1

Investigations of a Robotic Testbed withViscoelastic Liquid Cooled Actuators

Donghyun Kim, Junhyeok Ahn, Orion Campbell, Nicholas Paine, and Luis Sentis,

Abstract—We design, build, and thoroughly test a new type ofactuator dubbed viscoelastic liquid cooled actuator (VLCA) forrobotic applications. VLCAs excel in the following five criticalaxes of performance: energy efficiency, torque density, impactresistence, joint position and force controllability. We first studythe design objectives and choices of the VLCA to enhance theperformance on the needed criteria. We follow by an investigationon viscoelastic materials in terms of their damping, viscous andhysteresis properties as well as parameters related to the long-term performance. As part of the actuator design, we configurea disturbance observer to provide high-fidelity force controlto enable a wide range of impedance control capabilities. Weproceed to design a robotic system capable to lift payloads of32.5 kg, which is three times larger than its own weight. Inaddition, we experiment with Cartesian trajectory control up to2 Hz with a vertical range of motion of 32 cm while carrying apayload of 10 kg. Finally, we perform experiments on impedancecontrol and mechanical robustness by studying the response ofthe robotics testbed to hammering impacts and external forceinteractions.

Index Terms—Viscoelastic liquid cooled actuator, Torque feed-back control, Impedance control.

I. INTRODUCTION

SERIES elastic actuators (SEAs) [1] have been extensivelyused in robotics [2], [3] due to their impact resistance andhigh-fidelity torque controllability. One drawback of SEAs isthe difficulty that arises when using a joint position controllerdue to the presence of the elastic element in the drivetrain. Toremedy this problem the addition of dampers has been previ-ously considered [4]–[6]. However, incorporating mechanicaldampers makes actuators bulky and increases their mechanicalcomplexity.

One way to avoid this complexity is to employ elastomersinstead of metal springs. Using a viscoelastic material insteadof combined spring-damper systems enables compactness [7]and simplified drivetrains [8]. However, it is difficult toachieve high bandwidth torque control due to the nonlinearbehavior of elastomers. To address this difficulty, [9] modelsthe force-displacement curve of elastomer using a “standardlinear model.” The estimated elastomer force is employed ina closed-loop force controller. Unfortunately, the hysteresis inthe urethane elastomer destabilized the system at frequenciesabove 2 Hz. In contrast our controllers achieve a bandwidth of70 Hz. The study on [10] accomplishes reasonably good torquecontrol performance, but the range of torques is small to ensurethat the elastomer operates in the linear region; our design andcontrol methods described here achieve more than an order ofmagnitude higher range of torques with high fidelity tracking.

To sufficiently address the nonlinear behavior of elastomers,which severely reduce force control performance, we empiri-

cally analyze various viscoelastic materials with a custom-builtelastomer testbed. We measure each material’s linearity, creep,compression set, and damping under preloaded conditions,which is a study under-documented in the academic literature.To achieve stable and accurate force control, we study variousfeedback control schemes. In a previous work, we showed thatthe active passivity obtained from motor velocity feedback[11] and model-based control such as disturbance observer(DOB) [12] play an essential role in achieving high-fidelityforce feedback control. Here, we analyze the phase marginsof various feedback controllers and empirically show theiroperation in the new actuators. We verify the stability andaccuracy of our controllers by studying impedance control andimpact tests.

To test our new actuator, we have designed a two degree-of-freedom (DOF), robotic testbed, shown in Fig. 5. It integratestwo of our new actuators, one in the ankle, and another in theknee, while restricting motions to the sagittal plane. With thefoot bolted to the floor for initial tests, weight plates can beloaded on the hip joint to serve as an end-effector payload.We test operational space control to show stable and accurateoperational space impedance behaviors. We perform dynamicmotions with high payloads to showcase another importantaspect of our system, which is its cooling system aimed atsignificantly increasing the power of the robot.

The torque density of electric motors is often limited bysustainable core temperature. For this reason, the maximumcontinuous torque achieved by these motors can be sig-nificantly enhanced using an effective cooling system. Ourprevious study [13] analyzed the improvements on achievablepower based on thermal data of electric motors and proposedmetrics for design of cooling systems. Based on the metricsfrom that study, we chose a 120 W Maxon EC-max 40, whichis expected to exert 3.59 times larger continuous torque whenusing the proposed liquid cooling system. We demonstrate theeffectiveness of liquid cooling by exerting 860N continousforce during 5 min and 4500N peak force during 0.5s whilekeeping the core temperatures below 115◦C, which is muchsmaller than the maximum, 155◦C. We accurately track fastmotions of 2 Hz while carrying a 10 kg payload for endurancetests. In addition we perform heavy lift tests with a payloadof 32.5 kg keeping the motor temperatures under 80◦C.

The main contribution of this paper is the introduction of anew viscoelastic liquid cooled actuator and a thorough studyof its performance and its use on a multidof testbed. Wedemonstrate that the use of liquid cooling and the elastomersignificantly improve joint position controllability and powerdensity over traditional SEAs. More concretely, we 1) design

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a new actuator, dubbed the VLCA, 2) extensively studyviscoelastic materials, 3) extensively analyze torque feedbackcontrollers for VLCAs, and 4) examine the performance in amultidof prototype.

