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1 2013 IEEE/RSJ Internatinal Cnference n Intelligent Rbts and Systems (IROS) Nvember 3-7, Tky, Japan 'HVLJQRID1RYHO&RPSOLDQW'LIIHUHQWLDO6KDSH0HPRU\$OOR\ $FWXDWRU Zha Gu, Hayng Yu, Member, IEEE, and Liang-Bn Wee, Senir Member, IEEE bstract²this paper presents a nvel cmpliant differential (CD) Shape Memry lly (SM) actuatr with imprved perfrmance cmpared t traditinal SM actuatrs. This actuatr is cmpsed f tw antagnistic SM wires and a mechanical jint cupled with a trsin spring. The trsin spring is emplyed t reduce the ttal stiffness f SM actuatr and imprve the range f mtin. The antagnistic wires increase the respnse time as ne wire can be heated up while the ther wire is still in the cling prcess. Dynamic mdel f this actuatr was established fr cntrl design. Experimental results prved that this new actuatr can prvide larger utput range f mtin and faster respnse speed than traditinal SM actuatrs under the same cnditins. Sine wave tracking with 0.05 Hz, 0.08 Hz and 0.1 Hz were perfrmed and ur results demnstrated that this cmpliant actuatr has gd tracking perfrmance under simple PID cntrl. I. INTRODUCTION Shape Memry lly (SM) is an intelligent material that can remember its riginal shape at lw temperature and return t the pre-defrmed shape by heating abve a threshld temperature. This phenmenn knwn as the Shape Memry Effect (SME) is the result f a phase transfrmatin between martensite and austenite. SM wire, especially the Nitinl (Ni-Ti) wire, which has a strain rate f up t 8%, is the mst cmmnly used SM frms fr actuatr design. Cmpared t cnventinal (electric, hydraulic, and pneumatic) actuatrs r ther advanced (piezelectric and EP) actuatrs, SM actuatrs have the advantages f high pwer t weight rati, bi-cmpatibility, small size, and silence peratin, and these advantages make them suitable fr a wide range f applicatins [1], such as rbtic surgical systems [2] [3], sft rbtics [4], and airfil prfile cntrl [5]. Hwever, SM actuatrs als have the disadvantages f lw energy efficiency, slw respnse rate, nnlinearity, hysteresis and lw strain rate. Special mechanical design and nnlinear cntrl methds are needed t vercme these limitatins. SM wire can nly achieve unidirectinal actuatin, thus it is necessary t prvide a recvery frce via a weight, a spring r anther antagnistic SM wire t achieve bidirectinal mvement. Typically, there are tw classes f SM actuatrs [6]. One is the bias spring (BS) SM actuatr *Research Supprted by MINDEF/NUS/JPP Zha Gu is with Singapre Institute fr Neurtechnlgy (SINPSE), Department f Biengineering, Natinal University f Singapre, 9 Engineering Drive 1, Singapre , ( biegz@nus.edu.sg ). Hayng Yu is with Singapre Institute fr Neurtechnlgy (SINPSE), Department f Biengineering, Natinal University f Singapre, 9 Engineering Drive 1, Singapre , (crrespnding authr, phne: ; fax: ; bieyhy@nus.edu.sg). Liang-Bn Wee is with DSO Natinal Labratries, 20 Science Park Drive, Singapre , ( wliangb@ds.rg.sg). cmpsed f a SM element and a bias spring. This type f actuatr has slw respnse as the respnse speed is limited by the cling prcess. The ther type f actuatr design cnsists f tw antagnistic SM elements, called differential (DI) SM actuatr [7]. This type actuatr has faster speed f respnse than the BS SM actuatr, but it cnsumes mre pwer and the range f mtin is restricted by the antagnistic SM [8]. SM actuatrs with larger wrking range and quicker respnse are desirable in many fields [9][10][11]. T achieve these gals, a series f new SM-based actuatrs r mechanisms have been develped. Fr instance, Zhang and Yin [12] presented a SM-based artificial muscle