Tremor Suppression Through Impedance Control
Stephen Pledgie1, Kenneth Barner2, Sunil Agrawal3
University of Delaware
Newark, Delaware 19716
duPont Hospital for Children
Wilmington, Delaware 19899
1 Ph.D. Candidate, Biomechanics and Movement Science Program
2 Department of Computer and Electrical Engineering
3 Department of Mechanical Engineering
4 Extended Manipulation Laboratory
This paper presents a method for designing tremor suppression systems that achieve a
specified reduction in pathological tremor power through controlling the impedance of the hu-
man-machine interface. Position, rate, and acceleration feedback are examined and two tech-
niques for the selection of feedback coefficients are discussed. Both techniques seek a desired
closed-loop human-machine frequency response and require the development of open-loop hu-
man-machine models through system identification.
The design techniques were used to develop a tremor suppression system that was subse-
quently evaluated using human subjects. It is concluded that non-adaptive tremor suppression
systems that utilize impedance control to achieve a specified reduction in tremor power can be
successfully designed when accurate open-loop human-machine models are available.
Tremor is an involuntary, rhythmic, oscillatory movement of the body . Tremor
movements are typically categorized as being either physiological or pathological in origin.
Physiological tremor pervades all human movements, both voluntary and involuntary, and is
generally considered to exist as a consequence of the structure, function, and physical properties
of the neuromuscular and skeletal systems . Its frequency varies with time and lies between 8
and 12 Hz. Pathological tremor arises in cases of injury and disease and is typically of greater
amplitude and lower frequency than physiological tremor. In its mildest form, pathological
tremor impedes the activities of daily living and hinders social function. In more severe cases,
tremor occurs with sufficient amplitude to obscure all underlying voluntary activity [3, 4].
A number of digital filtering algorithms have been developed for the purpose of remov-
ing unwanted noise from signals of interest and have thus found application in tremor sup-
pression. Riviere and Thakor have investigated the application of adaptive notch filtering for the
purpose of suppressing pathological tremor noise during computer pen input [5, 6]. When a ref-
erence of the noise signal is available, adaptive finite impulse response (FIR) filters can produce
a closed-loop frequency response very similar to that of an adaptive notch filter . Gonzalez et
al. developed a digital filtering algorithm that utilized an optimal equalizer to equilibrate a
tremor contaminated input signal and a target signal that the subject attempted to follow on a
computer screen . Inherent human tracking characteristics, such as a relatively constant tem-
poral delay and over and undershoots at target trajectory extrema, were incorporated in a
“pulled-optimization” process designed to minimize a measure of performance similar to the
squared error of the tracking signal.
To improve an individual’s ability to perform manual tasks in a physical environment, it
is necessary to suppress tremor-related movements. This can be accomplished by applying re-
sistive forces to the user’s limb to attenuate movements that occur at or near tremor frequencies.
The mechanical impedance of the human-machine interface is altered due to the activity of a set
of actuators driven by a displacement feedback controller.
Several projects have investigated the application of viscous (velocity dependent) resis-
tive forces to the hand and wrist of tremor subjects for the purpose of suppressing tremor move-
ments [4, 7, 9, 10, 11]. Experimentation with varying levels of velocity dependent force feed-
back showed, qualitatively, that tremor movements could be increasingly suppressed with
increasing levels of viscous force feedback, but that concurrent resistance of voluntary move-
ment may occur.
Closed loop functional electrical stimulation (FES) has been shown to be effective in
suppressing tremor movements in patients with essential tremor, parkinsonian tremor, and cere-
bellar tremor [12, 13]. In this approach, tremorogenic muscles are stimulated out-of-phase to
cancel the tremor forces generated by affected muscles. Investigators were successful in deter-
mining closed loop configurations that attenuate 2 - 5 Hz tremor movements with minimal at-
tenuation applied to voluntary movements in the 0 – 1 Hz range.
Previous investigations into non-adaptive feedback tremor suppression systems have not
utilized quantitative performance criteria during the design of the feedback control system. They
addressed the question of whether or not velocity dependent resistive forces (damping) could ef-
fectively suppress tremor movements, but were not concerned with achieving a specified statisti-
cal reduction in the tremor.
