Electro-Hydrostatic Actuators with Series Dissipative Property and their Application to Power Assist Devices

Transcription

1 Proceedings of the rd IEEE RAS & EMBS International Conference on Biomedical Robotics and Biomechatronics, The University of Tokyo, Tokyo, Japan, September 26-29, 2010 Electro-Hydrostatic Actuators with Series Dissipative Property and their Application to Power Assist Devices Hiroshi Kaminaga, Tomoya Amari, Yamato Niwa, and Yoshihiko Nakamura Abstract The actuators used in wearable robots must behave compliant. This, however, is not easy mainly due to two reasons: lack of force measurement capability and lack of backdrivability. Both of above needs to be realized, but the latter issue lies in the actuation principle of conventional robot actuators. We have been investigating in the electro-hydrostatic actuators to realize backdrivability by minimizing friction due to the reduction. Still, the way to design actuator, considering backdrivability, including the one due to the internal leakage, was an open problem. We introduced the actuator model Series Dissipative Actuator to explain the actuator behavior. This model enables us to understand the roll of internal leakage in the hydraulic system and it shows the design guideline considering the backdrivability. In this paper, we show the method to apply SDA (Series Dissipative Actuator)concept on EHAs (Electro-Hydrostatic Actuators). Development of the actuator prototype targeted for use in lower limb is also presented and preliminary results in backdrivability evaluation is performed. I. INTRODUCTION One of the largest challenge in development of a wearable robot that assist human, is the realization of smooth and stable compliance. Unlike human muscles that have force sensitivity, natural compliance, and damping, robot actuator are often rigid and non-backdrivable. The method of using high power-high speed motor and high reduction ratio gear drives for robot actuation made significant contribution in mobility of robots; by enhancing power-weight ratio. This method, however sacrificed a basic functionality of actuator that was not relevant in industrial robots, Backdrivability. For robots to perform force sensitive behavior, both force sensing and backdrivability are necessary. There are many attempts to emulate compliant behavior using endeffector force sensor and/or joint torque sensor [1], [2]. However, these researches only give answers to one of the two aspects of force sensitive actuation. In field of motor control, backdriving operation is widely known and utilized as four-quadrant operation. However, when it comes to actuator system for mobile robots, including reducers and transmissions, this was not always the case, due to the reason mentioned previously. Series Elastic Actuator (SEA) [3] is a type of actuator that realize backdrivability with non-backdrivable actuators. This work was supported partially by Grant-in-Aid for Scientific Research (No ) for Research Fellowships of the Japan Society for the Promotion of Science for Young Scientists and partially by IRT Foundation to Support Man and Aging Society under Special Coordination Funds for Promoting Science and Technology from MEXT. H. Kaminaga, T. Amari, Y. Niwa, and Y. Nakamura are with Department of Mechano-Informatics, The University of Tokyo, Hongo, Bunkyo-Ku, Tokyo , Japan {kaminaga, amari, niwa, nakamura}@ynl.t.u-tokyo.ac.jp Fig. 1. Concept of Knee Power Assist with EHA They showed good compliant behavior and were applied to exoskeletal systems as [4] and [5]. However, SEA, from its nature, lacks the controllability in high frequency range. Usage of EHA (Electro-Hydrostatic Actuator) is yet another approach toward backdrivable actuator. EHA is a displacement type hydraulic actuator, that control hydraulic motor position with pump position. With appropriate design, whole actuator system becomes backdrivable as shown in [6], [7]. To treat backdrivable actuators, the concept of output backdrivability and total backdrivability were introduced [7]. Series Dissipative Actuator (SDA) [8] is an actuator concept that is complementary to SEA in the sense of its property in backdrivability. SDA has viscous element in between actuator input and output. Similar concept was first introduced by Chew et al. [9] as series damper actuator that add damper in between the reducer output and the load. However, their simple approach does not give solution to backdrivability under some circumstances as explained in following section. The dynamics decoupling produced by the damper is the basic priciple of output backdrivability of SDAs. From the investigation of dynamics, EHA is shown to be a member of SDA type actuator. The backdrivability of EHA can also be explained with SDA model. Our objective is to develop the design methodology of SDA, considering backdrivability of the actuator system. We also target on applying SDA technology to power assist device that extends human mobility. In this paper, we propose the design methodology of SDAs considering backdrivability property. This design methodology is applied to EHAs that were targeted for power assist device. Preliminary test on the prototype of the actuator is then carried out to verify the effectiveness of the design /10/$ IEEE 76

