GENERATION OF ROBUST ERROR RECOVERY LOGIC IN ASSEMBLY SYSTEMS USING MULTI-LEVEL OPTIMIZATION AND GENETIC PROGRAMMING

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1 Prceedngs f DETC 00 ASME 000 Desgn Engneerng Techncal Cnferences and Cmputers and Infrmatn n Engneerng Cnference Baltmre, Maryland, September 0-3 DETC000/CIE-4639 GENERATION OF ROBUST ERROR RECOVERY LOGIC IN ASSEMBLY SYSTEMS USING MULTI-LEVEL OPTIMIZATION AND GENETIC PROGRAMMING Cem M. BAYDAR (cbaydar@umch.edu) Kazuhr SAITOU (kazu@umch.edu) Department f Mechancal Engneerng and Appled Mechancs Unversty f Mchgan Ann Arbr, MI , USA ABSTRACT Autmated assembly lnes are subject t unexpected falures, whch can cause cstly shutdwns. Generally, these errrs are handled by human experts r lgc cntrllers. Hwever, these cntrller cdes are based n antcpated errr scenars and are defcent n dealng wth unfreseen stuatns. In ur prevus wrk (Baydar and Satu, 000a), an apprach fr the autmated generatn f errr recvery lgc was dscussed. The methd s based n three-dmensnal gemetrc mdelng f the assembly lne t generate errr recvery lgc n an ff-lne manner usng Genetc Prgrammng. The scpe f ur prevus wrk was fcused n fndng an errr recvery algrthm frm a predefned errr case. Hwever due t the gemetrcal features f the assembly lnes, there may be cases whch can be detected as the same type f errr by the sensrs. Therefre rbustness must be assured n the sense f havng a cmmn recvery algrthm fr smlar cases durng the recvery sequence. In ths paper, an extensn f ur prevus study s presented t vercme ths prblem. An assembly lne s mdeled and frm the gven errr cases ptmum way f errr recvery s nvestgated usng mult-level ptmzatn. The btaned results shwed that the nfrastructure s capable f fndng rbust errr recvery algrthms and mult-level ptmzatn prcedure mprved the prcess. It s expected that the results f ths study wll be cmbned wth the autmatc errr generatn, resultng n effcent ways t autmated errr recvery lgc synthess. INTRODUCTION Errr recvery plays an mprtant rle n autmated assembly systems snce these systems are pen t unexpected falures, whch can halt ther peratn. Generally, recvery algrthms fr such falures are antcpated by n-lne nvestgatn f the assembly lne by the experts, durng the desgn f assembly lnes. Anther apprach s usng Prgrammable Lgc Cntrller (PLC) cdes, whch are als manually cded, based n antcpated scenars. Hwever predctn f all scenars s mpssble, therefre these methds are nt flexble t slve the majrty f the prblems. An apprach f usng ff-lne synthess f errr dagnss and recvery lgc based n the three-dmensnal gemetry mdel f an entre assembly lne was dscussed n ur prevus wrk (Baydar and Satu, 000a). The scpe f ths wrk was fndng an errr recvery algrthm frm a predefned errr case. The system uses ne f the cmmercal assembly lne smulatn sftware (Wrkspace, 998), whch s cupled wth a develped cmputer prgram, t btan errr recvery lgc usng Genetc Prgrammng (Kza, 99). Prevus results shwed that, the system s capable f generatng recvery lgc fr cllsn errrs frm varus errr cases ndvdually. Hwever t des nt prvde rbust recvery lgc fr multple errr cases. The wrk dscussed n ths paper s an extensn f ur prevus study and amed t recver ths defcency. The fllwng sectn cntans nfrmatn n the prevus wrk dne n errr dagnss, hghlghtng the mprtance f havng a rbust recvery lgc as well as a bref summary n ur prevus apprach. Crrespndng authr Cpyrght (C) 000 by ASME