The objective of this research was the development of a methodology that incorporates
quantitative performance criteria as well as position, rate, and acceleration feedback into the de-
sign of a non-adaptive tremor suppression system. The remainder of this paper is divided into
six sections. Section 2 presents the results of an analysis of pathological tremor movements.
The design process for the tremor suppression system is described in Section 3. Next, a method
of system identification for the human-machine system is discussed. Sections 5 and 6 present the
methods and results of an evaluation of the system. Finally, the paper is completed with a brief
discussion and concluding remarks.
2. Analysis of Tremor Movements
An investigation into the spatio-temporal characteristics of tremor movements was per-
formed to gain insight into the spatial distribution and time-frequency properties of pathological
tremor movements. Previous investigations into tremor frequency have typically applied the
Fast Fourier Transform (FFT) algorithm to a sampled data sequence to obtain information re-
garding the exact frequency content of the data. However, no information with respect to the
evolution of the frequency content over time is generated with the FFT. It is for this reason that
a time-frequency analysis of pathological tremor movements was undertaken. The spatial distri-
bution of tremor movements was also examined. A tremor suppression system could potentially
take advantage of unique temporal and spatial distributions in the tremor.
A broad set of experiments was developed to examine the pertinent tremor characteris-
tics. Five tremor subjects ages 18 to 91 participated in the study.
The tremor subjects were qualitatively categorized with respect to the severity of their
tremor. Two subjects possessed the ability to write in a somewhat legible manner and received a
low severity label. Relatively large tremor amplitude that prevented legible writing was ob-
served in two of the subjects. The remaining tremor subject exhibited high variability in tremor
amplitude and, as such, received a variable severity label. The origin of the tremor in subjects B,
D, and E was unknown because no medical diagnosis was available.
The subjects performed target-tracking tasks while seated in front of a 17” computer dis-
play. The position of an on-screen cursor was controlled by manipulating a stylus attached to the
end-effector of the PHANToM, a small robotic arm used in haptic interfaces. The PHANToM is
an excellent platform for data collection because it has less than 0.1 N of static backdrive fric-
tion, an end-effector inertia of at most 100 grams with the motors disabled, a workspace of 13
cm x 18 cm x 25 cm, and a nominal end-effector position resolution of 0.03 mm.
Table 1. Subject Information.
Figure 1. Experimental Setup.
A target tracking task required the subject to follow an on-screen target with a cursor as it
propagated along a displayed straight line or sinusoidal pattern. The horizontal position of the
PHANToM’s end-effector controlled cursor location in a manner analogous to computer mouse
input. During a task, the subject’s elbow and forearm were permitted to rest upon a lightly pad-
ded surface (see Figures 1 and 2) and the stylus was grasped using the precision grip typically
employed during a writing task.
Pattern orientation, shape, and size as well as target velocity were systematically varied
across a number of target tracking tasks. The patterns that were displayed on the computer
screen were sinusoidal or straight line, horizontal or vertical in orientation, and were either 3
inches or 6 inches in length. Each sinusoidal pattern contained three complete cycles and there-
fore exhibited a spatial frequency of either 1 cycle/inch or 0.5 cycle/inch, as determined by the
pattern length. The targets that moved along the sinusoidal patterns completed one spatial cycle
in either 3 seconds or 6 seconds, corresponding to a temporal target frequency of either 0.333 Hz
or 0.167 Hz, respectively.
Figure 2. Illustration of the movements that are possible when grasping the stylus attached
to the end-effector of the robotic manipulator and with the forearm resting on a padded
surface. A.) X-direction movement (top view). B.) Z-direction movement (side view). C.)
Y-direction movement (side view).
Target movement initiated when the subject maintained his or her on-screen cursor loca-
tion within a designated “start area” for approximately one to two seconds. The tracking tasks
were stopped when the target had fully traversed the pattern. End-effector position was sampled
at 100 Hz throughout each task.
The frequency content of the tremor subjects’ movements was estimated using both
Welch’s average periodogram method as well as the Short-Time Fourier Transform (STFT) .
The STFT was formed by splitting the raw movement signal into overlapping segments (50 point
overlap), windowing each segment using a 100 point Hanning vector, and then calculating the
256 point zero-padded DFT for each segment. The filtered segments then contained an estimate
of the short-term, time-localized frequency content of the movement signal. Tremor frequencies
were selected as those frequencies at which the energy distribution contained a distinct peak.
