Fast Calibration for Robot Welding System with Laser Vision

Transcription

1 Fas Calbaon fo Robo Weldng Ssem h Lase Vson Lu Su Mechancal & Eleccal Engneeng Nanchang Unves Nanchang, Chna Wang Guoong Mechancal Engneeng Souh Chna Unves of echnolog Guanghou, Chna Absac Camea calbaon and obo hand-ee calbaon ae mpoan pas n applcaons of obos h vsons. A a o smulaneousl ca ou camea calbaon and obo handee calbaon s pesened n obo eldng ssem h lase vson. I s based on a cean elaon beeen hand-ee ma and ma of obo hand fame o obo base fame. Calbaon epemens ae pefomed n hs a usng specfcall desgned calbaon objecs. And all paamees o be calbaed ae solved ou n nonlnea leas squae opmaon mehod. 3D old coodnaes of 0 sample pons seleced fom a v-goove seam ae econsuced h he calbaon esuls. B conasng he eal coodnaes, aveage eo s 0.mm, hch s suffcen o he equemen of obo seam ackng. Keods obo eldng, camea calbaon, hand-ee calbaon, lase vson I. INRODUCION So fa, obos ae del used n eseach as ell as n ndusal poducon. When obos ae fed h vsual sensos, he can cach envonmen nfomaon hough he vsons o pefom specfc asks such as fndng, posonng and gaspng objecs. B he use of vson ssem, n ode o eale he ansfomaon fom D mage nfomaon o 3D nfomaon, he fs sep s o deemne he elaon beeen mage coodnaes and old coodnaes. hs poblem s he pocess of coodnaes calbaon and ncludes camea calbaon and obo hand-ee calbaon. Camea calbaon and hand-ee calbaon ae boh adonal poblems n obo applcaons, and vesale calbaon echnques ae pesened fo he momen[-5]. Camea calbaon s mosl based on pn-hole model, and no onl ncludes deemnng geomec and opcal camea feaues (nnsc paamees), bu also he 3D poson and oenaon of he camea elave o he old fame (ensc paamees). Man leaues have noduced mehods o calbae camea paamees[6-0]. hese mehods can be bascall soed no lnea soluon and nonlnea soluon. Lnea soluon s bef and quck, bu dsoon paamee s gnoed and pecson s no enough. So, nonlnea soluon s ofen used hen pecson s emphased[ ]. Robo hand-ee calbaon s o deemne he elave posons and oenaons of camea fame o hand fames. he geneal soluon fo hand-ee calbaon s o solve a homogeneous ansfomaon equaon as follos: AX XB () Whee X epesens he elave poson and oenaon ma of camea fame o obo hand fame, and A s ansfomaon ma of camea movemen and B s ha of obo hand movemen. A s deemned b o locaons n he camea fame and B s deemned b o obo hand posons[ 3]. In he applcaons of vson obos he camea paamees and he poson and oenaon of obo hand-ee boh need o be calbaed. Refeence [] make eensons o he sandad plane-based calbaon mehod and noduce ho o use pue anslaonal moons fo camea nnsc calbaon as ell as hand-ee calbaon. Bu hee ae o especve calbaon epemens, so much calculaon and me ae needed, and calbaon eo s cumulaed fom one epemen o he ne epemen. Paccall, n some specfc applcaons of vson obo, camea calbaon and obo hand-ee calbaon can be pefomed smulaneousl and calculaon s also geal educed. In hs pape smulaneous calbaon of camea and obo hand-ee s noduced fo he applcaon of obo eldng h lase senso. II. CALIBRAION A. Confguaon fo Lase Vson Robo Weldng Ssem In he aea of obo eldng, vson ssem s ofen used o deemne he eldng poson on okpece. Fg. shos he confguaon. Weldng och and lase vson ae gdl mouned on obo hand. Lase lgh fom he vson ssem s pojeced on eldng okpece and he nfomaon of V- goove s efleced on a lase lne. hen V-goove cene (eldng poson) can be ecogned fom he mage capued b he vson ssem. Afe he coodnaes ansfomaon of eldng poson fom mage fame o old fame, he dsplacemen of obo hand s conolled accodng o he old coodnaes of eldng poson. hen he och s /08 /$ IEEE RAM 008

