Int. J Latest Trends Computing Vol-2 No 3 September, 2011

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1 Fuzzy Logi and Neural Nework Conrol Syses for Baking up a Truk and a Trailer P D C R Jayarahna 1, J V Wijayakulasooriya 2 and S R Kodiuwakku 3 1,3 Deparen of Saisis and Copuer Siene, Fauly of Siene, Universiy of Peradeniya, Sri Lanka 2 Deparen of Elerial and Eleroni Engineering, Fauly of Engineering, Universiy of Peradeniya, Sri Lanka 1 hailkajayarahna@gailo, 2 jan@eepdnalk, 3 salukak@pdnalk 370 Absra: Today, opuer onrol syses have ahieved a highes posiion of heir appliabiliy hrough large sale indusries o saller aiviies suh as onrolling a oveen of an obje Espeially any researhes are being arried ou o develop onrol syses o auoae he oveens of vehiles as i is perfored by a huan being This paper presens onrol syses o onrol he baking up oion of a ruk and railer vehile ino a pariular loaion suh as a loading dok Salien feaure of hese syses is ha i an be applied o any vehile syse whih has a railer aahed o i Two separae onrol syses are used o ahieve he desired goal In he firs approah, he syse uses fuzzy logi while he seond approah uses an arifiial neural nework for he sae purpose The proposed onrollers are esed for differen iniial posiions and orienaions of he ruk and he railer using a siulaion odel ipleened wih he MATLAB ool boxes Coparisons of he resuls obained are also presened Under he ondiions onsidered for he siulaion i is observed ha he fuzzy logi based onrol syse is apable of onrolling he vehile wihin a larger area han ha of he neural nework based onrol syse Keywords: Copuer Conrol Syse, Baking Up, Tuk and Trailer, Fuzzy Logi, Arifiial Neural Nework 1 Inroduion To drive a vehile auraely a person needs o have a good praie Espeially ore skills are needed o drive a vehile bakward ino a pariular posiion preisely However, if i is a Truk and a Trailer vehile hings beoe uh ore opliaed In baking up a vehile ino a pariular posiion suh as a loading dok, he usual way of driving an ordinary vehile suh as a ar in bakward direion an no be direly applied for baking up a ruk wih a railer aahed o i Basially here are hree probles assoiaed wih he bakward oion of a ruk and a railer vehile whih ause diffiulies for a driver Firs one is ha he driver does no have a dire onrol over he railer Only possibiliy is o onrol he ruk so ha he railer whih is aahed o i oves owards he dok wih appropriae orienaions Anoher proble in his proess is ha when he relaive angle of he ruk wih respe o he railer is large, he driver an see only one side of he vehile There is no way for he driver o ge a good idea abou wha is happening a he oher side of Inernaional Journal of Laes Trends in Copuing IJLTC, E-ISSN: Copyrigh ExelingTeh, Pub, UK (hp://exelingehouk/) he vehile even wih he side view irrors unil he ruk aligns wih he railer Furherore, when he angle beween he ruk and he railer is very large i leads o a jakknife siuaion [5], [7] whih ay ause he railer o deah fro ruk When professional ruk drivers bak up he vehile hey always ry o keep he relaive angle beween he ruk and he railer as less as possible To ahieve his, drivers always bak up he vehile by repeaedly swihing beween forward and bakward oions unil he vehile aligns properly and finally baking up o he desinaion I is ore diffiul when he railer needs o be baked up wih no forward oveens peried The speifi proble reaed in his researh is of his kind Tha is he goal of his proje is o develop a opuer onroller syse o bak up a ruk and a railer ino he loading dok wih only bakward oion The purpose of any onroller syse is o observe he values of he inpus and o produe he values of he oupus aording o he relaionships defined beween he To onrol he oveen of an obje his proess needs o be perfored repeaedly unil he goal is e When i is no possible o odel aheaially here are wo widely used approahes of developing opuer onroller syses: Fuzzy Logi and Neural Neworks In his researh, wo onrollers for baking up he ruk and railer are designed and ipleened using hese wo ehniques separaely Also a siulaion odel is reaed using MATLAB o deonsrae and opare he perforanes of he onroller syses 2 Relaed Work Several aeps have been ade o realize a onrol syse for baking up a ruk and a railer ino a pariular posiion