1

Investigations of a Robotic Testbed with
Viscoelastic Liquid Cooled Actuators

arXiv:1711.01649v2 [] 8 Mar 2018

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

Abstract—We design, build, and thoroughly test a new type of
actuator dubbed viscoelastic liquid cooled actuator (VLCA) for
robotic applications. VLCAs excel in the following five critical
axes of performance: energy efficiency, torque density, impact
resistence, joint position and force controllability. We first study
the design objectives and choices of the VLCA to enhance the
performance on the needed criteria. We follow by an investigation
on viscoelastic materials in terms of their damping, viscous and
hysteresis properties as well as parameters related to the longterm performance. As part of the actuator design, we configure
a disturbance observer to provide high-fidelity force control
to enable a wide range of impedance control capabilities. We
proceed to design a robotic system capable to lift payloads of
32.5 kg, which is three times larger than its own weight. In
addition, we experiment with Cartesian trajectory control up to
2 Hz with a vertical range of motion of 32 cm while carrying a
payload of 10 kg. Finally, we perform experiments on impedance
control and mechanical robustness by studying the response of
the robotics testbed to hammering impacts and external force
interactions.
Index Terms—Viscoelastic liquid cooled actuator, Torque feedback control, Impedance control.

I. I NTRODUCTION
ERIES elastic actuators (SEAs) [1] have been extensively
used in robotics [2], [3] due to their impact resistance and
high-fidelity torque controllability. One drawback of SEAs is
the difficulty that arises when using a joint position controller
due to the presence of the elastic element in the drivetrain. To
remedy this problem the addition of dampers has been previously considered [4]–[6]. However, incorporating mechanical
dampers makes actuators bulky and increases their mechanical
complexity.
One way to avoid this complexity is to employ elastomers
instead of metal springs. Using a viscoelastic material instead
of combined spring-damper systems enables compactness [7]
and simplified drivetrains [8]. However, it is difficult to
achieve high bandwidth torque control due to the nonlinear
behavior of elastomers. To address this difficulty, [9] models
the force-displacement curve of elastomer using a “standard
linear model.” The estimated elastomer force is employed in
a closed-loop force controller. Unfortunately, the hysteresis in
the urethane elastomer destabilized the system at frequencies
above 2 Hz. In contrast our controllers achieve a bandwidth of
70 Hz. The study on [10] accomplishes reasonably good torque
control performance, but the range of torques is small to ensure
that the elastomer operates in the linear region; our design and
control methods described here achieve more than an order of
magnitude higher range of torques with high fidelity tracking.
To sufficiently address the nonlinear behavior of elastomers,
which severely reduce force control performance, we empiri-

S

cally analyze various viscoelastic materials with a custom-built
elastomer 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 various
feedback control schemes. In a previous work, we showed that
the 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-fidelity
force feedback control. Here, we analyze the phase margins
of various feedback controllers and empirically show their
operation in the new actuators. We verify the stability and
accuracy of our controllers by studying impedance control and
impact tests.
To test our new actuator, we have designed a two degree-offreedom (DOF), robotic testbed, shown in Fig. 5. It integrates
two of our new actuators, one in the ankle, and another in the
knee, while restricting motions to the sagittal plane. With the
foot bolted to the floor for initial tests, weight plates can be
loaded on the hip joint to serve as an end-effector payload.
We test operational space control to show stable and accurate
operational space impedance behaviors. We perform dynamic
motions with high payloads to showcase another important
aspect of our system, which is its cooling system aimed at
significantly increasing the power of the robot.
The torque density of electric motors is often limited by
sustainable core temperature. For this reason, the maximum
continuous torque achieved by these motors can be significantly enhanced using an effective cooling system. Our
previous study [13] analyzed the improvements on achievable
power based on thermal data of electric motors and proposed
metrics for design of cooling systems. Based on the metrics
from that study, we chose a 120 W Maxon EC-max 40, which
is expected to exert 3.59 times larger continuous torque when
using the proposed liquid cooling system. We demonstrate the
effectiveness of liquid cooling by exerting 860N continous
force during 5 min and 4500N peak force during 0.5s while
keeping the core temperatures below 115◦C, which is much
smaller than the maximum, 155◦C. We accurately track fast
motions of 2 Hz while carrying a 10 kg payload for endurance
tests. In addition we perform heavy lift tests with a payload
of 32.5 kg keeping the motor temperatures under 80◦C.
The main contribution of this paper is the introduction of a
new viscoelastic liquid cooled actuator and a thorough study
of its performance and its use on a multidof testbed. We
demonstrate that the use of liquid cooling and the elastomer
significantly improve joint position controllability and power
density over traditional SEAs. More concretely, we 1) design

