Viscous Pump for Highly BackdrivableElectro-Hydrostatic Actuator

Hiroshi Kaminaga, Hirokazu Tanaka, Kazuki Yasuda, and Yoshihiko Nakamura

Abstract— It is widely acknowledged that the actuator’sintrinsic backdrivability is important in realizing a forcesensitive behavior. It is desirable to realize such actuatorwith electric motor that is advantageous from power-to-weightratio and controllability point of view. Electro-HydrostaticActuator is a type of hydraulic actuators that can realizehigh backdrivability by reducing transmission friction and byproviding dynamics decoupling with an implicit serial damper.To farther enhance the backdrivability of a EHA, a pumpwith minimum static and Coulomb friction is necessary. Inthis paper, we introduce an EHA with viscous screw pumpthat minimizes static and Coulomb friction by eliminating themechanical contact between pump components. Viscous screwpumps also have the advantage that there is no pulsation inpressure due to the continuity of the force transmission fromthe rotor to the fluid. The property of the actuator, includingpulsation performance and impedance control performancewere evaluated on a prototype of EHA with a viscous screwpump.

I. INTRODUCTION

In the rapidly expanding field of robotics, robots thatinterface with human must be as force sensitive as humansare. Humans realize force sensitive behavior not only fromtheir proprioception but also from the backdrivability of themuscles. Such intrinsically backdrivable actuators are impor-tant in realizing high backdrivability even under contacts thatexceed control frequency. Typical examples of such contactsare impacts and collision with stiff objects.

The major burdens in realizing a highly backdrivable robotactuator are transmission friction and apparent inertia of themotor seen from the link, or the actuator output. This isthe major reason that the transmission-less actuators suchas McKibben artificial muscles [1] are used to achieve highbackdrivability. However, there still is a large advantage ofusing electric motor as mechanical energy source due to itshigh power density, position controllability, output linearity,and wide control bandwidth.

Series Elastic Actuators (SEAs) [2] and its derivatives asthe rotational SEA used in [3] and SERKA [4] are usedto realize backdrivability in motor based actuator systemwith gear drives. In the SEA type actuator, the motor sidedynamics is decoupled from link side by the spring, that

This work was supported by Research Grant from Fluid Power Tech-nology Promotion Foundation, Grant-in-Aid for Scientific Research (S)(No.20220001) of the Japan Society for the Promotion of Science, andGrant-in-Aid for Young Scientists (B) (No.90571571) of the Japan Societyfor the Promotion of Science. This work was also carried out in collaborationwith Nachi-Fujikoshi Corporation.

H. Kaminaga, H. Tanaka, K. Yasuda, and Y. Nakamura are withGraduate School of Information Science and Technology, The Uni-versity of Tokyo, 7-3-1 Hongo, Bunkyo-Ku, Tokyo 113-8656, Japan.{kaminaga,nakamura}@ynl.t.u-tokyo.ac.jp

Fig. 1. Viscous Screw Pump

reduces apparent inertia and motor side friction seen fromthe link side. The main advantage of SEA is that the actuatorcan be constructed by adding a component to a conventionalnon-backdrivable actuator. In SEA type actuators, to obtainhigh backdrivability, stiffness of the spring must be reduced.This, however, means reduction of resonance frequency thatresults in reduction of the position control bandwidth.

Variable compliance mechanisms as [5], [6], [7], [8] andvariable impedance actuators [9] are studied to overcome thisproblem by adjusting mechanical property with additionalactuator to obtain desirable property of backdrivability.

However, use of such actuator leads to higher complexityboth in mechanical and control point of view, which eventu-ally leads to additional weight and less reliability. The sourceof the problem lies in the transmission of the actuator.

In our previous research [10], [11], we developed robot ac-tuators with high backdrivability utilizing hydrostatic trans-mission, called Electro-Hydrostatic Actuators, or EHA. Thisactuator has complementary property to SEA type actuatorsas proposed in [12]. With EHA, controllability and backdriv-ability are not in trade-off relation.