Fuzzy Logi is he ehod ha has been used widely in os of he onrol syses [2]-[7] while Neural Nework approahes have also been invesigaed [1], [2] Soe onrol syses have been designed o onrol boh he forward and bakward oion of he vehile o redue he oplexiies in baking up ino a pariular loaion when he learane beween he railer and he posiion of he dok is no adequae [5] In soe oher aeps [2], [3], i has been assued ha here is an enough spae for he vehile o ove before i an be aligned o he final desinaion poin so ha only he bakward oion of he vehile is enough o reah he goal However, he onrol syse would no be able o guide he vehile ino he desired

2 371 posiion fro an iniial sae whih is loser o he final posiion unless i is only a dire oveen wihou any urning of he vehile In addiion, as disussed in [2] he oparisons of he wo ehods, fuzzy logi and arifiial neural neworks have also been ade However, alos all of he exising fuzzy logi onrol syses have designed onsidering only he disane in x direion fro he end poin of he vehile o he posiion of he dok assuing o have enough spae in Y direion The syses proposed in his paper onsidered he boh direions in odeling he onroller syse 3 Maerials and Mehodology In order o develop a onroller syse wo andidae sof opuing ehniques are used These ehniques are suarized here 31 Maerials Fuzzy Logi and Fuzzy Logi onrollers Fuzzy logi is a for of uli-valued logi derived fro fuzzy se heory o deal wih reasoning ha is approxiae raher han preise Therefore fuzzy logi is widely used when an approxiaed value is adequae raher han observing highly aurae value Sine i is no required o park he railer in he dok wih high auray fuzzy logi is used o develop he onroller A fuzzy inferene syse (FIS) essenially defines a nonlinear apping of he inpu daa veor ino a salar oupu, using fuzzy rules The apping proess involves inpu and oupu ebership funions, fuzzy logi operaors, fuzzy if hen rules, aggregaion of oupu ses, and defuzzifiaion Also a FIS wih uliple oupus an be onsidered as a olleion of independen uliinpu, single oupu syses There are four oponens in a Fuzzy Inferene Syse: he Fuzzifier, Inferene Engine, Knowledge Base and Defuzzifier These oponens are shown in figure 1 The knowledge base onains he linguisi rules ha have o be designed onsidering he knowledge of an exper of he field of onsideraion I is also possible o exra rules fro nueri daa One he rules have been esablished, he FIS an be viewed as a syse ha aps an inpu veor o an oupu veor The fuzzifier aps inpu nubers ino he orresponding fuzzy eberships This is required in order o aivae rules ha are in ers of linguisi variables The fuzzifier akes inpu values and deerines he degree o whih hey belong o eah of he fuzzy se via ebership funions The inferene engine defines apping fro inpu fuzzy ses ino oupu fuzzy ses I deerines he degree o whih he aneeden is saisfied for eah rule If he aneeden of a given rule has ore han one lause, fuzzy operaors are applied o obain one nuber ha represens he resul of he aneeden for ha rule I is possible ha one or ore rules ay fire a he sae ie Oupus for all rules are hen aggregaed During aggregaion, fuzzy ses ha represen he oupu of eah rule are obined ino a single fuzzy se Fuzzy rules are fired in parallel, whih is one of he iporan aspes of an FIS In an FIS, he order in whih rules are fired does no affe he oupu The defuzzifier aps oupu fuzzy ses ino a risp nuber Given a fuzzy se ha enopasses a range of oupu values, he defuzzifier reurns one nuber, hereby oving fro a se o a risp nuber Several ehods for defuzzifiaion are used in praie, inluding he enroid, axiu, ean of axia, heigh and odified heigh defuzzifier The os popular defuzzifiaion ehod is he enroid ehod whih alulaes and reurns he ener of graviy of he aggregaed fuzzy se Inpu Figure 1 Coponens of a fuzzy logi onroller Arifiial Neural Nework An arifiial neural nework is an aep o siulae he anner in whih he huan brain inerpres inforaion as deerined by urren knowledge of biology, physiology, and psyhology Neural neworks are faul oleran, exhibi he abiliy o learn and adap o new siuaions, and have he abiliy o generalize based on a liied se of daa Neural neworks an be used o solve highly nonlinear onrol probles I is a syse wih inpus and oupus and is oposed of any siple and