Formation Control For Wheeled Mobile Robots

Transcription

1 INTENATIONAL JOUNAL OF SCIENTIFIC & TECHNOLOGY ESEACH VOLUE 3, ISSUE 5, AY 2014 ISSN Formaton Contro For Wheeed obe obots tesh eshram, Dr. Sun Surve Abstract: ths paper descrbes work on ormaton or a group o wheeed mobe robots. Aso n ths paper we have tred to gve the deta normaton about the knematcs o wheeed mobe robot avaabe n varous teratures n a smper way. We are usng car-ke mobe robot where the eader mobe robot s controed to reach the desred poston, whereas the oower oows the eader robot wth some specc dstance and ange. Here we made an assumpton that the moton occurs n a 2D space wthout any obstace n ts path. The basc o knematc bcyce mode or a wheeed mobe robot s used n ths work. For controng the moton o robots we are usng uzzy ogc. As we know, Fuzzy ogc theory s subdvded nto two types, type-1 and type-2. For the moton contro o a car-ke mobe robot n ormaton we are usng the concept o Interva type2 uzzy ogc (IT2-FL). A new rue base s desgned or IT2-FL system and the smuaton s done n atab envronment aso the na resuts are gven to show the ecency and eectveness o the proposed uzzy controer. Index Terms: car-ke, mobe robot, IT2-FL, knematcs, eader-oower. 1 INTODUCTION In the ast 3 decades, the dea o robots dong human works has come to reaty whch was earer consdered as cannot be done and just an magnaton. obotcs devces and machneres are now becomng the part o human e. Now a days robots are very commony used n servce ndustry, armed orces, manuacture ndustry, etc. The one o the most chaengng and demandng ed o robotcs s wheeed mobe robots. One o the reasons or ths s mobe robot needs mobty that heps t to move unrestraned a over ts envronment. As gven n [1], a mobe robot can move ts surroundng n many derent ways. Thereore or a mobe robot, how t moves n ts envronment depends upon the type o approach used or ts moton. A substanta porton o wheeed mobe robotcs exporaton/research ncudes deveopng robot mode that mmc a car-ke moton wthout the hep o any human beng. Aso t has been seen as n case o we-known work n the ed o mobe robotcs the system strategy need not requred to be very compex even wth smper one we can acheve our desred resut. In case o mobe robotcs, sometmes t becomes necessary that to perorm a specc job we need group o mobe robot n ormaton. The requrement or ormaton o a group o mobe robot perormng a specc task has eads to the growth o a new research ed. The ormaton contro probem or mobe robots can be dened as ndng a system whch makes sure that the group o mobe robots can hod on a gven ormaton or precse set o ormatons. The objectve o ths work s to deveop eader-oower structure, such that mutpe mobe robots can move n a gven condton n ormaton. We are consderng an obstace ree envronment or our work. At rst we need to know how our o mobe robot move n ts surroundngs. For understandng ths process we need to understandng knematc equaton o moton. Knematcs s sad to be a geometrca or mathematca anayss o how our system behaves n ts envronment wthout takng nto consderng the orces that cause ths. tesh eshram s currenty pursung masters degree program n Eectroncs engneerng, Department o eectroncs, Fr. C..C.E., umba, aharashtra, Inda. E-ma: rtesh.b.meshram@gma.com Dr. Sun Surve s a proessor n Department o computer scence, Fr. C..C.E., umba, aharashtra, Inda. E-ma: surve@ragne.edu.n For understandng the Knematcs o car ke mobe robot rst we must know the type o whees we are usng n our case and aso the constraned apped due to t. In common case dsk type whees are used or a carke wheeed mobe robot. In case o smuaton, a car ke mode can be desgned usng smpe geometrc and trgonometrc concept or more understandng pease reer [2]. any contro approaches have been put orward to sovng the moton contro probem such game theory, mode predctve contro and so on. We have use Fuzzy ogc (type-2) n our case. Seong-Gon Kong n [4] presented a work n type1 uzzy ogc controer havng two nput and one output state varabe. x coordnate and vehce orentaton where the nput to the controer whereas the output s the vehce steerng ange. The rue