II. BACKGROUND

Existing actuators can be characterized using four criteria:power source (electric or hydraulic), cooling type (air or liq-uid), elasticity of the drivetrain (rigid or elastic), and drivetraintype (direct, harmonic drive, ball screw, etc.) [14], [15]. One ofthe most powerful and common solutions is the combination ofhydraulic, liquid-cooling, rigid and direct drive actuation. Thisachieves high power-to-weight and torque-to-weight ratios,joint position controllability, and shock tolerance. Existingrobots that use this type of actuators include Atlas, Spot, BigDog, and Wildcat of Boston Dynamics, BLEEX of Berkeley[16], and HyQ of IIT [17]. However, hydraulics are lessenergy efficient primarily because they require more energytransformations [18]. Typically, a gasoline engine or electricmotor spins a pump, which compresses hydraulic fluid, whichis modulated by a hydraulic servo valve, which finally causesa hydraulic piston to apply a force. Each stage in this processincurs some efficiency loss, and the total losses can be verysignificant.

The combination of electric, air-cooled, rigid, and harmonicdrive actuators are other widely used actuation types. Somerobots utilizing these actuator types include Asimo of Honda,HRP2,3,4 of AIST [19], HUBO of KAIST [20], REEM-C ofPAL Robotics, JOHNNIE and LOLA of Tech. Univ. of Munich[21], [22], CHIMP of CMU [23], Robosimian of NASA JPL[24], and more. These actuators have precise position controland high torque density. For example, LOLA’s theoreticalknee peak torque-density (129Nm/kg) is comparable to ours(107Nm/kg), although they did not validate their numberexperimentally and their max speed is roughly 2/3 of our maxspeed [22]. Compared to us, low shock tolerance, low fidelityforce sensing, and low efficiency gearboxes are commondrawbacks of these type of actuators. According to HarmonicDrive AGs catalog, the efficiency of harmonic drives may beas poor as 25% and only increases above 80% when optimalcombinations of input shaft speed, ambient temperature, gearratio, and lubrication are present. Conversely, the efficiency ofour VLCA is consistently above 80% due to the use of a ballscrew mechanism.

[25] used liquid cooling for electric, rigid, harmonicdrive actuators to enhance continuous power-to-weight ratio.The robots using this type of actuation include SCHAFTand Jaxon [26]. These actuators share the advantages anddisadvantages of electric, rigid, harmonic drive actuators, buthave a significant increase of the continuous power outputand torque density. One of our studies [13], indicates a 2xincrease in sustained power output by retrofitting an electricmotor with liquid cooling. Other published results indicate a6x increase in torque density through liquid cooling [14], [27],though such performance required custom-designing a motorspecifically for liquid cooling. In our case we use an off-the-shelf electric motor. In contrast with our design, these actuators

do not employ viscoelastic materials reducing their mechanicalrobustness and high quality force sensing and control.

Although the increased power density achieved via liq-uid cooling amplifies an electric actuator’s power, the rigiddrivetrain is still vulnerable to external impacts. To increaseimpact tolerance, many robots (e.g. Walkman and COMANof IIT [28], Valkyrie of NASA [29], MABEL and MARLO inUMich [30], [31], and StarlETH of ETH [32]) adopt electric,air-cooled, elastic, harmonic drive actuators. This type ofactuation provides high quality force sensing, force control,impact resistance, and energy efficiency. However, precisejoint position control is difficult because of the elasticity inthe drivetrain and the coupled effect of force feedback controland realtime latencies [33]. Low efficiency originating fromthe harmonic drives is another drawback.

As an alternative to harmonic drives, ball screws are greatdrives for mechanical power transmission. SAFFiR, THOR,and ESCHER of Virginia Tech [34]–[36], M2V2 of IHMC[37], Spring Flamingo of MIT [38], Hume of UT Austin [11],and the X1 Mina exoskeleton of NASA [39] use electric,air-cooled, elastic, ball-screw drives. These actuators showenergy efficiency, good power and force density, low noiseforce sensing, high fidelity force controllability, and lowbacklash. Compared to these actuators our design significantlyreduces the bulk of the actuator and increases its joint positioncontrollability. There are some other actuators that have specialfeatures such as the electric actuators used in MIT’s cheetah[40], which allow for shock resistance through a transparentbut backlash-prone drivetrain. However, the lack of passivedamping limits the joint position controllability of these typeof actuators compared to us.

III. VISCOELASTIC MATERIAL CHARACTERIZATION

The primary driver for using elastomers instead of metalsprings is to benefit from their intrinsic damping properties.However, the mechanical properties of viscoelastic materialscan be difficult to predict, thus making the design of anactuator based on these materials a challenging endeavor.

The most challenging aspect of incorporating elastomersinto the structural path of an actuator is in estimating or mod-eling their complex mechanical properties. Elastomers pos-sess both hysteresis and strain-dependent stress, which resultin nonlinear force displacement characteristics. Additionally,elastomers also exhibit time-varying stress-relaxation effectswhen exposed to a constant load. The result of this effect is agradual reduction of restoration forces when operating under aload. A third challenge when using elastomers in compressionis compression set. This phenomenon occurs when elastomersare subjected to compressive loads over long periods of time.An elastomer that has been compressed will exhibit a shorterfree-length than an uncompressed elastomer. Compression setis a common failure mode for o-rings, and in our application,it could lead to actuator backlash if not accounted for properly.

