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Automation & Robotics Research InstituteUniversity of Texas at Arlington

Automation & Robotics Research Institute The University of Texas at Arlington

F.L. LewisMoncrief-O’Donnell Endowed Chair

Head, Controls & Sensors Group

Wireless Sensor Networks


Wireless Sensor Networks2006 Conferences on Cybernetics & Intelligent Systems (CIS)

and Robotics, Automation, & Mechatronics (RAM)

Bangkok

GC I-Ming Chen


Localization of a Wireless Sensor Network with Unattended Ground Sensors and Some

Mobile Robots

Koushil SreenathMS Thesis, 2006

Frank Lewis, Dan PopaThe University of Texas at Arlington, United States


Localization - Contributions

Simultaneous Localization of WSNDistributed Kalman filtersGeometric constraints of radio connectivity

Adaptive Localization StrategyNavigate to a location to maximally reduce localization uncertainty.


Localization

Localization TechniquesRSSI – Signal strengthTOA – Time of ArrivalAOA – Angle of ArrivalSignal pattern matchingGeometric constraints

Range-free

Mobile Robot with GPS

UGS


1. Sensor Localization using Mobile Robot

[ ]TyxX αφ=

( )

⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢

⎣

⎡

=

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

==

αωα

φαφα

αφ sin

sincoscoscos

,L

vvv

yx

txaXt

t

t

&

&

&

&

&

⎥⎥⎦

⎤

⎢⎢⎣

⎡== Bot

y

BotxBotBot

kRσ

σσσ

00

,

const

BotyBot

yconst

BotxBot

xRangeRangeσ

σσ

σ == ,

1. At each discrete time instant,2. if robot broadcast received by sensor3. then4. Update sensor state and uncertainty estimates using KF measurement update equations.5. else6. Propagate estimates using time update equations.7. end if

Robot Dynamics

Sensor localization algorithm

[ ]Tiiik yxx =

ik

ik

ik

ik

ik

ik

ik wGuBxAx ++=+1

( ) ( ) ( )ik

ik

ik

ik

ix

ii RvQwPxx ,0,,0,,000 ===

⎥⎦

⎤⎢⎣

⎡=⎥

⎦

⎤⎢⎣

⎡=⎥

⎦

⎤⎢⎣

⎡=⎥

⎦

⎤⎢⎣

⎡=

1001

,1001

,0000

,1001 i

kik

ik

ik HGBA

Sensor Dynamics

ik

ik

ik QPP +=

−+1

ik

ik xx ˆˆ 1 =

−+

Sensor time update

1

11

11

1

11

−

+−

++

−−++ ⎥

⎦

⎤⎢⎣

⎡+= i

kkTi

kik

ik HRHPP

⎟⎠⎞⎜

⎝⎛ −+=

−+++

−+++

−++

ik

ik

ikk

Tik

ik

ik

ik xHzRHPxx 111

111111 ˆˆˆ

Sensor measurement update

Kalman Filter


1. Sensor Localization using Mobile Robot


2. Simultaneous Localization of Static Sensor and Mobile Robot

( ) ( )wtGtuXaX += ,,&

[ ][ ] ugs

kkugsugs

k

gpskk

gpsgpsk

vktXhZ

vktXhZ

+=

+=

),(

),(

( ) ( ) ( ) ( ) ( ) ( )ugsugsk

gpsgpsk RvRvQtwPXX ,0,,0,,0,,0 00 ====

( ) ( )⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

=

⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢

⎣

⎡

=

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

=

0000000000100001

,sin

sincoscoscos

, tGL

vvv

yx

tXat

t

t

αωα

φαφα

αφ&

&

&

&

[ ] [ ] ⎥⎦

⎤⎢⎣

⎡=⎥

⎦

⎤⎢⎣

⎡=

yx

ktXhyx

ktXh kugs

kgps ),(,),(

( )

( ) ( )

( ) ( )⎥⎦

⎤⎢⎣

⎡=

∂∂

=

⎥⎦

⎤⎢⎣

⎡=

∂∂

=

⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢

⎣

⎡−−−

=∂

∂=

00100001,

00100001,

0000cos000

sinsincoscos00cossinsincos00

),(,

XkXhXH

XkXhXH

Lvvvvv

XtXa

tXA

ugsugs

gpsgps

t

tt

tt

α

φαφαφαφα

Robot Dynamics( )( ) ( ) TT GQGtXPAPtXAP

tuXaX

++=

=

,ˆ,ˆ,,ˆˆ

&

&

Robot time update

( ) ( )( ) ( )[ ] ( )

( )[ ]kXhZKXX

tPXHKItP

RXHtPXHXHtPK

kugsugs

kkkk

kkugs

kk

ugsk

Tugskk

ugsk

Tugskk

,ˆˆˆ

ˆ

)ˆ()()ˆ(ˆ1

−−

−−

−−−−−−

−+=

−=

⎥⎦⎤

⎢⎣⎡ +=

Updates from UGS

( ) ( )( ) ( )[ ] ( )

( )[ ]kXhZKXX

tPXHKItP

RXHtPXHXHtPK

kgpsgps

kkkk

kkgps

kk

gpsk

Tgpskk

gpsk

Tgpskk

,ˆˆˆ

ˆ

)ˆ()()ˆ(ˆ1

−−

−−

−−−−−−

−+=

−=

⎥⎦⎤

⎢⎣⎡ +=

const

iyi

yconst

ixi

x

iy

ixiiiugs

k

RangeRange

PR

σσ

σσ

σσ

σσ

==

⎥⎥⎦

⎤

⎢⎢⎣

⎡=⎥⎦

⎤⎢⎣⎡ +=

,

00

,22

Robot measurement update

Updates from GPS

1. Navigate robot along desired path.2. Broadcast location information at discrete intervals.3. if broadcast from GPS received4. Update robot state and uncertainty estimates using GPS measurement equation.5. end if6. if broadcast from sensor received7. Update robot state and uncertainty estimates using UGS measurement equation.8. end if

Robot localization algorithm

⎥⎦⎤

⎢⎣⎡ +=

22 BotBotXYk PR σ

Robot measurement update

Jacobian linearization


2. Simultaneous Localization of Static Sensor and Mobile Robot


3. Simultaneous Adaptive Localization

1. Broadcast Navigation request, NAV-REQ, packet.2. Wait to receive Localization request, LOC-REQ, packets.3. for all LOC-REQ with the same friendly neighbor4. Combine uncertainty scalars of the requesting sensors.5. end for6. Pick friendly neighbor with maximum combined uncertainty scalar of the requesting sensors.7. if multiple maximas arise8. Among the maxima, pick the most localized friendly neighbor.9. end if10. Navigate around the picked friendly neighbor executing the simultaneous localization algorithm11. Repeat Steps 1-10 as required.

Adaptive localization algorithm

LOC-REQ packet flow

NAV-REQ packet flow

Formal Comm. Packet Structure & Protocol


Simultaneous Adaptive LocalizationAdaptive localization

Localization error Localized sensors


ARRI Distributed Intelligence & Autonomy LabDIAL

UnattendedGroundSensors

SmallmobileSensor-Dan Popa

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


Publications

K. Sreenath, F.L. Lewis and D.O. Popa, "Simultaneous Adaptive Localization of a Wireless Sensor Network," ACM Mobile Computing and Communication Review, submitted.


Conclusion

LocalizationSimultaneous localization of WSN

Localization of UGS by Mobile RobotLocalization of Mobile Robot by GPS & UGSJoint localization

Adaptive localization algorithmFormal communication packet protocol

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