F.L. Lewis, Assoc. Director for ResearchMoncrief-O’Donnell Endowed Chair

Head, Controls, Sensors, MEMS GroupAutomation & Robotics Research Institute (ARRI)

The University of Texas at Arlington

Wireless Sensor Networks for Monitoring Machinery, Human Biofunctions, and BCW Agents

Sponsored byIEEE Singapore SMC, R&A, and Control Chapters

Organized and invited by Professor Sam Ge, NUS

F.L. Lewis, Assoc. Director for ResearchMoncrief-O’Donnell Endowed Chair

Head, Controls, Sensors, MEMS GroupAutomation & Robotics Research Institute (ARRI)

The University of Texas at Arlington

Matrix Framework for Discrete Event Control

Organized and invited by Jing Bing Zhang

Sponsored bySIMTech &IEEE Singapore Control Chapter

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

F.L. LewisMoncrief-O’Donnell Endowed ChairHead, Controls and Sensors Group

http://ARRI.uta.edu/acs

Discrete Event Control & Decision-Making

Discrete Event Control

Objective:Develop new DE control

algorithms for decision-making, supervision, & resource assignment WITH PROOFS

Apply to manufacturing workcell control, battlefield C&C systems, & internetworkedsystems

• Patent on Discrete Event Supervisory Controller • New DE Control Algorithms based on Matrices• Complete Dynamic Description for DE Systems• Formal Deadlock Avoidance Techniques• Implemented on Intelligent Robotic Workcell• Internet- Remote Site Control and Monitoring• USA/Mexico Collaboration• Exploring Applications to Battlefield Systems

$75K in ARO Funding for Networked Robot Workcell Control$80K in NSF Funding for research and USA/Mexico Network

USA/Mexico Internetworked Control

Man/Machine User Interface

TexasTexas

Intelligent Robot Workcell

Dr. Jose Mireles- co-PI

DE Model State Equation:

Where multiply = AND & addition = ORwhere is the task or state logic

is the job sequencing matrix (Steward)is the resource requirements matrix (Kusiak)is the input matrixis the conflict resolution matrix

Matrix Formulation: DefinitionBased on Manufacturing Bill of Materials

DDucrcv uFuFrFvFx +++=

vFrF

uFDF

x

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

xSV vs =xSr rs =xSy y=

Compare with xk+1=Axk+Buk

Meaning of MatricesResources requiredPrerequisite jobs

Nextjob

NextjobFv

Fr

Conditions fulfilled

Nextjob Sv

Releaseresource Sr

Steward’s Task Sequencing Matrix Kusiak’s Resource Requirements MatrixBill of Materials (BOM)

Conditions fulfilled

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 Conveyor

unidirectional

conveyor

machinemachine

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)

Construct Resource Requirements Matrix Fr

Used 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

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

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!

Controller based on Matrix Formulation

Workcell

Matrix Formulation Discrete Event Controller

External events presentJobs completedResources releasedTasks completed

External EventsStart jobsStart resource releaseTask complete

Dispatchingrules

Resource allocation, task planning, task decomposition, Bill of Materials

Tasksc ompleted vc

Rule-Based Real-Time Controller

Cucurv uFuFrFvFx ⊗⊕⊗⊕⊗⊕⊗=

Job start logic

Resource release logic

Work Cell

. . .

uc

Partspresent u

R esourcer eleased rc

Partsin pin

Start tasks vs

Start resourcer elease rs

Output yProducts pout

Plant commands Plant status

Dispatching rules

Controller state monitoring logic

xSv VS ⊗=

xSr rS ⊗=

xSy y ⊗=Task complete logic

• 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 Petri NetsResources availableJobs complete

Trans. Trans.Fv Fr

Transition

Nextjobs Sv

Transition

Releaseresource Sr

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

Example

t1t2t3t4t5t6

t1t2t3t4t5t6

pinA p1t1 t2

p3t4 t5

p2 t3

p4 t6pinB

poutA

poutB

r1

r3

r2

⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

=

100001000000001000010000

x

⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

000010000001

⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

000010100000010001

Fv

OR/AND Algebra- Locating transitions firing from current marking

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

1110

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

001

⎥⎦

⎤⎢⎣

⎡00

Fr Fu

⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

110100

⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

000001

⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

000000

= , so x =

⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

110101

⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

001010

v r u

x = i.e. fire t2 and t4

Activity Completion Matrix F:

Activity Start Matrix S:

Complete DE Dynamic Formulation

][ yrvu FFFFF =

][ Ty

Tr

Tv

Tu SSSSS =

],,,[ yT

yrT

rvT

vuT

uT FSFSFSFSFSM −−−−=−=

PN Incidence Matrix:

PN marking transition equation:

Allowable marking vector:xFStmxMtmtm TT ][)()()1( −+=+=+

=⊕= kk mFx kyrvu POrvPIFFFF ][][ ⊕

Petri Net Marking Transition Equation--need to add Job Duration Times

)()()( tmtmtm pa +=

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

)()()1( txFtmtm aa −=+

TTT OrtimesvtimesOT ],,,[=

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

)()()( tmtmtm finishpp −=

)()()( tmtmtm finishaa +=

PN Marking VectorSplit transition equation in two steps

Add tokens

Subtract tokens when job complete

Add Time Duration Vector

Corresponds to Timed Places

Allows Direct Simulations- e.g. MATLAB

Jobs completedby Robot 1

Robot 1busy or idle

c.f. DE version of ODE23

Relation to Max-Plus Algebra

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

State equation

Output equations

Define timing matrices. Then max plus is

rFTSxFTSx rrrvvv +='

OPERATIONS IN OR-AND ALGEBRA

OPS. IN MAX-PLUS ALGEBRA

Can also include nonlinear terms- correspond to decisions

pinAp1t1 t2

p3t4 t5

p2 t3

p4 t6pinB

poutA

poutB

r1

r3

r2

⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

=

100001000000001000010000

x

⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

000010000001

⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

000010100000010001

Fv

Conflict Resolution for Shared Resources

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

1010

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

101

⎥⎦

⎤⎢⎣

⎡00

Fr Fu

⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

100100

⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

001001

⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

000000

= , so x =

⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

101101

⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

010010

v r u

Which one to fire?

But gives negativemarking!Cannot fire both.

Shared Resource- Two entries in same column

pinA p1t1 t2

p3t4 t5

p2 t3

p4 t6pinB

poutA

poutB

r1

r3

r2

⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

=

100001000000001000010000

x

⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

000010000001

⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

000010100000010001

Fv

Conflict resolution, add extra CR input and new matrix Fuc:

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

1010

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

101

⎥⎦

⎤⎢⎣

⎡00

Fr Fu

⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

100100

⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

001001

⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

000000

= , so x =

⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

101111

⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

010000

v r u

⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

001000000100

Fuc r2

⎥⎦

⎤⎢⎣

⎡01

Now only t5 fires

⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

000010

r2

Application- Intelligent Material Handling

Adept

Puma

CRS

12 Sensors!!

Machine 2

Machine 1

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

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 Conveyor

unidirectional

conveyor

machinemachine

Multipart 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

c.f. Kumar

Petri Net flow chart

R1U1

B1AA

B1AS R2U1

M1A

M1P

B2AA B3AA

R2U3 B2AS R3U1 B3AS R1U3 PAO

B1BA B2BA M2A B3BA

PBI R1U2 B1BS R2U2 B2BS R3U2 M2P R3U3 B3BS R1U4 PBO

R1A

R2AR3A

X1 X2 X3 X4 X5 X6 X7 X8 X9

X12 X13 X14 X15 X16 X17 X18 X19X11 X20

PAI X10

Start tasks/jobs

PC with High Level Controller

Dispatching rules

To Generate uc

Tasks: vSA

controller

controller controller CRS Puma 560 ADEPT One

Low level PD & PID controllers

Robots

Medium Level Tasks Controllers

RS232-1 RS232 -2 RS232-3

Robot 1

Task 4 Task 3

Task 2 Task 1

Robot 2

Task 3 Task 2

Task 1

Robot 3

Task 3 Task 2

Task 1

SAv~ Workcell data gathering

u

v

r

p

Sensors Machines

SBSin vrp ~,~,~

Jobs vSB

r SB

rSA, pin

Parts out

v SB

DAQ - card Analog & digital I/0

Rule-Based Real -Time ControllerController state monitoring logic

C u DDurv u FuFuFrFvFxC ⊗ ⊕⊗⊕⊗⊕⊗⊕⊗=

Job start logic

Sv =Sv x⊗

Task complete logicy =Sy x⊗

Resource release logic

xSr rs ⊗=

ucc.f. SaridisJim Albus

LabVIEW diagram of Controller

LabVIEW Controller's interface:

FrFv

Resources

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!!

U.S.-Mexico shared research

DE control via internet

Using Matrix DEC in LabVIEW

Texas