F.C.T. van der Helm
H. van der Kooij
Biomechanical Engineering, BMTI
University of Twente
P.O. Box 217, 7500AE Enschede
A Series Elastic- and
Actuation System for
Use as TorqueActuator
Within the context of impedance controlled exoskeletons, common
have a complex structure or are poor torque sources, due to gearing
or heavy nonlinearity. Considering our application, an impedance
controlled gait rehabilitation robot for treadmill-training, we de-
signed an actuation system that might avoid these drawbacks. It
combines a lightweight joint and a simple structure with adequate
torque source quality. It consists of a servomotor, a flexible Bowden
tic element. A basic model was developed that is shown to describe
the basic dynamics of the actuator well enough for design purpose.
in a gait rehabilitation robot. The demanded force tracking band-
widths were met: 11 Hz bandwidth for the full force range (de-
manded 4 Hz) and 20 Hz bandwidth for smaller force range (de-
manded 12 Hz). The mechanical output impedance of the actuator
could be reduced to hardly perceptible level. Maxima of about 0.7
than 2.5% of the maximal force output. These peaks were caused by
the stick friction in the Bowden cables.
Spring stiffness variation showed that both a too stiff and a too
maximum allowable controller gain. The relatively low control gain
then causes a larger effect of stick in the force output, resulting in
a less smooth output in general. Low spring stiffness, on the other
side, decreases the performance of the system, because saturation
will occur sooner.
KEY WORDS—actuator design, cable transmission, exo-
skeleton, impedance control, rehabilitation robotics
The International Journal of Robotics Research
Vol. 25, No. 3, March 2006, pp. 261-281
©2006 SAGE Publications
cb,s,tot= Stiffness of, index: b – Bowden cable; s – SE spring;
tot – Bowden cable and SE spring together [N/m]
Fa,m= Force, index: a – at actuator output; m – in the motor
km= Motor constant, gain from motor control command to
motor force [N/V]
KH= Gain of the uncontrolled actuator transfer function
KZ= Gain of the uncontrolled output impedance transfer
l = Spring-length [m]
M = Reflected motor mass [kg]
r = Radius of knee actuator disc [m]
R = Vector of sampled sine
T = Torque [Nm]
u = Control command [V]
x1,2,3= Position, index: 1 – on the motor side of the Bowden
cable; 2 – on the actuator side of the Bowden cable; 3 – on
the output side of the SE element [m]
y = Sampled measurement vector
ωe= Eigenfrequency [rad/s]
θ =Angular displacement corresponding to spring length
ζ = Damping coefficient
..l= Concerning a load
..ref= Reference value
∧= Estimated parameter
C = Controller transfer function
Hactuator= Transfer function of the uncontrolled actuator,
from control command to force output [N/V]
Hclosedloop= Transfer function of the feedback controlled
actuator, from reference force to actual force output
262THE INTERNATIONAL JOURNAL OF ROBOTICS RESEARCH / March 2006
Zactuator= Impedance transfer function of the uncontrolled
Zclosedloop= Impedance transfer function of the controlled
2.1. Exoskeleton Robots
Exoskeletons are a specific type of robots meant for interac-
basically an actuated skeleton-like external supportive struc-
ture. Such robots are usually meant for:
a. extending or replacing human performance, for exam-
ple in military equipment (Lemley 2002), or rehabili-
tation of impaired function (Pratt et al. 2004),
b. interfacing; creating physical contact with an illusion-
ary physical environment or object; these haptic de-
vices are usually referred to as kinaesthetic interfaces.
Possible applications appear for example in gaming
and advanced fitness equipment, or in creating “telep-
resence” for dealing with hazardous material or diffi-
cult circumstances from a safe distance (Schiele and
itation of arm functionality (Tsagarakis and Caldwell
2003) or gait (Colombo et al. 2002) after a stroke.
Every typical application brings about specific demands from
a mechatronical design viewpoint, on total concept as well as
on mechanical design, actuator selection and control outline
level. The actuator discussed in this article was designed for
use in an exoskeleton for gait training purpose, but might find
wider application in other types of exoskeleton robots. First
of all the specific application will be described, followed by
design, model and performance indication of the actuator.