2 moved fom cuen poson o he ne and eldng ask s auomacall pefomed b obo. Fg. Confguaon fo obo eldng h lase vson B. Camea Model Pnhole (pespecve) camea model s used n hs pape. Fg.. llusaes he basc geome of he camea model. o s he camea coodnae ssem. he ogn pon o s defned on he opcal cene and as s he same as he opcal as. Pon o' s he nesecon of opcal as and mage plane and he dsance beeen o and he mage plane s he focal lengh f of he camea. P s a pon n space, and p s s mage pon. Fg. Pnhole camea model Suppose, a pon n mage plane s denoed b m [, ], and a pon n old fame s denoed b M ] ae [,,. hen he homogeneous coodnaes m ~ [,,] and M ~ [,,,]. hen he elaon fom M ~ o m ~ s gven b : α c u0 ~ sm~ KM h K 0 β v , () Whee s s an aba scale faco, K s he camea nnsc paamee ma n hch ( u, v 0 0 ) s he coodnaes of camea pncpal pon, α and β ae he scale facos n and aes, and c denoes he skeness of o mage aes, and s he camea ensc paamee ma n hch ~ ae he oaon pa of he camea fame o he old fame and,, he anslaon pa. C. Hand-ee Model Suppose H s he ansfomaon ma of obo hand fame o he camea fame, 6 he obo hand fame o obo base fame, and R he camea fame o obo base fame. I s obvous ha he elaon of hese hee ma can be epessed as follos: R 6 H (3) Hee H s called hand-ee ansfomaon ma hch consss of oaon pa and anslaon pa h he same fom as ma. Snce lase vson s gdl mouned on obo hand n Fg., hand-ee ma H s a consan. D. Smulaneous Calbaon fo Camea and Hand-ee In he confguaon of obo eldng ssem shon n Fg., he base fame of obo s fed on he gound. So fo convenence, he old fame s defned as he same o he obo base fame. Fom equaon (), he follong equaon (4) s obaned: α c4 u07 α c5 u08 α3 c6 u0 α c u0 s β4 v07 β5 v08 β6 v0 β v0 7 8 ( α c4 u07 ) ( α c5 u08 ) ( α3 c6 u0 ) ( α c u0 ) ( 7 8 ) 0 ( β ) ( ) ( ) ( ) 4 v07 β5 v08 β6 v0 β v0 ( 7 8 ) 0 (4) Hee α, β, c, u 0, v 0, ~,,, ae unknon paamees, and,,,, ae knon fom specfc calbaon conol pons. In addon, accodng o he ohonomal of he oaon pa ~ n ma, he follong 6 equaons ae gven:,,, , , hus, hee ae 7 unknon paamees n all o be solved. As nonlnea equaons can be obaned fom each calbaon conol pon b equaon (4), 6 o moe calbaon conol pons, hch se up 8 o moe nonlnea equaons, ae needed o solve ou hese 7 unknon paamees. As 8 o moe nonlnea equaons ae used o solve 7 unknon paamees, hen he poblem becomes a common

3 nonlnea leas-squaes esmaon poblem ha can be solved h sandad nonlnea opmaon mehods. Gauss-Neon, Levenbeg-Maquad and quas-neon ae popula algohms fo nonlnea leas-squaes opmaon poblem[3]. Alhough he convegence of quas-neon algohm s moe effecve han he ohe o, calculaon s bg and s dffcul o modf Hesse ma. Gauss-Neon depends geal on he pecson of nal values o convege. Accodngl Levenbeg-Maquad s adoped n hs pape. As he old fame s he same h obo base fame, s obvous ha equaon (5) s concluded: R 6 H (5) hee ma s solved ou b nonlnea leas-squaes opmaon mehod, and ma 6 can be ansfomed fom he cuen oenaon quaenon o obo hand, hch can be ead ou fom he obo conolle. heefoe, he obo handee ma H s calbaed smulaneousl hen camea paamees ae calbaed as epessed b equaon (6): H (6) 6 III. EXPERIMEN ES he obo used o epemen n hs pape s a small ABB ac eldng obo and he vson ssem s Mea Lase Pobe. he confguaon s shon as Fg.. Fg.3 shos calbaon objecs hch ae o lle cubes h a hole n each. When lase lgh s pojeced o he o cubes along he dashed lne n Fg.3, a lase mage shon as Fg.4 s obaned, hch s 56 pels. Pon o 6 n Fg.3 ae calbaon conol pons, and he coespondng mage pons ae shon n Fg.4. Fg. 4 Lase mage fo calbaon objecs Image coodnaes of conol pons o 6 n Fg.4 ae eaced accodng o he follong flocha n Fg.5. Fs bnang Fg.4 a a heshold of ge value 50, and hnnng he lase lnes o keep one pel de. hen eacng end pons coodnaes of lase lnes b sucue elemens and *. Fnall sepeang he conol * pons o 6 b he coodnaes hch ae dffeen fom hose of non-conol pons. Wold coodnaes of conol pons ae ead n un fom obo conolle hen och goes o pon o 6 on calbaon objecs, especvel. he epemenal daa ae shon n able. Conol pons ABLE Coodnaes of conol pons Image coodnaes (pel) Wold coodnaes (mm) Fg.3 Calbaon objecs