siilar proessing eleens Eah of he proessing eleens has a nuber of inernal paraeers alled weighs Changing he weighs of an eleen will aler he behavior of he whole nework X Fuzzy onroller Fuzzifiaion 1 Knowledge Base Inferene Engine Σ Figure 2 Adaline Defuzzifiaion f(x) The proessing eleen used in an arifiial neural nework is known as he adapive linear neuron or Adaline Figure 2 illusraes a odel of he arifiial neural nework I has an inpu veor X={x i }, whih onains n nuber of oponens, a single oupu Y, and a weigh veor W={w i }, whih also onains n nuber of oponens Then he oupu Y equals o he su of inpus uliplied by he for of aivaion funion f(x) aording o he equaion (1) Y Oupu

3 372 s( X ) f n 1 i0 w i x i Y (1) The goal of a neural nework is o hoose he weighs of he nework o ahieve a desired inpu and oupu relaionship This proess is known as he raining of he nework When he weighs are kep onsan he oupu veor only depends on he urren inpu veor and is independen of he pas inpus During he raining proess he Adaline is presened wih an inpu X, whih auses is oupu o be y(x) The Adaline oupus d(x) insead of y(x) so ha he weighs are adjused o ause he oupu o be soehing ore lose o d(x) or o redue he differene beween he aual oupu y(x) and he desired oupu d(x) when X is presened as he inpu a he nex ie Many inpu, desired oupu pairs are used in he proess of raining of he weighs Afer he eah yle of raining a perforane easure is perfored o easure he aepabiliy of he urren oupu of he neural nework One of he widely used easures of he perforane of an Adaline is he ean squared error ( J ) If he observed error is greaer han soe hreshold value he gradien desen ehod illusraed by equaions (2) and (3) is applied o adjus he weighs n 1 ( ) J E d x f w x (2) i i i0 w Where, i new wi old 2x (3) d( x) y( x) f s( x) and f s is he firs derivaive of he funion f s This approah of Adaline an solve only linear ype probles Bu o solve nonlinear probles as i appears in os of he real world siuaion Adalines are onneed ogeher o fro ulilayer neural neworks as shown in figure 3 This is also known as he Layered feed forward neural nework Here he oupus of a one layer are onneed o he inpus of he nex layer so ha he oupu will be forwarded hrough he layers up o he oupu layer I has been proven ha a nework onsiss of only wo layers of Adalines an ipleen any nonlinear funion i 2 X Figure 3 Mulilayer neural nework Beause of he ineronneion of he single adalines o ake up he uli layered neural nework i is neessary o use a ore oplex raining algorih known as he Bak Propagaing learning algorih Here he weigh adjusens are no sraigh forward as in single layer Adeline beause he real oupu is assoiaed wih he weigh values of he iediae layer before he oupu layer whih is know as he hidden layer whih does no aquire he real inpu of he syse ausing he neessiy of sending he error bakward hough he previous layers of neurons o ake he weigh adjusens The bak propagaion algorih onverges o a se of weighs ha iniizes he eansquare error Siilar o he single Adaline nework, he equivalen error δ is defined for eah Adaline in he nework And if here are j nuber of inpus onneed o he oupu of he Adaline, he equaions (4) and (5) alulaes he equivalen error of he Adaline in he oupu layer and he equivalen error of he Adaline in any oher layer 1 1 w d ( x) y ( x) f s ( x) s x j j f(x) j (4) f ( ) w (5) Where, w j is he weigh of he onneion fro oupu of Adaline o he inpu of Adaline j 32 Mehodology As he firs sep he inpus for he onrol syses are deided onsidering he posiion and orienaion of he vehile as shown in he figure 4 Then he objeive of he onrol syses are o guide he rear end poin of he railer (x,y ) on o he posiion (x dok, y dok ) o park i perpendiular o he dok Tha is he value of he angle Φ had o be 90 degrees when he railer is parked However, he final posiion or he orienaion of he ruk is no aken in o onern as long as i is aahed o he railer and he railer is reahed he expeed final onfiguraions The enire proess is arried ou in hree differen sages as design of fuzzy logi onrol syse, design of neural nework onrol syse and he design of siulaion odel o deonsrae and opare he effeiveness of he designed onrol syses Σ Σ f(x) Σ Y

