Variable Impedance Control with an Artificial Muscle Manipulator Using Instantaneous Force and MR Brake

Transcription

1 1 IEEE/RSJ International Conferene on Intelligent Robots an Systems (IROS) November -7, 1. Tokyo, Japan ariable Impeane Control with an Artifiial Musle Manipulator Using Instantaneous Fore an MR Brake H. Tomori, S. Nagai, T. Majima an T. Nakamura, Member, IEEE Abstrat Highly rigi atuators suh as geare motors or hyrauli atuators are wiely use in inustrial robots. To obtain high-spee motion, it is neessary to inrease the atuator output as the robot weight inreases. In ontrast, humans perform motions using instantaneous fore, suh as jumping or throwing, via variable stiffness harateristis. We have evelope a one-egree-of-freeom manipulator with a variable rheologial joint using a straight-fiber-type artifiial musle an a magnetorheologial (MR) brake. With the generation of instantaneous fore, the ea an rise times erease ompare to the onventional metho. After the generation of an arbitrary instantaneous fore, we were able to ontrol the robot s arm position by applying an equilibrium fore on the joint. Furthermore, we were able to ontrol the vibrations of the arm by ontrolling the MR brake using an evaluation funtion. I. INTRODUCTION Highly rigi atuators suh as geare motors or hyrauli atuators are wiely use in inustrial robots. To obtain high-spee motion, it is neessary to inrease the atuator output as the robot weight inreases. In ontrast, humans perform motions suh as jumping an throwing using their musles an instantaneous fore. This instantaneous fore is reate by a high-spee hange in musle stiffness, whih hanges the potential energy in the musles to kineti energy. Therefore, systems require high ompliane an a high-spee stiffness hange to generate instantaneous fore, whih is iffiult to ahieve with highly rigi atuators. In aition, improve instantaneous motions are ahieve by aequately ontrolling variable impeane [1]. To generate instantaneous fore, we have evelope a straight-fiber artifiial musle [] [5] as a variable elastiity atuator. This artifiial musle has a high ontration perentage, high ontrative fore, an a long lifespan ompare to the Mibben-type rubber artifiial musle [6], H. Tomori is with the Faulty of Siene an Engineering, Department of Preision Mehanis Chuo University asuga, Bunkyo-ku, Tokyo , Japan (orresponing author: ; fax: ; h_tomori@bio.meh.huo-u.a.jp). S. Nagai is with the Faulty of Siene an Engineering, Department of Preision Mehanis Chuo University asuga, Bunkyo-ku, Tokyo , Japan ( s_nagai@bio.meh.huo-u.a.jp). T. Majima is with the Faulty of Siene an Engineering, Department of Preision Mehanis Chuo University asuga, Bunkyo-ku, Tokyo , Japan ( t_majima@bio.meh.huo-u.a.jp). T. Nakamura is with Chuo University asuga, Bunkyo-ku, Tokyo , Japan ( nakamura@meh.huo-u.a.jp). [7]. Moreover, the artifiial musle is lightweight an flexible an elivers high output. Furthermore, we use a magnetorheologial (MR) flui brake. The MR flui is a funtional flui whose apparent visosity an be hange reversibly at high spees by applying a magneti fiel [1]. Although the MR brake is a frition amper, it an be use as a variable visosity amper by ontrolling its apparent visosity. Therefore, we use this evie as a frition amper to generate instantaneous fore with a high-spee hange in stiffness an as a variable visosity amper to ontrol the vibration of motion. In previous stuies, Floreano [8] evelope a miniature jumping robot using a motor an a spring. However, the elasti oeffiient of the atuator use was onstant, an the instantaneous fore an position oul not be ontrolle inepenently. Although Niiyama [9] evelope a jumping robot using the Mibben artifiial musle, the jumping operation of this robot was esigne by trial an error, an the air-pressure-ontrol apabilities were inaequate. Furthermore, previous stuies have not allowe for visosity ontrol, an the ontrol of the motion generate by instantaneous