cmpsed f 16 parallel SM wires and a simple linear spring t imprve the driving frce and mimic the character f human muscle. Grant and Hayward [13] develped a differential SM actuatr cmprised f 12 SM wires in a helical arrangement t prduce larger mvements. Park, et,al [14] prpsed a differential spring-biased SM actuatr fr a bi-mimetic artificial finger. In this design, the spring was directly cnnected t the SM wire, which may absrb the cntractin length f SM wires and reduce the range f mtin f the jint. In the fields f assistive and rehabilitatin rbtics, cmpliant actuatrs have attracted cnsiderable attentin due t their ability f absrbing shcks, interacting with peple safely, string and releasing energy [15]. Many types f cmpliant actuatrs, such as Series Elastic ctuatr [16], Pneumatic rtificial Muscle [17] have been develped. Hwever, the utilizatin f advanced materials such as SM in cmpliant actuatr has nt been well investigated. The mtivatin f this paper is t develp a new cmpliant differential (CD) SM actuatr with a simple structure. trsin spring is emplyed t achieve better perfrmance ver traditinal DI SM and BS SM actuatrs. System mdels include the dynamics and cnstitutin equatins are established fr cntrl design. testing setup was designed t cmpare the prperties f this actuatr t the tw traditinal SM actuatrs. Furthermre, the psitin cntrl f this actuatr in step respnse and sinusidal tracking was investigated. II. COMPLINT DIFFERENTIL SM CTUTOR DESIGN. Cmpliant differential SM actuatr Inspired by the bilgical structure f human jint actuated by antagnistic skeletal muscles, we prpse a new cmpliant differential SM actuatr t mimic the extensin/flexin mtin f the bilgical jint. s shwn in Fig. 1(a), this cmpliant actuatr is cmpsed f tw antagnistic SM wires, a trsin spring and tw cylindrical cuplers. lad is applied n the cupler #1 by threaded cnnectin. Tw /13/$ IEEE 4925

2 antagnistic SM wires, behaving like artificial muscles, prvide the active frce fr bi-directinal mtin cntrl f the cuplers. The trsin spring, used t mimic the tendn, is packaged inside the cuplers. Tw legs f the trsin spring (0 deflectin, left hand wind) are restricted by the slts in the cuplers. The SM wires are directly cnnected t the cupler. The active cntractin frce prduced by the SM wire can be transmitted frm ne cupler t the ther by the trsin spring. The whle structure is simple and easy t implement fr different applicatins. In this design, we chse a trsin spring. Its stiffness is lwer than that f the SM wire. The spring will prvide the recvery frce fr the agnist SM wire and reduce the ttal stiffness f the actuatr. n encder can be assembled n the axis t get the rtatinal angle. respectively. Due t ks k, the rder f the passive stiffness 2 fllws kcd kbs k. DI Fig.1. CD mdel and prttype f the cmpliant differential SM actuatr B. Three types f SM actuatrs T cmpare the perfrmance f this actuatr with the tw traditinal SM actuatrs, we implement three cnfiguratins t represent three types f SM actuatrs using the same mechanical setup. They are (a) BS SM actuatr, (b) DI SM actuatr, (c) CD SM actuatr. Figure 2 includes the CD mdel and its equivalent mechanical mdel f each actuatr. Tw SM wires generate the tensile frce with a variable stiffness k i and a damping rati b (i=1, i 2). The trsin spring between tw SM wires transmits the cntractin frce with a cnstant stiffness k s.the damping between the spring and the mechanical part is b s. m, m 1 2 represents the mass f tw parts f the spring cupler respectively. The lad applied n the cupler #1 is represented as a mass m. Because f the small rtatinal lad speed, the effect f system damping