EEG Correlates of Motor Control Difﬁculty in Physical Human-Robot
Interaction: A Frequency Domain Analysis
Amirhossein H. Memar and Ehsan T. Esfahani
Abstract— This study investigates the relationship between
electroencephalogram (EEG) activity and motor control difﬁ-
culty during physical interaction with an admittance controlled
robot. Subjects performed a ﬁne cooperative manipulation
task, in which the motor control difﬁculty was manipulated
by altering admittance dynamics. To quantify motor control
difﬁculty, an interaction instability index is proposed based
on the spectral information of interaction forces. Regression
analysis is then performed to construct a model to estimate
motor control difﬁculty from EEG spectral features. The results
indicate the reliability of EEG signals as an indicator of motor
control difﬁculty in pHRI.
Physical human-robot interaction (pHRI) aims to integrate
the repeatability and accuracy of robots with problem solving
skills of humans to improve the overall performance in
a wide variety of robotic applications such as effortless
cooperative manipulation (co-manipulation) of heavy objects,
robot learning by demonstration and teleoperation. In such
applications, a compliant interaction is essential to achieve a
successful interaction and ensure the users’ safety.
Compliant interaction can be obtained by either imple-
menting active control methods (e.g., impedance/admittance
) or using actuators with passive compliant ele-
ments (e.g., variable stiffness actuators , ). The
impedance/admittance parameters can be modulated adap-
tively to further improve the pHRI performance. However,
it is challenging to ensure the stability of physical inter-
action due to the lack of information about human dy-
namics and the biomechanical impedance of human arm
which is subject-speciﬁc, conﬁguration-dependent, nonlinear,
and time-varying . Moreover, understanding the user’s
intention of pHRI, the so-called human intention inference,
is required to implement an appropriate adaptation. For
instance, a low virtual damping can facilitate cooperative
manipulation in terms of human effort, whereas, an increased
virtual damping may improve the accuracy in ﬁne and
accurate positioning by suppressing disturbances .
Although most of the proposed adaptive methods have
demonstrated an improved performance with respect to
a constant high/low compliance, an optimal method that
seeks to maximize perceived comfort by the users requires
objective measures of human mental states. For instance,
Gopinathan et al.  showed that a suitable adaptive stiff-
ness strategy depends on the task characteristics and varies
AH. Memar and ET. Esfahani are with the Department of
Mechanical and Aerospace Engineering, University at Buffalo
SUNY, Buffalo, NY, 14260 USA. email@example.com,
between individuals. Therefore, a reliable and continuous
estimation of motor control difﬁculty will enable designers to
assess the effectiveness of pHRI. It is specially important in
domains such as robotic rehabilitation  where maintaining
the optimal level of workload increases the motor-learning.
The effectiveness of pHRI is traditionally assessed by
subjective measures and questionnaires which require inter-
ruption of tasks. Moreover, participants’ self-reports may be
affected by a posteriori rationalization and desire to satisfy
implicit objectives of the researcher . Another approach
is the use of performance metrics (e.g., completion time) as
an indirect measure of difﬁculty. Nevertheless, the estimation
of task performance is impractical or prohibitive for many
real-world scenarios where sensing capabilities are limited.
Recently, neuroergonomic measures have been used to
assess the quality of human-machine interaction . Kulic
and Croft  used galvanic skin responses to determine
the participant anxiety in HRI. In their study, participants
observed the robot arm motions passively without physical
contacts. A signiﬁcant difference was revealed between a
safe and an unsafe motion planner due to the participants’
anxiety affected by the robot motions. Dehais et. al 
used ocular response, skin conductance and deltoid muscle
activity to evaluate the physical comfort in a hand-over task
with different motion planners. Novak et. al  studies a co-
manipulation task with a gravity and friction compensated
robot arm. They altered the difﬁculty of a virtual game
between trials and measured the workload. The workload
estimation performance for all the physiological modalities
was found to be signiﬁcantly better than random. Although a
compliant interaction was used in their study, task difﬁculty
was adjusted in terms of mental arithmetic and temporal
effort rather than the motor control difﬁculty of the pHRI.