4 Fg.5 Flocha of eacng mage coodnaes of conol pons In nonlnea leas-squaes opmaon, accodng o epeence and paamee anges, ake opmaon nal value as follos: 0 [ α β c u0 v ] [ ] (7) hen b Malab sofae, calbaon esuls ae obaned follong: α c u K 0 β v (8) R () H (0) Hee K and H ae fed and R vaes h dffeen posons of camea. IV. CALIBRAION ACCURACY 0 fames of pcues ee sampled fom a v-goove seam. Accodng o above calbaon esuls, mage coodnaes of he v-goove cene n he 0 fames of pcues ee conveed no 3D old coodnaes denoed b p (,, ) ( ~ 0). A he same me, n each fame of pcues, he eal old coodnaes of v-goove cene ee measued b obo conolle, hch as denoed b p (,, ) ( ~ 0). Compang p h p, and calculang aveage eo h equaon (), 0.mm as obaned fom he 0 sampled pcues, hch s suffcen fo obo seam ackng. 0 [ ] e ( ) ( ) ( ) N () V. CONCLUSION Camea calbaon and hand-ee calbaon ae ke poblems n he applcaons of vson obos. In hs pape, a mehod o smulaneousl calbae camea paamees and obo hand-ee ma s pesened. I s based on a specal elaon beeen hand-ee ma and ma of obo hand fame o base fame. Calculaon esuls of camea paamees and hand-ee ma ae obaned a one me. Epemens ae made o es he mehod, and he esuls sho ha he mehod s coec and feasble, and he calbaon pecson mees he need of obo seam ackng. Besdes, calbaon conol pons and opmaon algohm ae o mpoan facos o affec epemen esuls, so mpovng algohm and selecng moe conol pons h moe pecse coodnaes can lead o bee epemen esuls. REFERENCES [] R. Y. SAI, A Vesale Camea Calbaon echnque fo Hgh-Accuac 3D Machne Vson Meolog Usng Off-he-Shelf V Cameas and Lenses, IEEE, Jounal of obocs and auomaon, RA-3(4), (87). [] S. Rem, M. Dhome, J.M Laves and N. Dauche, Hand- Ee Calbaon, Inellgen Robos and Ssems,, (7). [3] L. M. Song, M. P. Wang, L. Lu and H. J. Huan, Hgh pecson camea calbaon n vson measuemen, Opcs & Lase echnolog, 3(7),43-40 (007). [4]Z. Y. Zhang, A fleble ne echnque fo camea calbaon, IEEE ansacons on Paen Analss and Machne Inellgence, (), (000). [5] S. F. Lu, D. W. Lu, J. L, e al, Smooh mehod fo oenaon coodnae of auonomous moble obo, ansacons of he Chnese Soce of Agculual Engneeng, 35(), 6- (004). [6] Y. Fang, L.Z. Gao and Z. H. Ln, he eseach on calbaon mehod of camea nnsc facos n he nellgen CMM nspecon ssem, Robo, 0(), 48-5 (8). [7] Z.Y. Zhang, Camea calbaon h one-dmensonal objecs, IEEE ansacons on Paen Analss and Machne Inellgence, 6(7), 8-8 (004). [8] J. Ean, R.E. Poppele, A sngle-camea mehod fo hee-dmensonal vdeo magng, Jounal of Neuoscence Mehods, 0, (00). [] X. Q. Meng, Z.Y. Hu, A ne eas camea calbaon echnque based on ccula pons, Paen Recognon, 36,55-64 (003).

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