The cause of backdrivability loss in EHA are frictions,especially static and Coulomb frictions. In the hydraulicmotor, we have proposed the structure to remove all contactseals except for the axis seal to minimize such frictiontorques [10]. However, in the volumetric pumps, that areutilized in majority of small hydraulic pumps for EHA, itis difficult to remove such friction because there are slidingcomponents such as gears, vanes, or cylinders.

Viscous type screw pump [13] (see Fig. 1) is a variationof turbo pumps that does not require mechanical contactsto generate pressure difference. Since the force transmissionbetween the screw and the fluid is symmetric, it is easily

2012 IEEE International Conference on Robotics and AutomationRiverCentre, Saint Paul, Minnesota, USAMay 14-18, 2012

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Fig. 2. Typical Configuration of Electro-Hydrostatic Actuator with FixedDisplacement Pump

deduced that this pump is backdrivable. This type of pumps iswidely used in the extruders of injection molding machines.If we utilize this pump in EHA, reduction in transmissionfriction can be pursued. Expected outcomes of the EHA witha viscous screw pump are as follows.

1) Low backdriving torque2) No pressure pulsationThe objectives of this paper is to propose viscous screw

pump based EHA for high backdrivability and to evaluate itsproperties. We use a viscous screw pump developed in [14]with the vane motor developed in [11] to form an EHA.Pressure pulsation performance and impedance control areevaluated on the prototype.

II. ELECTRO-HYDROSTATIC ACTUATOR WITH VISCOUSSCREW PUMP

An Electro-Hydrostatic Actuator is a type of a displace-ment type hydraulic actuator. The basic configuration of thisactuator consists of a hydraulic pump and a hydraulic motorconnected directly. The control of the hydraulic motor isdone with the control of the hydraulic pump. EHAs areusually equipped with the auxiliary circuits such as chargepump and over pressure protection relief valves. Typicalhydraulic schematic of a EHA is shown in Fig. 2.

In our previous studies [10], [12], [11], trochoid type innergear pumps were used. Gear pumps are advantageous insmall hydraulic systems due to its size and admissible power.However, gear meshing friction is inevitable that was thepotential cause of the backdrivability degradation.

Viscous pumps or friction pumps [15], [13], [16], [17],[18] generate pressure difference by the viscous frictionbetween the fluid and the rotor. From its principle, thepressure difference generated is proportional to the effectivelength of the fluidic path on the rotor and the velocity of thefluid-rotor interface. Screw type viscous pumps (hereafterdenoted as screw pumps) can be configured to have longfluidic path per the volume of the pump by placing the fluidpath in spiral along the cylindrical surface of the rotor. Also,the fluid path is located on the rotor where the velocity ismaximum.

Fig. 3. Basic Structure of Viscous Screw Pump

Screw pumps consist of two main components: a screw(rotor) and a sleeve (cylinder) as shown in Fig. 3. Rotatingscrew induces the shear stress on the fluid by the viscousfriction in the direction of the groove. The integral of theshear stress along the groove becomes the pressure differencebetween the ends of the screw.

There are theoretical studies on viscous screw pumps as[13], [19], [16]. The method of Asanuma [16], [20] wasadopted due to the simple form it leads to. In [16], the flowand torque characteristics are obtained by integrating Navier-Stokes equation in the Fourier series form.

From the result of [16] and [20], steady state relationshipbetween the generated pressure difference p1, the pumpspeed θ1, and the flow rate q1 is given in the form of(1). Similarly, the relation between the generated pressuredifference p1, the pump speed θ1, and the necessary torqueτ1 is given in the form of (2). Here ϕ is a parameter vectorcontaining the fluid property and the form factor of the screwpump such as viscosity, fluid density, screw diameter, groovedepth, groove width, groove pitch, and the gap amountbetween the screw and the sleeve. Q1, Q2, T1, and T2 arethe constants determined by the parameter ϕ.

q1 = Q1(ϕ)θ1 +Q2(ϕ)p1 (1)τ1 = T1(ϕ)θ1 + T2(ϕ)p1 (2)

Although the constants Q1, Q2, T1, and T2 are highlynonlinear function of the ϕ, the relation between p1, θ1, q1,and τ1 appears in a linear form.

