NGHIEN CUfU-TRAODOI gDlEU KHiiN ROBOT MEM BANG PHU'aNG PHAP NQI SUY SCr DUNG HAM DjNH DANG KET HOP VOI CO OHt BU KEP THE CONTROL OF FLEXIBLE MANIPULATORS APPLYING FORMAT FUNCTIONS IN COMBINATION WITH DOUBLE COMPENSATION Pham Thanh Long Trudng Dai hgc Ky thuat Cong nghiep, Dai hgc Thai Nguyen TOM TAT Mot cdc dgc diim quan trgng ciia robot mem Id a cho co cdu chap hdnh phdi lien tiic tich lHy vd gidi phdng thi ndng ddn hdi, ldm dnh hudng den tinh chinh xdc dgng hgc vd dgng luc hgc cua nd Bdi bdo ndy gidi thieu mgt quan diim xdy dung die lieu diiu khiin, nhdm dam bdo chinh xdc dgng hgc, dong thdi cd chi phi tinh todn hgp ly, phii hgp voi ndng luc cua hi thdng mdy tinh Biin dgng dan hdi cita ca cdu tgi mgt sd diem chudn xdc dinh thdng qua thuc nghiem Cdc die lieu biin dgng thuc nghiem duac thu thdp bdng cdc strain gauge vd mgch cdu wheatstone Sai sd tgi cdc diem chudn khdc thugc viing ldm viec dugc ngi suy tren quan diem sic dung hdm dinh dgng Ket qud cua buoc ndy sau dd duoc kit hgp vdi sa bit sai so theo hai buoc tho vd tinh de hiiu chinh vi tri cua diim cudi Kit qud dgt duac cho thdy ky thudt cd thi icng dung diiu khien cdc robot mim ddi hdi chinh xdc dgng hgc cao T\x khoa: Robot mim ngi suy, cdm biin sice cdng, bit sai so, cdu wheatstone, chi phi tinh todn ABSTRACT One of the important characteristics of flexible robots is the actuator which continuously accumulates and releases the elastic potential These processes affect the accuracy of robots This paper proposes a new approach of building control data to ensure kinematic accuracy as well as reasonable computation cost In addition, this method adapts to the capacity of computer systems The elastic deformation of the structure at some reference points can be determined by empirical data The Wheatstone bridge circuits and strain gauge are used in this paper content The deviation at reference points in the working domain is interpolated by using format functions The step result is then combined with the compensation scheme for errors, according to coarse-to-fine steps to adjust the position of the end point The obtained results show that the proposed method can be applied to control flexible robots which require high kinematic accuracy Keywords: Flexible robot, interpolate, strain gauge, compensation error, wheatstone cost calculation ISSN 0866 - 7056 TAP CHi CO KHi VIET NAM, S6 nam 2015 www.cokhivietnam.vn NGHIEN CUfU-TRAO DOI M O DAU Do ygu cau ve nang suat lao dgng cang cao ngn toe thao tac bang robot cung doi hoi phai dugc nang cao cung vdi tai trgng Idn han He qua cua viec la bign dang dan bdi cua he thong lam vi tri va hudng cua khau cudi sai lech nhigu so vdi tinh toan Viec thigt kg va dieu khien robot vi thg cung cSn cd nhirng thay ddi de dam bao dp cung vimg va dp chinh xae Cd hai khuynh hudng ca ban iing xu vg ky thuat cd the thay la: - Tinh toan lai kgt cau co du cung de dam bao phu hgp vdi miic tai trgng va van tdc cdng tac mdi; - Mgm