SLAM Algorithm for 2D Object Trajectory Tracking based on RFID Passive Tags

Transcription

1 2008 IEEE Inernaional Conference on RFID The Veneian, Las Vegas, Nevada, USA April 16-17, C2.2 SLAM Algorihm for 2D Objec Trajecory Tracking based on RFID Passive Tags Po Yang, Wenyan Wu, Mansour Moniri, Claude C. Chibelushi Faculy of Compuing, Engineering and Technology Saffordshire Universiy {p.yang, Absrac Tracking he physical locaion of nodes in a 2D environmen is criical in many applicaions such as camera racking in virual sudio, indoor mobile objecs racking. RFID echnique poses an ineresing soluion o localizing he nodes because he passive RFID ags could sore he posiion uni informaion according o unique ag ID. Based on ags paern, algebraic approach could solve he 2D rajecory racking problem. However, he racking accuracy of his approach is highly relaed o he ags posiion disribuion and posiion uni. I would be inaccurae for some erraic rajecory racking. Thus, we would ry o apply and evaluae he probabilisic approaches, such as SLAM (Simulaneous Localizaion and Mapping), ino RFID ag based rajecory racking. In his paper, we propose an RFID ag based SLAM algorihm for 2D rajecory racking. Also a echnique called Map adjusmen is proposed o increase he efficiency of he algorihm. The simulaion resuls show ha he approach could improve he accuracy for some pars of rajecory racking compared o RFID algebraic approach. The limiaion and fuure work are given in he conclusion. Keywords: SLAM, Paricle Filer, Localizaion, RFID,. 1. Inroducion RFID (radio frequency idenificaion) is an auomaic idenificaion sysem ha consiss of wo componens readers and ags [1]. A ag has an idenificaion ID sored in is memory ha is represened by oher informaion, such as posiion informaion. The RFID reader can recognize ags a high-speed and send daa wihin various disances. Recenly, he RFID echnology has been widely applied for he racking of moving physical objecs [2], especially in mobile robos racking and navigaion area [3] [4]. Therefore, he use of RFID sysem for 2D moving physical objec rajecory racking is a very crucial opic o research. There have been muliple localizaion mehods using RFID echnology. SpoON[5] is a well-known locaion sensing sysem which uilizes received signal srengh indicaion in RFID echnology o localize acive RFID ags. The SpoON echnique is an ad-hoc design which compares he differen received signal srengh measuremens of he acive ags o esimae he disance beween ags. LANDMAR [6] uilized similar principles o SpoON, and developed an algorihm o reflec he relaionship beween signal srengh and power levels on he LANDMARC sysem. However, hese mehods suffer from several drawbacks: (a) he accuracy only can reach meer uni due o he limiaion of signal srengh. (b) I incurs significan insallaion and mainenances coss. Then mehods for localizaion of passive RFID ags have been proposed based on wheher or no he ag is wihin he inerrogaion range of a reader. Lim [7] represens an effecive localizaion algorihm o increase he accuracy of RFID passive ags sysem. The core idea of he algorihm is o modify he disribuion of RFID passive ags in order o reduce he posiioning error. The advanage of localizaion based on passive RFID ags is o enhance he racking accuracy o cenimere uni pracically. However, i is inaccurae for some erraic rajecory racking. For he issue, we aemp o use he probabilisic approaches (SLAM) o esimae he rajecory by using disance informaion, insead of direcly observing he posiion informaion sored in RFID ags. SLAM sands for Simulaneously Localizaion and Mapping [8][9][10], and Localizaion deals wih he problem of rying o find he locaion of he moving objec, given a map of he surrounding environmen and some sensor reading daa. Mapping is he process of building and mainaining a model of he environmens. In he las several decades, SLAM (Simulaneous Localizaion and Mapping) echnology has been of grea ineres for /08/$ IEEE 165

