Automation & Robotics Research Institute The University of Texas at Arlington

F.L. LewisMoncrief-O’Donnell Endowed Chair

Head, Controls & Sensors Group

Talk available online athttp://ARRI.uta.edu/acs

Wireless Sensor Networks

II. ARRI Distributed Intelligence & Autonomy LabDIAL

UnattendedGroundSensors

SmallmobileSensor-Dan Popa

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

Distributed Intelligence and Autonomy Laboratory (DIAL)

Deadlock free dynamic resource assignment in multi-robot systems with multiple missions: a

matrix-based approach

Prasanna Ballal, Vincenzo Giordano, Frank LewisPrasanna Ballal, Vincenzo Giordano, Frank Lewis

by

Automation & Robotics Research Institute,University of Texas at Arlington

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:definition of

mission planning, resource allocation,

priority rules

U.S. Patent

Sensor readings

events

commands

Decision-making

Matrix Formulation: Definition

DDucrcv uFuFrFvFx +++=

multiply = AND & addition = ORoverbar = negation

Logical state equationCompare with xk+1=Axk+Buk

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

xSv vs =xSr rs =xSy y=

Compare with yk=CxkOutput equations

State vectorTask vector1= job complete

Resource vector1= resource available

Input vector1= event detected

Control inputpriority sequencingdeadlock avoidanceetc

Meaning of Matrices

Resources requiredPrerequisite jobs

Nextjob

NextjobFv

Fr

Conditions fulfilled

Nextjob Sv

Task Sequencing Matrix Resource Requirements Matrix

Releaseresource Sr

Conditions fulfilled

Resource Releasing MatrixTask Starting 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)

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

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 ∧∧∧∧∧=

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

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

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

Activity Completion Matrix

Complete DE Dynamical Description

][ yrvu FFFFF =

][ Ty

Tr

Tv

Tu SSSSS =

],,,[ yT

yrT

rvT

vuT

uT FSFSFSFSFSM −−−−=−=

xFStmxMtmtm TTT ][)()()1( −+=+=+

DDucrcv uFuFrFvFx +++=

PN incidence matrix

Marking transition equation

Activity Start Matrix

DE state equation

[ ]TTTTT yrvup =

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

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 =

!

DEC for WSN

Mission result:

False fire alarmRobot1 goes to

sensor 2Sensor 1

output:alarmRobot 1 picks

sensor 2Robot2 follows

robot1Sensor 3

measurementSensor 4

measurementRobot1 places

sensor 2Sensor2

measurement

Robot1 goes to sensor1

Robot2 smoke detection

Programmable Missions

Mission1-Task sequence

Mission 1 completedy1output

S2 takes measurementS2m1Task 11

R1 takes measurementR1m1Task 10

R1 deploys UGS2R1dS21Task 9

R2 takes measurementR2m1Task 8

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

UGS4 takes measurementS4m1Task 1

UGS1 launches chemical alertu1Input 1

Descriptionnotationmission1

Mission 2-Task sequence

Mission 2 completedy2output

R1 docks the chargerR1dC2Task 5

UGS3 takes measurementS3m2Task 4

R1 charges UGS3R1cS32Task 3

R1 goes to UGS3R1g S32Task 2

UGS1 takes measurementS1m2Task 1

UGS3 batteries are lowu2input

DescriptionnotationMission2

Fast Programming of Missions

⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜

⎝

⎛

=

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 priority

Simulation Results

Event traces

• Up means task in progress

• Down means resource in use

Mission 1 jobs

Mission 2 jobs

Resources

High Level Controller

Dispatching rules

To Generate uc

RS232 RS232 RS232

Wireless Network with Internet connection

- - Rule Based Real Time Controller

ucStart tasks/jobs

Mission result

Resource release

Sensor output u

Task completed v

Resource released r

Medium Level Tasks ControllersRobot 1

Task 1 Task 1

Robot 2

Task 1

Wireless sensors

Task 1

Robot 3

RS232

Pioneer arm

Cybermotion robot

Cybermotion robot

Xbow sensors

Environment

Task1

PC

urv uFrFvFx ⊗⊕⊗⊕⊗=xSv VS ⊗=

xSy y ⊗=xSr rS ⊗=

Finite state machine for each agent

UC-TDMA MAC protocol

Supervisor control level A

gent control levelN

etwork control level

Agents events

DEC Implementation

DDucrcv uFuFrFvFx +++=

DE controller on PC

Replaced by actual WSN

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

)()()1( txFtmtm aa −=+)1()1()1( +++=+ tmtmtm pa

System model

Duration times

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!!