In previous studies [13], [19], [16], assumed main applica-tion were pumping of fluid with very high viscosity. One ofthe reason was that the performance of the pump is greatlyaffected by the amount of the gap between the sleeve and theridge of the screw. Recent technology in precise machiningenabled us to have more control over the gap that, in turn,enabled us to apply the pump for lower viscosity fluid suchas hydraulic oil.

In [14], we developed screw pump rated for the values inTable I. The intended fluid is silicone oil with viscosity of100cSt. The relation of (1) and (2) were confirmed by theexperiment. Fig. 4 shows the outlook of the pump developedin [14].

It should be said that the efficiency of the current prototypeis very low compared to the trochoid pump we developed.With a same motor, screw pump can produce only about 30%of the power compared to the trochoid pump. It is known

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TABLE IDESIGN SPECIFICATION OF SCREW PUMP

Description Value UnitMaximum Discharge Pressure 1.2 MPa

Maximum Flow Rate 30× 10−6 m3/sec

Fig. 4. Outlook of Viscous Screw Pump

that the reason is the viscous friction between the screw andthe sleeve. Farther optimization on the design parameter isnecessary in improving the pumping performance.

This screw pump was combined with the vane motordeveloped in [11] to construct an EHA (see Fig. 5).

III. IMPEDANCE CONTROL OF ELECTRO-HYDROSTATICACTUATORS

EHAs are SDA (Series Dissipative Actuator) systems [12]that the link side and motor side dynamics are coupled withvelocity terms. Series dissipative actuator contains the ideaof series damper actuator [21] but not limited to simple serialphysical connection of damper to the output of the actuatorthat does not guarantee the backdrivability in high frequency

Fig. 5. Outlook of Hydraulic Vane Motor on Test Rig

TABLE IINOMENCLATURE OF PARAMETERS ON ELECTRO-HYDROSTATIC

ACTUATOR DYNAMICS

Symbol Descriptionθi Positionkij Constantsτfi Friction TorqueJi Inertiaτi External Torque

disturbance torque as in [21]. EHA is a type of SDA that canbe written in the form of (3).

d

dt

[θ1θ2

]= A

[θ1θ2

]−[

τf1/J1τf2/J2

]+B1τ1+B2τ2 (3)

Here, subscript 1 and 2 shows primary side (pump side)and secondary side (link side) respectively. Last two termsshow that the primary and secondary side torque can onlybe applied to dynamics of their own side. Usually τ1 is thecontrol input and τ2 is the disturbance torque, but they canbe treated in same way, which makes it easy to analyze thebackdriving behavior of the system. A, B1, and B2 are givenas follows.

A =

[−k11k13/J1 k12k13/J1k21k23/J2 −k22k23/J2

](4)

B1 =[1/J1 0

]T (5)

B2 =[0 1/J2

]T (6)

Since there is no coupling terms of position, link positionmeasurement is essential in EHA to have control of position.

In this paper, we use the method that combine inertia scal-ing 1 and disturbance observer based friction compensationoriginally proposed by Ott et al. [22] and Tien et al. [23]for a manipulator with joint torque sensors. The method wasadapted to hydraulic system in [24].

Inertia scaling feedback law is given by (8) [24]. It is easilyshown that this feedback changes the dynamics of pump sideequation of (3) by substituting (8) to lower equation of (3).Here J1 is the desired value of the pump inertia and p1 is thedischarge pressure of the pump. u is the new control inputto the inertia scaling controller to be used instead of τ1.

τ1 =1

αu+

(1− 1

α

)k13

(k11θ1 − k12θ2

)(7)

=1

αu+

(1− 1

α

)k13p1

α = J1/J1 (8)

Friction observer estimates the friction torque by compar-ing the momentum of the actual model and model withoutfriction. The estimated torque is then compensated in feed-forward manner. See [25], [26], [23] and [24] for detailedform of the compensation.

