indin 2012 beijing zongxia jiao yousef ibrahim … talks 2017/dec 2012 indin...input 1 u1 event-ugs1...
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INDIN 2012 BeijingZongxia Jiao Yousef Ibrahim EchoShaoping WangLiang YanFei Tao
ZhangJingbing
UTA Research Institute (UTARI)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 Control for Dynamic Resource Allocation in Networked Manufacturing Systems
He who exerts his mind to the utmost knows nature’s pattern.The way of learning is none other than finding patterns of the lost mind.
Meng Tze
Springer-Verlag 2006
Networked Supervisory Control (NSC)
Dynamic Resource Optimisation
Total Operations Visibility
Adaptive Real Time Factory Automation & Energy Management
Control Architecture; System Modelling and Analysis
ConstraintsQoS Mgt
Specifications
Interpretation
EnforcementDecisionExecuter
Monitored Events & Dynamics
ConfigurationContext Conditioning
Generic Rules
Local ControllerSensor/RFID Networks Wireless Devices
Optimisation Engine
Performance AnalysisEnergy
Labour
Material
Machine
Order
Quality
2
54
3
183%
Loading
Intelligent Fault Recovery
Real Time Task Sequencing
Sensors
MANAGING INDUSTRIAL INFORMATICS
Discrete Event Systems Task Sequencing Resource Assignment
Discrete Event Supervisory Control
Objective:Develop new DE control algorithms for decision-
making, supervision, & resource assignment
Apply to manufacturing workcell control, C&C systems, & i-networked systems
Results:• 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 missions Real-time event response Dynamic assignment of shared resources
UTARI 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
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 NetworksUTARI 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
Vincenzo Giordano
Mission1- Alarm DetectionTask sequence
mission1 notation Description
Input 1 u1 EVENT- UGS1 detects chemical alert
Task 1 S4m1 UGS4 takes measurement
Task 2 S5m1 UGS5 takes measurement
Task 3 R1gS21 R1 goes to UGS2
Task 4 R2gA1 R2 goes to location A
Task 5 R1rS21 R1 retrieves UGS2
Task 6 R1lis1 R1 listens for interrupts
Task 7 R1gS11 R1 gores to UGS1
Task 8 R2m1 R2 takes measurement
Task 9 R1dS21 R1 deploys UGS2
Task 10 R1m1 R1 takes measurement
Task 11 S2m1 S2 takes measurement
output y1 Mission 1 completed
Mission 2- Low BatteryTask sequence
Mission2 notation Description
input u2 EVENT- UGS3 batteries are low
Task 1 S1m2 UGS1 takes measurement
Task 2 R1g S32 R1 goes to UGS3
Task 3 R1cS32 R1 charges UGS3
Task 4 S3m2 UGS3 takes measurement
Task 5 R1dC2 R1 docks the charger
output y2 Mission 2 completed
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
Sample Team Mission scenario from J. Albus talk, ASC Orlando, Dec. 2008.
