A Probabilistic Approach for Mobile Robot Localization under RFID Tag Infrastructures

Transcription

1 A Probablsc Approach for Moble Robo Localzaon under RFID Tag Infrasrucures Dae-Sung Seo*, Daeheu Won*, Gwang-Woong Yang*, Moo-Sung Cho*, Sang-Ju Kwon** and Joon Woo Park*** * Dvson for Appled Robo Technology, KITECH, Ansan, Korea (Tel: ; E-mal:{sds, daehee, ygkgwg, moosung}@kech.re.kr) ** School of Aerospace & Mechancal Engneerng, HAU, Seoul, Korea (Tel: ; E-mal: sjkwon@hau.ac.kr) *** Fne Dgal Inc., Seoul, Korea (Tel: : jwpark@fnedgal.com) Absrac SLAM(Smulaneous localzaon and mappng) and AI(Arfcal nellgence) have been acve research areas n robocs for wo decades. In parcular, localzaon s one of he mos mporan ssues n moble robo research. Unl now epensve sensors lke a laser sensor have been used for he moble robo s localzaon. Currenly, as he RFID reader devces lke anennas and RFID ags become ncreasngly smaller and cheaper, he prolferaon of RFID echnology s advancng rapdly. So, n hs paper, he smar floor usng passve RFID ags s proposed and, passve RFID ags are manly used o denfy he moble robo s locaon on he smar floor. We dscuss a number of challenges relaed o hs approach, such as RFID ag dsrbuon (densy and srucure), ypng and cluserng. In he smar floor usng RFID ags, because he reader jus can senses wheher a RFID ag s n s sensng area, he localzaon error occurs as much as he sensng area of he RFID reader. And, unl now, here s no sudy o esmae he pose of moble robo usng RFID ags. So, n hs paper, wo algorhms are suggesed o. We use he Markov localzaon algorhm o reduce he locaon(x,y) error and he Kalman Fler algorhm o esmae he pose(θ ) of a moble robo. We appled hese algorhms n our epermen wh our personal robo CMR-P3. And we show he possbly of our probably approach usng he cheap sensors lke odomeers and RFID ags for he moble robo s localzaon on he smar floor. Keywords Localzaon, Kalman fler, Markov localzaon, SLAM, RFID, smar floor I. INTRODUCTION Unl a recen dae, Robos are used n few felds of ndusry and her uses have been lmed n a lle ask. They are fed a a ceran pon and jus carry ou same paerns of asks repeaedly. Bu, nowadays, robos can carry ou varous asks lke gude and guard as he echnologes of a robo are advancng rapdly. And a moble robo can go around place o place. A presen, he core echnology needed for a moble robo s localzaon. A robo should recognze her locaon n he envronmen o do varous ask elaboraely. So, he sudy for localzaon of a moble robo s made acvely. Anoher mporan echnology for a moble robo s a map buldng because a robo mus know he nformaon of he envronmen for localzaon. SLAM(Smulaneous localzaon and mappng) s he mehod o carry ou localzaon and map buldng smulaneously. In mos of he sudy, dead reckonng, passve land marks recognon and map based mehods have been used n med forms for SLAM. Odomery and nera sensors, vson and range fnders are used for hese mehods. These mehods have some demers. Naural landmarks recognon mehod usng vson requres hgh compung power and he laser range fnder s oo epensve. So, n hs paper, we used he passve RFID(Rado frequency denfcaon) ags for a smar floor envronmen and moble robo s localzaon. A RFID ag s small and nepensve and a robo can localze fas wh hs sysem. Frsly, we sugges he effcen arrangemen and sensng mehods of he RFID ags for a smar floor. There are some demers n he RFID ag based localzaon mehod. A RFID reader jus senses wheher a RFID ag s n s sensng range or no. So localzaon error occurs as much as he sensng range of a reader and s hard o ge he robo s accurae pose nformaon for hs error. So, n hs paper, we sugges he probably mehods o mprove hs problem. We use he Markov localzaon mehod o reduce he poson(x,y) error and Kalman Fler mehod o esmae he robo s pose(θ ). We can rase he measuremen accuracy of he robo s poson and pose usng he nepensve sensors lke odomery sensors and RFID ags. As he RFID ag becomes small and nepensve, he sudes for usng n varous felds have been carred ou rapdly. They mosly have been used n he dsrbuon ndusry. RFID ags can save he rackng and oher nformaon of moble objecs o manage hem effcenly [1]. Recenly, he RFID sysem s used as a sensor n he robo s feld. In mos of he prevous mehods, he RFID reader s fed and he objecs aachng he RFID ags move. Bu, n our RFID ag based localzaon sysem, many RFID ags are locaed a he place lke a room and offce, and he robo mouned a RFID reader goes around and recognzes hem. For hs reason, he mos mporan