2.2. Context: a Gait Rehabilitation Robot
We are developing a LOwer-extremity Powered ExoSkeleton
(LOPES) to function as a gait training robot.The target group
consists of patients with impaired motor function due to a
stroke (CVA).The robot is built for use in training on a tread-
more effective for patients and less demanding for physical
therapists. This claim is based on the assumptions that:
• intensive training improves both neuromuscular func-
tion and all day living functionality (Kwakkel et al.
• a robot does not have to be less effective in training
a patient than a therapist (Reinkensmeyer et al. 2004;
Richards et al. 2004),
• a well reproducible and quantifiable training program,
as is feasible in robot-assisted training, would help to
obtain clinical evidence and might improve training
quality (Reinkensmeyer et al. 2004).
The main functionality of LOPES will be replacing the
physiotherapists’mechanical interaction with patients, while
ments in the forward and sideward direction and in keeping
Within the LOPES project, it has been decided to realize
this concept by connecting the limbs of the patient to an “ex-
oskeleton” so that robot and patient move in parallel, while
walking on a treadmill (Figure 1). This exoskeleton is actu-
ated in order to realize well-chosen and adaptable supportive
ing enough foot clearance, stabilizing the knee, shifting the
walk as unhindered as possible, while offering a minimum of
necessary support and a safe training environment. Depend-
ing on training goals, some form of kinaesthetic environment
has to be added.This constitutes the main difference between
LOPES and the commercially available gait-trainers. Those
are either position controlled devices that overrule the patient
and/or allow only limited motions due to a limited number
of degrees of freedom, and/or are not fully actuated (Hesse
lenges of keeping balance and taking initiative in training.
et al. 2005).
In the control design of the exoskeleton in general two
of therapeutic interventions demanded in the LOPES project.
In one ideal mode, referred to as robot in charge, the robot
should be able to enforce a desired walking pattern, defined
technically characterized as a high impedance control mode.
In the other ideal mode, referred to as patient in charge, the
hindering him or her. This can be technically characterized
as a low impedance control mode. An intelligent controller
or intervention by a therapist then can vary the actual robot
behavior between these high and low impedance modes.
2.3. Impedance Control in Rehabilitation Robotics
In the robot-in-charge mode it is important that the robot has
enough bandwidth and power to realize the desired position-
ing performance with the desired, relatively high, impedance.
In the patient-in-charge mode it is important that interaction
troller, as is often applied in kinaesthetic (“force feedback”)
Veneman et al. /A Series Elastic- and Bowden-Cable-BasedActuation System 263
Hip abduction joints
Knee flexion joints
Hip flexion joints
Fig. 1. Preliminary design of an exoskeleton for the gait rehabilitation robot LOPES, with possible implementation of the
interfaces (Adams and Hannaford 2002). The schematic out-
line of this control setup is shown in Figure 2.
sure position and display force”. This implies that the quality
of the “haptic display” depends on the accuracy of the po-
sition sensors and the bandwidth and accuracy of the force
servos.This “force-bandwidth” will depend on both the robot
in general depends on these factors.
A fundamental limitation of impedance control is that the
impedance of the robot construction in every actuated degree
Figure 2). It could only be compensated for in the case of
a proper dynamical model of this impedance, and proper
measurements of position and velocity for stiffness (includ-
ing gravitation) and friction compensation respectively. Mass
compensation is only possible with explicit contact-force or
acceleration sensing.A solution for this limitation is to use a
lightweight, low-friction construction and a low-impedance
actuator, so that the impedance of the device is kept low
(Adams and Hannaford 2002). An important additional ad-
vantage of a lightweight, low-impedance actuated design is
its inherent collision safety (Zinn et al. 2004).
2.4. Actuator Demands in an Impedance Controlled
specific demands for the actuators in the robot. They should:
• be “pure” (low impedance) force sources;
• add little weight and friction to the moving robot con-
degree of freedom actuated by the considered actuator;
• be safe, even in case of failure;
• allow fast adjustment to the individual patient’s sizes;
• be powerful enough for the robot-in-charge task.
