Rapid Modelling and Grinding of Workpieces Inner-surface by Robot with Impedance Model Based Fuzzy Force Control Algorithm

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1 Rap Mollng an Grnng of Workpcs Innr-surfac by Robot wth Impanc Mol Bas Fuzzy Forc Control Algorthm Wang F, Luo Zhong an Lu Hongy School of Mchancal Engnrng & Automaton, Northastrn Unvrsty, , Shnyang, Chna Abstract To achv rap automatc grnng of workpcs nnr-surfac by nustral robot, a rap translatonal tcton stratgy of workpcs nnr-surfac an fuzzy forc control algorthm of grnng ar propos n ths papr Th rap translatonal tcton stratgy ntroucs a way to stablsh an nnr-surfac s mol quckly by rcorng ky ponts of th aal scton contour whch rflcts bg curvatur changs of th contour Th stablsh mol s fasbl but mprcson Th forc control algorthm s bas on mpanc mol To promot aaptablty to th mprcson of th stablsh nnr-surfac s mol, a fuzzy austng stratgy s ntrouc n th forc control algorthm By aoptng an austng factor, whch trmn by forc rspons an a fuzzy logc, th stratgy can aust th rfrnc tractory of mpanc mol n tm Takng avantag of propos tcton an forc control mtho, grnng prmnts shows that th contact normal forc mantans appromatly constant, th rlatv man rror s wthn 65%, an th matral rmoval thcknss of th nnr-surfac s appromatly consstnt Th propos stratgy's fasblty s vrf 1 Introucton Inustral robot s a tnncy n th manufacturng procss n INDUSTRIE 40[1] Whn robot contact wth a workpc, such lk grnng, burrng an polshng, complanc s ncssary for th robot[2] Morovr, th prcson of workpcs mol an workpcs locaton n ts g ar both mportant to th constrant machnng procss A Robrtsson tc stablsh a robot platform wth trnal fast opn snsor ntgraton systm, an mplmnt forc-controll grnng, fnshng an burrng prmnts wth th platform[3] In th prmnts, an off-ln programmng nclung path gnraton bas on work-pcs CAD mol s ntrouc n th hybr forc/poston control stratgs Consrng th poston an orntaton rrors of th workpc, H-Chan Song an Ja-Bok Song vlop a tool-path mofcaton mtho bas on a CAD mol an rct tachng By sttng a vrtual wall, th forc control bas on mpanc mol s us to applyng an accurat an stabl contact forc[4] Accuracy of workpcs affcts th prformanc of forc control ntnsvly To obtan accurat mol of th workpc, an off-ln pr-programmng s n n thos rsarchs r-programmng s obvously tmconsumng but bnfcal to forc control In orr to shortn th whol work tm, a lss-accurat mol of workpcs s accptabl Manwhl, aaptablty to th mprcson mol s put forwar to th forc control algorthm To solv th abov mnton problm, a rap translatonal tcton stratgy an fuzzy forc control algorthm, whch can stablsh a workpc s mol quckly an aapt th mprcson of th mol, ar propos n ths papr Mollng an grnng prmnts ar scrb n th n of th papr 2 Mol of th grnng robot systm Whn grnng a cavty s nnr-surfac wth a constant matral rmoval thcknss, th sktch map of th grn robot systm s shown n fgur1 Th cavty s assum to b a rotary shll Th robot has 5-DOF to grnng th nnr-surfac of th shll, nclung a translatonal ont, 2 rotatonal onts an a tool an a shll s rotatonal movmnt[5] Fgur 1 Sktch map of th grnng robot(1 1st arm, 2 2n arm, 3 3r arm, 4 grnng tool, 5 rotary shll s nnr-surfac) 21 Mol of th grnng robot Th Authors, publsh by ED Scncs Ths s an opn accss artcl strbut unr th trms of th Cratv Commons Attrbuton Lcns 40 (