2 ssue n he smar floor s how o arrange he RFID ags n he envronmen. II. RFID TAG SYSTEM A. RFID Tag Dsrbuon There are wo mehods n he RFID ag arrangemen lke he random unform dsrbuon mehod and he regular dsrbuon mehod. Many paerns of arrangemen are nroduced as a regular dsrbuon mehod such as he grd paern and he equlaeral rangulaon paern. Fgure 1. Random unform ags dsrbuon mehod If we arrange he RFID ags arbrarly bu a he regular densy by he random unform dsrbuon mehod lke Fgure 1, he probably ha he robo senses a RFID ag k s no zero a any poson. pag ( drecon ) 0 k Bu, f we arrange he RFID ags mananng he same dsance and paern by he regular dsrbuon mehod, he undesrable case ha a robo doesn sense any RFID ags can be occurred (1) pag ( drecon ) = 0 () k We can preven he occurrence of hs case by rasng he arrangemen densy of RFID ags. Bu f we rase he arrangemen densy of RFID ags, he cos rases oo and he collson problem ha a RFID reader senses oo many RFID ags occurs. In he case of applyng he regular dsrbuon, we mus arrange RFID ags mananng he regular dsance and paern, bu geng he localzaon nformaon s easy and we can apply n a robo s localzaon whou an addonal specal algorhm. In he case of usng he random unform dsrbuon, we can arrange RFID ags easly, bu he addonal poson seng algorhm for he RFID ags s requred because of he rregular dsances beween ags. In hs paper, we use he regular dsrbuon mehod and arrange he RFID ags n he equlaeral rangulaon paern whch provdes hgh probably n recognzng he ags. B. Tag Recognon Errors Localzaon error occurs as much as he sensng range of he RFID reader and s hard o ge he robo s pose nformaon because a RFID reader jus senses wheher a RFID ag s s sensng range or no. In hs paper, we suppose ha he robo s movng drecon s parallel o he vrual sragh lne where he RFID ags are lad and RFID ags come up o he sensng range of he RFID reader n he oppose drecon. Fgure 3 shows he localzaon error n he drecon of Y as. If he odomery nformaon s no accurae when he sensor gages he RF sgnal power or he RFID reader passes he deecon area, he errors specfed lke he equaons (3),(4) occur when he RFID reader senses he RFID ag. Y as : 0 p R (3) errory X as : p R p (4) errorx errory As we can see n Fgure 3, f he dsance beween he robo s (or reader s) cener and he RFID ag s can be measured when he robo movng, he RFID ag sysem s error can be correced. The cener of RFID reader also can be esmaed usng he connuous repea mode of he readng mode. In hs case, he robo use he nformaon of he odomery and he number of he answer from he RFID ags durng he RFID reader s n he sensng range of one RFID ag. a) Grd paern b) Equlaeral rangulaon paern Fgure. Regular ags dsrbuon mehods Fgure 3. Poson error

3 In hs paper, we use he probably mehods o reduce he localzaon error of he RFID sysem. As he resul, we can reduce he sensng error ha resuls from RFID reader s sensng range and rase he accuracy of localzaon even n he envronmen where he densy of RFID ags s low. III. LOCALIZATION WITH RFID TAGS The drecon (θ) s esmaed by he angle beween he wo RFID ags whch a robo passed one afer anoher. The robo s accurae poson nformaon s needed when sensng a RFID ag o esmae he robo s drecon precsely. Bu, wh he RFID ags based localzaon mehod, a robo canno fnd s accurae poson (, y). A robo jus can deermne wheher s near he poson (`, y`) of he nformed RFID ag n a ceran dsance. The dsance error beween he robo s real poson and he esmaed poson s proporon o he sandard devaon of he dsance beween he RFID ag and he RFID reader. So, we apply he Markov localzaon o fnd he robo s poson more accuraely and Kalman fler o esmae he robo s drecon. The accuracy of he poson and he drecon s relaed each