Cd hai khuynh hudng ca ban trong iing xu vg ky thuat cd the thay la: - Tinh toan lai kgt cau co khi du cung de dam bao phu hgp vdi miic tai trgng va van tdc cdng tac mdi; - Mgm hda chu d
Trang 1gDlEU 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 trong 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 do 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 do 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 do 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 do 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
Trang 2NGHIEN CUfU-TRAO DOI
1 M O DAU
Do ygu cau ve nang suat lao dgng ngay
cang cao ngn toe do thao tac bang robot cung doi
hoi phai dugc nang cao cung vdi tai trgng Idn
han He qua cua viec nay 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 trong iing xu vg ky
thuat cd the thay la:
- Tinh toan lai kgt cau co khi 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 ra 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 do 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 khi linh boat
Lien quan den viec xac dinh va bu sai sd
sii dung cac ham npi suy, van dg nay da dugc dg
capdenbdi AnjanappaM [1], trong dd, viec xac dinh va bii sai so dugc dat ra 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 2 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 nay chua thdng nhat dugc quy trinh chung sao cho xay dung sd lieu bu bien dang dugc nhanh chdng vdi khdi lugng tinh toan nhd han ma van dam bao do 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 thanh cac phan tir dang hop chii nhat va tinh toan sai sd dgng hgc do bien dang dan hdi ciia
ca cau bang phuang phap phan tu hiiu han hoac
do ludng bign dang nay bang thuc nghiem, trong
do, sii dung cam bien khoang each va cac khoi mau;
- Ngi suy sai sd tai cac diem khac trong 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
2 XAC DINH SAI SO DONG HOC CUA ROBOT M E M
De bii sai sd ve ca ban gom hai budc chinh la do 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 trong khau md hinh hda, ngu sai sd nay dugc xac dinh bang thuc nghiem ed the ke den tat ca cac nhdm nguygn nhan gay ra sai sd
nhu bign dang va khe hd co khi ^
ISSN 0866 - 7056
TAP CHi CO KHi VIET NAM, Sd 3 nam 2015
Trang 3Do dung lugng va tde do tinh toan ciia cac may tinh dgu bj gidi ban ngn chiing ta khong thg luu trii tit ca cac gia tri sai sd trong khong gian lam viec ciia may, viec xac dinh sai so ddng hgc tgi mdt digm cu thg thudng tren nguygn tac ngi suy
Do sai so tai cac
djpm diuan
Ngi suy sai so tai cac
Hinh 1: Sa do 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 trong khau md hinh hda, viec do bien dang
tranh dugc cae ldi nay va ciing thich hgp ban vdi
bai toan quy md Idn khi phai lay mlu d nhieu
diem chdt khac nhau
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 _±My
FlM-n^ M I 3K«( CRM
"^^li^^
• - • •• • ^
'm
*•••/
>
STRAIN O U J E E
k
•^^
smAiNOAuse
Hmh 3: Cdch ddn strain gauge lin khau
vd mgch cdu wheatstone
Trong dd: Md dun dan hdi E xac dinh tu
thi nghiem keo diit mSu dudi day
