Inll.Ｃ､n6e｢enceonlnteIIigentRobolsandSyslems LasVegas,NevadaOctober2003

P｢oceedingSofthe2003IEE曰RSl

Inll.Ｃ､n6e｢enceonlnteIIigentRobolsandSyslems LasVegas,NevadaOctober2003

AdaptiveAudioServohr MultirateRobotSystems

MakotoKUMON,ThkahiroSUGAWARA,KatuhiroMⅡKE,IkumMIZUMOrOandZentalWAI DepartmentofMechanicalEngineeringandMaterialsScienCe,KumamotoUniveI5ity

２３１－１，KUmkami,Kumamoto,860-8555,Japan EJ『miMJUmo"＠gpMEJmamom-UU.αQjP

ABSTRACT Obstac1esbctweenthetargetandd1ccamera・IIMhose lnthispaperbaMdioserv０Ｍ》orの】SEC"zwhichwas cases,animalsmayuseothersensorssuchasearsto

aservosystemusim】gaudioinfOnnationasfeedbackove1℃oｍｃCmiiculties･Ｔｈｅｓｅｎｓｅｏｆｈｅａｍｎｇｈａｓａｎ

ａｂｎｉＷｔｏsenseobjectsbehindObstaclessuChthat signalwasconsidered・SincethesampUngrateof

audiosignalandlhatofIDbotcontroHeraIeUsuany eyescannotrecognize・Thoughthesenseofhearing difhenMheSystemisabletobetreatedasamulti‐ maybethoughttobelessplecisethanthesenseof ratesystcm・ＳｉｎｃｅｉｔｉｓｇｅｎｅｒａｌｔｈａｔｔｈｅｓａｍｐＵｎｇ vision,itoffersenoughinfbnnationfbrdai1ytaSks・

rateoftheoUlPutisfasterthanthatoftheinput， ＦＤｒｅｘａｍｐｌｅ,skiUedpeOpleareabletowalkalong thecontmllercanobtainmoreinfbnnationthana waUswiththeireyesclosedonlybyliSteningechos single-rateservosystemByuSingthispmpemVban oftheirsteps[4]･Itisalsoworthnotingthatalldio infbrmationisusuanyldimensionaltimcSeriesand adaptiveauddoservosystemwaspmposed・Results

ofacomputersimulationandaexpeIimentshowed itisthOughttobeeaSiertoextractthecuewbich e6fectivenessofthemethod・ isrequhedby,acontmUersincevisUalinfmmation is2dimensionaltimeserieSwhichreqUiIcshuge l･INTRODUCTIONcomputationtOeXtractmeaningfUlinfbrmation・Ac- cordinglybaservoSystemusingaudioMbnnation Animalshavevarioussensingabilitiessuchas itselｆｂＷｈｉｃｈｉｓｃａＵｅｄａ腿diDseFTo・isconside1℃ｄ vision,hearing,tactnCpemeptionandsoon､T11ose

inthiSpapeⅢOneofinterestingapp1icationsof sensingabilitiesareusuallycombinedwiththeir

audioservoisasoPhisticatedhumanoidstalkingwith moＵｏｎｓａｎｄｉｔｍａkespossiblefbrthemtoadapt _humansｎ．

thesurroundingenvimnment､FOrexamp1e,eycsand

handsa1℃WellcoordinatedWhenananimaliscap‐Tbthisend,soundsignaliMequiredtObepro‐

､tulinganobjectandtheanimaliMbletosucceedcessedtoextractcuesl4]whichare剛mredbythe this・taskevenifthetaIgetismovmg．～ＣＯ別tldler・Ｉｎｏｒｄｅｒｔｏｃｘｔｍｃｔｔｈｅｃｕｅ，thercisa lnordertomakerobotsbesknlfilIasanimalsaｴe，methodwhichestimatesthepositionofthesound thesesensor-motioncoordinationhavebeenstudUed．souI℃ebyusing3CUmensionalworldmode】([6L【7])．