base used s a very common rue base used or mobe robot case, neary smar knd o rue base s gven n [5]-[7].We have desgned a new rue base havng 25 rues or our case. any tmes t s seen that the data that s used to deveop the rues or a uzzy system are uncertan. Due to the uncertanty, ke an uncertanty n coecton o normaton or a same case by derent peope, t becomes tough to decde what the exact vaue o membershp uncton s. The overa structure o uzzy sets n a uzzy system s to aow the handng and modeng o much o uncertanty usng type-1 uzzy sets. But Type-1 uzzy ogc systems are not abe to competey hande the ngustc or numerca uncertantes [9]. In such a case we need another knd o uzzy set or a uzzy system caed as type 2 uzzy set. A type-2 uzzy ogc system or controer uses notaton that are very much smar to that are used n a type-1 uzzy ogc controer such as membershp unctons, uzzy rues, t-norms operatons, uzzcaton, nerence, deuzzcaton. The ony derence s that addton o type reducton process beore deuzzcaton. The basc deas o IT2-FL n atab s expaned by Dongru Wu n [8] whereas Han hagras [9] expans the theoretca concept o type2 FLS n smpe anguage. The paper s arranged as oow Secton II gves knematc normaton o mobe robot aong wth knematc constrants, aso teng why we are havng these constrant and how our mobe robot move n ts envronment, secton III s ocused on our eader-oower ormaton probem. Secton IV gves the theoretca concept o Type2 uzzy ogc aong wth the proposed controer. Secton V shows the smuaton resuts whereas Secton VI tes the concuson. IJST

2 INTENATIONAL JOUNAL OF SCIENTIFIC & TECHNOLOGY ESEACH VOLUE 3, ISSUE 5, AY 2014 ISSN WHEELED OBILE OBOT The wheeed mobe robot can be o derent type, but as sad earer we are usng car-ke mode. Consder the car-ke robot shown n n gure. goba reerence rame, or more normaton on rotaton matrx pease reer [10]. Fg.1: The goba reerence rame and the robot oca reerence rame. The rst thng we need to know s Frames. Every object or as n our case mobe robot has ts own rame, generay caed as oca body rame. Not ony ths the envronment n whch the mobe robot s movng or dong hs work s aso consdered as rame, caed as goba or word rame, as you can see n gure 1, the word rame s represented by axes ( X Y ) G, G whereas robot oca body rame s represented by ( X, Y ) axes. For more normaton on rames pease reer [11]. Let pont p be consdered as the orgn o the body o mobe robot. The headng drecton or ongtudna drecton o the robot oca body rame s represented by axs X whereas the atera drecton o mobe robot oca body rame s represented by the axsy. The conguraton space o a mobe robot at any gven tme can be dened by a set o our state varabes. Bascay a conguraton space s a set o a varabe whch states what a system s dong at a gven tme. In case o conguraton scape o car-ke mobe robot,(x,y) represent the poston o the orgn pont p o the mobe robot oca body rame wth respect to word reerence rame, represent the orentaton ange o mobe robot whereas the steerng ange s represented by φ, t s the ange between mobe robot s ront whee and the mobe robot s ongtudna axs X. The conguraton space o mobe robots s gven as; x y q (1) 2.1 Knematc Bcyce ode As gven n [1], durng the course o the study we are consderng the mobe robot as a st body to whch whees are attached, operatng on a horzonta pane. Usng rotaton matrx we can map the poston o mobe robot t term o Fg. 2: Theoretca scheme o bcyce/car Usng bcyce mode we can streamne the Ackerman steered mode or a wheeed mobe robot. We can have bcyce mode by combnng the et and rght whees nto a par o snge whees at the center o the ront and rear axes as shown n dark back coor n Fgure 2. The equaton o moton or the knematc bcyce mode o a car can be understood rom [3]. Beore gong to knematc equaton o moton one mportant notaton we must know that s IC (nstantaneous center o rotaton). We know that the reguar whee that s dsk type whees have sdng restrctons. Thereore they have zero atera moton. As shown n gure 2, to show ths geometrcay we have to draw a ne caed as zero moton ne perpendcuar to the ongtudna axs o whees shown n dotted nes. The ntersecton pont o the zero moton ne o a whees gves a snge pont caed IC. Due to IC when a robot takes turn, the whee must be rong aong a crce such that the center ths crce s our pont IC and ts radus s represented by. The radus IC w be nnte when mobe robot s movng n straght ne. Thereore a mobe robot ke an Ackerman vehce as shown Fgure 2 may have a number o whees, but t s essenta t have a snge IC as n case o bcyce. Ths IC geometrc constructon ustrates how robot mobty depends on the number o constrants on the robot s moton but not the number o whees [1], [18]. 