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1 ISTANBUL UNIVERSITY JOURNAL OF ELECTRICAL & ELECTRONICS ENGINEERING YEAR VOLUME NUMBER : 004 : 4 : (6-70) REALIZATION OF REACTIVE CONTROL FOR MULTI PURPOSE MOBILE AGENTS Slm YANNİER Asf ŞABANOVİÇ Ahmt ONAT 3 Mchatoncs Laboatoy, Engnng and Natal Scncs Dpatmnt, Sabanc Unvsty, Ohanlı Mvk Tzla İstanbl, TURKEY E-mal: [email protected] E-mal: [email protected] 3 E-mal: [email protected] ABSTRACT Mobl obots a blt fo dffnt pposs, hav dffnt physcal sz, shap, mchancs and lctoncs. Thy a qd to wok n al-tm, alz mo than on goal smltanosly, hnc to commncat and coopat wth oth agnts. Th appoach poposd n ths pap fo mobl obot contol s actv and has layd stct that sppots mlt snso pcpton. Potntal fld mthod s mplmntd fo both tacl avodanc and goal tackng. Howv magnay focs of th tacls and of th goal pont a spaatly tatd, and thn sltng bhavos a fsd wth th hlp of th gomty. Poposd contol s tstd on smlatons wh dffnt scnaos a stdd. Rslts hav confmd th hgh pfomanc of th mthod.. Kywods: Atonomos Mobl Robot, Bhavo Abtaton, Bhavo Basd (Ractv) Contol, Mltagnt Systm, Potntal Fld Mthod. INTRODUCTION Most of th woks n th fld of mobl obotcs a basd on on of th followng assmptons: th th complt knowldg of th nvonmnt s a po known as ntodcd by th opato o obot has no a poy nfomaton abot th nvonmnt [-3]. Fst mthod s modl basd and gnally fd as dlbatv contol []. Rqmnt of a complt modl of th nvonmnt s th man dffclty n thos systms. Oth dawbacks of ths appoach a th hgh comptatonal pow and lag mmoy qmnts [,, 4]. Moov, thy do not ffctvly solv navgaton poblms n alwold applcatons wh mltpl movng tacls a nvolvd [5]. Scond appoach consds th task as a combnaton of mo lmntay tasks calld bhavos [4, 6, 7]. Pogammng th xcton of a gvn task thn dcs to fndng th pop combnaton of thos bhavos to podc th dsd task. Ths mthod s snso basd and fd as actv contol o bhavo basd contol [, ]. Many slts on bhavo-basd contol of mobl obots [4, 6, 7] wth vaty of tacl avodanc mthods [5, 8] a alady pblshd. Tnstl sd fzzy logc basd contolls n hs Rcvd Dat: Accptd Dat:

2 6 Ralzaton of Ractv Contol fo Mlt Ppos Mobl Agnts bhavo basd mappng obot [9]. A smla stdy s cad by Tsovlods also [0]. Lo and Chn sd bhavo basd mobl obot to avod dstbancs of th Intnt latncy n mot contol [, ]. Pak [3] has modfd bhavoal contols fo mlt-obot cass. Akn [4] xtndd bhavoal contol achtct fo mlt-obot contol. Estac [5] catd Bhavoal Synthss Modl dsgnd to facltat coopaton and coodnaton btwn mltpl obotc dvcs fo xcton of complx tasks. Fontan and Matac dmonstatd th applcaton of th dstbtd bhavo basd appoach to gnatng a mlt obot contoll [6]. Th a alady sval mplmntatons of pmtv bhavos sng vaty of mthods showng hgh pfomanc whn xctd fo on task at th tm only. Howv, onc mltpl goal alzaton, sch as avodng tacl whl achng a tagt pont, coms nto pct thn acton slcton s th ky ss. Fo acton slcton, Books sd sbsmpton achtct; ach lay ns n paalll, howv, th otpt of only on s xctd n a spcfc tm [4]. Althogh ths confgaton woks wll n lss cowdd aas sch as laboatoy tst bds, n a al wold applcaton slts w not so sccssfl. Consqntly, btt acton