A sequence of tasks triggered by detected events = A Mission
Task1 TT1 M1 R1 M2 R2 M4 …
Task2 TT2 M2 R2 M3 TT1 M2 …
Task3 TT1 M3 R1 M1 TT2 M1 …
Task flow information in Industrial Processing
T1 xport mill insert grind move smooth
T2 xport grind move High polish
xport grind
T3 xport polish insert mill xport mill
TT1 TT2 R1 R2 M1 M2 M3 M4xport 1 1mill 1grind 1Polish/smooth 1 1move 1insert 1High polish 1
1. Job sequencing
2. Resource Assignment
Task Sequencing Matrix - TSM
Task 1Task 2Task 3Task 4Task 5Task 6
Task 1Task 2Task 3Task 4Task 5Task 6
Task
1Ta
sk 2
Task
3Ta
sk 4
Task
5Ta
sk 6
Nextjobs
Prerequisitejobs
Used by Steward in ManufacturingTask Sequencing
Mission 1tasks
Mission 2tasks Partial order
time sequencing
Mission 1
Mission 2
Task
1Ta
sk 2
Task
3Ta
sk 4
Task
5Ta
sk 6
Mission 1tasks
Mission 2tasks
Contains same informationas the Bill of Materials(BOM)
Resource Assignment Matrix RAMUsed by Kusiak in ManufacturingResource Assignment
Contains informationabout required resources
Nextjobs
Prerequisiteresources
Task 1Task 2Task 3
Task 1Task 2Task 3
UG
S 1
UG
S 3
robo
t 1
UG
V 1
UG
V 2
UAV
1
Mission 1tasks
Mission 2tasks
RAM can change in real time as resources fail or are added
Discrete Event Systems Task Sequencing Resource Assignment
Discrete Event Controller
Workcell / WSNJobsdone
Resourcesavailable
Start jobs
Assign resources se
nsor
s
OutputsCommands
Trigger Eventsparts intargets detected
Discrete EventSupervisoryController
Computer software
FEEDBACK CONTROL
Darwin – Natural Selection of SpeciesVolterra – Population BalanceAdam Smith - EconomicsJames Watt – Steam Engine
SensoroutputsTaskscompleteResourcesavailable
Missioncomplete
StarttasksReleaseresources
Trigger events
TeamStatus Commands
Real-Time Decision Interrupts and Mission priority
Distributed Team
Messagepassing
Real-timeOperationalPhase
PlanningPhase
Force Commander Goal PrioritiesHigh-level Planning
Mission CommanderMission plan & goalsRequired operations
On-Site CommanderResources availableAssign manpower & platformsMaterial requirements planning
Chain ofCommand
PC, Laptop, PDA
PC, Laptop, PDA
PC, Laptop, PDA
C&C Rule-Based Discrete Event Controller for Distributed Networked Teams
What goes here?
Messagepassing
Rule-Based Controller = Discrete event system
IF Part A entersAND
Fixture 1 is availableAND
Robot 1 is available
THEN Robot 1 pick up part A AND
put into fixture 1
TWO TYPES of information-
Tasks just completed
Resources available
Task sequencing
Resource assignment
IF (tasks just completed) AND (resources available)THEN (perform next task)
tasks prerequisite resources neededt1 t2 t3 t4 r1 r2 r3
Rule 1 1 1 1Rule 2 1 1Rule 3 1 1Rule 4 1 1 1 1
rule firedR1 R2 R3 R4
Task 1 start 1Task 2 start 1Task 3 start 1Task 4 start 1
Rule i:IF (the tasks required as immediate precursors to task i are complete)
AND (the resources required for task i are available) THEN fire rule i
Introduce Rule Base
IF (rule i fires) THEN start task i
How to find the rules? Expert system?
Problems with:Redundant rulesInconsistent rules
How to implement the controller
Problems with:Real-time task sequencingDynamic resource assignmentBlocking phenomena
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
U.S. Patent
SensorStatus readingsevents
commands
Decision-making
Workcell / WSN
1001
cv
Job vector -Means jobs 1 and 4 have just completed
0110
cr
Resource vector -Means resources2 and 3 are available
Jobsdone
Resourcesavailable
Start jobs