2 mobile compuing and roboic researchers [11] [12] and applied ino racking and localizaion area. Our work focuses on he applicaion of he SLAM echniques mehodology adoped from mobile robo applicaion o RFID sysem area. In his paper, we propose a RFID ag based SLAM algorihm for 2D moving objec racking. Also a novel echnique called Map adjusmen is proposed o increase he efficiency of he algorihm. A simulaed experimen is conduced o analyze and evaluae he performance of his mehod. represens he real rajecory of moving objecs, and he RFID ag based rajecory of moving objecs. 2. Problem Sae As menioned above, in mos passive RFID ag racking sysem, heir sysem assumes perfec measuremens, and he posiions of he ags have o be known accuraely. In our research sysem, RFID passive ags are divided ino card ype and buon ype. The characerisic of ags vary he operaing range of he sysem, as shown in Table 1. Table 1. RFID passive ag characerisic Carrier Frequency MHz Type Card Buon Tag dimensions 3 cm 8 * 5 cm Tag surface area 7.06 cm2 40 cm2 Operaing range 14 cm 1 cm Thus, in RFID passive ag racking sysem, if we assume he RFID passive ags paern is based on a regular gird and each ag sored similar posiion informaion, shows as Fig 2. X Reader Area RFID Tag Fig. 2. RFID passive ag paern for racking However, based on he RFID passive ags paern, if we simulae a random erraic rajecory of moving objec, he posiion informaion use ineger array o represen he moving rajecory of objecs. Fig3 Y Fig 3. RFID reader rajecory and Real rajecory Table 2. The posiion daa of hese wo rajecories Time Seps Real (X,Y) RFID (X, Y) Therefore, i appears ha he RFID passive ag sysem have a weak abiliy o rack he erraic rajecory of moving objecs. The reason is ha he ag paern only can be calibraed as he ineger array o rack he moving rajecory, hus he accuracy is highly limied o he basic uni of ineger array. We can se he basic uni as differen numbers, such as 1cm, 5cm, and 10cm. However, i sill can no rack any unsable erraic rajecory, such as 1.05cm, 5.7cm, and 12.78cm since he mached ag posiion can no represen his figures. For his issue, since he probabiliy mehods can esimae he rajecory by disance informaion no only direcly observe he posiion figure, i has he poenial abiliy o solve his problem. 166

3 3 SLAM Algorihm for 2D Trajecory Tracking The aim of his algorihm is o achieve 2D range moving objecs racking by disance informaion (Fig4). This secion provides a comprehensive descripion of he implemenaion of sysem saes, sysem models and he paricle filer in his algorihm. The paricle filer in his SLAM algorihm is no exacly he same as he sandard paricle filer. In addiion, on he nex secion, we would apply his algorihm ino RFID passive ags based environmen. Feaure Poins: fixed poin o measure disance informaion. Moving Objecs: moving poins for 2D rajecory racking. Moving direcion: Disance informaion: Fig4. SLAM for 2D Objecs rajecory racking. 3.1 Sysem Sae and Model In his research work, i is assumed ha he observaion sysem is based on disance environmen, o successfully obain he range informaion. Thus we jus assume ha here are several feaures poins mouned in he surroundings, and he moving objec can receive he disance informaion wih ime seps.. Thus, feaure poins can be denoed as f n,wheren is an index of nodes. The locaion sae represens he posiion of moving objec, is defined as S :whereis index of ime seps: f n x f xs =, s, y = f y s (1) Having defined he feaure poins saes and locaion saes, he sysem sae, a ime, is hen: x s f 1, = f 2,... f n, Given he above overview of sysem sae, he objec node sars moving from an iniial posiion s 0 wihou prior knowledge of he feaure nodes, f1, f2,... f n.as he objec keeps moving i receives relaive range daa. Using hese sensor daa he SLAM algorihm ries o esimae he pah s 0: of he objec node. The observaion model ells he probabiliy of obaining an objec posiion a a cerain locaion sae. The Bayesian filer can be defined as a probabilisic disribuion: Pr( d s ),where d, s are he locaion sae and sensor reading, respecively. The sraigh observaion model is given by he following equaion: (2) d = g( f, s) = ( x x ) + ( y y ) + w (3) 2 2 s s f s f s Where x f ishecoordinaeofaimeframe, xs is he coordinae of he objec node, d is he relaive disance from he objec node o feaure poin n and w is he Gaussian noise characerizing he errors of he environmen. A each ime sep, he moving objec would receive observaion informaion from all feaure poins. The moion model characerizes he moving objec locaion saes over ime. I helps o predic he nex objec node locaion sae given he mos curren one. We assumed he arge objec moving rajecory is associaed wih direcion or speed of he movemen ha is random. Thus we use a 2D Gaussian model o approximae he moion. More specifically, when given he locaion sae s a he ime sep, o predic he 167

