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rr^3!t4Hi»rt ^XAC Dim DAC TINH CUA CAC THAM SO PHU TRONG BAI TOAN DONG HOC ROBOT SONG SONG DETERMINE THE PROPERTIES OF SUBPARAMETERS IN KINEMATIC PROBLEMS OF PARALLEL ROBOTS Pham Th^nh Long', Vu Dire Binh^ ' Truong Dai hpc Ky thuat C6ng nghiep, Dai hpc Thai Nguyen ^ Truong Dai hpc Cong nghiep Viet Tri Bai bao gi&i thieu mot phuong phap xdc dinh quy luat bien thien cua cac tham so phii bai toan dong hoc cua robot song song, tham so phu khong phai la tham so true tiep duac dieu khien song no co vai tro quan trong viec xdc lap cau hinh da chon cua ca cau chap hanh nham phan biet vai cac cau hinh kha dikhdc co the co tinh da nghiem ciia bai toan dong hoc robot Mot phuangphdp so tren co saphuong phap toi mi se cho phep xdc dinh cd tham so chinh va tham so phu bai bao la ca so de xay dung giai thuat dieu khien cdc he ca dien tic thieu dan dong Tir khoa: Thamsophu, robot song song, phuong phdp so, bdi toan dong hoc ABSTRACT This paper introduces a method to determine the variation of subparameters in kinematic problems of parallel robots The subparameters are not the parameters which are directly controlled, but they play an important role in setting up the preoptive configuration of the actuator and to distinguish the possible configurations caused by plural solutions of kinematic robotic problems A numerical method based on the optimized method will allow determining both major parameters and subparameters This paper is the base to build up the control algorithm of mechatronics systems which are under-actuated robots Keywords: Sub parameter, parallel robot, numerical method, kinematic TAP CHi CO KHI VIET NAM S6 nam 2014 www.cokhivietn a m problem NGHIEN CUTU-TRAODdl DAT VAN DE CO SO TOAN HQC CUA VIEC XAC D JNH THAM SO PHU Neu robot chu6i chi co nhieu nghiem a bai toan nguoc bai toan thuan luon co nghiem 3.1 Cac loai tham so ciia bai toan dong hoc nhat thi ca hai bai toan a robot song song deu CO nhieu nghiem Mot cau hinh c6ng tac cua CO cau chap hanh co nhiSu phuong an ngo vao, ciing nhu mot bp tham so tpa dp suy rong a ngo vao CO the cho nhieu cau hinh khac ciia phan chap hanh Do cau hinh dupe lira chpn cua phan chap hanh phai phu hap voi cac yeu cau cong nghe da dupe xac dinh tu truac, no khong phai la mot phuong an nghi nhien s6 cac phuong an co the co, mot bien phap phan biet chinh xac phuong an da chpn vai cac phuong an khong mong muon la can thiet CO Sd PHAN BIET CAC CAU HINH NGHIEM Gpi p^, la cau hinh cong tac mong muon va cac cau hinh khac a cimg cot voi no khong dap ling yeu cau cong nghe truong hop Do hai bai toan thuan va nguoc ciing co nhieu nghiem nen tao sy chong cheo quan he giiia hai tap tham s6 minh hoa nhu hinh Khi xuit nghiem P^ dieu khien bai toan thuan, cSu hinh mong muon co the bi nham lan voi cac phuong an khong mong muon dan den khong hoan nhiem vu cong nghe dat Joint space Hinh 2: Minh hoa cdc tham so cua robot song song Trong hinh a tren, moi chan co hai bac ty duoi dang hai khop ban le song chi co mot khop la chii dong, nhu vay, robot co ba bac tu bang voi so khau dSn Gia su khop chu dpng noi