL

UnattendedGroundSensors

SmallmobileSensor-Dan Popa

Testbed containing MICA2 network (circle), Cricket network (triangle), Sentry robots, Garcia Robots & ARRI-bots

Dan Popa

Programmable MissionsMission Programming and Execution

Mission Programming for Distributed Networks

R1

R2

R3

UGS1

UGS2

UGS3

UGS4

UGS5

Deploy & Program

Mission1-Task sequence

Mission 1 completedy1output

S2 takes measurementS2m1Task 11

R1 takes measurementR1m1Task 10

R1 deploys UGS2R1dS21Task 9


R1 gores to UGS1R1gS11Task 7

R1 listens for interruptsR1lis1Task 6

R1 retrieves UGS2R1rS21Task 5

R2 goes to location AR2gA1Task 4

R1 goes to UGS2R1gS21Task 3

UGS5 takes measurementS5m1Task 2


UGS1 launches chemical alertu1Input 1

Descriptionnotationmission1

Mission 2-Task sequence


R1 docks the chargerR1dC2Task 5


R1 charges UGS3R1cS32Task 3

R1 goes to UGS3R1g S32Task 2


UGS3 batteries are lowu2input

DescriptionnotationMission2

Fast Programming of Missions

WSN is also a Reentrant Flow Line!

PART B OUT PART A OUT PART A PART B

CRS

ROBOT 1

ROBOT 2

ROBOT 3

Machine 1

Machine 2

A(1)R1

A(2)R1 B(1)R1

B(2)R1

A(1)R2

A(2)R2

B(1)R2

B(1)R3

B(2)R3 A(1)R3

PUMA

ADEPT

Target/Event/ UGS/

UGS/

UGS/

Target/Event/

Routing and Dispatching Decisions are Needed

Discrete Event Supervisory Control

Objective:Develop new DE control algorithms for decision-

making, supervision, & resource assignment

Apply to manufacturing workcell control, C&C systems, & inetworked systems

• Patent on Discrete Event Supervisory Controller • New DE Control Algorithms based on Matrices• Implemented on Intelligent Robotic Workcell• Implemented on Wireless Sensor Networks• Internet- Remote Site Control and Monitoring

USA/Mexico Internetworked Control

Man/Machine User Interface

TexasTexas

Intelligent Robot Workcell

Fast programming of multiple missionsReal-time event responseDynamic assignment of shared resources

Discrete event controller

T asksco m p le ted v c

R u le-b ased rea l tim e con tro lle r

Cu curv uFuFrFvFx ⊗⊕⊗⊕⊗⊕⊗=

Job s ta rt lo g ic

R esource re lease lo g ic

W ireless Sensor

N etw o rk

. . .

u c

Se nsor ou tp ut u

R esourcere leased rc

S tart tasks v s

S tart reso urcere lease rs

O utp ut yM iss io n co m p le ted

P la nt co m m a nds P la nt s ta tus

D isp atch in g ru le s

C o ntro ller state m o nito ring lo g ic

xSv VS ⊗=

xSr rS ⊗=

xSy y ⊗= T ask co m p le te lo g ic

User interface:mission planning,

resource allocation, priority rules

Sensor readings

events

commands

Decision-making





Job s ta rt lo g ic


W ireless Sensor

N etw o rk

. . .

u c

Se nsor ou tp ut u


S tart tasks v s






xSv VS ⊗=

xSr rS ⊗=




U.S. Patent

Sensor readings

events

commands

Decision-making

DE Model State Equation:

DDucrcv uFuFrFvFx +++=

The Secret: multiply = AND & addition = OR

Tasks complete

Resources available

Targets / parts in

Decision/Command input

Task sequencing matrix – by Mission Planner

Resource assignment matrix – by onsite Leader

Fire next tasks

New Matrix Formulation for Supervisory Control

Compare with xk+1=Axk+Buk

US Patent

1001

cv

⎡ ⎤⎢ ⎥⎢ ⎥=⎢ ⎥⎢ ⎥⎣ ⎦

Means jobs 1 and 4 have just completed

0110

cr

⎡ ⎤⎢ ⎥⎢ ⎥=⎢ ⎥⎢ ⎥⎣ ⎦

Means resources2 and 3 are available

Job Start Equation:Resource Release Equation:Product Output Equation:

xSv vs =xSr rs =xSy y=

Compare with yk=Cxk

Output equations

Meaning of Matrices

Resources requiredPrerequisite jobs

Nextjob

NextjobFv Fr

Conditions fulfilled

Nextjob Sv

Task Sequencing Matrix Resource Requirements Matrix

Releaseresource Sr

Conditions fulfilled

Resource Release MatrixTask Start Matrix

Steward Kusiak

Construct Job Sequencing Matrix Fv

Part A job 1Part A job 2Part A job 3

Part B job 1Part B job 2Part B job 3

Par

t A jo

b 1

Par

t B jo

b 1

Par

t A jo

b 2

Par

t B jo

b 2

Par

t A jo

b 3

Par

t B jo

b 3

Nextjobs

Prerequisitejobs

Used by Steward in ManufacturingTask Sequencing

Contains same informationas the Bill of Materials(BOM)

Task 1

Task 2

Computer science task planners give the Fv Matrix

e.g. hierarchical HTFN task planners

Assembly Tree

a

b c

d e

0 1 1 0 00 0 0 0 00 0 0 1 10 0 0 0 00 0 0 0 0

a b c d eab

F cde

⎡ ⎤⎢ ⎥⎢ ⎥⎢ ⎥=⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦

Reorder tasks to get lower diagonal matrix = causal

Two 1’s in a row= assembly

Construct Resource Requirements Matrix FrUsed by Kusiak in ManufacturingResource Assignment

Contains informationabout factory resources

Nextjobs

Prerequisiteresources

Part A job 1Part A job 2Part A job 3

Part B job 1Part B job 2Part B job 3

Con

veyo

r 1C

onve

yor 3

Fixt

ure

1

Rob

ot 1

-IBM

Rob

ot 2

-Pum

aR

obot

3-A

dept

Example

ARRI

⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

=

100001000000001000010000

vF

⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

=

000010000100000000100001

TvS

⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

=

000010000001

uF

1 0 00 1 10 0 10 0 11 1 00 1 0

rF

⎡ ⎤⎢ ⎥⎢ ⎥⎢ ⎥

= ⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦

⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

=

010100000010001000

TrS

⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

=

100000010000

TyS

p1 p2 p3 p4 r1 r2 r3

p1 p2 p3 p4 r1 r2 r3

pinA pinB

poutA poutB

DDucrcv uFuFrFvFx +++=xSv vs =xSr rs =

xSy y=

crcv rFvFx +=

OR / AND Matrix Algebra

Example

)1()0()1(]101[ cbacba

x ∧∨∧∨∧=⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡=

)0()1()0( cbax ∨∧∨∧∨=

cax ∧=

)1()0()1( cbax ∧∨∧∨∧=

)1()0()1( cbax ∧∧∧∧∧=

De Morgan’s Laws

Don’t care about b

Easy to implement OR/ AND algebra in MATLAB

C= AB

for i= 1,Ifor j= 1,J

c(i,j)=0for k= 1,K

c(i,j)= c(i,j) .OR. ( a(i,k) .AND. b(k,j) )end

endend

Matrix multiply

• Formal rigorous framework• Complete DE dynamical description• Relation to known Manufacturing notions• Formal relation to other tools- Petri Nets, MAX-Plus• Easy to design, change, debug, and test• Formal deadlock analysis technique• Easy to apply any conflict resolution (dispatching) strategy• Optimization of resources• Easy to implement in any platform (MATLAB, LabVIEW, C,

C++, visual basic, or any other)

Advantages of the Matrix Formulation

Relation to Max-Plus Algebra

DDucrcv uFuFrFvFx +++=xSV vs =xSr rs =xSy y=

State equation

Output equations

Define diagonal timing matrices for job durations and resource release times.