To address these various engineering challenges we de-signed experiments to empirically measure the following fourproperties of our viscoelastic springs: 1) force versus dis-placement, 2) stress relaxation, 3) compression set, and 4)

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E-stopLoad cell

Elastic materialBelt driveBLDC motor

EtherCAT-based embedded control system

Ball screw drive

Displacement sensor

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Spring steelViton 75ABuna-N 90APolyurethane 90A

Increasing system bandwidth

(d) Stess relaxation (e) Dynamic response of four elastomertime (sec)

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EPDM 80APolyurethane 80AViton 75A

Spring steel

(b) Complession set (c) Force vs Displacement curveDispacement (m)

Forc

e (N

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Spring steelPolyurethane 90AReinforced Silicon 70ABuna- N 90A

Viton 75APolyurethane 80A

EPDM 80ASilicone 90A

Fig. 1. Viscoelastic material test. (a) The elastomer testbed is designed and constructed to study various material properties of candidate viscoelasticmaterials. (b) We measured each elastomers free length both before and after they were placed in the preloaded testbed. (c) A strong correlation betweenmaterial hardness and the materials stiffness can be observed. An exception to this correlation is the fabric reinforced silicone which we hypothesize hadincreased stiffness due to the inelastic nature of its reinforcing fabric. Nonlinear effects such as hysteresis can also be observed in this plot. (d) We commanda rapid change in material displacements and then measured the materials force change versus time for 300 seconds. Note that the test of reinforced silicone70A is omitted due to its excessive stiffness. (d) Although the bandwidths of the four responses are different, their damping ratios (signal peak value) arerelatively constant, which implies different damping.

frequency response, which will be used to characterize eachmaterial’s effective viscous damping. We built a viscoelasticmaterial testbed, depicted in Fig. 1(a), to measure each ofthese properties. We selected and tested the seven candidatematerials that are listed in Table I. The dimension of the testedmaterials are fairly regular, with 46mm diameter and 27mmthickness.

A. Compression set

Compression set is the reduction in length of an elastomerafter prolonged compression. The drawback of using mate-rials with compression set in compliant actuation is that thematerials must be installed with larger amounts of preloadforces to avoid the material sliding out of place during usage.To measure this property, we measured each elastomers freelength both before and after the elastomer was placed inthe preloaded testbed. The result of our compression setexperiments are summarized in Table I.

B. Force versus displacement

In the design of compliant actuation, it is essential to knowhow much a spring will compress given an applied force.This displacement determines the required sensitivity of aspring-deflection sensor and also affects mechanical aspectsof the actuator such as usable actuator range of motion andclearance to other components due to Poisson ratio expansion.In this experiment, we identify the force versus displacementcurves for the various elastomer springs. Experimental datafor all eight springs as shown in Fig 1(b). Note that there isa disagreement between our empirical measurements and theanalytic model relating stiffness to hardness, i.e. the Gent’srelation shown in [41]. This mismatch arises because in ourexperiments the materials are preloaded whereas the analyticalmodels assume unloaded materials.

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MaterialsCompression

set (%)Linearity

(R-square)Linear stiffness

(N/mm)Preloaded elastic

modulus (N/mm)Material damping

(Ns/m)Creep(%)

MaterialCost ($)

Spring steel 0 0.996 860.8 0 0 -

Polyurethane 90A 2 0.992 8109 112.5 16000 15.3 19.40

Reinforced silicone 70A 2.7 0.978 57570 798.7 242000 - 29.08

Buna-N 90A 2.8 0.975 11270 156.4 29000 25 51.47

Viton 75A 4 0.963 2430 33.7 9000 30.14 105.62

Polyurethane 80A 4.5 0.993 2266 31.4 4000 16.8 19.40

EPDM 80A 6.48 0.939 6499 90.2 16000 23.4 35.28

Silicone 90A - 0.983 12460 172.9 37000 10.7 29.41

TABLE ISUMMARY OF VISCOELASTIC MATERIALS

C. Stress relaxation

Stress-relaxation is an undesirable property in compliantactuators for two reasons. First, the time-varying force de-grades the quality of the compliant material as a force sensor.When a material with significant stress-relaxation propertiesis used, the only way to accurately estimate actuator forcebased on deflection data is to model the effect and then passdeflection data through this model to obtain a force estimate.This model introduces complexity and more room for error.The second reason stress-relaxation can be problematic is thatit can lead to the loss of contact forces in compression-basedspring structures.

The experiment for stress relaxation is conducted as follow:1) enforce a desired displacement to a material, 2) recordthe force data over time from the load cell, 3) subtract theinitially measured force from all of the force data. Empiricallymeasured stress-relaxation properties for each of the materialsare shown in Fig. 1 (c), which represents force offsets astime goes under the same displacement enforced. Note thateach material shows different initial force due to the differentstiffness and each initial force data is subtracted in the plot.

D. Dynamic response

In regards to compliant actuation, the primary benefit ofusing an elastomer spring is its viscous properties, which cancharacterize the dynamic response of an actuator in series withsuch a component. To perform this experiment, we generatemotor current to track an exponential chirp signal, testingfrequencies between 0.001Hz and 200Hz. Given the input-output relation of the system, we can fit a second order transferfunction to the experimental data to obtain an estimate ofthe system’s viscous properties. However, this measure alsoincludes the viscoelastic testbed’s ballscrew drive train friction(Fig. 1(a)). To quantify the elastomer spring damping inde-pendently of the damping of the testbed drive train, the latter(8000 Ns/m) was first characterized using a metal spring,and then subtracted from subsequent tests of the elastomersprings to obtain estimates for the viscous properties of theelastomer materials. Fig. 1(d) shows the frequency responseresults for current input and force output of three differentsprings, while controlling the damping ratio. The elastomershave higher stiffness than the metal spring, hence their naturalfrequencies are higher.

