Hybrid Motion Blending Algorithm of 3-Axis SCARA Robot using Parametric Interpolation

Transcription

1 Hybr Moon Blnng Algorhm of 3-Ax SCARA Robo ung Prmrc Inrpolon Auhor: J Hun Ju Won J Chung K Bom Pr Song Jo L K Sng L School of Mchronc, Chngwon Nonl Unvry Eml: uh87@n.com Tl: , Fx: Ar: School of Mchronc, Chngwon Nonl Unvry Chngwon, , Souh Kor ABSTRACT In orr o mplmn connuou-ph moon on robo, ncry o bln on on moon o nohr on moon nr v pon n rpzol form of on vlocy. Fr, h vlocy uprpoon ung prmrc nrpolon propo. Hybr moon blnng fn h blnng of ffrn wo yp moon uch blnng of on moon wh lnr moon, n h nghborhoo of v pon. Scon, hybr moon blnng lgorhm propo b on vlocy uprpoon ung prmrc nrpolon. By ung 3- x SCARA (Slcv Complnc Ambly Robo Arm) robo wh LbVIEW conrollr [], h vlocy uprpoon lgorhm ung prmrc nrpolon hown o rul n l vbron, compr wh PTP (Pon- To-Pon) moon n Km lgorhm []. Morovr, h hybr moon lgorhm mplmn on h robo ung LbVIEW [] progrmmng, whch confrm by howng h n-ffcor ph of on-lnr hybr moon. Kywor: Vlocy uprpoon, prmrc nrpolon, Hybr moon blnng, 3-x SCARA Robo, Connuouph. INTRODUCTION In gnrl, h movmn rgy of nurl robo cn b v no wo n,.., PTP (Pon o Pon) n CP (Connuou Ph) [3]. Erly nurl robo n m proucon ln hv bn mnly u for mpl n rv ob n whch PTP moon nough. In rcn, nurl robo whch houl b co-wor wh mchn ool r ncrngly n for prformng vrou ob, wll mpl hnlng or wlng. Accorngly, n orr o cop wh hgh-p hnlng of worpc for h coopron of nurl robo wh mchn ool or ohr vc, CP houl b mplmn o o ruc vbron n no, wll crng opron m. A hown n Fg. -(), h PTP moon cn rul n ll moon v pon. Whr, v pon rfrnc for plnnng nw ph from rng pon o nng pon whou ny ll moon. () PTP moon (b) CP moon Fg. PTP moon v. CP moon In orr o mplmn CP moon on robo, ncry o bln on on moon o nohr on moon nr h v pon n rpzol form of on vlocy hown n Fg.. In pcfc, blnng moon mn h uprpoon of h vlocy (rpzol) profl of on on moon gmn on nohr on moon gmn n rm of m, n h nrby of v pon. A rul, boh h cr of movng m n h rucon of vbron cn b obn. Km [] propo h blnng moon lgorhm, conrng ll h c of uprpoon. Bu Km lgorhm cnno prov hybr moon blnng uch blnng of on moon wh lnr moon bcu ffcv only for homognou blnng of on moon wh on moon. Hr h lnr moon mn h moon of whch on ngl (or vrbl) houl b obn from nvr nmc, gvn h lnr ph of n n-ffcor.