2

a new actuator, dubbed the VLCA, 2) extensively study
viscoelastic materials, 3) extensively analyze torque feedback
controllers for VLCAs, and 4) examine the performance in a
multidof prototype.
II. BACKGROUND
Existing actuators can be characterized using four criteria:
power source (electric or hydraulic), cooling type (air or liquid), elasticity of the drivetrain (rigid or elastic), and drivetrain
type (direct, harmonic drive, ball screw, etc.) [14], [15]. One of
the most powerful and common solutions is the combination of
hydraulic, liquid-cooling, rigid and direct drive actuation. This
achieves high power-to-weight and torque-to-weight ratios,
joint position controllability, and shock tolerance. Existing
robots that use this type of actuators include Atlas, Spot, Big
Dog, and Wildcat of Boston Dynamics, BLEEX of Berkeley
[16], and HyQ of IIT [17]. However, hydraulics are less
energy efficient primarily because they require more energy
transformations [18]. Typically, a gasoline engine or electric
motor spins a pump, which compresses hydraulic fluid, which
is modulated by a hydraulic servo valve, which finally causes
a hydraulic piston to apply a force. Each stage in this process
incurs some efficiency loss, and the total losses can be very
significant.
The combination of electric, air-cooled, rigid, and harmonic
drive actuators are other widely used actuation types. Some
robots utilizing these actuator types include Asimo of Honda,
HRP2,3,4 of AIST [19], HUBO of KAIST [20], REEM-C of
PAL 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 control
and high torque density. For example, LOLA’s theoretical
knee peak torque-density (129N m/kg) is comparable to ours
(107N m/kg), although they did not validate their number
experimentally and their max speed is roughly 2/3 of our max
speed [22]. Compared to us, low shock tolerance, low fidelity
force sensing, and low efficiency gearboxes are common
drawbacks of these type of actuators. According to Harmonic
Drive AGs catalog, the efficiency of harmonic drives may be
as poor as 25% and only increases above 80% when optimal
combinations of input shaft speed, ambient temperature, gear
ratio, and lubrication are present. Conversely, the efficiency of
our VLCA is consistently above 80% due to the use of a ball
screw mechanism.
[25] used liquid cooling for electric, rigid, harmonic
drive actuators to enhance continuous power-to-weight ratio.
The robots using this type of actuation include SCHAFT
and Jaxon [26]. These actuators share the advantages and
disadvantages of electric, rigid, harmonic drive actuators, but
have a significant increase of the continuous power output
and torque density. One of our studies [13], indicates a 2x
increase in sustained power output by retrofitting an electric
motor with liquid cooling. Other published results indicate a
6x increase in torque density through liquid cooling [14], [27],
though such performance required custom-designing a motor
specifically for liquid cooling. In our case we use an off-theshelf electric motor. In contrast with our design, these actuators

do not employ viscoelastic materials reducing their mechanical
robustness and high quality force sensing and control.
Although the increased power density achieved via liquid cooling amplifies an electric actuator’s power, the rigid
drivetrain is still vulnerable to external impacts. To increase
impact tolerance, many robots (e.g. Walkman and COMAN
of IIT [28], Valkyrie of NASA [29], MABEL and MARLO in
UMich [30], [31], and StarlETH of ETH [32]) adopt electric,
air-cooled, elastic, harmonic drive actuators. This type of
actuation provides high quality force sensing, force control,
impact resistance, and energy efficiency. However, precise
joint position control is difficult because of the elasticity in
the drivetrain and the coupled effect of force feedback control
and realtime latencies [33]. Low efficiency originating from
the harmonic drives is another drawback.
As an alternative to harmonic drives, ball screws are great
drives 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 show
energy efficiency, good power and force density, low noise
force sensing, high fidelity force controllability, and low
backlash. Compared to these actuators our design significantly
reduces the bulk of the actuator and increases its joint position
controllability. There are some other actuators that have special
features such as the electric actuators used in MIT’s cheetah
[40], which allow for shock resistance through a transparent
but backlash-prone drivetrain. However, the lack of passive
damping limits the joint position controllability of these type
of actuators compared to us.
III. VISCOELASTIC MATERIAL CHARACTERIZATION
The primary driver for using elastomers instead of metal
springs is to benefit from their intrinsic damping properties.
However, the mechanical properties of viscoelastic materials
can be difficult to predict, thus making the design of an
actuator based on these materials a challenging endeavor.
The most challenging aspect of incorporating elastomers
into the structural path of an actuator is in estimating or modeling their complex mechanical properties. Elastomers possess both hysteresis and strain-dependent stress, which result
in nonlinear force displacement characteristics. Additionally,
elastomers also exhibit time-varying stress-relaxation effects
when exposed to a constant load. The result of this effect is a
gradual reduction of restoration forces when operating under a
load. A third challenge when using elastomers in compression
is compression set. This phenomenon occurs when elastomers
are subjected to compressive loads over long periods of time.
An elastomer that has been compressed will exhibit a shorter
free-length than an uncompressed elastomer. Compression set
is 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 designed experiments to empirically measure the following four
properties of our viscoelastic springs: 1) force versus displacement, 2) stress relaxation, 3) compression set, and 4)

3

E-stop
Load cell
Displacement
sensor
Elastic material

EtherCAT-based
embedded
control system
Belt drive
BLDC motor

2500
2000
1500

Force (N)

1000

Ball screw drive

(a) Viscoelastic material Testbed

0
-500

Spring steel
Viton 75A
Polyurethane 80A
Polyurethane 90A
EPDM 80A
Reinforced Silicon 70A
Buna- N 90A
Silicone 90A

