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1
ADelayPredictionApproachforTeleoperation
over theInternet
TissaphernMirfakhraiand ShahramPayandeh
Abstract|Basedonthenotionofwavevariables,and
theideaofwave-integraltransmission,anewmethodis
suggestedtomatchthesystemparameterswithchanges
inthedelay.Anautoregressivemodel isusedasapre-
dictortoforecast thefuturevaluesofthedelay.The
predictionsareusedwithalook-up tabletotunethe
gainwithwhichthewaveintegralsaretobefedto
thesystem.Thisgainschedulingand tuningimproves
thesystemperformanceand decreasesthemismatch
betweenforcesand velocitiesat themasterand slave
sides.
Keywords|Teleoperation,Force-feedback,Internet.
I.Introduction
THEconceptofteleoperation beenaround fora
while[3]. Designand developmentoftelerobotic
systemswerefurthermotivatedwithintroductionofa
newubiquitousmeansofcommunication, i.e.theIn-
ternet.Alongwithgeneralproblemscaused bytime
delays,usingtheInternetasthemeansofcommuni-
cationcanresultinmoredi±cultiesinteleoperation
becauseofthevariabletimedelay.Thevariabletime
delayscanresultinwrongcommand order,decreased
control latencyand evenlostcommand packets.
Ithasbeenshown byAndersonand Spong[2]thatif
theforce and velocitysignalsaretransmittedasthey
arefromthemastersidetotheslavesideinthepres-
ence of force feedback,thesystemwill becomeunsta-
ble evenwiththesmallestdelays.Theysuggesteda
modi¯edcontrol law,whichwasbasedonthetransfer
functionofapasivetransmissionline,and guaranteed
thesystemstability.
BasedonAnderson'sideas,Niemeyerand others[5]
proposedthe conceptofWave variables.Usingthe
wavevariableswill resultinatwo-portcommunica-
tionlinethatispassivefromoutside.Thereforethe
stabilityofthesystemduringteleoperationisguaran-
teed.
Thewavevariablesareintroduced byrede¯ningthe
systempower°ow.LetFbetheforce appliedto a
systemand _xbethevelocityofmotioninthatpartof
thesystem.Usually,thepower°owisde¯nedasthe
productofane®ortand °owpairsuchas:
TissaphernMirfakhraiand ShahramPayandeh,Experimen-
talRoboticsLaboratory,SimonFraserUniversity,Burn-
abyBC,CanadaV5A1S6,Email: tmirfakh@cs.sfu.ca,
shahram@cs.sfu.ca.
P=_xTF(1)
Tointroduce thewavevariablesuand v,weassume
twostreamsofpowermovinginoppositedirectionsin
thesystem.Thismeanswehavedividedthepower
°owto a streamgoingfromthemastersidetowards
thesalveside(positivedirection) (1
2uTu)and astream
goingfromslavetomaster(1
2vTv).Inotherwords,we
assumethat themastersideisalwaysgivingenergyto
thesystem.Thisgivenenergymightbecomenegative
atinstants,meaningthat thepowertransferisactually
fromslavetomaster.
Therefore,tointroduce thewavevariables,we can
rede¯nethepower°owas:
P=1
2uTu¡1
2vTv(2)
Weassumethatuand varelinearcombinationsof
_xand F.Usingequation1 and 2,thewavevariables
can be calculatedintermsof_xand Fas:
u(t)=b_x(t)+F(t)
p2b
v(t)=b_x(t)¡F(t)
p2b(3)
Thetuningparameterbactsasaweightfunction
and changestherelativemagnitudeof_xand Fwith
respect toeachother.Anypairoftheabovevari-
ables(u;v;_x;F),can beselectedasinputoroutput
variablestothewave-transformerblock.Itispossible
toshowthat the communicationlineispassiveifthe
energystoredintheoutgoingwaveofvislimitedto
the energyofincomingwaveofu.Now, ifthesewave
variablesaretransmittedinsteadoftheactualforce or
velocitysignals,theoverall systemwould bepassive
and noinstabilitywill happen.
Figure1showstheoverall blockdiagramofthe
wave-basedteleoperationsystem.Theoperatorap-
pliesaforce Fhtothemastermanipulatorwiththe
mass ofMm.ThemastercontrollerisaPDcontroller
withthedampingfactorofBmand springfactorof
Km.Afeedbackforce isgenerated bythemastercon-
trollerbasedonthefeedbackwavevariables.Thisin-
putforce alongwiththefeedbackforce,will determine
thevelocityofmotionofthemastermanipulator.The
masterforce (Fm)and mastervelocity(_xm)arethen
codedintothewavevariableumusingequation3.This
2
wavevariableisthentransmittedthroughthe commu-
nicationlinetotheslaveside.