hda chu dgng, tiic la chap nhan ca cau chap hanh cd bien dgng dan hdi sau dd hieu chinh vi tri va budng khau cudi thong qua thay ddi mo hinh toan cua ddi tugng Nagarajan and Turcic [8] da dua he thdng cac phuong trinh ca ban cho he thdng cac khau dan hdi va khSu ciing Bricout et al [3] sir dimg phuang phap phSn hi hiiu han dg nghien cuu cac khSu dan hdi Moulin va Bayo [7] cung su dung cac phSn tii rdi rac hiiu ban dg thao luan vg quy dao diem cudi cho khau chap hanh mgm va cho thdy rang mdt giai phap quan he khong nhan qua cho moment xoan cho phep theo doi chuygn vj ciia khau chap hanh vdi chinh xac mong mudn Chang va Garmon [5] da phat trign mdt he thdng tuong duong tang cudng lien ket Cling (ERLS) md hinh su dung cac chuc nang tu nhien cho tay may mem va thu nghigm xac nhan cho md hinh lien kgt don da dugc thuc hien Zhu et al [9], xem xet md hinh tham sd ggp dg md phdng su theo doi vi tri cua diem cudi tren khau chap hanh tay may mgm lien kgt don Khalil va Gautier [6], su dung mdt md hinh dan hdi ggp cho cac he thdng ca linh boat Lien quan den viec xac dinh va bu sai sd sii dung cac ham npi suy, van dg da dugc dg capdenbdi AnjanappaM [1], dd, viec xac dinh va bii sai so dugc dat vai cac may cdng cu digu khien sd Fereira, K R, Liu, C R eung da phan tich viec ling dung cac md hinh bac dg bu sai sd hinh hgc tren cac trung tam gia cdng [2] Lin P D de cap den xac dinh va bu sai sd cho cac may cdng cu nhigu true [4] Nhuge digm cua cac cdng trinh chua thdng nhat dugc quy trinh chung cho xay dung sd lieu bu bien dang dugc nhanh chdng vdi khdi lugng tinh toan nhd han ma van dam bao chinh xac Trong bai bao nay, chung tdi de xuat mdt quy trinh de giai quygt van de xay dung sd lieu digu khien dpng hgc co cau robot mgm thdng qua bdn budc: - Chia ludi khdng gian cdng tac cua robot cac phan tir dang hop chii nhat va tinh toan sai sd dgng hgc bien dang dan hdi ciia ca cau bang phuang phap phan tu hiiu han hoac ludng bign dang bang thuc nghiem, do, sii dung cam bien khoang each va cac khoi mau; - Ngi suy sai sd tai cac diem khac khdng gian cong tac bang phuang phap su dung ham dinh dang; - Bu thd va danh gia sai sd cdn tdn tai; - Tinh toan lugng bu tinh va thuc hien bu tinh XAC DINH SAI SO DONG HOC CUA ROBOT M E M De bii sai sd ve ca ban gom hai budc chinh la bien dang kgt hgp ngi suy va loai trii sai sd dd, ve nguyen tac neu sai so dugc tinh toan bang mot phuong phap cu the nd cd the vap phai cac ldi khau md hinh hda, ngu sai sd dugc xac dinh bang thuc nghiem ed the ke den tat ca cac nhdm nguygn nhan gay sai sd nhu bign dang va khe hd co ^ ISSN 0866 - 7056 TAP CHi CO KHi VIET NAM, Sd nam 2015 www.cokhivietnam.vn NGHIEN CUfU-TRAO D | Do dung lugng va tde tinh toan ciia cac may tinh dgu bj gidi ban ngn chiing ta khong thg luu trii tit ca cac gia tri sai sd khong gian lam viec ciia may, viec xac dinh sai so ddng hgc tgi mdt digm cu thg thudng tren nguygn tac ngi suy Ngi suy sai so tai cac diem £ qua Do sai so