MODELING AND IDENTIFICATION OF A TWO-LINK FLEXIBLE MANIPULATOR

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1 ABC Sosu Ss caocs - Vo. 5 Cog b ABC Sco VII - Robocs Pag 9 ODELIN AND IDENIFICAION OF A WO-LINK FLEXIBLE ANIPULAOR og Auguso Bof jog.g@ga.co Fábo L.. Saos fsaos@a.b Cao Rogus Bao caob@ga.co Luz Caos Saova ós gos@a.b IA - Isuo coógco Aoáuca Dvsão Egaa câca-aoáuca. Paça a Euao os 5 São osé os Caos/SP BRASIL 89 Abs. I s wok w su og a fcao of a wo-k auao w caca fb sbu aog ks. a aaaus su s a wo-k fb auao ovg ozoa a v b wo busss DC oos. Ea aa coc s us fo ss fcao. A f soa o s v usg assu os o. Lagaga ao as o c uaos of oo. Acuaos a ssos a aso o o o v a co a c o of co ss. Kwos: og Ifcao Fb obos. INRODUCION saa assuo a oboc auaos coss o of g bos s va o fo sow oo a sa g focs. If fb s o ak o cou a gaao of ova c foac of obo oo ca occus. Fb afss sf as caca oscaos a sac fcos ga cocag oo coo of a caca a. If o s oscaos s sgfca av o cc of ova ask fb w b a ajo cosao a sg D Luca a Book 8. I s wok w su og a fcao of a wo-k auao w caca fb sbu aog ks. a aaaus s a wo-k fb auao v b wo busss DC oos a oo b os sa gaugs a cos. A uac ss ovs a fcoss cuso of a bow auao a ovs ozoa a. Bo oos a c w ucoa c sgas a a aa s oba oug a su w SPACE awa a sofwa og w ALAB - Suk. Fo og o of vw jo oo bw wo ks s saa o wo as of ca o k coas o covoa og a coss o o a f vous k as D Luca a Scao 99 a L a L. E fb k s cos b coag g sgs a s s. assu os o s ao o o oba a f-soa o a cus aoa gaz cooas a scb asc fcos. Lagaga ao s us o v o of oboc sucu. Ec uaos of oo a a assug fv sa fucos fo k. Acuaos a ssos a aso o o o v a co a c o of wo ss. Fuo aac ss fcao s o usg a aa. oca a a sus a coa o vf cu of o. oca fuc sos fucos a vaua usg ALAB sofwa. a s ogaz as foows: Sco gvs kac sco fo a aa wo-k fb auao. Kc a Poa gs a v Sco a Lagaga fouao s a. Ec fouao of a a sffss a a sa fucos a a A. Sco s vo o og of Acuaos a ssos sg a sa-s sao. Ea a oca sus a s Sco 5. Cocusos a aw Sco 6.. KINEAIC ODELIN Cos a wo-k fb auao w oa jos subjc o bg foao a ovs o a aa suf as sow Fg.. E k s o b a w. cooa sss a sabs: a ss X Y a wo ovg sss X assoca o k. g oo s Y scb b jo ags θ w os asvsa fco of k a abscssa < < w s g of fb a of k. ag bw cooas X Y a X Y s α θ θ w / a w cos aoao a.

2 ABC Sosu Ss caocs - Vo. 5 Cog b ABC Sco VII - Robocs Pag 9 X k k EI Y Y oo Y k θ θ oo X θ X oo k EI oo Vco [ ] Y Fgu. oc a Ia aas of wo-k fb auao ss a o aog fb a of k w sc o cooas X a [ ] s oso sa o bu w sc o cooas X Y as E. a. Vco ss of k w sc o cooas X Y a s o E. a. R θ R θ R α R α R α cos θ s θ R θ s θ cos θ 5 E k as wo g sgs o s s w cosa a s. c of ass of g sg s cua as:. Fo E. -5 s ossb o v sua of vocs o E. 6- w. I was cos aoaos >> a >> bcaus bg foaos a uc sa a k g.. sco-o s vovg oucs of foaos w gc. θ 6 θ θ 7 θ 8 θ θ 9