ESpeciallyWisionhasattractedmanyrBsearchers[1］ＨOWeveMhisapproaChtendstobecomp腕and

andInanyvision-basedorvision-guidedmotioncon- ３CmnensionalworldreconstmctiOnmaybemme tm1methodsfbrintenigentmachineshavebeen infbnnationthanlcquilcd･FUrthermoI巳,thesystem proposed[2][3)DWingtotheg剛pmgrcssofdigitalisprefer[edtobesimple・Thercfb[巳,itisproposedto processorS,itbecomeseasiertodesi印arObotwithfeedbackmteredsoundsignaMtSelfdireCUytothe visionsensorssuchasCCDcamelas急VisualservoI2］controllerinthispapeLGenemllyspeaking,ｓｉｎｃｅ ｉｓｏｎｅｏｆｃｏｎｔｍｌｓｃｈｅｍｅｓｕｓｉｎｇvisionsystemssamp1inglatesofi叩ut(commandstome(hanical tocontmlmbotsbyusingviSualinfbnnationwithsystems)andoutput(audioinfbrmation)ofthesystem simPlefbrmandithasbeenstudiedvigomusly． ／ｍｅｄｉｆｆBrent,theconsidercdsystemisamulti-】臼te Thou8hvisionsensorsoffbrrichinfbrmationofthesyStemwhichhasbeenStudied(e６９．［8]，［,]）Itis eIMmnmentamundthemboLthey肥quirealotofnatulH1thatsoundSi印alissampledaMasterrate

comPutationtoextmctintIinsicinfblmation,ｏｒａｃ"a thanthｅｍｔｅｗｈｉｃｈｍｂｏｔｓａＩ巳contmnedat・Owing Andthcyaresometimesinterferedbydeadanglesortothis,itispossibletoimplcvetheperfbmlanceof

W803p7860WD鯛17.00,2003IEEE１８２

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（）

0.1

鑿 ^{ServoMotor Con2mU1er 詞0}

-0.1

Fig’１．AudioServoSystem

-０．２ ‐100－５００５０ｍｏ

ａｅ

Ｆｉｇ２、Relationbetweentheoutputofthesystem(9)andthe orientatiOntothesoundsoume(仏）

theSys6emsincethesyStemisabletoObtainmore infmnationthanthecontmner比quiri9S・Inthispapen anadaptivecontmMhemefmaverySimPleaUdio servosystemispmposedbyusingthefast急、teoutput oflhesystem

lnSectionll,detailsofaudiOservosystemwhich isconsideH巳ｄｉｎｔｈｉｓｐ８Ｐｅｒａｒｅｓｈｏｗｎ.、lecontrO1 schemeisprOposedinSectionllLInortlertoshow effectivenessofthepmposedmethod,resultsofa ComputersimulatiOnandthoseofanexPerimentarc showninSeCtionSectionⅣandSectiOnV肥spec‐

tively・T11ensomeconcHudinglCmarksandfhtur己 worksaIMenoted(SectionVI)．

ＩＬＡｕＤＩＯＳＥＲｖｏＳＹｓＴＥＭ

Ｉｎｌｍｓｐａｐ甑ａｓe[vosyStemthatuseSaUdio infbnnationiscaUedqJudioSenJo3ysnem.hother wordMheObjectiveoftheaudioservosyStemisto makethestateofthcsystemconvelgetothedesired Statebyusingaudioinfbrmationitself

USUanyaudioinfbnnationcanbeObtainedatfaster ratethanattheratewhichmechaniCalmbotsystems arecontmUed・ForCxampIe,sUpPOsethataudiosig‐

､alissampledat44100Hz(CDmte)andthatarobot iscontrDUedbyaConlroI1erateaChO・Ssecondln thiscase,thesystemisabletoobtaintheaudiosignal

響2-20000timesfasteMlanthecontroU1eris aⅡ;】もtocontm】thembot､IT1isimPUesthattheaudio

servDsystemisabletoimpMethepeIfbnnanceof thecontmmerbyusingaudioinfbnnationduringtl1e salnplingPericdofthecontrolle凪

Figurc1・showsthesystemwhichisconsidcred inthispapelkTWomicmphonesa[eembeddedina dunmyheadwhichisattachedtoarObotsystem，

andthosencmPhonesobservethesoundfmma Speaker(soundsouzce).IMstheObjectivefbrthis systemtomakeonentationofthedummy-headd雌ct tothesoundsoumebyusingtheaudiOinfbrmation．

、】csignalfiommicmphonesisamplified,sampled aM4100Hzandpre-pmcessedbydigjtalsignalpm- cessor(DSP)asfOUows：

眺(ん)－鮒(ん）

ｇ(〃)＝ｌｇＩ(ん)|＋12〃(ｋ)|＋胸， ^（１）

Where軌(ん)ａｎｄ鮒(虎)repI巳sentthesigna】危om lefUhightmicmphonesattimc肺speCtivelyW(ん)is theoutputoEthesystemanditisthefilteredsignal fbrthecontrollelWoisasmallpositiveconstantto plpvcntthedenominatorof(1)fiomvanishing・