2 PREVIOUS WORK Errr dagnss s the key step befre determnng the recvery prcess. Cmplete dagnss must be perfrmed fr the effcent errr recvery. The establshed technques f Falure Mde and Effect Analyss (FMEA), Fault Tree Analyss (FTA) and Event Tree Analyss (ETA) have been n use fr many years (Khdabandehl, 997). FMEA s used t examne all pssble cmpnent falures and t dentfy ther frst rder and fnal effects n the system. FTA and ETA may be appled at varus levels fr examnng the errrs and falures n a system. FTA s a tp-dwn technque fr assessng the way n whch several falures can cause a sngle utcme r a system falure. ETA s a frward technque, whch may be used t examne the prpagatn f an ntatng event (r falure) wth the presence f a number f ther events, falures, faults r cndtns. Abu-Hamdan and El-Gzawy develped a knwledgebased system fr mntrng, dagnss and errr recvery fr the flexble assembly peratns (Abu-Hamdan and El-Gzawy, 994). The cntrl system cnssts f a dstrbuted netwrk f ntellgent sensng, actn and reasnng agents. Fr errr dagnss, an AND/OR type falure tree s cnstructed. The errr type s the gal nde (rt f the tree at the tp level). The errr causes are the sub-gals f the tree. The facts f the errrs (.e. sensr falure) are represented as the leaves f the sub-gals. The use f fault trees as a database f run-tme fault detectn s dscussed n (Vsnsky et al., 994). An expert system s embedded t the system t mntr the faults and mantan the prbablty f falure fr each nde wthn the tree. Tw fnte state machnes (FSM) are used. The User/executve FSM handles the nteractn between the user and the rbt whle; the Crtc FSM s respnsble fr the safety f the rbt system. Other prpsed tw methds are knwn as Falure Reasn Analyss (FRA) and Multple Outcme Analyss (MOA), whch are dscussed n (Hardy et al., 989). FRA s based n fndng an explanatn f the falure and tres t derve a plan fr recvery by usng a falure tree. The tree cntans actn ndes and falure ndes. The data abut the type f the errr are cllected frm the tree and passes t a planner mdule. In MOA, the states f the wrkcell are n cnsderatn. Detectng the devatn f the states frm the expected nes reveals the fact f falure. After an errr s detected, avalable data and gathered data are used t cnclude a predefned recvery strategy. All f the systems dscussed abve are fcused n dagnss and recvery by usng expected errr cases. Hwever, due t the gemetrcal nature f the assembly lnes, there can be errrs, whch have the same errr type (.e. cllsn) but need t be recvered by usng a prcedure dfferent frm the antcpated case. Fr example a cllsn errr can be ccurred n many dfferent ways durng an assembly prcess. The dagnss f ths falure wth the develped systems dscussed abve can reveal the cause f the errr crrectly. Hwever t may nt be pssble t detect the exact lcatn f the cllsn, whch s very mprtant fr the recvery prcedure. If the lcatn s dfferent frm the antcpated place, the mplemented recvery lgc algrthm may nt be useful. Therefre rbust ways f recvery lgc must be nvestgated. In ur prevus study (Baydar and Satu, 000a), a pssble way f errr recvery n ff-lne manner was dscussed. A sample assembly lne was mdeled three-dmensnally usng a cmmercal sftware package. The archtecture f the system s summarzed n Fgure. The system uses a cmmercal sftware package called Wrkspace (Wrkspace, 998). A sftware mdule was develped and cupled wth the Wrkspace. Ths mdule s respnsble frm the generatn f recvery lgc usng Genetc Prgrammng (Kza, 99). The generated prgrams are tested wth the cmmercal sftware and evaluated based n ther perfrmance. After that, evlutn prcess takes place accrdng t the perfrmance f each prgram. Case studes demnstrated that the develped system s effcent t fnd the ptmum recvery lgc frm a gven cllsn case. Fr the errr recvery language, KAREL Rbt Language was selected. The cmmands fr ths language are used t manpulate the rbt fr the recvery prcess. Fgure.: System Archtecture. Cpyrght (C) 000 by ASME