Then max plus is

rFTSxFTSx rrrvvv +='

OPERATIONS IN OR-AND ALGEBRA

OPS. IN MAX-PLUS ALGEBRA

Can also include nonlinear terms- correspond to decisions

Relation to Petri NetsResources availableJobs complete

Trans. Trans.Fv Fr

Transition

Nextjobs Sv

Transition

Releaseresource Sr

UTA

ARRI

pinA p1t1 t2

p3t4 t5

p2 t3

p4 t6pinB

poutA

poutB

r1

r3

r2

⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

=

100001000000001000010000

vF

⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

=

000010000100000000100001

TvS

⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

=

000010000001

uF

⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

=

000010100000010001

rF

⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

=

010100000010001000

TrS

⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

=

100000010000

TyS

p1 p2 p3 p4 r1 r2 r3

p1 p2 p3 p4 r1 r2 r3

pinA pinB

poutA poutB

Jobs along path

Resources off path

Task 1

Task 2

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

001110001

More About Fv

J2

J5

J6

J1 J3 J4

Two 1’s in same col. = Routing (Job Shop)

Two 1’s in same row = Assembly

J3

J4

J5

J1

J2

J6

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

001110001

More About Fr

J2

J5

J6

R1 R2 R3

Two 1’s in same col. = Shared Resource

Two 1’s in same row = Job needs multiple res.

J5

R2

R3

R1

J2

J6

DECISIONNEEDED!

DECISIONNEEDED!

Activity Completion Matrix

Complete DE Dynamical Description

][ yrvu FFFFF =

[ ]T T T T Tu v r yS S S S S=

],,,[ yT

yrT

rvT

vuT

uT FSFSFSFSFSM −−−−=−=

xFStmxMtmtm TTT ][)()()1( −+=+=+


PN incidence matrix

Marking transition equation

Activity Start Matrix

DE state equation

T T T T Tm u v r y⎡ ⎤= ⎣ ⎦

Include Process Times in Places

)()()( tmtmtm pa +=

)()()1( txStmtm Tpp +=+

)()()1( txFtmtm aa −=+

TTT OrtimesvtimesOT ],,,[=

TtxSdiagttTtmdiagtT Tsamplependppend })({])([})({)1( +−=+

Split up marking vector

Add tokens

Take away tokens

Wait for process durations

Allows easy MATLAB simulation of DE systems


)()()1( txStmtm Tpp +=+

)()()1( txFtmtm aa −=+

)1()1()1( +++=+ tmtmtm pa

Duration time counting routine

1. Rules- fire transitions

2. Add tokens to places

3. Wait until jobs finish

4. Take tokens from places

5. Find updated vectors for DE state equation

Controller

System model

6. [ ] )( pmyrvu TTTTT =

PNMarkingTransitionEq.

Mission / Task 1-Job sequence


S2 takes measurementS2m1Task 11


R1 deploys UGS2R1dS21Task 9


R1 gores to UGS1R1gS11Task 7

R1 listens for interruptsR1lis1Task 6

R1 retrieves UGS2R1rS21Task 5

R2 goes to location AR2gA1Task 4

R1 goes to UGS2R1gS21Task 3



UGS1 launches chemical alertu1Input 1

Descriptionnotationmission1

Mission / Task 2-Job sequence


R1 docks the chargerR1dC2Task 5


R1 charges UGS3R1cS32Task 3

R1 goes to UGS3R1g S32Task 2


UGS3 batteries are lowu2input

DescriptionnotationMission2

Fast Programming of Missions / Tasks

⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜

⎝

⎛

=

100000000000100000000000100000000000110000000000010000000000010000000000011000000000001100000000000