fore has not been suffiiently evelope. Therefore, we propose the generation of instantaneous fore via a high-spee variable stiffness hange in artifiial musles an MR brakes in a manipulator joint. Furthermore, we ontrol the manipulator arm position by applying an equilibrium fore to the joint. We also ontrol the vibration of the arm using the MR brake as a variable visosity amper. These methos enable us to inepenently ontrol the spee, position, an vibration of the arm. In this paper, we propose a metho for generating instantaneous fore with a one-egree-of-freeom (1DOF) manipulator using artifiial musles an an MR brake in the joint an valiate this propose metho experimentally an via simulation. Next, we ontrol the arm position by inreasing the stiffness of the joint. Then, we propose a visosity ontroller for the MR brake using an evaluation funtion for vibration ontrol. To esign this ontroller, we use a nonlinear ynami harateristis moel of the manipulator. II. 1DOF MANIPULATOR WITH ARIABLE RHEOLOGICAL JOINT A. Straight-Fiber-Type Artifiial Musle The evelope in our laboratory has a tubular shape an is mae of natural rubber latex. Fig. 1 shows a shemati of the /1/$1. 1 IEEE 596

2 artifiial musle. The musle struture inlues a lengthwise arbon fiber layer. Consequently, when air pressure is applie to the musle, it expans in the raial iretion an ontrats lengthwise. The ontratile fore is then use as an atuator. The artifiial musle is flexible an lightweight an provies high output. Furthermore, its elastiity hanges with the applie air pressure. Figure. 1DOF artifiial musle manipulator Figure 1. Shemati of fiber-ouble-layer-type artifiial musle B. MR Flui Brake To generate instantaneous fore, a rapi hange in stiffness is require. Therefore, we fouse on the MR flui brake. By applying a magneti fiel, the apparent visosity of the MR flui an be hange in several milliseons. This evie has a frition amper funtion that an be use for a high-spee hange in the stiffness of the manipulator joint. In aition, it an be use as a variable visosity amper to ontrol the arm s vibration by ontrolling its apparent visosity. In this stuy, we use an MRB-17- (LORD Co.) MR flui brake. Fig. illustrates MRB-17-, an Table 1 gives its speifiations. The MR flui in this evie generates frition on the isk surfae by the magneti fiel. Thus, this mehanism an halt the arm s rotation. MR flui Rotor Coil Figure. Configuration of MR brake D. Funtion of the manipulator This manipulator has variable stiffness, visosity, an elastiity in its joint. Thus, the manipulator an perform the following tasks: The manipulator inepenently ontrols the arm position an joint stiffness by ontrolling the elastiity of eah musle. It halts the arm motion using the MR brake as a frition amper. Elasti energy an be aumulate in the musle by inreasing its elasti fore (i.e., by applying the brake). By quikly releasing the brake, the manipulator generates instantaneous fore from the aumulate elasti energy. Elasti energy an also be aumulate by inreasing the stiffness of the joint using both musles, whih have an opposing relationship. Thus, the manipulator generates kineti energy by hanging the equilibrium of the ontratile fore of musles. The MR brake an be use as a variable visosity amper by ontrolling its apparent visosity. It an ontrol the vibration of the arm. In this paper, we explain the seon task in setion I, the first task in setion, an the fourth task in setion I. TABLE I. SPECIFICATION OF MR BRAE III. NONLINEAR DYNAMIC CHARACTERISTICS MODEL OF THE MANIPULATOR Term Parameter Diameter (mm) 9. With (mm) 6.6 Weight (kg) 1.4 Maximum torque (Nm) 7 Minimum torque (Nm) <.4 Max urrent value (A) 1 C. 1DOF Manipulator Fig. shows the evelope 1DOF artifiial musle manipulator. In this manipulator, two artifiial musles are arrange in parallel. The belt pulley transmits the ontrative fore of the artifiial musles to the rotation axis. The MR brake is fixe to the first joint through