4 locaion sae s + 1 a he ime + 1, we draw a number of paricles randomly from a 2D Gaussian disribuion wih zero-mean. These paricles will form a circle wih origin as and is radius is deermined by he sandard deviaion of he 2D Gaussian disribuion. 3.2 Paricle Filer SLAM Algorihm Based on above he sysem model given above, he daa srucure of M paricles is illusraed in Figure 5: Camera Locaion feaure 1 feaure 2 feaure n Paricle 1 x,y x,y x,y x,y Paricle 2 x,y x,y x,y x,y Paricle 1M x,y x,y x,y x,y Iniializaion Iniializaion is a mos imporan sage in all SLAM algorihms. In his paricle filer based SLAM i is o iniialize he locaion sae and feaure saes in each paricle. The iniializaion process can be quie ricky when a single measuremen is no enough o consrain a feaure locaion in all dimensions. This problem will bring grea ambiguiy abou he feaure saes a he beginning of he algorihm. In his research work, we would use he firs wo measuremens o obain a rough idea of where he nex locaion saes should be, i.e. in which quadran he sae is. Then a random poin is chosen in ha quadran o be he nex locaion sae Weighing Afer he iniializaion, he moion model is applied o all paricles. More specifically, he locaion sae of each paricle will be replaced wih a new one generaed from he moion model while he feaure poins sae of each paricle will remain unchanged. Figure 6 is an example showing one paricle being applied he moion model. Figure 5 Daa srucure of paricles Each paricle has 2 (n + 1) saes: 2 locaion saes and 2n feaure poins saes. In a mahemaical form, each paricle is: x =< s, f, f,... f > =< > (4) m m m m m 1, 2, n, m m m m ( xy, ),( xy, ) 1,,( xy, ) 2,,...( xy, ) n, Where he superscrip m is he index of he paricle, he m subscrip indicaes he ime sep, s is he locaion m of he moving objec and, fn, represens feaure n. The paricle filer algorihm is hen operaing on a se of paricles x. Each ieraion of he algorihm can be m divided ino he following sages: Iniializaion, Weighing all he paricles, Map Adjusmen, Resampling Since he paricle filer SLAM algorihms have been invesigaed by researchers in mobile robos area for long ime [13][14][15][16]. For he iniializaion, weighing all he paricles, and resampling, we would apple he sandard Fas SLAM [17] approach o implemen, however, he MAP Adjusmen is our new exension o enhance he efficiency of algorihm. Fig 6. Apply he moion model o paricle Before applying he moion model, he paricle has an esimaion of he locaion sae a ( xs, ys) and esimaion of Feaure 1 a ( x f1, y f 2). Afer applying he moion model he locaion sae is replaced wih ( xs, ys ) while he esimaion o Feaure 1 remains unchanged. In Figure 6, ( xs, ys ) is he prediced locaion sae and d is he prediced observaion. Then he weigh of each paricle should be deermined by he difference beween he prediced observaion and real observaion. Hence his paricle will have a high weigh. In a probabilisic mahemaical form, he weigh of each paricle is given by: w = Pr( d f, s )Pr( f s, d ) df (5) m m m n n 0: 1 0: 1 n 168

5 Where he superscrip m is he index of he paricle, subscrip is ime sep, is feaure n, and is he observaion. Equaion 6 is implemened by calculaing he real observaion under a Gaussian disribuion wih mean and sandard deviaion deermined by he observaion noise. More specifically, he weigh of each paricle is calculaed using he following equaion: 2 ( dd ) 2 (2 ) 1/ 2 2 w= 2 e (7) allfeaures Map Adjusmen The Map Adjusmen is a novel echniques invened in his paper. Is inspiraion comes from he landmark updae in FasSLAM [16] where he landmark (feaure) esimaes are updaed using EKF. The EKF approach is no suiable in his SLAM problem due o he non-linear and no inverible observaion model. The basic idea of Map Adjusmen is as follows: For each paricle, afer applying he moion model and weighing, when he observaion is received, each feaure s sae is hen adjused so ha he difference beween he prediced observaion and real observaion is smaller. Figure 7 Illusraion of he Map Adjusmen he esimaion o feaure A will be closer o he real one. How far he grey circle should be moved depends on he difference beween en d and d, and depends on he radius r. In his implemenaion we use he following equaion o calculae he movemen: ( ) movemen p* d = d (8) r where p is a parameer which mus be specified manually based on experimens. By using he Map Adjusmen, he accuracy of he esimaion o feaures can be grealy improved, or can be mainained bu fewer paricles are required Resampling Resampling is he las sep in each ieraion, which is very similar o he one in Paricle Filer Localizaion. In his process, paricles wih large weigh will be duplicaed while hose wih small weigh will be deleed he sum of all weighs of all paricles should remain unchanged. Therefore before he resampling a normalizaion operaion is carried ou which normalize he weigh of all paricles so ha hey sum up o RFID Passive Tag Based SLAM In RFID passive ag sysem, if we could apply his SLAM algorihm, firsly we need o deermine some fixed feaure poins, since i is a 2D rajecory racking, we would choose simple four fixed poins A. B, C, D as he feaure poins, and he objec moving rajecory would be consrained ino he area. Secondly, he RFID reader has a ani-collision funcion, which can deec more han one passive ag each ime. Based on his, we can exend our SLAM algorihm from single ag racking o muliple ags racking, and hen esimae he mean of he ag posiion as he objecs moving posiion. As shown in Fig 8: A one paricle example of he Map Adjusmen is as follows: a he beginning, a disance measuremen of feaure A is received hence we pu is esimaion on a circle (wih a radius of he disance r). Then he moion model is applied which moves he locaion sae from ( xs, ys) o ( xs, y s ) (he grey riangle). If he black circle is he real locaion of feaure A, hen a new observaion d will be received. Then we compare he real observaion d wih he prediced observaion d. Obviously d is smaller hen d so he esimaion o feaure A is moved o he dashed circle. By doing so X Fig 8. Ani-collision of RFID reader Reader Area RFID ags Feaure Poins (ABCD) Y 169