Ontheslavesidethewavevariableisreceivedafter
goingthroughthetimedelay.Thenthewavevariable
isdecodedagain usingequation3.Thedesiredslave
velocity(_xsd)isgiventotheslave controller,which
generatestherequiredforce ontheslavemanipulator.
ThiscontrollerisaPDcontrollerwiththedamping
factorofBsand thespringconstantofKs.Theslave
manipulatorhasamass ofMs,and isreceivingthe
force Fethroughcontactwiththe environment.
Fig.1.Theoverall systemblock diagram.
Inthispaperwesuggestusing a delaypredictorto
predict thefuturevalueofdelay.Introducing a delay
predictorinawave-basedteleoperationsystemcanim-
provetheperformance throughfeedbackingtheinte-
gralsofthewavevariables.Bytuningthevalueofthe
feedbackgainfortheintegrals,someofthelostprop-
ertiesofthesignalcan berestoredtheoverall delay
can bereducedforforce-precisionorvelocity-precision
tasks.
Thepaperisorganizedasfollows:SectionII ex-
plainstheidea oftransmittingthewavevariableinte-
gralsalongwiththeoriginalwavevariablestoimprove
systemperformance.Theintegrals somehowrepresent
the energyofthewavevariables.Soifthe energydif-
ference isfed backtothesystemwithyacertaingain,
theperformance can beimproved.Tuningthisgain
accordingtothemagnitudeofthetimedelayhelps
theperformance,butrequiresaforecastknowledgeof
thedelay value.SectionIII discussesoursuggested
methodtopredict thefuturevaluesofthedelay.In
sectionIV,weusethesepredictionstotunethesys-
temthroughteleoperation.SectionVincludes some
concludingremarks.
II.WaveIntegralTransmission
Depending onthetaskin hand,and whetherwe
want tomatchforcesorvelocities,therewill always
besomemismatch betweenforcesand velocitiesat the
masterand slavesides.Evenifthemismatch between
thevelocitiesis small, the errorwill causethepositions
ofthetwomanipulatorstodriftapartgraduallyas
timepasses.
Oneperformance improvementstrategyistransmit-
tingwaveintegrals.Asthewavevariablesthemselves
carryinformationabout theforcesand velocitiesof
thetwomanipulators,theirintegralswill encodemo-
mentumand position.Thustransmittingthewave
integralsmeans someinformationabout theposition
ofthemanipulators.Althoughtheoreticallythepo-
sitioninformationcan bedecodedfromtheoriginal
wavevariablesbyintegratingthevelocities,theposi-
tionerrorwill increasegraduallybecauseofnumerical
integrationmethodsused.Transmittingthewavein-
tegralswill solvethisproblem.
Niemeyerand Slotine[6], hadsuggestedtotransmit
thewaveintegralsU(t)=Rudtand E(t)=Ru2dt
alongwiththewavevariablesthemselvestoimprove
theteleoperation performance.E(t)isthewave en-
ergy,meaningthe energythatisbeingtransmitted by
thewavestreaminacertain direction.
Theysuggested using a ¯lterto obtainacorrected
versionofus,denotedasuout,fromtheintegralof
thewavevariableU(t)=Rudtand theintegralofthe
squareofthewavevariableE(t)=Ru2dt(Figure2).
Fig.2.The con¯gurationofthe communicationlinkusinga
reconstruction ¯lteras suggestedbyNiemeyerandSlotine
The¯lterisde¯nedas
uout(t)=(®E(t)
U(t)ifU(t)6=0
0ifU(t)=0(4)
where®isaconstant thatcanmodifytheshape
ofthe¯lter response.The¯lterimpulseresponsesfor
®=1,®=1:5 and ®=2 areplottedin ¯gure3.
Theidea oftransmittingwaveintegralswasfurther
investigated byYokokohji, Imaida,and Yoshikawain
[7]. Theysuggestedthat theintegralofthemasterside
wavevariable(um)should be calculated numerically
up tothetimeofeachtransmissionand thenshould
besentalongtotheslaveside.