3 The man dsadvantage f the prevus system s due t ts nsuffcency t generate rbust recvery lgc frm multple errr cases. As t s stated befre, a part presentatn errr can be resulted n a cllsn errr n dfferent ways at dfferent places n three-dmensnal space durng the assembly prcess. Therefre, a rbust recvery algrthm shuld be nvestgated fr the recvery frm dfferent cllsn cases. PROPOSED APPROACH Genetc prgrammng s an extensn f genetc algrthms, amed t prduce useful cmputer prgrams autmatcally t slve a specfc prblem. The term Genetc Prgrammng was frst ntrduced by Kza (Kza, 99). It uses the same wrkng prncples f Genetc algrthms. Genetc algrthms were frst ntrduced by Hlland (Hlland, 975). They brrw ther termnlgy and wrkng prncples frm the blgy. Bascally, prblem varables are cded nt strngs lke chrmsmes n blgcal systems. Each strng s a member f the ppulatn, representng a slutn fr the prblem. The am s maxmzng a ftness functn based n the defned bjectve f the prblem. Tw basc peratrs are used fr the evlutn prcess. The frst peratr, whch s called crssver, s respnsble fr takng tw strngs as parents and cmbnng them t prduce better strngs as chldren. The secnd peratr s called mutatn whch has the advantage f ntrducng sme dversty t the ppulatn by changng the values n a strng randmly. Genetc prgrammng requres effcent representatn f the search space wth the defntn f several crtcal varables fr the ppulatn. As n ur prevus study, a chrmsme structure s defned fr each lne wthn a recvery algrthm. The maxmum number f lnes s lmted t 0. The number f members n the ppulatn s determned as 00. The crssver prbablty s taken as 0.9 and t s drectly prprtnal wth the ftness value f the recvery algrthm. Tw parents are selected based n ther ftness value and the crssver peratn takes place by lcatng a crssver pnt between the prgrams. In rder t ntrduce varance t the ppulatn, dynamc mutatn was appled wth a prbablty f changng between 0.05 and 0.05 dependng n the nature f the ppulatn. Durng ths study as n ur prevus wrk part placement errrs, whch result n cllsn, are studed. Cllsn calculatns are perfrmed by usng the cmmercal sftware package s abltes. The bjectve s defned as t mnmze the part placement errr between the fnal pstn and ts desred pstn n the fxture. A dstance functn between the recvered pstn and the desred pstn s used fr the bjectve functn. Therefre the prblem s a sngle bjectve ptmzatn prblem wth the bjectve functn: Durng the recvery prcedure, tlerances fr the fnal pstn f the wrkpece are determned as 5 mm fr a successful assembly peratn n all dmensns. x x 5 () y y 5 (3) z z 5 (4) The prblem s handled n tw phases: Slvng a relaxed prblem fr n dfferent errr states t reach an ntermedate state. Frm the btaned ntermedate state, slvng the rgnal prblem t reach a desred state. At frst, several cllsn cases are slved n parallel t fnd a recvery algrthm, whch enables reachng a cmmn state fr all f the cases. Fr ths step, the same bjectve functn s used but ths tme the cnstrants are relaxed frm 5 mm. t 5 mm. The reasn fr relaxng the cnstrants t 5 mm s t fnd a cmmn pnt near t the desred lcatn. A feasble wrkng envelpe s defned arund the fxture fr the rbt mvement. It s amed that ths knd f mult-level mplementatn makes the prblem much easer t reach an ntermedate state when the prblem s relaxed. In the secnd step, after the ntermedate state s btaned a new prblem f recvery prcedure s defned by takng ths ntermedate state as the ntal state and the desred state as the gal state. Cnstrant values are als restred t 5 mm. Cubcal wrkng envelpe s reduced t half sze and nvestgatn n a secnd errr recvery algrthm s dne. Fnally tw errr recvery algrthms are cncatenated t btan rbust recvery lgc fr n dfferent number f errr cases. The cmplete prcedure s summarzed n Fgure. Mnmze ( x x ) + ( y y) + ( z z ) () Fgure.: Mult-level ptmzatn Prcedure. 3 Cpyrght (C) 000 by ASME