More specifically, it is required that the actuators should
be able to modulate their output force with 12 Hz for small
forces, and 4 Hz for the full force range. Maximum torques
differ per joint, and range from 25 to 60 Nm. Joint powers
range up to 250Watt per joint. These numbers were based on
study of the human gait cycle and the motion control range of
264THE INTERNATIONAL JOURNAL OF ROBOTICS RESEARCH / March 2006
Fig. 2. Basic outline of an impedance controlled device, applied on robotic therapy. Here the connections between device and
patient are taken as a part of the patient impedance, so that the device can be considered rigidly connected to the ‘patient’.
x indicates position, F forces.
1991) was studied to obtain maximal needed torques, speeds
control were studied to estimate maximum expected force-
control speed and accuracy of a common therapist.
The resulting actuator bandwidths are typically lower, and
the forces typically higher than in the specifications of com-
mon kinaesthetic devices which are intended for haptic dis-
play of a virtual object, but not to assist humans. Actua-
tors usually selected for kinaesthetic devices are either heavy
(like direct drive electro-motors) or poor force actuators (like
geared DC motors), or suffer from moderate suitability for a
rehabilitation setting due complex nonlinear behavior or lack
of safety (like pneumatic muscles or cylinders) (Robinson
2000). The alternative to use spatial transmissions (e.g., ca-
bles) generally hinders fast adjustment of the exoskeleton to
individual body sizes.
2.5. Article Outline
In this article an actuator will be presented that is feasible for
facilitating both low- and high-impedance control modes.
To avoid the mentioned drawbacks of conventional ac-
tuator technology a flexible Bowden-cable-based transmis-
sion is combined with a spring based feedback force control
loop. This allows for flexibly detaching the actuator from the
robot frame, while achieving appropriate force control per-
formance. The working principle is related to Series Elastic
Actuation (SEA) (Robinson 2000). The important difference
with standard SEA is the use of a Bowden cable transmis-
sion and the detachment of the power source from the robot
frame. A fundamental issue therefore is whether this adapta-
tion, which is expected to worsen performance, still allows
sufficient performance of the actuator system.
First, the construction of the proposed actuator system
will be presented. Secondly, a model of the actuator will be
derived, covering the basic dynamics. Such a model would
be useful for scaling this actuator for specific applications.
This model will be compared with measurements. Finally,
the achieved controlled performance will be shown. Perfor-
mance is defined as force tracking performance for the robot-
in-charge task, and amount of reduction of output impedance
for the patient-in-charge task.
3. Design of a Bowden-Cable-Driven Series
The basic idea in designing the actuator was to detach the ac-
dered, while little weight is added to the robot construction,
compared to the relatively heavy electro motors.
in an exoskeleton (Figure 3) as for example hip and knee
will be lost and no safety threat will occur to due unidirec-
tional forces. This choice implies that the force transfer from
the cables to the disc is friction based. The same applies to
the cable connecting the springs; to prevent slipping, strips of
high-friction synthetic material have been fixed on the inside
of the disk. Slippage would not affect the force output but
could shorten the motion range.
The power transmission from motor to joint is realized by
use of so called Bowden cables. A Bowden cable is a type
of flexible cable used to transmit power by the movement of
an inner cable relative to a hollow outer cable, generally a
spiral steel wire with a plastic outer sheath, often containing
an inner liner to reduce friction. Because Bowden-cables in-
troduce orientation-, speed- and tension-dependent friction,
friction compensation is needed. The angles of the curves in
Veneman et al. /A Series Elastic- and Bowden-Cable-BasedActuation System 265
Fig. 3. A global lay-out of the proposed actuator system. The actuated joint can be lightweight as the motor is placed on the
fixed world. On the right the final design of the joint alone is shown.
Fig. 4. The picture shows the actuated joint, the other side (not visible) of the Bowden cables is connected to a second disk
driven by a servo-motor; the latter side is situated on the fixed world.The cable with the two springs is the connection between
the actuated disk and the joint output axis. Numbered parts: 1. sensor mounts, 2. joint end-stop, 3. upper connection side of
the joint, 4. lower connection side of the joint, 5. set of two pretensioned compression springs, realizing a rotational spring
around the main joint axis; the series elastic element of the actuator, 6. set of two pairs of uninterrupted Bowden cables,
connected to the motor, transferring force to the actuator disk via friction. 7. actuator disk; this disk can rotate independently
of both connection sides of the joint, or rather, it is connected to them via a force coupling, not an angle coupling.