Thecontronercontro1stheorientationofthc

dummy=headbyusingIhenlter己dsigMll9(彫).Let denotetheOrientationofthedUmmy-headasO(k)．

Inthispap甑thefbllowingsilnplecaseisconsiderCd・

Thembot,onwhichthedummy-headisiixed,has onlyldegreeOffiBedom,i､e・mtationalmotion,and commandstOtherobota1℃acceptedtwiceasccond・

mecommandindicatesthedeshCddilectionofthe

dummy-headanditisprOcessedbytheservomotor controllerbnlesettlingtimeoftheservomotoris aboutO3seconddependingonthemagnitudeOfthe

cOmmand．}

NOwbdefinetheangledeaSfbllowS：

“(ん)＝0(ん)－ぬ，（２）

where8drepresentstheorientationofIhesound soumaWiththisnotation,thecontmlObjectiﾊﾉecan beIBwrittenasletOb(虎)→Oasルーoobyusing audiosignalg(ん).Nmethatthesystemmustnot reqUir巳thevalueofOtl・

ｎＤｅ剛ationbetweengandtheangleOeisidenti‐

fiedIhmughexperimcntsanditisshowninFignlre2．

１８３

AuthorizedIIcenseduseIimltedto:KumamotoUniversityTrialUse｢､DownloadedonAugusta2009atO5:１３fiDmlEEEXplore・RestricUonsapply．

WhenthesoundsourccislocatedinnDntofthe

dummy-head，ｔｈａｔｉｓ－９０ｏ＜０ｅ＜９０．，yis monotonicaUyincleasingwithrｅｓｐｅｃｔｔＭｂａｎｄｙ ｉｓａＩｍｏｓｔＯｗｈｅｎＯｂ＝0.nlelefOrc,ｉｔｉｓｎａｔｕｍ】

tomodeMhelelation(oranoutputfilnctionofthe system)betweenWanMeasfbllows：

ｖ(ん)＝50e(代)，、（３）

wherMisanon-zeroconstant・ThisimpUesthat Oe(ん)＝Ｏ幹w(ん)＝０，

andthatthecontmlobjectivMe(ん）→Ocanbe achicvedwhenV(ん）→0.TheIBfbre,itcanbe conclUdedlhattheaudioservosystemisabletobe implementedbyuSingsoundsignamromthedunｍｙ‐

head．

theconve堰encemte,thevalueofK(〃T)isEequM

tobeequaltMhatof；sincethecontmllcrmakes

８e((冗十1)T)becomeOInthisp叩飢amcihod toestimatethisadCquatevaluewithoutap巾冗 infOrmationof6becauseitisnoteaｓｙｔｏｍｅａｓｕｒｅ ｔｈｅｖａｌｕｅｏｆ６・

Ｎｏｗ,HBcallthatthecontm1peliodoftheservo motorcontmllerisTtimeslongerthanlhatofthe audiomiclopmcessorwhichhandlessignalsfrom lnicloPhonescmbeddediMhedunmny-head・ms meansthatlhevalueofW(A)isaN'ailableateach step,ｉ・ａｆｂｒＶｋ・AssumhngthatthesoundsouIceis nxed,thefOllowingrClationholds：

；-鵜}三妄篝)-;{筈;三;{;+（７）

ｉｆ"(ん＋1)－w(ん)≠o

WhenthevalueoM(k)ateachMsavailable,the valueof6canbeidentinedbyusing(7)durinｇｏｎｅ ｓａｍｐｌｉｎｇｐｅｒｉｏｄｏｆＵｌｅｓｅｒｖｏｍｏtorcontroUmThis updatinglawisimplelnentablesince（７）ｄｏｅｓｎｏｔ ｒ己qUireth9valueofOd・

ＩＭＳＩMULATION

InordertovalidatelheeffectivenessofUHepm- posedmethod,resultsofanumeIica1simUlationaIe showninthissection・

DynamicsoftherObotar己modenedasnrstPorder disc剛esystemasfbllow：

０(､T＋ｋ＋1)＝0.50(7,T十h)＋0.5u(､T）

ＶＡＥ[O…Ｔ－１]．（８）

Ｌｅｔｕｎｉｔｏｆｔｉｍｅｏｆｔｈｉｓｓｙｓｔｅｍｂｅ0.1second・It meanMhatthcstateO(片)issamp1edateaChO.ｌ second・Hence，ｍｅｓｅｔｔｌｉｎｇｔｉｍｅｏｆｔｈｅｓｙｓｔｅｍｉｓ ａboutO432secondAndtheinputsi印a】ｕ(vZT)is conunandedateach5seconds(i､c､Ｔ＝５０).Audio signalg(ん)iSassumedtobedilcctlyavaiIab】eateach O1secondwilhoutusing(1)．

