DEEP (Displacement Estimation Error Back-Propagation) Method for Cascaded ViSPs (Visually Servoed Paired Structured Light Systems)

Transcription

1 DEEP (Dsplacemet Estmato Error Back-Propagato) Method for Cascaded VSPs (Vsually Servoed Pared Structured Lght Systems) Haem Jeo 1), Jae-Uk Sh 2), Wachoel Myeog 3), Yougja Km 4), ad *Hyu Myug 5) 1), 3), 5) Dept. of Cvl ad Ev. Egg., KAIST, 291 Daehakro, Daejeo , Korea 2), 4), 5) Robotcs Program, KAIST, 291 Daehakro, Daejeo , Korea 5) ABSTRACT I ths study, a dsplacemet estmato error back-propagato (DEEP) method for multple vsually servoed pared structured lght systems (VSPs) s proposed. The VSP s composed of two sdes facg each other, each wth oe or two lasers, a 2-DOF mapulator, a camera, ad a scree. By calculatg postos of the projected laser beams o the screes ad rotato agles of the mapulators, 6-DOF relatve dsplacemet betwee two sdes ca be estmated. To apply the system to massve cvl structures such as log-spa brdges or hgh-rse buldgs, etre structure should be parttoed ad multple VSPs are placed each partto a cascaded maer. Etre shape of the structure s motored by multplyg estmated dsplacemets from VSP modules. I the multplcato, however, the error resdg estmated dsplacemet s propagated through the parttos. To solve the problem, DEEP method whch uses the Newto-Raphso formulato spred by the error back-propagato algorthm eural etwork s proposed. I ths method, the estmated dsplacemets are updated reverse order by mmzg the propagato error. The error at the last module ca be obtaed by calculatg the dfferece of the 6-DOF relatve dsplacemet estmated from VSP ad the postos measured from precse GPS or topographcal surveyg. The performace of the proposed DEEP method has bee verfed from varous smulatos, ad the results show that t reduces the propagato error sgfcatly. 1. INTRODUCTION As structural dsplacemet motorg s cosdered oe of mportat categores of structural health motorg (SHM), varous sesors or systems have bee developed (Balageas 2006). Especally, vso sesor-based drect dsplacemet measuremet 1), 2), 3), 4) Graduate Studets 5) Professor 2758

2 system have bee wdely researched due to tremedous developmet of vso sesor techology. Most of the vso-based dsplacemet measuremet system stalls targets o a structure ad a camera wth a zoomg capablty captures the targets from a far (Lee 2006, Park 2010). Sce the dstace betwee the targets ad the camera s log, t s sestve to evrometal chages such as llumato or weather codto. Moreover, most of vso-based dsplacemet measuremet systems measures 2 or 3- DOF dsplacemet. To resolve these problems, a vsually servoed pared structured lght system (VSP) has bee developed (Jeo 2011). The VSP, whch s a later verso of a pared structured lght system proposed by Myug et al. (Myug 2011, Myug 2012), s composed of two sdes facg each other, each wth oe or two lasers, a camera, ad a scree. The lasers project ther parallel beams to the scree o the opposte sde ad the camera ear the scree captures the mage of the scree. To make laser beams appear o the scree all the tme, a 2-DOF mapulator holds the laser(s) ad cotrols the pose of laser(s). The relatve 6-DOF dsplacemet ca be estmated by calculatg three postos of the projected laser beams ad rotato agles of the mapulators. I comparso wth other vso-based dsplacemet motorg systems, VSP s robust to the evrometal chages due to ts uque cofgurato, the dstace betwee the camera ad the scree s short such as 20 cm. To apply VSP to real cvl structures, multple modules should be placed parttos a cascaded maer ad motor the dyamc movemet of the etre structure. I other words, the etre shape of structure ca be estmated by multplyg the estmated dsplacemet from multple modules. However, the mult-module system has a major drawback that the error resdg the estmated dsplacemet s propagated through the multplcato. To solve ths problem, a dsplacemet estmato error back-propagato (DEEP) method whch uses the Newto-Raphso formulato spred by the error back-propagato algorthm mult-layer eural etworks s proposed ths paper (Jeo 2013). The remader of ths paper s orgazed as follows. I Secto 2, desg ad kematcs of VSP s brefly descrbed. The detals of DEEP method s troduced Secto 3. I Secto 4, smulatos are performed to verfy the performace of the proposed method. Coclusos are dscussed Secto VISUALLY SERVOED PAIRED STRUCTURED LIGTH SYSTEM (VSP) Multple modules of vsually servoed pared structured lght system (VSP) ca be appled to cvl structures by stallg mult-modules a cascaded maer as show Fg. 1. Isde the dashed le box the fgure, detals of VSP are llustrated. As show the fgure, VSP s composed of two sdes facg each other, each wth oe or two lasers, a camera, ad a scree. The lasers project ther parallel beams to the scree o the opposte sde ad the camera ear the scree captures the mage of the scree. As the dstace betwee the camera ad the scree s short such as less tha 20 cm, the system s robust to the evrometal chages. To cotrol projected laser beams appear o the scree all the tme, a 2-DOF mapulator was added. I other words, the mapulator holds the laser(s) ad cotrols the pose of laser(s). By calculatg postos of the projected laser beams o the screes ad rotato agles of the mapulators, 2759