a gear. As a result, it is possible to apply a brake to the rotation axis. A. Outline of the Manipulator Moel We built a manipulator moel taking the ynami harateristis of the artifiial musle into aount. This manipulator moel allows for an analytial approah to the ontrol problem. Fig. 4 shows the shemati of the moel, whih onsists of three parts. The first part is a mehanial equilibrium moel [], [5] that treats the stati harateristis of the musle. With this moel, the relationships between pressure, loa, an ontration are linearize. The seon part is a moel ontaining elements relate to the ynami harateristis of the air musle system, inluing a pressure valve [11] [1]. The thir part is a manipulator loa system moel. We ombine these three parts into one manipulator moel. 597

3 x rp rp Figure 4. Shemati of the manipulator C. Dynami Charateristis Moel of the Artifiial Musle This setion esribes the ynami harateristis moel of the artifiial musle. In this moel, the input is the target pressure from the ontrol part, an the output is the ontratile fore of the artifiial musle. The flowhart of this moel is shown in Fig. 5. Elements relate to the ynami harateristis of the artifiial musle inlue the spee response of the solenoi valve, ease of passing air in the air tube, an pressure an volume hanges. B. Mehanial Equilibrium Moel In this setion, we esribe the mehanial equilibrium moel that treats the stati harateristis of the manipulator [], [5]. The artifiial musles are iffiult to ontrol beause they are highly nonlinear in ontration, ontratile fore, an pressure. Therefore, we use a mehanial equilibrium moel to ontrol the artifiial musle. Through this mehanial equilibrium moel, the internal pressures P 1 an P [MPa] of an artifiial musle an be alulate from the joint rigiity j [Nm/ra], loa torque τ l [Nm], an target angle θ of the arm [ra]. In the alulations, α is the onstant that approximates the relationship between the extent of ontration an iameter, l is the initial length [m], is the initial iameter [m], is the elasti oeffiient [N/m ], a is a oeffiient between pressure an spring onstant of an artifiial musle [N/(m.MPa)], t is the thikness of the rubber [m], M is the oeffiient of the fiber of artifiial musle, n is the number of fibers, b is the with of the fiber [m], Ψ is angle slak of wire [ra], an r p is the pulley raius [m]. Figure 5. Nonlinear moel of the straight-fiber-type artifiial musle 1) Spee response of the solenoi valve First, we obtaine the spee response of the solenoi valve experimentally an onlue that it followe a seon-orer lag system with a ea time. The harateristis of the solenoi valve are shown in equation (9), where T 1 =.5 [s], T =.5 [s], an L =.4 [s]: P (, ) [ G 1 11 j a ( ) G ( ) G G ( ) G /[ G ( ) G r ( ) G 1 ( ) G p ( ) ( ) G 1 1 ( 1) j a1 (, ) P1 a a P G ( ) 1i i G i a1 a ( )] 1 G ( ) G iti li sini i osi i i i ( ) i M i tan nb i i 1 ( )] 1 1 sl G( s) e T1s 1 Ts s 15s 75 T s 1 T s 1 s 15s 75 1 (9) ) Air pressure propagation in a pipeline Next, we onstrute a moel of the air tube that transmits pressure from the solenoi valve to the artifiial musles. The whole system, whih inlues the air tube an the insie of the solenoi valve, is expresse using the soni onutane C, aoring to JIS B 89 [14]. When the internal pressures of the artifiial musle an solenoi valve are etermine, the mass flow rate of the air that flows into the insie of the artifiial musle, i.e., q m [g/s], is given by equations (1) an (11). We etermine the soni onutane experimentally: l sin os l sin M ( ) tan i i i i i i i G i i i i i i i 4nb i i i xi i ( 1.4) ( l x ) x l i i i l i i q ( P, P) Cp m u.58 P/ Pu 1 u T T u P / Pu 1 1 (1) x 1 rp 1 rp P / Pu