2.2 Knematc Equaton o oton As we sad earer we are consderng car as a rgd body movng on the pane. The conguraton or posture o the vehce can be descrbed wth three coordnates n the word.derentatng wth respect to tme we rame q ( x, y, ) can wrte the conguraton o mobe robot n terms o veocty q ( x, y, ). L s the dstance between the ront and rear whees. I the steerng ange φ s set at some xed vaue, the car w traves n a crcuar moton and the radus o the crcuar moton s. et the speed o robot be Vx n drecton and Vy n Y drecton. The speed o the vehce ny drecton s zero because the whees cannot sp sdeways. Thereore we have Vx=V and Vy=0. Thus we can represent the moton o vehce usng two dmensona rotaton matrx as [10][11] X IJST

3 INTENATIONAL JOUNAL OF SCIENTIFIC & TECHNOLOGY ESEACH VOLUE 3, ISSUE 5, AY 2014 ISSN x vsn y vcos x and y are vector components o near veocty v and s the orentaton ange o mobe robot oca body rame w.r.t word rame. The next task s to derve the equaton or anguar veocty. The anguar veocty s gven as v From trgonometry L tan (3), reer gure 2. Thus the anguar veocty o mobe robot becomes v tan L (4) 2.3 Knematc Constrants These constrants are aso reerred as nonhoonomc constrants where the system has restrctons n ts veocty, but the mportant pont to be noted that these restrctons do not cause any restrctons n ts postonng. From a knematc pont o vew, the man characterstc o wheeed robots s the nonhoonomc rong wthout sppng constrant o the whees on the oor, whch orces the vehce to move tangentay to ts man axs. Ths reduces the set o accessbe veoctes at each tme makes the path pannng probem partcuary dcut. Vewed another way, the system s oca movement s restrcted, but not ts goba movement. athematcay, ths means that the veocty constrants cannot be ntegrated to gve poston constrants. The nonhoonomc constrants can be derved rom equaton 3 as; xsn y cos 0 (5) The constrant o rong wthout sppng means that and must be consstent wth the drecton o rong, they are not ndependent [20]. Ths means that the robot cannot change poston and drecton ndependenty. 3 LEADE-FOLLOWE FOATION Leader oower strategy can be o varous types ke there can many eaders and many oowers or one eader and many oowers and so on. In our case we have use one eader and much oower strategy. For smpcaton we have assumed that the oower aready have normaton where the robot s. The equaton or our ormaton ramework s as oows Fg. 3: Leader-Foower Formaton strategy x x d y y d Where ( x, y ) and ( x, y ) are poston o oower and eader mobe robot respectvey whereas and are the orentaton o oower and eader robots respectvey. D s the desred dstance between eader and oowers. 4 TYPE 2 FUZZY LOGIC Type1 uzzy ogc has been used rom around It was ntroduce by Zadeh. Ten years ater he ntroduces type 2 uzzy ogc whch s consdered as an extenson o type 1 uzzy ogc. Type1 uzzy ogc rom the tme o ts ntroducton has been used n number o appcaton. But there s a probem n type 1 uzzy ogc, the membershp grade or the degree o truth or each nput s a crsp vaue rangng rom 0 to 1 reer [13][19]. In many case ths works qute we and produces an output or a system such that t can do ts job eectvey. Fuzzy ogc systems are wdey used due to ther abty to mode and hande uncertanty. But some tme t s not possbe usng type 1 uzzy ogc system. Thus n ths case type two uzzy ogc s used. Type-2 uzzy sets ncreased scope or modeng uncertanty better. Uncertanty can be o derent type e.g. In uzzy ogc we deas wth words, but words mean derent to derent peope [12][14]-[16][19].For understandng the concept o Interva type2 uzzy ogc pease reer[13]-[15] A type 2 uzzy set s descrbed by ootprnt o uncertanty and secondary membershp uncton. A type 2 uzzy set s sad to be bonded by two type1 uzzy set. A type-2 uzzy set s bounded rom beow by a Lower embershp Functon (LF) rom above by an Upper embershp Functon (UF). The area between LF and UF s caed ootprnt o uncertanty(fou). IJST