3 the relatve 6-DOF dsplacemet ca be estmated. Fg. 1 Applcato of multple vsually servoed pared structured lght system to cvl structures. Detals of VSP ca be foud sde a dashed le box. The kematcs of VSP defes a geometrc relatoshp betwee the observed data, postos of the projected laser beams, m = [ A O, B O, B Y] T ad estmated dsplacemet p = [x, y, z, θ, φ, ψ] T (Jeo 2011). Here A O s the projected beam o scree A ad B O ad B Y are the projected beams o scree B. x, y, ad z are the traslatoal dsplacemet alog X, Y, ad Z axes, respectvely, ad θ, φ, ad ψ are the rotatoal dsplacemet about X, Y, ad Z axes, respectvely. By usg trasformato matrces, A T B ad B T B', ad a posto of the stalled laser o sde B, the A O ca be obtaed as follows: A A B O T T B TB ZAB (1) where A T B s the trasformato matrx that trasforms the coordate from scree B to scree A, Z AB s the dstace from scree A to scree B, B T B' s the rotato matrx cossts of motor ecoder formato of the mapulator o sde B, B T B' =R x (-θ Bec ) R z (- ψ Bec ) where θ Bec ad ψ Bec are rotated agles of the mapulator B about X ad Z axs, respectvely. I the same way, B O, ad B Y ca be easly obtaed by usg B T A ad A T A as follows: B T A' AB, B A O T T L 0 Z 1 (2) A B B A T Y TA TA' L 0 ZAB 1 (3) where A T A s the rotato matrx cossts of ecoder formato of mapulator A ad L s the offset of a stalled laser posto from a ceter of a scree X drecto. As z = 0 o screes, z compoet of A O, B O, ad B Y vectors should be zero. By applyg these costrats, the kematc equato ca be derved as follows: M O O O O Y Y (4) A A B B B B x y x y x y where A O x ad A O y deote the x ad y compoet of A O, respectvely. T 2760

4 To estmate the dsplacemet from the kematc equato M, a o-teratve method amed cremetal dsplacemet estmato (IDE) method was proposed (Jeo 2012). I ths method, the dsplacemet s updated from the prevously estmated dsplacemet by calculatg a dfferece of the prevous ad curret observed data. 3. DISPLACEMENT ESTIMATION ERROR BACK-PROPAGATION (DEEP) To apply VSP to massve cvl structures such as log spa brdges or hgh rse buldgs, multple modules should be stalled a cascaded maer. I other words, etre shape of the structure ca be motored by multplyg estmated dsplacemet from each module. I the multplcato, however, the error resdg the estmated dsplacemet s propagated through the multplcato. To solve ths problem, a dsplacemet estmato error back-propagato (DEEP) method whch uses the Newto-Raphso formulato spred by the error back-propagato algorthm multlayer eural etworks s proposed (Jeo 2013). The propagato error s compesated from the last to the frst module reverse order. The propagato error ca be defed as the dfferece betwee the absolute posto at the last module calculated from other sesors such as precse GPS or topographcal surveyg ( p ) ad the VSP (P ) as follows: E P P (5) where P ca be calculated by multplcato of trasformato matrces of estmated dsplacemet D 1 through D where deotes the umber of modules. The relatve dsplacemet betwee adjog -th module, P, ca be estmated as follows: P f( gd ( ) gd ( ) gd ( ) gd ( )) (6) 1 1 gd ( 1 1 where f s a fucto that trasforms a homogeeous trasformato matrx to a vector ad g s a fucto that trasforms a vector to a homogeeous matrx. To update the estmated dsplacemet, the Newto-Raphso formulato wth a learg rate, α, s formulated as follows: D( k1) D( k) J E (7) D where J D = E/ D s the Jacoba of the error ad J + D s the pseudo-verse of J D. The Jacoba matrx ca be represeted usg the cha rule of partal dfferetato, yeldg Eqs. (8) - (10). As ca be see Eq. (8), the relatve dsplacemet at the -th module s updated by the Newto-Raphso formulato. By usg the cha rule, Eq. (8) ca be formulated as Eq. (9). As E/ P s 1, Eq. (9) ca be smplfed to Eq. (10). D ( k1) D ( k) J ( P P) (8) D E P D( k) ( P P) P D (9) 2761

