Biped Walking of Passive Dynamic Walker with IPMC Linear Actuator

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1 Biped Walking of Passive Dynamic Walker with IPMC Linear Actuator N. Kamamichi 1,Y.Kaneda 1, M. Yamakita 1,3,K.Asaka 2,3 and Z. W. Luo 3 1 Tokyo Institute of Technology, Meguro-ku Oh-okayama Tokyo, JAPAN 2 Special Division for Human Life Technology, AIST, Midirigaoka Ikeda Osaka, JAPAN 3 Bio-Mimetic Control Research Center, RIKEN, Anagahora Shimoshidami Moriyama-ku Nagoya, JAPAN {nkama,ykaneda,yamakita}@ctrl.titech.ac.jp Abstract: We are developing a linear artificial muscle actuator using ionic polymer-metal composites (IPMC) which is an electro-active polymer that bends in response to electric stimuli and the goal of our study is to apply the actuator to robotic applications especially to a biped walking robot. In this paper, we will describe an empirical model of the actuator and demonstrate walking simulations of a small-sized biped walking robot called Wire Walker. Keywords: Passive Dynamic Walking, Artificial Muscle Actuator, IPMC, EAP 1. Introduction The study of humanoid robot and bipedal walking is one of the most active research area in robotics. Humanoid walking has been already demonstrated, however, energy-effective gait design and safe control against outside environment and human being are not confirmed completely yet. One of the solutions for energy-effective gait design is exploiting the natural dynamics of a walking robot. McGeer studied a simple unpowered walking machine which is well known to as passive dynamic walking 1). A bipedal robot with suitable parameters can walk down a gentle slope without any driving force utilizing only gravity effect and its physical dynamics, and generates a stable periodic gait automatically. The gait pattern of passive walker can be considered to be natural and energy-efficient. In our previous works 2, 3, 4), we have studied some application methods of gait synthesis for active walking on the level ground based on the passive dynamic walking. A control strategy based on passive dynamic walling has properties of automatic gait generation and realization of dynamic-based control. The validity of proposed methods had been investigated by numerical simulations and experiments. In the experimental verification, we considered that the geared motor was not able to exploit the natural dynamics fully, and soft actuation should be needed in order to exploit the natural dynamics. For biped walkers, soft and light actuators with back-driveability should be needed to realized energy-effective gaits by taking advantage of the natural dynamics and the gravity effect. Some researchers have applied soft actuators to biped walking robots, e.g., Direct Drive torque motor, MIT Leglab s Series Elastic Actuator 5), pneumatic McKibben muscle actuator. The study of M. Wisse et al. is especially excellent, they constructed a 2D autonomous walking machine: MIKE 6) which is actuated by McKibben muscle actuators, and demonstrated its stable and energy-effective walking on the level ground. In this paper, we apply a high polymer gel actuator, Ionic Polymer-Metal Composite(IPMC), to a biped walking robot. High polymer gel actuator is one of the candidates of artificial muscle actuators due to their softness and miniaturizability. For several decades, electro-active polymers(eap) 7), which respond to electric stimuli with shape change, received little attention because of their actuating limitation. During last ten years, development of EAP materials with large displacement and quick response changed the potential capability, and EAP received much attentions of engineer and researcher from many disciplines, e.g., robotics, medical service, toy industry. Ionic Polymer-Metal Composite(IPMC) actuator is one of the most promising EAP actuators for applications. The output force of IPMC actuator is still small, however, we proposed a new concept of unitization in order to realize desired characteristic 8). The structure of our proposed actuator can be easily constructed, and the actuator transform bending motion into linear motion. The elementary units can be connected in parallel and series in order to realize desired displacement and force. In this paper, we explain the structure of the actuator, and identify an empirical model of the actuator. Numerical simulation of a small-sized bipedal walking based on the model and basic experiment are demonstrated. 2. Ionic Polymer-Metal Composite (IPMC) Ionic Polymer-Metal Composite (IPMC) is an EAP material that bends in response to an electrical activation, and produced by chemically plating gold or platinum on a perfluorosulfonic acid membrane which is known as an ion-exchange membrane. When input voltage is applied to metal layers of the both surface, it bends in high speed (Fig. 1). The phenomenon of this motion was discovered by Oguro et al. in ). The charac-

