CIRCULAR GRATING ECCENTRIC TESTING AND ERROR COMPENSATION FOR ROBOT JOINT USING DOUBLE READING HEAD

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1 10 th April 013. Vol. 50 No JATIT & LLS. All rights rsrvd. ISSN: E-ISSN: CIRCULAR GRATING ECCENTRIC TESTING AND ERROR COMPENSATION FOR ROBOT JOINT USING DOUBLE READING HEAD 1 MING CHU, JING-ZHOU SONG, 3 YAN-HENG ZHANG, 4 HAN-XU SUN 1 Asstt Prof., School of Automation, Bijing Univrsity of Posts and Tlcommunications, Bijing, China Assoc. Prof., School of Automation, Bijing Univrsity of Posts and Tlcommunications, Bijing, China 3 Assoc. Prof., School of Automation, Bijing Univrsity of Posts and Tlcommunications, Bijing, China 4 Prof., School of Automation, Bijing Univrsity of Posts and Tlcommunications, Bijing, China 1 chuming_bupt@bupt.du.cn, sjz008@bupt.du.cn, 3 zyh60@163.com, 4 hxsun@bupt.du.cn ABSTRACT Th circular grating is usd as th masurmnt standard componnt in th robot joint-angl tst systm, howvr th masurmnt rror is invitabl du to th installation ccntricity. In ordr to corrct th masurmnt rror, both th compnsation modl and ccntric dtction tst ar ndd to b invstigatd. Firstly, th compnsation modl about angular rror is dducd according to th rlationship btwn th angular rror and th ccntric paramtrs. Scondly, w proposd a mthod to dtct th grating ccntricity and ccntric dirction by using doubl rading had. Th ccntric paramtrs of grating is obtaind from th Lissajous plot, which is gnratd by th composit signals. Finally, th xprimnt rsults show that th amndd angular accuracy has bn gratly improvd. Kywords: Robot Joint-Angl Masurmnt, Circular Grating, Error Compnsation, Eccntricity Ranging, Eccntric Dirction Tst 1. INTRODUCTION For th robot motion control systm, th srvo motors ar usually usd as th driving componnt [1], whil th various typs of snsors (i.. vision snsor [], torqu snsor, vlocity snsor and position snsor [3], tc.) ar usually usd as th masuring componnts. Th robot joint-angl tst systm can b usd to masur th output accuracy of th robot joint-angl position, and provid rsarch basis for th transmission charactristics of th joint flxibl parts and th intrnal snsor calibration [3]. Th circular gratings ar usd as angl position masurmnt componnt and as circular of th joint angl accuracy masurmnt. Masuring accuracy of th grating dirctly dcids th prformanc of th joint-angl tst systm and application rang. Howvr, an ccntricity is invitabl btwn th gratings and joint-shaft during installation, and th ccntricity lads to masuring angl rror. Thrfor, th grating masuring angl nd b amndd to guarant th masuring accuracy. At prsnt, th amnding rsarch for circular grating masuring angl mainly concntrats on th masurmnt rror causd by th ccntricity. In [4], Guo analyzs th ffct of ccntricity on grating masuring angl. In [5] and [6], Yu and Zhang analyz th xprssion of grating masuring angl rror by using Fourir sris xpansion mthod and raliz th masurmnt of grating masuring angl rror through 3 facs polygon calibration mthod. Wang and Gao idntify and amnd th grating installation ccntricity rror basd on th simulatd annaling algorithm, on can s [7] and [8]. In [9], Zhu uss four rading hads mthod to liminat th influnc of grating ncodr ccntricity and vibration. Howvr, th prsnt work do not discuss that how to masur ccntric rror (ccntricity and ccntric dirction) undr th difficult assmbly and adjustmnt condition. In th robot joint-angl tst systm, th masurd joint nd rinstallation for th diffrnt rquirmnts, thus th ccntric paramtrs will b sriously changd. Using calibration and idntification mthod to amnding th grating involvs high cost, long tim and complx opration, and this mthod can not b applid to th masurmnt systm whr th shaft changs rpatdly. In ordr to masur th ccntric rror mor fficintly and convnintly and to amnd th grating masuring angl, this papr proposd a mthod to dtct th grating ccntricity and 161