1Inertia scaling is the feedback control that reduces apparent inertia ofthe motor.

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Let us assume that the inertia is reduced to J1 by inertiascaling. Also let us assume that the motor side friction iscompensated by friction compensation. The dynamics of theEHA is modified to (9).

d

dt

[θ1θ2

]= A

[θ1θ2

]−[

0τf2/J2

]+ B1u+B2τ2 (9)

A, B1 are given as follows.

A =

[−k11k13/J1 k12k13/J1k21k23/J2 −k22k23/J2

](10)

B1 =

[1/J10

](11)

Note that the form of the dynamics is preserved with thecontrol.

The state feedback of the EHA system with positionfeedback is given as follows.

u = K[θ1 θ2 θ2

]T(12)

Where K is the gain matrix of R1×3.The resultant dynamics is given by:

d

dt

θ1θ2θ2

=

([A 0

0 1 0

]+

[B1

0

]K

) θ1θ2θ2

−

0τf2/J2

0

+

[B2

0

]τ2 (13)

Following selection of gain K gives approximateimpedance control with damping Dref and stiffness Gref

for reference position and velocity of θ2 = θ2 = 0 at lowacceleration [10].

K =

[0 −k13

k23Dref −k13

k23Gref

](14)

IV. EXPERIMENTS

A. Pressure Pulsation Performance Evaluation

The pressure fluctuation or ripple regarding the pumprotation is called pulsation. Pulsation is caused by dis-continuous change in energy transmission caused by dis-continuous change in chamber volume. Pulsation is innatein all volumetric pumps as gear pumps, vane pumps, andpiston pumps. Pulsation in EHA leads to fluctuation ofthe output torque and inaccurate pressure measurement thatharms torque controllability.

Since the pumping principle of the screw pump is pureenergy transmission via continuous shear stress it is expectedthat the screw pump generates stable and smooth pressurewithout pulsation.

We evaluated the pressure stability performance of thescrew pump by measuring pressure while applying constanttorque to the pump. The pulsation performance was thencompared with the result of trochoid pump developed in[11]. The output of the pump was plugged to realize zerodischarge flow.

TABLE IIIPULSATION EVALUATION BY STANDARD DEVIATION. UNITS ARE IN

MPa

Screw Pump Trochoid PumpMean Std. Deviation Mean Std. Deviation0.034 4.2 ×10−6 0.038 2.0 ×10−5

0.050 2.6 ×10−6 0.049 3.7 ×10−6

0.075 3.4 ×10−6 0.070 7.2 ×10−6

TABLE IVPARAMETER IDENTIFICATION OF k13 AND k23

Input torque to pump Estimated valueτ1 (Nm) k13 (MPa · s) k23 (MPa · s)

0.048 0.0025 0.220.064 0.0028 0.260.080 0.0027 0.210.096 0.0027 0.23

Average 0.0027 0.23

Table III shows the mean value and the standard deviationof measured pressure data.

As expected, we can observe pressure ripple for the dataof trochoid pump. In reality, we also observe some ripplefor screw pump as well. The reason for this is expectedthat the screw is making microscopic contact with the sleevedue to the eccentricity of the axis. However, the ripple ofthe screw pump is smaller compared to the trochoid pump.This difference is observed as the standard deviation of thepressure value listed in Table III. For the similar pressuremean value, screw pump produces less pressure fluctuation.The data showed that in screw pump the pulsation amount isconstant against the discharge pressure, where trochoid pumpshowed larger pulsation for smaller discharge pressure, henceat lower pump speed. The efficacy of the screw pump wasexperimentally confirmed with this result.

Using the result of this experiment, parameter k13 andk23 were identified using least square method. The identifiedparameter are listed in Table IV. There were small fluctuationobserved, so the average of the parameters across τ1 wereused as the parameters for the control in following sections.