E. Selection of Polyurethane 90A

A variety of other experiments were conducted to strengthenour analysis and are summarized in Table I. Based on theseresults, Polyurethane 90A appears to be a strong candidatefor viscoelastic actuators based on its high linearity (0.992),low compression set (2%), low creep (15%), and reasonablyhigh damping (16000 Ns/m). It is also the cheapest of thematerials and comes in the largest variety of hardnesses andsizes.

IV. VISCOELASTIC LIQUID COOLED ACTUATION

The design objectives of the VLCA are 1) power density, 2)efficiency, 3) impact tolerance, 4) joint position controllability,and 5) force controllability. Compactness of actuators is alsoone of the critical design parameters, which encourage usto use elastomers instead of metal springs and mechanicaldampers. Our previous work [13] shows a significant im-provement in motor current, torque, output power and systemefficiency for liquid cooled commercial off-the-shelf (COTS)electric motors and studied several Maxon motors for com-parison. As an extension of this previous work, in this newstudy we studied COTS motors and their thermal behaviormodels and selected the Maxon EC-max 40 brushless 120 W(Fig. 2(e)), with a custom housing designed for the liquidcooling system (Fig. 2(h)). The limit of continuous currentincreases by a factor of 3.59 when liquid convection is usedfor cooling the motor. Therefore, a continuous motor torqueof 0.701 N ·m is theoretically achievable. Energetically, thisactuator is designed to achieve 366 W continuous powerand 1098W short-term power output with an 85% ball screwefficiency (Fig. 2(b)) since short-term power is generally threetime larger than continuous power. With the total actuatormass of 1.692 kg, this translates into a continuous power of216W/kg and a short-term power of 650W/kg. The liquidpump, radiator, and reservoir are products of Swiftech whichweight approximately 1kg. By combining convection liquidcooling, high power brushless DC (BLDC) motors, and ahigh-efficiency ball screw, we aim to surpass existing electricactuation technologies with COTS motors in terms of powerdensity.

In terms of controls, a common problem with conventionalSEAs is their lack of physical damping at their mechanicaloutput. As a result, active damping must be provided fromtorque produced by the motor [42]. However, the presence of

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(a) Timing belt transmission(b) Ball screw drive(c) Load cell(d) Actuator output

Opposite side

(e) BLDC Motor(f) Quadrature encoder(g) Temperature sensor(h) Liquid cooling jacket(i) Tube connector

(j) Polyuretane elastomer(k) Compliance deflection sensor(l) Mechanical ground pivot(m) Quadrature encoder (deflection)

Rubber part

Motor part

Load part

ground

Fig. 2. Viscoelastic Liquid Cooled Actuator. The labels are explanatory. In addition, the actuator contains five sensors: a load cell, a quadrature encoderfor the electric motor, a temperature sensor, and two elastomer deflection sensors. One of the elastomer deflection sensors is absolute and the other one is aquadrature encoder. The quadrature encoder gives high quality velocity data of the elastomer deflection.

signal latency and derivative signal filtering limit the amountby which this active damping can be increased, resultingin SEA driven robots achieving only relatively low outputimpedances [33] and thus operating with limited joint positioncontrol accuracy and bandwidth. Our VLCA design incor-porates damping directly into the compliant element itself,reducing the requirements placed on active damping effortsfrom the controller. The incorporation of passive damping aimsto increase the output impedance while retaining complianceproperties, resulting in higher joint position control bandwidth.The material properties we took into consideration will beintroduced in Section III. The retention of a compliant elementin the VLCA drive enables the measurement of actuator forcesbased on deflection. The inclusion of a load cell (Fig. 2(c)) onthe actuators output serves as a redundant force sensor and isused to calibrate the force displacement characteristics of theviscoelastic element.

Mechanical power is transmitted when the motor turns aball nut via a low-loss timing belt and pulley (Fig. 2 (a)),which causes a ball screw to apply a force to the actuator’soutput (Fig. 2(d)). The rigid assembly consisting of the motor,ball screw, and ball nut connects in series to a compliant vis-coelastic element (Fig. 2(j)), which connects to the mechanicalground of the actuator (Fig. 2(k)). When the actuator applies aforce, the reaction force compresses the viscoelastic element.The viscoelastic element enables the actuator to be more shocktolerant than rigid actuators yet also maintain high outputimpedance due to the inherent damping in the elastomer.

V. ACTUATOR FORCE FEEDBACK CONTROL

To demonstrate various impedance behaviors in operationalspace, robots must have a stable force controller. Stable andaccurate operational space control (OSC) is not trivial toachieve because of the bandwidth interference between outerposition feedback control (OSC) and inner torque feedbackcontrol [11]. Since stable torque control is a critical componentfor a successful OSC implementation, we extensively studyvarious force feedback controls.