3 ABC Sosu Ss caocs - Vo. 5 Cog b ABC Sco VII - Robocs Pag 9 θ θ α θ θ α cos θ θ θ α θ θ α cos θ θ θ α α θ θ α α cos θ. LARANIAN ODELIN Lagaga cacs s a -fouao of cassca cacs a uss cosvao of g. I Lagaga cacs uaos of oo of a ss of acs a v b sovg Lagag uaos. kc g a oa g V a cou o cua Lagaga L V Los. kc g of wo-k fb auao Fg. su of foowg cobuos: b j j kc oaoa g of g bo of o of a oca a bass s: b θ kc g of g sgs of ks E. 5 s o o of a of g sg a ass of sg. E sg as a cosa a s aog sg. j j σ j j j j j j 5 W σ θ σ θ σ α σ α. kc g of g bos oca bw ks E. 6 s o o of a of bo ca a fs k bo ca a sco k a su of bos ass. θ α 6. kc g of aoa a of sco k s: W / α 7 kc g of fb k w a s s: 8 j W cos aso kc asaoa g of co w ass oso a : 9

4 ABC Sosu Ss caocs - Vo. 5 Cog b ABC Sco VII - Robocs Pag 95 oa g of ss s u o asc oa of fb k w asc ouus E a sco o of aa s I. No gavaoa oa g s cos bcaus ss ovs o ozoa a. V EI assu os o s ao o o oba a f-soa o a cus aoa gaz cooas a scb asc fcos. fco s saa a s: j φ δ j j W cos 5 os fo fs k a 5 os fo sco k. Dfg... φ φ... φ ] [ g δ... δ ] [ a a cua A. a g δ... δ ] [ [ φ ] E. bcos E.. sa uaos g foua of Lagaga L V s v fo E. 6- a as a fuco of a vco of θ g θ θ δ K δ δ K δ gaz cooas [ ] [ ] θ g. Euao s Lagag uao o Eu-Lagag uao. L L f f τ τ s vco of gaz focs o ss. As su of Lagaga ao E. vs uaos of oo w s a a s Coos vco a cfuga focs a K s sffss a as cua A. W [ ] K f. ACUAORS AND SENSORS ODELIN gaz focs vco f s E. s a fuco of uao ou jo of bass τ a jo bw wo ks τ. E uao s a DC cc oo as sow Fg.. Sso u. og s o s f as a fuco u vco [ ] Pow Souc oo Coo Pow Cov oo oo A Co. SPACE k k Af Sa augs Af Accos Af os Fgu. Ea su

5 ABC Sosu Ss caocs - Vo. 5 Cog b ABC Sco VII - Robocs Pag 96 E oo as a coo a coo ca b s a ou o. A ou o voag sga ov b SPACE s cov o a oooa cu sga a oooa o aau cu a cosa:. ou ga b DC oo τ s.. τ s oooa o u voag w k s oo ou τ k 5 sug ou τ s cou cug ou fco w c v s fco cosa: τ τ c θ 6 v Fo E. 5-6 s ossb o f τ as fuco of a θ w. τ k c θ 7 v Usg E. 7 s ossb o f f as fuco of u a Euao ca b w as: P K Qu 8 I I Q k P c v 9 W I s a a s zo a. W f sa vco a ouu vco Es. -. Fgu sows u vco u wo c sgas a ouu vco. [ θ θ δ K δ δ K δ θ θ δ K δ δ K ] δ [ ] sg sg c sga v c sga Ss sg sg Fgu. Ius a ouus of ss Lazao of E. 8 aou a b cos θ bcos a b a a s θ bcos. Euaos - a sa-s sao w A s sa a B s u a C s ouu a a D s ffowa a Ogaa. as A B u C Du a A K b a b I P B a b Q