is neglected. We mainly cnsider the stiffness f these actuatrs. The passive stiffness f each actuatr is k k, k ( k k ) / ( k k ) BS S DI 2 k k, 2 2 CD s s Fig.2. CD mdels and equivalent mechanical mdels fr three SM actuatrs: (a) BS SM actuatr; (b) DI SM actuatr; (c) CD SM actuatr. III. MODELING THE COMPLINT DIFFERENTIL SM CTUTOR The mdel f the actuatin system includes the dynamics and kinematics f the actuatr as well as the cnstitutive equatins, transfrmatin equatins and the heat transfer dynamics f the SM wire.. Dynamics and Kinematics simplified mdel f the actuatr is shwn in Fig.3. The cuplers are actuated independently under the functin f SM wires, the rtatinal angle f each cupler is defined as T, 1 2 T, which is relative t the y axis. Fig.3. Schematic diagram f the CD SM actuatr, F 1,F 2 are the active frces f the upper and lwer SM wires respectively, F s is the trsin spring frce, r 1, r 2 represent the mment arm, r s is the radius f trsin spring. The dynamic equatin f each cupler is given by 4926

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4 fast cntrl n the jint mtin. The rule fr each wire is shwn in Equatin (10) (11). V V 0 heating Upper SM wire: ut ' T t (10) V 0 ' T 0 cling V V 0 heating Lwer SM wire: ut ' T d (11) V 0 ' T! 0 cling IV. EXPERIMENTL SETUP ND RESULTS. Experimental setup n experimental setup has been develped t evaluate the perfrmance f this CD SM actuatr. small irn stick is cnnected t the actuatr as the lad fr testing. Figure 6 shws the schematic diagram f the cntrl hardware and picture f the experimental setup, respectively. Tw antagnistic NiTi SM wires (Dynally, Inc.) are selected in ur actuatr design. Their prperties are summarized in Table I. The diameter f each SM wire d is 250m. ngular psitin is measured by a shaft encder (Omrn E6B2-CWZ1X) with a reslutin f 2500 pulses per turn. NI-PCI-6221 DQ card is used t cllect the data and prvide the analg vltage utputs with a full-scale range f ±10 V t an amplifier. Tw channel analg vltages were augmented by the amplifier with a gain f 3.125V/V and applied n tw SM wires separately. The test was implemented n a Lab VIEW platfrm (Natinal Instruments, Inc.) n a PC. TBLE I. PRMETERS OF THE CD SM CTUTOR Parameter Value Parameter Value E M 28GPa d 250m E 75GPa w U g/cm s f M s 88 C C u 10 m T amb 20 C 10MPa/ K 98 C C m 10MPa/ K 72 C C p M f 62 C w R 20/m r1, r 2 l1, l m V 0 k s N m/ J/kg C 4 m k, k m1, m2 10g r 2 6.8u 10 kg/m 10mm 25MPa 3714~10348N/m 7.5mm B. Perfrmance cmparisn fr three SM actuatrs We cmpare this new SM actuatr with the ther tw SM actuatrs in tw aspects: range f mtin and respnse speed. We apply the same utput vltage (1V) n the upper SM wire f these actuatrs. The current acrss the SM wire is 0.42, and the lwer SM wire wrks as a variable stiffness spring. ccrding t the <RXQJ VPRGXOXV f SM wire in tw transfrmatin phases, the range f its stiffness is linearly changed frm 3714N m t 10384N m.the stiffness f trsin spring is selected as N m/1 ; its equivalent stiffness t extensin spring is 1031N m. The stiffness f trsin spring is lwer than that f the SM wire. Experimental results fr three actuatrs, including the heating and cling phases f the upper SM wire, are shwn in Fig. 7. The results indicate that the CD SM actuatr prvides largest angular range f mtin. The maximum angular mtin f the CD SM actuatr is clse t 30, while BS SM actuatr is limited t 20 and DI SM actuatr prvides nly 13. This limitatin in angular mtin is due mainly t the high stiffness f the antagnist SM wire. 40 BS DI CD 30 Fig.6. (a) Blck diagram cnfiguratin f the psitin cntrl system and (b) experimental setup fr testing. ngle (deg.) Same starting pint f cling Time (s) Fig.7. Experimental angular psitin f three SM actuatrs under the same applied current. The dynamic respnse f the three actuatrs shw a slight psitin versht befre reaching steady-state, see Fig.7. This behavir is explained with the aid f the heat dynamics, equatin (8). During the heating phase, the SM wire 4928