oher. We can rase he accuracy of he drecon by rasng he accuracy of he poson, and esmae he robo s poson n he area where he robo canno sense he any RFID ags by esmang he robo s drecon precsely. A. Poson esmaon In hs secon, we show he process o esmae he robo s poson (, y) applyng he Markov localzaon. We use he -dmenonal array of wh he resoluon of 1cm 1cm o show he belef sae of he robo s poson. In general, 3-dmenonal arrays are used o fnd he robo s poson (, y, θ) n he Markov localzaon. Bu n hs paper, we suppose ha a robo s a he cener of he array and lm he belef sae o 70cm from he robo. If l s he robo s poson represened as (, y), l s he robo s rue locaon and L s he sae varable of robo s locaon, he robo s poson belef Bel( L = l) a me s defned lke he equaon (5) as a probably densy. In hs equaon, Bel( L = l) = PL ( = l s1, K,, a1, K, ) (5) a and s are he npu daa of he moon model and he percepon model a me. Frsly, he moon model s used o esmae he robo s presen poson. In hs model, he probably a he presen poson Bel( L = l) s dependen on he probably a he prevous poson Bel( L 1 = l'). The moon model wh he conrol npu a -1, s specfed as a condonal densy lke he equaon (6). PL ( = l L = l', a ) Bel( L = l'). (6) The probably ha he robo s poson s l a me s specfed lke he equaon (7) from he oal probably and he Markov assumpon[4]. Bel( L = l) = PL ( = l L = l', a ) Bel( L = l') ' l The condonal densy PL ( = l L 1 = l', a 1) Bel( L 1 = l') s represened usng he -dmenonal array of 1 1 wh he resoluon of 1cm 1cm. The probably a he poson (l, l y ) s specfed lke he equaon (8). ( + l) + ( y+ ly) Bel( L = l) = η ep d σd l + θ an θ y l + y ep d σθ d = + y y θ = an In hs equaon, Δ and Δy are he dsance ha he robo moves n sragh along wh a -as and a y-as, l, l are he robo s poson n he -dmenonal array, y η s normalzer and σd, σ θ are he varances of he robo s movng dsance and drecon change. The robo s poson s renewed by he percepual model when here s he npu of useful sensor daa. In hs case, Bel( L = l) s defned lke he equaon (9) (7) (8) Bel( L = l) = η Ps ( ) l Bel( L = l) (9) In hs equaon, η represens he probably densy normalzer Ps ( s, a ) whch s ndependen 1, K, 1, K, of L. The Gaussan PDF(probably densy funcon) was used for he sensor model of he RFID ag sysem lke he equaon (10). ( d agcp ) 1 σ Pm( d ) l = ep (10) σ π

4 In hs equaon, σ s he sandard devaon of he sensng values of he RFID sysem, ag s he real cener poson of he RFID ags and d s he poson of a pon represened n he sensor model. The accurae robo s poson s no found by he RFID reader n sensor model because he RFID reader jus can senses wheher a RFID ag s n he sensng area or no. So we used he sensor model for he robo s poson esmaon o mprove hs problem. B. Pose esmaon In he Prevous secon, we suggesed he mehod o reduce he robo s poson error resuls from he sensng dsance of RFID ag sysem applyng he Markov localzaon. In hs secon, we sugges he mehod o esmae he robo s pose θ. For applyng he sandard Kalman fler model, we suppose ha he robo s sysem model s a Lnear Dynamc Sysem and corruped by he whe nose represened as a Gaussan dsrbuon. We use he sysem model of he sandard wo-wheeled moble robo o esmae he degree of he robo s locaon change (Δ, Δy, Δθ). Δ, Δy s he same value used n he equaon (8) of he secon A. We om predcon equaon, orrecon equaon, error covarance propagaon equaon because hey are general equaons used n he Kalman fler model. cp lke he equaon (11). We can fnd he poson of σ n he Gaussan funcon. We can fnd he poson ( p-ma, y p- ma) showng he hghes probably (p ma) and hen, n he drecon + and -, search he poson ( -, + ) where he probably s less han 1/8 of p ma. Ths s he poson of σ n Gaussan funcon. σ y s founded n he same way. ( p ma p ma + ) ma, σ ma ( yp ma y, yp ma y+ ) (11) σ y = σ θ ma( σ :, σ y : ) ma( σ :, σ y : ) an l In hs equaon σ p : s he sandard devaon of poson derved form Gaussan PDF. Ths equaon shows ha he sandard devaon of θ s dependen on he sandard devaon,y. The robo s pose error s reduced by he process of predcon and correcon. IV. EXPERIMENTS Fgure 4. The Pose Esmaon Mehod