2 Th ynamc mol of an n-lnk rg-ont manpulator n ont coornat s scrb by Mqq () Cqqq (,) Gq () τ J F (1) T (,) ( ) whr qqq, q, q corrspon to th onts poston, vlocty an acclraton vctors, rspctvly M (q) s th nn postv-fnt nrta matr Cqq) (,) s th n n cntrptal an Corols matr G (q) s th n 1 vctor of gravtatonal trms n workspac s th n 1 ont nput torqu J rprsnts th n6 Jacoban matr Th robot ynamc mol n th Cartsan spac can b rv from formula(1): M () C (,) G () J τ F (2) T T 1 whr ( B) M J MJ, an ( ) T G J G C (,) ) J ( C MJ J J 1 -T 1 1 ( )J 22 Contour tctng an mollng of th nnr-surfac Usually, th contour of th shll s nnr-surfac has grat ffrnc wth ts CAD mol, caus th shll s craftng procss An poston rrors nvtably occur whn a workpc s plac n th g, shown n fgur2 Th CAD mol can not b us rctly n robot s grnng procss Thrfor, th nnr-surfac s mol ns to b stablsh to guarant th accurat grnng procss Fgur 2 Locaton an shap rror of an nnr-surfac s contour 221 Rap translatonal tcton stratgy Whn th actual contour of th shll nnr-surfac has grat ffrnc wth ts CAD mol, th mol coul b us as a rfrnc only F a lasr snsor, splacng th grnng tool, n th n of th robot manpulator Wth th CAD mol as rfrnc, tctng th nnrsurfac s aal contour, th tcton coul b conuct accorng to th followng stps 1 Actuatng th manpulator nto th cavty, lt th n of th manpulator locat appromatly n th ml of th cavty Th sral numbr of ths cavty s aal scton rprsnts by ( 0,1,, m) 2 Takng th CAD mol as rfrnc, lt th lasr bam b prpncular to th suppostonal nnr-surfac St th orntaton of th n-ffctor as th ntal orntaton Actuat th manpulator n th ntal orntaton untl th lasr snsor got a val ata quall to D, whch s th man of th lasr snsor s masurng rang Calculat ths frst tcton pont s coornaton valu 0 n th bas coornat systm accorng to th robot s knmatcs mol 3 Mantanng th n-ffctor s gstur, lt th paralll moton of lasr bam b along wth on aal rcton of th cavty untl th snsor s output D out chang out of rang f Whn snsor s output chang out of rang, whch mans D out D f, th pont tct can b rcor as ( 1,2, t) 4 On th bass of mantanng th lasr bam stckng on tcton pont, austng n-ffctor s poston an gstur, lt lasr snsor s output b quall to an lasr bam b prpncular to th ln form by 1 an 5 Rpatng stp 3 an 4 wth rcton 1 untl lasr snsor got no val output, a srs [ 0 1 t ] wll b rcor 6 Actuatng th manpulator rturn to th status of th frst pont 0, an rpatng stp 3 to 5 n th oppost rcton, srs [ t 1 t 2 n ] wll b rcor 7 Rsttlng an combnng th srs [ 0 1 t ] an [ t 1 t 2 n ] along wth th cavty s aal rcton, th rsttl srs [ 0 1 n ] wll sktch an aal contour of th cavty s nnr-surfac, shown as fgur3 8 Rotatng th cavty n a small gr an rpatng 1 1 stp 1 to 7, srs [ k ] wll b rcor Whr, k, rprsntng th quantty of rcor ponts, s trmn by complty of th aal contour 9 Rpatng stp 1 to 8, aftr th whol aal contours bng tct, ky ponts of th cavty s nnrsurfac wll form a bvctor as ( 1,2, k, 1,2, m ) Fgur 3 Dtcton ponts srs of a cavty s nnr-surfac contour 222 Smulaton of translatonal tcton stratgy D 2

3 Sttng f as 05mm an 2mm, th tcton smulaton rsults ar shown n Fg 4 an Fg 5 whr M, D an K ar rspctvly th sr nrta, ampng an stffnss matrcs of th manpulator-nvronmnt systm F s th sr contact forc btwn manpulator s n-ffctor an th constrant surfac, an ar th actual poston, vlocty an acclraton of th robot manpulator, rspctvly, an s rspctvly th sr tractory, vlocty an acclraton 32 Rfrnc tractory s fuzzy austng stratgy Assumng an K to b th actual poston an stffnss of th constrant surfac can b rprsnts as: Fgur 4 Dtcton wth 05mm f F (4) K Usually, th accurat an K ar unavalabl Lt an K n th naccurat valu c an K c rplac th formula(4) An th appromat K c s usually prntal Accorng to th appromatly rough functon, th rfrnc tractory shoul b: F r c (5) Kc Fgur 5 Dtcton wth 2mm f Th smulaton rsults shown that th translatonal tcton stratgy propos abov s fasbl Morovr, th smallr f s th mor accurat th mol goanna b Howvr, th mol s not tal nough It only nclus svral ky ponts that can rflct bg curvatur changs of th contour Thrfor, th mol stablsh by propos rap translatonal tcton stratgy s fasbl but mprcson An ntllgnt forc control algorthm whch can b aaptv th mprcson s n To promot aaptablty of th control algorthm, an ntllgnt prcton an austng of th rfrnc tractory s ntrouc nto th mpanc mol [7] 3 Forc control algorthm Snc th stng mprcson of both contour mol an locaton of th nnr-surfac, th forc control algorthm shoul b aaptv to th mnton rror A fuzzy forc control stratgy bas on mpanc control mol s propos 31 Impanc control mol Usng th followng mpanc mathmatc mol [6]: M D K F F ( ) ( ) ( ) (3) Fgur 6 Rfrnc tractory austng Establsh th rfrnc tractory ntllgnt austng law n scrt form as: ( k1) ( k) ( k) (6) r r c whr k s fn as th currnt momnt r ( k 1) s th prctv poston of rfrnc tractors n tm k 1 ( k) r s th rfrnc tractory n tm k Th trm () k c s an austmnt bas on th prct locaton an gomtrc rror: 3

