Line Matching Algorithm for Localization of Mobile Robot Using Distance Data from Structured-light Image 1

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1 Advacd Scc ad Tchoogy Lttrs Vo.86 (Ubqutous Scc ad Egrg 015), pp L Matchg Agorthm for Locazato of Mob Robot Usg Dstac Data from Structurd-ght Imag 1 Soocho Km 1, Chaho Park 1, Sooyog Y 1 1 Dpartmt of Ectrca ad Iformato Egrg, Sou Natoa Uvrsty of Scc ad Tchoogy, soochuss@avr.com, cpktph@soutch.ac.kr, suy@soutch.ac.kr Abstract. Dstac masurmt s ssta for autoomous mob robot. A actv ragg ssor basd o th structurd-ght mag obtas dstac data of a st of objct pots o a asr strp. Ths papr ams to propos a agorthm for xtracto of sgmts from th dstac data ad matchg wth a gv goba map of vromt. By usg ths agorthm, a mob robot s ab to ocaz ts posto ad hadg ag th vromt. Exprmts for matchg ad ocazato ar coductd by usg dstac data from th actv ragg ssors to vrfy th prformac of th proposd agorthm. Kywords: structurd-ght mag, actv ragg, matchg, ocazato, mob robot 1 Itroducto I ordr to achv sf-ocazato ad autoomous avgato for a mob robot, a dstac masurmt systm s prrqust to obta spata map of th robot s vromt [1]. Amog th may kds of ragg ssors, th structurd-ght mag basd ssor has may advatags: ffct computato mag procssg, robustss agast ambt ght ad cost-ffctvss []. Th structurd-ght magg systm projcts a asr strp oto vromta objct ad capturs th rfctd ght by a camra. Dstac of a st of objct pots o th asr strp ca b computd basd o th traguato. Bcaus th dstac data cotas th formato about th vromt, t s possb to ocaz a mob robot by matchg th masurd dstac data wth a gv vromta objct map. May studs ar avaab o th matchg agorthm for ocazato of a mob robot [3], [4]. Th vromta objct map s gray gv th form of sgmts. A curvd objct s possby approxmatd by a st of sgmts aso. 1 Ths rsarch was supportd by Basc Scc Rsarch Program through th Natoa Rsarch Foudato of Kora (NRF) fudd by th Mstry of Educato, Scc ad Tchoogy ( ) Corrspodg author ISSN: ASTL Copyrght 015 SERSC

2 Advacd Scc ad Tchoogy Lttrs Vo.86 (Ubqutous Scc ad Egrg 015) Ma am of ths papr s to propos a matchg agorthm for a st of dstac data from a structurd-ght mag wth a gv vromta objct map th form of sgmts. A ffct agorthm for xtracto of a sgmt from masurd st of dstac data s aso proposd ths papr. L Sgmt Extracto Fg. 1 shows a xamp of asr structurd-ght mag. Th ragg ssor basd o th structurd-ght mag obtas a st of dstac data of pots o a projctd asr strp[5],[6]. Fg. 1. A xamp of asr structurd-ght mag ad dstac data of a st of pots o a asr strp Fg.. Ag at P cas of 4 Fg. 3. Px os o th ag I ordr to rprst th masurd st of dstac data wth svra sgmts, two d pots of a sgmt shoud b dtrmd. I cas that thr s a dscotuous pot th masurd data, t s smp to dtrm th d pot of a sgmt. I th othr cas that two sgmts ar coctd, a corr pot shoud b foud out as th d pot of a sgmt. As ustratd Fg., a ag at P btw th vctors r P P ad f P P ar dfd as foows: c o s 1 r r f f (1) 38 Copyrght 015 SERSC

3 Advacd Scc ad Tchoogy Lttrs Vo.86 (Ubqutous Scc ad Egrg 015) th whr dots th r product, P s th px posto th masurd data, ad P ad P ar th ( ) th ad th ( ) th px postos rspctvy wth a fxd trva. Th crtro for P to b a corr pot s dscrbd as foows: ad ( 1) 1 Eq. () mps that s a oca mmum wth. Fg. 3 shows th fuc of px os o th ag accordac wth. Wh thr s ot ay os o px P, th ag shoud b th fgur. If th amout of os o P s y axs, th ag bcoms or cas of 1 or 4 rspctvy as show th fgur. Thus, th fuc of px os o th ag bcom smar as th trva s crasd. Howvr, f s st too arg, t may caus a oss of corr pot a short sgmt. Thus, th sz of shoud b dtrmd by takg th amout of px os to cosdrato. Fg. 4 s th graph of th ag by appyg (1). From two d pots of a sgmt, th ctr of th sgmt ad th umbr of masurd data pots o th sgmt ca aso b obtad. () Fg. 4. Ag wth rspct to at 4 3 Matchg ad Locazato I Fg. 5 (a), P ad P dot two d pots of a sgmt. Th ctr of th sgmt s P P c P ad s th umbr of data pots o th sgmt. It s assumd that th goba map s modd by th poygoa objcts. Th mod Fg. 5 rprsts a sd of a poygoa objct th vromt. As xpad Fg. 5, th arst mod s chos as a targt for ach masurd sgmt. To choos th targt, th shortst dstac btw a mod ad th ctr of a sgmt s usd. Th targt s dscrbd as P u r (3) whr P s a pot o th targt, crta ra umbr. u s th ut orma vctor, ad r s a Copyrght 015 SERSC 39

