NGHIEN CirU-TRAO DOI
"MiNG DUNG MANG N O R O N
DE GIAI BAI TOAN DONG HOC NGl/CJC TAY MAY
APPLICATION OF NEURAL NETWORK FOR THE PURPOSE OF SOLVING THE KINETIC PROBLEM WITH COUNTER
CUTTER JIBS
TS. Lyong Hong Sam, KS. Nguyin Viet Hung Trucmg Dai hoc Tran Dai Nghia
TOM TAT
Bai todn dong hoc nguac Id mot phdn quan trong, chiem mot phdn l&n trong cdc nghien cim ve lay mdy. Co nhieu phucmg phdp gidi bdi todn dong hoc nguac, tuy nhien moi phucmg phdp deu co uu nhugc diem rieng. Trong bdi bdo ndy, chimg toi giai thieu mot phuang phdp m&i gidi bdi todn dong hoc ngitffc cho tay mdy bdng viec ung dung mang naron. Phuong phap nay, to ra hieu qud nhdt la duac tra giiip manh me vd todn dien cua mdy tinh vdphdn mem Matlab. Kit qud nghien cieu ndy duac img dung cho bdi todn dieu khien vd cdc bdi todn khac ve tay mdy.
Tir khoa: Mang naron; Bdi todn dong hoc nguac.
ABSTRACT
The inverse kinematics plays an important role, account for a large part in the study of manipulators.
There are many methods to solve this problem, each method has its own advantages and disadvantages.
In this paper, we introduce a new method of solving the problem of inverse kinematics for manipulators with artificial neural network application. This method proved effective, especially with the strong am comprehensive support of computer and Matlab .software. The results of this study are applied to control problems and other problems in manipulators.
Keywords: Neural networks; Inverse kinematics.
TAP CHi CO KHi V I £ T NAM, S6 3 nam 2014 www.cokhivietnam.vn
NGHIEN CUU - TRAO DOI 1. GIOI THIEU
Nhiem vu cua bai toan ddng hgc ngugc la xac dinh cac gia tri cua bidn khdp q_, (i=l,...n) khi biet trudc vi tri va hudng ciia ban kep Robot.
Viec nghien ciiu giai bai toan ddng hgc ngu'gc cho rdbdt la mot ITnh vuc dugc r^t nhidu nha nghien ciiu quan tam vi Idi giai cua nd la ca sd dd didu khien ban kep den vi tri cho trudc.
Cd ba phuang phap truydn thdng thudng dugc sir dung dd giai bai toan ddng hgc ngugc:
Phuang phap giai tich, phuang phap hinh hgc va phuang phap lap.
Phu-ffng phap giai tich: Xac dinh cac bidn khdp q,, q,, q^ theo cac bidn vi tri. Dd xac dinh gia tri cua cac bien khdp nay ta phai giai n phuang trinh vdi n in sd vdi robot cd n bac Ur do. Phuang phap nay Ididng dam bao duy nhit nghiem [I].
Phu-ffng phap hinh hoc: Bang each chilu he tga do ciia khau len true tga do X ^ va Y ,. Phuang phap nay, cd the dugc diing de giai cho bit ki tay may nao da biet hinh dang hinh hgc. Han chd cua phuang phap nay la nghiem dang hrdng minh cho ba khdp dau tien phai tdn tai ve phuang dien hinh hgc [2].
Phu-OTig phap lap: Giai bai toan dgng hgc ngugc bang each lap lai cac bien khdp nham xac dinh cac bien khdp phu hgp neu phuang phap nay hdi tu tdi mot Idi giai duy nhat. Tuy nhien, vdi tay may cd so bac tu do Idn, ddi khi se Ididng hoi tu nen khdng dam bao viec dieu khien tay may theo thdi gian thuc.
LTng dung mang naron de giai bai toan ddng hgc ngugc da cd mot sd cdng trinh nghien ciiu [1], [3]. Trong bai bao nay, chiing tdi gidi thieu viec su dung mang naron truyen thang vdi giai thuat Back propagation de giai bai toan ddng hgc TAP
ngugc cho tay may Scorbot ER-VII. Ket qua dat dugc da chiing minh rang mang naron cd the giai bai toan ddng hgc ngugc tay may cd n bac tu do, do chinh xac cao, bao dam dugc thdi gian thuc cho dieu khien tay may.
2. BAI TOAN DONG HOC THUAN TAY MAY SCORBOT ER-VTI
Hinh 1: Sa do ddng hgc cua tay may Scorbot- ERVIL
Tay may Scorbot ER-VII cd sa do ddng hgc nhu hinh 1. Giai bai toan ddng hgc thuan theo phuang phap dimg ma tran thuin nhit do Denavit J. & Hartenberg R.S. [3]. Phuang h-inh dgng hgc bai toan thuan nhu sau;
= A,.A3.A3,A^.A5^
1 j -
tu.
nz
0 S j - S-y Sz
0
ax a,.
Qz 0
Vx Pv Pz
1
(2.1)
Trong do: Cac ma tran A^ mo ta vi tri va huong cua Idiau thir i so voi Ichau thii i-1.