-1000

Reinforced silicone 70A

Viton 75A
Buna-N 90A
Polyurethane 80A

Polyurethane 90A
Spring steel

500

EPDM 80A

-1500
-2000

0

1

2

3

4

5

-2500

6

-5

Compression set (%)

-4

-3

-2

-1

0

1

2

3

Dispacement (m)

5
10 -4

(c) Force vs Displacement curve

Phase (deg)

Force (N)

Magnitude (dB)

(b) Complession set

4

time (sec)

(d) Stess relaxation

Increasing system bandwidth

Spring steel
Viton 75A
Buna-N 90A
Polyurethane 90A

Frequency (Hz)

(e) Dynamic response of four elastomer

Fig. 1. Viscoelastic material test. (a) The elastomer testbed is designed and constructed to study various material properties of candidate viscoelastic
materials. (b) We measured each elastomers free length both before and after they were placed in the preloaded testbed. (c) A strong correlation between
material hardness and the materials stiffness can be observed. An exception to this correlation is the fabric reinforced silicone which we hypothesize had
increased stiffness due to the inelastic nature of its reinforcing fabric. Nonlinear effects such as hysteresis can also be observed in this plot. (d) We command
a rapid change in material displacements and then measured the materials force change versus time for 300 seconds. Note that the test of reinforced silicone
70A is omitted due to its excessive stiffness. (d) Although the bandwidths of the four responses are different, their damping ratios (signal peak value) are
relatively constant, which implies different damping.

frequency response, which will be used to characterize each
material’s effective viscous damping. We built a viscoelastic
material testbed, depicted in Fig. 1(a), to measure each of
these properties. We selected and tested the seven candidate
materials that are listed in Table I. The dimension of the tested
materials are fairly regular, with 46mm diameter and 27mm
thickness.
A. Compression set
Compression set is the reduction in length of an elastomer
after prolonged compression. The drawback of using materials with compression set in compliant actuation is that the
materials must be installed with larger amounts of preload
forces to avoid the material sliding out of place during usage.
To measure this property, we measured each elastomers free
length both before and after the elastomer was placed in
the preloaded testbed. The result of our compression set
experiments are summarized in Table I.

B. Force versus displacement

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

4

Materials

Compression Linearity
set (%)
(R-square)

Linear stiffness
(N/mm)

Spring steel

0

0.996

860.8

Polyurethane 90A

2

0.992

8109

Preloaded elastic
modulus (N/mm)

Material damping
(N s/m)

Creep
(%)

Material
Cost ($)

0

0

-

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 I
S UMMARY OF VISCOELASTIC MATERIALS

C. Stress relaxation

E. Selection of Polyurethane 90A

Stress-relaxation is an undesirable property in compliant
actuators for two reasons. First, the time-varying force degrades the quality of the compliant material as a force sensor.
When a material with significant stress-relaxation properties
is used, the only way to accurately estimate actuator force
based on deflection data is to model the effect and then pass
deflection 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 that
it can lead to the loss of contact forces in compression-based
spring structures.
The experiment for stress relaxation is conducted as follow:
1) enforce a desired displacement to a material, 2) record
the force data over time from the load cell, 3) subtract the
initially measured force from all of the force data. Empirically
measured stress-relaxation properties for each of the materials
are shown in Fig. 1 (c), which represents force offsets as
time goes under the same displacement enforced. Note that
each material shows different initial force due to the different
stiffness and each initial force data is subtracted in the plot.

A variety of other experiments were conducted to strengthen
our analysis and are summarized in Table I. Based on these
results, Polyurethane 90A appears to be a strong candidate
for viscoelastic actuators based on its high linearity (0.992),
low compression set (2%), low creep (15%), and reasonably
high damping (16000 N s/m). It is also the cheapest of the
materials and comes in the largest variety of hardnesses and
sizes.

D. Dynamic response
In regards to compliant actuation, the primary benefit of
using an elastomer spring is its viscous properties, which can
characterize the dynamic response of an actuator in series with
such a component. To perform this experiment, we generate
motor current to track an exponential chirp signal, testing
frequencies between 0.001Hz and 200Hz. Given the inputoutput relation of the system, we can fit a second order transfer
function to the experimental data to obtain an estimate of
the system’s viscous properties. However, this measure also
includes the viscoelastic testbed’s ballscrew drive train friction
(Fig. 1(a)). To quantify the elastomer spring damping independently of the damping of the testbed drive train, the latter
(8000 N s/m) was first characterized using a metal spring,
and then subtracted from subsequent tests of the elastomer
springs to obtain estimates for the viscous properties of the
elastomer materials. Fig. 1(d) shows the frequency response
results for current input and force output of three different
springs, while controlling the damping ratio. The elastomers
have higher stiffness than the metal spring, hence their natural
frequencies are higher.