2 elementary unit Figure 3: Basic concept of IPMC linear actuator Figure 1: Bending behavior of IPMC actuator Figure 2: Structure of IPMC actuator teristics of IPMC are as follows: Driving voltage is low. (1 2 [V]) Speed of response is fast. (> 100 [Hz]) It is durable and stable chemically. (It is possible to bend over times) It is a flexible material. It moves in water and in wet condition. Miniaturization and weight saving is possible. It is silent. 0[V] 2.5[V] By exploiting the characteristics, IPMC actuators have been applied to robotic applications such as active catheter 10, 11, 12), a wiper for nanorover 13), a micropump 14), a fish-type underwater robot 12, 15), micromanipulator 16) and a distributed actuation device 17). It, however, also has disadvantages that actuation force is still small and that input voltage is restricted to the range that electrolysis of ionic polymer dose not occur. In order to improve the performance, developments of ionic polymer menbrance and plating method are required. 3. IPMC Linear Actuator In this section, a concept of linear actuator and the structure of its elementary unit is explained, and a performance of the actuator is analyzed from experimental results. load Laser Displacement Meter IPMC Actuator [current] Computer Figure 4: Experimental setup [position] [voltage] 3.1 Structure of Linear Actuator We propose an effective structure of actuator that transform bending motion into contracting motion. Fig. 2 shows the structure of the elementary unit. This elementary unit consists of four IPMC films and one side of the unit is formed from a pair of films which are connected by a flexible material. When input voltage is applied to electrodes of surface with anode outside, each membranes bend outside, then the actuator is constricted. An actuation force and displacement of each units are small, however, the elementary units are able to be connected in parallel and series as in Fig. 3, so the actuator can realize desired force and displacement. By shifting series of the elementary units by half pitch to avoid interferences as in Fig. 3, total actuator is made compact, and high power/volume and miniaturization are realized. 3.2 Characteristics of Actuator In order to check the characteristics of the actuator, we carried out fundamental experiments. Fig. 4 shows the experimental setup. In this experiment, one edge of the actuator is fixed on a board floated on the water surface to reduce effects of the weight of electrodes and ties. Displacement of the linear actuator was measured by a laser displacement meter. IPMC film which we used in this experiment is Nafion R 117(DuPont) plated with gold, and the amount of gold on the surface of membrane is about 10 [mg/cm 2 ]. The elementary unit was made from four IPMC films which were cut into ribbons with a width of 2 [mm] and length of 20 [mm], and the total length of actuator unit is about 40 [mm]. The maximum displacement was more than 10 [mm] under a step voltage

3 $ # "! (a) displacement (b) current $ # "! (a) displacement % % % (b) current % % % Figure 5: Step response with various inputs Figure 6: Step response with various loads of 2.5 [V], though the response of the actuator varies depending on its condition. Response in Step Voltage Fig. 5 shows the response in a step voltage without loads, where step input voltages of 1.5, 2.0, and 2.5 [V] were applied at 0 [s]. From (a), it can be seen that the peak value of displacement enlarges as input voltage increases. When the step voltage is applied, IPMC membrane bends toward anode side quickly and bends back gradually. The linear actuator has such a characteristic behavior. From (b), it is observed that the current increased sharply at the moment when the input voltage is applied, then it decreased exponentially. The peak value of current increases as input voltage does. Response with Loads Fig. 6 shows the response in step voltage with loads, step input voltage of 2.5 [V] was applied in loading. As the load is increased, displacement becomes small but the current does not almost change. Fig. 7 shows the response in step load. A constant load is added on after 1 [s]. Displacement becomes large in proportion to weight of loads. 