Brain monitoring and in particular EEG has become the
most studied physiological indicator of workload due to its
high temporal resolution  and thus has been used in
this study to continuously and unobtrusively estimate motor
control difﬁculty. For this purpose, participants performed
a path-tracking task in which an admittance controlled arm
is used to enable compliant interaction. Controller intrinsic
dynamics is used to manipulate motor control difﬁculty by
decreasing the virtual damping and making the precise guid-
ance more difﬁcult. A quantitative measure representing the
instability of the motions is extracted from spectral analysis
of interaction forces to estimate motor control difﬁculty. EEG
spectral power density and coherence features are used to
investigate EEG correlations with motor control difﬁculty
using multiple linear regression analysis.
2018 IEEE Haptics Symp. 2018, San Francisco, USA
Accepted for publication by IEEE. c
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Fig. 1. Experimental setup and the locations of EEG sensors.
Fig. 2. Block diagram of the admittance controller.
II. MATERIALS AND METHODS
A. Experimental Setup
Figure 1 shows the experimental setup used in this study.
B-Alert X24 wireless headset (Advanced Brain Monitoring
Inc., Carlsberg, CA, USA) was used to record non-invasive
EEG signals from 20 locations based on the 10/20 interna-
tional EEG system which are shown in Fig. 1. EEG signals
were referenced to linked mastoid electrodes located behind
ears. To provide the visual information regarding visuomotor
tasks and end-effector position, a computer display was
placed in the front of subjects. A light-weight 6-DoF robot
arm, SCHUNK PowerBall , equipped with a force/torque
sensor at the end-effector was used for pHRI task.
An admittance controller with null stiffness was imple-
mented to provide a compliant behavior such that users
can lead the robot motions in the Cartesian space. The
controller consisted of two feedback loops (outer and inner)
as depicted in Fig. 2. The outer loop establishes a second
order dynamics between the input force and end-effector
position in the Cartesian space, whereas, the internal loop
tracks the desired velocities in the joint space. In the outer
loop, the interaction forces acquired from the force sensor
are mapped to the desired end-effector velocity based on the
admittance function Ycto establish (1).
where vc∈R6denotes the desired end-effector veloc-
ity; fh∈R6is the interaction force and torque vector;
Md,Cd∈R6×6are the admittance parameters indicating
the inertia and damping of the desired compliance respec-
tively. vcis then transformed into the desired velocity in the
joint space ( ˙
qc) using the inverse Jacobian J−1(q)as (2),
The robot motion controller (inner loop) tracks the desired
joint velocities based on a closed-loop feedback scheme jD
by applying torques to the joints of the robot with intrinsic
-5 0 5
x (cm) -5 0 5
Boundary Tracked Path
Fig. 3. Sample tracks of co-manipulation with (a) HD, and (b) LD mode.
impedance of jZr. A local PI controller for each joint was
used for tracking the desired velocity.
B. Experimental Scenario
Participants were asked to perform a ﬁne co-manipulation
task by guiding the end-effector between the boundaries of
a star-shaped path that is shown in Fig. 3. The primary error
metric was deﬁned as the total number of times that an
individual crosses the virtual boundaries over the 3 minutes
experiment. Each participant experienced two conditions in
which the controller dynamics was altered using a low
damping (LD) and high damping (HD). Only the damping
parameter of the admittance control was subjected to change
since it has been identiﬁed as the most dominant parameter
that affects the interaction with compliant controllers .
The robot resistance is lower for the LD thus the human
effort decreases. However, low damping may cause unstable
interaction since the controller dynamics gets closer to its
unstable region. The resulting over-responsive motions of the
robot will be seen as overshoots in co-manipulation. This
instability is more pronounced in precise co-manipulations
since humans tend to increase arm stiffness to achieve higher
precision and resistance to disturbances . In our study,
we exploit this dynamics between humans and an admittance
controller to increase motor control difﬁculty via decreasing
the damping and making the co-operation harder.
To compensate the effect of user’s arm weight, the motion
of the end-effector was restricted to the X-Y plane. The
maximum velocity of the joints was also limited to 0.6
rad/sec to increase the safety of interaction. In both con-
ditions, Mdwas set to Diag([3,3,3,0.1,0.1,0.1]), while,
Cdwas set to Diag([80,80,80,10,10,10]) for the HD, and
Diag([20,20,20,6,6,6]) for the LD condition. These values
are obtained experimentally to ensure a stable co-operation
with HD and a more difﬁcult interaction with LD condition.
This difference can be observed in the sample tracked paths
shown in Fig 3.