The correcon sep s processed when a robo senses a RFID ag. In hs sep, he sandard devaon σ s needed, bu σ and σ y of he RFID ag and sensor are oo bg o be used n he correcon and σ θ canno be found drecly. In hs paper, we sugges he mehod o fnd he sandard devaon (σ, σ y, σ θ ). Fgure 4 shows he correcon process n he case ha he robo sensed he h RFID ag and moved n a sragh lne and senses he (+1)h RFID ag rgh away. If he robo senses a RFID ag, we can fnd he poson showng he hghes probably ha he robo may be. We suppose as he poson where he robo s. Then he robo s poseθ mus be correced as much as Δθ. The mehod o appromae he sandard devaons σ, σ y from he belef sae map of he Makov localzaon s We smulae RFID based localzaon sysem applyng he Kalman fler and Markov localzaon. In hs smulaon, we apply he sandard model for Moon model. I has mosly been used n prevous sudy. We arrange RFID ags a 500mm nervals by he grd paern mehod and use he anenna of whch radus s 100mm. Fgure 5 shows he resuls of he smulaon. Ths Fgure shows he resuls of correcon of X-Y and X-Y-θ applyng our localzaon algorhm. If a robo fnds s poson X-Y usng only he poson nformaon geng from he RFID ags, he localzaon error ncreases connuously. In he Fgure 5-a), before a robo come no he slanng lned area A and fnd a RFID ag, he robo canno recognze s correc locaon. And fnd s correc locaon a he momen ha he robo senses he Tag-A. So we esmae he robo s pose θ applyng he Markov localzaon and he Kalman fler localzaon algorhm. As he resul, The localzaon error can be reduced remarkably as we can see n Fgure 5-b). And he localzaon error s reduced n proporon o he number ha he robo senses he RFID ags.

5 The RFID sysem we consruc s showed n Fgure 6. Ths sysem consss of he V70D5P0 RFID ag and he V70-HMC73T RFID reader of OMRON. And he frequency of he RFID s13.56mhz. We mouned hs RFID reader o he CMR-P3 whch was developed as a dfferenal ype n KITECH. a) V70-HMC73T RFID reader b) V70D5P0 RFID ag a) RFID based X-Y esmaon Fgure 7. Elecromagnec nducve RFID sysem [OMRON] V. CONCLUSIONS b) RFID based X-Y-θ esmaon Fgure 5. Resuls of he smulaon In hs paper, we consruc he smar floor usng he RFID ags based on he resuls of our smulaon. Bu we arrange he RFID ags by he equlaeral rangulaon paern because he probably ha he robo senses he RFID ags s hgher han n he grd paern mehod. Fgure 6 shows he paern of he arrangemen of he RFID ags of smar floor. Fgure 6. RFID ag dsrbuon In hs paper, we analyss he effcen arrangemen mehod of he RFID ags for he smar floor. We sugges he sensor model of he RFID ag o reduce he robo s localzaon error applyng he Markov localzaon and he Kalman fler localzaon algorhms. Especally, we can rase he accuracy of he robo s localzaon by correcng he robo s pose θ and he X-Y poson. In he prevous sudy, some range fnders have been used wh RFID ag sysems for he localzaon. They used he RFID ag sysem for poson recognon and correced he robo s pose θ usng range fnders. Bu we carry ou wo process only usng he RFID ags. We reduce he error of he robo s pose θ applyng our localzaon algorhm. Bu sll has nfluence on he locaon error slghly. Furhermore, f he robo doesn move n he sragh lne beween wo RFID ags, he error wll ge bgger. So, we wll connue he sudy o reduce hs error. And he sudes abou he mos suable RFID ag densy and he pah plannng algorhm are needed for he mos suable localzaon. REFERENCES [1] J. Brusey, M.Harrson, Ch. Floerkemeer, and M. Flecher. Reasonng abou uncerany n locaon denfcaon wh RFID. IJCAI-003 Workshop on Reasonng wh Uncerany n Robocs, 003. [] Drk Hahnel, Wolfram Burgard, Deer Fo, Ken Fshkn, and Maha Phlpose, Mappng and Localzaon wh RFID Technology, Proceedngs of he IEEE Inernaonal Conference on Robocs and Auomaon (ICRA)., pp , 004. [3] Jürgen Bohn and Fredemann Maern, Super-Dsrbued RFID Tag Infrasrucure, Proceedngs of he nd European Symposum on Amben Inellgence, Sprnger-Verlag, pp. 1-1, 004. [4] H. Bruynnk, Bayesan probably, 00. [5] D. Fo, W. Brugard, and S. Thrun, Markov localzaon for moble robos n dynamc envronmens., Journal of Arfcal Inellgence Research 11, pp , 1999.