2 Jon Vlocy P P = MAX () ( mx cclfcor) P P = MAX (3) ( mx clfcor) Tm Fg. Suprpoon of vlocy In h ppr, hybr moon blnng lgorhm nclung vlocy uprpoon propo by ung prmrc nrpolon. By ung 3-x SCARA robo wh LbVIEW conrollr, h mpl lgorhm hown o rul n l vbron, compr wh PTP moon n Km lgorhm. Morovr, h hybr moon lgorhm mplmn on h robo ung LbVIEW progrmmng, whch confrm by howng h n-ffcor ph of on-lnr hybr moon.. VELOCITY SUPERPOSITION USING PARAMETRIC INTERPOLATION For vlocy uprpoon, h boh cclron/clron m n conn-p m houl b h m for ll h on of robo. Th cn rul n mooh moon wh low vbron. Th vlocy uprpoon ung prmrc nrpolon cn b r by fnng h m,, whch pcf p whou cclron n clron con: ( + ) = (4) whr mx h mxmum cclron for h -h on; mx h mxmum clron for h -h on. Th cclfcor n clfcor r h conn rngng 0 o. Th ol m of movmn,, gv by = + + (5) ol ( ) Whn + <, h ngv vlu from quon (4). In h c, o b 0, whch chng h rpzol vlocy profl no rngulr on. Thn quon (4) bcom + = (6) If w um mx cclfcor =, quon () bcom ol P P = V (pfcor [0,]) () mx pfcor P P = (7) whr h numbr of on; n, r h n n r pon, rpcvly; V mx h mxmum p of h -h on. Th pfcor conn rngng from 0 o. For xmpl, Spfcor cn b lc 0.7 whn r p o b 70% of h mxmum on p. Nx, h mxmum of ( =,, n, n: h numbr of on gr of from),.., cn b lc, whch cn b u for clculng h long cclron m, conn-p m, h long clron m (whch r llur n Fg. ) ung quon (), (3) n (4), rpcvly. P P whr nc h on numbr corrponng o h long cclron m. Smlrly, f w uppo mx clfcor =, quon (3) l o P P = (8) whr no h on numbr corrponng o h long clron m. W cn ly fn by olvng h quon (6), (7) n (8). Conqunly w hv P P = (9) ( P P + P P ) P P = (0) ( P P + P P ) Fg. Trpzol vlocy profl

3 B on quon (9) n (0) whch m boh cclron n clron m b h m for ll h on, h prmr u() cn b nrouc follow: P ( u( )) = P u( )( P P ), u [0,] () whr u() pn from 0 o, hvng y rol of ynchronzng ll h on n cclron n clron m. Hr nc h numbr of on x; P no h n poon of -h on, P no h r poon of -h on. I cn b worh nocng h u() P, whl u() 0 P. Epclly h prmr u() no h ro of h mov nc l urng lp m o h ol movmn L, whch cn b fn by l u( ) = () L 3: C ol ol ( ol ) u( ) = (6) ( + + ) By ubung quon (4), (5) n (6) o quon (), h poon of -h on m cn b clcul by ung h prmr u(). Rfrrng o Fg. 4, h vlocy uprpoon ung prmrc nrpolon cn b propo follow: 0 < b P u ( )) = P v u ( )( P P ) (7) ( < b b v P ( u( ), u( ) = P u )( v P ) u ( )( P P ) (8) ( v v Th mnng of l n L r llur n Fg. 3. I houl b noc h h prmr u() cn b ppl o ll h on mulnouly. 3 b P ol u ( )) = P v u ( )( P P ) (9) ( v v Tol movmn = L whr h ubcrp v no h v pon. Th ubcrp, n 3 mn h con, n 3, rpcvly, hown n Fg. 4. Th uprpoon m, b < b, houl b lc h l m bwn h clron m of h prcng rpzol vlocy profl n h cclron m of h followng on. Vlocy 3 Fg. 3 Mnng of l n L Th ol movmn L cn b ly rv follow: L = v + v + v (3) whr v nc h conn-vlocy hown n Fg. 3. Th prmr u() cn obn for 3 c follow: C : 0 < u( ) = (4) ( + + ) C : < ol u ( ) = (5) ( + + ) b Fg. 4 Concp of vlocy uprpoon Tm Whn compr wh Km blnng lgorhm, h propo vlocy uprpoon lgorhm ung prmrc nrpolon mor conc bcu o no hv o conr ll h c of uprpoon. Morovr h con of xprmn wll how h h propo lgorhm cn rul n l vbron whn mplmn on 3-x SCARA robo, n compron wh Km blnng lgorhm of on moon. b ol

