A Neural Network Approach for Inverse Kinematic of a SCARA Manipulator

Transcription

1 Itertl Jurl f Rbts d Autmt (IJRA) Vl N Mrh 5~6 ISSN: A Neurl Netwrk Arh fr Iverse Kemt f SCARA Multr Phd Jh BB Bswl Dertemet f Idustrl Desg Ntl Isttute f Tehlg Rurkel 7698 Id Artle If Artle hstr: Reeved M 5 Revsed J Aeted J 5 Kewrd: D-H Prmeters Frwrd Kemts Iverse Kemts MLP Neurl Netwrk SCARA Multr ABSTRACT Iverse kemt s e f the mst terestg rblems f dustrl rbt The verse kemts rblem rbts s but the determt f jt gles fr desred Crtes st f the ed effetrit mrses f the mutt eed t fd the jt gles fr gve Crtes st d rett f the ed effetrs t trl rbt rm There s uque slut fr the verse kemts thus eessttg lt f rrte redtve mdels frm the sft mutg dm Artfl eurl etwrk s e suh tehque whh be gfull used t eld the etble results Ths er rses strutured rtfl eurl etwrk (ANN) mdel t fd the verse kemts slut f -df SCARA multr The ANN mdel used s mult-lered eretr eurl etwrk (MLPNN) where grdet deset te f lerg rules s led A ttemt hs bee mde t fd the best ANN fgurt fr the rblem It s fud tht mult-lered eretr eurl etwrk gves mmum me squre errr Crght Isttute f Adved Egeerg d See All rghts reserved Crresdg Authr: Phd Jh Dertemet f Idustrl Desg Ntl Isttute f Tehlg Rurkel 7698 Odsh Id Eml: jh_7@htmlm INTRODUCTION The rbt multr s msed f serl h f rgd lks eted t eh ther b revlute d/r rsmt jts Eh rbt jt lt s usull defed reltve t the eghburg jt The relt betwee suessve jts s tg hmgeeus trsfrmt mtr tht hs rett d st dt f rbts Rbt trl ts re eeuted the jt rdtes whle rbt mts re sefed the Crtes rdtes Cvers f the st d rett f rbt multr ed-effetrs frm Crtes se t jt se s lled s verse kemts rblem Ths s f fudmetl mrte lultg desred jt gles fr rbt multr desg d trl I mst rbt lts the desred sts d retts f the ed effetrs re sefed b the user Crtes rdtes The rresdg jt vlues must be muted t hgh seed b the verse kemts trsfrmt [] Fr multr wth degree f freedm t stt f tme the jt vrble s deted b = (t) = d st vrbles b j = (t) j = m The relts betwee the ed-effetrs st (t) d jt gle (t) be rereseted b frwrd kemt equt ( t) f ( ( t)) () Where f s ler tuus d dfferetble fut Jurl hmege: htt://esjurlm/le/deh/ijra

2 IJRA ISSN: O the ther hd wth the desred ed effetrs st the rblem f fdg the vlues f the jt vrbles s verse kemts whh be slved b ( t) ' f ( ( t)) () Iverse kemts slut s t uque due t ler uert d tme vrg ture f the gverg equts [] The dfferet tehques used fr slvg verse kemts be lssfed s lgebr gemetr d tertve The lgebr methds d t gurtee lsed frm sluts I se f gemetr methds lsed frm sluts fr the frst three jts f the multr must est gemetrll The tertve methds verge t l sgle slut deedg the strtg t d m t wrk er sgulrtes[] [] The frwrd kemt equts lws hve uque slut d the resultg Neurl et be used s strtg t fr further refemet whe the multr des beme vlble Artfl eurl etwrk esell MLP (mult-lered eretr) s used t ler the frwrd d the verse kemts equts f fve degrees freedm (DOF) rbt rm [] Ths usuervsed methd lers the futl reltsh betwee ut (Crtes) se d utut (jt) se bsed lled dtt f the mg b usg the multr tself uder jt trl d dtg the slut bsed mrs betwee the resultg lts f the multr s ed effetrs Crtes se wth the desred lt [5] The smult d mutt f verse kemts usg multler eretr eurl etwrk s rtulrl useful where less mutt tmes re eeded suh s rel-tme dtve rbt trl [6] If the umber f degrees f freedm reses trdtl methds wll beme mre mle d qute dffult t slve verse kemts [7]M reserh trbuts hve bee mde relted t the eurl etwrk-bsed verse kemts slut f rbt multrs [8] The reset wrk rses verse kemts sluts bsed strutured MLP tht be tred qukl Althugh the use f ANN s t ew the feld f mult-bjetve d NP-hrd rblem t rrve t ver resble tmed slut the mult lered eurl etwrk (MLPNN) hs t bee tred t slve verse kemts rblem wth -DOF multr MLP eurl etwrk s used t fd verse kemts slut whh elds multle d rese sluts wth etble errr d re sutble fr rel-tme dtve trl f rbt multrs [9] The stud f revus wrk shws tht the mst f the reserhers [] d []hve dted methds lke ANN ANFIS et fr smle rblem The fetures f MLPNN re fud qute mthg d hee sutble fr the reset rblem hvg mlet d vlvg multle rmeters Therefre the m m f ths wrk s fused mmg the me squre errr f the eurl etwrk-bsed slut f verse kemts rblem The result f eh etwrk s evluted b usg dret kemts equts t bt frmt but ther errr I ther wrds the gles bted fr eh jt re used t mute the Crtes rdte fr ed effetr The trg dt f eurl etwrk hve bee seleted ver resel Esell ulered dt eh eurl etwrk hve bee hse d used t bt the trg set f the lst eurl etwrk KINEMATIC MODELING OF SCARA MANIPULATOR The Devt-Hrteberg (D-H) tt d methdlg re used ths set t derve the kemts f rbt multr The rdte frme ssgmet d the DH rmeters re deted Fgure d lsted Tble resetvel where t reresets the ll rdte frmes t the fve jts resetvel reresets the ll rdte frme t the ed-effetr where θ reresets rtt but the Z-s α rtt but the X-s trst lg the Z-s d trst lg the X-s Sl Tble The D-H Prmeters (degree) d (mm) (mm) (degree) θ =± =5 θ =± =5 8 d =5 θ d =5 A Neurl Netwrk Arh fr Iverse Kemt f SCARA Multr (Phd Jh)