slcton mthods w ndd []. Many sachs sggstd and appld fzzy logc basd contolls [9, 7, 8]. Th advantag of fzzy logc s that potntally conflctng fnctons can b fsd n a natal and smooth way, so that a asonabl dcson can b mad to sv both fnctons. Mochada poposd an Emotonal Mchansm smla to th hman motonal mchansm as a solton [9]. Th dvlopmnt of satsfactoy contol mthod fo an atonomos mobl obot that can b pat of a mltagnt systm s stll an opn poblm. Fo sch a systm, on can dntfy a nmb of qmnts, Mltgoal sppot: contol of a mobl obot mst fnd th way to slct th acton that svs a maxmm nmb of goals at th sam tm. Robstnss: n th cas of fals o onos adngs of th snsos, th obot mst stll show manngfl bhavo wthn lmts. Platfom ndpndnc: t shold b applcabl to mobl obots wth dffnt physcal sz, shap, mchancs and lctoncs. Coopatv: a mobl obot contol mst b opn fo adonal contols that wll gd th obot to b a pat of a mltagnt systm. Th goal of ths wok s to psnt a nw stct fo th mobl obot moton contol systm, capabl of bng a bldng block of an ntllgnt agnt. Th st of th pap s oganzd as follows. Scton dscbs th plant. Th whol contol that s dsgnd s psntd n Scton 3. Scton 4 psnts th smlaton slts of th poposd mthod a psntd. Conclsons and aas fo ft sach a psntd n Scton 5.. Plant Th plant conssts of two man ntts: agnts and tacls... Smplfd Modl of Agnts Sampl mobl agnt s dffntal dv typ, nonholonomc obot gnally fd as "whl st" as shown n Fg. Knmatcs of sch a obot can asly b mnd assmng no slp at ts [0], x = v cos y = v sn = ω, v = ω = ( v + v ) R L ( v v ) L R L () 3 wh q = ( x, y, ) R s th stat of th obot psntd by poston and th ontaton n x,, L dnots th wold coodnat fam ( ) w y w lngth of th axs jonng dvn whls and v s th vlocty of th cnt of th two dvng whls. Vaabls that shold b contolld a ght and lft whl s lna vlocts, v R and v L spctvly, whch may asly b tanslatd nto th tanslatonal and otatonal vlocty = v, ω R fo convnnc [0]. vaabls ( ) Slm YANNİER, Asf ŞABANOVİÇ, Ahmt ONAT

3 Ralzaton of Ractv Contol fo Mlt Ppos Mobl Agnts 63 Fg. Whl st s sd as sampl physcal agnt.... Snsos of th Agnt Slctd agnts hav two majo typs of snsos. Fst typ s fo ntnal sag and s ncssay fo fdback contol, sch as ncods to ct th poston and/o vlocty of th dvng motos. Scond typ snsos a fo ctng th nvonmntal stats sch th plac of th tacls by ltasonc dstanc snsos... Obstacls Fo pactcal asons w a fng to all physcal objcts psnt n th nvonmnt (ncldng oth agnts) as tacls. Obstacls a ntts that a th pvntng th agnt to mov o lmtng ts actons. 3. PROPOSED SOLUTİON, SYSTEM LAYER DESIGN Poposd contol s a layd stct fomd ot of two typs of lays: paalll and sal as shown n Fg. Paalll lays a comptnc lays that a pfomng th own tasks ndpndntly and most podcng an otpt n th fom of dsd vlocty and ontaton chang. Sal lays on th oth hand a th connctons of th paalll lays to th hadwa. Dtals of ach lay a psntd n th followng sctons. Fg. Stct of th poposd solton. 