NGHIEN CUfU - TRAO D I MI^N G\0\ HAN CHUYEN DONG VA QUV DAO TRANG THAI CHUYEN DONG T | UU CUA ROBOT C N G NGHIEP THE LIMITED ZONE OF MOTION AND OPTIMAL TRAJECTORY OF INDUSTRIAL ROBOT TS Le Van Ngy', ThS Pham Cong Kiem^ ThS Nguyin Van Huynh^ 'VienVIELINA ^Trudng Dai hpc Cdng nghiep Ha Npi ^Trudng Dai hpc Ky thuat Cdng nghiep, Dai hpc Thai Nguyen TOM TAT Bdi bdo trinh bdy phuang phdp xdc dinh quy dao trgng thdi chuyin dpng toi mi, dua vdo dieu kien gi&i han dpng luc hpc de xdc dinh mien gioi hcin chuyen dpng vd tinh chdt ciia tdt cd cdc quy dao trqng thdi chuyen dpng thupc miin Ap dung cho viec xdc dinh quy dao trang thdi chuyen dpng toi uu thai gian vd toi uu ndng lupng cho cdc giai doan cda mpt chu trinh chuyin dgng cua tay mdy co khau quay Tur khoa: Robot; Gi&i han; Chuyen dpng; Quy dao; Toi uu; Thoi gian; Ndng luang This paper presents the method for determining the optimal trajectory based on limited condition of dynamics to define the limited motion zone and the characters of all of trajectories in that zone Its application to determination for the optimal trajectories of time and energy for periods in motion cycle of manipulator with two rotary links Keywords: Robot; Limit; Motion; Trajectory; Optimal; Time; Energy ISSN 0866 - 7056 TAP CHf CO KHl VIET NAM, Sd nam 2015 www.cokhivietnam.vn NGHIEN CUfU-TRAOD6| GlOfI THEEU Viec dieu khiln chuydn dpng ciia robot cong nghiep tu trang thai ban ddu din trang thai cuoi cho trudc cd thd dupe thuc hien theo vd so quy dao chuyen dpng khdc nhau, vi vay, can phai chpn quy dao chuydn dpng tdi uu theo muc tieu dugc dat Viec dp dung cdc ly thuylt dilu khien tdi uu kmh diin cho bai todn cdn gap nhieu khd khan vi cac ly thuylt chi Id nhiing dieu kien can md khong du, cac ket qua dat dugc CO tinh tuong ddi, cd the chua phai la tdi uu Trong ung dung, hien nay, ngudi ta thuong dung nhung chuang trinh phan mem tinh todn dl xac dinh gia tri ham muc tieu cho mpt sd lupng ban che ciia cac trudng hpp cd the xdy rdi chpn mpt gia tri dd theo nghia tuong ddi tdt cd tpa dp la^^vd tdc dp la^^^de dat dupe muc tieu dinh trudc Sy biln ddi trang thai chuyen dpng tai mpt diem dugc bieu thi bai quan he ciia bien ddi dqvkdq, tacd: dq _ dqjdt _ q dq dq/dt q hoac iii- = i- dq (2) q Y nghia hinh hpc cua (2) Id dp doc tai mpt diem cua quy dao trang thai chuyen ddng Tai mdi diem trang thai cho trudc (g, q)ihi tir (1) De khac cac phuc ban che tren day, bdi ta cd A{q),B{q,q)q vdC(g)la xac dinh Vi u bao se de xuat phuang phap xdc dinh quy dao cd gidi ban, u^