gia, vay cac tham s6 tpa dp suy rong tren mo hinh g6m ba tham s6{6^,0j,6^) Neu de y rang he phuong trinh lien ket dpng hpc cua robot noi tren gom phuong trinh, chiia tham so la ngoai ba goc dong vai tro tham so tpa dp suy rong ba tham so g6c mo ta cosin chi huong cua cac doan b|, b^, b^ so voi cac doan a,, a , a^ chinh la cac goc tao boi doan va bi ciia moi mot chan Ba goc co vai tro xac dinh huong cua cac d6t chan bj, b^, b^ va dupe gpi la tham so phu Gia sii giii nguyen ba tham s6(^|,^2'^3) nhu hinh ve, neu thay doi cac tham so phu se nhan e gii^a hai tap tham so qua bai toan dupe vi tri va huong khac cua tam di dpng, dong hoc chinh la he qua ciia tinh da nghiem bai toan thuan Vay, vi tri va huong ciia \km di dpng Di phan biet duac cac phuong an vai xac dinh nhat bang mot bp tham so phu va can can cu vao cac thong tin hay cac dac mot bp tham so tpa dp suy rong, dieu co nghia di6m dpng hpc lam cho phuong an kh6ng la neu giai bai toan dpng hpc chi tim tpa dp suy gi6ng phuong an kia, chung t6i gpi cac thong tin rong la chua du, dii cac tham so phu khong tham gia tryc tiep vao dieu khien he ^ la tham s6 phu TAP CHI CO KHI VIET NAM, S6 nam 2014 www.cokhivietnam.vn NGHIEN CtfU-TRAOD6l 3.2 Co SO" toan hpc xac dinh tham so phu duong tron ^400; - Ciu hinh thay th6 [2] chpn hai d6t chan c6 dp Co nhiSu phuong phap giai bai toan dpng dai nhu va bang 80 hpc chi xac dinh tham s6 di6u khiSn ma khong xac dinh tham s6 phu Neu quan sat he phuong trinh dpng hpc lap dupe cho mot robot bat ky CO th8 nhan thiy so phuong trinh lien kk luon bing t6ng s6 tham so phu va tham so tpa dp suy rong Ben canh do, phuong trmh lien ket chira cac tham s6 m6 ta vi tri va huong cua khau cuoi, nen s6 lupng phuong trinh luon nho hem tong s6 Hinh 3: Duong cong quy dgo khong gian cong tac cua robot tham so cua mo hinh Trong bai toan ngupc cho truoc cac tham s6 vi tri va huong cua khau cuoi, s6 phuong trinh lai bing s6 tham s6, bai toan du dieu kien de tim ca tham s6 tpa dp suy rong va tham so phu, cin ghi nhan gia tri ciia tham so phu buac Trong bai toan thuan, da biet truoc cac tpa dp suy rong, muon tim chinh xac cau hinh nao chi can gan them bp tham so phu cua phuong an tim dupe buoc giai bai toan nguoc vao phuong trinh lien ket, bai toan thuan luon cho chinh xac cau hinh chap hanh da chpn Diem mau chot cua phuong phap la can gan lai gia tri cua tham so phu da biet a bai toan nguoc vao mo hinh toan ciia bai toan thuan de giam quy mo cua bai toan thuan be hon quy mo cua bai toan ngupc Vi du duoi day img dung phuong phap giai bai toan ngupc trinh bay o [2] voi robot Stewart ghoch lam ro hon dieu Theo npi dung cua [2] can thay the cau hinh d6 bac bai toan ve dang bac nham giai bing phuong phap GRG Theo hiiih 4, vi robot CO chan nen moi chan ngoai cac tham so tpa dp suy rong ^2, ™i i ^ 1-6 co hai tham so cosin chi huong \k9^^,0^, vai i = 1-6, tiic la toan bp mo hinh CO tham so tpa dp suy rong va 12 tham so phu can xac dinh theo phan tich tren Toan bp mo hinh gom 18 duong dac tinh can xay dung, bai toan thupc dang thieu dan dpng vi chi sir dung dpng CO tinh tien dieu khien 18 bien so T"^ / ' • ; '' ','] li (, b\ «: B' i, ^—.