19

18

17

16

15

14

13

12

11

1

xxxxxxxxx

Fv

⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜

⎝

⎛

=

000000000010000000000000000000000110000000000000000000111100000

19

18

17

16

15

14

13

12

11

1

xxxxxxxxx

Fr

⎟⎟⎟⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜⎜⎜⎜

⎝

⎛

=

100000100000100000100000100000

26

25

24

23

22

21

2

xxxxxx

Fv

⎟⎟⎟⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜⎜⎜⎜

⎝

⎛

=

000000000000010010000000000000000010000100

26

25

24

23

22

21

2

xxxxxx

Fr

Mission 1 matrices

Mission 2 matrices

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140

10

20

30

40

50

60

70 1S4m1S5m1R1gS21R2gA1R1rS21R1lis1R2m1R1gS11R1dS21R1m1S2m

2S1m2R1gS32R1cS32S3m2R1dC

R1R2UGS1UGS2UGS3UGS4UGS5

Time [s]

mobile wireless sensor network DE simulation priority 2-->1

Reso

urce

s

M

issi

on2

M

issi

on 1

u2

u1

0 20 40 60 80 100 120 140 0 20 40 60 80 100 120

10

20

30

40

50

60

70 1S4m1S5m1R1gS21R2gA1R1rS21R1lis1R2m1R1gS11R1dS21R1m1S2m

2S1m2R1gS32R1cS32S3m2R1dC

R1R2UGS1UGS2UGS3UGS4UGS5

Time [s]

mobile wireless sensor network DE simulation priority1-->2

Reso

urce

s

Mis

sion

2

M

issi

on1

u1

u2

Simulation 2 –change mission/task priority

Simulation Results

Event traces

• Up means task in progress

• Down means resource in use

Mission/Task 1 jobs

Mission/Task 2 jobs

Resources

R1gS1

R1lis R1m

X21 X2

2 X23 X24 X25 X26

X15 X16 X1

7 X18 X19S5m

R2gA

R1rS2

R2m

R1dS2 S2m

UGS2

UGS1

R1

u1

u2

R1gS3S1m R1cS3 S3m R1dC y2

Mission2 result

y1 Mission1 result

UGS3

R1gS2

S4m

X14X13X

12

X11

UGS4

UGS5 R2

PN Equivalent of Missions/Tasks

Mission/Task 1

Mission/Task 2

Discrete event controllerImplementation




Job s ta rt lo g ic


W ireless Sensor

N etw o rk

. . .

u c

Se nsor ou tp ut u


S tart tasks v s






xSv VS ⊗=

xSr rS ⊗=




U.S. Patent

Sensor readings

events

commands

Decision-making

R1u1

R1u2

R1u3

R1u4

R2u1

R2u2

R2u3

R3u1

R3u2

Discrete events

Results of LabVIEW Implementation on Actual Workcell

Compare with MATLAB simulation!

We can now simulate a DE controller and then implement it,Exactly as for continuous state controllers!!

Shared resources circular waits

S4m2

S1m1

X21 X22 X23 X24 X

25 X26

R1cS11 R1dC1

S3

R1

u1

u2

S3m2 R1gA2 R2mS22 S2m2 R2gC2

y2 Mission2 result

y1 Mission1 result

S2

X14X1

3X12X11

S4

X27 X28

R2

R1gD2

S1

Critical subsystems cannot get fullShared Resources- which jobs to dispatch first?

LBFS always works – but too conservative

What is LBFS for multipart path systems?

Shared resources circular waits

S4m2

S1m1

X21 X22 X23 X24 X

25 X26

R1cS11 R1dC1

S3

R1

u1

u2


y2 Mission2 result

y1 Mission1 result

S2

X14 X1

3X12X11

S4

X27 X28

R2

R1gD2

S1

Critical subsystems cannot get full

= Initial resources available

ARRI Intelligent Material Handling (IMH) Cell3 robots, 3 conveyors, two part paths

Need Supervisors to limit WIP in Critical Systems

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180

1R1gS11S1m1R1dC

2R1gA2S3m2R2mS22S2m2R2gC2S4m2R1gA

S1R1S2R2S3S4

Time [s]

Mobile wireless sensor network DE simulationRe

sour

ces

Mis

sion

2

Mis

sion

1

Event time trace

Simulation results

Deadlock!