4 INTENATIONAL JOUNAL OF SCIENTIFIC & TECHNOLOGY ESEACH VOLUE 3, ISSUE 5, AY 2014 ISSN Fg. 4: 3D vew o nterva type-2 uzzy set In g.4, x s nput, u s prmary membershp uncton, ( x, u ) s secondary membershp uncton and the area A shaded n red coor s represented by FOU. It s the 3 rd dmenson o secondary membershp uncton and the FOU area whch maps the uncertanty o prmary membershp n secondary membershp uncton and heps us to hande and mode uncertanty n etter way than type 1 uzzy set. Fg: 2D vew o secondary membershp or nterva type2 uzzy ogc set. Bascay type2 uzzy ogc s subdvded nto two type a) Genera type2 uzzy ogc, b) Interva type2 uzzy ogc. I the vaue a secondary membershp s 1 or a ponts, we speak o an nterva type-2 set and we are uncertan about a specc quantty, we can use type-2 sets whose degrees o membershp whch are themseves uzzy. Ths s caed Genera type2 uzzy set [9]. Due to the uzzy-uzzy set nature o type 2 uzzy set, means the prmary membershp uncton o type1 uzzy set s now agan represented another membershp uncton (secondary membershp uncton) thereore the genera type-2 FLC s computatonay very exhaustve and expensve whereas the cacuaton becomes straghtorward n case o IT2-FL whch w heps us to use a uzzy controer or rea tme contro probems. Aso a detas o how to use IT2 FSs n a uzzy ogc system have been worked out whereas n case o Genera type2 uzzy ogc the rea tme mpementaton s st an area o research Due to ths reason we see that most o the appcatons usng type-2 uzzy ogc are based on Interva Type-2 FLCs that uses nterva type-2 uzzy sets. The man dcuty n understandng o Type2 uzzy set s ts 3D nature. But whe usng Interva type 2 uzzy set the 3 rd Fg: 2D vew o nterva type uzzy ogc wth FOU area n red shaded area dmenson does not provde any new or addtona normaton. It s the LF, UF and FOU area that competey descrbe the IT2 FLS. Thus we can say that t s the FOU area whch heps us to determne the uncertanty n 2D nstead o 3D. Aso whe computng we can say that nstead o computng ony one type1 uzzy set now we are computng two type1 uzzy set one or LF and other or UF. 4.1 Type-2 uzzy ogc controer The IT2-FLC n our case has 3 state varabes. Two or nput and one or output. The nput state varabes are dr. whch represents the x postonng o mobe robot and whch represents the orentaton ange o mobe robot. The output state o IT2-FLC s whch represent the steerng command to the mobe robot. The dr. ranges rom 0 to 300, ranges rom -150 to 340. Derent vehces have derent maxmum turnng ange rangng rom -90 to 90 degree. So n our case we consdered the steerng ange 38. So ranges rom -38 to 38. The ngustc terms are very common, used n rue base are n uzzy ogc. ue Base dr. Tabe 1: Fuzzy rues base tabe PB PS ZE NS NB PH NB NB N N PS PL N N NS PS P ZE NS NS ZE PS PS NL NS ZE PS P P NH PB PB PB P P IJST

5 INTENATIONAL JOUNAL OF SCIENTIFIC & TECHNOLOGY ESEACH VOLUE 3, ISSUE 5, AY 2014 ISSN Where NH, negatve hgh; NL, negatve ow ZE, zero PL, postve ow PH, postve hgh NB, negatve bg N, negatve medum NS, negatve sma ZE, zero PS, postve sma P, postve medum PB, postve bg 4.2 Type-reducer and deuzzcaton The output processor ncudes a type-reducer and deuzzer. The type-reducton method s an extenson o type-1 deuzzcaton obtaned by appyng the Extenson Prncpe to a specc deuzzcaton method. The type-reduced set usng the centrod can be expressed as [17]; 4, ),( , ),( , ),( ,2.6850),( , ) ( , ), ( , )} The nta, na poston o group o mobe robots n eader oower ormaton aong wth ther tra s shown beow. Y [ y, y ] ; T r y 1 1 y ( y ) B ( y ) B y r 1 1 y ( y ) B ( y ) B Fg.6: Inta poston o robots The output o deuzzcaton step o FLS s obtaned by summng the vaue o y and y obtaned rom type reducton step and dvde t wth two, as shown on equaton, ths w gve us the steerng vaue. y r y yr 2 