Automatic design of fuzzy control systems for autonomous mobile robots

AUTOMATIC DESIGN OF FUZZY CONTROL SYSTEMS FOR AUTONOMOUS MOBILE ROBOTS I. Ba u one1, F. J. Mo eno-Velo1, S. Sánchez-Solano1, R. Ma ín de Aga 2, A. Olle o2 1 Ins i u o de Mic oelec ónica de Se illa (IMSE). A d. Reina Me cedes, s/n. Edi . CICA, 41012, Se illa, SPAIN 2 Dep. Ingenie ía de Sis emas y Au omá ica. E.S.Ingenie os. Camino Descub imien os s/n. 41092, Se illa, SPAIN [email p o ec ed] P oc. 28 h Annual Con e ence o he IEEE Indus ial Elec onics Socie y (IECON’2002), pp. 2457-2462, Se illa, No embe 5-8, 2002. © 2002 IEEE. Pe sonal use o his ma e ial is pe mi ed. Howe e , pe mission o ep in / epublish his ma e ial o ad e - ising o p omo ional pu poses o o c ea ing new collec i e wo ks o esale o edis ibu ion o se e s o lis s, o o euse any copy igh ed componen o his wo k in o he wo ks mus be ob ained om he IEEE. This ma e ial is p esen ed o ensu e imely dissemina ion o schola ly and echnical wo k. Copy igh and all igh s he ein a e e ained by au ho s o by o he copy igh holde s. All pe sons copying his in o ma ion a e expec ed o adhe e o he e ms and cons ain s in oked by each au ho ’s copy igh . In mos cases, hese wo ks may no be epos ed wi hou he explici pe - mission o he copy igh holde . Abs ac - This pape desc ibes he design and implemen- a ion o a uzzy con olle o au onomous mobile obo s. The ool X uzzy 3.0, de eloped a he IMSE (Ins i u o de Mic oelec ónica de Se illa) has been used o design a con olle o he Romeo 4R au onomous ehicle designed and buil a he “Escuela Supe io de Ingenie os”, Uni e si y o Se ille. The pape p esen s he design o he con olle and eal expe imen s wi h Romeo 4R demons a ing he e iciency o he con olle . I.INTRODUCTION Some o he maneu e s ha should be pe o med by an au onomous mobile obo , such as pa king in a gi en place, a e easily pe o med by any human d i e wi h a bi o p ac ice. The way in which human d i e s usually exp ess hei con ol ac ua ion o pe o m a maneu e (b ake, s ee ing wheel, e c.) is no qui e p e- cise bu a he uzzy. We nei he need exac in o ma- ion om he en i onmen o om ou ehicle o ca y ou a success ul maneu e . Mos o he imes, we apply a heu is ic knowledge which can be exp essed linguis- ically by mo e o less chained i - hen ules. Fuzzy logic p o ides a ma hema ical amewo k o ansla e hese linguis ic and symbolic concep s in o nume ical da a which can be handled by elec onic ci cui s. Many wo ks ha e been epo ed in he li e a u e which show he e ficiency o uzzy con olle s implemen ed in so - wa e (gene al-pu pose p ocesso s) o ha dwa e (appli- ca ion specific p ocesso s) [1-2]. As happens o any design p ocess, i is e y in e es - ing o employ CAD ools when designing a uzzy con- olle . This is pa icula ly ue nowadays when educing he cos and he ime- o-ma ke o a p oduc a e d i ing o ces o he indus y. In he las ew yea s se e al CAD ools ailo ed o he uzzy sys em design ha e been c ea ed [3-5]. The CAD en i onmen employed in his pape is X uzzy 3.0, which has been de eloped a he IMSE (Ins i u o de Mic oelec ónica de Se illa) wi h he objec i e o being an open en i onmen wi h he leas possible lim- i a ions [6]. Wi h his gene al objec i e, X uzzy 3.0 is based on an specifica ion language (XFL3) ha eases he desc ip ion and manipula ion o complex uzzy sys ems hanks o he use o use -defined membe ship unc ions, uzzy ope a o s (including linguis ic hedges), and ule bases (admi ing hie a chical s uc- u es) [7]. This objec i e has also mo i a ed he use o Ja a as he p og amming language o X uzzy 3.0. This means he use