The spatial distribution of the tremor movements was calculated by first isolating the
higher frequency tremor “noise” component with a 5th order IIR highpass filter and then counting
the number of data points within each cell of a two dimensional mesh. This process lead to the
creation of a two dimensional histogram of the tremor movement that occurred during a particu-
lar task. All analyses were performed using MATLAB.
As shown in Table 2, little variation was observed in the tremor frequencies across the
various target tracking tasks. Subject C consistently exhibited tremor with two distinct fre-
quency components and subject A’s tremor was by far the most variable and possessed a rather
broad distribution of energy with a mild peak.
Mean Freq. [Hz]
Std. Dev. [Hz]
Each category of tremor (low, moderate, and variable) exhibited a unique time-frequency
relationship, as illustrated in Figure 3. The level of color on the plot indicates the intensity of the
movement at a particular time and frequency. Warm colors, such as red and orange, indicate
greater power at a particular frequency and cool colors, such as blue, correspond to a lower
power level. Coloration observed at or below approximately 1 Hz represents the voluntary
movement and that above 1 Hz can be attributed to tremor movement. Constant frequency and
magnitude characterized the moderately severe tremor movements of subjects B and C (Figure
3.A). Low severity tremor (Figure 3.B) occurred at a relatively constant frequency but with
variable magnitude during the task. Subject A’s tremor was highly variable (Figure 3.C).
The spatial distribution of tremor movements was found to be non-uniform for all of the
subjects. In general, the spatial distributions were highly elliptical (see Figure 4), indicating a
predominant direction of tremor movement.
Three conclusions regarding the pathological tremor characteristics of the participants
were made based on the results of the target tracking tasks: 1.) Tremor frequency is relatively in-
variant with respect to the direction and speed of movement. 2.) Tremor frequency during task
performance is relatively constant, but the intensity, or amplitude, of the tremor may vary. 3.)
Tremor movements possess non-uniform spatial distributions.
Table 2. Mean tremor frequencies with standard deviations over all target-tracking tasks as
determined using Welch’s average periodogram method .
Figure 3. Representative time-frequency plots that show the evolution of the power spec-
trum over the course of a single trial. “Warmer” colors indicate greater power and “cooler”
colors indicate less power. A.) Moderate Tremor of subject C. B.) Low Tremor of subject
D. C.) Variable Tremor of subject A.
Figure 4. Representative example of the non-uniform spatial distribution of tremor move-
ments. The tremor component was extracted from the raw position signal with a 5th order IIR
high pass filter. A.) Plot of subject C’s tremor movements from a target tracking task. B.)
Two-dimensional histogram of the tremor movements shown in plot A. Increased levels of
coloration indicate a greater concentration of tremor movement data points within that re-
These conclusions suggested that the methodology behind the design of the tremor sup-
pression system could include the assumption of a constant tremor frequency. While this as-
sumption is justifiable over relatively short periods of time, it may not hold for tasks of long du-
ration. As such, the tremor frequency may need to be periodically re-estimated online to ensure
that the feedback controller is properly configured.
One could also pursue a tremor suppression system that intervenes only along the princi-
pal direction of the tremor movement. Such an approach would exploit the highly elliptical
tremor traces mentioned above and would lead to a feedback controller that is spatiotemporally
tuned to the user’s tremor.
3. Modification of the Human-Machine Frequency Response
To correctly configure the feedback controller, one must have a model that captures the
essential features of the human-machine system when not acted upon by external forces. The
open-loop properties of the human-machine system were modeled with a linear second order
time-invariant transfer function, as shown in the forward path of Figure 5. The plant possesses a
mass M, damping C, and stiffness K that represent the combined properties of the human limb
and the robotic arm as viewed at the end-effector of the PHANToM. This approach was moti-
vated by the work of Dolan et al. and Hollerbach on the impedance characterization of the hu-
man arm [15, 16].
Figure 5. Closed-loop human-machine system with 2nd order negative feedback.
