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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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3
E-stopLoad cell
Elastic materialBelt driveBLDC motor
EtherCAT-based embedded control system
Ball screw drive
Displacement sensor
Frequency (Hz)
Phas
e (d
eg)
Mag
nitu
de (d
B)
Spring steelViton 75ABuna-N 90APolyurethane 90A
Increasing system bandwidth
(d) Stess relaxation (e) Dynamic response of four elastomertime
(sec)
Forc
e (N
)
(a) Viscoelastic material Testbed
-5 -4 -3 -2 -1 0 1 2 3 4 510-4
-2500
-2000
-1500
-1000
-500
0
500
1000
1500
2000
2500
Compression set (%)0 1 2 3 4 5 6
Reinforced silicone 70A
Buna-N 90APolyurethane 90A
EPDM 80APolyurethane 80AViton 75A
Spring steel
(b) Complession set (c) Force vs Displacement curveDispacement
(m)
Forc
e (N
)
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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5
(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
Frequency (Hz)
Phas
e (d
eg)
-40
-20
0
20
40
60
100 101 102-225
-180
-135
-90
-45
0
41.034.0
47.6 42.8
17.7
Phase margin
Mag
nitu
de (d
B)
Open-loopPDmPIDmPDfPDm + DOB
s
(b)
(c)
(a)
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)
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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
10
20
30
Torq
ue (N
m)
JPos
(rad
)
time (sec)
x 103
Act
uato
r for
ce (N
) Motor temperature ( oC
)
time (sec)
commandsensed
0 1 2 3-3
-2
-1
0
1
2
3
4
5
20
30
40
50
60
70
80
90
100
110
Act
uato
r for
ce (N
)
Motor tem
perature ( oC)
time (sec)0 50 100 150 200 250 300 350
-500
0
500
1000
0
50
100
150
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
Torq
ue (N
m)
Hip
pos
ition
(m)
time (sec)
Ank
leK
nee
14 16 18 20 22 24-0.1
00.10.2
14 16 18 20 22 24
0.8
1
14 16 18 20 22 24-200
20
14 16 18 20 22 24304050
commandsensed
(a) Impedance control
Compliant in horizontal direction
Stiff in vertical direction
(b) Operational space impact test
Torq
ue (N
m)
Hip
pos
ition
(m)
time (sec)
Ank
leK
nee
10 12 14 16 18-0.1
00.10.2
10 12 14 16 18
0.8
1
10 12 14 16 18
-20
-10
0
10 12 14 16 1830
40
Hitting down
(c) Fast up and down (1.7 Hz)
1 1.5 2 2.5
-0.1
0
0.1
1 1.5 2 2.50.60.70.80.9
-0.05 0 0.050.6
0.65
0.7
0.75
0.8
0.85
0.9
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
1
1.5
0.5 1 1.5 2 2.5 3 3.5
-0.4-0.2
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
2.22.42.6
6.5 7 7.5 84
5
6
6.5 7 7.5 8-200
0200
-1000100200
6.5 7 7.5 8
0100200
-600-400-2000200400
Join
t pos
ition
(rad
)K
nee
Ank
le
commandjoint encodermotor encoder
Join
t tor
que
(Nm
)K
nee
Ank
le
Mechanical pow
er (W)
joint torquemechanical power
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5-3000-2000-1000
01000
30
35
40
45
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5-4000
-3000
-2000
-1000
40
60
80
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
500
1000
1500
Ankle
Knee
Act
uato
r for
ce (N
) 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