3 ISSN: IJRA Vl N Mrh : The trsfrmt mtr A betwee tw eghburg frmes O d O s eressed equt () s Fgure D-H frmes f the SCARA rbt A = s s s s s s s d () B substtutg the D-H rmeters Tble t equt () the dvdul trsfrmt mtres A t A be bted d the geerl trsfrmt mtr frm the frst jt t the lst jt f the multr be derved b multlg ll the dvdul trsfrmt mtres( T ) A A A A T () Where ) ( reresets the st d ) ( ) ( ) ( d reresets the rett f the ed-effetr The rett d st f the ed-effetr be lulted terms f jt gles d the D-H rmeters f the multr re shw fllwg mtr s: d d s s s s (5) t t s (6)

4 IJRA ISSN: s s s t t (7) d d (8) s t (9) s It s bvus frm the reresett gve equts (7) thrugh (9) tht there est multle sluts t the verse kemts rblem The bve dervts wth vrus dts beg tke t ut rvde mlete ltl slut t verse kemts f rm S t kw whh slut hlds gd t stud the verse kemts ll jts vrbles re bted d mred usg frwrd kemts slut Ths ress s bee led fr d d t hse the rret slut ll the fur sets f ssble sluts (jt gles) lulted whh geerte fur ssble rresdg sts d retts usg the frwrd kemts MULTI-LAYERED PERCEPTRON NEURAL NETWORK APPLICATION FOR SCARA MANIPULATOR It s well kw tht eurl etwrks hve the better blt th ther tehques t slve vrus mle rblems Iverse kemts s trsfrmt f wrld rdte frme (X Y d Z) t lk rdte frme ( d d ) Ths trsfrmt be erfrmed ut/utut wrk tht uses ukw trsfer fut MLP eurl etwrk's eur s smle wrk elemet d hs ll memr A eur tkes mult-dmesl ut d the delvers t t the ther eurs rdg t ther weghts Ths gves slr result t the utut f eur The trsfer fut f MLP tg the ll memr uses lerg rule t rdue reltsh betwee the ut d utut Fr the tvt ut tme fut s eeded Cet weghts Bs Iut P P d P Outut d Iut Ler Hdde Ler Hdde Ler Outut Fgure Mult-lered eretr eurl etwrk struture We rse the slut usg mult-lered eretr wth bk-rgt lgrthm fr trg The etwrk s the tred wth dt fr umber f ed effetr sts eressed Crtes A Neurl Netwrk Arh fr Iverse Kemt f SCARA Multr (Phd Jh)