4 373 x dis Φ Φ - Φ y Φ Φ (x,y ) Sine i is opliaed o define he rule base for a fuzzy logi syse wih four inpu variables wo separae fuzzy logi syses are used o obain he seering angle for he urren sae of he vehile Firs one is a adani ype fuzzy syse whih akes x dis, y dis and Φ as he inpus and produes a value for he relaive angle beween he ruk and he railer, (Φ - Φ ) req, whih is required for he railer o be oved o he dok fro he urren posiion of he railer Then he oupu obained fro he firs fuzzy logi syse and he urren value of he relaive angle beween he ruk and he railer (Φ - Φ ) urr are used as inpu o he seond sugeno ype fuzzy syse as shown in he figure 6 whih alulaes he neessary seering angle () as he oupu y dis (x dok,y dok ) Figure 4 Inpu and oupu variables of he fuzzy logi onrol syses x x dis y dis Φ (Φ - Φ ) urr Fuzzy Logi 1 (Φ - Φ ) req Fuzzy Logi Fuzzy Logi Conrol Syse Aording o he figure 4 he disane o he rear end poin of he railer along he posiive x direion (x dis ) and along he posiive y direion (y dis ) fro he posiion of he dok (x dok,y dok ), he orienaion of he railer wih respe o he posiive x direion (Φ ) and he relaive angle beween ruk and railer (Φ - Φ ) are he inpus o he onrol syse o produe he seering angle () of he ruk as he oupu A single fuzzy logi onroller syse whih akes four inpu variables and produes one oupu is designed as shown in he figure 5 The working range of he onroller syse is aken as a square area of 100 eers a side Then he ranges of eah inpu and he oupu are aken as shown in he able 1, in he sae easureen sales as hey appear in a real ruk and railer vehile All easureens of lenghs are aken in eers and he angles in degrees x dis y dis Φ (Φ - Φ ) Fuzzy Logi Figure 5 Design of he single fuzzy logi onroller The inpu and oupu of he syse are given in Table 1 Table 1 Inpus and oupus of fuzzy logi syse Variable Type Range Uni x dis Inpu -50 o +50 eer y dis Inpu 0 o +100 eer Φ Inpu -180 o +180 degree (Φ - Φ ) Inpu -90 o +90 degree Oupu -60 o +60 degree Figure 6 Design wih he wo fuzzy logi syses The designed fuzzy logi syse is ipleened using he MATLAB Fuzzy Logi Toolbox Mebership funions of boh riangular shaped and rapezoidal shaped are used o define eah of he inpus and oupu of he wo fuzzy syses The rule base of he FuzzyLogi1 is ipleened wih 189 rules whereas FuzzyLogi2 syse onained 49 rules 322 Arifiial Neural Nework Conrol Syse A feed forward bak propagaion neural nework is ipleened and rained using he MATLAB Neural Nework Tool Box onsidering he posiion of he rear iddle poin of he railer (x,y ), he orienaion of he railer wih respe o he posiive x direion (Φ ) and he orienaion of he ruk wih respe o he railer (Φ ) are aken as he inpus o produe he neessary seering angle () as he oupu aording o figure 7 The ranges of he inpus and he oupu are again onsidered as shown in he able 2 Then he arifiial neural nework is designed inluding a firs layer onsiss of 25 hidden neurons wih a TANSIG ransfer funion where as he oupu layer having only one neuron wih a PURELIN ransfer funion The raining daa se is olleed by anually driving he vehile ino he dok fro differen iniial posiions and differen iniial angles using a siulaion odel developed in MATLAB Here several aeps had o be ade o adjus he nuber of neurons in he hidden layer o have a beer raining perforane Also a raining daa are olleed saring fro he iniial onfiguraions whih are only slighly differen fro he final desired onfiguraions This is done o obain a beer raining perforane so ha a leas he os useful oveens ould be onrolled by he neural

5 374 nework onrol syse o be opared wih he fuzzy logi onrol syse Furher ore he area where he syse an onrol he vehile is redued o a square area of 20 eer a side o obain beer raining perforane The inpu and oupu o he syse are given in Table 2 Table 2 Inpus and oupus of neural nework syse variable ype Range unis x Inpu -10 o +10 eer y Inpu 0 o +20 eer Φ Inpu 0 o 360 degree Φ Inpu 0 o 360 degree Oupu -60 o +60 degree Φ vsin ( ( k 1) ( L (8) Where, Φ - Orienaion wih respe o he horizonal line L - Lengh of he vehile - Seering angle v - Veloiy of he vehile δ - Tie sep (x,y) - he poin of he vehile whih should ove o a pariular posiion To deonsrae he effeiveness of he wo onroller syses for onrolling he baking up oion of he ruk and railer vehile a siulaion odel is ipleened using he vehile kineai