2 Fig. 2. Fig. 3. Conceptual Diagram of Series Elastic Actuation Conceptual Diagram of Series Dissipative Actuation II. SERIES ELASTIC ACTUATOR AND SERIES DISSIPATIVE ACTUATOR MODEL SEA (Series Elastic Actuator) [3] is one type of elastic joint mechanism that was developed to enhance actuator backdrivability with non-backdrivable reducer. SEA intentionally put spring in series to the power transmission to decouple link side dynamics from motor side dynamics. The model of SEA is essentially same with the normal elastic joint model proposed by Spong [10] and given by (1). J out θout +K(θ out θ in /N)=τ out τ out f J in θin K(θ out θ in /N) N = τ in τ in f (1a) (1b) Here, θ in and θ out are motor and link side position respectively. τ in is the motor torque and τ out is the external torque from link side. τf in and τf out are motor and link side friction torques. K is the stiffness of the spring connecting the reducer output and the link. N is the reduction ratio of the transmission. SEA is a type of actuator with coupling between input side equation and output side equation by position difference. The idea of SEA can further be generalized to form of (2). Here i and ī are as follows. J i θi +K i 1θ i K i 2θ ī = τ i τ i f (2) (i,ī) {(in,out),(out,in)} (3) Coefficients K{1,2} i involve stiffness. Conceptual diagram of SEA is shown in Fig. 2. From (1), the minimum output backdriving torque [7] is τf out when no torque is exerted from the motor (τ in = 0). This is a significant reduction in minimum backdriving torque because if the output and input of the actuator is coupled rigidly, minimum backdriving torque is τf out +Nτf in (See Fig. 2). Hence, for the system with large N, minimum backdriving torque becomes large, deteriorating backdrivability. As a dynamically complementary system, there is actuator that input and output connected via viscous element. In such system, the dynamic model can be expressed in the form of (4) with coefficients involving damping factor D{1,2} i. We named this type of actuators Series Dissipative Actuators [8]. J i θi +D i 1 θ i D i 2 θ ī = τ i τ i f (4) As in the case of SEA, minimum backdriving torque in SDA is reduced significantly. Since the nominal model of SDA in (4) is first order, the oscillation is less likely to occur compared to SEA that is second order system. EHA is an example of SDA type actuator. Detailed model of EHA is described in section III. Although the dynamic model of SEA and SDA are similar, their behavior are complementary. Coupling term of SEA serves as a low-pass filter, so the high frequency force is not transmitted. This feature is desirable if the actuator system is not total backdrivable. Contrary, coupling term of SDA serves as high-pass filter, so the high frequency force is transmitted. A total backdrivable actuator is necessary to achieve high backdrivability with SDA for this reason. In other word, if total backdrivability is achieved, then both backdrivability and controllability can be high in wide frequency range. This is the reason that series damping actuator in [9] is not sufficient as a backdrivable actuator. Viscoelastic coupling, serves as band-pass filter; output backdrivability can be improved at certain frequency. For the SEA, reduction of stiffness is necessary in output backdrivability enhancement, which result in reduction of resonance frequency. Thus, in SEAs, control bandwidth and output backdrivability are in trade-off relation. In SDA, there is no resonance frequency induced by the transmission. However, improvement of output backdrivability and transmission efficiency are in trade-off relation. III. MODEL OF ELECTRO-HYDROSTATIC ACTUATOR EHA is a class of servo motor driven displacement control type hydraulic system with typical architecture shown in Fig. 4. The equation of motion of an EHA is given as follows [7]: J i θi = k i 3p i τ i f( θ i,p i, p)+τ i = k i 1k i 3 θ i +k i 2k i 3 θ ī τ i f( θ i, θ ī, p)+τ i (5) (i,ī) {(p,m),(m,p)} (6) Here, the parameters used in the equation is explained in Table I.k{1,2,3} i are constants determined by form and hydraulic properties, such as pump thickness and hydraulic viscosity. Similar to the discussion in previous section, subscript and superscript i are either p or m. p show pump parameters and m show hydraulic motor parameters. Subscript and superscript ī shows other side of i, thus if i = p then ī = m and Vice Versa. Although it is not intuitive from the mechanical structure of the actuator, from (5), it can easily be seen that EHAs are SDA type actuators. It is know from out previous study [6], 77