Ms2 + Cs + K
a1s2 + a2s + a3
Second order negative feedback was generated by the manipulator to create the
closed-loop system depicted in Figure 5, which has the transfer function
M a s
C a s
The feedback coefficients a1, a2, and a3 impact the effective mass, damping, and stiffness of
the closed-loop system in an additive fashion. The magnitude response of the closed-loop sys-
tem is a function of the plant parameters M, C, and K as well as the feedback coefficients and
can be expressed as
Figure 6. Illustration of the magnitude response modification technique. The closed loop
system increases the attenuation at the tremor frequency while ideally not impeding lower
frequency voluntary movements.
The feedback coefficients are selected to increase the attenuation at a specified tremor
frequency and preserve the low frequency magnitude response of the open-loop system. Figure
6 illustrates the design methodology. The closed-loop system produces a desired attenuation Ad
at a designated tremor frequency ωt, but it does not introduce additional attenuation at frequen-
cies below a designated passband frequency ωp. While effective in many cases, it should be
noted that this tremor suppression technique is not well suited for individuals whose tremor fre-
quency lies very close to voluntary movement frequencies.
Setting ω to zero in Equation (2) reveals that a nonzero position feedback coefficient a3
will introduce undesirable low frequency attenuation in the closed-loop system. For this reason,
the position feedback coefficient a3 is set to zero.
The first technique for selecting the feedback coefficients permits the selection of either
the rate or acceleration feedback coefficient. First, the open-loop magnitude response of the hu-
man-machine system at a tremor frequency ωt is determined by evaluating Equation (1) with
estimates of the plant parameters and zero feedback. Next, a desired level of closed-loop at-
tenuation for movements at the tremor frequency is selected and used to evaluate one of the fol-
lowing expressions depending on whether acceleration (a1) or rate (a2) feedback is desired.
The second technique for selecting the rate and acceleration feedback coefficients di-
rectly addresses the issue of preserving the low frequency magnitude response of the open-loop
human-machine system. In this case, two additional frequency-attenuation pairs are selected: the
zero frequency gain of the open-loop system and the open-loop attenuation at a frequency ωp
that represents the highest frequency for which the closed-loop magnitude response should ap-
proximate the open-loop magnitude response (see Figure 6). A general least-squares fitting algo-
rithm is used to select the feedback coefficients that will produce a closed-loop magnitude re-
sponse that is a least-mean-square approximation to the desired response described by the
4. System Identification
The apparent mass, damping, and stiffness of the open-loop human-machine system are
required in order to select the appropriate rate and acceleration feedback coefficients. These pa-
rameters were estimated by approximating the frequency response of a discrete-time auto regres-
sive moving average (ARMA) human-machine model with a second order continuous-time
To generate the ARMA model of the human-machine system, a band-limited zero-mean
white noise force profile was applied by the manipulator while the tremor subject grasped the
attached stylus. The subjects were asked not to actively intervene while the manipulator moved
their limbs throughout the workspace. The resulting movement profile was then sampled at 1
kHz and filtered using a 20th order adaptive FIR filter to remove the active tremor component
that does not arise from the physical properties of the system. The adaptive FIR filter that was
employed was typical of those utilized in noise cancellation applications where a reference of the
noise signal is available . Next, the least-squares modified Yule-Walker method was em-
ployed to determine the coefficients of the ARMA model . The discrete-time frequency re-
sponse of the ARMA model was then mapped, in a least-squares sense, to a second order con-
The tremor suppression technique described in Section 3 was evaluated on tremor sub-
jects C, D, and E, as subject B was unavailable and the variable tremor of subject A was not suit-
able for evaluation. The experimental setup was identical to that during the target-tracking tasks.
The basic procedure was to first develop the open-loop human-machine models, select suitable
feedback coefficients, and then implement and evaluate the system.
Once the open-loop human-machine models were developed, the feedback coefficients
required to produce 10 dB and 20 dB of tremor attenuation were calculated. Three feedback
configurations were examined: strictly rate feedback, strictly acceleration feedback, and the
combination of rate and acceleration feedback (via the least-squares method). The feedback
system was implemented using the PHANToM robotic manipulator.