equaions As illusraed in he figure 9, he ruk and he railer are onsidered as wo separae vehiles so ha he oion of he ruk is onrolled by he seering angle of he ruk and he relaive angle beween he ruk and he railer working as he seering angle for he railer The veloiy of he vehile is onsidered as a onsan Φ L Φ (x,y ) Φ (x,y ) (Φ - Φ ) (x dok,y dok ) Figure 7 Inpu and oupu variables of he neural nework onrol syses x Φ (x,y ) L 323 Siulaion Model Vehile kineais addresses he aheaial odel of he oion of a vehile There are aheaial equaions o alulae he nex posiion of he vehile onsidering he urren posiion of he vehile, veloiy, seering angle and he diensions of he vehile For a general vehile as shown in he figure 8, L (x,y) Φ v Figure 8 Vehile kineais here are hree dynai equaions (6) (8) o desribe he oveen of he vehile [3], x( k 1) x( vos ( (6) y( k 1) y( vsin ( (7) X Figure 9 Use of vehile kineais for ruk and railer The above hree general vehile kineais equaions are applied o find he oordinaes of he nex posiion of he rear end poin of he ruk (x,y ) using (9) (11) x ( k 1) x ( vos ( (9) y ( k 1) y ( vsin ( (10) vsin ( ( k 1) ( (11) L Also he orienaion of he nex sae of he oion of he railer is alulaed using he vehile kineais equaion (12) and he nex posiion of he rear end poin of he railer is alulaed by applying rigonoeri equaions using he poin (x,y ) and he lengh of he railer using (13) and (14) (x,y ) Φ

6 375 vsin( )( ( k 1) ( L x ( k 1) x ( L os ( (12) (13) y ( k 1) y ( L sin ( (14) 4 Resuls and Disussion Afer he ipleenaion, boh onroller syses were esed for various iniial saes A graphial user inerfae ipleened in MATLAB was used o deonsrae he oveen of he vehile, pah of he oveen and he final posiion and orienaion of he vehile Figure 10 shows he pah of he oion of he vehile using fuzzy logi onroller where he saring oordinaes of he rear end poin of he railer was (309, 216) onsidering he oordinaes of he dok as (0,0) and he values of Φ and Φ were 66 and 80 respeively Here he final posiion was observed as -034, 012 and he orienaion as 9079 degrees These values represens ha he final posiion had a deviaion of 34 enieers along he negaive x direion and he variaion of he final orienaion fro he expeed angle is 079 degrees In oparison o he diensions of he ruk and railer vehile his deviaion of he posiion and he expeed final orienaion an be onsidered as a suessful baking up siuaion onrolled by he designed fuzzy logi onrol syse Table 3 and able 4 represen he resuls for soe of he suessful perforanes of he fuzzy logi onrol syse and he arifiial neural nework onrol syse respeively Iniial posiion and orienaion of he vehile Table 4 Suessful resuls of Neural Nework onroller Iniial sae Final sae x y Φ Φ x y Φ In addiion, he graphs were ploed o visualize he variaions of he sraigh line disane fro he dok o he rear end poin of he railer, disane fro he dok o he rear end poin along he x direion and he variaion of he orienaion of he railer over he ie Aording o he figure 11 he graph on op shows he variaion of he sraigh line disane fro he dok o he rear end poin of he railer wihin he ie period ha he vehile had been oving bakward while he graphs on boo righ and boo lef shows he variaion of he disane along x direion and he variaion of he orienaion of he ruk wih in he sae ie period respeively Pah of he oion Posiion of he dok Final posiion and orienaion of he vehile Figure 10 Siulaion of he ruk and railer Table 3 Suessful resuls of fuzzy logi onroller Iniial sae Final sae x y Φ Φ x y Φ Figure 11 Variaions of onrol variables Coparison of he wo onrol syses Sine he neural nework onroller is designed in he range of a squired area of 20 eers of eah side he oparisons were ade only wihin his region The graphs of he variaions of he sraigh line disane fro urren posiion o he dok and he variaions of disane along X direion and he variaions of he orienaion of he railer wih respe o ie were used