IV. V ISCOELASTIC L IQUID C OOLED 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 also
one of the critical design parameters, which encourage us
to use elastomers instead of metal springs and mechanical
dampers. Our previous work [13] shows a significant improvement in motor current, torque, output power and system
efficiency for liquid cooled commercial off-the-shelf (COTS)
electric motors and studied several Maxon motors for comparison. As an extension of this previous work, in this new
study we studied COTS motors and their thermal behavior
models and selected the Maxon EC-max 40 brushless 120 W
(Fig. 2(e)), with a custom housing designed for the liquid
cooling system (Fig. 2(h)). The limit of continuous current
increases by a factor of 3.59 when liquid convection is used
for cooling the motor. Therefore, a continuous motor torque
of 0.701 N · m is theoretically achievable. Energetically, this
actuator is designed to achieve 366 W continuous power
and 1098W short-term power output with an 85% ball screw
efficiency (Fig. 2(b)) since short-term power is generally three
time larger than continuous power. With the total actuator
mass of 1.692 kg, this translates into a continuous power of
216W/kg and a short-term power of 650W/kg. The liquid
pump, radiator, and reservoir are products of Swiftech which
weight approximately 1kg. By combining convection liquid
cooling, high power brushless DC (BLDC) motors, and a
high-efficiency ball screw, we aim to surpass existing electric
actuation technologies with COTS motors in terms of power
density.
In terms of controls, a common problem with conventional
SEAs is their lack of physical damping at their mechanical
output. As a result, active damping must be provided from
torque produced by the motor [42]. However, the presence of

5

(e) BLDC Motor

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

(f) Quadrature encoder
(g) Temperature sensor
(h) Liquid cooling jacket

Opposite side

Motor part
Rubber part
Load part

(i) Tube connector

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

ground

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

signal latency and derivative signal filtering limit the amount
by which this active damping can be increased, resulting
in SEA driven robots achieving only relatively low output
impedances [33] and thus operating with limited joint position
control accuracy and bandwidth. Our VLCA design incorporates damping directly into the compliant element itself,
reducing the requirements placed on active damping efforts
from the controller. The incorporation of passive damping aims
to increase the output impedance while retaining compliance
properties, resulting in higher joint position control bandwidth.
The material properties we took into consideration will be
introduced in Section III. The retention of a compliant element
in the VLCA drive enables the measurement of actuator forces
based on deflection. The inclusion of a load cell (Fig. 2(c)) on
the actuators output serves as a redundant force sensor and is
used to calibrate the force displacement characteristics of the
viscoelastic element.
Mechanical power is transmitted when the motor turns a
ball nut via a low-loss timing belt and pulley (Fig. 2 (a)),
which causes a ball screw to apply a force to the actuator’s
output (Fig. 2(d)). The rigid assembly consisting of the motor,
ball screw, and ball nut connects in series to a compliant viscoelastic element (Fig. 2(j)), which connects to the mechanical
ground of the actuator (Fig. 2(k)). When the actuator applies a
force, the reaction force compresses the viscoelastic element.
The viscoelastic element enables the actuator to be more shock
tolerant than rigid actuators yet also maintain high output
impedance due to the inherent damping in the elastomer.
V. ACTUATOR F ORCE F EEDBACK C ONTROL
To demonstrate various impedance behaviors in operational
space, robots must have a stable force controller. Stable and
accurate operational space control (OSC) is not trivial to
achieve because of the bandwidth interference between outer
position feedback control (OSC) and inner torque feedback
control [11]. Since stable torque control is a critical component
for a successful OSC implementation, we extensively study
various force feedback controls.

Jm (kg m2 )

bm (N m s)

mr (kg)

br (N s/m)

kr (N/m)

3.8e−5

2.0e−4

1.3

2.0e4

5.5e6

TABLE II
ACTUATOR PARAMETERS

The first step in this analysis is to identify the actuator
dynamics. The transfer functions of the reaction force sensed
in the series elastic actuators (elastomer deflection) are well
explained in [43]. When the actuator output is fixed, the
transfer function from the motor current input to the elastomer
deflection is given by
Px =

xr
ηkτ Nm
=
, (1)
2 + m )s2 + (b N 2 + b )s + k
im
(Jm Nm
r
m m
r
r

where η, kτ , Nm , and im are the ball screw efficiency,
the torque constant of a motor, the speed reduction ratio of
the motor to the ball screw, and the current input for the
motor, respectively. The equations follow the nomenclature in
Fig. 3(a). We can find η, kτ , and Nm in data sheets, which are
0.9, 0.0448 N · m/A, and 3316 respectively. The gear ratio of
the drivetrain is computed by dividing the speed reduction of
pulleys (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 measurement
from the load cell by the elastomer deflection. The other
parameters are estimated by comparing the frequency response
of the model and experimental data. The frequency response
test is done with the ankle actuator while prohibiting joint
movement with a load and an offset force command. The
results are presented in Fig. 3 with solid gray lines. Note that
the dotted gray lines are the estimated response from the transfer function (measured elastomer force/ input motor force)
using the parameters of Table. II. The estimated response and
experimental result match closely with one another, implying
that the parameters we found are close to the actual values.
We also study the frequency response for different load
masses to understand how the dynamics changes as the joint
moves. When 10kg is attached to the end of link, the reflected

6

(a)
VCLA

-149

o

27.5 Hz

Fig. 3. Frequency response of VLCA. Gray solid lines are experimental data
and the other lines are estimated response with the model using empirically
parameters.