Assign resources
sensors
Output status vectorscommands
Eventsparts intargets detected
DE Model State Equation:
DDucrcv uFuFrFvFx
The Secret: multiply = AND & addition = OR
Tasks complete
Resources available
Trigger Events / parts in
Decision/Command input
Task sequencing matrix – by Mission Planner
Resource assignment matrix – by onsite Leader
Rule vectorFire 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
Binary mathematics- LOGIC not real numbers
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
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
First- Sequence the Mission or Job Tasks
Task sequencing Matrix- TSM
Production Planner / Mission Commandershould specify intent, not details
A general class of missions consisting of sequenced tasksEach task has a well-defined entry state and exit state – Kevin Moore
I. Planning / Programming Phase
Computer science planners (e.g. HTN) give information equivalent to TSM
Construct Task Sequencing Matrix - TSM
Task 1Task 2Task 3Task 4Task 5Task 6
Task 1Task 2Task 3Task 4Task 5Task 6
Task
1Ta
sk 2
Task
3Ta
sk 4
Task
5Ta
sk 6
Nextjobs
Prerequisitejobs
Used by Steward in ManufacturingTask Sequencing
Mission 1tasks
Mission 2tasks Partial order
time sequencing
Mission 1
Mission 2
Task
1Ta
sk 2
Task
3Ta
sk 4
Task
5Ta
sk 6
Mission 1tasks
Mission 2tasks
Contains same informationas the Bill of Materials(BOM)
Computer science task planners give the Fv Matrix
e.g. hierarchical HTN 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
v
a b c d eab
F cde
Two 1’s in a row= assembly
Task Sequence
Reorder tasks to get lower diagonal matrix = causal
0 0 0 0 00 0 0 0 01 1 0 0 00 0 0 0 00 0 1 1 0
v
e d c b aed
F cba
Warfield
Second- Assign the Resources
Resource Assignment Matrix - RAM
Job Shop ForemanField Commander
I. Planning / Programming Phase
Construct Resource Assignment Matrix RAMUsed by Kusiak in ManufacturingResource Assignment
Contains informationabout required resources
Nextjobs
Prerequisiteresources
Task 1Task 2Task 3
Task 1Task 2Task 3
UG
S 1
UG
S 3
robo
t 1
UG
V 1
UG
V 2
UAV
1
Mission 1tasks
Mission 2tasks
RAM can change in real time as resources fail or are added
Assign the resources – shop foremanAssembly 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
v
a b c d eab
F cde
Two 1’s in a row= assembly
a
bc
d e
1 2 1 2
0 0 1 00 1 0 10 0 1 00 0 1 01 0 0 1
f f R R
r
ab
F cde
Robot 1
Fixture 1
Robot 1Fixture 2
Robot 2
Robot 2
Multiple 1’s in a col. MeansShared resource
SensoroutputsTaskscompleteResourcesavailable
Missioncomplete
StarttasksReleaseresources
Trigger events
TeamStatus Commands
C2 Rule-Based Discrete Event ControllerRule State equation
Task start equationResource release equation
Real-Time Decision Interrupts and Mission priority
Distributed Team
MessagepassingMessage
passing
Real-timeOperationalPhase
PlanningPhase
vs
rs
vc
rc
u
uD
x vc , rc
vs, rs
Force Commander Goal PrioritiesHigh-level Planning
Mission CommanderMission plan & goalsRequired operations
Battalion CommanderResources availableAssign manpower & platformsMaterial requirements planning
program Fv
Chain ofCommand
PC, Laptop, PDA
PC, Laptop, PDA
PC, Laptop, PDA program Fr
C&C Rule-Based Discrete Event Controller for Distributed Networked Tea
Discrete Event Systems Task Sequencing Resource Assignment
Discrete Event Controller How does DEC Work?
DDucrcv uFuFrFvFx xSv vs xSr rs
xSy y
Discrete Event Controller
How does it work?
The secret:addition = ORmultiply = AND
.OR.
.AND.