5 56 ISSN: rdtes d the rresdg jt gles The dt sst f the dfferet fgurts vlble fr the rm A blk dgrm f the struture s shw Fgure The sgls O j re reseted t hdde ler eur the etwrk v the ut eurs Eh f the sgls frm the ut eurs s multled b the vlue f the weghts f the et w j betwee the resetve ut eurs d the hdde eur The etwrk uses lerg mde whh ut s reseted t the etwrk lg wth the desred utut d the weghts re djusted s tht the etwrk ttemts t rdue the desred utut Weghts fter trg t megful frmt wheres befre trg the re rdm d hve meg Net ut f hdde eurs (fr k uts) = k w h j j j () The utut O mj f hdde eur s fut f ts et ut s desrbed equt () The sgmd fut s: Outut mj h e () Oe the ututs f the hdde ler eurs hve bee lulted the et ut t eh utut ler s lulted smlr mer s equt () f ' ( )( d m ) () ( )( d ) () m m m Where d s the trget r desred vlue d O m s the tul vlue frm utut eur fter gg thrugh the feed frwrd lult The errr lult ws mlemeted eur-b-eur bss ver the etre set (eh) f tters Ths errr vlue δ ws used t erfrm the rrte weght djustmets f the weght et betwee the utut ler d hdde ler kl f '( ) w ( ) w h h lh l h h lh l l l kl () Where δ h the errr vlue f the hdde ler s δ l s the errr vlue f the utut ler O h s the utut f the sgmd fut d W lh s the et weghts betwee the utut d hdde lers The weght hges were lulted rdg t equt () w( ld) w( ew) [ w( ld)] (5) The m f the trg hse s t mme ths verge sum squred errr ver ll trg tters The seed f vergee f the etwrk deeds the trg rte d the mmetum ftr α I ths wrk tw hdde ler eurl etwrk wth three utsp P d P d fur ututs θ θ d d θ ws tred usg the bk-rgt lgrthm desrbed erler lg trjetr f the edeffetr the - le RESULTS AND PERFORMANCE ANALYSIS The rsed wrk s erfrmed the Mtlb Neurl Netwrks Tlb I ths wrk the trg dt sets were geerted b usg equts () thrugh (9) A set f dt ws frst geerted s er the frmul fr the ut rmeter P P d P rdtes mm These dt sets were the bss fr the trg evlut d testg the MLP mdel Out f the sets f dt 9 were used s trg dt d were used fr testg fr MLP s shw Tble The fllwg rmeters were tke: IJRA Vl N Mrh : 5 6

6 IJRA ISSN: Tble Cfgurt f MLPNN Sl Prmeters Vlues tke Lerg rte Mmetum rmeter Number f ehs Number f hdde lers 5 Number f uts 6 Number f utut 7 Trget dtsets 8 Testg dtsets 9 9 Trg dtsets Bk-rgt lgrthm ws used fr trg the etwrk d fr udtg the desred weghts I ths wrk eh bsed trg methd ws ledthe frmult f the MLPNN mdel s geerled e d t be used fr the slut f frwrd d verse kemts rblem f multr f fgurt Hwever sef fgurt hs bee sdered the reset wrk l t llustrte the lblt f the methd d the qult f the slut vs-à-vs ther ltertves methds Tble gves the dt fr st f jts determed thrugh ltl slut d tht bted frm MLPNN mdel SN Tble Cmrs betwee ltl slut d MLPNN slut st f jts determed thrugh ltl methd st f jts determed thrugh MLPNN methd θ θ d θ θ θ d θ Sl Regress Ceffet (R) Me Squre Errr Tble Regress lss Eh Number Reslut thrugh AdetOe rbt wth smrt trller user s gude Reslut thrugh MLPNN mm 99mm A Neurl Netwrk Arh fr Iverse Kemt f SCARA Multr (Phd Jh)

7 58 ISSN: Ths s sstet wth ur lm tht t s gd strteg t tr the ANN wth gd reresettve set f fed trgets sts sted f vrble trget sts fr the lerg ress tht wll trdue se the t fut d m result r vergee The me squre urves shw Fgure thrugh Fgure 6ehbt the buldg kwledge redure fr the ew th tht gves dt fr the suess f the rsed mdel As shw result the used slut methd gves the he f seletg the utut whh hs the lest errr the sstem Hee the slut be bted wth less errr s shw Fgures () thrugh (6) fr the best vldt erfrme f the bted dt wth the desred dt Geerlt tests were rred ut wth rdm trget sts shwg tht the lered MLP geerle well ver the whle se Frm Tble we uderstd the me squre errr fr ll jt vrbles s qute lser t er The regress effet lss s er Tble tht shws 999% mthg fr ll jt vrbles whh s etble fr bttg verse kemts f the SCARA multrresluts f the AdetOe SCARA rbt gve Tble (bted frm AdetOe rbt wth smrt trller user s gude) re mred wth the reslut bted frm the MLPNN mdel Fgure 7 reresets the grhl vew f regress lss Fgure Me squre errr fr IJRA Vl N Mrh : 5 6