266THE INTERNATIONAL JOURNAL OF ROBOTICS RESEARCH / March 2006
the actual friction. Also wear and (pre-)tension of the cables
are important factors. Because these parameters are hardly
observable and their effects complexly interrelated, it is im-
control alone. Acceptable compensation may be achieved by
introducing a feedback force control loop. This requires a
force measurement located after the cable transmission.
We chose to use springs for force measurement. A spring
sensor, as its length can be considered proportional with the
force. Two compression springs were connected to the actu-
ator disk with a cable so that a torque spring is created in
between the actuator disk and the lower segment. The two
compression springs are pre-tensioned with the maximally
desired force, so that the connecting cable will always be un-
der tension during operation.
length can be considered proportional to the force output.
A higher compliance in the force sensor allows for higher
control gains in the feedback spring length control loop. This
way a better force control performance and actuator impact
resistance can be achieved. Adverse effects of for example
play and stick in transmissions can also be decreased this
The concept is similar to Series Elastic Actuation (SEA),
treated extensively in Robinson (2000). Its theoretical frame-
tuator presented here. The differences with Robinson (2000)
are that we constructed a rotational joint instead of a linear
(this has been implemented before, by Torres-Jara and Banks
(2004), but that design was meant for use in the motor axis),
integrated the actuator with the robot joint and added a Bow-
den cable transmission (common cable drives have been used
with SEA before, for example in the “Spring Turkey” (Pratt
et al. 2001)).
the bandwidth of the actuator compared to common SEA, as
it introduces friction and compliance into the position con-
trol loop. On the other hand, it is possible to select a heavier
motor, as the motor weight is of no importance in this setting
and a larger motor inertia will increase the bandwidth of the
actuator, as a smaller gear-ratio, thus a smaller reflected mass
can be used (Robinson et al. 1999).
Basic design parameters, besides the choice of motor and
gearing, are the actuator disk diameter and the stiffness of the
springs. The diameter is a compromise between size of the
joint versus low tension (thus friction) in the cables.The stiff-
minimal endpoint impedance combined with optimal nonlin-
ear (cable-) friction compensation (Robinson et al. 1999).
The proposed actuator was designed and built to function
as a knee joint. With this set-up (Figure 2.2, Extension 1,2),
all presented measurements were carried out. It has an ap-
proximate peak torque output of 30 Nm. Four Bowden cables
as series elastic element, as described in Table 1.
4. Model of theActuator
4.1. Linear Model
A basic model is assumed to be sufficient to describe the es-
sential linear behavior of the actuator (Robinson 2000; Sugar
model is presented as a translational Ideal Physical Model
(IPM, Figure 5).This means that all parameters and variables
were converted to the linear motion of the cables on the joint
disk. Conversions from the rotational to the translational do-
main and vice versa do not affect model behavior. In addition
to the IPM a control scheme is given (Figure 6).
model, obtained when the output axis is fixed, or fourth-order
obtained when a freely movable load with second-order dy-
namics is added. Basic elements are:
• the inertia M, which is dominated by the motor inertia,
• the stiffness ctot, which dominated by the combination
of the Bowden cable-stiffness cband the series elastic
element stiffness cs, as ctot=
• the load, which typically has specific second-order dy-
namics Ml, dl, cl.
This implies that in this model the mass/inertia of cables,
springs and knee cable disk were neglected. The use of a
current/torque-controlled servomotor is presupposed, but not
necessary; an alternative would be a voltage/velocity con-
The important transfer functions, which will also be mea-
sured and estimated, are:
• the actuator behavior, that is the transfer from control
command (u) to actual output force (Fa), or possibly
spring length (l).
• the force tracking, that is the transfer from reference
erence spring length (lref) to actual spring length (l).
refcs) to the actual force (Fa), or also from ref-
• the output impedance, that is the transfer from external
position (x3) to force output (Fa), or also from external
position (x3) to the actual spring length (l).