negation
Octav Pastravanu
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
Boolean Matrix multiply
Rule i:IF (the tasks required as immediate precursors to task i are complete)
AND (the resources required for task i are available) THEN fire rule i
Proper Functioning of DEC
DEC Gives a Rule base that is: Consistent Nonredundant
Can add code to guarantee: No blocking phenomena
DEC performs dynamic real-time task sequencing and resource assignment
Does not need to know durations times of jobs
Interleaves the tasks of multiple missions depending on mission priority
Guaranteed Performance due to DEC Structure
Properness of the DEC Rulebase
• 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
Discrete Event Systems Task Sequencing Resource Assignment
Discrete Event Controller How does DEC Work? Relation to Existing ModelsMax-PlusPetri nets
Relation to Max-Plus Algebra
DDucrcv uFuFrFvFx xSV vs xSr rs xSy y
State equation
Output equations
Define diagonal 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
Diagonal Timing Matrices
Relation to Petri Nets
DDucrcv uFuFrFvFx xSV vs xSr rs xSy y
State equation
Output equations
x= transition vector – fire the rules
v, r = place vectors – store the current situation (tokens)
Relation to Petri NetsResources availableJobs complete
Trans. Trans.Fv Fr
Transition
Nextjobs Sv
Transition
Releaseresource Sr
r3
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
pinA p1t1 t2
p3t4 t5
p2 t3
p4 t6pinB
poutA
poutB
r1
r2Jobs along path
Resources off path
Mission 1
Mission 2
DDucrcv uFuFrFvFx xSV vs xSr rs , ,
Discrete Event Systems Task Sequencing Resource Assignment
Discrete Event Controller How does DEC Work? Relation to Existing Models Complete DE Description and Simulation
Complete Dynamical Description of DE Systems
xFStmxMtmtm TTT ][)()()1(
DDucrcv uFuFrFvFx Petri Net Marking transition equation
DE state equation
Activity Completion Matrix ][ yrvu FFFFF
[ ]T T T T Tu v r yS S S S S
],,,[ yT
yrT
rvT
vuT
uT FSFSFSFSFSM
PN incidence matrix
Activity Start Matrix
T T T T Tm u v r y Marking vector
Details -
xSr rs xSV vs
xSy y
Start equations
Allows easy MATLAB simulation of DE systems
DDucrcv uFuFrFvFx
)()()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.
Wireless Sensor NetworksUTARI 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
Mission 1 - Alarm DetectionJob sequence
mission1 notation Description
Input 1 u1 UGS1 launches chemical alert
Task 1 S4m1 UGS4 takes measurement
Task 2 S5m1 UGS5 takes measurement
Task 3 R1gS21 R1 goes to UGS2
Task 4 R2gA1 R2 goes to location A
Task 5 R1rS21 R1 retrieves UGS2
Task 6 R1lis1 R1 listens for interrupts
Task 7 R1gS11 R1 gores to UGS1
Task 8 R2m1 R2 takes measurement
Task 9 R1dS21 R1 deploys UGS2
Task 10 R1m1 R1 takes measurement
Task 11 S2m1 S2 takes measurement
output y1 Mission 1 completed
Mission 2- Low Battery ChargeJob sequence
Mission2 notation Description
input u2 UGS3 batteries are low
Task 1 S1m2 UGS1 takes measurement
Task 2 R1g S32 R1 goes to UGS3
Task 3 R1cS32 R1 charges UGS3
Task 4 S3m2 UGS3 takes measurement
Task 5 R1dC2 R1 docks the charger
output y2 Mission 2 completed
Fast Programming of Multiple 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
Mission 1 matrices
1 2 3 4 5
21222
2 3242526
0 0 0 0 01 0 0 0 00 1 0 0 00 0 1 0 00 0 0 1 00 0 0 0 1
v
t t t t t
xxx
Fxxx
21222
2 3242526
1 2 1 2 3 4 50 0 1 0 0 0 01 0 0 0 0 0 00 0 0 0 0 0 00 0 0 0 1 0 01 0 0 0 0 0 00 0 0 0 0 0 0
r
R R S S S S Sxxx
Fxxx
1 1
2 2
0,
0v r
v rv r
F FF F
F F
Mission 2 matrices
Block together matrices from multiple missions
Can all be done automatically in software
TSM RAM
Missions use the same Team resources
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 job in progress
• Down means resource in use
Mission 1 jobs
Mission 2 jobs
Resources
Resource Percent Utilization
Simulation of Steady-State Behavior
Bottleneck Detection
Discrete Event Systems Task Sequencing Resource Assignment
Discrete Event Controller How does DEC Work? Relation to Existing Models Complete DE Description and Simulation Implementation
Discrete event controllerImplementation
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
U.S. Patent
Sensor readings
events
commands
Decision-making
Wireless Sensor NetworksUTARI 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
VR interface Panoramic view of the configuration of the mobile WSN during real-world experiments
Actual Implementation of DEC
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!!