5 SIULATION The eectveness o the uzzy controer s demonstrated here. Ths secton ays out the smuaton envronment created n atlab, and ts resuts. The smuaton was desgned to match the car as cosey as possbe. The maxmum number o Wheeed obe obot that can be handed by our controer s 7. At rst we w enter the number o vehce we want or our smuaton. Once the numbers o vehces are entered. We w enter the coordnates o rst vehce. The output o smuaton s shown beow; Fg.7: Fna poston o robots enter the No o vehces : - 7 enter poston 1 or 2 : - 1 enter x ocaton :-10 to 150: enter y ocaton : - 10 to 60 : - 60 The steerng commands to the eader mobe robot are as oow { , , , , , , , , , , , , } The new postons o mdpont p o robot oca body rame are {( , ),( , ),( , ),( , ),( , )( IJST Fg.8: Tra o obots 6 CONCLUSION The Fuzzy controer shows the moton contro o car-ke mobe robot very cose to reastc moton o car n rea word. obe robot moton contro s a good condton or testng a type-2 uzzy ogc controer because o the uncertantes nvoved whe nteractng wth the mobe robot movng n ts envronment n rea-tme. In ths paper, we have shown the 245

6 INTENATIONAL JOUNAL OF SCIENTIFIC & TECHNOLOGY ESEACH VOLUE 3, ISSUE 5, AY 2014 ISSN ormaton strategy o a group o car-ke mobe robot n eaderoower structure. We have aso gven the detaed normaton about the knematcs o wheeed mobe robot. The ecency o IT2-FL controer wth rue base s aso shown or controng the group o mobe robots movng whe they are n ormaton. Ths s conrmed by smuaton resuts. The controer s based on smpe and then rues The uture research work w ocus on extendng the smuaton resuts to more genera appcatons such as empoyng swtchng o mobe robots postons, obstace avodance, rea tme contnuous path trackng and mantanng ormaton between eader and oower robots takng nto consderaton o robot dynamcs, mode uncertantes. EFEENCES [1] oand Segwart and Iah. Nourbakhsh, Introducton to Autonomous obe obots, [2] Aejandra Barrera, obe obots Navgaton, Pubshed by In-Teh arch [3] Jarrod. Snder, Automatc Steerng ethods or Autonomous Automobe Path Trackng, obotcs Insttute, Carnege eon Unversty, Pttsburgh, Pennsyvana, February [4] Seong-Gon Kong and Bart Kosko, Adaptve Fuzzy Systems or Backng up a Truck-and-Traer, IEEE Tansactons On Neura Networks, Vo. 3, No. 2, arch [5] James A. Freeman, Fuzzy Systems or Contro Appcatons: The Truck Backer-Upper, The athematca Journa, [6] Guanrong Chen, Trung Tat Pham Introducton to Fuzzy Sets, Fuzzy Logc, and Fuzzy Contro Systems, CC Press, Bern, [13] Jerry. ende, obert I. John and Feong Lu, Interva type-2 uzzy ogc systems made smpe, IEEE Trans. on Fuzzy Systems, vo. 14, No. 6, pp , [14] Jerry. ende and obert I. John, Type-2 uzzy sets made smpe, IEEE Trans. on Fuzzy Systems, vo.10, No. 2, pp , [15] Qan Lang and Jerry. ende, Interva Type-2 Fuzzy Logc Systems: Theory and Desgn, IEEE Transactons On Fuzzy Systems, VOL. 8, NO. 5., October 2000 [16] Nesh N. Karnk, Jerry. ende Type-2 Fuzzy Logc Systems IEEE Transactons On Fuzzy Systems, Vo. 7, NO. 6, DECEBE [17] Nesrne Bakout, obert John, Ade. AmInterva Type-2 Fuzzy Logc Contro o obe obots,journa o Integent Learnng Systems and Appcatons, , 4,2012. [18] B B V L Deepak, Daya Parh, Knematc Anayss O Wheeed obe oobt, J. Automaton & Systems Engneerng 5-2 (2011). [19] Jerry ende, typ2 2 uzzy set and systems: An Overvew IEEE Computatona Integence agazne,vo.2,no.1,pp.20-29,february 2007 [20] Aonzo Key, A Vector Agebra Formuaton o Knematcs o Wheeed obe obots, Carnege eon Unversty, 2010 [7] Amar Khoukh, Luc Baron, arek Baaznsk, Fuzzy Parkng anoeuvres O Wheeed obe obots, Natura Scence And Engneerng esearch Counc o Canada, ay 5, [8] Dongru Wu A Bre Tutora on Interva Type-2 Fuzzy Sets and Systems, petepubs [9] Han Hagras and Chrstan Wagner, Introducton to Interva Type-2 Fuzzy Logc Controers - Towards Better Uncertanty Handng n ea Word Appcatons, IEEE SC enewsetter,2009. [10] Greenwood D.T., Prncpes o Dynamcs 2 nd Edton, Prentce_Ha,1987. [11] Steven. LaVae, Pannng Agorthm Pubshed by Cambrdge Unversty Press,2006. [12] Oscar Casto and Patrca en, Type-2 Fuzzy Logc: Theory and Appcatons, Sprnger-Verag, IJST