3 Fig. 4. Basic Structure of EHA Fig. 5. Analogic Structure of EHA TABLE I NOMENCLATURE Symbol Description (units) Prismatic Revolute θ i Position (m) Angular position (m) J i Mass (kg) Moment of inertia (kg m 2 ) τf i Friction force (N) Friction Torque (Nm) τ i External force (N) External torque (Nm) p i Pressure difference (Pa) p Amount of pressurization (Pa) [7], that EHAs become both output and total backdrivable if designed properly. This total backdrivability is important in SDA to maintain high backdrivability at all frequency range as mentioned in previous section, making EHAs suitable actuator for realizing backdrivability. The linear part of equation (5) can be treated with resistance network analogy shown in Fig. 5. Here, V {p,m} are external forces, Z {p,m} are internal impedances, I {p,m} are currents, r {p,m,λ1,λ2} are resistances respectively. The dynamics of Fig. 5 is given by (7). Z i I i = r i ( 1 r i Σ r ) I i + r ir ī Σ r I ī +V i (7) Here Σ r = r p +r m +r λ1 +r λ2. By choosing parameters as (8) to (12), (5) and (7) becomes identical. In equations (8) to (11), i mean either p or m. Here, kd i is the constant that converts generalized speed of the pump and the hydraulic motor to flow rate and kl i is the flow admittance of internal leakage in the pump and the hydraulic motor. Thus, putting flow rate in the transmission tube Q, itisgivenbyq = kd i θ i kl ip i. k λ is the flow resistance in the whole transmission tube. From the analogy perspective, V i corresponds to p i of mechanical system, I i to flow rate, r i to flow resistance respectively. Refer to [7] for farther details on EHA model. ( ) 1 d Z i = J i dt +ki fv (8) k i d ki 3 I i = k i d θ i (9) V i = τ i /k i 3 (10) r i = 1/k i l (11) r λ1 +r λ2 = k λ (12) This fundamental architecture of the EHA can be regarded as impedance modifying attenuator. That means the impedance seen from input side and impedance seen from output side is different. This implies that the backdrivability design can be performed using the concept of impedance matching. Namely, impedance seen from pump should match Z p in order to transmit maximum power from the pump. the impedance seen from hydraulic motor should be as small as possible. However, this is not that simple because reduction of Z i leads to reduction of r i that leads to loss in the transmission. Though, in general, Z m and r m should be chosen relatively large intentionally, in order to realize high backdrivability. This design approach provides tool to introduce impedance matching technique that are used commonly in electronics field. When the SDA has viscoelastic coupling, or when the bulk modulus of the hydraulic oil is explicitly considered, the equation of motion becomes very complicated. Using the proposed method, the design process still show the clear design guideline of impedance matching, that simplifies the design without struggling with the complicated dynamics equation itself. A. Design Concept IV. MECHANICAL DESIGN Our objective for this paper is to develop a single joint power assist exoskeleton for the knee joint. We focused on properties of EHA on following points: 1) Force controllability. Since the actuator is backdrivable, we have more sensitivity and control over force. 2) Durability. In hydraulic system, force is transmitted with large surface area, which disturbs stress and enhances the durability. 3) Actuator placement freedom. In hydraulic system, there is placement freedom for actuator component because pump and hydraulic motor are not rigidly connected. Heavy devices can be placed near the center of mass to enhance mobility. Fig. 1 shows the concept diagram of the power assist to be developed. Hydraulic motor is attached to knee and rest of the system including pump, controller, and battery are attached to hip. Designed EHA structure is shown in Fig. 6. Following issues are two large challenges in using an EHA as an actuator for wearable robot application. 1) Avoid oil leakage without degrading backdrivability. 2) Realize small and light system. To realize low friction without leakage, oil seal evaluation was performed using a test rig in order to select seal with most adequate property. To realize small and light system, we designed hydraulic system that can bear over 4.5(MPa) 78