4 3. HYBRID MOTION BLENDING ALGORITHM USING PARAMETRIC INTERPOLATION A mnon n Scon, hybr moon blnng fn h blnng of ffrn wo yp moon uch blnng of on moon wh lnr moon, n h nghborhoo of v pon. In h ppr, hybr moon blnng lgorhm propo b on vlocy uprpoon ung prmrc nrpolon. Th yp of moon cn b clf no 3 cgor; on moon, lnr moon, n crculr moon. In h ppr, on n lnr moon r xcluvly lc for xplnon. Rfrrng o quon (), on moon gmn cn b crb by PTP moon n Km lgorhm []. Th on-lnr (hybr) moon blnng wll b lo xprmn on h robo o h h blnng moon wll b hown o rc on-lnr ph. In vnc, ncry o ummrz Km lgorhm [] n h followng. For h vlocy uprpoon of h fr rpzol vlocy profl wh h con on hown n Fg. 5, Km lgorhm compo of 8 c hown n Fg. 5. In prculr, Fg. 6-(c) llur h c n whch h rcon of wo vlocy profl r oppo o ch ohr,.., (v_mx) (v_mx) < 0. Hr v_mx n v_mx r h conn p of h fr n h con vlocy profl, rpcvly, hown n Fg. 5. J ( u( )) = J u( )( J J ), u [0,] (0) whr J(u()) no on poon; h ubcrp n nc n n r, rpcvly. Smlrly, lnr moon gmn cn b gvn by L( u( )) = P u( )( P P ), u [0,] () whr L(u()) no poon of n n-ffcor n Crn coorn. Epclly P n P nc h n n r poon of h n-ffcor n Crn coorn. Equon cn b r-wrn n on coorn follow: : m from r pon o v pon : m from v pon o n pon Fg. 5 Concp o f Km blnng J ( u( )) = InvKn( L( u( ))) = InvKn( P u( )( P P )), u [0,] () whr InvKn( ) no h nvr nmc roun. Th propo hybr moon blnng houl b mplmn n on coorn on h b of m x. For xmpl, h ( )-h on moon gmn n h - h lnr moon gmn cn b bln n on coorn follow: J B ( u ( ), u ( )) = InvKn( L( u ( ))) + J ( u ( )) J (3) = InvKn( L( u ( ))) u ( )( J,, J, ) () [Fr clron m Scon cclron m] whr h uprcrp no h numbr of on x. 4. EXPERIMENT In orr o llur h ffcvn of h propo hybr moon blnng, h vlocy uprpoon ung prmrc nrpolon (cn b rm on-on moon blnng), whch b of hybr moon blnng, wll b xprmn on h 3-x SCARA [4] robo wh LbVIEW conrollr n compr wh h rul of boh (b) [Fr clron m > Scon cclron m]

5 y x (c) (v_mx) (v_mx) < 0 40mm 00mm Fg. 6 8 c of uprpoon for Km lgorhm In h mnwhl, h propo vlocy uprpoon ung prmrc nrpolon n Scon cn ovrlp wo vlocy profl brfly. In orr o compr h prformnc of h propo vlocy uprpoon wh Km lgorhm n h ronl PTP moon (no blnng), h cul mplmnon of 3 lgorhm r prform by ung h 3-x SCARA robo hown n Fg. 7. A hown n Fg. 8, h LbVIEW moon vc wh grphcl progrmmng h bn u for h conrollr of h robo [5]. () (b) Fg. 9 Exprmn conon of 3 x-scara robo For h prformnc of 3 lgorhm nclung PTP, Km lgorhm n h propo vlocy uprpoon ung prmrc nrpolon, h vbron murmn ung h FFT (F Fourr Trnform) nlyzr of Zonc h bn crr ou hown n Fg. 0. Fg. 0 Vbron murmn of 3 x-scara robo Fg. 7 3-x SCARA robo Fg. 8 Grphcl Progrmmng of LbVIEW Exprmn conon r follow. followng. B on h Crn coorn pcf n Fg. 9-(), h r pon (-00, 00), whr h n pon (00, 00) wh v pon of (0, 440), hown n Fg. 9-(b). Th pfcor, cclfcor n clfcor r 0.5, rpcvly, for h mxmum (conn-p) vlocy of 50 r/ n h mxmum cclron/clron (500 r/ ). Th rul of vbron murmn for 3 lgorhm r llur n Fg., n 3, rpcvly. A xpc, h lp m of PTP lgorhm for movng h robo from h r poon o h n poon h long, 6, compr wh ohr lgorhm (bou 3 ). Th roo-mn-qur (rm) vlu of vbron cclron n h un of grvonl cclron (g) r l Tbl. I cn b noc h h propo vlocy uprpoon ung prmrc nrpolon cn ruc h vbron cclron by / of h vbron cclron for PTP, by / of h vbron cclron for Km lgorhm. Thrfor cn b conclu h h propo vlocy uprpoon (pcfclly on-on blnng) lgorhm ung prmrc nrpolon cn b ffcv n rulng low vbron wh f movmn, compr o h xng lgorhm of PTP n Km lgorhm. 6 Fg. Rul of vbron murmn for PTP