3.3 Model Identification In order to know the capability of the linear actuator for robotic system, we identify the linear actuator as a mathematical model. IPMC actuators have been modeled in various ways in consideration of the physical and chemical phenomenon 18, 19), however, it is difficult to represent these models by systems of ordinary differential equation because of its complexity. In this paper, in consideration of model-based control, we identify the actuator as a linear time invariant model with a static nonlinearity from input-output data 20) using a subspace identification algorithm. % % % Figure 7: Response with various loads First, the model of the actuator is assumed to be represented by a system of Fig. 8. This model has two inputs and one output, and consists of two sub-system, P 1 (s) andp 2 (s), which are connected in series. P 1 (s) is a system with one input v, input voltage, and one output f 1 which is a force generated by electric stimuli. P 2 (s) is a system with one input force f 2 which is exerted to the actuator, and one output y, displacement of actuator. f 2 is assumed to be the difference between f 1 and f l. P (s) is defined as P 2 (s)p 1 (s). In order to conduct the simulations that the actuator is applied for a mechanical system, we need to identify both of sub-systems. It is difficult to add two inputs simultaneously, so we first assume that they are linear time invariant (LTI) systems, and identify them as following procedure: 1. Identification of P (s): Measure a response from input voltage v to displacement y, then compute the system P (s) = P 2 (s)p 1 (s) from input-output data using a subspace identification algorithm. 2. Identification of P 2 (s): Measure a response from load f l to displacement y, then compute the system P 2 (s) from input-output

4 f l v P 1 f 1 f 2 y P 2 b u h m h Figure 8: Block diagram m l m l g a θ 1 (x, y) θ 2 l = a b Figure 10: Experimental walking machine and its ideal model (a) displacement. u h # " f actuator r pulley (b) input voltage. Figure 9: Identification result with LTI model Figure 11: Actuator model of hip joint data using a subspace identification algorithm. 3. Computation of P 1 (s): Compute the system P 1 (s) asp 2 (s) 1 P (s). In procedure 1 and 2, we performed the system identification using N4SID function 21) in MATLAB. Fig. 9 shows a comparison between experimental result and simulated result using the identification model. It is shown that a quick transient of simulated result is nearly equal to the experimental one. But in part of slow decay, there is a little error between them. As the results of identification with linear approximate model, the characteristics of the actuator is captured, however, we have to identify the characteristics in consideration of nonlinear effects to obtain an appropriate model especially in large operating range. It is reasonable to assume that actuator has many nonlinear characteristics and one of the most influential factor is dynamics of load since the bending characteristics of the films highly depends on the load. In order to include the effect, we identified the actuator as Hammerstein model that consists of static nonlinearity and LTI system, where the static nonlinearity is followed by a LTI system in a cascade connection. Please see reference 8) for the detail. 4. Application to Biped Walker This section addresses an application of the actuator to a small-sized biped walking robot. 4.1 Model of Biped Robot In this paper, a simplest planar walking model, so-called compass-gait walker, is chosen as a target system. Fig. 10 shows the experimental walking machine and its ideal model, and Table 1 shows the values of the parameters. Because of the symmetric structure, the motion is constrained in a sagittal plane and the robot can be regarded as a two-legged robot. A heel-strike collision is assumed to be inelastic and without sliding in the simulation. The robot with suitable parameters can walk down a gentle slope without any driving force, and generates a stable periodic gait. Our biped model with the parameters has the nature of the passive dynamic walking. We consider the walking with actuators at hip joint on a slope or a level ground. To actuate the hip joint, contractive force of linear actuator transforms into torque by the structure as Fig. 11. We assume that one joint is actuated by a pair of linear actuators, then the hip joint of the robot is able to be rotated clockwise and counterclockwise as in this figure.

5 " " Table 1: Parameters of walking machine Actuator r m l leg mass [kg] m h hip mass [kg] total mass [kg] a lower part of leg 0.05 [m] b upper part of leg 0.05 [m] l leg length 0.10 [m] r radius of hip pulley [m] g gravity acceleration 9.81 [m/s 2 ] θ 1,θ 2 leg angle [rad] u h hip torque [N m] l m θ Figure 13: Experimental setup of swinging a pendulum #" % %! Figure 14: Experimental result (a) angular positions! # # " (b) input = = = ing cycle is so fast and the walking motion is generated with quick transient motion and small displacement of the actuator. Fig. 12 shows the simulated results of walking on a level ground. The number of units connected in parallel and series is set as 4 and 3, respectively, and the radius of pulley is set as r =0.004 [m]. In this simulation, we applied a square pulse as input voltage whose cycle is 0.48 [s] and whose amplitude is 2.5 [V]. From this results, it can be seen that the oneperiodic walking gait is generated and the walking cycle synchronizes with the cycle of the input signal. Figure 12: ground (c) stick diagram Simulated results of walking on a level 4.2 Numerical Simulation We conducted walking simulations using MATX 22) and we use LTI model as the actuator model since a walk- 4.3 Experiment We carry out the experiments of swinging a pendulum as preliminary tests for walking experiments. Fig. 14 shows the result. The weight of a small pendulum is [kg] and a length is 0.1 [m]. We applied a square pulse as input voltages whose cycle is 0.5 [s] and whose amplitude is 3.0 [V]. In comparison with simulated results, the amplitude decreases slightly under the influence of frictions or modeling error, but it is confirmed that the motion is enough fast to realize a bipedal walking. 