tai cac djpm diuan Bii kg) Robot mem Hinh 1: Sa nguyin ly bd sai sd tay robot mem 2.1 Xic dinh biln d^ng ciia khau bang thuc nghiem Trong qua trinh tinh toan bien dang bang phuang phap phan hiiu ban ed the vap phai cac sai sd khau md hinh hda, viec bien dang tranh dugc cae ldi va ciing thich hgp ban vdi bai toan quy md Idn phai lay mlu d nhieu diem chdt khac FlM-n^ •-• _±My ~E^ EJ 0) Trong dd: Md dun dan hdi E xac dinh tu thi nghiem keo diit mSu dudi day • ^ •• • ^ 'm *•••/ Dau tien can xac dinh chinh xac md dim dan hoi E cua vat lieu che tao khau dan hdi, thdng qua cac quan he co hpc sau day se xac dinh dugc bign dang ciia nd _(7 M I 3K«( CRM "^^li^^ STRAIN O U J E E >k •^^ smAiNOAuse Hmh 3: Cdch ddn strain gauge lin khau vd mgch cdu wheatstone Robot sii dung thi nghiem cua chiing tdi trinh bay d day gdm ba khau (robot ba khau phang) chigu dai khau: 1-^5 a, = 250, 3^-250, a3-165 mm Hmh 2: Mdu keo thu vgt lieu che tgo khau de tim E Vdi tai trgng mang ban tay la 400 (N), minh hga sai lech vi tri ciia tam ban tay tai cac diem thg bien bang dudi day dat dugc thdng qua ba cau trgn ba khau Bdng 1: Minh hga kit qud bien dgng bdng strain gauge Siem L y thuyet Y(mm) 557.0499 532.49422 331.24851 Z(mm) 313.2039 372.5993 492.2819 Ket qna Y(mm) Z(mm) 557.2459 312.94749 532.7112 372.35227 331.3334 492-22789 ISSN 0866 - 7056 TAP CHi CO KHi VIET NAM, Sd nam 2015 www.cokhivietnam.vn Sai so bien d a n g ^(mm) &(min) 0.619 0.256 0.217 0.247 0.085 0.0534 NGHIEN CUfU-TRAODdi 2.2 Phinmg phap noi suy diing ham dinh dang Chia khdng gian cdng tac cua robot mdt sd biiu ban cac phan tii bang cac Idp mat phang song song vdi cac mat tao bdi cac true ciia he quy chigu co sd gan vdi gia cua robot Giao digm ciia cac mat dinh hinh cac phan tu dang hop chii nhat va cac dinh ciia nd dugc gpi la didm chuan Tiiy theo quy dao ciia diem cudi trgn robot, ngudi dieu khign can xac dinh sai sd vi tri va hudng tai cac digm chuan cu thg bang each thuc ngliiem hoac thdng qua cac tinh toan dan gian He thdng sai sd d cac digm sau dd diing lam CO sd dg ndi suy sai sd d cac diem trung gian khac ciia quy dao Vigc lam day nhanh dugc qua trinh tinh toan sai sd da thay the bai toan tinh hoac sai sd la bai toan cd chi phi tinh toan Idn bang bai toan ndi suy la bai toan cd chi phi tinh toan nhd ban {r=-1;s=+1;t=-1) '^^^1.'-% Hinh a Hinhb Hinh 4: a) Sa chia luai khdng gian cdng tdc cua robot trin mat chiiu dimg vd chiiu bdng; b) Hi toa (r, s, t) cho cdc hdm dinh dgng trin phdn tu dgng hop H4m dinh dang cho phSn tii tren hinh xac dinh nhu sau: Ar, = - ( l + r X l - s ) ( l + t ) V, = i ( i + / - X i - - s X i - v , = - | ( i + »-Xi+ 5X1 + N,=Ul + rX\ + s)0.