—•' o' AI ^' A, '>' Hinh 4: So vong kin mot chan cdu hinh goc (trai) va sa vong kin cdu hinh thay the (phai) TINH TOAN MINH HOA vOl ROBOT STEWART GHOCH Dieu khien robot Stewart ghoch bam theo quy dao la duong cong ghenh duoi dang giao tuyen ciia hai mat try co duong kinh 50 nhu hinh 3, robot CO tham so nhu sau: - Tam di dpng la mot hinh luc giac npi tilp duong tron ^400; - Tam CO dinh la mot hinh luc giac npi ti§p Hinh 5: Bdi toan dong hoc nguoc robot Stewart ghocggidi bdng phuong phdp GRG TAP CHI CO KHI VIET NAM, S6 nam 2014 www.cokhivietnam.vn NGHigN CUfU - TRAO Dpi Hinh 6: Do thi bien thien cdc tham so phu t^j — t^^ ung voi quy dao cho truac Hinh 7: D6 thi biSn thien cdc tham sdphu t^^ - t^^ img vai quy dao cho truoc Hinh 8: Do thi bien thien cdc toa suy rong L, - L^ cua robot img vai quy dgo cho truoc TAP CHi CO KHi VIET NAM, S6 nam 2014 www.cokhivietnam.vn NGHIEN CUfU - TRAO D | KET LUAN Bai bao da trinh bay mot phuong phap s6 cho phep tim dupe cac tham s6 tpa dp suy rong song song voi viec xac dinh cac tham so phu Khi thyc hien bai toan thuan co su tham gia cua cac tham so phu ben canh cac tham so tpa dp suy rong, chiing t6i luon xac lap dupe quan he nhit giiia hai diem a hai khong gian khac Day la diem ma nhieu phuong phap khac khong quan tam Viec phan biet cac cau hinh nghiem can cii' tren cac tham so phu la hoan toan hop ly va logic ve mat toan hpc, hi§u biet sau ve dpng hpc la can cu tin cay de kiem soat dupe qua trinh lam viec cua robot mot each chic chan.*;* Ngay nhan bai: 05/4/2014 Ngay phan bien: 10/5/2014 Tai liSu tham khao: [1] Bien dich Tran The San, Casa nghien cuu vdsdngtgo robot, NXB Thong ke Ha Npi (2002) [2] Pham Thanh Long, Nguyen Thi Hong Cam, Nguyen Thanh Chung, Su dung cdu hinh thay the bdi loan dong hoc Robot, Tap chi KH&CN cac Truong Dai hpc Ky thuat, s6 65, ttang 81-85, Ha N6i (2012) [3] Lung - Wen Tsai, Robot Analysis: The Mechanics of Serial and Parallel Manipulators, John Wiley & Sons, New York, 1999 [4] L S Lasdon, A D Warren, A Jain, and M Ratner (1978), Design and Testing of a generalized reduced gradient code for nonlinear Programming, ACM Trans Math Software 4,(1), pp 34-50 [5] Domagoj Jagobovic, Ocjena ucinkovitosti postupaka za rjesavanje kinematike Stewartowih paralelnih mehanizama, MAGISTARSKI RAD, zagreb 2001, Pages 81 [6] Pham Thanh Long, A New Method to Solve the Reverse Kinematic Robot Problem, pp 43 - 46 ISTS (2012) TAP CHi CO KHi VIET NAM, S6 nam 2014 www.cokhivietnam.vn ... space Hinh 2: Minh hoa cdc tham so cua robot song song Trong hinh a tren, moi chan co hai bac ty duoi dang hai khop ban le song chi co mot khop la chii dong, nhu vay, robot co ba bac tu bang voi... s6 cho phep tim dupe cac tham s6 tpa dp suy rong song song voi viec xac dinh cac tham so phu Khi thyc hien bai toan thuan co su tham gia cua cac tham so phu ben canh cac tham so tpa dp suy rong,... cong tac cua robot tham so cua mo hinh Trong bai toan ngupc cho truoc cac tham s6 vi tri va huong cua khau cuoi, s6 phuong trinh lai bing s6 tham s6, bai toan du dieu kien de tim ca tham s6 tpa
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