(b)

Open-loop
PDm
PIDm
PDf
PDm + DOB

60

Magnitude (dB)

Experiment result

40
20
0
-20
-40
0

Phase margin

-45

47.6

-90

41.0

1) Proportional (P) + Derivative (Df ) using velocity signal
obtained by a low-pass derivative filtered elastomer
deflection
2) Proportional (P) + Derivative (Dm ) using motor velocity
signal measured by a quadrature encoder connected to
a motor axis
The second controller (PDm ) has benefits over the first one
(PDf ) with respect to sensor signal quality. The velocity of
motor is directly measured by a quadrature encoder rather than
low-pass filtered elastomer deflection data, which is relatively
noisy and lagged. In addition, Fig. 4 shows that the phase
margin of the second controller (47.6) is larger than the first
one (17.1).
To remove the force tracking error at low frequencies, we
consider two options: augmenting the controller either with
integral control or with a DOB on the PDm controller. To
compare the two controllers, we analyzed the phase margins
of all the mentioned controllers. First, we chose to focus on
the location where the sensor data returns in order to address
the time delay of digital controllers (Fig. 4 (a) and (c)). Next,
we have to compute the open-loop transfer function for each
closed loop system. For example, the PDf controller’s closed
loop transfer function is

kr Px
kp (Fr − e−T s Fk ) + Fr − kd,f Qd e−T s Fk ,
N
(2)
where Fk , Fr , T , and Qd are the measured force from a
elastomer deflection, a reference force, a time delay, a low
pass derivative filter, respectively.For convenience, we use N
instead of the multiplication of three terms, ηkτ Nm . When

34.0

-225
10

(c)

42.8
17.7

-135
-180

mass to the actuator varies from 1500kg to 2500kg because
the length of the effective moment arm changes depending on
joint position. In Fig. 3(b), the bode plots are presented and
the response is not significantly different than the fixed output
case. Therefore, we design and analyze the feedback controller
based on the fixed output dynamics.
For the force feedback controller, we first compare two
options, which we have used in our previous studies [11],
[12]:

Fk =

kr

-3dB

Phase (deg)

Inf. mass
2500 kg
2000 kg
1500 kg

0

10

1

10 2

Frequency (Hz)

VCLA

kr

s

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

gathering the term with e−T s of Eq. (2), we obtain
Fk
kr Px (Kp + 1)/N
=
.
Fr
1 + e−T s kr Px (Kp + Kd,f Qd )/N

(3)

Then, the open-loop transfer function of the closed system
with the time delay is
open
PPD
= kr Px (Kp + Kd,f Qd )/N.
f

(4)

We can apply the same method for the PIDm and PDm +DOB
controllers.
The transfer function of PIDm , which is presented in
Fig. 4(c), is
1
kr Px 
(Fr − e−T s Fk )(Kp + Ki ) + Fr
Fk =
N
s
(5)
Fk 
−T s
− Kd,m e
sNm
.
kr
Then it becomes
Fk
kr Px (Kp + Ki /s + 1)/N
=
.
Fr
1 + e−T s Px (kr (Kp + Ki /s) + Kd sNm )/N

(6)

When we apply a DOB instead of integral control, we need
the inverse of the plant. In our case, the plant of the DOB is
PDm , which is similar to Eq. (6) except that Ki and e−T s are
omitted:
kr Px (Kp + 1)
PPDm (= Pc ) =
.
(7)
N + Px (kr Kp + Kd,m sNm )

7

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

The formulation of PDm including the DOB, which is shown
in Fig. 4(c), is
Fk =

kr Px (Kp + 1)(Fd − e−T s Pc−1 Qτ d Fk )
, (8)
(N + e−T s Px (kr Kp + Kd,m sNm )) (1 − Qτ d )

the hip, and the foot is fixed on the ground. With this testbed,
we intended to demonstrate coordinated position control with
two VLCAs, the viability of liquid cooling on an articulated
platform, cartesian position control of a weighted end effector,
and verification of a linkage design.
The two joints each have a different linkage structure that
was carefully designed so that the moment arm accommodates
the expected torques and joint velocities as the robot posture
changes (Fig. 5). For example, each joint can exert a peak
torque of approximately 270 N m and the maximum joint
velocity ranges between 7.5 rad/s and 20+ rad/s depending
on the mechanical advantage of the linkage along the configurations. The joints can exert a maximum continuous torque
of 91 N m at the point of highest mechanical advantage. This
posture dependent ratio of torque and velocity is a unique
benefit of prismatic actuators.
Given cartesian motion trajectories, which are 2nd order Bspline or sinusoidal functions, the centralized controller computes the torque commands with operational space position
and velocity, which are updated by the sensed joint position
and velocity. The OSC formulation that we use is
−1
τ = AJhip
(ẍdes + Kp e + Kd ė − J˙hip q̇) + b + g,

(11)

where A, b, and g represent inertia, coriolis, and gravity
joint torque, respectively. ẍdes , e, and ė are desired trajectory
acceleration, position and velocity error, respectively. q̇ ∈ R2
is the joint velocity of the robot and τ is the joint torque. Jhip
is a jacobian of the hip, which is a 2 × 2 square matrix and
assumed to be full-rank.