C. Participants and Procedure
11 subjects (8 males and 3 females) were recruited from
University at Buffalo School of Engineering to participate in
an IRB-approved experiment. Participants’ ages ranged from
23 to 34 (mean age 27.5) and they had normal or corrected to
normal vision. Participants were instructed to guide the robot
end-effector by holding a handle attached to the force/torque
sensor. As the feedback for visuomotor tasks, the position of
the end-effector in the X-Y plane was displaced on the users’
monitor via a circular cursor. After brieﬁng on the objectives
of the experiment, participants received a practice session
of co-manipulation in free space, without any particular
path, to get familiar with the two damping conditions of
the admittance control. The order of experimental conditions
were permuted randomly for each participant to balance the
learning effects. To obtain subjective measures, subjects were
asked to complete a NASA TLX questionnaire  upon the
completion of each experimental condition.
D. EEG Data Analysis
EEG signals were band-pass ﬁltered (0.1-70 Hz) and then
digitalized with a sampling rate of 256 Hz. They were
transmitted then from the headset via a Bluetooth link to
a nearby PC. The B-Alert recording software was used to
automatically remove eye blinks and muscle movements
artifacts . Spectral power density and coherence analysis
was then performed on clean EEG signals.
Spectral power density reﬂects speciﬁc regional activity in
an isolated fashion, whereas, the coherence between channel
pairs corresponds to the inter-regional functional connectiv-
ity. It quantiﬁes the level of synchrony between two signals at
a speciﬁc frequency and it ranges from 0 to 1. A Hamming
window with 50% overlap was used to extract power and
coherence estimates using Welch’s method from 2-second
epochs. Features were extracted from 6 frequency bands
including: theta (4-7 Hz), lower-alpha (8-10 Hz), higher-
alpha (11-13 Hz), lower-beta (14-22 Hz), higher-beta (23-35
Hz) and gamma (36-44 Hz). EEG alpha-attenuation at low-
alpha is associated with the state of alertness and expectancy,
whereas, high-alpha is mainly related to semantic memory
information processing . Accordingly, the division of
alpha band to low and high range are common in studying
psychomotor efﬁciency .
120 spectral power measures (Nch ×Nfwhere Nch = 20
and Nf= 6 are the number of channels and bands, respec-
tively) and 1140 coherence measures (Nch×(Nch−1)
were extracted from each 2-sec epoch. However, only the
EEG coherences between frontal midline region (Fz) and the
rest of electrodes were considered for analysis in this study.
Therefore, a feature vector of 114 elements ((Nch −1)×Nf)
was used as the EEG connectivity measure.
EEG activity at Fz is predominantly inﬂuenced by premo-
tor area (motor planning) in the 10/20 international EEG sys-
tem. Functional connectivity between premotor and motor,
temporal, parietal and occipital regions are commonly used in
neuropsychology to study sensorimotor control. These func-
tional connectivities have been found to be correlated with
motor planning, somatosensory and visuomotor integration
processes . For instance, the coherences of Fz with other
cortical regions have been found to be signiﬁcantly affected
by cognitive-motor task difﬁculty in a Tetris game .
E. Quantiﬁcation of Motor Control Difﬁculty
The direct and continuous measurement of motor control
difﬁculty is not easily achievable, therefore, an indirect
measure is used to estimate and quantify the level of motor
control difﬁculty. A dimensionless index in the frequency
domain is proposed to distinguish between the low frequency
input components of the intended human motions and the
unintended high frequency oscillations of the robot due to the
controller instability. In other words, it is assumed that the
bandwidth of the human arm motions in voluntary controls is
relatively low  while robot motions caused by admittance
instability mostly appear in the frequency bands higher than
human voluntary control.
Frequency domain analysis of pHRI in terms of end-
effector position  and interaction force  have been
investigated in previous studies to develop haptic stability
observers for detecting and suppressing unstable oscillations
of haptic devices. Dimeas and Aspragathos  demon-
strated that spectral analysis based on the position data
is mostly valid for back-drivable haptic devices, whereas,
spectral analysis of interaction forces is more appropriate
for an admittance controlled robot. This is because an
admittance controller acts as a low pass ﬁlter and attenuate
high frequency components of the control force inputs.
Inspired by , , we used frequency domain analysis
of force data to quantify instable behaviors as an indirect
measure of motor control difﬁculty. We used the Fast Fourier
Transform (FFT) of interaction forces to extract the mag-
nitude Pf(ω)of the frequency components ω. Force data
were down-sampled to 128 Hz and then segmented to 2-
seconds data epoch (aligned with EEG signals). A Hamming
window with 50% overlap was applied on each segment.