０blisgivenasaslowsqumBwave：

鮴)={洲11Ｗ≦`三ｍ0伽十m） _（９）

ｗhe"、isapositiVeintegenThecycleof帥egins

lOaudiosamplingstep(１second）priortod1atof contlO1cycle・TT1erehC,theservosystemreSponds totheChangeofOdwith4seconddclay・

InoldertocomPutethecontlo1inputtL(ｎＴ)，

ｔｈｅｖａｌｕｅｏｆＫ(冗T)withtheupdatingldw(7)is rcquired・Whenthembotstops,Cry(ん)＝D(ん－１)，

ｌｌＬＣｏＮＴＲｏＬＳｃＨＥＭＥ

ＩｎｍｄｅｒｔｏｍａｋｅｔｈecontroUerassimpleas possib1e,thefbllowinglinearoutlputfbedbaCkcontrol

sChemeisadopted：

皿(､T)＝－Ｋ(洞T)w(､T)，（４）

．ｗher已沌rcpIesents血ｅｎｕｍｂｅｒｏｆｔｈｅｃｏｎｔｍｌｓｔｅｐ ａｎｄＴｒｅｐ【esentstheperiodofthecontlol・THmeis sc2dedsuchthattheunitoftimeisequa1Iotheperiod ofaudiosignaL皿(，zT)andＫ(冗T)ICP[csentcontmI signaltOthemotorconnoUerandanadaptivefbed‐

backgainrBspcctiveUy・ItisassumedthatIhemotor

contmUercontmlstheo[ientationoflherubOt(0(ん)）

ｓｕＣｈｌｈａｔ

Ｏ((冗十1)T)＝0(，zT)＋u(冗T)．（５）

Ｂｙ(2),(3),(4)ａｎｄ(5)

０e((冗十1)T）＝０。(河T)＋u(泥T）

＝,e(価)一Ｋ("T)w(､T）

＝０e("T)－Ｋ(､T)処(７２T）

＝（１－Ｋ(，zT)5)ぬ(〃T)．（６）

WhenＯ〈Ｋ(価)〈；,(6)showsthMe＝O

isanasymptotica11ystableeqUiUMumpointatthe samplingrateT､Therefbre,thecontmlobjectiveis achievedwhenK(7,T)isasmallpositiveconstant・

Howevemtmaybetooconservativeto】etthevalue ofKbeaveIysmallpoSitiveconstant・Ｉｔｍｅａｎｓ

【hｅｓｍａｎｅｒｔｈｅｖａｌueofpositiveKis，ｔｈｅlonger thesystemtakestoconverge・InOrdertoimprove theperfblmanceofthesystenMhevalueofK(〃T）

mustbctunedadeqUately・Ｆｒｏｍｔｈｃｖｉｅｗｐｏｉｎｔｏｆ

184

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(7)cannotbecomputedbecauseitsdenominator vaniShes・nlerBfbrMheupdatingIaw(7)ismodined

asfbllows：

Ｋ(k)＝ ^（10）

|鑑静鵬ﾄD''三m）

LettheinitialvalueOfKbeK(O)＝0.1．

InthissectioMnidealzdationbctweeny(k)and Oe(ん)whichismodeMby(3)isConSidered・The outputfmnctionismodemedas：

ｇ(ん)＝1000(0(ｋ)－(9.(ｋ))．（11）

ThefefbHMheoptimaM1ueofKis；＝OOOL

FigUrc3showsnumeIicalresults・ThefirstEgure (Fig.3:a)showsthelcSponscofw(脂).At1hebegging ofthesmulatioM(k)variedwidelybutitColweIged toOastimCpassedn血swasbecausetheinitialva1ue oM,iMr(0)＝Oﾕ,waslOOtimeslaIgerthanthe ,adequatevalueofiMndthesystemwasmstableat thebegimingof血esimmatioM(舟)convergedtoO fbralmostanykbumhevalueofitwasnotOdunng theperiOdfiomwhenOdChangedtowhencontrol inputwasissued．‐