Veneman et al. /A Series Elastic- and Bowden-Cable-BasedActuation System 267
Table 1. Stiffness of the Different Springs and Their ResultingAngular StiffnessAround the JointAxis
Catalogue Value (kN/m)
High compliance spring
Medium compliance spring
Low compliance spring
Angular Stiffness [Nm/rad]
c [Nm ]
d [Nsm ]
c [Nm ]
Fig. 5. Outline of the essential dynamics of the actuator: the Ideal Physical Model (IPM) of the actuator. All degrees of
freedom are transferred to the translational domain. Fmis the motor force, x1the position of the motor mass, x2the position
of the actuator disk, which is the disk connecting Bowden cables with series elastic element, x3the position of the output
axis, which may be connected to a load or to the fixed world, or be left open, in which case basically a very small load mass
is connected. The system dynamics are described by the mass M, the stiffness of the Bowden cable cband the stiffness of the
series elastic element cs, and the damping d, and an arbitrary load defined by specific second-order dynamics Ml, dl, cl.
(x - x )=l
Fig. 6. Flow scheme of the IPM from Figure 5, without load and with an added controller. In this scheme ctotis the resulting
stiffness of cband cs, both the outputs Fa, the output force and l, the measured spring length, are defined. kmis the transfer
from control command u to actual motor force Fmand is taken to be a pure gain. lref, the reference length and l are defined as
input and output to show the position control loop. The actuator output force is Fa. Tracking considers the transfer from lref
to the output force or the actual spring length, and output impedance considers the transfer from x3, the position of the output
axis, to the output force.
268THE INTERNATIONAL JOURNAL OF ROBOTICS RESEARCH / March 2006
Depending on the situation it might be more feasible to
use deflection (l), forces (F), torques (T), or disk rotation
(θ) as in- and output. These conversions are all linear factors,
following Figure 7.
In the case that the load has infinite impedance (x3fixed),
Faof the uncontrolled actuator is
(jω)2+ 2ζωe(jω) + ω2
which is similar to a standard damped second-order system,
as described with the last term of the equation in terms of
system gain (KH = km) eigenfrequency (ωe) and damping
ratio (ζ ζ ζ). These three parameters can then be estimated from
A controller can be added, resulting in a closed loop trans-
C · Hactuator|Z=∞
1 + C · Hactuator|Z=∞
The output impedance, which is the transfer from x3to F(=
sl), is in the uncontrolled (u = 0) case
(jω)2+ 2ζωe(jω) + ω2
Note that both ωeand ζ ζ ζ are the same as in (1), but that KZ
differs from KH.
In the case that the controller is switched on and lref= 0,
the output impedance transfer function becomes
(jω)2+ 2ζωe(jω) + (1 + C?) · ω2
Typical model behavior
The typical dynamics of the modeled system, as described
by the transfer functions (1) and (3), is given in Figure 8.
enced in case of feedback control by changing the controller
C. For the case of a PID controller the influence of changing
the three basic parameters of a PID controller are given in
Fig. 7. Conversions as necessary to switch between several
in- and out-put definitions. cs is the stiffness of the series
This model can be used to predict the basic dynamics of
the system from design parameters. To validate the model, its
by a comparison of model output with measurements. Iden-
tification will be done by Process Model Identification, opti-
as described in Ljung (1999, 2003). All measurements were
done at sample rate 5 kHz, and down-sampled where needed
for proper identification. As input signal a crest-optimized
multisine signal was used, containing frequencies from 0.1–
20 Hz or 0.1–30 Hz. For reference also higher-order fits or
other identification methods were performed; this will then
be mentioned. To obtain a quality measure for the model fits,
the variance-accounted-for factor was chosen, which is de-
1 −var?y − ˆ y?
where y is the measurement output and ˆ y the output of the
model, using the same input.AVAF factor of 100% indicates
a perfect fit.
To obtain an overall transfer function of the system, mea-
surements with varying amplitudes were done to obtain an
average fit. This identification was done for all three differ-
ent springs, altering the stiffness of the series elastic element,
frequency is calculated, as determined by the reflected mass
(14 kg) and the series stiffness of the Bowden cable and the
4.2. Expected Nonlinearities
predictions and measurements may be expected due the
Veneman et al. /A Series Elastic- and Bowden-Cable-BasedActuation System 269
Typical model behaviour
Fig. 8. Qualitative model behavior. Bode plots of the uncontrolled actuator transfer H (1) and output impedance transfer Z (3),
both scaled to 0 dB gain, and both calculated for the same realistic system. The high frequent gain of the impedance transfer
is equal to the stiffness ctot.