5 underges a phase change that persists till an energy balance between the pwer input and the pwer lss is reached. This energy transfer als crrespnds t the temperature respnse f SM wire. During the cling phase, we bserved that the rate at which the CD SM actuatr returned t the relaxed state is faster than the ther actuatrs. This faster rate f the CD SM actuatr is prvided by stred energy in the trsin spring. The abve results clearly indicate that the CD SM actuatr prvide large wrking range under the same current stimulating cnditin, as well as mre efficient energy utilizatin cmpared t the ther tw actuatrs. C. Step respnse The experimental respnses t a series f step inputs were examined n this new SM actuatr. single channel and tw-channel cntrls were applied fr a cling speed perfrmance cmparisn. In ne channel cntrl, the upper SM wire was actively heated and the antagnistic SM wire was passive. In tw-channel cntrl, when the real psitin was larger than the reference, the antagnistic SM wire wuld be activated t reduce the versht and increase the cling prcess. phase, the average fall time frm 20 t the 10 and frm 10 t 0 is apprximately 6 secnds. The jint angle reduced slwly t the set pint under the recvery frce frm the trsin spring. T reduce the fall time, a secnd PI cntrller was prvided t the lwer SM wire. Figure 8(b) shws the step respnses t the desired steps f 10 and 20. Cmpared t the ne channel cntrl, the rise time reduces t abut 1s. Despite an versht in the heating phase, the psitin angle tends t stable sn due t the integral gain. Meanwhile during the cling phase f upper SM wire, the secnd SM wire wuld be heated t increase the cling speed. The fall time f step input frm 20 t 10, 10 t 0 reduces t abut 2.5 s. These figures clearly shw that the rise and fall times f step respnses have decreased significantly. The respnse speeds bth in the heating and cling phase are increased. This clearly demnstrates that ur prpsed actuatr design and cntrl methd have achieved better perfrmance than the cnventinal SM actuatr. D. Tracking respnse This part presents the tracking respnses f the CD actuatr t a series f sinusidal inputs with frequencies f 0.05 Hz, 0.08Hz and 0.1 Hz using the prpsed cntrl methd. It can be seen that the tracking perfrmance fr 0.05 Hz is better than 0.08Hz and 0.1Hz in Fig. 9 (a) (b) (c).the tracking errr fr 0.05Hz, 0.08Hz and 0.1 Hz is abut-1 ~1, -1 ~1.5, -2.5 ~1.5 respectively. s the frequency f the sine wave increases, the errr increases gradually, the system begins t lag behind the desired respnse due t the slw respnse speed f the actuatr. (a) (b) Fig.8. (a) One channel cntrl fr the CD SM actuatr and (b) tw channels cntrl fr the CD SM actuatr Figure 8(a) shws respnses t desired steps f 10 and 20 in ne channel cntrl. In terms f time-dmain specificatin, during the heating phase, the average rise time t the 10 step input is apprximately 3.5 s. Fr the respnse t a 20, it is slightly lng and requires apprximately 5 secnds. This is expected, as the set pint is further away frm the zer psitin, s it takes a lnger time fr the actuatr t reach the desired set pint. During the cling (a) 0.05 Hz 4929