5 P D( k) ( P P) D The estmated dsplacemets are updated from the last to the frst module reverse order. Usg the updated dsplacemet calculated the prevous step, the error ad Jacoba are calculated ad the the dsplacemet s updated by mmzg the propagato error. I geeral, the relatve dsplacemet at each module s updated as follows: (10) D( k1) D( k) J ( P P) (11) D P P P 1 P P 1 1 ( ) ( ) P 1 P 2 P D D ( k ) ( P P ) (12) where =,, 1. Sce the umber of dsplacemet varables s more tha the umber of costrats p, there ca be umerous solutos that mmze the propagato error. Therefore, we assume that the updated rage of the estmated dsplacemet, ΔD, s lmted by two costrat values. The costrat values are determed by cosderg physcal lmtatos of the motors or error covarace of the VSP. Ths dea was partally from the cotrol strategy used for redudat mapulators. Istead of usg the Newto-Raphso formulato, the gradet descet formulato ca be used. Detals of DEEP method wth the gradet descet formulato ca be foud Jeo (2013). 4. SIMULATIONS To verfy the performace of the proposed DEEP method, smulato wth sx, ad te modules have bee performed as follows. The predefed absolute postos, p,, p, are set at frst. The, the 6-DOF dsplacemet betwee two adjog modules s estmated by usg VSP wth IDE method. Afterwards, the propagato error s calculated by multplyg the estmated dsplacemets. The DEEP method s appled (a) Fg. 2 Smulato results wth sx ad te modules. Sold le wth astersk: groud truth. Dot dashed le wth crcle: estmated 2762dsplacemet from VSP. Dotted le wth rectagle: updated dsplacemet by usg DEEP method (b)

6 ad the estmated dsplacemets are updated reverse order. The updated dsplacemet s set to boudares f t exceeds the upper ad lower lmts. The calculato of the propagato error ad the dsplacemet update step are repeated utl L 2 orm of the propagato error at the last module becomes smaller tha the error threshold. I ths paper, the learg rate, lmts, ad error threshold are set to 0.1, [±0.01m, ±0.01m, ±0.15m, ±1, ±1, ±1 ], ad 1.0 x 10-4, respectvely. The lmts are determed based o the error covarace of VSP from prevous expermetal tests. The dstace betwee each module s set to be 10 m. The smulato results wth sx ad te modules are show Fg. 2(a) ad 2(b), respectvely. I the fgure, the sold le wth astersk dcates the groud truth, the dotdashed le wth crcle s the estmated dsplacemet usg VSP, ad the dotted le wth rectagle s the updated dsplacemet by usg DEEP method. As show the fgure, the proposed DEEP method reduces the propagato error. 5. CONCLUSIONS To apply VSP to massve cvl structure, multple modules should be stalled a cascaded maer ad etre shape of structure ca be estmated by multplyg estmated dsplacemet from VSP. I the multplcato, however, dsplacemet estmato error ca be propagated. I ths paper, therefore, a dsplacemet estmato error back-propagato (DEEP) method, whch uses the Newto-Raphso formulato spred by the error back-propagato algorthm of the mult-layer eural etworks, for multple VSPs s proposed. I ths method, a propagato error at the last module s calculated at frst, ad the the estmated dsplacemet from VSP at each partto s updated reverse order by usg the proposed DEEP that mmzes the propagato error. To verfy the performace of the proposed method, varous smulatos have bee performed. The results show that the propagato error s sgfcatly reduced after applyg DEEP method. ACKNOWELDGEMENT Ths study was supported by the Natoal Research Foudato of Korea (NRF) ad fuded by the Korea govermet (Grat No ). Mr. Myeog s supported by Korea Mster of Mstry of Lad, Trasport ad Martme Affars (MLTM) as U-Cty Master ad Doctor Course Grat Program. REFERENCES Balageas, D., Frtze, C.P. ad Guemes, A.(eds) (2006), Structural Health Motorg, New Jersey: Joh Wley & Sos, Ic. Lee, J.J. ad Shozuka, M. (2006), Real-tme dsplacemet measuremet of a flexble brdge usg dgtal mage processg techques, Exp. Mech., 46(1), Park, J.W., Lee, J.J., Jug, H.J. ad Myug, H. (2010), Vso-based dsplacemet measuremet method for hgh-rse buldg structures usg parttog approach, NDT & E It., 43(7),

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