B. Impedance Control Performance of Screw Pump BasedEHA

In this research, an impedance controller consists of inertiascaling, friction compensation, and compliance control. Theability to achieve low impedance is one of the measure inimpedance control because achieving high impedance is ingenerally easier.

Inertia scaling is the control that reduces apparent inertiaof the pump side dynamics by torque feedback. To reproducesmaller apparent inertia, larger the feedback gain becomes.However, the minimum value of the apparent inertia isusually limited by torque signal quality. In EHA, torquesignal is substituted by pressure difference acting on pump.

In screw pumps, as we have shown in previous section,we obtain smooth pressure signal without ripple. From thisfact, we can expect the screw pump based EHA to realize

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TABLE VSTIFFNESS EVALUATION OF THE IMPEDANCE CONTROLLER

Actual StiffnessDesired Stiffness Forward Reverse

Stiffness Error Stiffness Error(Nm/rad) (Nm/rad) (%) (Nm/rad) (%)

2.0 2.2 8.4 2.0 1.64.0 4.3 7.9 4.3 7.86.0 6.4 5.9 6.1 2.0

lower apparent inertia than conventional EHAs.We put the EHA under inertia scaling and compliance

control. By applying force on the wire that is attached tothe output linkage in Fig. 5, torque was applied to the vanemotor. External torque was measured with a force gaugeattached to the wire being pulled. Position of the vane motorwas measured with the link side encoder.

Several amounts of inertia scaling factor were tested withsame controller stiffness to see the effect of inertia scaling.By observing displacement-torque relation, effect of inertiascaling becomes visible as reduction of friction, that in turnis observed as reduction of hysteresis. By observing time-torque relation, effect of inertia scaling becomes visibleas the amount of the torque required for the acceleration,but considering the resolution of the output axis encoderand noise produced by numerical differentiation, time seriescomparison is difficult. Thus, in this paper, the effect ofinertia scaling was observed with the friction reduction effectof the inertia scaling.

Fig. 6 shows the test result seen in displacement-torquerelation. The figure includes three runs of the experiment foreach curve. Gref in the figure shows the desired stiffnessvalue. From the figure, it can be observed that the inertiascaling is stable with the apparent inertia down to 1/20 of thephysical value. We call the configuration of desired inertiascaled down to 1/n as 1:n. From our previous studies, inertiascaling was only useful roughly down to 1:10 on the EHAwith the trochoid pump [24] and roughly down to 1:4 onharmonic drive based torque sensing joint [27]. It shows theadvantage of the screw pump on inertia scaling. Reductionof the hysteresis is observed in Fig. 6 as an effect of frictionreduction of inertia scaling.

The change in the slope in Fig. 6 is due to the reduction ofviscous friction in the pump due to the inertia scaling. Thedata for no inertia scaling (1:1), the loop shows erratic shape.The desired stiffness is very low that the torque generatedby the compliance control is smaller than the friction in thesystem. The error between the slope angle of the desiredstiffness and the case of 1:20 inertia scaling contains theestimation error of the k13.

Fig. 7 shows the result of impedance controller test withvariable desired stiffness. All the data were acquired with1:10 inertia scaling and friction compensation. This figureshows that the stiffness is reproduced with the small error.The value of the desired and actual stiffness is shown inTable V.

Fig. 6. Effect of Inertia Scaling in Compliance Control in Displacement -Torque Relationship. Gref=4Nm

Fig. 7. Result of Impedance Control. Dashed line shows reference valueof the stiffness.

V. CONCLUSIONS

In this paper, we proposed the construction method ofan Electro-Hydrostatic Actuator (EHA) using viscous screwpump to enhance backdrivability and torque controllabilityof the actuator, intended for realizing highly force sensitiveactuator. We have investigated the intrinsic backdrivabilityof the EHA in previous study [14]. We treated the torquecontrollability that still was an open problem. In this paper,torque controllability problem was treated as performanceevaluation of pump pulsation, inertia scaling capability, andthe impedance control.