NeXtfigU1℃3:bShows泥SponsesofO(ん)and8d(ん）

WithreSpecttotime・Sincelcsponsesbecamesteady periodiccyclesasitwasshowniniigure3:aresults ofthehrst300secondsa配ｓｈｏｗｎinfbnowing ligmreSmDisfigUI巳showMhatO(ん)trackedOlf(だ）

veHyweUthoughtheIBexistedadelaybecauseof phasediif垣IBncebetweeMdandu､Itisworthnoting thatO(脂)tmckeMbl(ん)withinafewcontru1step・

nMeSponseofK(A)iSShowniMgure3:cand thissupportsthatthesystelnsuitablyadaptedthe valueofK(ん)tolheOptimalvaluebyusingthe Updatinglaw(12)m1isimpliesthattheeffbctiveness oftheupdatinglaｗ(12)wasvalidated､Itisobvious

thatu(vDT)wasboundCdsinceX(ん)and9(ん)ｗｅ泥

bounded(iigureM）

Thmughthissimulation，itisthoughtthatthe pmposedmethodcanbeeffeCtiVetoasimP1eaudio servosyStemevenifp[巳ciseinfbnnationofmicrC- phonesisnOtgivenα〃oｱi､moughthCmodc1of mic1xmllonealray(3)or(11)consideI巴dinthispaper issimPle,thisappmachisapplicableasfaraMhe Idationbetween〃ａｎｄＯｅｃｏｍ己spondingto(7)can beObtaincd･ｍｅｒｅ１ａｔｉｏｎｉｓｎｏｔ亜quiredtobea sca1areqUatiOn,、or・tobetherelationbetweenAth‐

ＳｔｅｐａｎｄＡ;＋lth-step・EvenmorccomplexmultistCp

易

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100２００３０ ０

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nOnlinearrelationcanbeconsideｌＣｄａｓｆａｒａｓａｎ ｕＪｎｑｕｅＳｏｌｕｔｉｏｎｉｓａｂｌｅｔｏｂｅｃｏｍｐｕｔｅｄｗｉｄｌｉｎｏｎｅ

contlolstep．

ＪｕｎＩｕ

VhExpERIMENT

ｒ

Ｔｈｅpmposedmethodwasa1sotestedbya”al robotsystem

ThediagramofthesysteInisshowniniigureland aphotogmphofthefiontviewofthelobotisshown iniiguIe4・Adumny-headwasmadeofaheadofa manikin,TWoeleCtretmicmphoneswereinsertedits earholesandpinnasmadefromclayweIeattaChed・

ＳｉgnaMiommicmphoneswelcampnnedaｎｄｓａｍ‐

pledbymUlti-channelADconverter(FOSTEXVM 88）TheuMheywereencodedasS/PDFsignaland trZlnsmittedtoDSP(MrrHeIonDSP6067anda soundsi印alpmcessingmoduleAP21gO)viaoptical fibercables・ＴｈｅＤＳＰｄｅｃｏｄｅｄＳ/PDIFsi印aland computedmovmgavemgeofsignalsinorderfbr noisereductionThepIe-interedsignalwaSpro‐

cessedbyamamcontmUer(PCﾉﾊﾞrcompatibleper‐

･Son剴computer)andthepmposedcontroUercompute theinputu､ＴｈｅｄｕｍｎＷ国headwasa1taChedondhe tipofamanipulator⑯mSUBISmE1ec・MOvemas‐

terEX),OnlytheMistofthemanipulatorwaScomP mandedtoMateandotherjointsweMixedtokeep thedumny･headUpIightposition・Themanipulator acceptcdutWiceasecondviaRS232Candthe settIｉｎｇｔｉｍｅｏｆｔｈｅｍｂｏｔｗａｓａｍＵｎｄ0.5second・

NotethatIheprcRpmcessedsignａｌｗａｓｓａＩ叩】edat 44100HzandtheinputuwassamPledat2HZ・

TT1eorientationofthedunny-hｅａｄｗａｓｍｅａＰ ｓｕｒｅｄｂｙａ３Ｄｍｏｔｉｏｎ･scnsorCJECTbkinMDP- A3U7）whichwasattaChedtotheshoulderofthe dununy-headThesignalfhomthemotionscnsorwas transmittedviaUSBtothcmaincontmllcrandthc orientationwassamPIedateaChOOO8sccond、

SinceaudiosignalwasstronglydistuIbedbythe noisemmamotoMndiosignaljustaKertheinput uwasissuedwasignｍｅｄａｎｄｏｎｌｙ４０００ｐｏｉｎｔｓ

