Modeling of a Single DOF Force Feedback Teleoperaion Sye Mehe Ie Can Dede and Sabri Tounoglu Florida Inernaional Univeriy Deparen of Mechanical and Maerial Engineering Miai, Florida 3374 cdede00@fiu.edu Abrac The objecive of hi paper i o decribe he odeling of a ingle degree-of-freedo (DOF eleoperaion ye by uing he Malab ofware ool. Modeling a eleoperaion ye coni of he odeling of he dynaic and kineaic of wo ubye a well a he counicaion line beween he o couple he ye and uer inerface o inerac wih he ye. The ubye of a eleoperaion ye are he aer and he lave. In hi paper, ubye are choen o have a ingle degree-of-freedo. A conan ie-delay i alo odeled o ee he effec of ie delay on he abiliy of eleoperaion. The wave variable echnique i hen inroduced o enhance he abiliy of he ye. Preliinary iulaion reul are alo preened in an effor o deonrae he ue of he developed odel. Inroducion Hazardou and unrucured ak found in nuclear reacor, pace applicaion, iliary ue, edical operaion and deep-ea exploraion ofen eploy eleoperaed ye. More recenly, pace exploraion uch a he Space Saion developen effor and iion o Mar have renewed he inere in hi area. Teleoperaion decribe wo ye ha are dian fro each oher and coupled in a way ha boh end and receive coand fro each oher. The inforaion en fro he aer o he lave conroller i he poiion and/or velociy coand and he inforaion en fro he lave o he aer i uually he force coand. The force feedback fro he lave provide valuable inforaion o he aer o receive he feeling of he condiion he lave face in order o iprove he operaor abiliy o perfor he anipulaion wih all or no error, which could ave he lave fro exering unneceary aoun of force o he environen. The ie delay beween he aer conroller and he lave robo ha been een a a doinan facor of inabiliy in eleoperaion. In order o overcoe hi proble, Anderon and Spong in 989 [] inroduced he wave variable echnique, which i furher udied by Nieeyer and Sloine [], [3]. Nieeyer alo udied hi echnique on iedelayed force-reflecing eleoperaion ye in hi dieraion [4]. Thi echnique iply focue on how o ake he energy creaed a a reul of he ie delay zero in order o guaranee paiviy, which will reul in a robu ye if ubjeced o conan ie delay. The wave variable ehod i furher dicued in he nex ecion. The odeling of he ubye of he eleoperaed ye i decribed in he hird ecion. Alo he odeling of counicaion line beween he ubye and he uer inerface i illuraed in hi ecion. Preliinary reul of he developed eleoperaion iulaion are preened in he fourh ecion for differen iulaion ak. The fir iulaion for eleoperaion i carried ou for he ye having no ie delay o oberve he be perforance ha i can have for he coupled aer and lave ye. In he econd iulaion, ie delay i inroduced wihou any copenaion or a echnique o guaranee abiliy o ee how he ye perforance and abiliy i affeced. In he hird iulaion, he wave variable echnique i applied o he eleoperaed ye in he preence of ie delay. Finally differen wave ipedance er are exained for he ae iulaion. Uilizing preliinary iulaion reul of he iulaion, he neceiy of he wave variable ehod and he Proceeding of he 7h Florida Conference on Recen Advance in Roboic, Univeriy of Cenral Florida, Orlando, Florida, May 6-7, 004.