From the investigation on the pump pulsation, the screwpump showed 30% reduction of the pulsation against thetrochoid pump in worst case. The data showed that in screwpump the pulsation amount is constant against the dischargepressure, where trochoid pump showed larger pulsation forsmaller discharge pressure, hence at lower pump speed.The evaluation was done with the standard deviation of thepressure signal at similar discharge pressure.

The stability of the pressure signal made a large contribu-

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tion on the inertia scaling capability. In trochoid based EHA,inertia scaling of 1:10 of the physical value was roughlythe stability limit. For the screw pump based EHA, wehave stably realized 1:20 inertia scaling. Considering that therough stability limit of inertia scaling in gear driven torquesensing joint is 1:5, screw pump based EHA showed largeadvantage.

The impedance control was implemented by combiningthe inertia scaling, friction compensation, and the compliancecontrol. The compliance control showed reproduction ofstiffness with error within 8.4% in forward direction in worstcase. In the reverse direction, the maximum error was 7.8%.

The results above showed the efficacy of the proposedEHA system as the force sensitive actuator that can beapplied on force sensitive robots.

REFERENCES

[1] V. L. Nickel, J. Perry, and A. L. Garrett, “Development of UsefulFunction in the Severely Paralyzed Hand,” J. Bone Joint Surg. Am.,vol. 45, pp. 933–952, 1963.

[2] 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. 399–406.

[3] H. K. Kwa, J. H. Noorden, M. Missel, T. Craig, J. E. Pratt, and P. D.Neuhaus, “Development of the ihmc mobility assist exoskeleton,” inProc. of IEEE Int’l Conf. on Robotics and Automation, 2009, pp. 2556–2562.

[4] J. S. Sulzer, R. A. Roiz, M. A. Peshkin, and J. L. Patton, “A HighlyBackdrivable, Lightweight Knee Actuator for Investigating Gait inStroke,” IEEE Trans. on Robotics, vol. 25, no. 3, pp. 539–548, 2009.

[5] R. Van Ham, B. Vanderborght, M. Van Damme, B. Verrelst, andD. Lefeber, “MACCEPA, The Mechanically Adjustable Complianceand Controllable Equilibrium Position Actuator: Design and imple-mentation in a biped robot,” Robotics and Autonomous Systems,vol. 55, no. 10, pp. 761–768, 2007.

[6] J. W. Hurst, J. E. Chestnutt, and A. A. Rizzi, “The Actuator with Me-chanically Adjustable Series Compliance,” IEEE Trans. on Robotics,vol. 26, no. 4, pp. 597–606, 2010.

[7] S. Wolf, O. Eiberger, and G. Hirzinger, “The DLR FSJ: Energy BasedDesign of a Variable Stiffness Joint,” in Proc. of IEEE Int’l Conf. onRobotics and Automation, 2011, pp. 5082–5089.

[8] M. Howard, D. J. Braun, and S. Vijayakumar, “Constraint-BasedEquilibrium and Stiffness Control of Variable Stiffness Actuators,”in Proc. of IEEE Int’l Conf. on Robotics and Automation, 2011, pp.5554–5560.

[9] Y. Ikegami, K. Nagai, R. C. V. Loureiro, and W. S. Harwin, “Designof Redundant Drive Joint with Adjustable Stiffness and DampingMechanism to Improve Joint Admittance,” in Proc. of IEEE Int’l Conf.on Rehabilitation Robotics, 2009, pp. 202–210.

[10] H. Kaminaga, J. Ono, Y. Nakashima, and Y. Nakamura, “Develop-ment of Backdrivable Hydraulic Joint Mechanism for Knee Joint ofHumanoid Robots,” in Proc. of IEEE Int’l Conf. on Robotics andAutomations, 2009, pp. 1577–1582.

[11] H. Kaminaga, T. Amari, Y. Niwa, and Y. Nakamura, “Development ofKnee Power Assist using Backdrivable Electro-Hydrostatic Actuator,”in Proc. of IEEE/RSJ Int’l Conf. on Intelligent Robots and Systems,2010, pp. 5517–5524.