S4m
R1gS2
R1rS2
R2m
R1dS2
S2m
R1gS3
S3m
S5m
R2gA
R1lis
R1gS1
R1m
S1m
R1cS3
R1dC
Utilization time trace of the WSN- Experimental results
Remote Site Programming and DEC
Man/Machine User Interface
USA/Mexico Internetworked Control
TexasTexas
Intelligent Robot Workcell
Fast programming of multiple missions Real-time event response Task sequencing Dynamic assignment of shared resources
DEC
LabVIEW
Discrete Event Systems Task Sequencing Resource Assignment
Discrete Event Controller How does DEC Work? Relation to Existing Models Complete DE Description and Simulation Implementation Analysis of DEC and Blocking Phenomena
Shared resourcescircular waits
S4m2
S1m1
X21 X2
2 X23 X2
4 X25 X2
6
R1cS11 R1dC1
S3
R1
u1
u2
S3m2 R1gA2 R2mS22 S2m2 R2gC2
y2 Mission2 result
y1 Mission1 result
S2
X14 X1
3X12X1
1
S4
X27 X2
8
R2
R1gD2
S1
Circular Blocking - Critical subsystems cannot get full
= Initial resources available
Shared resourcescircular waits
S4m2
S1m1
X21 X2
2 X23 X2
4 X25 X2
6
R1cS11 R1dC1
S3
R1
u1
u2
S3m2 R1gA2 R2mS22 S2m2 R2gC2
y2 Mission2 result
y1 Mission1 result
S2
X14X1
3X12X1
1
S4
X27 X2
8
R2
R1gD2
S1
Critical subsystems cannot get fullShared Resources- which jobs to dispatch first?
LBFS always works – but too conservative
S4m2
S1m1
X21 X2
2 X23 X2
4 X25 X2
6
R1cS11 R1dC1
S3
R1
u1
u2
S3m2 R1gA2 R2mS22 S2m2 R2gC2
y2 Mission2 result
y1 Mission1 result
S2
X14 X1
3 X12 X1
1
S4
X27 X2
8
R2
R1gD2
S1
rrW FSG Wait Relation Graph
Easily found from matrices
Richard Wysk- Circular Waits cannot become Circular BlockingsCritical Siphons Cannot Get Full
Deadlock Analysis- easy with matrix DEC
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
C
FFCFSC vT
rT
vrTsSc =
where denotes the element-by-element matrix ‘and’ operation.
Find critical siphons
CS cannot get empty
Implement in Real Time
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!
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 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
2R1gA2S3m2R2mS22S2m2R2gC2S4m2R1gA
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
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
Deadlock avoidance software here at top-
Decision-making
Sensor readings
events
commands
Decision-making
Discrete Event Systems Task Sequencing Resource Assignment
Discrete Event Controller How does DEC Work? Relation to Existing Models Complete DE Description and Simulation Implementation Analysis of DEC and Blocking PhenomenaReal-Time Structural Changes in Resources and TasksFailure Recovery
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
Sensor readings
events
commands
Real-timeDecision-making
Mission Planner Modifies Matrices on the Fly
DEC= Real-time decisioncontrol loopWith guaranteed performance
S4m2
S1m1
X21 X2
2 X23 X2
4 X25 X2
6
R1cS11 R1dC1
S3
R1
u1
u2
S3m2 R1gA2 R2mS22 S2m2 R2gC2
y2 Mission2 result
y1 Mission1 result
S2
X14X1
3X12X1
1
S4
X27 X2
8
R2
R1gD2
S1
Adding Resources of Different Type
R3
Add columns to Fr
,r r
old resourcesF old F new col r
new resource
Done by mission planner
S4m2
S1m1
X21 X2
2 X23 X2
4 X25 X2
6
R1cS11 R1dC1
S3
R1
u1
u2
S3m2 R1gA2 R2mS22 S2m2 R2gC2
y2 Mission2 result