3. BAI TOAN DONG HOC NGlTOC Trong bai nay, chiing toi giai bai toan dong hgc tay may Scorbot- ERVII nhSm IciSm chiing ' CHl CO KHi VIET NAM, S6 3 nam 2014
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NGHIEN ciiu - TRAO DOI
i 0 U U
0 - 1
0 0
0 0 - 1 0
Pr Pv v?
1
Icet qua giai bang mang noTon. De co nghiem duy nhat chiing toi giai trong trucmg hcrp ban Icep cua tay may phai luon vuong goc voi mat phang XDY.
De don gian trong qua trinh xac dinh cac bien lihcip, huong ciia ban iiep dugc co dinh. Khi do vi tri va huong cua ban icep so voi goc tga do dugc the hien nhu sau:
(2.2)
Can bang cac phan tir cua phuong trinh (2.2) ta dugc cac piiucmg trinh bai toan dgng hgc ngugc tay may Scorrbot- ERVII.
4. MANG NOBON TRUYEN THANG NHIEU L 6 P
Mang noron truyen thfing nhigu lap (Feedforward networlc) gom co mot Icjp vao, mot lop ra, CO the khong co hoac co nhiSu lop jn. M6i noron thii q o Icjp an lien Icgt voi Igp vao bjng trgng s6 V^ va lien kit voi Icjp ra bang trgng s6 W_^; vai j = 1, 2....,m; q=l, 2.../; I = 1, 2..., u.
4.1. Luat hoc lan truyen ngu-ffc Luat hgc Ian truyen ngugc (Back propagation leaming rule) cho mang truySn thSng nhiiu Icjp da dugc Bryson va Ho da xuji nam 1969 [4].
Cho truoc cap mlu tin hieu vao-ra {(x*i,d*')}
vai k=l,2...,p. Luat hgc lan truyan ngugc thuc hien hai qua trinh hgc cap dir lieu mlu.
0 giai doan dau, bg mlu tin hieu vao x lan truyen theo chiSu thuan tir lop vao qua cac leip In den Icjp ra de tao ra tin hieu ra y.
Giai doan thii hai, sai lech e ^ (d - y) dugc la truyen ngugc lai tir Icjp ra qua icjp an ve lop vao CO nhiem vu diSu chinh lai gia tri trgng s6 giiij cac lap sao cho tin hieu ra y bam theo dugc tin hieu mau dau ra d.
4.2. Bo mlu diing de huSn luyen mang Bg mau diing de huiin luyen mang noron dugc lay tir cac phuong trinh (2.1). Voi gia tri ciia cac goc quay dugc xac dinh trong khoang:
0° < e, £ 125°; -90" < 6j < 0»; 0° < 6, <90';
-90°< e_< 0°; 63= 9, va diju kien: 6^+ 6,+ 6,= 0.
Mang naron dugc sit dung nhu sau (hinh 2):
Hinh 2; Cdu true cua mang noron diing digiai bdi todn dong hoc nguac.
5. KET LUAN
Mang naron truy6n thing ba lop voi giai thuat Back propagation dugc xay dung dua vao toolbox ciia Matlab. DS huln luyen mang nhini xac dinh bg trgng s6 thich hgp, chung toi dung bg du: lieu huln luyen g6m 700 mlu, bg dii liei kiem chiing g6m 300 mlu dS kiSm tra kat qua, Mang g6m 28 nut In dugc xac dinh blng cacli thu nghiem voi ham truyan sigmoid kat qui buac dau nhu sau:
g TAP CHi CO KHi VIET NAM, S6 3 nam 2014 www.cokhivietnam.vn
NGHIEN ClfU-TRAO DOI
100 ISO 2 0 0 2 5 0 3 0 0 C 0 2
so 100 200 250 300
(a) (b)
|_]f*vrYf,p^iTt^M^^ Ij^^HM^Mivf^iWh
(c) (d)
200 25t3 S O M A U U C M T S A
(d)
Hinh 3: Sai lech cua cdc gdc thela. duac tim tie mgng naron sau htidn luyen so vdi bd dit- lieu kiem tra a- thetal; b- Theta2; c- Theta3; d- Theta4; e- ThetaS
Vdi sai sd cua gia tri theta nhu hinh 3, cd the ket luan rang mang naron da hgc dugc Idi giai cua bai toan ngugc vdi do chinh xac cd the chap nhan dugc trong vung gidi ban ciia cac bien di chuyen. Cd the ndi rang mang naron vdi cau true va bd trgng sd viia tim dugc chinh la Idi giai cua bai toan ddng hgc ngugc cho tay may Scorbot ER-VIL<*
Ngay nhan bai: 12/01/2014 Ngay phan bien: 15/02/2014
Tai lieu tham khao:
[1]. Sreenivas Tejomurtula, Inverse kinematics in robotics using neural networks, M.S. Thesis, Louisiana State University, (1998).
[2]. C.S.G.Lee and M.Ziegler, A geometnc approach in solving the inverse kinematics of puma robots. University ofMichigan,1983.
[3]- Tapomayukh Bhattacharjee, Arindam Bhattacharjee. A Study of neural network based Inverse kinematics solution for a planar three joint robot with obstacle avoidance.
[4]. Pham Hiiu Diic Due, Mgng naron & img dung trong dieu khien tuddng, NXB. Khoa hoc va Ky thuat, (2009).
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