o an ad an ageous objec -o ien ed me hodology and he flexibili y o execu ing X uzzy 3.0 in any pla o m wi h JRE (Ja a Run ime En i on- men ) ins alled. This pape desc ibes how X uzzy 3.0 can help he use o iendly design a uzzy sys em o con olling he pa king maneu e s o Romeo 4R, an au onomous mobile obo de eloped a he Escuela Supe io de In- genie os (ESI) o he Uni e si y o Se ille [8]. Sec ion II shows he desc ip ion p ocess o he uzzy sys em. Sec ion III explains how he beha io o he con olle can be e ified by moni o ing he in e ence p ocess as well as simula ing he con olle in a closed loop wi h a model o he obo . Once he sys em has been designed and alida ed, X uzzy 3.0 allows i s syn hesis in o se - e al p og amming languages. Sec ion IV shows how he con olle is syn hesized as a C code and in eg a ed in o he so wa e execu ed by he compu e ha con- ols Romeo 4R. Se e al expe imen al esul s o diago- nal pa king maneu e s a e included o illus a e he e ficiency and obus ness o he designed con olle . II.FIRST STEP:DESCRIPTION PROCESS OF THE FUZZY CONTROLLER Pa king a ehicle a a gi en place has been a p ob- lem usually add essed in he li e a u e o illus a e he capabili ies o neu al and uzzy con olle s. A ypical goal is o back up a ehicle so as o a i e a a desi ed loading dock a a igh angle wi h he ho izon al [9]. The inpu a iables conside ed in hese epo ed con- olle s a e he x posi ion o he ehicle and he ehi- cles´s o ien a ion angle wi h he ho izon al. The ou pu con ol a iable is he equi ed s ee ing angle (see Fig- Au oma ic Design o Fuzzy Con ol Sys ems o Au onomous Mobile Robo s I. Ba u one1, F. J. Mo eno-Velo1, S. Sánchez-Solano1, R. Ma ín de Aga 2, A. Olle o2 1 Ins i u o de Mic oelec ónica de Se illa (IMSE-CNM). A d. Reina Me cedes, s/n. Edi . CICA, 41012, Se illa, SPAIN 2 Dep. Ingenie ía de Sis emas y Au omá ica. E.S.Ingenie os. Camino Descub imien os s/n. 41092, Se illa, SPAIN [email p o ec ed] This wo k has been pa ially suppo ed by he Spanish CICYT P ojec s TAP99-0926-C04-01 and TIC2001-1726. u e 1). The speed magni ude as well as he backwa d di ec ion o d i ing a e cons an . These epo ed con- olle s a e e ficien whene e he ehicle is a he a om he loading dock bu ail i i is nea he dock and wi h a bad o ien a ion angle, like ha in Figu e 1. The pa king p oblem ha we add ess in his pape is mo e complex and ealis ic: ou au onomous obo has o pa k a a desi ed place, a i ing backwa d and a a igh angle, bu i could d i e backwa d and o wa d o achie e success om any s a ing posi ion and o ien a- ion. The app oxima ion we ha e aken o design his con olle is o di ec ly emula e wha we would do as d i e s. In his sense, ou fi s con ol ac ion is o decide he di ec ion o d i ing ( he sign o he speed): backwa d o o wa d, and he magni ude o he speed. This decision is dynamic because i akes in o accoun no only he cu en posi ion and o ien a ion o he ehicle bu also i s p e ious speed. This knowledge is included in o a ule base ha we call “di ec ion”. In addi ion, he cons ain s imposed by Romeo 4R ha e o be conside ed when deciding he new speed. Fo example, Romeo has no an elec onically con- olled b ake cu en ly, and i is impo an o ensu e ha he d i ing di ec ion changes so ly. This means ha he con olle should ne e decide o go o wa d a a a he high speed i p e iously, he ehicle was d i - ing backwa d a a a he high speed. This kind o con- s ain s a e conside ed by a ule base ha we call “b ake”. The inpu a iables o his ule base a e he speed decided by he ule base “di ec ion” and he p e- ious speed. I s ou pu is he new speed ha will