Jm(kgm2) bm(Nm s) mr(kg) br(N s/m) kr(N/m)

3.8e−5 2.0e−4 1.3 2.0e4 5.5e6

TABLE IIACTUATOR PARAMETERS

The first step in this analysis is to identify the actuatordynamics. The transfer functions of the reaction force sensedin the series elastic actuators (elastomer deflection) are wellexplained in [43]. When the actuator output is fixed, thetransfer function from the motor current input to the elastomerdeflection is given by

Px =xrim

=ηkτNm

(JmN2m +mr)s2 + (bmN2m + br)s+ kr

, (1)

where η, kτ , Nm, and im are the ball screw efficiency,the torque constant of a motor, the speed reduction ratio ofthe motor to the ball screw, and the current input for themotor, respectively. The equations follow the nomenclature inFig. 3(a). We can find η, kτ , and Nm in data sheets, which are0.9, 0.0448 N ·m/A, and 3316 respectively. The gear ratio ofthe drivetrain is computed by dividing the speed reduction ofpulleys (2.111) with lead length of the ball screw (0.004m)using the equation 2π × 2.111/0.004.

However, we need to experimentally identify kr, br, Jm,and bm. We infer kr by dividing the force measurementfrom the load cell by the elastomer deflection. The otherparameters are estimated by comparing the frequency responseof the model and experimental data. The frequency responsetest is done with the ankle actuator while prohibiting jointmovement with a load and an offset force command. Theresults are presented in Fig. 3 with solid gray lines. Note thatthe dotted gray lines are the estimated response from the trans-fer function (measured elastomer force/ input motor force)using the parameters of Table. II. The estimated response andexperimental result match closely with one another, implyingthat the parameters we found are close to the actual values.

We also study the frequency response for different loadmasses to understand how the dynamics changes as the jointmoves. When 10kg is attached to the end of link, the reflected

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-3dB

Experiment result

Inf. mass2500 kg2000 kg1500 kg

27.5 Hz

-149o

Fig. 3. Frequency response of VLCA. Gray solid lines are experimental dataand the other lines are estimated response with the model using empiricallyparameters.

mass to the actuator varies from 1500kg to 2500kg becausethe length of the effective moment arm changes depending onjoint position. In Fig. 3(b), the bode plots are presented andthe response is not significantly different than the fixed outputcase. Therefore, we design and analyze the feedback controllerbased on the fixed output dynamics.

For the force feedback controller, we first compare twooptions, which we have used in our previous studies [11],[12]:

1) Proportional (P) + Derivative (Df ) using velocity signalobtained by a low-pass derivative filtered elastomerdeflection

2) Proportional (P) + Derivative (Dm) using motor velocitysignal measured by a quadrature encoder connected toa motor axis

The second controller (PDm) has benefits over the first one(PDf ) with respect to sensor signal quality. The velocity ofmotor is directly measured by a quadrature encoder rather thanlow-pass filtered elastomer deflection data, which is relativelynoisy and lagged. In addition, Fig. 4 shows that the phasemargin of the second controller (47.6) is larger than the firstone (17.1).

To remove the force tracking error at low frequencies, weconsider two options: augmenting the controller either withintegral control or with a DOB on the PDm controller. Tocompare the two controllers, we analyzed the phase marginsof all the mentioned controllers. First, we chose to focus onthe location where the sensor data returns in order to addressthe time delay of digital controllers (Fig. 4 (a) and (c)). Next,we have to compute the open-loop transfer function for eachclosed loop system. For example, the PDf controller’s closedloop transfer function is

Fk =krPxN

(kp(Fr − e−TsFk) + Fr − kd,fQde−TsFk

),

(2)where Fk, Fr, T , and Qd are the measured force from aelastomer deflection, a reference force, a time delay, a lowpass derivative filter, respectively.For convenience, we use Ninstead of the multiplication of three terms, ηkτNm. When

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krVCLA

VCLA kr

Fig. 4. Stability analysis of controllers. Phase margins of each controllersand open-loop system are presented.

gathering the term with e−Ts of Eq. (2), we obtain

FkFr

=krPx(Kp + 1)/N

1 + e−TskrPx(Kp +Kd,fQd)/N. (3)

Then, the open-loop transfer function of the closed systemwith the time delay is

P openPDf = krPx(Kp +Kd,fQd)/N. (4)

We can apply the same method for the PIDm and PDm+DOBcontrollers.

The transfer function of PIDm, which is presented inFig. 4(c), is

Fk =krPxN

((Fr − e−TsFk)(Kp +Ki

1

s) + Fr

−Kd,me−TssNmFkkr

).

(5)

Then it becomesFkFr

=krPx(Kp +Ki/s+ 1)/N

1 + e−TsPx(kr(Kp +Ki/s) +KdsNm)/N. (6)

When we apply a DOB instead of integral control, we needthe inverse of the plant. In our case, the plant of the DOB isPDm, which is similar to Eq. (6) except that Ki and e−Ts areomitted:

PPDm(= Pc) =krPx(Kp + 1)

N + Px(krKp +Kd,msNm). (7)

7

Fig. 5. Robotic testbed. Our testbed consists of two VLCAs at the ankleand the knee. The foot of the testbed is fixed on the ground. The linkagesare designed to vary the maximum peak torques and velocities depending onpostures. As the joint positions change, the ratios between ball screw velocities(L̇0,1) and joint velocities (q̇0,1) also change because of effective lengths ofmoment arms vary. The linkages are designed to exert more torque when therobot crouches, which is the posture that the gravitational loads on the jointsare large.