4 The advantages f usng a mult-level ptmzatn prcedure are as fllws: Tryng t slve a relaxed prblem wll eventually result n less number f teratns than the sngle-step ptmzatn case snce an ntermedate state s defned; there wuld be less number f functn evaluatns. The recvery algrthms, whch are btaned fr reachng the fnal state frm the ntermedate state can be stred as sub-rutnes and may be used fr the recvery f smlar errr cndtns later. A ftness functn s defned ndvdually fr all errr cases. These functns are taken as the nverse f the bjectve functn as ndcated thrugh Eq. (5) and (6) where n s the number f errr cases. Therefre the prblem s cnverted nt a maxmzatn prblem. =,,..., n (5) f = (6) ( x x ) + ( y y ) + ( z z ) The verall ftness f a recvery prgram s defned as ts average ftness mnus the abslute value f the devatn between ths average value and the mnmum ftness value amng the n cases as t s shwn n Eq. (7). The varables w and w determne the weght f each term. By usng ths knd f defntn, perfrmance varance fr recvery prgram s penalzed and rbustness s tred t be assured. f = (8) ( x x ) + ( y y ) + ( z z ) Same prcedure s appled fr the secnd part f the prblem. The btaned recvery algrthm fr the secnd part s cmbned wth the ne btaned n the frst part and rbust recvery lgc s btaned. In the Genetc Prgrammng part, same ppulatn structure frm ur prevus study s used. As an mprvement frm ur prevus study, durng the evlutn prcess eltsm (Gldberg, 989) s als ntrduced. The recvery prgrams are ranked based n ther ndvdual case perfrmance. After that, best prgrams fr each case are cmbned t get better slutns n the prblem dman. The case studes shwed that ths type f mplementatn ncreased the perfrmance f the system. It was bserved that, there culd be recvery prgrams, whch perfrm effcently fr nly small prtn f the errr cases and cmbnatn f these prgrams wuld result n better prgrams fr generatn f the rbust recvery. The mplemented system s tested n several case studes. The results demnstrated that the system s verall perfrmance s effcent t fnd rbust recvery lgc. CASE STUDIES A mdel assembly lne s cnstructed by usng Wrkspace smulatn sftware and the detals are gven n (Baydar and Satu, 000a). An IRB6000 type ndustral rbt s used fr the part placement prcedure durng the assembly prcess. Fgure.3 shws the mdel f the assembly lne and the desred pstn f the wrkpece n the fxture. f f f = w w ABS mn f (7) n n There can be cases where the maxmum varance s ccurred between the average ftness and the maxmum ftness. Hwever, thse types f cases are nt penalzed t keep the better slutns n the search space. Detaled nfrmatn n the evlutnary cdng f the prblem s gven n (Baydar and Satu, 000b). The frst step f ptmzatn s cmpleted when a rbust recvery algrthm s fund. Ths recvery algrthm makes all f the cases t reach the ntermedate state. After that, the prblem s renewed. The btaned ntermedate state s defned as the nly errr case t be recvered and the fnal state s taken as the gal state. At ths stage, ne ftness functn s defned such as n Eq. (8). Fgure.3: Mdeled Assembly Lne. 4 Cpyrght (C) 000 by ASME

5 In the fllwng case studes, sx dfferent cllsn pnts are generated randmly between the wrkpece and the fxture. These sx errr cases are studed n tw dfferent case studes. In case studes, the assumptn s made n that the part s held n the grpper after the cllsn and repstnng can be detected prperly. Case Study : Three cllsn pnts (n=3) are studed t fnd a rbust recvery algrthm. Tw f these pnts are taken frm ur prevus study. Fgures 4-6 shw thse cllsn pnts. At frst the frst level f ptmzatn s accmplshed. Ths s cmpleted n 0 generatns (cuntng the ntal randm generatn as the frst generatn). Fgure.6: 3 rd Cllsn Pnt n Case Study. The pstnal errrs after the 0 th generatn at the ntermedate state are gven n the fllwng