At theslaveside,theintegralofthereceivedwave
variable^us(t)iscalculatedsimilarlyand isthencom-
paredwiththenumericvalueoftheintegralreceived
3
Fig.3.Theimpulseresponseofthereconstruction ¯ltersug-
gestedbyNiemeyerandSlotinefor®=1,®=1:5and®=2
fromthemasterside.Thedi®erence (¢),can be cal-
culatedas:
¢(t)=Zum(t)¡Z^us(t)
¢can beinterpretedasameasureofchangeinen-
ergyofthesignal, and will befed backto^ustore-
storethelostenergy(Figure4).¢(t)isaddedtothe
receivedwavevariable,^us(t),ampli¯ed byacertain
gain,hereaftercalled¾.Finallywe calculatetheslave
wavevariableas:
us(t)=^us(t)¡¾¢(t)=us(t)¡¾(Zum(t)¡Z^us(t))
(5)
Fig.4.The con¯gurationofthe communicationlinkusinga
reconstruction ¯lteras suggestedbyNiemeyerandSlotine
Yokokohjietal. [7]had noticedtheimportance of
thegainofthisfeedback(¾)and hadmentionedthat
thevalueofthegainshould be chosensuchthat the
systemiswell compensated,butat thesametimenot
tosensitivetodisturbances.However,theyhad not
suggestedapracticalwaytotunethisgain.
Oursimulations showthat theoptimalvalueofthis
gain,to obtainthesmallesterrorvariesasthemag-
nitudeofthetimedelaychanges.Thismeansthatat
every valueofT(t),the errorinforce/velocitycan be
minimizedifthemagnitudeof¾ischosenaccordingly.
Thereforeifthefuturetimedelayisknown,alook-
up table can beformedforthepurposeof¯nding a
¾valuethatresultsinthesmallestmismatch between
theforcesorvelocitiesat themasterand slavesides.
Thisideawill bediscussedin detail insectionIV
Thequestion nowishowto obtainanaprioriknowl-
edgeoftherandomtimedelayoftheInternet.Inother
wordsweneedtopredict thefuturevalueofthedelay
tobeabletotunethegaintoitsoptimalvalue.The
nextsectionaddressesthemethodofprediction.
III.ModelingandPrediction
TheInternet time-delaysarerandomprocesses.A
randomprocess isarandomvariablethevalueofwhich
alsodependsontime.Althoughrandomprocessesare
randomand thereforeunpredictable,modelscan be
created basedontheirpastvaluestopredict thefu-
turevaluesoftheprocess withsome error.Themost
widelyusedmodelsfor randomprocessesaretheMov-
ingAverage(MA)Modeland theAutoregressive(AR)
model. Themoving averagemodelactsbasicallyas
alowpass ¯lterontheincomingsignal, and predicts
thefuturevalueofthesignaltobetheaverageofits
pastvalues.However,averagingdisregardsall ofthe
highlystochasticbehavioroftheprocess.ThusanMA
model isnotadequateforahighlystochasticprocess
suchastheInternet timedelay.Therefore,theautore-
gressivemodelhastobeusedforthedelayprediction
application.Forastudyofalternativedelayprediction
approaches see [10].
A.Modelderivation
Anautoregressive(AR)model isamodelthatre-
latesthevalueofthesignalat timentoitsvaluesat
timen¡1through
x[n] =
N
X
i=1
aix[n¡i] + w[n](6)
wherex[n] isthesignalwewant tomodeland Nis
theorderofourARmodel, whichcan beselectedas
adesign parameter[4]. w[n] iswhitenoisewithauto-
correlation
E[w[n]w¤[n]]=¾2
w±[n](7)
where¤indicatescomplexconjugate,¾2
wisthevari-
ance ofthenoiseand theoperatorE[] takesthe ex-
pectedvalueoftheparameterappearingbetweenits
brackets.
4
Itisdesiredto¯nd the coe±cientsa1;a2;a3; :::aN
suchthatifthelastNvaluesofxareknown(x[n¡
1];x[n¡2]; :::x[n¡N]),thenextvalueofx(x[n])can be
predicted usingequation6withthesmallesterrorcom-
paringtoitsactualmeasuredvalue.Itcan beshown
[4]that theoptimalvaluesofaisto givethesmallest
errorbetweenthepredictedvalueand theactualmea-
suredvalueofxarethesolutionsoftheYule-Walker
matrixequation[1].