y1 Mission1 result
S2
X14 X1
3X12X1
1
S4
X27 X2
8
R2
R1gD2
S1
Adding New MissionMay need new resources
May make new SHARED resourcesAdds new pathMission Agent Coordinator
1 1
2 2
0,
0v r
v rv r
F FF F
F F
Block together matrices from multiple missions
Can all be done automatically in software
Missions use the same Team resources
Self Healing – without human intervention
New task entersMachine breakdownUnexpected delays/processing time changes
Automatically handled by DEC
Add New Task Path-Sequence jobs for new tasks - FvAssign resources for new jobs - Fr
Redistribute jobs to other resources – change Fr onlineReroute in case of failures- decision needed in task path
John Wiley, New York, 2006
S4m2
S1m1
X21 X2
2 X23 X2
4 X25 X2
6
R1cS11 R1dC1
S3
R1
u1
u2
S3m2 R1gA2 R2mS22 S2m2 R2gC2
y2 Mission2 result
y1 Mission1 result
S2
X14 X1
3X12X1
1
S4
X27 X2
8
R2
R1gD2
S1
Faults and Maintenance
Maintenance Agent Coordinator
Send to maintenance:ScheduledFault detected
Adds new pathMaintenance Jobs
Repair resource
Distributed Decision on Communication Graph Topology
Discrete Event Systems Task Sequencing Resource Assignment
Discrete Event Controller How does DEC Work? Relation to Existing Models Complete DE Description and Simulation Implementation Analysis of DEC and Blocking Phenomena Real-Time Structural Changes in Resources and Tasks
Failure Recovery Distributed Decision and DEC
over Communication Networks
Strongly connected if for all nodes i and j there is a path from i to j.
( 1) ( )i
i ij jj N
w k d w k
Standard consensus algorithm in a graph
Agents reach consensus if the graph is strongly connected
Distributed Decision on Communication Graph Topology
Distributed Resource Assignment Over Networks
DDucrcv uFuFrFvFx xSv vs xSr rs xSy y
Introduce Skill vector and skill matrix
v c c u D Dx F v s F u F u
Skills required
Nextjob
Skill Requirements Matrix
Skills required by jobs
Do not pin down the actual resources used. Only the skills needed.
Resources
Skills
Skill-Resource Matrix
r
1 1 0 0 00 1 0 0 11 0 1 0 10 0 1 1 0
r
The Ops. Res. Assignment problem- assign resources to skills
max ij ijskills j agents i
c z ij jskills i
z Cap 1ijres j
z rZ
1 0 0 0 00 1 0 0 00 0 0 0 10 0 1 0 0
Z
Assigned resource matrixOne ‘1’ in each row
v c r c u D Dx F v F r F u F u
rF Z
Can solve the assignment problem using distributed processing usingAuction algorithmsBundle-based algorithm
Resource req. matrix is
v c c u D Dx F v s F u F u
Heterogeneous Robots Consensus-based Allocation
The Heterogeneous Robots Consensus-based Allocation (HRCA) is a distributed iterative planning approach based on the Consensus-Based Bundle Algorithm (CBBA)1
Each agent iterates between 2 nested Stages: HRCA: Decentralized auction-based algorithm for heterogeneous robotsStage 1 (Consensus-based Bundle
Costruction):Phase 1: Bundle Filling(greedy selection of tasks)Phase 2: Conflict Resolution(consensus stage)
Stage 2 (Bundle Check)Phase 3: Bundle resize(overloaded bundles are partially emptied with criteria that tend to minimize the loss in terms of score
Communication with neighbors robots is required in phases 2 and 3 only.