3.. Lay 0: Low-Lvl Moton Contoll Lay 0 psnts all hadwa sch as th body of th obot, actatos, dvs and spd/poston contolls, whls, snsos tc. Moov, ths s th lay wh th fnc vlocty and dcton nfomaton fom hgh lvls a convtd to fnc whl vlocts n socalld low-lvl moton contoll. Fnally, th otpt of ths contoll consttts spd fncs fo whl vlocty contolls. Fst, sng actal poston of th obot ( x, y) togth wth th fnc vlocty v f and ontaton, fnc poston of th obot f can b obtand, x y f f = v = v f f cos sn f f Thos two fncs can b combnd, f f f () = x + y (3) wh cosponds to th dstanc fom th f ogn of th wold coodnat fam to th obot s fnc poston. Obvosly, th contol shold b slctd sch that poston os = x x and = y y can b kpt x f y f nd ctan thshold. Pojcton of thos two os on to th vlocty and stng dcton axs (dnotd wth sbscpt and spctvly) can b fond. Slm YANNİER, Asf ŞABANOVİÇ, Ahmt ONAT

4 64 Ralzaton of Ractv Contol fo Mlt Ppos Mobl Agnts = x = cos + x y sn + sn y cos (4) W can thn calclat coctd vals fo th fnc vals and coctd os as co co co = + = = σ f f f (5) co co co = + = = f f σ f Choosng = v R + v L and = v R vl (6) as contols and sng q-3, q- bcoms; = = L (7) Not that s popotonal to v whl s popotonal to = ω. Th contol shold b chosn sch that componnts of th postv dfnt Lyapnov T fncton canddat γ = σ σ 0 satsfy Lyapnov stablty cta. Snc both qatons a ndpndnt, w can s componntws contol, wh componnts of th o vcto a spaatly contolld to tnd to zo. Spaatng γ to ts componnts; γ = σ σ = D σ σ ( σ + D σ ) = 0, =, (8) wh, γ 0 and γ 0, fo =, and fo som constant D > 0. In th abov qaton, th σ o ( σ + D σ ) s zo. f σ + D σ s zo fo σ 0, thn obvosly ( ) σ wll tnd to zo. Solvng abov qaton fo dsct tm systms wh small comptatonal dlays a nglctd w obtan [0]; k k k k (( ) ) = + + D σ σ (9) k k k k = + (( + D ) σ σ ) wh stands fo dsct tm ntval, and k dnots th k th tm ntval. Claly, k k blongs to th cnt tm ntval whl psnts th past val. Fnally, actal fncs fo th ght and lft whl vlocts that wll b sd by svo contolls a fond as, f v = ( + ) R (0) f v = L ( ) 3.. Lay : Obstacl Avodanc () Fo tacl avodanc, potntal fld mthod s sd [, ]. Ths mthod s patclaly attactv bcas of ts smplcty and compatblty wth dffnt typ of snsos. Th basc concpt of th potntal fld mthod s to fll th obot s nvonmnt wth an atfcal potntal fld catd by magnay focs of th fom, A F = ˆ d () wh A s a constant scalng facto, d s th dstanc btwn tacl and agnt fom snso adngs, and ˆ s th dcton fom th agnt to th tacl. By th way, tacls pl th obot. Moov, th nvs popotonalty nss sgnfcant ncas n foc magntd whn th agnt s clos to tacls, whch cas stong acton to avod collsons. Snc th foc s th ngatv gadnt of th fld ( F U ( d ) = ), th agnt can calclat th potntal fld catd by snsd tacls at any pont n th spac (Fg 3). Nvthlss, th agnt mght not b abl to ct vy tacl psnt n th nvonmnt snc ths dpnds on nmb, ontaton and ang of th snsos. Thfo, th xpncd potntal fld mght b slghtly dffnt fom th xpctd on. Fg 3. Potntal fld catd by two tacls. Slm YANNİER, Asf ŞABANOVİÇ, Ahmt ONAT