6 5. CONCLUSION Fg. Rul of vbron murmn for Km lgorhm Fg. 3 Rul of vbron murmn for h propo vlocy uprpoon Tbl Vbron cclron of 3 lgorhm Algorhm g [rm] n g [rm] Tm x-coor. n y-coor, () PTP Km Algorhm Propo Algorhm A l, h fnl xprmn of hybr moon (pcfclly on-lnr) blnng lgorhm gvn by quon (3) h bn prform o how ffcvn by mng h pn ch o h robo rw h ph of n-ffcor hown n Fg. 4. Th cn vrfy h h propo hybr moon blnng wor ffcnly for fbl mplmnon. V pon 3 Lnr nrpolon 3 Jon nrpolon Fg.4 Ph of Hybr Moon Blnng In gnrl, h movmn rgy of nurl robo cn b v no wo n,.., PTP n CP. In orr o mplmn CP moon on robo, ncry o bln on on moon o nohr on moon nr v pon n rpzol form of on vlocy. Fr, h vlocy uprpoon ung prmrc nrpolon h bn propo. Hybr moon blnng fn h blnng of ffrn wo yp moon uch blnng of on moon wh lnr moon, n h nghborhoo of v pon. Scon, hybr moon blnng lgorhm h bn propo b on h vlocy uprpoon ung prmrc nrpolon. By ung 3-x SCARA robo wh LbVIEW conrollr, h vlocy uprpoon lgorhm ung prmrc nrpolon h bn hown o rul n l vbron, compr wh PTP moon n Km lgorhm. Morovr, h hybr moon lgorhm h bn uccfully mplmn on h robo ung LbVIEW progrmmng, whch h bn confrm by howng h n-ffcor ph of on-lnr hybr moon. 6. ACKNOWLEDGMENT Th rrch w fnnclly uppor by h Mnry of Commrc, Inury n Enrgy (MOCIE) n Kor Inurl Tchnology Founon (KOTEF) hrough h Humn Rourc Trnng Proc for Rgonl Innovon 7. REFERENCES [] Nonl Inrumn Corporon. Moon conrol Funmnl cour Mnul, [] D. Y. Km, Dvlopmn of nw wvng Algorhm ung Bzr Spln n A uy on h Rlzon of CP(Connuou Ph) Moon wh Jr Connuy, Mr of Engnrng r, School of Mchronc, Chngwon Nonl Unvry, 004. [3] K. S. Fu, R.C. Gonzlz n C.S.G L,, ROBOTICS, pp49-00 [4] J. H. Ju. Mon-Crlo Smulon Tchnqu for Erro r Anly of 3-x SCARA Robo ung Obrvbly, MSV07.pp0-07 [5] J. H. Km. Prooypng n Vulzon Tchnqu of 3-x SCARA Robo Ung DOE n LbVIEW, MSV07.pp34-40 [6] Nonl Inrumn, LbVIEW Funmnl, 005