5. Conclusions We have discussed the development of linear actuator using IPMC materials in order to apply a soft actuator to biped walking robot. The elementary unit of the actuator was constructed, and its empirical model was identified from input-output data. Based on the empirical model, we demonstrated walking simulations of a

6 biped walking robot. Now we are planing to test the validity of the actuator using an experimental walking machine. In order to apply the artificial muscle actuator to a general robotic system, there exists a lot of problem such as limitation of output force, however, we think the mutual evolution of improvement of actuator technology and design of control system is important for further applications. References [1] T. McGeer, Passive dynamic walking, The Int. Journal of Robotics Research, Vol. 9, No. 2, pp , [2] F. Asano et. al., A novel gait generation for biped walking robots based on mechanical energy constraint, Proc. of IEEE/RSJ Int. Conf. on Intelligent Robots and Systems(IROS), pp , [3] F. Asano and M. Yamakita, Virtual gravity and coupling control for robotic gait synthesis, IEEE Trans. on Systems, Men and Cybernetics, Part A: Systems and Humans, Vol. 31, No. 6, pp , [4] M. Yamakita et. al., Virtual coupling control for dynamic bipedal walking, Proc. of IEEE/RSJ Int. Conf. on Intelligent Robots and Systems(IROS), pp , [5] D. W. Robinson et. al., Series elastic actuator development for a biomimetic walking robot, Proc. of IEEE/ASME International Conference on Advanced Intelligent Mechatronics(AIM), pp , [6] M. Wisse and J. van Frankenhuyzen, Design and construction of MIKE; a 2D autonomous biped on passive dynamic walking, Proc. of Int. Symp. on Adaptive Morion of Animals and Machines(AMAM), [7] Y. Bar-Cohen, Electro-active polymers: current capabilities and challenges, Proc. of SPIE Int. Symp. on Smart Structures and Materials, EAPAD, [8] M. Yamakita et. al., Development of artificial muscle actuator using ionic polymer with its application to biped walking robots, Proc. of SPIE Int. Symposium on Smart Structures and Materials, EAPAD, [9] K. Oguro et al., Bending of an ion-conducting polymer film-electrode composite by an electric stimulus at low voltage, Journal of Micromachine Society, Vol. 5, pp , (in Japanese) [10] S. Guo et al., Micro catheter system with active guide wire, Proc. of IEEE Int. Conf. on Robotics and Automation (ICRA), pp , [11] S. Sawa et al., Polymer electrolyte actuator with gold electrodes, Proc. of SPIE Int. Symp. on Smart Structures and Materials, EAPAD, Vol. 3669, pp , [12] EAMEX Corporation, [13] Y. Bar-Cohen et al., Challenges to the application of IPMC as actuators of planetary mechanisms, Proc. of SPIE Int. Symp. on Smart Structures and Materials, EAPAD, Vol. 3987, [14] S. Guo et al., Development of a new type of capsule micropump, Proc. of IEEE Int. Conf. on Robotics and Automation (ICRA), pp , [15] S. Guo et al, Development of underwater microrobot using ICPF actuator, Proc. of IEEE Int. Conf. on Robotics and Automation (ICRA), pp , [16] S. Tadokoro et al., Multi-DOF device for soft micromanipulation consisting of soft gel actuator elements, Proc. of IEEE Int. Conf. on Robotics and Automation (ICRA), pp , [17] S. Tadokoro et al., Development of a distributed actuation device consisting of soft gel actuator elements, Proc. of IEEE Int. Conf. on Robotics and Automation (ICRA), pp , [18] K. Asaka and K. Oguro, Bending of polyelectrolyte membrane platinum composites by electric stimuli Part II. Response kinetics, Journal of Electroanalytical Chemistry, 480, pp , [19] S. Tadokoro et al., A dynamical model of ICPF actuator considering ion-induced lateral strain for molluskan robotics, Proc. of IEEE Int. Conf. on Robotics and Automation (ICRA), pp , [20] K. Mallavarapu et al., Feedback control of the bending response of ionic polymer-metal composite actuators, Proc. of SPIE Int. Symposium on Smart Structures and Materials, EAPAD, Vol. 4329, pp , [21] P. Van Overschee and B. De Moor, N4SID: Subspace algorithms for the identification of combined deterministic-stochastic systems, Automatica, 30(1), pp , [22] M. Koga, Numerical Computation with MATX, Tokyo Denki University Press, (In Japanese)