2 10 th April 013. Vol. 50 No JATIT & LLS. All rights rsrvd. ISSN: E-ISSN: ccntric dirction by using doubl rading had. And using th grating ccntric masuring angl rror modl, th masurmnt systm can b amndd.. ROBOT JOINT-ANGLE TEST SYSTEM Th robot joint-angl tst systm can tst th positioning accuracy, output shaft angl hystrsis and vlocity prformanc of flxibl joints undr diffrnt loads. Th hardwar systm of th jointangl tst systm ( as shown in Figur 1) includs robot joint, torqu snsor, load, grating ncodr, uppr computr and data acquisition card, tc.. Th grating is connctd with joint-shaft to masur th output-angl. Th joint output is connctd with torqu snsor through couplr, and th load is connctd with th othr nd of torqu snsor. Robot joint Circular Grating Torqu Snsor Load grating masuring angl rror mainly includs grating installation ccntric rror, baring radial rror and grating strip rror, tc.. W can us high prcision baring and grating to nsur th rang of baring radial rror and grating strip rror. Th main sourc of rror coms from grating installation ccntric rror, which affcts th systm masuring accuracy to a larg xtnt. During th installation, gomtric cntr of grating and rotation cntr of masuring shaft don t coincid, which causs ccntric rror. Eccntric rror is a rgular systm rror, and th rror changs with angl priodic, thus amndd compnsation can b usd to liminat th ccntric rror [10, 11]. Th following thsis will discuss th rlationship btwn ccntric rror and masuring angl. Rading Had A θ OD θ OM Eccntric Dirction θ ' I Fig.1 Framwork Of Robot Joint-Angl Tst Systm Robot joint is a high prcision srvo systm, and th position of singl joint is controlld in th rang of 1 arc-sconds, so th high masuring rquirmnts about th circular grating is ndd. During th actual masurmnt, th rlativ ccntricity btwn th grating and masurd shaft affcts th masurmnt accuracy sriously. It is difficult to assmbl and adjust th gratings, and th ccntricity can not b dtctd by microscop. Furthrmor, th ccntric paramtrs btwn th grating and joint-shaft will chang whn th joint is rinstalld. At this tim, th tst fficincy will dcras if using calibration mthod. Hnc, an fficint and convnint mthod should b proposd to masur th grating ccntric rror and amnd th angl-rror causd by th ccntricity. 3. AMEND RESEARCH OF GRATING MEASURING ANGLE ERROR CAUSED BY ECCENTRICITY Whn using gratings to masur rotation motion, th angl position rror is priod. Th sourcs of R Zro Fig. Angular Error Rsulting From An Eccntricity Error As shown in figur, analyzing th angl rror causd by ccntricity, O M is grating gomtric cntr, O D is masuring shaft rotation cntr aftr installation, is ccntricity, R is th grating optical radius, taking ccntric dirction OO D M as rfrnc, th angl scannd by photolctric snsor is θ '. Du to ccntricity, actual angl of grating is θ, thus ccntric masuring rror θ is θ = θ θ' (1) According to gomtric rlationship, w can obtain sin θ ' tan θ = R+ cos θ ' () 16