WemeasuredthedelayfromtheSimonFraserUni-
versity(SFU),BC,Canadatoanumberofdi®erent
destinationsaround theworld. [1]. Theresultsillus-
tratedinthepresentpaperweremeasuredfromthe
communicationlinktotheDataCommunicationIn-
corporation(DCI)inIran,whichliesalmostonthe
exactoppositesideoftheglobetoSFU.Asthedelays
oftheInternetareknowntohaveaquasi-periodicpro-
¯leoveraweek[9], we createourmodelbasedonthe
delay valuesobserved duringaweek.Thismodel is
then usedtopredict thebehaviorofthedelayover
theweekaftertheobservations.Delaysaremeasured
severaltimeseverydayand apiecewisemodel iscon-
structedfromall setsofresults.
Thesamplingtimeswerearbitrarilyselectedtobe
12:00AM,4:00AM,8:00AM,12:00PM,4:00PMand
8:00PMeveryday.Theseparticulartimeswerese-
lectedsuchthat theyfall in di®erent timesoftheday,
representingverylow,veryhighand averagedatatraf-
¯cload.Starting ateachoftheabovetimes,thedelay
wasmeasured24 timesusingthepingutility.The
experimentswere continuedfor2weeks.
Foreachexperiment,theRootMean Square(RMS)
errorwascalculatedfordi®erentmodelorders,topick
anorderthatgivesusthesmallesterror.The errors
versusthemodelorderNareplottedin ¯gures5.a
and 5.b.The errorseemstobedecreasingwhenthe
modelorderNisincreased.To avoid unnecessarily
large computation,N=24 wasacceptedasbeinglarge
enoughforourpurpose.
Figure6shows6setsofour24 modelparameters,
calculatedat thesixmeasurement timesduringacer-
tain day.
B.Predictingdelays
Once themodel iscreated basedonthedatafrom
measurements,thevaluesobtainedfromthismodeling
process areusedtopredict thebehaviorofthesystem
duringthesecond week.Thisprocess ofmeasuring,
modeling and predictingwill continueduringteleoper-
ation.In ¯gure7,thepredictionsare comparedwith
theactualvaluesofthedelayobtainedthroughmea-
surement.Thepredictionand therealmeasuredval-
uesareless then%20 di®erent,exceptat timesof fatal
crashesatoneofthemasterand slave computers.
Fig.5.ModelparametersforconnectionwiththeDCIsystem
on Saturday,plotted at the6measurement times.
Fig.6.ModelparametersforconnectionwiththeDCIsystem
on Saturday,plotted at the6measurement times.
Fig.7.Predicted delays(dashed)comparedtotheactualvalues
ofdelays(solid)oftheDCIseverduringthesecondweek.
IV.WaveIntegralGainScheduling
Inourscenario,theoperatorappliesaforce inthe
formofasquarepulsewiththemagnitudeof2Nto
5
amastermanipulatorwith unitmass (Mm=1Kg).
Thismanipulatoriscontrolled byaPDcontrollerwith
sti®ness factorof0.5N=m(P)and dampingfactorof
1N=m=s(D).Thiscontrollermovesthemasterma-
nipulatorbyrespondingtothevelocitydictated by
theoperatorand thevelocitythatisobtained bythe
feedbacksystemthroughthenetwork.
Themastersidewavetransformerconvertstheforce
and velocitysignalstoum,whichistobetransmitted
throughthe communicationline.Thewaveimpedance
bischosentobe equalto 1,to give equalweight to
theforce and velocitiesatbothmasterand slavesides.
Thedelayofthe communicationline(T(t)) isassumed
tobevariableand will bediscussedfurtherbelow.
Theslavesidesystemisassumedtobe exactly
similartothemasterside.Sotheslavesidewave
transformerworkswithawaveimpedance alsoequal
to 2;theslavemanipulatoralsohasaunitmass
(Ms=1Kg)and the controllergainsare exactlythe
sameasthoseofthemasterside.Theslavema-
nipulatorisassumedtobeinteractingwithanen-
vironment,consisting ofaspring(k=1N/m)and a
damper(B=0.5N/m/s).Themanipulatorispushing
thespring againstasolidwall, whilebeingheld bya
damper.
ThedelayoftheslaveÃmastercommunicationlink
is supposedtobe equaltothatofthemaster!slave
link, i.e.T(t).Wealso assumethat thereisnoscaling
betweenthemasterand slavesides.