4 T ( ), (11) qm Pu Cpu Tu where T is the normal onition temperature [], ρ iniates the normal onition ensity [kg/m ], C iniates the soni onutane [kg.s/m ], an P u iniates the upstream sie pressure insie the solenoi valve [MPa]. In aition, T u is the air temperature [], P is the ownstream sie pressure insie the artifiial musle [MPa], an γ is the ritial pressure ratio. ) Pressure hange in the artifiial musle Next, the ompation property of air, whih is a harateristi peuliar to an air pressure system, is onsiere. A state equation an express the ompation property of a flui. Equation (1) is obtaine by ifferentiating an transforming this state equation. Then, the pressure hange P/t insie the artifiial musle is expresse in terms of q m, the inner volume of the artifiial musle [m ], an pressure P. 1 1 P RT qm P t t (1) P,, P, qm, t t where R is the gas onstant [Pa.m.g 1. 1 ] an к is the ratio of speifi heat. 4) Generating ontratile fore in the artifiial musle The pressure harateristi of the artifiial musle is expresse in equation (1) using the mehanial equilibrium moel. The ontratile fore F [N] of the artifiial musle is expresse in terms of its internal pressure P an ontration x [m]. Note that G 1, G, an G use equations (), (4), an (5), respetively. F( x, P) PG G1 G 5) olume hange in the artifiial musle We moele the hange in the volume apaity aoring to the ontration of the artifiial musle. First, the artifiial musle beomes irular, as shown in Fig. 6. Then, the inner volume of the musle [m ] an be expresse as follows: Figure 6. Shape moel of the artifiial musle viewe along the z-axis D. Loa System Moel of the Arm First, we alulate the riving torque of the arm from the ontratile fores F 1 an F of the two opposing artifiial musles as follows: ( F F) r, 1 where r p is raius of the pulley. Then, the angular aeleration of the arm is alulate from the forwar kinetis: ( ) (, ), m l I1 I where I 1 is the inertia of the arm, I is the inertia of the loa [Nm.s ], τ l is the loa torque [Nm], an τ m is the amping torque of the MR brake [Nm]. I. GENERATING INSTANTANEOUS FORCE A. Metho for Generating Instantaneous Fore In this hapter, we explain the generation of instantaneous fore using the MR brake, as shown in Fig. 7. This MR metho has three steps: 1) hol the joint rotation using the MR brake as a frition amper, ) aumulate elasti energy in the artifiial musle on one sie by applying air pressure, an ) generate instantaneous fore by releasing the MR brake. p l l 4 l os l 4 sin l l sin sin 1 Figure 7. Generation of instantaneous fore using the MR metho B. Seletion of Initial Pressure for the Artifiial Musle Aoring to the MR metho, the steay-state position of the arm epens on the initial pressure of the artifiial musle. No air pressure is ae in the musle uring the manipulator rive, so it is neessary to alulate the initial pressure to raise the loa to the esire arm angle. However, this pressure hanges with hanges in the volume an ontratile fore of the musle. 599

5 Therefore, we obtaine the experimental relationship between the volume an pressure of the artifiial musle. In the experiment, the initial pressure was applie to the artifiial musle, an the pressure an ontration were reore. The volume of the artifiial musle was alulate from the ontration using equation (14). The experimental result in Fig. 8 shows that the pressure is proportional to volume. This relationship oes not epen on the initial pressure. We express this relationship using the following approximate equation, where P is the initial pressure an the initial volume: P P.14 Aoring to this approximate equation, the initial pressure of the artifiial musle was alulate from the initial volume an the esire pressure an volume. The esire pressure was alulate from the esire angle an loa torque using the mehanial equilibrium moel. The esire volume was alulate from the ontration an esire angle using equation (14). Finally, the initial volume was alulate from the initial angle following the proeure use to alulate the esire volume. Pressure [MPa] P =.5 {MPa] P =.15 [Mpa] P =. [MPa] y = -.14x y = -.14x +.9 y = -.1x olume [m ] Figure 8. Relationship between pressure an volume of artifiial musle C. Instantaneous Fore Generation Experiment In this setion, we