7 376 o ake he oparisons Figure 12 shows he oparison of he oveen onrolled by he (a) fuzzy logi onrol syse and (b) neural nework onrol syse Boh syses were esed fro he sae iniial saes wih he values x =227, y =1932, Φ =7862, Φ =9818 (a) Fuzzy logi (b) Arifiial neural nework Figure 12 Coparison of he wo onroller syses Fro figure 12 i an be observed ha he neural nework onroller allows a sharp urn of he railer han ha of he fuzzy logi onroller Also he figure 13 illusraes he graphs whih represen he variaions of he sraigh line disane fro he dok o he rear end poin of he railer, variaion of he disane alone posiive X direion and he variaion of he orienaion of he railer were opared The doed line of he graphs represens he variaions of he variables when he neural nework onroller is used and he sraigh lines represen he variaions of he sae variables when fuzzy logi onroller is used Figure 13 Coparison of he variaion of onrol variables he bakward oion of he ruk and railer vehile ino he loading dok, he fuzzy syse ould be developed in shor period of ie for a large range of saring posiions han ha of he neural nework onroller The diffiuly wih he neural nework onroller is ha here is finding he appropriae nuber of neurons in he hidden layer Only possibiliy is o assign differen onfiguraions for he nework and observe he perforane of he raining for he sae daa se This is a uh ie onsuing proess and os of he ie i reahes he loal inia poins sopping furher raining of he nework However in fuzzy onroller all he possible onfiguraions of he ruk and he railer has o be defined in he rule base where as he neural nework onroller has he abiliy of generalizaion so ha i an produe orre oupu for soe onfiguraions whih were no in he raining daa se Furherore, in he siulaions perfored under he onsan veloiy he oion of he vehile guided by he neural nework onrol syse reahes he goal aking less ie opared o he oion onrolled by he fuzzy logi onrol syse Bu here is a higher variaion of he orienaion of he railer when he neural nework is used so ha if he seering angle is ade o be hanged ehanially i us be apable of handling rapid hanges of he angle 5 Conlusion The goal of his researh was o design and develop a opuer onroller syse o auoae he baking up oion of a ruk and railer vehile ino he loading dok Two onroller syses were developed using fuzzy logi and a neural nework respeively The perforanes of he onrols were opared using graphial represenaions of he onrol variables over he ie Wih he fuzzy logi onroller syse he ruk and railer an be onrolled suessfully o ove ino he loading dok fro os of he seleed saring onfiguraions of he vehile wihin a squire area of 100 eers of eah side And i is observed ha when he disane along he Y direion is large a he saring poin of he vehile he final posiion and orienaion of he vehile is uh loser o he expeed values han ha of saring fro a posiion wih sall Y disane Beause of he lengh of he railer i needs soe spae in Y direion o align wih he desired final angle and he posiion when using boh of hese onrol syses The neural nework onroller was rained o onrol he ruk and railer wihin a range of a squire area of 20 eers of eah side wih a daa se of sall variaions fro he desired final onfiguraions of he ruk and he railer Sine i did no perfor well in he raining phase he oupu ha an be ahieved fro neural nework onroller is less han ha of he fuzzy logi onroller syse In oparison of he fuzzy logi onroller syse and he neural nework onroller syse of onrolling

8 377 Referenes [1] Derrik H Nguyen, Bernard Widrow, Neural Neworks for Self-Leaning Conrol Syses, IEEE Conrol syses agazine, April 1990 [2] Seong-Gon Kong, Bar Kosko, Coparison of Fuzzy and Neural Truk Baker-Upper Syse, IJCNN Inernaional Join Conferene on Neural Neworks (Ca No90CH2879-5), Vol 3, June 1990 [3] Seong-Gon Kong, Bar Kosko, Adapive Fuzzy Syses for Baking up a Truk-and-Trailer, IEEE Transaions on neural neworks, Vol 3,No 2, Marh 1992 [4] Jaes A Freean, Fuzzy Syses for Conrol Appliaions: The Truk Baker-Upper, The Maheaial Journal Miller Freean Publiaions, Vol 4, Issue 1, 1994 [5] Graha J Eaherley, Eil M Periu, A Fuzzy Conroller For Vehile Rendezvous and Doking, IEEE Transaions on insruenaion and easureen, Vol 44, No 3, June 1995 [6] Andri Riid, Ennu Rusern, Fuzzy Logi in Conrol: Truk Baker-Upper Proble Revisied, sienifi lieraure digial library and searh engine, 2001 hp://wwwduee/andri/eosed/bupdf [7] Doen Novak, Dejan Dovžan, Sion Oblak, eniled "Auoaed Parking Syse For A Truk And Trailer", Inernaional Culural and Aadei Meeing of Engineering Sudens (ICAMES), 2007 hp://sfeuniljsi/iaes/07/auoaed_parking_ Syse_For_A_Truk_And_Trailerpdf