The formulation of PDm including the DOB, which is shownin Fig. 4(c), is

Fk =krPx(Kp + 1)(Fd − e−TsP−1c QτdFk)

(N + e−TsPx(krKp +Kd,msNm)) (1−Qτd), (8)

where Qτd is a second order low-pass filter. Then the transferfunction isFkFd

=krPx(Kp + 1)

N(1−Qτd) + e−Ts (NQτd + Px(krKp +Kd,msNm)).

(9)The open-loop transfer function is

P openPDm+DOB =NQτd + Px(krKp +Kd,msNm)

N(1−Qτd)(10)

The bode plots of P openPDf , PopenPDm

, P openPIDm , and PopenPDm+DOB

are presented in Fig. 4(b). The gains (Kp, Kd,m, Ki) are thesame as the values that we use in the experiments presented inSection VII-A, which are 4, 15, and 300, respectively. The PDfcontroller uses KdNm/kr for Kd,f to normalize the derivativegain. The cutoff frequency of the DOB is set to 15Hz becausethis is where the PDm+DOB shows a magnitude trend similarto the integral controller (PIDm). The results imply that thePDm+DOB controller is more stable than PIDm with respectto phase margin and maximum phase lag. This analysis is alsoexperimentally verified in Section VII-A.

VI. ROBOTIC TESTBED

We built a robotic testbed shown in Fig. 5. To demon-strate dynamic motion, we implemented an operational spacecontroller (OSC) incorporating the multi-body dynamics ofthe robot. We designed and built a robotic testbed (Fig. 5)consisting of two VLCAs - one for the ankle (q0) and onefor the knee (q1). The design constrains motion to the sagittalplane, the robot carries 10kg, 23kg, or 32.5kg of weight at

the hip, and the foot is fixed on the ground. With this testbed,we intended to demonstrate coordinated position control withtwo VLCAs, the viability of liquid cooling on an articulatedplatform, cartesian position control of a weighted end effector,and verification of a linkage design.

The two joints each have a different linkage structure thatwas carefully designed so that the moment arm accommodatesthe expected torques and joint velocities as the robot posturechanges (Fig. 5). For example, each joint can exert a peaktorque of approximately 270 Nm and the maximum jointvelocity ranges between 7.5 rad/s and 20+ rad/s dependingon the mechanical advantage of the linkage along the config-urations. The joints can exert a maximum continuous torqueof 91 Nm at the point of highest mechanical advantage. Thisposture dependent ratio of torque and velocity is a uniquebenefit of prismatic actuators.

Given cartesian motion trajectories, which are 2nd order B-spline or sinusoidal functions, the centralized controller com-putes the torque commands with operational space positionand velocity, which are updated by the sensed joint positionand velocity. The OSC formulation that we use is

τ = AJ−1hip(ẍdes +Kpe+Kdė− J̇hipq̇) + b+ g, (11)

where A, b, and g represent inertia, coriolis, and gravityjoint torque, respectively. ẍdes, e, and ė are desired trajectoryacceleration, position and velocity error, respectively. q̇ ∈ R2is the joint velocity of the robot and τ is the joint torque. Jhipis a jacobian of the hip, which is a 2 × 2 square matrix andassumed to be full-rank.

VII. RESULTS

We first conducted various single actuator tests to showbasic performance such as torque and joint position controlla-bility, continuous and peak torque, and impact resistance. Sub-sequently, we focused on the performance of OSC using therobotic testbed integrated with DOB based torque controllersto demonstrate actuator efficiency and high power motions.

A. Single Actuator Tests

Fig. 6(a) shows the experimental results of our frequencyresponse testing as well as the estimated response based onthe transfer functions. We compare three types of controllers:PDm, PIDm, and PDm + DOB. As we predicted in theanalysis of Section V, the PDm +DOB controller shows lessphase drop and overshoot than PIDm. The integral controlfeedback gain used in the experiment is 300 and the cutofffrequency of the DOB’s Qτd filter is 60Hz, which showssimilar error to the PIDm controller (Fig. 6(b)). Another testpresented in Fig. 6(c) also supports the stability and accuracyof torque control. In the test, we command a ramp in jointtorque from 1 to 25Nm in 0.1s. The sensed torque (blue solidline) almost overlaps the commanded torque (red dashed line).

Fig. 6(d) is the result of a joint position control test designedto show that VLCAs have better joint position controllabilitythan SEAs using springs. In the experiment, we use a jointencoder for position control and a motor quadrature encoderfor velocity feedback. To compare the VLCAs performance

8

(c) Torque fast response

(d) Position fast response

Erro

r (dB

)

Frequency (Hz) time (sec)

Reference

(b) Error magintude and chirp test trajectories

Frequency (Hz)

Open Open (estimated)

(estimated) (estimated)

(a) Frequency responses of different controllers

Phas

e (d

eg)

Mag

nitu

de (d

B)

(e) Continous force and core temperature

(f) peak force

1.6 1.8 2 2.2 2.4 2.6 2.80

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ue (N

m)

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uato

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ce (N

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commandsensed

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core temperature (w/ liquid)actuator force

core temperature (w/o liquid)

1.6 1.8 2 2.2 2.4 2.6 2.8

-2.4

-2.2

-2

-1.8

(exp.) command(exp.) sensed

(sim.) elastomer(sim.) metal spring

Fig. 6. Torque Feedback Control Test. (a) Experimental data and estimated response based on the transfer functions are presented. Estimated response ofPD controller is identical to the PD+DOB since DOB theoretically does not change the transfer function. The plot show PD+DOB shows better performancein terms of less overshoot and smaller phase drop near to the natural frequency. (b) We choose integral controller feedback gain that shows similar accuracyof PD+DOB’s. The left is error magnitude of three controllers. PD controller has larger error than the other two controller in the low frequency region. Theright is torque trajectories in the time domain.