where Qτ d is a second order low-pass filter. Then the transfer
function is
VII. R ESULTS
Fk
kr Px (Kp + 1)
.
=
We first conducted various single actuator tests to show
Fd
N (1 − Qτ d ) + e−T s (N Qτ d + Px (kr Kp + Kd,m sNm ))
(9) basic performance such as torque and joint position controllability, continuous and peak torque, and impact resistance. SubThe open-loop transfer function is
sequently, we focused on the performance of OSC using the
N Qτ d + Px (kr Kp + Kd,m sNm )
open
robotic testbed integrated with DOB based torque controllers
PPD
=
(10)
m +DOB
N (1 − Qτ d )
to demonstrate actuator efficiency and high power motions.
open
open
open
open
The bode plots of PPD
,
P
,
P
,
and
P
PDm
PIDm
PDm +DOB
f
are presented in Fig. 4(b). The gains (Kp , Kd,m , Ki ) are the A. Single Actuator Tests
same as the values that we use in the experiments presented in
Fig. 6(a) shows the experimental results of our frequency
Section VII-A, which are 4, 15, and 300, respectively. The PDf response testing as well as the estimated response based on
controller uses Kd Nm /kr for Kd,f to normalize the derivative the transfer functions. We compare three types of controllers:
gain. The cutoff frequency of the DOB is set to 15Hz because PD , PID , and PD + DOB. As we predicted in the
m
m
m
this is where the PDm +DOB shows a magnitude trend similar analysis of Section V, the PD + DOB controller shows less
m
to the integral controller (PIDm ). The results imply that the phase drop and overshoot than PID . The integral control
m
PDm +DOB controller is more stable than PIDm with respect feedback gain used in the experiment is 300 and the cutoff
to phase margin and maximum phase lag. This analysis is also frequency of the DOB’s Q filter is 60Hz, which shows
τd
experimentally verified in Section VII-A.
similar error to the PID controller (Fig. 6(b)). Another test
m

VI. ROBOTIC T ESTBED
We built a robotic testbed shown in Fig. 5. To demonstrate dynamic motion, we implemented an operational space
controller (OSC) incorporating the multi-body dynamics of
the robot. We designed and built a robotic testbed (Fig. 5)
consisting of two VLCAs - one for the ankle (q0 ) and one
for the knee (q1 ). The design constrains motion to the sagittal
plane, the robot carries 10kg, 23kg, or 32.5kg of weight at

presented in Fig. 6(c) also supports the stability and accuracy
of torque control. In the test, we command a ramp in joint
torque from 1 to 25N m in 0.1s. The sensed torque (blue solid
line) almost overlaps the commanded torque (red dashed line).
Fig. 6(d) is the result of a joint position control test designed
to show that VLCAs have better joint position controllability
than SEAs using springs. In the experiment, we use a joint
encoder for position control and a motor quadrature encoder
for velocity feedback. To compare the VLCAs performance

8

20
10

1.8

2

2.2

2.4

2.6

2.8

-1.8

JPos (rad)

Phase (deg)

(c) Torque fast response

Open (estimated)
(estimated)
(estimated)

-2

-2.4
1.6

1.8

2

2.2

2.4

2.6

70
1
60
0

50
40

-2
-3

2.8

30

0

1

2

3

time (sec)

20

(f) peak force

(d) Position fast response
Actuator force (N)

80

1000

150

500

100

0

-500

time (sec)

50

actuator force
core temperature (w/ liquid)
core temperature (w/o liquid)
0

50

100

150

200

250

0
350

300

Motor temperature (oC)

Error (dB)

(a) Frequency responses of different controllers

Frequency (Hz)

90

2

time (sec)

Reference

100

-1

(sim.) metal spring
(sim.) elastomer
(exp.) command
(exp.) sensed

-2.2

Frequency (Hz)

110

3

0
1.6

Open

x 103

4

command
sensed
Actuator force (N)

Magnitude (dB)

5

Motor temperature (oC)

Torque (Nm)

30

time (sec)

(e) Continous force and core temperature

(b) Error magintude and chirp test trajectories

Fig. 6. Torque Feedback Control Test. (a) Experimental data and estimated response based on the transfer functions are presented. Estimated response of
PD controller is identical to the PD+DOB since DOB theoretically does not change the transfer function. The plot show PD+DOB shows better performance
in terms of less overshoot and smaller phase drop near to the natural frequency. (b) We choose integral controller feedback gain that shows similar accuracy
of 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. The
right is torque trajectories in the time domain.
Load cell (solid holding)
Load cell (w/ elastomer)
Rubber deflection (solid holding)
Rubber deflection (w/ elastomer)