5 Ralzaton of Ractv Contol fo Mlt Ppos Mobl Agnts 65 In many applcatons, th plsv foc dctly nflncs th motons of th obot by th s of classcal Nwtonan law F = ma wh F s th nt foc assmd to mov th obot, m s th mass (mo gnally sd as a scalng facto) and a s th cospondng obot acclaton vcto []. Howv, F s always n th dcasng potntal dcton, and thfo obot s bondd to mov oppost dcton of th ncontd tacl gadlss of th poston of th goal pont. A btt appoach s to fnd th way to mak obot follow th tacl bonday so that t can go aond t to ach oth sd wh pobably goal pont s locatd. Fst, w dcompos F nto ts componnts: on along vlocty dcton of th agnt F and oth n th dcton ppndcla to t, F. F = F cosθ θ = θ, () F = F snθ π θ π wh θ s th ontaton of F (fom obot to th tacl) n wold coodnat fam. Fo a saf tavl, th agnt mst b ontd to kp F, th foc along th hadng dcton, f mnmm o gnally zo, F = 0. Th at of chang of thos componnts s, F = F F = F θ snθ = F θ cosθ = F ( θ ) sn ( θ ) cosθ θ (3) Fom h, on can concld that contol of both F and F s fasbl by changng ontaton of th obot. Ths fact may b sd fo stablshng stct n whch th tacl avodanc lay wll b sd to chang ontaton of th agnt ths nflncng fnc moton nstad of ntfng wth low-lvl moton contol. Ths way th moton contol loop s mbddd n th tacl avodanc loop. By psntng tacl avodanc loop as two dmnsonal systm, F =, F (4) = on can dsgn an contoll followng th sam stps as n moton contol. W can now dfn os to b mnmzd, = F = F f f F F (5) Usng Lyapnov Fncton canddat T γ = 0 and pocd dscbd n scton 0 w obtan, k, k = =, k, k + +, k, k (( + D ) ), k, k ( + D ) ) Usng q-4 and q-6 togth sn = cosθ θ = θ tan (6) (7) wh θ s th fnc ontaton catd by tacl avodanc lay fo a collson f path. All vals n th abov qaton a fo th psnt tm. Fo pactcal asons, th otpt of ths lay s convtd to th dsd chang n th ontaton = θ (8) bfo snt to th nxt lay. As on can s th tacl avodanc contoll has th sam stct as moton contoll. Thy a stctally connctd n sch a way that lay modfs th bhavo fncs of th moton contol lvl Lay : Dv Towad Goal Pont () Potntal fld mthod s not only sd fo tacl avodanc pposs bt also fo goal tackng. In potntal fld mthod, th agnt s focd mov towad th gon of th spac wh th potntal catd by tacls s mnmm. Howv, ths dos not ns th obot to ach a spcfc pont namly th goal pont. Howv, f n adon to th magnay plsv focs (q-), an attactv foc towad th goal pont s addd, mnma of th potntal fld wll occ at that pont (Fg 4). Ths foc has gnally th fom, F at = B d ˆ (9) Slm YANNİER, Asf ŞABANOVİÇ, Ahmt ONAT

6 66 Ralzaton of Ractv Contol fo Mlt Ppos Mobl Agnts wh B s a constant scalng facto, d s th dstanc to th goal pont and ˆ s th dcton fom th agnt to that pont. In most applcatons, ths foc s smmd wth th plsv focs and th sltant foc s sd to navgat th obot accodng to th classcal Nwtonan law F = ma. Howv, n cas of conflcts lk an tacl btwn th movng agnt and th goal pont, obot wll b focd to mov to oppost sd to avod that tacl f no adonal pcaton s takn. Moov, many local mnmms may appa n th nvonmnt, spcally clos to th passags lk doo opnngs tc, and n gnal, obots a stck at thos ponts. By followng th sam asonng n w can asly fnd th at of chang of th goal focs as, G G = F = F at at θ snθ = θ cosθ = w obtan o contol vaabls Th os to b mnmzd a, = G = G f f G G and (). () Usng Lyapnov Fncton canddat T γ = 0 and pocd dscbd n scton 0 w obtan, k, k =, k + =, k +, k, k (( + D ) ), k, k ( + D ) ) (3) Usng q- and 3 togth, Fg 