6 Therefore, if we assume he number of RFID reader can deec RFID passive ags is N, hen we can ge N se of disance informaion, finally we can ge he moving objec node posiion by means of he passive ags esimaed value. RFID passive ags paern is regular grid, he ime seps is 135. Therefore, we can ge a random rajecory, he solid line represens he real rajecory, and he do line represens he RFID reader rajecory. The able 3 shows some posiion daa of wo rajecories. ( Pos _ ag1 + Pos _ ag Pos _ ag Posiion _ obj = n) N (9) The summary of he whole RFID sensor-based SLAM program, as shown in Fig.9: Fig 10. Simulaion random of rajecory Table 3. The posiion daa of wo rajecories Fig.9 The RFID Tag-based SLAM algorihm 5. Simulaion Resuls For he experimen, we simulae a random erraic moving objec rajecory in a 2D environmen by Malab. The goal of his simulaion is o evaluae he accuracy and efficiency of his RFID ag based SLAM soluion, and o invesigae if his algorihm has enhanced he accuracy for 2D moving objec racking. In all he simulaed daases, we assumed ha here are four fixed feaure poins in he environmen, which are easy and simple, Feaure A: (10, 10), Feaure B: (22, 0), Feaure C: (-12, -16), Feaure D: (-5,15). And he Time Seps Real (X,Y) RFID (X, Y) The Assumpion based on hese daa, we can ge he disance informaion of each RFID ags and hen use hem o esimae he rajecory. 5.1 Single Tag SLAM Firsly, we can apply our algorihms ino single ag deecion siuaion. In his case, he numbers of RFID readers deeced over ime is jus one. Thus, we can ge he resuls as Fig

7 Fig 11. Single Tag SLAM From Fig 11, we can find ha excep he iniial esimaion posiion, he esimaion pah has no much differen wih he RFID pah. And he iniial esimaion posiion error could no be considered because he SLAM algorihm iniialized as an unknown posiion and feaure poins. Therefore, we only enlarge he obvious differen ime seps beween RFID pah and Esimaion pah and evaluae he resuls. The algorihm applied for single ag deecion siuaion performance no quie well for our arge. Fig 12. Muliple Tags SLAM 5.2 Muliple Tags SLAM Afer single ag SLAM experimen, we evaluae he muliple ags SLAM siuaion. If we assume he RFID deecion RFID reader area is a circle wih radius 1.2, hen we can ge oher four Passive RFID Tags o esimae he pah. Someimes Tags posiion value is he same, we also can use he algorihm o esimae i. (see Fig 12) From he Fig 12, we can find ha some pars of he RFID pah are differen wih he Mean of esimaion pah. The Fig are oo small so ha we can no see quie clear wheher improve he esimaion or no. Thus, we enlarge he differen area wih ime seps and enlarge hem o compare wih he real pah. Because he iniial seps are no sable due o he feaure of algorihm, and final seps are sraigh pah, hey are no considered in our research work. We only enlarge wo middle pars of ime seps and (Fig 13 and Fig 14). From hese wo figures, i is appear ha he esimaion pah can represen he movemen of real erraic rajecory pah beer han he RFID pah. Fig 13. Time Seps Fig 14. Time Seps