[12] H. Kaminaga, T. Amari, Y. Katayama, J. Ono, Y. Shimoyama, ,and Y. Nakamura, “Backdrivability Analysis of Electro-HydrostaticActuator and Series Dissipative Actuation Model,” in Proc. of IEEEInt’l Conf. on Robotics and Automations, 2010, pp. 4204–4211.

[13] H. S. Rowell and D. Finlayson, “Screw Viscosity Pumps,” Engineer-ing, vol. 114, pp. 606–607, 1922.

[14] H. Kaminaga, H. Tanaka, K. Yasuda, and Y. Nakamura, “Screw Pumpfor Electro-Hydrostatic Actuator that Enhances Backdrivability,” inProc. of 11th IEEE-RAS Int’l Conf. on Humanoid Robots, 2011, pp.434–439.

[15] N. Tesla, “Turbine,” United States Patent No.1061206, 1913.[16] T. Asanuma, “Study on the Sealing Action by Viscous Fluid (The 1st

Report, On the Pump-performances of a Screw-type Viscous Pump),”Journal of JSME, vol. 17, no. 60, 1951, in Japanese.

[17] H. G. Elrod, “Some Refinements of the Theory of the Viscous ScrewPump,” Trans. ASME J. of Lubrication Technology, vol. 94, pp. 83–93,1973.

[18] I. Etsion and R. Yaier, “Performance Analysis of a New ConceptViscous Pump,” Trans. ASME J. of Tribology, vol. 110, pp. 93–99,1988.

[19] M. L. Booy, “Influence of Channel Curvature on Flow, PressureDistribution, and Power Requirements of Screw Pumps and MeltExtruders,” Trans. ASME J. of Engineering for Industry, vol. 86, pp.23–30, 1964.

[20] T. Asanuma, “Study on the Sealing Action by Viscous Fluid (The 2ndReport, On the Sealing-performances of a Screw-type Viscous Pump),”Journal of JSME, vol. 17, no. 60, pp. 126–130, 1951, in Japanese.

[21] C.-M. Chew, G.-S. Hong, and W. Zhou, “Series Damper Actuator: ANovel Force/Torque Control Actuator,” in Proc. of 4th IEEE-RAS Int’lConf. on Humanoid Robots, 2004, pp. 533–546.

[22] C. Ott, A. Albu-Schaffer, and G. Hirzinger, “A passivity basedcartesian impedance controller for flexible joint robots.part i:torquefeedback and gravity compensation,” in Proc. of IEEE Int’l Conf. onRobotics and Automation, 2004, pp. 2659–2665.

[23] L. Tien, A. Albu-Schaffer, A. De Luca, and G. Hirzinger, “FrictionObserver and Compensation for Control of Robots with Joint TorqueMeasurement,” in Proc. of IEEE/RSJ Int’l Conf. on Intelligent Robotsand Systems, 2008, pp. 3789–3795.

[24] H. Kaminaga, H. Tanaka, and Y. Nakamura, “Mechanism and Con-trol of Knee Power Augmenting Device with Backdrivable Electro-Hydrostatic Actuator,” in Proc. of 13th World Congress in Mechanismand Machine Science, no. A12 534, 2011, pp. 1–10.

[25] A. D. Luca and R. Mattone, “Actuator Failure Detection and IsolationUsing Gneralized Momenta,” in Proc. of IEEE Int’l Conf. on Roboticsand Automation, 2003, pp. 634–639.

[26] ——, “Sensorless Robot Collision Detection and Hyrid Force/MotionControl,” in Proc. of IEEE Int’l Conf. on Robotics and Automation,2005, pp. 999–1004.

[27] T. Kawakami, K. Ayusawa, H. Kaminaga, and Y. Nakamura, “High-fidelity joint drive system by torque feedback control using highprecision linear encoder,” in Proc. of IEEE Int’l Conf. on Roboticsand Automation, 2010, pp. 3904–3909.

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