4 Fig. 6. Structure of Developed Hydraulic System Fig. 7. Outlook of Developed Hydraulic Motor TABLE II EHA DESIGN PARAMETER Description Value Motor rated output 100 (W) Oil Viscosity 100 (cst) Maximum operating pressure 4.6 (MPa) Reduction ratio 449 Pump displacement 360 (mm 3 /rev) Hydraulic motor displacement (mm 3 /rev) Maximum Torque 30 (Nm) at10(rpm) Maximum Speed 55 (RPM) that is higher operating pressure than that of our previous works [6], [7]. B. Actuator Design Since the knee joint of human basically is a hinge joint, we chose the rotary output hydraulic motor. This way we can minimize the chance of exoskeleton being an obstacle, especially when the knee is bent, that were issues in [11], [4] that use linear actuators. As pump, we chose trochoid type inner gear pump from its large displacement per pump size. As hydraulic motor, we chose vane motor, which can produce large torque with same pressure relative to its package volume. We used symmetric double vane structure to cancel radial internal force produced by hydraulic pressure. Output axis of the hydraulic motor is supported with angular bearings with light axial pre-loading to realize low-friction and precise movement, and to bear large radial external force. Friction parameters for oil seals were identified with a test rig. See Table II for design specification. Pressurization is vital in closed circuit hydraulic system as EHA to avoid cavitation [12]. To avoid cavitation, minimum hydraulic pressure in the system must be sufficiently high; this is called pressurization. Charge pump is used to give pressurization to closed circuit upon assembly of the system as in Fig. 4. However, in normal operation, charge pump is not necessary if amount of pressurization is kept. In this research, we developed miniature accumulator integrated in pump that enables us to detach charge pump to reduce size and weight of the system in normal operation. Calculation proposed in [7] was used to calculate the hydraulic component dimension. Fig. 7 shows developed vane motor and Fig. 8 shows developed pump. Hydraulic motor assembly is equipped with motor side pressure sensor. Pump assembly is equipped with Fig. 8. Outlook of Developed Pump. Miniature accumulator and connection to charge pump is on the bottom side. pump side pressure sensor, accumulator, charge circuitry, and safety relief circuitry. V. EXPERIMENTS A. Oil Seal Friction Identification To estimate the power output with the method presented in previous section, we must identify friction parameter of the oil seals. Also, the specified friction parameters in manufacturer s catalogs are not performed under same condition. We developed test rig as shown in Fig. 9 to evaluate oil seals from different manufacturers under same test condition. We tested the oil seal for axis diameter of 18(mm). For the test of static friction, torque applied to the axis was measured with force gauge. For the test of dynamic friction (Coulomb and viscous friction), torque was measured with current supplied to DC motor. Torque constant was calibrated with force gauge for measurement consistency. Fig. 11 shows the result for static friction measurement. For oil seal (b), leakage was examined for pressure above 2(MPa). For oil seal (d), leakage was examined for pressure above 3(MPa). Fig. 12 shows the result for dynamic friction measurement. It is interesting that the gradient differs product to product. Hence it was concluded that the oil seal to be used mainly for speed below 1000(RPM), oil seal (a) is suitable. TABLE III MASS OF WEARABLE ROBOT SYSTEM Part Mass Pump (g) (Dry Weight, Design Value) Motor 541 (g) (Dry Weight, Design Value) Total 1124 (g) (With Oil, Measured Value) 79

5 Fig. 9. Apparatus for Oil Seal Friction Identification. Torque applied to the axis was measured with force gauge for static friction test and motor current for dynamic friction test. Fig. 12. Result of Dynamic Friction Test Under Different Pressurization. Symbols (a) and (c) corresponds to the symbols in Fig. 10. Fig. 10. Cross Sections of Low Friction Oil Seals Under Test For usage mainly above 1000(RPM), oil seal (c) behaves better. From this result we use oil seal (a) for hydraulic motor and (c) for pump. B. Torque - Speed Performance To evaluate the power output performance of the developed EHA, actual torque - speed characteristics was measured. Torque was applied to the actuator by weight through wire and pulley as shown in Fig. 13. Applied torque was measured with force gauge attached in between the wire and the weight. Simulation results were calculated with the method in [7] with the identified friction parameters. The comparison of the simulated data and measured data is shown in Fig. 14. From the result, we satisfied the speed but lacked the torque. The major cause for this result is Fig. 11. Result of Static Friction Test Under Different Pressurization. Symbols (a) to (d) corresponds to the symbols in Fig. 10. Fig. 13. Test Apparatus for Output Power and Backdrivability Test expected to come from excessive gap between the hydraulic components. Using the analogy of Fig. 5, r p and r m were smaller than the design value. Those values are inverse-cubic proportional to the gap value and thus sensitive. The reason that the speed requirement was satisfied is that the k i fv in Z i is also dependent on gap value (they