iproveen i ake on he perforance of he ye are dicued in he concluion ecion of hi paper. Wave variable echnique The block diagra below uarize he wave variable ehod in a raighforward anner. The caering ranforaion define he ranforaion of he velociy and force feedback inforaion o he wave variable. Figure. Scaering ranforaion for eleoperaion wih ie delay By uing he noaion developed in [], he caering ranforaion i decribed a follow: u u v v ( F + bx& d b ( F + bx& b ( bx& F b ( bx& d F b ( where x& and x& are he repecive velociie of he aer and he lave. F h i he operaor orque and F e i he environen orque. F i he force refleced back o he aer fro he lave robo. F i he force inforaion en fro he lave o aer. x& d i he velociy derived fro caering ranforaion a he lave ide. u and v are he wave variable. The power, P in enering a ye i defined a he calar produc beween he inpu vecor x and he oupu vecor y. Such a ye i aid o be paive if and only if T Pin x yd Eore ( ( τ E (0 ( 0 0 ore where E ( i he energy ored a ie and E (0 i he iniial ored energy. The power ino he counicaion block a any ie i decribed by P ( x& ( F ( x& ( F ( (3 in d d In cae of he conan counicaion delay, where T i a conan, u ( u ( T v ( v ( T (4 Subiuing hee equaion ino (3, and auing ha he iniial energy i zero, i i copued ha he oal energy ored in he counicaion during he ignal raniion beween aer and lave i given by E 0 in P ( τ dτ ( x& ( τ F ( τ x& ( τ F ( τ dτ 0 ( u ( τ v 0 T d d ( τ + v ( τ u ( τ dτ ( u ( τ + v ( τ dτ 0 (5 and, herefore, he ye i paive independen of he agniude of he delay T. In oher word, he ie delay doen produce energy if he wave variable echnique i ued. Therefore, i guaranee abiliy for he ie-delayed eleoperaion. Developen of he eleoperaed ye odel in Malab The eleoperaed ye ainly ha wo ubye: The aer conroller, which i a one-dof joyick, and he lave robo, which i alo odeled a a one-dof lider. Thee wo ub-ye are odeled in Malab uing he Siechanic block of Siulink. The ub-ye are hown in Figure and 3 below. The orque inpu applied by he operaor on he joyick, denoed by Joy_Ou in he block diagra (Figure, i fed ino he join acuaor of he joyick wih he force feedback inforaion fro he lave robo and he joyick pring dynaic oupu, Torque of Spring. The Spring&Daper block i ued o odel a pring ye o ove he joyick o he null poiion when here i no oher orque applied o i. I i copoed of iple Siulink block ha uliply he poiion and velociy feedback wih cerain Proceeding of he 7h Florida Conference on Recen Advance in Roboic, Univeriy of Cenral Florida, Orlando, Florida, May 6-7, 004.
gain o ake he block ac a a pring-daper ye. Force feedback inforaion fro he lave i eiher en while here i a ie delay by Slave_FF or while here i no ie delay by Force_FB, which i wiched by he Tie_Dly wich inpu generaed fro he ain window. The re of he block of Figure i he block fro Siechanic library of Siulink o odel he kineaic and dynaic of he joyick. The Siechanic block ha are ued o develop he aer and he lave robo are briefly inroduced below. : Ground block ground one ide of a join block o a fixed locaion in he World coordinae ye. oion can be eaured by he Join Senor block if he block are aached o hi block. : Body block repreen a uerdefined rigid body. Body block i defined by a, ineria enor and coordinae origin. : Body Senor block eaure linear/angular poiion, velociy, and/or acceleraion of a Body block wih repec o a pecified coordinae ye. : Join Iniial Condiion block e he iniial linear/angular poiion and velociy of oe or all of he priiive in a join block. : Join Acuaor block acuae a join block priiive wih he generalized force/orque or linear/angular poiion, velociy, and acceleraion oion ignal. : Join Senor block eaure linear/angular poiion, velociy, acceleraion, copued force/orque and/or reacion force/orque of a join priiive. : Revolue join block repreen one roaional degree of freedo. I can be driven by he Join Acuaor block and i oion can be eaured by he Join Senor block if he block are aached o hi block. Figure. Maer (joyick ub-ye window Figure 3 how he Siulink window of he odeled lave robo. The kineaic and dynaic of he robo i alo odeled wih he Siechanic library of Siulink. Differen han he aer, he lave ha one priaic join which enable i o work like a lider echani wih one degree of freedo. The lave robo iply ake he velociy coand fro he aer, Slave_V_W, if here i a ie delay or i i wiched o ake he velociy coand fro he aer oupu direcly, Po_FB, by he help of he Tie_Dly wich and copare i wih i velociy feedback Slave_V o feed he neceary inforaion o he PD conroller. Alo, i end he neceary oupu o creae he force inforaion in ean of proxiiy o he odeled wall, by he poiion of ielf Slave_P. : Priaic join block repreen one ranlaional degree of freedo. I can be driven by he Join Acuaor block and i Figure 3. Slave ub-ye window Proceeding of he 7h Florida Conference on Recen Advance in Roboic, Univeriy of Cenral Florida, Orlando, Florida, May 6-7, 004.