4. Potntal fld catd by two tacls and a goal pont. sn = cosθ θ θ = tan (4) In o applcaton, w dlbatly slctd to tat thos focs spaatly n two dffnt lays, n od to avod sch poblms. Th attactv foc F s fst dcomposd nto ts at componnts: on along vlocty dcton of th agnt G and oth n th dcton ppndcla to t G. G G = F at cosθ = F snθ at, at θ = θ π θ π (0) To obtan an ontaton towad th goal pont th foc along th hadng dcton mst b f maxmzd G = F, whl th oth at f componnt s focd to b mnmm G = 0. wh θ s th fnc ontaton catd by dv towad goal lay to mov th obot towad th qstd locaton. Fo pactcal asons, th otpt of ths lay s convtd to th dsd chang n th ontaton = θ (5) bfo bng snt to th nxt lay Bhavo Abtaton Unlss dsabld by a hgh lay, (Lay ) s wokng and podcng an otpt,. In adon, onc th obot snss an tacl, (Lay ) wll podc anoth otpt,, that s most pobably n conflct wth th oth on. Slm YANNİER, Asf ŞABANOVİÇ, Ahmt ONAT

7 Ralzaton of Ractv Contol fo Mlt Ppos Mobl Agnts 67 Agnt mst avod tacls whl dvng towad th goal pont. Thfo, and mst b combnd sch that both qst a patally flflld. Fo ths ppos, sally placd bhavo abtaton lay calclatng th wghtd sm of and to tansmt th vlocty and ontaton fncs, to th low-lvl moton contoll, s poposd. In ths pocss, wghts a not constant and a calclatd fom gomtcal latonshps. Assmng that th agnt s movng towad th goal pont, whl avodng an tacl n mdway as shown n Fg 5 blow. Obsvng th staton, w can s that whn th angl btwn vctos F and v s clos to π, tacl avodanc mst gan mpotanc. On th oth hand, f ths angl s clos to π thn tacl s clos to th th sd of th obot and thfo th collson has low pobablty. In ths cas, th mpotanc of mst b ncasd. Mathmatcally ths can b shown as, f = + A + B (6) wh s th actal ontaton of th obot and A and B a th complmntay constants A + B = that psnts th wghts n th smmaton. Thy a both sd as sqa to ncas smoothnss n th fnc ontaton f and a dvd sng θ : th angl btwn vlocty v of th obot and plsv foc F : ( max) fo θ = π A = B = (7) 0 ( mn) fo θ π Fg 5: Optmm and non-optmm path xampl fo an agnt whl avodng an tacl. In ths lay, vlocty fnc s not changd. Howv, a dclaton whn an tacl s ctd and acclaton whn th path s f cold also b addd n ths lay. Th otpt of ths lay s th fnc vlocty f f v and ontaton that s snt to th lowlvl moton contoll wh th moto vlocts a calclatd and contolld accodngly. 3.5.Lay 3: Enablng and Dsablng Fats In dffnt applcatons dng gnal s, bcas of possbl stctons, a spcfc bhavo may b qd to b dsabld, as n th xampl of a mobl obot that nds to stop and chag t-slf at th staton. Th thd lay of th poposd algothm s sponsbl of th nablng and dsablng of th th fats: Dv Enabl (Mov o Stop): Th dsd task may q bng statonay at a gvn pont as n th cas of a ca obot that s clos nogh to ts load to gasp t. Dv Towad Goal Enabl ( Enabl): It may also b ncssay to dsabl lay. Fo xampl, f th agnt s stck among tacls and cannot mov smply bcas of th confgaton, t may b sfl to tmpoaly dsgad th goal. Obstacl Avodanc Enabl: Th a cass wh vn tacl avodanc mst b dsabld. A foklft appoachng to a box to hold t mst dsabl ths lay snc othws t wll b focd to mov away by th commands of lay. In