• ^ 1 1-^5
Robot sii dung trong thi nghiem cua chiing tdi trinh bay d day gdm ba khau (robot ba khau phang) chigu dai khau:
a, = 250, 3^-250, a3-165 mm Vdi tai trgng mang trong ban tay la 400 (N), minh hga sai lech vi tri ciia tam ban tay tai cac diem do thg bien trong bang dudi day dat dugc thdng qua ba cau do trgn ba khau
Hmh 2: Mdu keo thu vgt lieu che tgo khau de tim E
Bdng 1: Minh hga kit qud do bien dgng bdng strain gauge
S i e m
1
2
L y thuyet
Y ( m m )
5 5 7 0 4 9 9
532.49422
3 331.24851
Z ( m m )
313.2039 372.5993 492.2819
K e t q n a do
Y ( m m )
557.2459 532.7112 331.3334
Z ( m m )
312.94749 372.35227 492-22789
S a i so bien d a n g
^(mm)
0.619 0.217 0.085
& ( m i n )
0.256
0 2 4 7 0.0534
Trang 4NGHIEN CUfU-TRAODdi 2.2 Phinmg phap noi suy diing ham dinh dang
Chia khdng gian cdng tac cua robot
thanh mdt sd biiu ban cac phan tii bang cac Idp
mat phang song song vdi cac mat tao thanh bdi
cac true ciia he quy chigu co sd gan vdi gia cua
robot Giao digm ciia cac mat nay 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 ro-bot, 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 nay sau dd diing lam
CO sd dg ndi suy sai sd d cac diem trung gian khac ciia quy dao Vigc lam nay day nhanh dugc qua trinh tinh toan sai sd do da thay the bai toan tinh hoac do 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
7 {r=-1;s=+1;t=-1)
'^^^1.'-%
Hinh a Hinhb Hinh 4: a) Sa do chia luai khdng gian cdng tdc cua robot trin mat chiiu dimg vd chiiu bdng;
b) Hi toa do (r, s, t) cho cdc hdm dinh dgng trin phdn tu dgng hop
H4m dinh dang cho 8 phSn tii tren hinh 2 xac dinh nhu sau:
Ar, = - ( l + r X l - s ) ( l + t )
v , = - | ( i + »-Xi+ 5X1 + 0
( l - r ) ( l + j X l + 0
.V, = i ( i + / - X i - - s X i - 0
N,=Ul + rX\ + s)0.-t)
-V, = i ( l - r X l + ^ X l - 0
(2)
ISSN 0866 - 7056
TAP CHi CO KHi VIET NAM, 53 3 nam 2015
Trang 5Nhu 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 8 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 + + N„TJ„ (5)
He quy chieu r,s,t dat tai trgng tam cua
phin hi ngn cd cdng thiic chuyen true:
' - ^ (3)
Trong do:
7 ^(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 dd: a, b,c xac dinh theo binh 2, toa - - u x *u u—_ ^ , 1 , • , tinh toan boic thuc nghiem;
n: Sd digm chuan tren phan hi
(4) Kgt hgp vdi dii lieu do d phan 2.1, ndi Nhu vay, cac gia tri (r, J, t) nay bign suy mdt quy dao diy du gdm 6 digm chdt nhu
thign trong doan [-1,1] dudi day
dp trpng tim cua phan tii dang xet:
Bdng 2: Minh hga kit qud ngi suy sai so tgi cdc diim chdt cua quy dao
Diim
1
2
3
4
5
6
L y tliuyet
Y(nini)
557.0499
562.94209
532.49422
612.24907
331.24851
372.49315
Z ( m m ) 313.2039 324.7715 372.5993 238.1441 492.2819 519.2782
Ket qua do Y(ram) 557.2459 563.1421 532.7112 612.3841 331.3334 372.6722
Z ( m m ) 312.94749 324.49849 372.35227 247.77106 492.22789 519.18172
Sai s6 biin dang 5y(nim) 0.619
0.2
0.217 0.135 0.085 0.179
5z(nim) 0.256 0.273 0.247 0.373 0.0534 0.0965
3 BU SAI SO THEO HAI Bl/OC
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:
Do anh huong cua ngoai lire bien dang
cua cau triic lam cho vi tri va dinh huong thuc tk
se la:
- • ' , • ' , P ,
- P,
1
(6)
- (»1,±R,,,.) Iji,±ip„„) <P.±»,)
Trang 6NGHIEN CUfU-TRAODdi
Vdi (7) xiy dyng hi (6) va bign dang do 3.2 Qua trinh bii tinh
dugc bang thuc nghiem T]= (U^,U ,u„q>^,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):
(8)
iTu digm cua each lam nay la giam dugc
dang ke sai sd vi tri digm cudi so vdi khi khdng
bu, tuy nhien, su ban chg cua each lam nay d chd
nd khdng the bii dugc su giam tim vdi ciia mdi
khiu Do khi da bi udn cong thi tim vdi ludn la
diy cung trong khi ngu khdng bidn dang tam vdi
phai la chigu dai cung, cd thg thiy ro digu dd
trong hinh 5
- (",+R0.,
L-) (",+?'.D 6
) Ip.^f-u,)
1
Hinh 5: Quan hi giua cdc vi tri trong khi ldm viic
Theo binh ve 5, mudn digm cudi la A thi
thuc tg khi chiu lue p, dieu khien bang cac tham
sd ddng hgc ly tudng kigm tra tren cac phan mem
FEM chi ra diem eudi thuc tg la B De khac phuc
trong budc bii thd liy C lam digm cudi thay the
cho A ngn trong ciing digu kien digm cudi se la D
gin vdi A hon nhigu so vdi B, phep bii da mang
lai bieu qua
Tuy nhign, lugng AD chinh la lugng
khong thg giam nhd hon ngu chi bii mdt lin ma
nguyen nhin d chd khi khiu bi udn cong nhu
dudng net diit trdn binh 5, tam vdi cua nd hi
giam di
De khac phuc su giam tim vdi do khiu bi udn cong, khdng khd dg thiy r5ng ngu D mudn triing vao A sau khi bien dang diy dii thi trudc khi chiu luc tii diem C tren hmh 5 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((|)))
Hinh 6: Su hinh thdnh diem thay Ihi khi bu linh
Ggi CE la hinh chigu vudng gdc cua AD len khau d trang thai dS lay doi xiing khi 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 trong lin bu thii hai; d trang thai
dn dinh sau khi khau bien dang dan hdi day du digm E se tiem can dgn digm mong mudn A gan ban so vdi digm D Dg nhan thay d lan bii thii n lugng bu tao thanh mdt chudi don dieu giam bi chan dudi:
4 KET QUA NOI SUY BANG HAM DpVH DANG KET HOfP BU KEP
Dg minh hga cho quy trinh bii dua ra d trgn, trong muc nay trinh bay cac kgt qua nhan dugc khi ket hgp ba quy trinh gdm do sai sd bing strain gauge, npi suy bang ham djnh dang
va bu kep cho mdt quy dao gdm 6 diem key thuc
hign tren robot ba khiu nhu sau ^
ISSN 0866 - 7056 TAP CHi CO KHi VIET NAM, Sd 3 nam 2015
Trang 7Bdng 3: Minh hga kit qud bii kep trin robot ba khau
Dien
1
1
5
Moiw muon
Y
557.0499
562.94209
612-24907
372 49315
Z
313 2039
372,5993
23R 1441
492,2819
519 2782
Till
^ •
557 2459
563 1421
532.7112
612 3841
3J1 3334
372-6722
IfCti
Z
3 1 2 9 4 7 4 9
3 2 4 4 9 S 4 9
2 4 7 7 7 1 0 6
5 1 9 18172
B u I
^ •
557 0 4 2 7
532 44S1
3 J I 2 4 8 3
372 4 9 1 7
Z
3 1 3 2 0 5
3 2 4 7 8 S
3 7 2 6 3 4
4 9 2 2 8 1
S a i s
Sv
0 0071
- 0 0 2 1 8 0,0461
0 0 0 0 2
o b u l
&z
0 , 0 0 1 5
• 0 0 3 6 5 4 0.(XH01
- 0 (XKXM
B u 2
&
5 5 7 0 4 9
5 6 2 9 4 2 5
6 1 2 , 2 4 7 3
3 7 2 4 9 3
Sz
315 2 0 2 9
324 " " 2 4
23S 1432
4 9 ; 2 S I 5
5 1 9 2 7 8
S a i so b ^ :
&
OUOUUN
0 (ll](W3
0 n o i s :
n 00(109
b ;