8 The Fig 15 and Fig 16 illusrae he X and Y value of he objec 2D rajecory esimaion. Fig 15. X value for esimaion pah Fig 16. Y value for esimaion pah Finally, he able 3 would show he average X and Y error over ime seps beween RFID pah and esimaion pah. The resuls illusrae he algorihm performs well for muli-passive ags siuaion and improves he accuracy. Table3AverageErroronXandY Time Seps Errors RFID Pah vs Real Pah Esimaion Pah vs Real Pah Axis X Y X Y Value Conclusion and Fuure work Trackinghephysicalnodesina2Denvironmenis a criical research opic in many applicaions such as indoor mobile objecs racking. RFID echniques are he new approach for achieve he aim. In his paper, a RFID passive ag based SLAM algorihm has been designed and implemened o solve he problem of 2D moving objec rajecory racking based on radiional RFID sysem. The simulaion resuls show ha he algorihm would improve he RFID sysem accuracy for erraic rajecory. The main difficulies in his algorihm research are he non-accuracy linear observaion model, he moion model wihou direcion informaion. The fuure work would carry on he exension of he algorihm wih direcion informaion and be applied in 3D environmen. References [1]. K.Finkenzeller. RFID Handbook. Wiley,2003. [2]. P.Wilson, D. Prashanh and H. Aghajan. Uilizing RFID Signaling Scheme for Localizaion of Saionary Objecs and Speed Esimaion of Mobile Objecs, IEEE Conf. RFID pp [3]. O. Kubiz, Mahias 0. Berger, Marcus Perlick, Rene Dumoulin, "Applicaion of Radio Frequency Idenificaion Devices o Suppor Navigaion of Auonomous Mobile Robos," IEEE Conf. Vehicular Technology, vol. 1, pp , [4]. K.Yamano, K.Tanaka, M.Hirayma, E. Kondo, Y. Kimuro and M. Masumoo, "Self-localizaion of mobile robos wih RFID sysem by using suppor vecor machine," Proc. IEEEIRSJ In. Conf on Inelligen Robos and Sysems, vol. 4, pp , Sep. 28-Oc. 2, [5] J. Highower, C. Vakili, G. Borriello, and R. Wan. Design and Calibraion of he SpoON Ad-Hoc Locaion Sensing Sysem, Seale, WA, Augus [6]L.Ni,Y.Liu,Y.ChoLau,A.Pail,LANDMARC: Indoor Locaion Sensing Using Acive RFID. Wireless Neworks 10, p , Kluwer Academic Publishers. Neherlands, [7] H.S.Lim, B.S.Choi and J.M.Lee. An Efficien Localizaion Algorihm for Mobile Robos based on RFID sysem. In Proc, SICE-ICASE, 2006, pp [8] A. Ward, A. Jones, and A. Hopper. A New Locaion Technique for he Acive Office. IEEE Personal Communicaions, pp , [9] R. A. Brooks. A robo ha walks: Emergen behavior from a carefully evolved nework. IEEE Journal of Roboics. and Auomaion, 2: pp , [10] S. Thrun, D. Fox, W, Burgard and F. Dellaer. Robus mone carlo localizaion for mobile robos. Arificial Inelligence, vol. 128, no. 1-2, pp [11] M. Pupilli and A. Calway. Real-ime camera racking using a paricle filer. In Proc. Briish Machine Vision Conference, pp ,2005. [12]. A. J. Davison. Real-ime simulaneous localisaion and mapping wih a single camera. In Proc. IEEE Inernaional Conference on Compuer Vision, pp , [13] A.J. Davison and D.W. Murray. Simulaneous Localizaion and Map-Building Using Acive Vision. IEEE Trans. Paern Analysis and Machine Inelligence, vol. 24, no. 7, pp [14].M.H.DegrooandM.J.Schervish,M.Probabiliy and saisics. 3rd ed: Addison-Wesley [15] J. M. Buhmann, W. Burgard, A. B. Cremers, D. Fox, T. Hofmann, F. E. Schneider, J. Srikos and S. Thrun. The mobile robo rhino. AI Magazine, 16(2): pp , [16] Thrun, S., Monemerlo, M., Koller, D., Wegbrei, B., Nieo, J. and Nebo, E., FasSLAM: An efficien soluion o he simulaneous localizaion and mapping problem wih unknown daa associaion, J. Machine Learning Research, 2004, [16] M. Monemerlo, S. Thrun, D. Koller and B. Wegbrei. FasSLAM 2.0: An improved paricle filering algorihm for simulaneous localizaion and mapping ha provably converges. In Proc. Inernaional Join Conference on Arificial Inelligence, pp ,