esribe the generation of instantaneous fore using the MR metho. In the experiment, the initial pressure was alulate using equation (17) with the esire arm angle of 6[eg] an a loa of 8. [N]. Fig. 9 shows the results obtaine from the onventional metho as well as the experimental an simulation results obtaine from the MR metho. The onventional metho uses step input an torque feebak [15]. Table shows the ea an rise times. The results show that the ynami harateristis moel of the manipulator effetively reproues the manipulator system harateristis. Furthermore, we onlue that the initial pressure was orretly etermine using equation (17). For the experimental results of the MR metho, Table shows that the ea time ereases by 68% an the rise time ereases by 1% when ompare with the onventional metho. Angle [eg] Desire angle Conventional metho MR metho (experiment) 1 MR metho (Simulation) Figure 9. Experimental an simulation results TABLE II. DEAD AND RISE TIMES Term alue Dea time (s) Rise time (s) Step response MR metho (Experiment) MR metho (Simulation) APPLYING EQUILIBRIUM FORCES FOR POSITION CONTROL Although the manipulator generate instantaneous fore, the initial pressure epene on the esire angle of the arm. Furthermore, this approah oes not ontrol the arm s joint stiffness after this motion. Therefore, we propose the appliation of an equilibrium fore to the joint to ahieve position ontrol as shown in Fig. 1. With this metho, the manipulator an ontrol the arm position after an arbitrary instantaneous fore is applie. First, the manipulator generates instantaneous fore using an arbitrary initial pressure. Next, air pressure is applie to the musles to help ontrol the arm position an joint stiffness. In the propose metho, aitional air pressure was alulate using equations (1) an (). However, we annot simply apply air pressure after the arm reahes the esire angle beause of the response elay of air pressure. Therefore, we etermine the proper timing requirement as follows. Figure 1. Applying equilibrium fore for position ontrol loa A. Pressure Timing As shown in Fig. 11, we alulate t b from t a an t to etermine the proper time to apply aition pressure, where t a 54

6 is the time when the arm reahes the esire angle obtaine experimentally an t is the response lag of the pressure alulate using equation (18). In aition, both artifiial musles nee ifferent value of t, beause these musles are applie ifferent pressure. Therefore, eah t were etermine by taking into aount both musles. Angle [eg] t a t b t =t a - t b Time [se] [s] Figure 11. Presure timing Qm = 66. P t P P m Q Here an P are the volume an pressure of a musle, respetively, when the arm reahes the esire angle with joint stiffness, an Q m is the volume flow rate [m /s] of air from the solenoi valve to the musle. B. Experiment for Applying Equilibrium Fores for Position Control We applie pressure to the musles to ontrol the arm position an joint stiffness after the generation of instantaneous fore. In this experiment, we generate instantaneous fore with an arbitrary initial pressure an then applie air pressure to the musles in orer to establish an equilibrium fore an ahieve the esire joint angle. The time of pressure aition is t b, whih is alulate in setion.a. Figs. 1 an 1 show the experimental results for eah initial pressure. The esire angles were an 6 [eg], joint stiffness was.7 [Nm/eg], loa was 8. [N], an initial pressures were.,.5, an.4 [MPa]. From these results, we ontrolle the arm position by applying an equilibrium fore to the joint for eah initial pressure an esire angle. Furthermore, joint stiffness was ontrolle after applying an equilibrium state. Angle [eg] Desire angle Initial pressure. [Mpa] Initial pressure.5 [Mpa] Initial pressure.4 [Mpa] Figure 1. Experimental result of applying an equilibrium fore (esire angle was [eg]) Angle [eg] Desire angle Initial pressure. [Mpa] Initial pressure.5 [Mpa] Initial pressure.4 [Mpa] Figure 1. Experimental