3 10 th April 013. Vol. 50 No JATIT & LLS. All rights rsrvd. ISSN: E-ISSN: Aftr installing gratings and masuring shaft, thr is a fixd phas rlationship btwn grating zro lin dirction and ccntric dirction, which is ccntric phas angl I, zro lin rotation angl, which is th radout angl of snsor θ s θ = θ' + I (3) S Bring (3) into (), th rlationship btwn θ s and θ is sin( θs I) θ = arctan R+ cos( θ I) S (4) Whn sin( θs I) = 1, th masuring rror causd by ccntricity gts its maximum, and maximal rror valu is θ max = arctan (5) R According th abov analysis, th masuring rror causd by ccntricity changs with rotation angl, rror valu θ can b xprssd as function of masuring shaft rotation angl θ s. Exprssion (5) is a modl of rror compnsation, masuring angl rror is rlatd to two constant paramtrs, ccntricity and ccntric dirction. W can amnd grating masuring angl rror through ths two paramtrs. 4. GRATING ECCENTRIC TEST RESEARCH To obtain ccntric rror angl compnsation formula compltly, th grating ccntric paramtrs nd to b tstd. According to grating masuring angl principl, monochromatic light mittd by lasr gnrats intrfrnc fring through grid lin of grating. Aftr photolctric rcivr rcivs intrfrnc pattrn optical signal, sinusoidal signal can b obsrvd in th oscilloscop. Whn grating is ccntric, th sinusoidal signals tstd by rading hads of diffrnt position in circumfrntial dirction at sam momnt hav phas diffrnc [1]. Considring this fatur, w can tst th grating ccntricity and ccntric dirction according to composition of sinusoidal signals of diffrnt phass. Two photolctric rading hads collct strip signals. Rading had-1 and had- ar installd in position A 1, A rspctivly, taking rotation cntr O D as cntr (shown in Figur 3). Du to th ccntricity btwn grating gomtric cntr and rotation shaft, it lads to diffrnt grating numbrs of rading had-1 and had- through th sam tim, which mans two photolctric rading hads don't pass sam lngth in optical circumfrnc at sam tim. As a rsult, th tstd sinusoidal signals of rading had-1 and had- hav diffrnt frquncy and phas. A Had- O D E B O M A 1 ϕ Had- 1 Fig.3 Illustration Of Two Snsor Tsting Eccntricity Error Nxt mak furthr analysis of rlationship btwn ccntricity and rcivd signal phas diffrnc. Whn shaft rotats along a fixd dirction, th lngth diffrnc that rading had-1 and had- pass in optical circumfrnc is AB. According to Small Angl Approximation Thory, AB AB, OME AA 1. According to gomtric similarity shown in Figur 3, lngth diffrnc AB can b xprssd as AB O E= sinϕ (6) M Whr ϕ is th angl btwn ccntric dirction and lin AA 1. Th corrsponding angl valu of lngth diffrnc AB in th lctric strip signal cycl is th phas diffrnc of tstd sinusoidal signals two rading hads. And th rlativ phas diffrnc of 163

10 th April 013. Vol. 50 No.1 005-013 JATIT & LLS. All rights rsrvd. ISSN: 199-8645 www.jatit.

Th phas diffrnc btwn th rading had-1 and had- changs with shaft angl.

4 10 th April 013. Vol. 50 No JATIT & LLS. All rights rsrvd. ISSN: E-ISSN: rcivd signals of rading had-1 and had- can b xprssd as sinϕ ψ1 = 360 (7) d Whr d is grating pitch, 360 rprsnts th angl valu in a lctric strip signal cycl. Th phas diffrnc btwn th rading had-1 and had- changs with shaft angl. Whn th shaft rotats a circl, th ccntric distanc diffrnc of rading had-1 and had- will rach th xtrm point twic (shown in Figur 4), which corrspond rspctivly th two points that rcivr- rads whn ccntric dirction crosss AA 1. From minimum, grating rotats 180 anti-clockwis to rach maximum, during which th total phas diffrnc that two rading hads hav rad is ψ. Transforming th xprssion furthr, th formula of ccntricity is ψ = d (8) Had- 1 Thus, contrasting th composit signal of two rading hads can calculat th phas diffrnc of diamtr position signals aftr a circl, thus dtrmining th ccntricity and ccntric dirction. Putting ccntricity and ccntric phas angl ψ into formula (4), amnding formula of masuring angl rror causd by ccntricity can b obtaind compltly. 5. MEASURING EXPERIMENT AND RESULTS 5.1 Eccntric Error Masuring Exprimnt Robot Joint Oscilloscop A 1 O E O D O E Had-1 Had- Fig.5 Exprimnt of Eccntricity Error Dtction Min A Had- Ma x Fig.4 Illustration of Eccntric Extrm Position From th momnt whn rading had- has rad th xtrm point, th grating continus to rotat 90 dgr, th ccntric dirction will b consistnt with th dirction of AA 1. Thrfor, aftr acquiring th phas xtrm point from th oscilloscop, th ccntric dirction of grating can b dtrmind according to th orthogonal rlation,. Rading had-1 and had- ar installd in th snsor holdr of manipulator joint tst systm grating. Rcivr gts its lctricity through a 5v rgulatd powr supply, and channl-1 and channl- of oscilloscop ar connctd to th signal output of rading had-1 and had- rspctivly (shown in Figur 5). Elctric signals transformd by rading had- 1and had- ar composd as Lissajous plot through two channls of oscilloscop. Basd on Lissajous plot, th corrsponding phas diffrnc (th sam sinusoidal signal frquncy is rquird) can b rad. Th mthod is as follows: X is th distanc btwn two intrsctions of plot and horizontal axis, X 0 is projction lngth of 164