ｂｅｆｂｒｅＵｌｅｔimewhenuwasissuedweleuscd、

Fmrthermore,inolderfbrnoisereduction，average ofK(denotedasK)wascomputedbyusingthose

valuesasfbUows：

ＤｕｏｎＤｅｎｓｏｒ

Fig.４．ＦｍｎＭｅｗｏ肋erObot(dummy-headmicmPhoneswilh pinnas）．

００

伽釦削剥 ［恕已⑪｛創自く

II2tim6lsec14S6

Fig､５．RcsUltofcxpenment(RespmseofonentahonemraB withrespecttotimet）

where

K(k)＝

(;{号三ｉＨ鮒臘-,'2三…）

InthiseXperimenMhevalueofK(ん)wasseMoO

ⅥhenU(胸)－"(ん－１)wassmallenoughUsingthis K,thecontmlinputTLwascomputedas：

皿((冗T)＝－Ｋ("zMnT)．

え(他+l1Tトホ臘皇繩⑩…） nlesoundsourcewasinstaUedinlmeterftontof

thembotDandtheinitialoIientationofthedummy‐

186

Aulhonzedlicenseduselimltedto:KumamotoUnive屑ityT｢ialUse｢.、ownIoadedonAugust612009atO5:１３hDmlEEEXplore、Restrictionsapply．

mensionalmanipu1atorwinbethenextstCpSince theoutputfimctionmode1Iedby(3)wasthesimp1est case,theoutputfimctionmustbegeneralize｡､From theviewpointofsoundsignaIpIDcessmg,pmpcmes

ofnoiseorsOUndsou1℃eshouIdbetal6enintoaccount

todetectthesoundsignalinsteadofusiｎｇａｓinm1e filterthatwasusedinlhispapeIKAndthougMhe soundsourcewasassumedtobeinstal】edinfiontof thedununy-head,thisassumptionshou1dbe妃laXed andthembotmustbeabletodistinguiShlhesoUnd sourccfmmanydirectiond

VILAcKNowLEDGEMENTs

mｓｓｔｕｄｙｗａｓｓＵｐｐｏｒｔｅｄｉｎｐａｒｔｂｙＵＤｅＪapan SocietyfbrthePmmotionofScience．

ｖ、、REFERENcEs

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浬

oItil:傷[scc]ｊ４５

Ｆｉｇ､６．Resultofexpemiment(ReSponseoftheadaptivegainK withrBspeCttotimc〃

headwas-70degIee､Asitwasshowninthesim- ulationabove,thetmnsientreSponsemayovershoot dependUngontheinitialvalueofK､Therefbre,the veryfirStcommandwas5xcdto泌(－５)＝２０and

timewassettobeOwhenthesecondcommandwas issued

FigU1℃sandFigu唖6showthereSponseofu(〃T)＋

⑫(価)ａｎｄＫ(〃T)respCctivelyBincetheservo contmlleroflhemanipulatormadcOC(("＋1)T)恩Ｌ 皿(〃Z1)十日e(”の,Figure5showSOb(刀T).Thefig‐

meShowsthatthesystemsuccCededtomakethe dummyごheadfacetothesoundsouIce・Ｔｈｅ卿ation betweenりａｎｄＯｅｉｓＳｈｏｗｎｉｎＦｉｇｕＩｅ２ａｎｄｔｈｅ ｅｓtimatedoptimalvalueofKis438・HOwevelb Figuｴe6showsthatKwasabout80atmost,ａｎｄ itdecayedsoonafterOevanishedItisconsidered thatKwasestimatcdsmaUerbccauseK(脂)＝Ｏ Ｗｈｅｎｇ(片＋1)－U(ﾊ）得OHowevenIhesystem wasabletoachievedtheObjectivewithin2stepand itwasacceptableeventhoughthevalueofXwas smanerthantheOptimalvalue・Thelcfb応,itcanbe concludedthateffectivenessofthelDmposedmethod wasvalidatedbythisexpeliment・

VLCONCLUSION

InthiSpap瓢theadaptiveaudioservosystemwas considereCMmediBferenceofmtesbetweenaudio

systemandloboticmotorsystemistalQenintoac- count,andaSimPIeadaptiveschemeisprOposedby usingthispmpertyResultsofacOmputersimulation andanexperimentshowedvalidityofthismelhod・

Asourfhtulewollk,moregeneralcomplexaudio scrvosys6emisneededtobestudied.]POrexample，

Zdimensionalaudiosewosysteｍｕｓｉｎｇｍｍｈｉｄｉ‐

187

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