sch an applcaton dsablng snsos s not a stabl solton snc ths contol shas all avalabl soc to th nt layd stct. 3.6.Lay 4: Long Tm Mmoy Lays Most of th sachs am to cat mobl obots that can wok n hazados nvonmnts sch as a dp sa, ncla plants and polltd aas wh hmans may not svv. Gnally, th obot mst cod som data sch as tmpat, ncla adaton, alttd tc. and cay t to th bas staton wh fth analyss s don. Smlaly a ca obot that s wokng n a factoy, mst kp a log of what s tanspotd. Slm YANNİER, Asf ŞABANOVİÇ, Ahmt ONAT

8 68 Ralzaton of Ractv Contol fo Mlt Ppos Mobl Agnts Sch knd of data loggng wok shold b alzd n ths lay. Howv, pocssng of ths data o actons latd to th staton mst b appld n th pp lay Lay 5: Us Dfnd Lays In al obotcs applcatons, most of th tm th s an xtnal hadwa, whch mst b contolld. A mobl obot may hav a obot am montd on top of t togth wth a stabl nd-ffcto to alz tasks sch as pantng a wall. In atomatd ca, th obot mst hav hadwa to gasp, lft, mov and lav objcts. Th contol latd to ths hadwa o any modfcaton to th xstng contol lays (sch as changng fnc vals of th foc contol lays) shold b don fom ths lay. Contol placd n ths lay, as all oth lays, hav accss to th snso data, and to all low lvl blocks. If ths lay wll gnat a modfcaton qst n fnc vlocty and ontaton of th low-lvl moton contoll ths mst b don thogh bhavo abtaton lay that wll b modfd accodngly Lay 6: Commncaton Commncaton s th only lnk btwn th agnts and th s. Hgh lvl command sch as mov to ( x, y), stat/stop xcton of tasks and low lvl commands sch as dsabl, opn gpp a snt to th agnt sng ths lnk. Smlaly, collctd data by th agnt s tansmttd to th s and oth agnt by ths lnk. Moov, commncaton can safly b sd n mlt-obot collaboaton wh small tm dlays d to th tansmsson tm a not mpotant. Ths lay mst b at th top lay fom wh t can ach and modfy all oth lays. Any stabl commncaton mthod can b appld. 4. SIMULATIONS AND RESULTS Poposd contol fo mobl obots s tstd on th dvlopd smlaton tool wttn n C++ pogammng langag. Ths smlaton cod, conssts of a co whch s a collcton of otns and xpmnts that a dfnng th xpmntal stp and thn callng otns n th ncssay od. Rslts a shown sng a smpl GUI. 4.. Statonay Obstacls In ths xpmnt, only on agnt s placd n th nvonmnt togth wth fo statonay tacls. Agnt s told to tavs towad th oth sd of th nvonmnt (s Fg 6). What s xpctd fom th agnt s a smooth and saf navgaton thogh tacls. Agnt mst dct tslf towad th goal pont nlss an tacl s snsd. In sch a cas, th dcton of navgaton mst b changd to go aond th tacl at a saf dstanc. Ths s xactly what s vd n th xpmnt. Fthmo, n ths fg, w also s claly th wok don by th bhavo abtaton: whn th agnt gts clos to th tacl, t was movng dctly to th tacl. Th foc contol algothm nflncd th obot to chang ts dcton sch that, th obot statd to mov aond th tacl. At th pont shown wth an aow n Fg 6, tacl s not btwn th agnt and th goal pont anymo. Consqntly, th bhavo abtaton nhbts th otpt fom th tacl avodanc lay ntl th agnt achs to th snsblty ang of th tacl. A smla bhavo s vd wth th two oth tacls. Fg 6. Avodanc of statonay tacls. 4.. Movng Obstacls In ths xpmnt, w tstd th acton of th agnt to th movng tacls. As shown n Fg 7, an agnt s placd at th pont S and told to mov to th pont T. Fo oth agnts, wth tacl avodanc lay dsabld, a also placd to th nvonmnt (MO, MO, MO3 and MO4). 3 4 Slm YANNİER, Asf ŞABANOVİÇ, Ahmt ONAT