10 th April 013. Vol. 50 No.1 005-013 JATIT & LLS. All rights rsrvd. ISSN: 199-8645 www.jatit.org E-ISSN: 1817-3195 plot on th horizontal axis, X / X0 = ω, and th phas diffrnc ψ =arcsin( w).

5 10 th April 013. Vol. 50 No JATIT & LLS. All rights rsrvd. ISSN: E-ISSN: plot on th horizontal axis, X / X0 = ω, and th phas diffrnc ψ =arcsin( w). Th mthod of obtaining phas diffrnc is as follows. Firstly, th ccntric xtrm position nd to b dcidd. Sinc th masurd shaft rotats along on dirction, w can obsrv th motion trail of Lissajous plot. Whn th motion dirction changs, rcord th minimum point and th phas diffrnc ψ, thn gt th maximum point and min th phas diffrnc ψ max. Aftr gtting th xtrm point, rcord th changing cycls of Lissajous plot during th rotation, namly th priodicity in th phas diffrnc n. Through th abov rcord, us th following formula to calculat th ccntricity ( ψ n ψ ) d (9) max min = Using th MicroE-R10851 grating in th xprimnt, and th pitch is 0μm. Through th masurmnt and calculation, th grating ccntricity aftr installation is 6.9μm, and th ccntric phas angl is 34.96º. Taking ths ccntric paramtrs into formula (4), formula of rror compnsation causd by ccntricity can b obtaind compltly. 5. Masurmnt Exprimnt Vrification In ordr to vrify improvmnt ffct on th masurmnt accuracy of robot joint-angl tst systm aftr amnding th grating ccntric masuring angl rror. Putting th rror compnsation formula into th rror amnding program of tst softwar, tak th angl as amnding angl. Taking masuring angl of 4- prism as standard angl (shown in Figur 6), masur th angl vry 15, and rcord th standard angl valu, th masuring valu bfor amnding, th masuring angl aftr amnding, rspctivly. Th contrast of masuring angl rror bfor and aftr th amnding is shown in Figur 6. From Figur 6, th plot of th masuring angl rror bfor amnding is a sin curv which mans grating masuring angl rror mainly is systm rror. Aftr ccntric rror amnding, th masuring angl rror rang is apparntly rducd. On can s that th grating angl-rror bfor and aftr amnding ar rspctivly arc-sconds and 38. arc-sconds, which mans th rror is dcrasd narly 78%. Thus, th circular grating masurmnt prcision is improvd gratly. Error (Arc-scond) Error (Arc-scond) 4-Prism Circular Grating Light Pip Display Scrn Fig.6 Th 4-Prism Masurmnt Systm Position (Dgr) (a) Th Grating Angl-Error Bfor Amnding Position (Dgr) (b) Th Grating Angl-Error Aftr Amnding Fig.7 Angular Error Bfor/Aftr Compnsation 6. CONCLUSION 165