Figure 4 how he counicaion beween he aer and he lave. Force feedback inforaion i creaed wih he FF Coand in Figure 4. FF acivaion block ene he conac of he lave robo wih he environen and enable he force feedback inforaion o be en o he aer by wiching fro zero inpu block o he FF Coand block. There are four oher wiching condiion o enable uage of he wave variable echnique for he ie-delayed eleoperaion. Thee wiche are operaed by he inpu Wave_Vrb generaed fro he ain window. The re of he block of he Counicaion Line block are ued o inegrae he wave variable ehod ino he counicaion line beween he aer and he lave. The aoun of ie delay i e hrough he Tie Delay block. echnique o he ye wih a conan ie delay. Thi wich alo generae an inpu, Wave_Vrb, for he wiching in he Counicaion Line block. Figure 4. Counicaion line block window The ain conrol window of eleoperaion i illuraed in Figure 5. The ubye are arked wih Maer (Joyick and Slave. The generaion of ie delay and he applicaion of he wave variable ehod o he counicaion line are realized in he Counicaion Line block of he ain conrol window. The operaor ineracion o apply orque o he joyick i accoplihed hrough he joyick wih he ag Operaor Torque Inpu. The aer robo (joyick oion under he influence of he orque inpu fro he operaor and he force feedback provided fro he lave robo i oberved fro he joyick wih he ag eniled Acual Joyick Moion. The oion of he lave robo (lider i oberved fro he lider on he ain conrol window wih he ag Slider Moion. There are alo wo wiche ha appear on he ain conrol window of eleoperaion. The fir one wih he ag Tie Delay On/Off i o enable he ie delay on he counicaion line of he ye. Thi wich generae an inpu, Tie_Dly, for he wiching in he aer and he lave robo. The econd wich wih he ag Wave Variable On/Off enable he applicaion of he wave variable Figure 5. Main eleoperaion inerface window Preliinary iulaion reul for eleoperaion The fir iulaion in hi udy i conduced for a counicaion line having no ie delay, which will give an idea of an ideal cae where he wo ub-ye are coupled perfecly wihou any reaon for inabiliy (due o ie delay. The econd iulaion i carried ou for a ie delay of 0.5 econd and in he abence of wave variable echnique. Thi iulaion provide inforaion on how ie delay play a role in he abiliy of eleoperaion. Finally, he la iulaion i done for a ie delay of 0.5 econd in he preence of wave variable o guaranee abiliy in eleoperaion. The cenario for each iulaion i e for he operaor o apply a eady orque o he aer conroller (joyick o end a conan velociy coand o he lave. The lave lider proxiiy enor i e o 50 inche and herefore a i aep o go beyond 50 inche, he lave lider Proceeding of he 7h Florida Conference on Recen Advance in Roboic, Univeriy of Cenral Florida, Orlando, Florida, May 6-7, 004.