4 Advacd Scc ad Tchoogy Lttrs Vo.86 (Ubqutous Scc ad Egrg 015) Rotato by posto r ad trasato by x, y wth rspct to th rfrc C of th robot mak th d pots of th sgmt as P R ( )( P C ) C T ( x, y ) (4) r r whr P ad P rprst a d pot bfor ad aftr th trasformato rspctvy. Th squard dstac btw th trasformd d pot ad th targt (3) s dfd as th matchg rror as foows: s R ( )( P C ) C T ( x, y ) u r r r R ( )( P C ) C T ( x, y ) u r r r whr P ad P ar th two d pots of th sgmt. Th, th tota matchg rror s rprstd by sum of th wghtd matchg rrors of a sgmts: S R ( )( P C ) C T ( x, y ) u r r r s R ( )( P C ) C T ( x, y ) u r r r Th wght s th umbr of a data pots o a sgmt. I ordr to gt th amout of rotato ad trasato ( x, y) that mmzs th tota matchg rror (6) by th ast-squar mthod, th rotatoa matrx R ( ) s arzd as foows[11]: c o s( ) s ( ) 1 R ( ) s ( ) c o s( ) 1 By srtg (7) to (6) ad takg a drvatv wth rspct to ad ( x, y) t s possb to gt th amout of trasato ad rotato that mmzs th tota matchg rror as foows: whr x 1 A B E 1 1 y C D F A 1 B M ( P C ) u u u t r u (5) (6) (7), (8) C B t D M ( P C ) u r E ( r P u ) u F ( r P u ) M ( P C ) u I (9), M s gv by r (9) 40 Copyrght 015 SERSC

5 Advacd Scc ad Tchoogy Lttrs Vo.86 (Ubqutous Scc ad Egrg 015) 0 1 M 1 0 Wh th amout of trasformato x, y, s obtad from (8), th stmatd postur x, y, r r r shoud b updatd as foows: x, y, x x, y y, r r r r r r (10) (11) Th matchg procss from (3) through (11) shoud b rpatd ut th matchg rror (9) bcoms smar tha a prdfd vau. (a) Bfor matchg Fg. 5. Matchg agorthm (b) Aftr matchg 4 Exprmts To vrfy th prformac of th proposd matchg agorthm ad th rsut of ocazato, xprmts ar coductd by usg a array of ragg systm basd o th asr structurd-ght. Fg. 6 shows th rsut of th map matchg ad th ocazato agorthm. Th omdrctoa dstac data masurd at a ukow robot postur s dpctd by rd sgmts Fg. 6 (a) ad th rsutat robot postur aftr th matchg s rprstd by a dark trag Fg. 6 (b). Th amout of trasformato to updat th robot postur s x, y, , 3 0.0, o from th matchg agorthm. (a) Bfor matchg (b) Aftr matchg ad updat Fg. 6. Data matchg ad th sf-ocazato Copyrght 015 SERSC 41

6 Advacd Scc ad Tchoogy Lttrs Vo.86 (Ubqutous Scc ad Egrg 015) 5 Cocuso For th ocazato of a mob robot ukow vromt, a ragg ssor s rqurd to masur a dstac to a vromta objct. Th actv ragg ssor basd o th structurd-ght mag obtas a st of dstac data o a asr strp. I ordr to match th masurd dstac wth a vromt objct map gv th form of sgmts, sgmts shoud b xtractd from th masurd data st. I ths papr, a ffct xtracto ad a matchg agorthm ar proposd basd o a ast-squard rror. Th matchg agorthm dvopd ths papr to assocat btw sgmts xtractd from th masurd omdrctoa dstac data ad poygoa mod of th goba objct map. Sc th matchg agorthm usd oy two d pots of a sgmt to assocat wth a dg of th poygoa mod, t s ffct computato tha a covtoa pot to pot matchg agorthm. Th proposd xtracto ad matchg agorthms wr vrfd through xprmts by usg ragg ssors basd o th structurd-ght mag. Rfrcs 1. Camro, S., Probrt. P.: Advacd gudd vhcs-aspcts of th Oxford AGV Projcts, Word Sctfc, Lodo (1994). Ja, R., Kastur, R., Schuck, B.: Mach Vso, McGraw-H (1995) 3. Cox, I.: Bach-a xprmt gudac ad avgato of a autoomous robot vhc. IEEE Trasactos o Robotcs ad Automato, vo. 7, o., pp (1991) 4. Cox, I., Kruska, J.: O th Cogruc of Nosy Imags to L Sgmt Mods, Proc. of It Cof. o Computr Vso, pp (1988) 5. Y, S., Suh, J., Hog, Y., Hwag, D.: Actv Ragg Systm Basd o Structurd Lasr Lght Imag, Proc. of SICE, Tawa, pp (010) 6. Sh, J., Y, S.: Actv Ragg Ssors Basd o Structurd Lght Imag for Mob Robot, LNEE, vo. 40, pp (013) 4 Copyrght 015 SERSC