Letusde¯netheforce errortobethemaximum
mismatch betweentheforcesat themastersideand
theslaveside.
Ferr =maxfFm(t)¡Fs(t¡T(t))g(8)
Thevelocityerroris similarlyde¯nedasthemax-
imum mismatch betweenthevelocitiesat themaster
sideand theslaveside.
_xer r =maxf_xm(t)¡_xs(t¡T(t))g(9)
Oursimulationstudies showthatforevery valueof
T,thereisavalueof¾tominimize the error.
Figure8showsthebehavioroftheabovementioned
errorswithchangesinTand ¾.Itcan beseenthat
forevery valueofT,thevalueof¾can be chosensuch
that the errorisminimized.ForeachTin ¯gure8,the
topsurface ofoneofthe errorbarsispainted blackto
showtheoptimalvalueof¾.Inthesame¯gure,the
hatchedsquares showsomelimitations,wherethesys-
tembecomesunstableduetothe choice ofanimproper
¾.At thosevaluesof¾theamountofenergyfedto
thesystemforcompensationismorethan necessary
and thatmakesthesystemnon-passiveand unstable.
Whenoperating,thedelaypredictorwill estimate
thefuturevalueofthedelay.Thisestimatedvalueof
Fig.8.Force andvelocityerrorsatdi®erentestimated delays
fordi®erentvaluesof¾.
Tisthen used bythegainschedulertosearchina
look-up tablelike¯gure8to¯nd theoptimalvalue
ofthegain¾.Figure9,comparesthesystemperfor-
mance withtheoptimalvalueof¾withthesystem
performance with nocompensation.Itisvisiblethat
thesalveforce followsthedesiredforce more closely
whencompensationisadded.
Itshould benotedthat thevalueof¾tominimize
theforce error, isnotalwaysthesameasthevalueof¾
tominimize thevelocityerror.Thiscan beseenfrom
¯gure8,wheretheblackpainted pathontheforce
errorplot(8.b), isdi®erentfromtheblackpainted path
onthevelocityerrorplot(8.a).
Figure10 showsthevelocitiesonthemasterand
slavesides,withand withoutacompensationgainthat
minimizestheforce error.Itcan beseenthatalthough
applyingthe compensationgainof¾=0:5hasthebest
compensatione®ectontheforce, itactuallyincreases
thedi®erence between_xmand _xs.
Also atlargedelays, ifthe¾value exceedsacertain
valuethesystemgoesunstable.Thehatchedsquares
in ¯gure8representsuchcases.Thisinstabilitycan
be explained bynotingthataddingthe¾-path,we
areviolatingthe conditionsofpassivityas statedin
Niemeyer'scalculationsin[8]. Thusifweadd too
muchfeedbacktothesystem,wemightend up with
positivefeedback,whichtendstodestabilize thesys-
tem.
6
Fig.9.ForcesatE(T(t))=500 msandE(T(t))=700 ms
Fig.10. _xm,_xswithoutcompensationand_xswith¾=0:5
thatminimizestheforce error.
Therefore,whenthefuturevalueofthedelayispre-
dicted,we can usealook-up tablesimilartotheblack
pathin ¯gure8toretunethesystem.Thiswaychoos-
ingtheoptimalvalueof¾canminimize ourerroron
force orvelocity,orboth.When dealingwithlarge
delaysthevalueof¾hastobeset tozero,to guaranty
thepassivityofthesystemand tokeepstableopera-
tion.Forexample, ifthepredictedvalueforT(t)is
1second, itisoptimaltoset¾=0:5basedon ¯gure
8.aifaminimalforce errorisintended.Also¾=0:2
will resultinminimalvelocityerrorasisvisiblefrom
¯gure8.b.
V.Conclusions
Amethodis suggestedtodecreasethe errorbetween
forces/velocitiesofthemasterand slavemanipulator.
Thefuturevalueofthevariabletimedelayispredicted
basedonitspastvaluesusing anAutoregressive(AR)
model. Alook-up tableisthen usedto¯nd avalueof
thewaveintegralfeed-forwardgain¾tominimize the
errorbetweentheforce/velocitiesofthemasterand
slavemanipulators.Bytuningthegaintothisopti-
malvalue,someofthelostpropertiesofthesignalcan
berestored,the errorbetweenthemasterand slave
forces/velocitiesisdecreasedand theoverall teleoper-
ationsystemperformance isimproved.
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