table. Nte that these values are btaned wth the relaxed cnstrants. Table.: Pstnal Errrs at the Intermedate State. Crdnate: Errr (mm): X: Y: Z: 5 Fgure.4: st Cllsn Pnt n Case Study. After reachng the ntermedate state, secnd level f ptmzatn s started by regeneratng the ppulatn. After the 7 th generatn a lcal ptmum s fund. Table. shws the fnal placement errrs fr the fnal state. Nte that n ths case rgnal cnstrant values are restred. Table.: Pstnal Errrs at the Fnal State. Crdnate: Errr (mm): X: 5 Y: 3 Z: 3 Fgure.5: nd Cllsn Pnt n Case Study. Ttally, 7 generatns are needed t reach the rbust recvery algrthm and t s cmpsed f 6 lnes between the BEGIN and END cmmand. Fr the frst stage f the ptmzatn the recvery algrthm cntans lnes f cde. In the secnd stage, 4 addtnal lnes are added t the cde. The recvery algrthm s gven belw. 5 Cpyrght (C) 000 by ASME

6 ROUTINE RecveryCase BEGIN -- Ths prtn f the cde belw belngs t the frst level Mve T POS( -798, -794, -09, 50, 50, 0,'RUFB') Mve T POS( -704, -708, -970, 50, 80, 0,'RUFB') --Ths prtn f the cde belw belngs t the secnd level Mve T POS( -78, -66, -08, 40, 0, 0,'RUFB') Mve Away -5 Mve T POS( -78, -66, -08, 40, 0, 0,'RUFB') Mve T POS( -7, -694, -990, 90, 90, 0,'RUFB') End RecveryCase In Table 3 the hstry f the bjectve functn s gven. It s bserved that a fluctuatn ccurred between the 0 th and th generatn. The reasn s that the secnd stage f the ptmzatn s ntated at the th generatn wth a new generatn f ppulatn. Ths can be seen frm Fgure.7 als. Nte that the ftness functn s nversely prprtnal wth the bjectve functn therefre t s ncreasng thrughut the study. Ftness Value.80E-0.60E-0.40E-0.0E-0 Wrst.00E-0 Best 8.00E-0 Average 6.00E E-0.00E E Generatn Number Fgure.7: Optmzatn Prgress f the st Case Study. Table.3: Change n the Objectve Functn. Generatn Objectve Functn Case Study : A dfferent set f three pnts s selected at ths tme t test the perfrmance f the system. These three cllsn pstns are gven n Fgures 8-0. Ths tme t tk 7 generatns t reach the ntermedate state. The pstnal errr n each dmensn at the ntermedate state s gven n the Table.4 belw. Table.4: Pstnal Errrs at the Intermedate State. Crdnate: Errr (mm): X: 9 Y: 9 Z: 8 The perfrmance f the rbust recvery algrthm s tested n each errr case ndvdually and t s fund that the prcedure s wrkng prperly. Fgure.8: st Cllsn Pnt n Case Study. 6 Cpyrght (C) 000 by ASME

7 ROUTINE Recvery BEGIN -- Ths prtn f the cde belw belngs t the frst level Mve Relatve VEC (0, -70, -8) Mve Near POS (-70, -655, -006, 50, 0, 0,'RUFB') By 43 --Ths prtn f the cde belw belngs t the secnd level Mve Near POS (-733, -730, -005, 80, 0, 0,'RUFB') By -74 Mve Near POS (-73, -688, -99, 70, 0, 0,'RUFB') By -5 Mve T POS (-7, -70, -986, 90, 90, 0,'RUFB') END Recvery Table.6: Change n the Objectve Functn. Fgure.9: nd Cllsn Pnt n Case Study. Generatn Objectve Functn Fgure.0: 3 rd Cllsn Pnt n Case Study. After ths pnt, secnd level f ptmzatn s ntated. The secnd state s reached the lmts f the fnal state n 4 generatns. The fnal placement errrs are gven n the fllwng table. Table.5: Pstnal Errrs at the Fnal State. Crdnate: Errr (mm): X: 5 Y: 5 Z: Ttally generatns are requred t gather the rbust recvery cde. Tw recvery algrthms are cmbned and a rbust recvery fr these three cases s btaned. The fnal algrthm s cmpsed f 5 lnes between the BEGIN and END cmmands as gven belw. The frst lnes are frm ntal state t ntermedate state, whle the rest f them are fr the recvery frm ntermedate state t fnal state. The change n the bjectve functn s gven n Table 6. The change n the bjectve functn frm ntermedate state t fnal state s smth n ths case. Hwever, as t can be seen frm Fgure. the average ftness f the members drpped at the 8 th generatn snce a new ppulatn s generated fr the secnd level ptmzatn prcess. It s realzed that the average value ncreased between 8 th and 0 th generatns and ths helped the best ftness t ncrease n th generatn. It s nted that the secnd level f ptmzatn cnverged n 4 generatns n ths case. Durng the case studes, three errr states are cnsdered fr each case study. Hwever the number f cases n the ntal set can be ncreased t btan rbust recvery lgc fr n number f cases. Ftness Value.60E-0.40E-0.0E-0.00E E E E-0.00E E Generatn Number Wrst Best Average Fgure.: Optmzatn Hstry f the nd Case Study. 