with that of spring-based SEAs, we present simulation resultsfor a spring-based SEA on the same plot as the experimentresult for the VLCA. The green dashed line is the simulatedstep response of our actuator and the yellow dotted line isthe result of the simulation model using the same parametersexcept the spring stiffness and damping. The spring stiffnesswas selected to be 11% of the elastomer’s, based on theresults of our tests in Section III, and the damping for thespring case was set to 8000 Ns/m which only includes thedrivetrain friction. The results show a notable improvement injoint position control when using an elastomer instead of asteel spring.

Fig. 6(e) shows the continous force and the motor core tem-perature trend with and without liquid cooling. The observedcontinous force is 860N and the motor core temperature settlesat 115◦C with liquid cooling. Fig. 6(f) is the the result of short-term torque test. In the experiment, we fix the output of theactuator and command a 31A current for 0.5s. The observedforce measured by a loadcell (Fig. 2(c)) is 4500N, which isa little smaller than the theoretically expected value, 5900N.Considering that the estimated core temperature surpassed107◦C (< 155◦C limit), we expect that the theoretical valueis reasonable. Thus, we conclude that the maximum forcedensity of our actuator is larger than 2700N/kg and potentially3500N/kg.

Fig. 7 shows loadcell and elastomer force data from theimpact tests. In the tests, we hit the loadcell connected to theball screw (Fig. 2(c)) with a hammer falling from a constantheight while fixing the actuator in two different places to

-2 0 2 4 6 8 10 12 14-1000

-500

0

500

1000

time (ms)

Act

uato

r for

ce (N

)

95% interval

Load cell (solid holding)Load cell (w/ elastomer)Rubber deflection (solid holding)Rubber deflection (w/ elastomer)

Fig. 7. Impact test. 83 trials are plotted and estimated with gaussian process.We can see the deflections of the elastomer, which imply that the elasticelement absorbes the external impact force.

compare the rigid actuator to viscoelastic actuator response. Inthe rigid scenario, outer case of ballnut, a blue part in Fig. 2,is fixed to exclude the elastomer from the external impactforce path. In the second case, we fixed the ground pin of theactuator, which is depicted by a gray part in Fig. 2(l), to seehow the elastomers react to the impact.

The impact experiment is challenging because the numberof data points we can obtain is very small with a 1ms updaterate. To overcome the lack of data points, we estimate themean and variance of 83 trials by gaussian process regression.The results presented in Fig. 7 imply that there is no significantdifference in the forces measured by the loadcell in bothcases, which is predictable because the elastic element isplaced behind the drivetrain. However, the elastomer does

9

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m)

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leK

nee

14 16 18 20 22 24-0.1

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(a) Impedance control

Compliant in horizontal direction

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(c) Fast up and down (1.7 Hz)

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-0.05 0 0.050.6

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time (sec)

commandsensed

Fig. 8. Operational Space Impedance Control Test. (a) The robotdemonstrates different impedance: stiff in the vertical direction and compliantin the horizontal direction. The high tracking performance of force feedbackcontrol results in the overlapped commanded and sensed torques. (b) Toshow the stability, we hit the weight with a hammer while operating theimpedance control. Even under the impact, force control show stable andaccurate tracking. (c) The robot demonstrates a 1.7Hz up and down motionwhile carrying 10kg weight at the hip, and shows a position error of less than2.5cm.

play a significant role in absorbing energy from the impactwhich is evident from large elastomer deflection in the secondcase. Thus, the presence of the elastic element mitigates thepropagation of an impulse to the link where the actuatorgrounds.

B. Operational Space Impedance Control

Fig. 8 shows our OSC experimental tests (Section VI)carrying a 10kg weight. In the first test presented in Fig. 8(a),the commanded behavior is to be compliant in the horizontaldirection (x) and to be stiff in the vertical direction (y).When pushing the hip with a sponge in the x direction, therobot smoothly moves back to comply with the push, but itstrongly resists the given vertical disturbance to maintain the

0.5 1 1.5 2 2.5 3 3.50

0.5

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1.5

0.5 1 1.5 2 2.5 3 3.5

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00.20.40.6

servodrive

Wk

/ Wm

Wk

/ Wb

5 (sec)310.50.3

time (sec)

power supply

electricmotor

joint

Wb Wm WkAverage efficiency

Fig. 9. Efficiency analysis of the ankle actuator. Efficiencies of mechanicalsystem using electrical power has 3 steps from a power supply to robot joints.The graph shows the ratio of the mechanical power of the ankle joint and themotor power and the ratio of the joint power and power supply’s input power.

commanded height. To show the stability of our controller, wealso test the response to impacts by hitting the weight with ahammer (Fig. 8(b)). Even when there are sudden disturbances,the torque controllers rapidly respond to maintain good torquetracking performance as shown in Fig. 6(d).

Fig. 8(c) shows the tracking performance of our systemwhile following a fast vertical hip trajectory. While travel-ing 0.3m with 1.7Hz frequency, the hip position errors arebounded by 0.025m. This result demonstrates that our systemis capable of stable and accurate OSC, which is challengingbecause of the bandwidth conflict induced by its cascadedstructure.