result of applying an equilibrium fore (esire angle was 6 [eg]) I. IMPEDANCE CONTROL WITH INSTANTANEOUS FORCE BY A 1DOF MANIPULATOR A. isosity Control of MR Brake Using an Evaluation Funtion As mentione in setion, we were able to apply an equilibrium fore to the joint an ontrol the arm position after generating instantaneous fore. However, we still experiene arm vibration an overshoot, as shown in Figs. 1 an 1. Thus, we ontrolle the arm vibration an overshoot using the MR brake as a variable visosity amper by ontrolling its apparent visosity. Then, we introue a ontroller to hange the apparent visosity oeffiient of the MR brake aoring to the motion of the arm. We use the following evaluation funtion [16]. f I ( r, r) r { A( ) B r } s Here A an B are weighting oeffiients an B = 1 A, r is the visosity oeffiient [Nm.s/eg], θ is angle of the arm [eg], θ s is the vibration ontrol start angle [eg], an θ f is the vibration ontrol finish angle [eg]. The first term is the element of interferene of the brake torque to the arm, an the 541

7 seon term is the element of smoothness of hange in the visosity oeffiient. In aition, using the variational metho in equation () an solving Euler s equation, we obtain the following: Here s is the initial value of the visosity oeffiient, f is the final value, an s = [Nm.s/eg] an θ s = [eg]. Using this funtion, we an ontrol the visosity of the MR brake aoring to the angle of the arm. Fig. 14 shows the relationship between the arm angle an the visosity oeffiient when f is.9 [Nm.s/eg], an θ f is 6 [eg]. Figure 14. Relationship between arm angle an visosity oeffiient B. Simulation for isosity Control Design To use the evaluation funtion to ontrol the visosity of the MR brake, we must etermine the parameters f an A. In this paper, we obtaine these parameters by try an error using simulation. To this en, we simulate the MR metho with the apparent visosity ontrol. Fig. 15 shows the simulation results. The initial pressure was.5 [MPa], loa was 8. [N], the weighting oeffiient A was.7, an the final value of the visosity oeffiient f was.9 [Nm.s/eg]. Angle [eg] - s s f r( ) e - f f = θ e - e - e A B r( θ ) f = f f f - se e - f e f - e s = s r( θ ) Desire angle Simulation result 1 (A=.7, f=1.) Figure 15. Simulation result with apparent visosity ontrol - C. Impeane Control with Instantaneous Fore by MR Brake Using the Evaluation Funtion We ontrolle the vibration an overshoot of the arm using the MR brake as a variable visosity amper. We applie the arm position ontrol esribe in setion here as well. We use the MR brake as follows: The apparent visosity of the MR brake was ontrolle by the evaluation funtion. The weighting oeffiient A was.7, an the final value of the visosity oeffiient f was 1. [Nm.s/eg], whih were eie by simulation. The apparent visosity of the MR brake was fixe at.1 [Nm.s/eg]. This onition was hosen experimentally to obtain stable response without vibration an overshoot of the arm. The apparent visosity of the MR brake was fixe at [Nm.s/eg]. The loa was 8. [N], the esire angle was 6 [eg], an the joint stiffness was.7 [Nm/eg]. The experimental results are shown in Fig. 16. From this figure, the simulation results in Fig. 15 reproue the experimental results. In aition, owing to the apparent visosity ontrol, the arm s vibration an overshoot erease without suffering interferene from the MR brake in the rise setion. This result was ompare with the results of the fixe apparent visosity. Angle [eg] Desire angle Experimental result with apparent visosity ontrol (A=.7, f=1.) Experimental result with fixe apparent visosity (.1 [Nm.s/eg]) Experimental result with fixe apparent visosity ( [Nm.s/eg]) Figure 16. Experimental results with apparent visosity ontrol II. CONCLUSION In this paper, we propose a metho for the generation of instantaneous fore using an MR brake to proue a hange in musle stiffness. Using this metho, we were able to emonstrate that the ea an rise times erease ompare with the onventional metho with experiments an simulations. We also applie an equilibrium fore to the joint for position ontrol. With this metho, the manipulator an ontrol the arm position after an arbitrary instantaneous fore is applie. 54