Influence of PID controller parameters on output impedance
Impedance |Z| [dB]
Fig. 9. Effect of increasing the several terms of the PID controller (C) on the output impedance transfer (4). Changing these
terms should of course always consider stability issues. It is clear that at high frequencies the impedance always becomes the
same physical parameter ctot. This value has in the plot been scaled to 0 dB.
270THE INTERNATIONAL JOURNAL OF ROBOTICS RESEARCH / March 2006
Table 2. Parameters of the Second-Order Model StructureAccording to (1,1) as Identified from Measurements forAll
Three Sets of Springs.Also the Model Predicted ωe
High compliance spring4.3
Medium compliance spring5.4
Low compliance spring 5.4
ones are as follows.
force Fm; it is neither a linear nor a pure static relation,
box play, complex friction) and an electric current con-
trol scheme is needed for servo-motor torque control,
which has its own dynamics, albeit of high frequency
compared to the measurements range.
• The real friction is not damping, as the friction of a
Bowden cable is complex and depends on many pa-
rameters. Also gearbox and other elements contribute
• The force of the motor, Fm, is limited (at higher ve-
locities depending on the actual ˙ x1, via a maximal
power). This introduces saturation effects in the sys-
tem. From former studies on SEA it is known that
closed loop bandwidth for large forces (large force
ing parameters, and using the linear model for prediction and
design. Most of the described nonlinearities are expected to
result in an amplitude dependency of the transfer functions.
model parameters like before, but for input several constant
input signal amplitudes. For every spring three (RMS) ampli-
tudes were measured and fit on the same second-order model.
of a changing friction on the model parameters.
M, which is also the eigenfrequency of
the model transfer of the uncontrolled actuator (1).
4.3. Performance of the Actuator
The developed model was mainly meant for design purposes.
The performance of the actuator can be considered indepen-
dently of such model assumptions. In this chapter several is-
sues are considered that determine the feasibility of the ac-
tuator for the described application: compare Hayward and
cation of the achievable performance with the presented type
of actuation. The joint is as much as possible used in the way
it will be used in the final design of the rehabilitation robot.
The performance will be considered in four consecutive
1. Quality of spring based force measurement: how well
can the output force or torque be determined by only
measuring the deflection of the series elastic element?
frequency can the output force of the actuator be mod-
ulated using a basic control scheme?
3. Reduction of the output-impedance: how well can the
same controller decrease the output impedance of the
4. Fidelity (or distortion) of force output: how severely is
the force output distorted by system nonlinearities?
All four issues or measurements will be described shortly
defined, as this determines performance. The optimal course
of a Bowden cable would be straight, as bending introduces
friction and play. A realistic standard situation was defined
in which the Bowden cables are bent over 90◦with a radius
of 0.8 m. For the sake of conciseness, measurements were
only carried out on the medium compliance spring, unless
4.3.1. Quality of Spring-Based Force Measurement
As the springs in the joint are used for force measurement
in the control loop, a measurement is done to determine how
well the spring deflection reflects the actual force output. To
check this, the joint was fixed on both sides, on one side via
a 6D force sensor. From the force sensor measurements the
output based on the spring deflection. As reference input a
ramp signal was used. Both signals were filtered at 30 Hz.
The low compliance spring was used as worst-case example.
Veneman et al. /A Series Elastic- and Bowden-Cable-BasedActuation System 271
4.3.2. Bandwidth of Force Tracking with Fixed Load
ator, only a straightforward controller will be presented. The
objectives of the controller design were to improve the ex-
tent and accuracy of the force control, to reduce the apparent
friction and inertia when back driven, and to reduce the sensi-
tivity to load impedance variations. The force command was
interpreted as a desired spring length, which then was con-
trolled in a feedback loop, resulting in a torque command to
the servo-motor of the actuator.
A tuned PID controller is the most straightforward choice,
and can be designed based on the open-loop behavior of the
of Ziegler and Nichols. This method has been used to tune a
Due to the amount of noise in the spring length measure-
ment (LVDT), the differential action of the controller intro-
the encoder measurement of the motor position was used in
the differential part of the controller.
This concept of sensing, load position together with actu-
ator velocity, is also generally known to be a workable, con-
ditionally stable concept for fourth-order systems (Groenhuis
1991). An alternative would be to design an optimal state
space controller based on a measured open-loop transfer.