0 O I W 6 3 I) 1)0089
0 ( X ) 0 9 4
0.00005
Sai i6 khdnf! bu
&
a 6 1 9 0.2
0 3 1 7
a i 3 5
0.179
6z 0.256
0.247
0,0534
5 KET LUAN
Ky thuat ma bai bao trinh bay cho phep hieu chinh do chinh xac eho cac robot mem; Viec
chiing minh dugc each lam nay dam bao do chinh xac yeu cau trong hai lan bu tuong duang vdi eae giai thuat bu hdi quy ciia cac tie gia khac da cdng bo Sai sd d cac lin bu la mdt chudi dan dieu giam bj chan dudi, tiic ia khi sd lan bii tidn tdi vd ciing thi sai sd ve khdng, cd nghia la giii thuat bii ndi trgn cd thg cho do chinh xac bit ky vdi so lan bii thich hgp
Toan bg qua trinh bu da thay the cac giii thuat cd chi phi Idn bang giai thuat ndi suy cd chi phi be ban lam day nhanh qua trinh tinh toan, do digm liy miu khdng nhat thigt tning vdi quy dao ngn viec ndi suy sai sd cho cac quy dao khac nhau khdng can do sai sd chuan nhieu lin, sd lieu diu vao ciia bai toan ndi suy cd the xiy dung theo hai each, do bang thuc nghiem hoac tinh toan theo ly thuygt phan tii hiiu han
Ky thuat npi suy ham dinh dang du da dugc cdng bd ling dung hieu qua trgn cac trung tam gia cdng ddi hdi do chinh xae cao, song nd ciing cd the ling dung hieu qua tren robot, ciing mpt quy trinh nhu trgn cd the trign khai trgn cac robot cd ciu tnic khac nhau vdi sir kg den nhieu hon cac thanh phan bign dang ciia khau.*t*
Ngay nhan bai: 08/02/2015
Ngay phan bien: 12/3/2015
Tai lifu tham khao:
[1] Anjanappa M Enor correction methologies and control strategies for numerical control machining; ASME,Vol 7, 1988
[2] Ferreira, K E, Liu, C R; An analytical quadratic model for geometric error of machining center; journal
of manufacturing systems, April 1986
[3] J.N Bricout, J.C Debus, P Micheau, A finite element model for the dynamics of flexible manipulator, Mechanism and Machine Theory 25 (1)(1990) 119-128
[4] Lin P D; Error analysis, measurement and compensation for multi - axis machine; Northwestern university phD Disser 1989
Trang 8NGHIEN CUfU - TRAO Ddi
[5]- L.W Chang, K.P Gannon, A dynamic model on a single link flexible manipulator, ASME Journal of Vibration and Acoustics 112(1990) 13 8-143
[6] W KhaUl, M Gautier, Modeling of mechanical systems with lumped elasticity Proceedings of the IEEE
Intemational Conference on Robotics and Automation 4 (2000) 3964-3969
[7] H Moulin, E Bayo, On the accuracy of end-point trajectory tracking for flexible arms by noncausal inverse dynamic solutions, ASME Journal of Dynamic Systems, Measurement, and Control 113 (1991) 320-324
[8] S Nagarajan, D.A Turcic, Lagrangian formulation of the equations of motion for the elastic mechanisms with mutual dependence between rigid body and elastic motions Part 1: Element level equations, and Part II: System equations, ASME Joumal of Dynamic Systems, Measurement, and Control 112(2) (1990) 203-214, and 215-224
[9] G Zhu, S.S Ge, T.H Lee, Simulation studies of tip tracking control of a single-hnk flexible robot based
on a lumped model, Robotica 17 (1999) 71-78
ISSN 0866 - 7056
TAP CHi CO KHi VI$T NAM S6 3 nam 2015