6 10 th April 013. Vol. 50 No JATIT & LLS. All rights rsrvd. ISSN: E-ISSN: Masuring angl rror causd by grating installation ccntricity is an important factor which affcts grating masurmnt accuracy. Th papr studis th rlationship btwn ccntric paramtrs and grating masuring angl, and dducs compnsation formula of grating masuring angl rror causd by ccntricity. This rror compnsation modl has gnrality and can b applid to othr photolctric masurmnt angl systm. This papr puts forward a mthod of tsting grating ccntricity and ccntric dirction through phas diffrnc of two rading hads rcivd signals, and gts th masuring angl rror compnsation formula. Without incrasing larg tst instrumnt, amnd th grating masuring angl in a short tim. Th rsults of masurmnt xprimnt show that grating masurmnt rror has bn dcrasd narly 5 tims aftr amnding, and masuring accuracy satisfis rquirmnts of joint tst systm. 7. ACKNOWLEDGMENTS This work was supportd in part by th Spcializd Rsarch Fund for th Doctoral Program of Highr Education ( ), Scintific and tchnological innovation projcts of Gnral Armamnt Dpartmnt(ZYX ), th National Natural Scinc Foundation of China ( ) and th National High Tchnology Rsarch and Dvlopmnt Program of China (01AA ). REFRENCES: [1] Chandra Skhar O. and Chandra Skhar K., Spac vctor modulation & fuzzy PID spd controllr for dirct torqu control induction motor driv, Journal of Thortical and Applid Information Tchnology, Vol. 35, No. 1, 01, pp [] Zhang Z.B., Song Y.S., Wang H.X., t al., "An approach of corrcting th rrors in th vision navigation systm for fild robot", Journal of Thortical and Applid Information Tchnology, Vol. 44, No. 1, 01, pp [3] HAN B, Dsign and implmntation of a modular tst systm for th flxibl manipulator, China: Bijing Univrsity of Post and Tlcommunication Dgr thsis, 009. [4] GUO Y.K., LI Y.H., LI Q.X., t al.. Error compnsation for ccntric motions of circular gratings, Journal of Tsinghua Univrsity (Sci&Tch), Vol. 45, No., 005, pp [5] YU L.D., DING Y. and CHENG F.T., Compnsation of Angl Masurmnt Error of Circular Gratings for Paralll Dual-joint Coordinat Masuring Machin, Journal of Nanjing Univrsity of Scinc and Tchnology (Natural&Scinc), Vol. 33, No. 5, 009, pp [6] ZHANG L.S. and GUAN B.L., Error corrction and its application to multi-joint CMM rsarch, Mtrology & Masurmnt Tchnology, Vol. 7, No. 4, 007, pp [7] WANG W, LIN K, GAO G.B., t al., Eccntricity paramtr idntification of angl snsors for articulatd arm CMMs, Optics and Prcision Enginring, Vol. 18, No. 1, 010, pp [8] GAO G.B., WANG W., LIN J., t al.. Error compnsation and paramtr idntification of circular grating angl snsors, Optics and Prcision Enginring. Vol. 18, No. 8, 010, pp [9] ZHU F., WU Y. and LIU C.C, Eliminating Influnc of Grating Encodr s Eccntricity and Vibration to Moir Frings Signal by Four Rading Hads, Acta Optica Sinica, Vol. 31, No. 4, 011, pp [10] HAGIWARA Nobumi, SUZUKI Yoshihisa and MURASE HIDEAKI, A mthod of improving th rsolution and accuracy of rotary ncodrs using a cod compnsation tchniqu, IEEE Trans on Instrumntation and Masurntm, Vol. 41, No. 4, 199, pp [11] HONG X., XU ZH.J. and YANG N, Error compnsation of optical ncodr basd on RBF ntwork, Optics and Prcision Enginring, Vol. 16, No. 4, 008, pp [1] Portman V. and Pschansky B., Phasstatistical mthod and dvic for high prcis and high-fficincy angular masurmnts, Prcision Enginring, Vol. 5, No. 4, 001, pp

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