end force inforaion o he aer wih repec o he diance violaed beyond he lii. During all hi ie, operaor ill exer he conan orque o he joyick o ake he lave lider ove in he ae direcion. Thi ype of operaion i likely o caue an ocillaory oion abou he conrain, which hould be daped o a poiion ju above he lii of 50 inche due o he eady operaor orque inpu. Figure 6 i preened o depic he effec of wave variable ehod on he abiliy of eleoperaion. The olid line in he plo repreen he lave oion in he abence of wave variable echnique for he counicaion beween he aer and he lave. The dahed line how he lave repone in he preence of wave variable. I can be oberved fro he figure ha when he wave variable ehod i no acivaed he lave oion ocillae wihou any daping o converge he oion o a eady ae. A he wave variable ehod i acivaed, he oion of he lave i daped and herefore converged o a poin ju above he liiing value of 50 inche. Perforance of wave varibale for 0.5 ec delay wih repec o no conrol over he delay Slave Poiion (inch 55 50 45 40 35 30 5 Wave variable no acive W ave variable acive 0 0 40 60 80 00 0 40 60 80 00 Tie (ec Figure 6. Effec of wave variable echnique on a 0.5 econd ie-delayed eleoperaion achieve he ak of a able repone for a conan ie delayed eleoperaion. Slave Poiion (inch Perforance of wave variable wih repec o an ideal eleoperaion wih no ie delay 55 50 45 40 35 30 5 No ie delay 0.5 ec delay wave var. acive 0 0 40 60 80 00 0 40 60 80 00 Tie (ec Figure 7. Side effec of wave variable wih regard o he ideal eleoperaion wih no ie delay When elecing he wave ipedance for he wave variable conroller, one hould be very careful no o ake he eleoperaion ye unable. Tuning of he wave ipedance er, b, enable he poibiliy o change he characeriic of he eleoperaion ye a i i oberved in Figure 8. A he wave ipedance er increae, i i furher oberved ha he ocillaion agniude increae while he ocillaion frequency decreae. Thi ean ha an increae in he ipedance er caue he anipulaor o ele in eady ae in a longer ie period wih larger overhoo in raniion ae. Alo, a anoher oucoe of hi iulaion, he wave ipedance er hould be eleced in oe range ha will no caue inabiliy. The range cae ou o be beween 400 and 800 for he ye iulaed. 60 Effec of wave ipedance "b" on he perforance of he wave variable While enhancing he abiliy of eleoperaion wih a conan ie delay, he decreae in he anipulaion peed caued by he applicaion of wave variable echnique can alo be oberved fro he above figure. Figure 7 illurae he lave oion for he cae wih and wihou ie delay. The wave variable ehod i applied o he eleoperaion ye when ie delay i odeled. Slave Poiion (inch 55 50 45 40 35 30 5 b450 b600 b750 Even if he wave variable are acive for a conan ie delay, rie for he ocillaion agniude wih repec o he ideal eleoperaion cae can be oberved fro Figure 7. While he agniude of he ocillaion increae and anipulaion peed decreae, in hi iulaion, wave variable ill 0 0 0 40 60 80 00 0 40 60 80 00 Tie (ec Figure 8. Perforance variaion of he wave variable echnique due o he wave ipedance Proceeding of he 7h Florida Conference on Recen Advance in Roboic, Univeriy of Cenral Florida, Orlando, Florida, May 6-7, 004.
Concluion In hi aricle, he heory of wave variable echnique, odeling of a -DOF eleopearion and hree iulaion reul of hi eleoperaion ye are preened. Alhough he ain ak i planned o be he ae for each iulaion, acivaion and deacivaion of he wave variable in iulaion provided a beer underanding of he neceiy of he wave variable in conan ie delayed eleoperaion. The wave variable enhance he abiliy of conan ie delayed eleoperaion, bu i end o increae he agniude of he overhoo and caue a decreae in he anipulaion peed relaive o he ideal cae when no ie delay are involved. Alo, uning of he wave ipedance er for an opiu anipulaion peed and overhoo i required. The nex ep for he coninuing udy of wave variable will be he inveigaion of he effec of differen ie delay agniude on eleoperaion, and how he wave variable ehod handle i. Reference [] R. J. Anderon, and M. W. Spong, Bilaeral Conrol of Teleoperaor wih Tie Delay, IEEE Tranacion on Auoaic Conrol, AC-34, No. 5, pp. 494-50, May 989. [] G. Nieeyer, and J. Sloine, Sable Adapive Teleoperaion, Inernaional Journal of Oceanic Engineering, Vol 6, No., pp 5-6, 99. [3] G. Nieeyer, and J. Sloine, Toward Force- Reflecing Teleoperaion Over he Inerne, Proc. IEEE In. Conf. Roboic and Auoaion, ICRA, pp. 909-95, Leuven, Belgiu, 998. [4] G. Nieeyer, Uing Wave Variable in Tie Delayed Force Reflecing Teleoperaion, Ph.D. Thei, MIT, Cabridge, Maachue, 996. [5] C. Ki, Developen and Teleoperaion of Roboic Vehicle, Proc. AIAA Unanned Unliied Sye, Technologie and Operaion Conference, San Diego, California, 003. Proceeding of he 7h Florida Conference on Recen Advance in Roboic, Univeriy of Cenral Florida, Orlando, Florida, May 6-7, 004.