1000

Actuator force (N)

with that of spring-based SEAs, we present simulation results
for a spring-based SEA on the same plot as the experiment
result for the VLCA. The green dashed line is the simulated
step response of our actuator and the yellow dotted line is
the result of the simulation model using the same parameters
except the spring stiffness and damping. The spring stiffness
was selected to be 11% of the elastomer’s, based on the
results of our tests in Section III, and the damping for the
spring case was set to 8000 N s/m which only includes the
drivetrain friction. The results show a notable improvement in
joint position control when using an elastomer instead of a
steel spring.
Fig. 6(e) shows the continous force and the motor core temperature trend with and without liquid cooling. The observed
continous force is 860N and the motor core temperature settles
at 115◦C with liquid cooling. Fig. 6(f) is the the result of shortterm torque test. In the experiment, we fix the output of the
actuator and command a 31A current for 0.5s. The observed
force measured by a loadcell (Fig. 2(c)) is 4500N, which is
a little smaller than the theoretically expected value, 5900N.
Considering that the estimated core temperature surpassed
107◦C (< 155◦C limit), we expect that the theoretical value
is reasonable. Thus, we conclude that the maximum force
density of our actuator is larger than 2700N/kg and potentially
3500N/kg.
Fig. 7 shows loadcell and elastomer force data from the
impact tests. In the tests, we hit the loadcell connected to the
ball screw (Fig. 2(c)) with a hammer falling from a constant
height while fixing the actuator in two different places to

500

0

95% interval

-500

-1000

-2

0

2

4

6

8

10

12

14

time (ms)
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 elastic
element absorbes the external impact force.

compare the rigid actuator to viscoelastic actuator response. In
the rigid scenario, outer case of ballnut, a blue part in Fig. 2,
is fixed to exclude the elastomer from the external impact
force path. In the second case, we fixed the ground pin of the
actuator, which is depicted by a gray part in Fig. 2(l), to see
how the elastomers react to the impact.
The impact experiment is challenging because the number
of data points we can obtain is very small with a 1ms update
rate. To overcome the lack of data points, we estimate the
mean and variance of 83 trials by gaussian process regression.
The results presented in Fig. 7 imply that there is no significant
difference in the forces measured by the loadcell in both
cases, which is predictable because the elastic element is
placed behind the drivetrain. However, the elastomer does

Ankle

command
sensed

20
0

power
supply

14

16

18

20

22

24

14

16

18

20

22

24

40

Wm

Wb

0.2

Hip position (m)

joint

electric
motor

50

30

0
-0.1

14

16

18

20

22

24

1

Wk

Average efficiency

1.5

0.1

Wk / W m

Compliant in
horizontal direction

servo
drive

-20

Knee

Stiff in
vertical direction

Torque (Nm)

9

1
0.5

0.8
14

16

(a) Impedance control

22

0

0.6
0.4

-20
12

14

16

18

40

12

14

16

18

Hip position (m)

0.1

10

12

10

12

14

16

18

14

16

18

1

time (sec)

(b) Operational space impact test

0.9

0.1

0.85

0

0.8

-0.1
2

command
2.5
sensed

0.9

0.75
0.7

0.8

0.65

0.7
0.6

0.6

1.5

time (sec)

1.5

2

2.5

3

3.5

5 (sec)
3
1
0.5
0.3

0.2
0
-0.2

0.5

1

1.5

2

2.5

3

3.5

0
-0.1

0.8

1

1

time (sec)

0.2

1.5

0.5

-0.4

30
10

1

0

24

Wk / W b

Ankle

20

-10

10

Knee

Torque (Nm)

Hitting down

18

time (sec)

2

2.5

-0.05

0

0.05

(c) Fast up and down (1.7 Hz)
Fig. 8. Operational Space Impedance Control Test. (a) The robot
demonstrates different impedance: stiff in the vertical direction and compliant
in the horizontal direction. The high tracking performance of force feedback
control results in the overlapped commanded and sensed torques. (b) To
show the stability, we hit the weight with a hammer while operating the
impedance control. Even under the impact, force control show stable and
accurate tracking. (c) The robot demonstrates a 1.7Hz up and down motion
while carrying 10kg weight at the hip, and shows a position error of less than
2.5cm.

play a significant role in absorbing energy from the impact
which is evident from large elastomer deflection in the second
case. Thus, the presence of the elastic element mitigates the
propagation of an impulse to the link where the actuator
grounds.
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 horizontal
direction (x) and to be stiff in the vertical direction (y).
When pushing the hip with a sponge in the x direction, the
robot smoothly moves back to comply with the push, but it
strongly resists the given vertical disturbance to maintain the

Fig. 9. Efficiency analysis of the ankle actuator. Efficiencies of mechanical
system 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 the
motor power and the ratio of the joint power and power supply’s input power.