Schematic Event Sequence for Mission Performance

Shared resources circular 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

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!

One Step Look Ahead Deadlock Avoidance Policy

Some Definitions:

• Circular Waits-Circular waits (CW) among resources are a set of resources ra, rb,… rwwhose wait relationship among them are ra rb … rw and rw ra.

• Simple CW-Simple CWs (sCW) are primitive CWs which do not contain other CWs.

• Critical siphons, Sc- The critical siphon of a CW is the smallest siphon containing the CW. Note that if the critical siphon ever becomes empty, the CW can never again receive any tokens. This is, the CW has become a circular blocking.

•Siphon job set Js-Siphon-job set, Js, is the set of jobs which, when added tothe set of resources contained in CW C, yields the criticalsiphon.

•Critical Subsystems Jo-The critical subsystems of the CW C, are the job sets J(C) from that C not contained in the siphon-job set Js of C. That is Jo = J(C)\ Js.

One Step Look Ahead Deadlock Avoidance Policy ctd…

Deadlock AnalysisThe Circular Waits are key to deadlock analysis (Wysk).CW are difficult to find from the Petri Net.

The CW are given directly from our matrices by the Wait Relation Matrix

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.

When a CW becomes blocked, one has Deadlock. To avoid this, examine the Critical Siphons. CS are difficult to find using Petri Nets.

The CS are given directly from our matrices by the columns of matrix

⎥⎥⎦

⎤

⎢⎢⎣

⎡ ∧C

FFCFSC vT

rT

vrTsSc =

Where vector Cs is the projection of C into the shared resources in the CW

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

)()()()( vdTvdvdvdo FCSCFCCFJ ∧=∧=

Matrix formulation for Jo

)())(( ioio CmCJm <

Deadlock Avoidance Strategy- MAXWIP Policy

One Step Look Ahead Deadlock Avoidance Policy ctd…

Critical Subsystems Jo

Deadlock analysisResources

Circular Waits Ci Co

Circular waits Matrix

Tasks

Critical subsystems Jo

Critical subsystems Matrix

Resources

ResourcesW

Digraph Matrix

Gurel’s algorithm

Matrix operations

Maxwip policy )())(( ioio CmCJm <

Initial number of tokens in circular wait Ci should always be greater than the number of tokens in the corresponding critical subsystem

Deadlock avoidance

⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

=

111111111110111101111100100010010001

oC

⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

=

011111101101111110000110011011011001100000011000000000000011

oJ

R1cS1 R1dC S3m S2m S4mS1m R1gA R2mS2 R2gC R1gD

S1 S2 S3 S4 R1 R2

Circular wait matrix Critical subsystem matrix

Deadlock avoidance

Motion with Deadlock Avoidance

Motion with no Deadlock Avoidance

Charger

UGS

Sentry robot

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

New Work—Modify resource assignments on-line as sensor nodes fail or are added

DDucrcv uFuFrFvFx +++=

Add or modify columns of Fr

Deadlock avoidance still works if there are no Key resources-1-step look ahead.

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

R2 R4 R5

t3 R2A t5 t7 R4A t9

Pi1 t1 B1 t2 R1A t4 B2 t6 R3A t8 B3 t10 R5A t11 Po1

B1 R1 B2 R3 B3

Choices in routing- select resource for next job

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

DDucrcv uFuFrFvFx +++=

New Work-A new matrix algebra to implement Dempster-Shafer decisions

∑=∩

=ACB

jiji

CmBmAm )()()( 212,1

).()( 21 jiCB

CmBm∑≠∩ φ

Implement the DS Rule of Combination

Make the state equation

∑≠∩

=0

)()(AB

BmaPl

Plausibility

∑⊂

=AB

BmABel )()(Belief

xSv vs = xSr rs =Make the output equations

Implement