be adop ed by Romeo. The second decision is o selec he p ope angle o he wheels once we ha e decided o d i e backwa d o o wa d. The speed selec ed by he ule base “b ake” oge he wi h he x posi ion and he o ien a ion o he ehicle a e he inpu a iables o ano he ule base ha we call “wheel”. As a esul o ou knowledge emula ion, he uzzy con olle ha we ha e ob ained is a hie a chical sys- em wi h he s uc u e shown in Figu e 2. The global inpu a iables a e he posi ion (x, y), o ien a ion (angle), and p e ious speed (olddi ) o he obo ; and he ou pu a iables a e he s ee ing wheel angle (wheel) and he new speed (di ec ion). We ha e employed X uzzy 3.0 o desc ibe his con- olle . X uzzy 3.0 di ides he desc ip ion o a uzzy sys em in o wo pa s. One pa is he logical defini ion o he sys em (i s s uc u e, he membe ship unc ions ha ep esen he uzzy se s, and he ules o each ule base). This pa can be defined ia g aphical use in e - aces by using he ool x edi o by edi ing di ec ly a “.xfl” file. The o he pa is he ma hema ical defini ion o he di e en unc ions ha appea in he logical de - ini ion (membe ship unc ions, connec i e ope a o s, de uzzifica ion me hods, linguis ic hedges, e c.). This pa can be defined ia g aphical use in e aces by using he ool x pkg o by edi ing di ec ly a “.pkg” file. This wo old defini ion allows us o c ea e and use ou own membe ship unc ions, de uzzifica ion me h- ods, e c. In ou case, all he ma hema ical unc ions employed a e desc ibed in he xfl.pkg file p o ided wi h X uzzy 3.0. Fo example, he de uzzifica ion me hod employed in he ule base “wheel” is he Fuzzy Mean me hod, which calcula es he weigh ed a e age o he consequen single on alues. This p o ides a so in e pola ion among he 7 single on alues conside ed o ep esen he wheel angle. On he o he side, he de uzzifica ion me hod ha we employ in he ule bases “di ec ion” and “b ake” is a me hod ha we call “MaxLabel”. I selec s he single on consequen o he ule whose ac i a ion deg ee is maximum, because he decision made by hese ule bases has o be c isp: o - wa d o backwa d bu no an a e age o bo h. The desc ip ion o he MaxLabel me hod can be seen in Figu e 3. This figu e illus a es he g aphical in e ace o he ool x pkg whe ein he X uzzy use can define new uzzy ope a o s (logical connec i e, linguis ic hedges, membe ship unc ions, o de uzzifica ion me hods). wheel (x,y) Fig. 1: Example o he diagonal pa king p oblem. he objec i e angle ehicle angle Fig. 2: S uc u e o he designed con olle . x angle di ec ion y olddi b ake wheel di ec ion wheel We ha e used he ool x edi o speci y he logical defini ion o ou con olle , as can be seen in Figu e 4. The membe ship unc ions employed a e: 5 uzzy se s o co e he x posi ion; 1 single on alue and 3 uzzy se s o co e he y posi ion; 7 uzzy se s o co e he o ien a ion; 5 single on alues o co e he speed (i s sign eflec s he d i ing di ec ion); and 7 single on al- ues o co e he s ee ing wheel angle. The speed alues a e a he slow as co esponds o pa king maneu e s (be ween -1m/s and 1m/s). The wheel angle alues a e limi ed by he maximum cu a u e ha Romeo can apply. Figu e 5 shows he window o x edi whe ein we ha e defined he membe ship unc ions o he o ien a- ion a iable. The ule bases can employ di e en ma hema ical unc ions o ep esen he uzzy ope a o s. Fo exam- ple, he ule bases “di ec ion” and “wheel” use di e - en de uzzifica ion me hods, as commen ed abo e. Figu e 6 illus a es he window o x edi whe ein we ha e selec ed he ma hema ical unc ions o he uzzy ope a o s in he ule base “di ec ion”. An ad an age o X uzzy 3.0 is ha he use can