9 Ralzaton of Ractv Contol fo Mlt Ppos Mobl Agnts 69 S MO 3 4 Fg 7. Avodanc of movng tacls. Dng th xpmnt, agnt confontd fo movng tacls, smlatng hmans o ollng balls, on by on. Fst confontaton happnd wth MO (s ccld aa makd as n Fg 7). Th agnt actd qckly to avod th tacl. As xpctd, ths acton was fast snc both th foc and ts dvatv s sd n contol. Whn th path was cla to th obot, t ontd t-slf towad th tagt pont T, ntl nxt confontaton. Smla bhavo s vd fo MO, MO3 and MO4 confontatons. W s claly that th agnt movs natally and safly n th aa wh t nconts movng tacls contnosly. 5. CONCLUSION MO3 MO In ths wok, w sggstd a nw appoach fo alzaton of actv contol of mobl obots. Ths nw alzaton dvds th contol nto lays. Each lay has ts own task and goals to b accomplshd. Otpts fom ach lay a collctd n bhavo abtaton. In th whol contol, bhavo abtaton s th only pat that can dctly nflnc th moton of th obot, xcpt som possbl s applcatons sch as an mgncy stop command. Th poposd appoach fo alzaton sppots mlt goals. Rachng to a spcfc pont whl avodng tacls s a smpl mlt goal xampl fo a mobl obot. Thos two basc goals fo a mobl obot a alady n th contol, and wokng n hamony. Fth goals can asly b dfnd n th appopat lay of contol. Ths way, th adons of th nw lays to th mobl obot contol wll agmnt chnss of th bhavos vd and wth coct mplmntatons wll ncas th pfomanc vd. G MO4 Poposd contol s tstd on smlatons, and dffnt scnaos a stdd. Espcally, th cass that a poblmatc to many oth appoachs a nvstgatd. Som of th slts a shown n th pvos chapt. Th smlaton slts confmd th hgh pfomanc of th mthod. Moov, sam slts show that som of th dawbacks comng fom th nat of th appld contol a avodd. Fthmo, fom ths slts, w can concld that th poposd contol s a potntal altnatv fo mobl obots contol opatng n dynamc nvonmnts and/o as an agnt n mltagnt systm. REFERENCES [] R. C. Akn, Bhavo-Basd Robotcs. Cambdg, Mass.: MIT Pss, 998. [] J. Fb, Mlt-Agnt Systms: An Intodcton to Dstbtd Atfcal Intllgnc. Halow, Eng.: Addson-Wsly, 999. [3] W. L. X and S. K. Tso, "Snso-Basd Fzzy Ractv Navgaton of a Mobl Robot thogh Local Tagt Swtchng" IEEE Tans. on Systms, Man and Cybntcs, Pat C, vol. 9, pp , 999. [4] R. A. Books, "A Robst Layd Contol Systm fo a Mobl Robot" MIT Atfcal Intllgnc Laboatoy, Massachstts A.I. Mmo 864, Sp [5] K.-T. Song and C. C. Chang, "Ractv Navgaton n Dynamc Envonmnt Usng a Mltsnso Pdcto" IEEE Tansactons on Systms, Man and Cybntcs, Pat B, vol. 9, pp , 999. [6] R. A. Books, "A Robot That Walks; Emgnt Bhavos fom a Caflly Evolvd Ntwok" MIT Atfcal Intllgnc Laboatoy A.I. Mmo 09, Fb [7] R. A. Books, Camban Intllgnc: Th Ealy Hstoy of th Nw A.I. Cambdg, Mass.: MIT Pss, 999. [8] A. Stnhag and R. Schon, "Th Dynamc Appoach to Atonomos Robot Navgaton" psntd at IEEE Intnatonal Symposm on Indstal Elctoncs, ISIE' 97, 997. Slm YANNİER, Asf ŞABANOVİÇ, Ahmt ONAT

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