C. Efficiency Analysis

Fig. 9 explains the power flow from the power supply to therobot joint. Input current (Ib) and voltage (Vb) are measuredin the micro-controllers and the product of those two yieldsthe input power from the power supply. θ̇m is measured by thequadrature encoder connected to the motor’s axis (Fig. 2(f))and τm is computed from kτ im with im measured in themicro-controller. Joint velocity is low-pass derivative filteredjoint positions measured at the absolute joint encoders. Thetorque (τk) is computed from projecting the load cell dataacross the linkage’s effective moment arm.

In this test, the robot lifts a 23kg load using five differentdurations to observe efficiency over a range of different speedsand torques. The results are presented in Fig. 9 with thedescription of three different power measures. The sensedtorque data measured by a load cell is noisy; therefore, wecompute the average of the drivetrain efficiency for a clearercomparison. The averages are the integrations of efficiency di-vided by the time durations. Here we only integrate efficiencywhile the mechanical power is positive, to prevent confoundingour results by incorporating the work done by gravity.

10

6.5 7 7.5 81.82

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que

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) Motor temperature ( oC

)

Pow

er (W

)

time (sec)

totalankleknee

(a) 2Hz up and down motion (b) Heavy weight lift

actuator forcemotor temperature

Fig. 10. High power motion experiment. (a) Joint position data from joint encoder and motor encoder are shown. In this experiment, the maximum observedtorque of the ankle joint is 250 Nm and the maximum observed mechanical power of the knee joint is 310W. (b) The robot lifts by 0.3m a 32.5 kg loadduring 0.4s. There is still a safety margin with respect to the limits equal to 5900N and 155◦C.

The experimental results show that the drivetrain efficiencyis approximately 0.89, which means that we lose only a smallamount of power in the drivetrain and most of the torquefrom the motor is delivered to the joint. This high efficiencyindicates only minor drivetrain friction, which is beneficial fordynamics-based motion controllers.

D. High Power Motion Experiment

To demonstrate high power motions such as fast verticaltrajectories and heavy payload lifts, we use the motor positioncontrol mode, which uses the quadrature encoders attacheddirectly to the motor for feedback. Fig. 10(a) presents theresults of a test comprised of 2Hz vertical motion with 0.32m of travel while carrying a load of 10 kg at the hip.With respect to mechanical power, the knee joint repeatedlyexerts 305W, which is close to the predicted constant power(360W). Although the limited range of motion makes it hardto demonstrate continuous mechanical power, these resultsconvincingly support our claim of enhanced continuous powerenabled through liquid cooling.

Fig. 10(b) presents another test in which the robot lifts a32.5kg weight. We can see that the robot operates in the saferegion (≤ 5900N and ≤ 155◦C) while demonstrating highpower motion.

VIII. CONCLUDING REMARKS

Overall our main contribution has been on the design andextensive testing of a new viscoelastic liquid cooled actuatorfor robotics.

One of the tests addressed is impedance control in theoperational space instead of joint impedance control. It is oftenthe case that humanoid robots require impedance control inthe operational space. For instance, controlling the operationalspace impedance can enable improved locomotion behaviorssuch as running. Our controllers demonstrate that we cancontrol the impedance in the Cartesian operational space asa potential functionality for future robotic systems. The useof liquid cooling has allowed to sustain high output torquefor prolonged times as shown in the experiments of Fig.

6(e). As we can see, when turning off liquid cooling thetemperature rises quickly above safety limits whereas whenturning on the cooling we can sustain large payload torquesfor long periods of time. The use of elastomers versus steelsprings has demonstrated a clear improvement on joint positionperformance as shown in Fig. 6(d). This capability is importantto achieve a large range of output joint or Cartesian spaceimpedances.

In the future we will explore further reducing the sizeof our viscoelastic liquid cooled actuators. Maintaining thecurrent compact design structure we can still reduce anothersignificant percentage the bulk of the actuator by exploringnew types of bearings, ballnut sizes and piston bearings at thefront end of the actuator. We will also explore using differentmaterial for the liquid cooling actuator jacket. The currentpolyoxymethylene material is easily breakable and developscracks due to the vibrations and impacts of this kind of roboticapplications. In the future we will switch to sealed metalchambers for instance. Further in the future we will considerdesigning our own motor stators and rotors for improved per-formance. We expect this kind of actuators to make their wayinto full humanoid robots and high performance exoskeletondevices and we look forward to participate in such interestingfuture studies.

ACKNOWLEDGMENTThe authors would like to thank the members of the

Human Centered Robotics Laboratory at The University ofTexas at Austin for their help and support. This work wassupported by the Office of Naval Research, ONR Grant[grant #N000141512507] and NASA Johnson Space Center,NSF/NASA NRI Grant [grant #NNX12AM03G].

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I IntroductionII BackgroundIII viscoelastic material characterizationIII-A Compression setIII-B Force versus displacementIII-C Stress relaxationIII-D Dynamic responseIII-E Selection of Polyurethane 90A

IV Viscoelastic Liquid Cooled ActuationV Actuator Force Feedback ControlVI Robotic TestbedVII ResultsVII-A Single Actuator TestsVII-B Operational Space Impedance ControlVII-C Efficiency AnalysisVII-D High Power Motion Experiment

VIII Concluding RemarksReferences