7 Cpyrght (C) 000 by ASME

8 DISCUSSIONS AND FUTURE WORK In ths paper an apprach fr the generatn f rbust recvery algrthms s presented. The mplemented system s an extensn n the nfrastructure that was develped n ur prevus study. Snce part msplacement errrs are wdely ccurred durng assembly prcess, recvery fr the cllsn errrs s studed. Hwever, the system s nt lmted t the cllsn errrs nly and ther errr types can be studed t recver n the future. The prcedure nvlves mult-level ptmzatn prcess cupled wth genetc prgrammng. In the frst step, several errr states are studed n parallel t fnd a cmmn recvery algrthm fr the relaxed prgram. After that n the secnd stage the slutn f the relaxed prblem s taken as the nly state t be recvered fr the rgnal prblem. Fnally the recvery algrthms fr bth stages are cmbned t get a rbust recvery algrthm. It s bserved that ths prcedure: Smplfes the prblem f slvng dfferent errr states. Tryng t slve a relaxed prblem wll eventually result n less number f teratns than the sngle-step ptmzatn case. Therefre the cmputatn speed wuld be ncreased. Gldberg D., Genetc Algrthms n Search, Optmzatn and Machne Learnng, Addsn-Wesley, Readng, MA, 989. Kza J. R., Genetc Prgrammng: On the Prgrammng f Cmputers by Natural Selectn, MIT Press, Cambrdge, MA., 99. Khdabandehl K., Analyses f Rbt Systems usng Fault and Event Trees: Case Studes, Relablty Engneerng and System Safety 53, 47-64, 996. Hardy N., Barnes D., Lee M., Autmatc Dagnss f Task Faults n Flexble Manufacturng Systems, Rbtca 7, 5-35, 989. Hlland J., Adaptatn n Natural and Artfcal Systems, MIT Press, Cambrdge, MA, 975. Vsnsky M.L., Cavallar J.R., Walker I.D, Expert System Framewrk fr Fault Detectn and Fault Tlerance n Rbtcs, Cmputers n Electrcal Engneerng 0(5), 4-435, 994. Wrth R., Berthld B., Kramer A., Peter G., Knwledge Based Supprt f System Analyss fr the Analyss f Falure Mdes and Effects, Engneerng Applcatns n Artfcal Intellgence 9(3), 9-9, 996. Wrkspace v.4 Educatnal User Gude Manual, 998. Leads t a rbust errr recvery algrthm, whch can be used fr dfferent errr states (.e. cllsn errrs ccurred at dfferent pnts n an assembly lne). Althugh three states (n=3) are cnsdered fr each case study, ths prcedure can be appled t larger number f states. Due t ts gemetrcal features, each assembly lne has dfferent number f crtcal states t be cnsdered. Therefre errr samplng by usng the statstcal mdel f the dmensnal and functnal errrs must be nvestgated fr each lne n rder t fnd rbust recvery algrthms fr each errr case. The future studes are amed n ths type f errr case analyss by usng Mnte-Carl methd. REFERENCES Abu-Hamdan M. G., El-Gzawy A. S., Cmputer Aded Mntrng System fr Flexble Assembly Operatns, Cmputers n Industry, Vl. 34, pp. -0, 997. Baydar C., Satu K., Off-lne Errr Recvery Lgc Synthess n Autmated Assembly Lnes by usng Genetc Prgrammng, 000 Japan-USA Sympsum n Flexble Autmatn, 000a. Baydar C., Satu K., A Genetc Prgrammng Framewrk fr Errr Recvery n Assembly Systems, Genetc and Evlutnary Cmputatn 000 Cnference, Las Vegas, Nevada, 000b. Brnyjlfssn S., Arnstrm A, Errr Detectn and Recvery n Flexble Assembly Systems, The Internatnal Jurnal f Advanced Manufacturng Technlgy, Vl.5, pp. -5, Cpyrght (C) 000 by ASME