The transfer of the feedback controlled actuator was deter-
at force amplitudes of 1, 2, 4 and 8 Nm were measured.
Additional measurements were done with cables bent over
180◦with a radius of 0.4 m. Such a configuration should be
bending. Force tracking transfer functions were identified us-
30 Hz. The signal was crest optimized, to prevent appearance
functions were directly calculated from the output response
and this signal, averaged over several frequencies and then
checked on validity of estimations calculating the coherence
of the result.
4.3.3. Reduction of the Output Impedance
In relation to the patient-in-charge mode it is interesting to
determine how low the impedance of the output axis can be
controlled. This is also called the backdriveability of the de-
vice or actuator. The uncontrolled actuator itself is already
backdriveable, but still has, depending on the actual configu-
ration, quite high impedance, caused by the large friction of
the cables and the reflected mass of the motor. In our case the
motor has a relatively low gearing (8:1), so the reflected mass
is also low, but in general this might become considerable.
The output impedance is measured by imposing a position
trajectory upon the output axis of the joint, by hand, and then
measuring the interaction force between robot and hand. The
hand was considered feasible as disturbance source, given
the intended application of the actuator. The spring length
was used as force measurement. The transfer from joint an-
gle to actuator torque then is the mentioned impedance. The
impedance was measured both in the controlled and uncon-
trolled situation, to show the improvement obtained by using
a force feedback loop. The measurements for the controlled
situation were done using the same force control settings as
above, while using a zero reference force. It appeared that the
power spectrum of the hand perturbations ranged from about
0.7 to 4 Hz. In addition, time domain plots of force response
4.3.4. Force Fidelity
quencies compared to the input signal. Several metrics can be
defined to characterize the amount of distortion or its inverse,
the fidelity of the system: how undistorted the output signal
is compared to the input. The importance of such a metric
for actuator comparison was recognized by Morell and Salis-
bury (1998) and by Hayward and Astley (1996). To quantify
fidelity the following procedure was used (which differs from
the method of the mentioned authors).
As input signal a pure sine was used, the output then was
measured and scaled to fit the input signal optimally, using an
RMS-based optimal fit. This way both gain and phase shift
are compensated for and solely the remaining (frequency-
) distortion can be measured. To quantify the corresponding
was used, defined as
1 −var (y − R)
where y is the vector of the sampled measurement and R the
vector of the sampled sine, that was scaled to fit the mea-
surement. Fidelity of 100% indicates a perfectly undistorted
The fidelity of outputs of both the uncontrolled and the
controlled actuator were measured as a function of the fre-
quency. In both cases the output torque was tuned to have a
peak value of about 2 Nm magnitude. In the case of the open
loop measurement the control command was a sine of a given
frequency, which was increased in amplitude until the output
nal is the vector y. In case of the closed-loop measurement,
the reference was set to amplitude 2 Nm. Again the sampled
torque output signal was used as vector y. The measurements
were filtered with a 100 Hz first-order Butterworth filter.
272 THE INTERNATIONAL JOURNAL OF ROBOTICS RESEARCH / March 2006
5.1. Feasibility of the Model
5.1.1. Overall Linear Model
The parameters K, ωeand ζ, as defined in (1) were estimated
by fitting a general second-order model on the measurement
data. The coefficients of these fits are shown in Table 2. In
addition, the ωe, as predicted by the model, according (1)
To show how well a second-order model fits a measure-
ment, the overall second-order fit for the low-compliance
spring was compared with both a third-order PMI fit and
an optimal-order state space identification (Ljung 1999)
order fit only is a rough estimate of the actual system. The
order estimate, and considerably higher for the higher-order
fits: 85% and 86%. These results appeared to be similar for
each spring stiffness.
Mis given for varying stiffness. These results are
also shown in the Bode plots of Figure 10.
5.1.2. Amplitude Dependency
to the amplitude of the input signal. For comparison also the
with excessive curvature of the Bowden cables.
In general, it appears that the relative contribution of the
friction or damping is larger for small command amplitudes,
as the identified damping ratio increases. The best identifi-
cations were achieved with the medium compliance spring
(VAF 86–91%). The low compliance spring (VAF 71–87%)
and the high compliance spring (VAF 70–87%) systems were
estimated slightly worse. For high compliance this is due to
the fact that the system is identified as more heavily damped.