8 IJRA ISSN: Fgure Me squre errr fr Fgure 5 Me squre errr fr d A Neurl Netwrk Arh fr Iverse Kemt f SCARA Multr (Phd Jh)

9 6 ISSN: Fgure 6 Me squre errr fr () (b) () (d) Fgure 7 Grhl vew f regress IJRA Vl N Mrh : 5 6

10 IJRA ISSN: CONCLUSION The emhss f ths er ws ml the ltf ltl d eurl etwrk slut f verse kemts f -df SCARA rbt multr Mthemtl mdels rel ssumg the struture f the mdel dved whh m be sub-tml Csequetl m mthemtl mdels fl t smulte the mle behvur f verse kemts rblem I trst ANN s bsed the ut/utut dt rs t determe the struture d rmeters f the mdel Mrever the lws be udted t bt better results b resetg ew trg emles s ew dt beme vlble I the reset rblem the errr vlue (me squre errr) s erl er whh s ver muh etble whe mre t the res fgures d reetblt errr vlues f tl multr Frm the reset stud t s bserved tht the MLP gves mmum me squre errr fr reslut d jts vrbles s erfrme de Ths rtfl eurl etwrk bsed jt gles redt mdel be useful tl fr the rdut egeers t estmte the mt f the multr urtel REFERENCES [] MS Alshms et l Mdellg d smult f SCARA rbtusg sld dms d verft bmatlab/smulk Itertl Jurl f Mdellg Idetft d Ctrl ; 5() [] MA Al-Khedher et l SCARA Rbt Ctrl usg Neurl Netwrks th Itertl Cferee Itellget d Adved Sstems (ICIAS ) [] SM Rft et l Imrvg Trjetr Trkg f Three As SCARA Rbt UsgNeurl Netwrks 9 IEEE Smsum Idustrl Eletrs d Alts (ISIEA 9) Otber -6 9 Kul Lumur Mls [] R Kker Relblt-bsed rh t the verse kemts slut f rbts usg Elm s etwrks Egeerg Alts f Artfl Itellgee [5] A Srvs d MJ Ngm Neur-Fu bsed Arh fr Iverse Kemts Slut f Idustrl Rbt Multrs It J f Cmuters Cmmuts & Ctrl 8; : - [6] AT Hs et l A dtve-lerg lgrthm t slve the verse kemts rblem f 6 DOF serl rbt multr Adves Egeerg Sftwre 6; 7: -8 [7] ML Hust M Pfurer d HP Shrker A ew d effet lgrthm fr the verse kemts f geerl serl 6R multr Mehsm d Mhe Ther 7; : 66-8 [8] AT Hs et l Artfl eurl etwrk-bsed kemts Jb slut fr serl multr s ssg thrugh sgulr fgurts Adves Egeerg Sftwre ; : [9] A Olru et l Asssted Reserh d Otmt f the rer Neurl Netwrk Slvg the Iverse Kemts Prblem Preedgs f Itertl Cferee Otmt f the Rbts d Multrs [] WM Jsm Slut f Iverse Kemts fr SCARAMultr Usg Adtve Neur-Fu Netwrk Itertl Jurl Sft Cmutg (IJSC) ; () [] RV Mrg d P Sgb Iverse kemts d gemetrll buded sgulrtes revet f redudt multrs: A Artfl Neurl Netwrk rh Rbts d Autmus Sstems 5; 5; 6-76 BIOGRAPHIES OF AUTHORS Phd Jh grduted Prdut Egeerg the er 7 frm ITGGU Blsur Id He hs mleted Msters Mehl Egeerg wth Selt Prdut Egeerg 9 frm Ntl Isttute f Tehlg Rurkel Id After shrt stt s Leturer Mehl Egeerg t RCET Bhl he jed Dertmet f Idustrl Desg Ntl Isttute f Tehlg Rurkel s Reserh Fellw Hs reserh terests lude Rbts Mufturg Presses sft mutg tehques d Develmet f Otmt tls Dr BB Bswl grduted Mehl Egerg frm UCE Burl Id 985 Subsequetl he mleted hs MTeh d PhD frm Jdvur Uverst Klkt He ws fult f Mehl Egeerg t UCE Burl frm 986 tll d the jed Ntl Isttute f Tehlg Rurkel s Prfessr d urretl he s the Prfessr d Hed f Dertmet f Idustrl Desg He hs bee tvel vlved vrus reserh rjets d ublshed mre th 9 ers t Ntl d Itertl levels the res f reserh beg rbts utmt mtee egeerg d dustrl rgt He ws vstg Prfessr t MSTU Msw d vstg setst t GIST Suth Kre A Neurl Netwrk Arh fr Iverse Kemt f SCARA Multr (Phd Jh)