6 this new actuatr and the tw cnventinal SM actuatrs have been cnducted fr perfrmance cmparisn. Psitin cntrl experiments fr step respnse and sine wave tracking demnstrated that this nvel cmpliant actuatr has faster respnse speed, larger utput range. The respnse speed f SM actuatr can be further increased t faster and mre rbust jint mtin with better cntrl methds. We are currently develping advanced cntrller t imprve the perfrmance f this actuatr and develping applicatins fr rehabilitatin rbtic and surgical rbtic systems. (b) 0.08 Hz (c) 0.1Hz Fig.9. Sine tracking respnse with (a) 0.05 Hz, (b) 0.08 Hz and (c) 0.1Hz. V. CONCLUSION nvel CD SM actuatr using tw antagnistic SM wires and a trsin spring has been prpsed t imprve the perfrmance f traditinal SM actuatrs. Experiments fr REFERENCES [1]. Nespli, S. Besseghini, S. Pittacci, E. Villa, and S. Viscus, ³The high ptential f shape memry allys in develping miniature mechanical devices: review n shape memry ally mini-actuatrs, Sensrs and ctuatrs, vl. 158, pp , Mar [2] P. Sears and P. Dupnt, ³ steerable needle technlgy using curved cncentric tubes, in IEEE/RSJ Int. Cnf. Intell. Rbts Syst., Beijing, China, frm Oct. 9-15, 2006, pp [3] R. Webster,. M. Okamura, and N. J. Cwan, ³Tward active cannulas: Miniature snake-like surgical rbts, in IEEE/RSJ Int. Cnf. Intell. Rbts Syst., Beijing, China, frm Oct. 9-15, 2006, pp [4] S. Kim, E. Hawkes, K. Chy, M. Jldaz, J. Fleyz, and R. Wd, ³Micr artificial muscle fiber using NiTi spring fr sft rbtics, in IEEE/RSJ Int. Cnf. Intell. Rbts Syst., St. Luis, US, frm Oct , 2009, pp [5] F. Peng, X.-X. Jiang, Y.-R. Hu, and. Ng, ³pplicatin f shape memry ally actuatrs in active shape cntrl f inflatable space structures, in Prc. IEEE Cnf. ersp., 2005, pp [6] C. Liang and C. Rgers, ³Design f shape memry ally actuatrs, J. Intell. Mater. Syst. Struct., vl. 8, pp , [7] R. B. Grbet and R.. Russell, ³ nvel differential shape memry ally actuatr fr psitin cntrl, Rbtica, vl. 13, pp , [8] M. Mallem and V. Tabrizi, ³Tracking cntrl f an antagnistic shape memry ally actuatr pair, IEEE Trans. Cntrl Syst. Technl., vl. 17, pp , [9] H. shrafiun, M. Eshraghi, and M. H. Elahinia, ³Psitin cntrl f a three-link shape memry ally actuated rbt, J. Intell. Mater. Syst. Struct., vl. 17, pp , [10] S. Z. Yan, X. J. Liu, F. Xu, and J. H. Wang, ³ gripper actuated by a pair f differential SM springs, J. Intell. Mater. Syst. Struct., vl. 18, pp , May [11] E. T. Esfahani and M. H. Elahinia, ³Stable walking pattern fr an SM-actuated biped, IEEE-SME Trans. Mechatrn., vl. 12, pp , Oct [12] J. J. Zhang and Y. H. Yin, ³SM-based binic integratin design f self-sensr-actuatr-structure fr artificial skeletal muscle, Sensrs and ctuatrs, vl. 181, pp , Jul [13] D. Grant and V. Hayward, ³Variable structure cntrl f shape memry ally actuatrs, IEEE Cntrl Syst. Mag. vl. 17, pp , Jun [14] V. Bundh, E. Haslam, B. Birch, and E. J. Park, ³ shape memry ally-based tendn-driven actuatin system fr bimimetic artificial fingers, part I: design and evaluatin, Rbtica, vl. 27, pp , [15] R. Van Ham, T. G. Sugar, B. Vanderbrght, K. W. Hllander, and D. Lefeber, ³Cmpliant ctuatr Designs, IEEE Rbt. utm. Mag., vl. 16, pp , Sep [16] G.. Pratt and M. M. Williamsn, ³Series elastic actuatrs, in IEEE/RSJ Int. Cnf. Intell. Rbts Syst., Pittsburgh, US, frm ug. 5-9, 1995, pp [17] C. P. Chu and B. Hannafrd, ³Measurement and mdeling f McKibben pneumatic artificial muscles, IEEE Rbt. utm. Mag., vl. 12, pp , Feb [18] C. Liang and C. Rgers, ³One-dimensinal thermmechanical cnstitutive relatins fr shape memry materials, J. Intell. Mater. Syst. Struct., vl. 1, pp , [19]. R. Shahin, P. H. Meckl, J. D. Jnes, and M.. Thrasher, ³Enhanced Cling f Shape-Memry lly Wires Using Semicnductr Heat-Pump Mdules, J. Intell. Mater. Syst. Struct., vl. 5, pp , Jan