During the evaluation of the system, tremor subjects were asked to grasp the stylus at-
tached to the end-effector and manipulate it slowly throughout the entire workspace. Initially,
the robotic arm was disabled so that the power of the open-loop tremor movements could be cal-
culated. The feedback configurations were then individually implemented and applied during
separate trials. During each trial, the robotic arm operated at 1 kHz. The reduction in the tremor
movement power was used as a measure of the tremor attenuation achieved in the closed loop
Tables 3, 4, and 5 present the estimated mass, damping, and stiffness values of the hu-
man-machine system. These values represent the combined parameters of both the human and
the robotic arm. Subjects A and C, who possessed the most severe tremor, also exhibited the
greatest stiffness (i.e. rigidity).
It was found that the level of damping required for the “strictly rate feedback” configura-
tion designed to generate 20 dB of tremor attenuation was prohibitively large. For this reason,
the ability of the system to create 20 dB of tremor attenuation using strictly rate feedback was
Table 3. Mass estimates for the open-loop human-machine system [kg].
Table 4. Damping estimates for the open-loop human-machine system [Ns/m].
Table 5. Stiffness estimates for the open-loop human-machine system [N/m].
Table 6. Average tremor energy reduction with associated standard deviations [dB].
Rate & Accel.
10.679 ± 2.873
7.752 ± 2.203
8.811 ± 1.893
14.391 ± 3.258
15.073 ± 2.829
Table 6 shows the average levels of tremor attenuation achieved with each feedback con-
figuration. When a 10 dB reduction in tremor amplitude was sought, rate feedback provided, on
average, the best performance. The combination of rate and acceleration feedback provided the
best average performance when 20dB of tremor attenuation was sought. In general, the three
feedback configurations produced similar reductions in tremor power and speak to the feasibility
of the design and modeling process. An additional phase of experimentation will be required in
order to determine whether this method of tremor suppression is best suited for individuals with
particular pathologies as well as which feedback configuration is superior under certain condi-
tions. The subjects did indicate that the 20dB feedback configurations felt more resistive than
their 10 dB counterparts.
Figure 7 shows subject C’s performance on a pattern-tracing task. A desired spatial tra-
jectory was displayed on the computer screen and the subject was instructed to trace the pattern
with a cursor controlled through manipulating the stylus. Both rate and acceleration feedback
were applied in an attempt to achieve 20 dB of tremor attenuation.
7. Discussion and Conclusions
Two techniques for the design of non-adaptive tremor suppression systems that utilize
impedance control have been developed. Both methods utilize quantitative frequency domain
performance criteria during the selection of the gain in rate and acceleration feedback pathways.
The issue of preserving voluntary movement in the presence of adequate tremor suppression can
be addressed when rate and acceleration feedback are combined.
The ability of the system to produce a desired level of tremor attenuation depends upon
the accuracy of the parameters in the open-loop human-machine model. In this project, the me-
chanical properties of the human limb were the primary determinant in the overall physical be-
havior of the human-machine system. As such, it is natural to expect a configuration dependent
impedance of the human-machine interface due to the length-tension and force-velocity charac-
Figure 7. Qualitative example showing the effect of second order feedback on the pattern
tracing performance of subject C. Combined rate and acceleration feedback was applied
in an effort to achieve 20 dB of tremor attenuation. The tremor power was reduced by
11.34 dB in the “x” direction and by 20.59 dB in the “y” direction. A.) Desired spatial pat-
tern. B.) Performance without feedback forces. C.) Improved performance with feedback
teristics within the bi-articular muscles of the limb as well as the inertial properties of the limb
segments. A constant-coefficient second order linear model is unable to represent such a de-
pendence. For this reason, localized inaccuracies of the human-machine models may exist and
lead to degraded performance. Because the subjects performed tasks that did not require large
joint excursions, the errors introduced by the configuration dependent impedance were tolerable.
Additionally, a model developed under the conditions of a relaxed and primarily passive limb
may not be applicable under the conditions of an actively controlled limb. There may exist a
more suitable method of system identification that can be employed to model the properties of an
It is suggested that future investigations utilize adaptive feedback that seeks an “optimal”
level of tremor reduction. The average power of the user’s movements could be taken as the cost
function for either an adaptive FIR filter or the Weighted-Frequency Fourier Linear Combiner
(WFLC) developed by Riviere and Thakor [11, 12]. The existence of a physical plant in the
system will, in all likelihood, require the use of a noise reference signal that has been pre-filtered
using a model of the plant
Improved tremor suppression may also be achieved with the use of higher order feed-
back. Such systems will provide for better control of the closed loop frequency response but
may suffer from significant noise amplification and instability problems.