S4m2

S1m1

X21 X22 X23 X24 X

25 X26

R1cS11 R1dC1

S3

R1

u1

u2


y2 Mission2 result

y1 Mission1 result

S2

X14X1

3X12X11

S4

X27 X28

R2

R1gD2

S1

Critical subsystems cannot get full

Finding the critical subsystems= CW resources

= crit. syst.= P invariant minus the critical siphon= added output job places to make up critical siphon

Deadlock Analysis- easy with matrix DEC

CS cannot get empty

⎥⎥⎦

⎤

⎢⎢⎣

⎡ ∧C

FFCFSC vT

rT

vrTsSc =

where denotes the element-by-element matrix ‘and’ operation. ∧

Find critical siphons Shared resources in C

rrW FSG = (in AND/OR algebra)

i.e. if gij=1 then resource j waits for resource i

Use string algebra to find a matrix C, wherein each column represents a circular wait.

Find circular waits

Wait relation graph- Wysk

Binary basis for p-invariants

compute the Critical System for each CS using

cSPCSysCrit ∧=..

Critical systems cannot take up all resources

)()()()( vdTvdvdvdo FCSCFCCFJ ∧=∧=

)())(( ioio CmCJm <

Output transitions of CW

Input transitions of CW

Critical systems

Critical systems cannot get full

Simplified calculations

MAXWIP dispatching

Deadlock Avoidance Dispatching MAXWIP Policy


Deadlock Avoid Software Selects Dispatching Input uD





Job s ta rt lo g ic


W ireless Sensor

N etw o rk

. . .

u c

Se nsor ou tp ut u


S tart tasks v s






xSv VS ⊗=

xSr rS ⊗=


Deadlock avoidance software here at top-

Decision-making

Sensor readings

events

commands

Decision-making

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180

1R1gS11S1m1R1dC


S1R1S2R2S3S4

Time [s]

Mobile wireless sensor network DE simulation

Reso

urce

s

M

issi

on2

M

issi

on1

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180

1R1gS11S1m1R1dC


S1R1S2R2S3S4

Time [s]

Mobile wireless sensor network DE simulation

Reso

urce

s

Mis

sion

2

Mis

sion

1

Event time trace without deadlock avoidance

Event time trace with deadlock avoidance

Simulation results

New Work --Deadlock Avoidance for Free-Choice Routing Systems

Problems with the old formulae for deadlock-need to make critical subsystems include alternate routing resources

t1

t2

t3

t4

t5

t6

t7

t8

t9

t10

t11

t12

t13

R1

R2

B1 B2 B3

M1

M2

r1a r1b

r2a r2b

b1 b2 b3

m1

m2Pin Pout

Decision Places- Choices in routing- select resource for next job

t1

t2

t3

t4

t5

t6

t7

t8

t9

t10

t11

t12

t13

R1

R2

B1 B2 B3

M1

M2

r1a r1b

r2a r2b

b1 b2 b3

m1

m2Pin Pout

= CW resources= added output job places to make up critical siphon= crit. syst.= P invariant minus the critical siphon

Does not work- t7 can still fire“Sneak out places”

t1

t2

t3

t4

t5

t6

t7

t8

t9

t10

t11

t12

t13

R1

R2

B1 B2 B3

M1

M2

r1a r1b

r2a r2b

b1 b2 b3

m1

m2Pin Pout

= CW resources= add other CW containing the decision place output transitions= added output job places to make up critical siphon= crit. syst.= P invariant minus the critical siphon

Can have deadlock

Cannot have deadlock

Partitions CW into Equivalence Classes

Discrete Event Decision & Control - UTA talks/Xian PN 08.pdf · r J2 J5 J6 R1 R2 R3 Two 1’s in...

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Transcript of Discrete Event Decision & Control - UTA talks/Xian PN 08.pdf · r J2 J5 J6 R1 R2 R3 Two 1’s in...