commanded height. To show the stability of our controller, we
also test the response to impacts by hitting the weight with a
hammer (Fig. 8(b)). Even when there are sudden disturbances,
the torque controllers rapidly respond to maintain good torque
tracking performance as shown in Fig. 6(d).
Fig. 8(c) shows the tracking performance of our system
while following a fast vertical hip trajectory. While traveling 0.3m with 1.7Hz frequency, the hip position errors are
bounded by 0.025m. This result demonstrates that our system
is capable of stable and accurate OSC, which is challenging
because of the bandwidth conflict induced by its cascaded
structure.
C. Efficiency Analysis
Fig. 9 explains the power flow from the power supply to the
robot joint. Input current (Ib ) and voltage (Vb ) are measured
in the micro-controllers and the product of those two yields
the input power from the power supply. θ̇m is measured by the
quadrature encoder connected to the motor’s axis (Fig. 2(f))
and τm is computed from kτ im with im measured in the
micro-controller. Joint velocity is low-pass derivative filtered
joint positions measured at the absolute joint encoders. The
torque (τk ) is computed from projecting the load cell data
across the linkage’s effective moment arm.
In this test, the robot lifts a 23kg load using five different
durations to observe efficiency over a range of different speeds
and torques. The results are presented in Fig. 9 with the
description of three different power measures. The sensed
torque data measured by a load cell is noisy; therefore, we
compute the average of the drivetrain efficiency for a clearer
comparison. The averages are the integrations of efficiency divided by the time durations. Here we only integrate efficiency
while the mechanical power is positive, to prevent confounding
our results by incorporating the work done by gravity.

7

7.5

8
200
100
0
-100

0
7

joint torque

7.5
mechanical power

8
400
200
0
-200
-400
-600

200
100
0
6.5

7

7.5

Mechanical power (W)

Ankle

7

200
-200
6.5

Knee

8

5
4
6.5

Joint torque (Nm)

7.5

8

(a) 2Hz up and down motion

Ankle

0

45
40

-1000

35

-2000
-3000
0

0.5

1

1.5

2

2.5

actuator force
3
3.5
4
motor
temperature

30
4.5
80

Knee

-1000

60

-2000
-3000

40

-4000
0

Power (W)

Ankle
Knee

6.5
6

1000

Actuator force (N)

command
joint encoder
motor encoder

2.6
2.4
2.2
2
1.8

0.5

1

1.5

2

2.5

3

3.5

4

Motor temperature (oC)

Joint position (rad)

10

4.5

total
ankle
knee

1500
1000
500
0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

time (sec)

(b) Heavy weight lift

Fig. 10. High power motion experiment. (a) Joint position data from joint encoder and motor encoder are shown. In this experiment, the maximum observed
torque of the ankle joint is 250 N m and the maximum observed mechanical power of the knee joint is 310W. (b) The robot lifts by 0.3m a 32.5 kg load
during 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 efficiency
is approximately 0.89, which means that we lose only a small
amount of power in the drivetrain and most of the torque
from the motor is delivered to the joint. This high efficiency
indicates only minor drivetrain friction, which is beneficial for
dynamics-based motion controllers.
D. High Power Motion Experiment
To demonstrate high power motions such as fast vertical
trajectories and heavy payload lifts, we use the motor position
control mode, which uses the quadrature encoders attached
directly to the motor for feedback. Fig. 10(a) presents the
results of a test comprised of 2Hz vertical motion with 0.32
m of travel while carrying a load of 10 kg at the hip.
With respect to mechanical power, the knee joint repeatedly
exerts 305W, which is close to the predicted constant power
(360W). Although the limited range of motion makes it hard
to demonstrate continuous mechanical power, these results
convincingly support our claim of enhanced continuous power
enabled through liquid cooling.
Fig. 10(b) presents another test in which the robot lifts a
32.5kg weight. We can see that the robot operates in the safe
region (≤ 5900N and ≤ 155◦C) while demonstrating high
power motion.

6(e). As we can see, when turning off liquid cooling the
temperature rises quickly above safety limits whereas when
turning on the cooling we can sustain large payload torques
for long periods of time. The use of elastomers versus steel
springs has demonstrated a clear improvement on joint position
performance as shown in Fig. 6(d). This capability is important
to achieve a large range of output joint or Cartesian space
impedances.
In the future we will explore further reducing the size
of our viscoelastic liquid cooled actuators. Maintaining the
current compact design structure we can still reduce another
significant percentage the bulk of the actuator by exploring
new types of bearings, ballnut sizes and piston bearings at the
front end of the actuator. We will also explore using different
material for the liquid cooling actuator jacket. The current
polyoxymethylene material is easily breakable and develops
cracks due to the vibrations and impacts of this kind of robotic
applications. In the future we will switch to sealed metal
chambers for instance. Further in the future we will consider
designing our own motor stators and rotors for improved performance. We expect this kind of actuators to make their way
into full humanoid robots and high performance exoskeleton
devices and we look forward to participate in such interesting
future studies.
ACKNOWLEDGMENT

VIII. C ONCLUDING R EMARKS
Overall our main contribution has been on the design and
extensive testing of a new viscoelastic liquid cooled actuator
for robotics.
One of the tests addressed is impedance control in the
operational space instead of joint impedance control. It is often
the case that humanoid robots require impedance control in
the operational space. For instance, controlling the operational
space impedance can enable improved locomotion behaviors
such as running. Our controllers demonstrate that we can
control the impedance in the Cartesian operational space as
a potential functionality for future robotic systems. The use
of liquid cooling has allowed to sustain high output torque
for prolonged times as shown in the experiments of Fig.

The authors would like to thank the members of the
Human Centered Robotics Laboratory at The University of
Texas at Austin for their help and support. This work was
supported 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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