6 ouu a C a ffowa a D a sow E. 9- w s ga of co ouu ov sg s sa gag ouu a s o ouu as E. -7. } { θ 5 } { α θ θ 6 sg sg sg 7 θ 8 [ ] [ ] [ ] [ ]. sg sg sg sg P K P K C 9 Q Q D Euaos - vs fuc sos fucos s H w f j s π s co agua fuc. oca o fuc sos fucos s H a s Fg.. D B A I C H s s 5. EXPERIENAL RESULS a aaaus s sow Fg.. fuc ag s was o 7 Hz oug o f wo fs vbao os. wo ucoa c sw sgas a a o oos o w casg fucs fo o 7 Hz a ao casg fo 7 o Hz. Daa s coc a 5 sas sco oug a su w SPACE awa a sofwa og w ALAB a Suk. Wc o s us o sa ow sca s as Ljug a a 99. E coc sga was v sgs w 5% ova o soo cuv a a Hag wow was us. s ocu s coa a ALAB fuco fsa gag a fuc sos fucos. oc aas w asu bu fco cosas a a aas w ajus usg aac fcao. objcv fuco s uaac o bw oca a a gas o cosg bas ffc bw a of oca a a gas. oca aas w u zg uvaab objcv fuco usg ALAB fuco fco. If oca a a fuc sos fucos of cos sa gags a os a coa Fg.. ABC Sosu Ss caocs - Vo. 5 Cog b ABC Sco VII - Robocs Pag 97

7 ABC Sosu Ss caocs - Vo. 5 Cog b ABC Sco VII - Robocs Pag 98 Fgu. oca a a fuc sos fucos of ssos 6. CONCLUSION s a s og a aac fcao of a wo-k auao w wo fb ks. D o was v bas o Lagaga ao assug wo os of vbao fo k. Ssos a uao w aso o vg a co s of uaos of oo. g jo oo bw wo ks was saa o wo as coas o covoa og a coss o o a f vous k. Rg sgs a s of ks w cos o o ov og. ass of cao ssos affcs ss sos a s aso cos og. oca o as b sua a coa o a sus. Paac fcao succssfu f oca a a fuc sos fucos.

8 ABC Sosu Ss caocs - Vo. 5 Cog b ABC Sco VII - Robocs Pag ACKNOWLEDEENS auos ak CNP Coso Noa Dsvovo Cífco coógco fo oog a suog s s. 8. REFERENCES D Luca A. a Book W. 8 Robos w Fb Es I: Scao B. a Kab O. Sg Habook of Robocs Sg D Luca A. a Scao B. 99 Cos-Fo D o of Paa uk Lgwg Robos IEEE asos o Sss a a Cbcs v L S. a L C. Hb Coo Sc fo Robus kg of wo-lk Fb auao oua of Ig a Roboc Sss v Los N. A. câca Aaíca.. São Pauo: Eoa Lvaa a Físca. v Ljug L. a a. 99 og Of D Sss Pa III Ifcao Pc Ha c Ogaa K. Egaa coo oo.. S.Pauo Paso Pc Ha RESPONSIBILIY NOICE auos a o sosb fo aa cu s a. APPENDIX acs a K. Euao s a a s s a cua usg E. : θ θ g g o o K θ τ θ τ g K g o o v w v. o v w o

9 w v. o Z v w v Z EI K EI K W cos cosa aas of caca os: o v w Z a. a cos θ a b s sc a as a u b cos θ K s a a s θ a as a s u b s θ. Lazao aou as o b a a. Sa uaos j φ. fco s saa a s E.. E fb k a b o as Eu-Bou ba sasfg uao: EI A Po boua coos a os a bas a of k. k a s uc sa a u bos as so s asoab o assu k cosa a bas D Luca a Scao 99. Boua coos a of k cos baac of bg o a sa foc: A A L D EI A L D EI A5 ABC Sosu Ss caocs - Vo. 5 Cog b ABC Sco VII - Robocs Pag

10 ABC Sosu Ss caocs - Vo. 5 Cog b ABC Sco VII - Robocs Pag a A6: W L L L. W cos az cooas δ ca b f as: jω j D. L δ A6 j j Souos fo sa uaos φ a v fo Eu-Bou ba uao A a fo a φ j β C cos β C s β C cos β j C j s j j j j j j A7 W β ω EI. Ag boua coos. A-A o A7 as o: j j j C j C j j C j A8 C ass boua coos A-A5 a o A7 a o a uao ss A9. C j [ β ]. F j A9 C j No-u souos fo C j C j a o ossb f a of a β j fuc uao A. a cos fs souos fo β a j D. F s u ag o L j cos β cos β s β cos β cos β s β L β j j L L j s β cos β cos β s β cos β cos β j j j β j j j j j β j j j A C j C j Rag cosas a fou usg E. A9 g o a sca fo. s sca fo s cos usg a suab oazao as E. A. φj A Fgu 5. Sa uaos φ j