are reciprocal to the gap amount). Another cause was the error of friction estimation of pump side. As mentioned in previous section, the parameter for oil seal was identified for seal diameter of 18(mm). This value was scaled to 4(mm) under assumption that the friction value per unit surface area at contact is constant regardless of the seal size. It is expected that this simple scaling was inaccurate. C. Intrinsic Backdrivability Realization of high backdrivability is necessary in realizing force sensitive robot systems. Advantage of EHA is that it can realize output backdrivability regardless of reduction ratio. This is a significant advantage against mechanical transmissions as gear drives. However, ease of backdriving is heavily dependent on oil seal friction at output axis of EHA because this friction cannot be measured and controlled without external torque sensor, which is often bulky and heavy. Since our target is wearable robot application, it is desirable to eliminate additional weight of torque sensor. For the backdrivability evaluation test, we used the appa- 80

6 Fig. 14. Torque - Speed Output Performance of Developed EHA at 22.6(V) Applied to Motor TABLE IV COMPARISON BETWEEN CALCULATED AND MEASURED BACKDRIVE TORQUE (Nm) Pressurization(MPa) Measured Output Backdrive Torque less than 0.20 Expected Output Backdrive Torque Measured Total Backdrive Torque Expected Total Backdrive Torque ratus shown in Fig. 13. Test results are shown in Table IV. As a result, we confirmed output backdrivability was less than 200(mNm). Actual output backdriving torque is smaller, but with the combination of link side encoder resolution, force gauge resolution, and test arm length (moment arm), 200(mNm) was the measurement limit. Total backdriving torque exceeds calculated value largely at the pressurization of 1.5(MPa). This is expected to come from the friction parameter estimation error, for the same reason we explained in previous section. The pump axis oil seal friction torque was more sensitive to the pressurization than we expected. At pressurization of 0.5(MPa) and 1.0(MPa), the test results show good fit to the expected data. VI. CONCLUSION In this paper, we reported the methodology of developing Series Dissipative Actuator using Electro-Hydrostatic Actuator structure, considering the backdrivability. The prototype of the actuator targeted for the use in a power assist device was developed and evaluated. Followings are the conclusions: 1) We proposed the concept of Series Dissipative Actuators (SDAs) that is in contrast to Series Elastic Actuators (SEAs) with the fundamental dynamics equations. We showed that an EHA is a SDA type actuator and its behavior can be explained by resistor network analogy. This explanation enables us to treat the backdrivability design using impedance matching technique, which is applicable also to the system with higher complexity. However, since the parameters in the analogy have nonlinear couplings, inverse problem of finding design parameter from impedance matching is not as simple as in the case of electric impedance matching. Farther investigation is necessary to derive actual design procedure. 2) Design concept of splitting EHA to power unit and motor unit was presented. System driven with 100 (W) brushless DC motor was designed to meet specification of maximum torque being 30(Nm) at 10(RPM) and 55(RPM). All range of specification can be covered with continuous operating region. Total system weight is 1124(g) including all components except battery. 3) Oil seal property was measured and used in simulation. From the power output evaluation, we lacked in the maximum torque that is expected to come from following three issues: the gap in hydraulic components are larger than the designed value; oil seal parameter scaling method used for pump seal was not accurate. Oil seal evaluation with actual diameter is necessary for fateher investigation. 4) We succeeded in realizing the output backdrivability at less than 0.5(%) of maximum torque. Even for this small friction, from the basic test on the oil seals, we confirmed there is no leakage from the oil seal with this configuration. REFERENCES [1] A. Albu-Shäffer, C. Ott, and G. Hirzinger, A Unified Passivity-based Control Framework for Position, Torque and Impedance Control of Flexible Joint Robots, The Int l J. of Robotics Research, vol. 26, no. 1, pp , [2] T. Kawakami, K. Ayusawa, H. Kaminaga, and Y. Nakamura, Highfidelity joint drive system by torque feedback control using high precision linear encoder, in Proc. of IEEE Int l Conf. on Robotics and Automation, 2010, in print. [3] G. A. Pratt and M. M. Williamson, Series Elastic Actuators, in Proc. of IEEE/RSJ Int l Conf. on Intelligent Robots and Systems, vol. 1, 1995, pp [4] J. E. Pratt, B. T. Krupp, C. J. Morse, and S. H. 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