8 We esigne the apparent visosity ontrol of the MR brake using a nonlinear ynami harateristis moel of the manipulator in orer to ontrol the vibration an overshoot of the arm. Finally, we ontrolle the vibration an overshoot of the arm by ontrolling the apparent visosity of the MR brake using an evaluation funtion. As a result, the manipulator an ontrol the arm position, joint stiffness, vibration, an overshoot using the instantaneous fore. [15] Y. Miorikawa an T. Nakamura, ariable Rheologial Joints Using an Artifiial Musle Soft Atuator an Magneto-Rheologial Fluis Brake, Intelligent Robotis an Appliations 9 (ICIRA9), pp , 9. [16] S. Nagai, H. Tomori, Y. Miorikawa, an T. Nakamura, The Position an ibration Control of the Artifiial Musle Manipulator by ariable isosity Coeffiient Using MR Brake, Pro. the 7th Annual Conferene of the IEEE Inustrial Eletronis Soiety (IECON11), pp. 7 1, 11. III. FUTURE STUDY In future, we plan to alulate the initial pressure for the generation of instantaneous fore in orer to realize the esire spee an fore. We also plan to evelop a multi-dof manipulator ontrolle by instantaneous fore. In aition, we will test an arbitrary arm motion through experimentation. REFERENCES [1] D. Braun, M. Howar, an S. ijayakumar, Optimal variable stiffness ontrol: formulation an appliation to explosive movement tasks, Autonomous Robots, vol., no., pp. 7 5, 1. [] T. Nakamura, N. Saga, an. Yaegashi, Development of Pneumati Artifiial Musle base on Biomehanial Charateristis, in Pro. IEEE Int. Conf. Inustrial Tehnology (ICIT ), pp [] T. Nakamura an H. Shinohara, Position an Fore Control Base on Mathematial Moels of Pneumati Artifiial Musles Reinfore by Straight Glass Fibers, in Pro. IEEE Int. Conf. Robotis an Automation (ICRA 7), pp [4] T. Nakamura, Experimental Comparisons between Mibben type Artifiial Musles an Straight Fibers Type Artifiial Musles, in Pro. SPIE Int. Conf. Smart Strutures, Devies an Systems III, p , 6. [5] H. Tomori an T. Nakamura, Theoretial Comparison of Mibben-Type Artifiial Musle an Novel Straight-Fiber-Type Artifiial Musle, Int. J. Autom. Teh., vol. 5, no. 4, pp , 11. [6] G.. lute, J. M. Czernieki, an B. Hannafor, Mibben Artifiial Musles: Pneumati Atuators with Biomehanial Intelligene, Pro. IEEE/ASME Int. Conf. Avane Intelligent Mehatronis 1999, pp [7] C. P. Chou an B. Hannafor, Stati an Dynami Charateristis of Mibben Pneumati Artifiial Musles, Pro. IEEE Int. Conf. Robotis an Automation 1994, pp [8] M. ova, M. Shlegel, J.-C. Zufferey, an D. Floreano, A Miniature Jumping Robot with Self-Reovery Capabilities, Pro. IEEE/RSJ Int. Conf. Intelligent Robots an Systems, pp , 9. [9] R. Niiyama, A. Nagakubo, an Y. uniyoshi, Mowgli: A Bipeal Jumping an Laning Robot with an Artifiial Musuloskeletal System, Pro. IEEE Int. Conf. Robotis an Automation (ICRA 7), pp [1] B. J. Park, C. W. Park, S. W. Yang, H. M. im, an H. J. Choi, Core-Shell Type Polymer Coate-Carbonyl Iron Suspension an Their Magnetorheology, ERMR8, p. 1, 8. [11] H. Tomori, H. Maea, an T. Nakamura, Orbit Traking Control of 6-DOF Lubber Artifiial Musle Manipulator Consiering Nonlinear Dynamis Moel, Trans. Japan So. Meh. Eng., Series C, vol. 77, no. 779, pp , 1. [1] H. Tomori, H. Maea, an T. Nakamura, Orbit Traking Control of 6-DOF Lubber Artifiial Musle Manipulator onsiering Nonlinear Dynamis Moel, 15th ROBOTICS Symp., pp , 1. [1] H. Tomori, Y. Miorikawa, an T. Nakamura, Constrution of Nonlinear Dynami Charateristi Moel of Pneumati Artifiial Rubber Musle Manipulator using MR Brake, Journal of Intelligent Material Systems an Strutures, vol., no. 9, pp , 1. [14] JISB89, Air pressure-apparatus for ompressive flui-the test metho of a flow harateristi, Japanese Stanars Assoiation,. 54