The estimations with the 180◦bent cables were poor (VAF
53–67%), due to the heavily increased stick friction in this
5.2. Actuator Performance
5.2.1. Quality of Spring-Based Force Measurement
A representative measurement (Figure 12) shows the force
estimate based on the spring deflection compared to the ac-
tual torque output, as measured by the force sensor. The
low-compliance spring was chosen, as it was the worst-case
5.2.2. Bandwidth of Force Tracking with Fixed Load
ing to (1), are given in Figure 13. The medium-compliance
spring was used. RMS amplitude of the input signal and the
Bowden cable curvature were varied. The effects on these re-
sults of varying spring stiffness can be concluded from eq.
(1), Figure 10 and Table 3.
large force bandwidth of the system, which is the worst case
The performance of the feedback controlled actuator with the
implemented PID controller is presented in Figure 14. The
RMS amplitude of the input was varied.
It can be seen that the controlled bandwidth of the actuator
is over 20 Hz for the measured range of torques in a nor-
mal Bowden cable course. For small torques the transfer falls
off already at a lower frequency. Closed loop bandwidths for
gains the closed loop transfers for any compliance can be ad-
Robinson 2000), unless saturation limits are reached.
In the case that the cable is excessively bent, the effects
of friction increase dramatically, as could already be noticed
in the uncontrolled actuator Bode plot. The controlled actua-
tor bode plot also shows a dramatic decrease of performance
5.2.3. Reduction of the Output Impedance
The reduction of output impedance as achieved by using the
PID controller with a zero reference force is presented in a
Bode plot (Figure 16).
From this figure it can be concluded that a reduction of
10–13 dB (factor 3–4.6) of impedance can be realized with
feedback control in the frequency range of application. The
values of the torques range from negligible up to 0.7 Nm for
around 4 Hz motion. The noticeable effects of cable stick
forces on the output force are also reduced. The time domain
subject connected to this joint confirmed that the controlled
impedance was low enough to experience unhindered lower
5.2.4. Force Fidelity
best-fit sine at 2 Hz, and Figure 19 for 20 Hz. A best-fit sine
is used instead of the reference sine, as at this point solely
the distortion of the signal is addressed, not phase shift or
amplification.The values for fidelity and distortion according
to the given definition show that this quality metric is quite
sensitive. One should be careful to qualify seemingly high
factors as “good”.
As expected, the low-compliance spring gave the most
distorted force output (comparison between springs is not
Veneman et al. /A Series Elastic- and Bowden-Cable-BasedActuation System 273
Influence of compliance on transfer estimate
model measurement fits).
Comparison of several model fits
Fig. 11. Comparison of a fit onto the proposed second-order model structure compared to a third-order fit and an optimal
sixth-order parametric fit. VAF-factor for the second-order fit is 71%, for the third-order fit 85% and for the sixth order 86%.
This indicates that a third-order model might predict the system behavior more adequately (low-compliance spring).
274 THE INTERNATIONAL JOURNAL OF ROBOTICS RESEARCH / March 2006
Table 3. Parameters of the Second-Order Model StructureAccording to eq. (1)
High compliance spring
Medium compliance spring
Low compliance spring
Medium compliance spring
Note: Identified from Measurements WithVaryingAmplitudes u for all Three Sets of Springs.All Measurements Were Done
With a Curvature of 90◦Over 0.8 m, Except the Last One Which Was Done With a Curvature of 180◦Over 0.4 m
Torque measurement linearity
Fig. 12. Representative comparison of torque determined from an LVDT measurement of spring deflection versus torque
determined from a force sensor measurement. The reference for the torque was a ramp signal controlled on the spring
measurement (low-compliance spring).
Veneman et al. /A Series Elastic- and Bowden-Cable-BasedActuation System 275
Uncontrolled actuator response
Fig. 13. Response of the uncontrolled actuator. Bode plot of the transfer from input control command to output joint torque.
The fits are optimal parametric fits of appropriate order (medium-compliance spring).
Controlled actuator response - 90º
Fig. 14. Bode plot of the closed loop transfer from reference torque to actual torque. The RMS amplitude of the reference was
varied. Here the orientation was 90◦with a bending radius of 0.8 m (medium-compliance spring).