eely modi y he ma h- ema ical unc ions ha desc ibe hese linguis ic ope a- o s (wi h he ool x pkg men ioned abo e). We ha e also used x edi o define he ules o each ule base. The XFL3 language employed by X uzzy 3.0 eases he ansla ion o linguis ically exp essed ules because admi s linguis ic hedges like “mo e o less equal o”, “sligh ly equal o”, e c., and ela ions like “g ea e han” o smalle han”. Fo ins ance, one o he ules in he ule base “di ec ion” is: ‘i (y is “equal o” nea and x is “s ongly equal o” cen e and angle is “equal o g ea e han” le small and angle is “equal o smalle han” igh small) hen di is backwa d’. III.SECOND STEP:OFF-LINE VERIFICATION PROCESS OF THE FUZZY CONTROLLER Al hough he defini ion o he uzzy con olle ansla es ou expe knowledge, we migh ha e o go - en o conside some si ua ions o no conside p op- e ly o he ones. This is why pe o mance o he con olle has o be e ified p io o expe imen wi h Romeo 4R. Fo his pu pose, we ha e employed h ee e ifica ion ools o X uzzy 3.0: x 3dplo ,x m and x sim. The ool x 3dplo allows us o isualize he beha io o one o he con ol a iables e sus wo o he ones. Fig. 3: G aphical use in e ace o he ool x pkg. Fig. 4: Main window o x edi . Fig. 5: Membe ship unc ions o he ehicle o ien a ion. Fig. 6: Window o x edi o selec he uzzy ope a o s. This is e y use ul o s udy, o ins ance, i ou con ol- le is sa e enough o a oid c ashes wi h a possible pa emen a y=0. Figu e 7 shows he su ace co e- sponding o he new speed decided by he con olle agains he y posi ion and he o ien a ion o Romeo, when he x-posi ion coo dina e is ze o and he p e ious speed was -1m/s. We can see ha i he y posi ion is nea ze o and he angle is no qui e ze o, he con olle decides o s op o be e s aigh en he ca by d i ing o wa d in subsequen s eps. The ool x m is e y use ul o moni o how is wo k- ing he in e ence p ocess. Fo ins ance, i we wan o know why he new speed is -1m/s when he x posi ion is ze o, he p e ious speed was -1m/s, he y posi ion is 2 m and he angle is 180º, we can use x m as shown in Figu e 8 o disco e ha he ule esponsible o his decision is he ule 30 o he ule base “di ec ion”: ‘i (y is “equal o” nea and x is “equal o” cen e and (angle is “smalle han” le o “g ea e han” igh )) hen di is backwa d’. Al hough wi h he p e iously men ioned ools we can analyze he con olle i sel , a e y impo an s ep in any con ol design is o simula e he con olle wo k- ing in a closed loop wi h he plan . Fo his simula ion, we ha e employed he ool x sim o X uzzy 3.0. The beha io o ou plan , Romeo 4R, has been desc ibed by he bicycle kinema ic model [10], conside ing a fi s -o de dynamic esponse in he se ling o he speed and he wheel angle imposed by he con olle . The ou pu s o he simula ion pe o med by x sim can be sa ed o a log file o pos e io g aphical ep esen a- ion. As an example, Figu e 9 illus a es he simula ed beha io o Romeo 4R when i s a s (wi h speed 0) a x=3.9m, and y=9m, wi h an angle o 90º. The a ows indica e he d i ing di ec ion and he shaded one ma ks he s a ing poin . Wi h his o -line simula ion, we can analyze he obus ness o ou con olle agains pe u ba ions. Fo ins ance, i he ue speed aken by Romeo 4R is 40% g ea e han ha imposed by he con olle and we epea he simula ion o Figu e 9, he esul s ob ained a e shown in Figu e 10. IV.THIRD STEP:ON-LINE VERIFICATION PROCESS OF THE FUZZY CONTROLLER Once checked ha ou sys em is obus enough, we ha e e ified i s con ol beha io wi h he ue plan , Romeo 4R. This obo is an elec ical ehicle p o ided wi h a se o senso s and ac ua o s ha make i capable o au onomous na iga ion (Figu e 11). The in o ma- ion collec ed by he senso s and ha equi ed by he ac ua o s is cen alized by a compu e placed a he back o he obo and which also implemen s he con- ol algo i hms. In ou pa king applica ion, he com- pu e has o go e n a mo o con ol ca d which in u n go e ns, independen ly, he s ee ing and ac ion elec- ical mo o s o Romeo. These elec ical mo o s has o ecei e, espec i ely, he wheel angle and new speed commands om ou con olle . In addi ion, he mo o Fig. 7: S udying he beha io o he a iable “di ec ion”. Fig. 8: Moni o ing he in e ence p ocess. F ig. 9: Simula ing he con olle wi h a model o Romeo 4R. 0 2 4 6 8 10 12 -2-1012345 ✧ ✧✧✧✧✧✧✧ ✧✧✧✧✧✧ ✧✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧✧ ✧ ✧ ✧ ✧ ✧✧ ✧ ✧ ✧✧ ✧✧ ✧ con ol ca d eads he di ec ion and ac ion encode s o he engines. These measu es, oge he wi h he in o ma ion p o ided by a gy oscope ha e o be p o- cessed by he compu e o es ima e he cu en posi- ion, o ien a ion and speed o he obo , which a e he inpu a iables equi ed by ou con olle . The compu e ope a es wi h Linux and all he d i - e s o he senso s and ac ua o s ha e been w i en in C code. In addi ion, an in e ace has been de eloped ha include a wide se o unc ions (p og ammed in C++) o wo k easily wi h senso s and ac ua o s. Ha ing his in e ace, he inclusion o ou con olle is as simple as gene a ing i s C code. Fo his ask, we ha e employed he syn hesis ool x c o X uzzy. Despi e execu ing he con ol code and all he o he equi ed ou ines, he compu e ope a es a eal ime wi hou p oblems because a con ol cycle pe iod o 100 ms is enough o ou applica ion. Figu e 12 shows wo examples o expe imen al a- jec o ies ollowed by Romeo when s a ing a di e en posi ions (ma ked by he shaded a ows) and wi h di - e en o ien a ions. Compa ing Figu e 12a wi h Figu e 9 we can see ha expe imen al esul s do no di e e y much om simula ed esul s. Figu e 13a illus a es he e olu ion in ime o he wheel angle e e ence gi en by he uzzy con olle (in solid line) and he eal angle aken by Romeo (in dashed line), o he expe imen in Figu e 12a. We can see how he angle e e ence changes so ly (as a conse- quence o he Fuzzy Mean de uzzifica ion me hod applied by he ule base “wheel”) and how i is ol- lowed apidly by he eal angle. Figu e 13b compa es he e olu ion in ime o bo h he speed e e ence (in solid line) and he eal speed (in dashed line) co esponding o he expe imen in Figu e 12a. In his case, he e e ence changes ab up ly (because o he MaxLabel de uzzifica ion me hod applied) and he dynamic o he eal speed is slowe Fig. 10: Simula ing he con olle wi h pe u ba ions. 0 2 4 6 8 10 12 -2 -1 0 1 2 3 4 5 ✧✧✧✧✧✧ ✧✧✧✧✧ ✧✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧✧ ✧ ✧ ✧ ✧ ✧✧ ✧ ✧✧ ✧ ✧✧ ✧✧ ✧✧ ✧✧ ✧✧✧ ✧✧✧ ✧✧✧ ✧✧✧ ✧✧✧✧ ✧✧✧✧✧ ✧✧✧✧✧✧ ✧✧✧✧✧ Fig. 11: Romeo 4R success ully pa ked. Fig. 12: Expe imen al esul s. 0 2 4 6 8 10 12 -2 -1 0 1 2 3 4 5 ✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧ ✧ ✧ ✧✧✧✧ ✧✧✧✧✧ ✧ ✧ ✧✧✧ ✧ ✧ ✧✧ ✧ ✧✧✧✧ ✧ ✧ ✧ ✧ ✧✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧✧ ✧✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧✧ ✧ ✧ ✧✧✧ ✧ ✧ ✧✧ ✧ ✧ ✧ ✧ ✧ ✧✧✧✧ ✧✧✧ ✧ ✧ ✧✧ ✧✧✧✧✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧✧ ✧ ✧ ✧ ✧✧✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧✧✧ ✧✧✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧✧ ✧ ✧ ✧✧✧✧ ✧✧✧✧ ✧ ✧ ✧✧✧✧ ✧ ✧ ✧✧✧✧ ✧✧✧✧✧✧✧✧✧✧ ✧ ✧ ✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧ -2 0 2 4 6 8 0 2 4 6 8 10 12 14 ✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧ ✧ ✧ ✧✧✧✧ ✧ ✧ ✧✧✧ ✧ ✧ ✧ ✧✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧✧✧✧✧✧ ✧✧✧✧ ✧✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧✧ ✧ ✧ ✧✧ ✧ ✧ ✧✧✧✧ ✧✧✧✧✧ ✧✧✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧✧ ✧ ✧ ✧ ✧ ✧✧ ✧ ✧ ✧✧ ✧ ✧ ✧ ✧✧✧ ✧ ✧✧✧✧✧✧✧ ✧✧ ✧✧ ✧ ✧ ✧ ✧ ✧✧ ✧✧ ✧✧ ✧ ✧ ✧✧ ✧✧ ✧ ✧ ✧ ✧ ✧✧ ✧ ✧ ✧ ✧✧ ✧✧ ✧ ✧✧ ✧ ✧ ✧✧ ✧✧ ✧✧ ✧ ✧ ✧✧ ✧✧✧ ✧ ✧✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧✧ ✧✧ ✧ ✧ ✧✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧ ✧✧ ✧ ✧ ✧ ✧ ✧ ✧✧ ✧ ✧ ✧ ✧✧✧ ✧ ✧✧ ✧ ✧ ✧ ✧ ✧ ✧✧ ✧ ✧✧✧ ✧ ✧ ✧✧ ✧ ✧✧ ✧ ✧✧✧ ✧ ✧ ✧ ✧ ✧ ✧✧ ✧✧ ✧ ✧✧✧✧✧✧✧✧ ✧✧✧✧✧✧✧✧✧✧ ✧✧✧✧ ✧ ✧ ✧✧✧ ✧✧✧ ✧ ✧ ✧✧✧ ✧ ✧ ✧ ✧ ✧ ✧✧✧ ✧ ✧ ✧ ✧✧✧ ✧✧✧ ✧✧✧ ✧ ✧✧✧✧✧✧✧✧✧✧✧ ✧✧✧✧✧✧✧✧✧✧ ✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧✧ (a) (b) han ha o he eal angle. The wo hwhile ac shown by his figu e is ha he obo is con olled e ficien ly o commu e so ly be ween d i ing backwa d and o - wa d, hus mee ing he imposed equi emen s. V.CONCLUSIONS The au oma ic design and implemen a ion o uzzy con ol sys ems in ol es a numbe o ac i i ies ela ed o he defini ion o he con olle , including i s logical s uc u e and he ma hema ical defini ion o unc ions, he o -line e ifica ion o he con olle by means o simula ion and he on-line e ifica ion and es ing wi h he eal p ocess. This pape p esen s he applica ion o he X uzzy 3.0 ool o he design o he uzzy con olle o au ono- mous ehicles. Pa icula ly he design and implemen- a ion o a con olle o he Romeo 4R is desc ibed. The esul s ob ained wi h he eal ehicle a e simila o he simula ion esul s and Romeo 4R is able o pe o m success ully a pa king maneu e e en when he ehicle is ini ially close o he pa king posi ion, wi h a bad o i- en a ion, and ha ing o maneu e au onomously o pa king. Fu u e wo k will include a compa ison o he p e- sen ed uzzy logic me hod wi h o he echniques based on he consecu i e execu ion o pa h planning, gene a- ion and con ol echniques in di e en p ac ical cases. VI REFERENCES [1] Munaka a, T., Jani, Y., Fuzzy sys ems: an o e iew, Communica ions o he ACM, Vol. 37, N. 3, 1994. [2] Sugeno, M., Ed., Indus ial Applica ion o Fuzzy Con ol, No h-Holland, pp. 19-40, 1985. [3] Home page o FuzzyTech: h p://www. uzz- y ech.com [4] Home page o FIDE: h p://www.ap onix.com/ ide/ [5] Home page o TILShell: h p://www.o ech eng .com/ uzzy/TilShell.h ml [6] F. J. Mo eno-Velo, I. Ba u one, S. Sánchez-Solano, A. Ba iga, "X uzzy 3.0: A De elopmen En i on- men o Fuzzy Sys ems", P oc. 2nd IEEE In . Con . on Fuzzy Logic and Technology (EUS- FLAT’2001), pp. 93-96, Leices e , 2001. [7] F. J. Mo eno-Velo, S. Sánchez-Solano, A. Ba iga, I. Ba u one, D. R. López, “An Speci ica ion Lan- guage o Fuzzy Sys ems”, Ma hwa e & So Com- pu ing, Vol. 8, No. 3, pp. 239-253, 2001. [8] A. Olle o, B. C. A ue, J. Fe uz, G. He edia, F. Cues a, F. López-Pichaco and C. Nogales. “Con ol and pe cep ion componen s o au onomous ehi- cles guidance. Applica ion o he Romeo Vehicles". Con ol Enginee ing P ac ice, Vol. 7, No. 10, pp 1291-1299, Oc obe 1999. [9] S.-G. Kong, B. Kosko, “Compa ison o Fuzzy and Neu al T uck Backe -Uppe Con ol Sys ems”, Chap e 9 in Neu al Ne wo ks and Fuzzy Sys ems, B. Kosko, P en ice Hall, 1992. [10] Y. Zhao, S. L. Bemen , “Kinema ics, Dynamics and Con ol o Wheeled Mobile Robo s”, P oc. IEEE In . Con . on Robo ics and Au oma ion, pp. 91-96, Nice, 1992. Fig. 13: E olu ion o : (a) wheel angle e e ence (solid line) and eal angle (dashed line), (b) speed e e ence (solid line) and eal speed (dashed line). 515253545 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 ime (s) cu a u e (m-1) ime (s) speed (m/s) 5 15253545 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 (a) (b)