-t) (l-r)(l+jXl + -V, = i ( l - r X l + ^ X l - 7/, = i ( l - r X l - ^ X l + Ar8 = i ( l - r X l - ^ X l - f ) ISSN 0866 - 7056 TAP CHi CO KHi VIET NAM, 53 nam 2015 www.cokhivietnani.vn (2) NGHIEN CUfU - TRAO edi Nhu vay, gia su sai sd d tam ciia phan tu Sai sd vi tri hoac hudng tai mgt didm hop ndi tren la bidt trudc thi dinh ciia nd cd the chuSn bat ky dugc ngi suy qua ham dinh dang: ndi suy duoc sai sd theo cac ham dinh dang noi trgn theo trinh tu sau: ^ = ^i'?! + ^2^/2 + He quy chieu r,s,t dat tai trgng tam cua phin hi ngn cd cdng thiic chuyen true: ' - ^ (3) + N„TJ„ (5) Trong do: ^(u^,Uy,u^,g)^,g)y,p^)\a sai so vi tri hoac hudng tai mdt digm chuin bat ky dang can tinh; J], sai so da bigt tai cac diem chuan thdng qua Trong - toan - boic u xthuc *u nghiem; u—_ ^ dd: , a, b,c ,xac dinh • ,theo binh 2, toa tinh dp trpng tim cua phan tii dang xet: n: Sd digm chuan tren phan hi (4) Kgt hgp vdi dii lieu d phan 2.1, ndi Nhu vay, cac gia tri (r, J, t) bign suy mdt quy dao diy du gdm digm chdt nhu thign doan [-1,1] dudi day Bdng 2: Minh hga kit qud ngi suy sai so tgi cdc diim chdt cua quy dao Diim L y tliuyet Y(nini) Z(mm) Ket qua Y(ram) Z(mm) 557.0499 313.2039 557.2459 312.94749 0.619 0.256 562.94209 532.49422 324.7715 563.1421 0.2 0.273 372.5993 238.1441 532.7112 324.49849 372.35227 0.217 0.247 612.3841 247.77106 0.135 0.373 492.2819 331.3334 372.6722 492.22789 0.085 0.0534 519.18172 0.179 0.0965 612.24907 331.24851 372.49315 519.2782 BU SAI SO THEO HAI Bl/OC Do anh huong cua ngoai lire bien dang cua cau triic lam cho vi tri va dinh huong thuc tk se la: 3.1 Qua trinh bu thd Ky hieu ma tr£n tea dp thuc bieu dien the cua robot a vi tri mong muon la: - •', Sai s6 biin dang 5y(nim) 5z(nim) •', - P, iP,±u,) (6) - (»1,±R,,,.) Iji,±ip„„) ^,g)^,q)f) Trong khdng gian cdng tac cua robot, de bu trOr anh hudng ciia bign dang kg tren cin digu khien ciu tnic dua khiu tac dpng cudi dat den tu the sau thay vi dgn (6): - (",+R0., ) (",+?'.D ) Ip.^f-u,) L- De khac phuc su giam tim vdi khiu bi udn cong, khdng khd dg thiy r5ng ngu D mudn triing vao A sau bien dang diy dii thi trudc chiu luc tii diem C tren hmh cin cdng thgm vao phuang ciia khau mdt doan bang hinh chigu vudng gdc cua doan AD len khau d trang thai chua chiu luc (AD.cos((|))) (8) iTu digm cua each lam la giam dugc dang ke sai sd vi tri digm cudi so vdi khdng bu, nhien, su ban chg cua each lam d chd nd khdng the bii dugc su giam tim vdi ciia mdi khiu Do da bi udn cong thi tim vdi ludn la diy cung ngu khdng bidn dang tam vdi phai la chigu dai cung, cd thg thiy ro digu dd hinh Hinh 6: Su hinh thdnh diem thay Ihi bu linh Ggi CE la hinh chigu vudng gdc cua AD len khau d trang thai dS lay doi xiing bu thd nhu hinh 5, vi gdc giira AD va CE (ki hieu ) dii nhd de ed thg xem gin diing CE = DA (tam giac can thay vi vudng), nhu vay, diem E la diem thay thg cho digm C lin bu thii hai; d trang thai dn dinh sau khau bien dang dan hdi day du digm E se tiem can dgn digm mong mudn A gan Hinh 5: Quan hi giua cdc vi tri ldm viic ban so vdi digm D Dg nhan thay d lan bii thii n lugng bu tao mdt chudi don dieu giam bi Theo binh ve 5, mudn digm cudi la A thi chan dudi: thuc tg chiu lue p, dieu khien bang cac tham sd ddng hgc ly tudng kigm tra tren cac phan mem (9) LimU^