In conclusion, it has been demonstrated that a non-adaptive tremor suppression system
can be designed such that movements at a designated frequency experience a specified level of
attenuation. When second order feedback is present, additional frequency domain constraints,
such as the preservation of lower frequency voluntary movements, can be addressed.
This research was funded by the National Institute on Disability and Rehabilitation Re-
search (NIDRR) of the U.S. Department of Education under grant #H133E30013.
 A. Anouti, and W. Koller. Tremor disorders: diagnosis and management. The Western Jour-
nal of Medicine, 162(6):510 – 514, 1995.
 R. Stiles. Lightly damped hand oscillations: acceleration related feedback and system
damping. J. Neurophysiology, 50(2):327 – 343, 1983.
 B. Adelstein, M. Rosen, and M. Aisen. Differential diagnosis of pathological tremors ac-
cording to mechanical load response. Proc. of the RESNA 10th Annual Conf., 829 – 831, 1987.
 A. Arnold, M. Rosen, and M. Aisen. Evaluation of a controlled-energy-dissipation-orthosis
for tremor suppression. J. Electromyography and Kinesiology, 3(3):131 – 148, 1993.
 C. Riviere, and N. Thakor. Assistive computer interface for pen input by persons with
tremor. Proc. RESNA 1995 Conf., 440 – 442, 1995.
 C. Riviere, and N. Thakor. Modeling and canceling tremor in human-machine interfaces.
IEEE Engineering in Medicine and Biology, 15(3):29 – 36, 1996.
 Q. Xu. Control strategies for tremor suppression. Unpublished master’s thesis, University of
 J. Gonzalez, E. Heredia, T. Rahman, K. Barner, and G. Arce. Filtering involuntary motion of
people with tremor disability using optimal equilization. Proc. IEEE Int. Conf. On Systems,
Man, and Cybernetics, 3(3), 1995.
 S. Beringhause, M. Rosen, and S. Haung. Evaluation of a damped joystick for people dis-
abled by intention tremor. Proc. of the RESNA 12th Annual Conf., 41 – 42, 1989.
 M. Rosen, A. Arnold, I. Baiges, M. Aisen, and S. Eglowstein. Design of a controlled-
energy-dissipation-orthosis (CEDO) for functional suppression of intention tremors. J. Reha-
bilitation Research and Development, 32(1):1 – 16, 1995.
 B. Morrice, W. Becker, J. Hoffer, and R. Lee. Manual tracking performance in patients
with cerebellar incoordination – effects of mechanical loading. Can. J. Neurol. Sci. 17(3):275-
 M. Javidan, J. Elek, and A. Prochazka. Attenuation of pathological tremors by functional
electrical stimulation II: clinical evaluation. Ann. Biomed. Eng. 20:225-236, 1992.
 A. Prochazka, J. Elek, and M. Javidan. Attenuation of pathological tremors by functional
electrical stimulation I: method. Ann. Biomed. Eng. 20:205-224, 1992.
 J. Proakis, and D. Manolakis. Digital Signal Processing: Principles, Algorithms, and Ap-
plications. (3rd ed.). Prentice Hall, Upper Saddle River, New Jersey, 1996.
 J. Dolan, M. Friedman, and M. Nagurka. Dynamic and loaded impedance components in
the maintenance of human arm posture. IEEE Trans. Systems. Man, and Cybernetics, 23(3):698
– 709, 1993.
 K. Hollerbach, and H. Kazerooni. Modeling human arm movements constrained by robotic
systems. Advances in Robotics ASME, DSC-Vol.42:19 – 24, 1992.
 S. Haykin. Adaptive Filter Theory. (2nd ed.). Prentice-Hall, Englewood Cliffs, New Jersey,
Stephen Pledgie: email@example.com
Kenneth Barner: firstname.lastname@example.org
Sunil Agrawal: email@example.com
Tariq Rahman: firstname.lastname@example.org