1. Assign resources to skills a priori
2. Assign resources to skills at each event occurrence
1 1 0 0 00 1 0 0 11 0 1 0 10 0 1 1 0
r
1 0 0 0 00 1 0 0 00 0 0 0 10 0 1 0 0
Z
Overall skill-resource matrix
1 1 0 0 00 1 0 0 11 0 1 0 10 0 1 1 0
r
Skill-resource matrix for fireable jobs
Assigned resources at k-th event
TWO CHOICES
Description of the network
1 2 3 4 5
1
2
3
4
5
1 1 1 0 01 1 1 1 01 1 1 1 00 1 1 1 10 0 0 1 1
r r r r r
r
r
r
r
r
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
Resource Interaction GraphT
r rF F Defines an undirected graph that shows which resources are involved in the same tasks with each other
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
( )Tr r
Defines an undirected graph that shows which resources need to bid for skillsIt shows which resources may be in competition to supply skills for the tasks
( )T Tr rF F Z Z
Resource interaction graph is
A more fully connected graph is
Logical Consensus
To agree on the status of tasks done and resources available
( 1) ( )i ij jj
w k d w k Standard consensus algorithm in a graph
( 1) ( ( ))i j ij jw k d w k
Let be a semiring. Then the following consensus algorithm converges( , )
Take as logical .or.as logical .and.
To get logical consensus
1. S. Bogdan, F.L. Lewis, Z. Kovacic, and J. Mireles, Manufacturing Systems Control Design: A Matrix Based Approach, Springer-Verlag, London, 2006.
2. D. Tacconi and F.L. Lewis, “A new matrix model for discrete event systems: application to simulation,” IEEE Control Systems Magazine, pp. 62-71, Oct. 1997.
3. B. Harris, F.L. Lewis, and D.J. Cook, “Machine planning for manufacturing: dynamic resource allocation and on-line supervisory control,” J. Intelligent Manufacturing, vol. 9, pp. 413-430, 1998.
4. F.L. Lewis, A. Gurel, S. Bogdan, A. Doganalp, O. Pastravanu, “Analysis of deadlock and circular waits using a matrix model for flexible manufacturing systems,” Automatica, vol. 34, no. 9, pp. 1083-1100, 1998.
5. A. Gurel, S. Bogdan, and F.L. Lewis, "Matrix approach to deadlock-free dispatching in multi-class finite buffer flowlines," IEEE Trans. Automatic Control, vol. 45, no. 11, pp. 2086-2090, Nov. 2000.
6. B. Harris, D. Cook, F.L. Lewis, “A matrix formulation for integrating assembly trees and manufacturing resource planning (MRP) with capacity constraints,” J. Intelligent Manufacturing, vol. 13, no. 4, pp. 239-252. August 2002.
7. S. Bogdan, F.L. Lewis, Z. Kovacic, A. Gurel, and M. Stajdohar, “An implementation of the matrix-based supervisory controller of flexible manufacturing systems,” IEEE Trans. Control Systems Technol., vol. 10, no. 5, pp. 709-716, Sept. 2002.
8. V. Giordano, J.B. Zhang, D. Naso, and F.L. Lewis, “Integrated supervisory and operational control of a warehouse with a matrix-based approach,” IEEE Trans. Automation Science & Engineering, vol. 5, no. 1, pp. 53-70, Jan. 2008.
9. P. Ballal and F.L. Lewis, “Condition-based maintenance using dynamic decisions by Petri nets and Dempster Shafer theory: a matrix-based approach,” Trans. Inst. Measurement and Control, vol. 31, no. 3/4, pp. 323-340, June/Aug. 2009.
10.C.K. Pang, G. Hudas, M. Middleton, C.V. Le, O.P. Gan, and F.L. Lewis, "Discrete Event Command and Control for Networked Teams with Multiple Military Missions" J. Defense Modeling and Simulation, to appear, 2011.
11.A. Gasparri, D. Di Paola, G. Ulivi, D. Naso, F. Lewis, “Decentralized task sequencing and multiple missions control for heterogeneous robotic networks,” Proc. IEEE Int. Conf. Robotics and Automation, 2011, to appear.
12.D. Di Paola, A. Gasparri, D. Naso, and F.L. Lewis, “Decentralized Discrete-Event Modeling and Control of Task Execution for Robotic Networks,” Proc. IEEE Conf. Decision & Control, Maui, Dec. 2012, to appear.
References