4 () k ( k1) () k k () k (7) c c c c p whr, p() k p() k p( k 1) rprsnts th tnncy of th austng rror Sttng F ( k) p( k) ( k), rprsnts th appromatly Kc actual poston of th constrant surfac, p( k) p( k) c( k) appromatly rflcts th stanc from th rfrnc tractors to th actual surfac k c s th aaptng scal factor trmn by a fuzzy controllr Th nput of th fuzzy controllr s p ( k ) Th lngustc varabls assgn to p an kc ar EX an KC Th corrsponng fuzzy substs ar A an B Th st A comprss VB, B, M, S an VS, whch rspctvly not vry bg, bg, ml, small an vry small Th st B comprss KB, BK, KM, SK an KS, whch not vry bg, bg, ml, small an vry small rspctvly Th fuzzy ruls for nput EX an output KC ar shown n Tabl I Tabl 1 Fuzzy Control Ruls for Th Output KC EX VB B M S VS KC KB BK KM SK KS Rplacng th, an wth r, r an r n formula(3), fn u as th control rul It coul b uc as: 4 Dtctng an grnng prmnt Th grnng robot systm s shown n Fg 8 Th CAD mol of cavty s nnr-surfac s avalabl but has a grat ffrnc wth th actual obct Frstly tctng th nnr-surfac of th shll wth a lasr snsor, th 3D mol of th nnr-surfac coul b bult as fgur 9 Thn cutng th grnng procss bas on th propos fuzzy forc control algorthm, wth an pct contact forc 5N, th forc rspons s shown n fgur 10 Fgur 8 Grnng prmnt of a rotary shll s nnr-surfac u M D K F F 1 1 ( r r ) (8) whr, r r, r r an r r Combnng formula(1) an (8), th on torqu control law of th forc control mol wth rfrnc tractory onln ntllgnt austng coul b: τ J [ M u C G F ] (9) T 33 Impanc mol bas forc control Th control law s shown n Fg 3 Whn robot s n a constrant moton, th mpanc bas ntllgnt forc controllr wll b mplmnt to prform a constant forc btwn th robot n-ffctor an constrant surfc Fgur 9 Rconstruct 3D mol of th rotary shll s nnr-surfac fn/n t/s Fgur 10 Normal forc rspons wth pct 5N Fgur 7 Schm of th mpanc mol bas forc control Fg 10 shows that th contact normal forc btwn manpulator s n-ffctor an th constran nnrsurfac s controll to b aroun ts pct valu Th 4

5 fluctuaton n th rspons s caus by naccurat mol of th nnr-surfac an mpact of th manpulator s movmnt from fr movmnt to a rstrant movmnt n th vry bgnnng of th grnng procss Morovr, whn grnng procss s n tm 50~70s, thr s fluctuaton bcaus that th curvatur of th constran surfac s vry small an chang rastcally Takng avantag of propos fuzzy forc control stratgy, rror of contact normal forc fluctuat n [-03, 02]N, wth rlatv rror wthn 5% Ovrall, n th whol grnng procss, th rlatv man rror of normal contact forc from th pct valu s wthn 65% Th matral rmoval thcknss of th nnr-surfac s appromatly consstnt 5 Concluson To grn a cavty s nnr-surfac automatcally wth robot, a rap translatonal tcton stratgy an fuzzy forc control algorthm ar propos n ths papr A compnous mol coul b stablsh quckly by followng th rap translatonal tcton stratgy whch vlop to rcor ky ponts of th nnr-surfac s contour Takng avantag of th fuzzy forc control algorthm bas on mpanc control algorthm, th matral rmoval thcknss n grnng procss can b controll to b appromatly consstnt Th forc control algorthm s aaptv to th contour mol s mprcson, an mantan th contact forc b appromatly constant qual to th pct valu wth rlatv man rror 65% Th prnc of ths rsarch provs an mportant rfrnc for th practcal applcaton Rfrncs 1 J F Wan, H Ca, K L Zhou 2015 ICIT, 135(2015) 2 Y Shot, J Akyama, H Yosha, Y Haraa Robotcs an Automaton, IEEE Intrnatonal Confrnc on Robotcs an Automaton, 1, 788(1995) 3 A Robrtsson, T Olsson, R Johansson, tc rocngs of th 2006 IEEE/RSJ Intrnatonal Confrnc on Intllgnt Robots an Systms, 2743(2006) 4 H C Song, J B Song Intrnatonal Journal of rcson Engnrng & Manufacturng, 14(1), 85(2013) 5 F Wang,H Y Lu, Z Luo Optcs an rcson Engnrng, 21(6),1479(2013) 6 M K Vukobratov, A G Roc Journal of Intllgnt an Robotc Systms, 18(2), 191(1997) 7 F Wang, Z Luo, H Y Lu, L Wang 2010ROBIO, 1555(2010) 5