Periodograms were averaged to estimate spectral power and
results were normalized according to the overall window
power. The index used for the quantiﬁcation of motor control
difﬁculty was deﬁned as (3),
where ω0is the smallest non-zero frequency component
of the FFT; ωmis the maximum frequency component of
interest for summation which must be less than Nyquist
frequency; ωcis the cross-over frequency to distinguish
between intended and unintended motions which is between
ω0and ωm. The index (IR) ranges from 0 to 1 and a
larger value indicates lower interaction stability and higher
difﬁculty in motor control accordingly. To minimize the
effect of sensor noise on the IR, the value of ωmmust be
chosen around the maximum bandwidth of the robot motions.
The selection of ωc, however, is not trivial since an optimal
value is task-speciﬁc and varies between individuals with
different arm impedance and skill levels.
F. Regression Analysis
234 EEG measures (120 spectral power and 114 coher-
ences) were obtained from each 2-sec epoch. A Stepwise
Multiple Linear Regression (SWMLR) method was used for
dimensionality reduction and identifying the most dominant
predictors. In this model, the EEG measures were predictor
variables and the motor difﬁculty index (IR) was the re-
sponse variable. SWMLR is a numerical approach that itera-
tively enters/removes predictors with signiﬁcant/insigniﬁcant
main effect on the regression model. Although SWMLR
cannot handle nonlinearities, it is a simple and robust method
to reduce the dimensionality of large EEG measures .
The Mahalanobis distance was used in SWMLR to enter or
remove predictors, with a threshold of 0.05 on p-value for
entering and 0.1 for removing a predictor.
Since the SWMLR assumes predictors belong to a multi-
variate normal distribution, a logarithmic transformation was
applied on the spectral power density measures  and
Fisher’s Z-transformation on the coherences to normalize
their distributions . Combined EEG measures of all
the subjects were used for the SWMLR and then selected
predictors are used to ﬁt a multiple linear regression model
to the response variable. To stabilize intra-individual variance
and minimize the effect of individual differences, predictor
variables were transformed into z-scores based on the distri-
bution of each subject. To evaluate the performance of the
constructed linear model to estimate motor control difﬁculty
and distinguish between the two manipulation conditions,
predicted responses are reported for each subject.
III. RES ULTS
A. Behavioral and Subjective Assessment
Subjective and performance data were analyzed primarily
to examine the experimental design and difﬁculty manipu-
lation of the tasks. A paired-sample t-test was performed to
compare subjects’ performance between the two conditions.
The number of intersections with the start-shaped boundaries
was used as the primary error metric and the results are
shown in Fig. 4a. Statistical analysis revealed signiﬁcantly
higher errors (lower performance) with low-damping than
high-damping condition (t(10)= −3.7,p<.005).
To further explore the effect of damping on the interaction,
the average magnitude of interaction forces in the X-Y
plane ( 1
TRT||Fh||dt) was also computed. Fig. 4b shows the
obtained results across the subjects. As expected, a paired-
sample t-test revealed higher interaction forces in the high-
damping than low-damping condition (t(10)=4.2,p<.005)
indicating a lower physical effort for low-damping.
An overall perceived workload score, ranging from 0 to
100, was calculated using the weighted combination of the
six dimensions of NASA TLX. Weights for the combined
workload score were calculated based on a set of 15 paired
comparisons between the 6 dimensions as instructed in .
The results of perceived workload are shown in Fig. 4c
(a) (b) (c)
Force Magnitude (N)
Combined NASA Score
HD LD HD LD HD LD
Fig. 4. (a) error metric, (b) average magnitude of interaction forces, and
(c) weighted NASA score. Error bars represent one standard deviation.
Frequency (Hz) Frequency (Hz)
Fig. 5. (a) Unscaled and (b) scaled spectral power of the interaction forces
averaged across the subjects. Shaded error bars is one standard deviation.
and statistical analysis revealed a signiﬁcantly higher work-
load for the co-manipulation with low-damping than high-
damping (t(10)=−4.6,p<.001) which is consistent with the
performance results. The behavioral and self-report results
indicate that although the smaller damping facilitated the co-
manipulation with lower interaction forces, the difﬁculty of
controlling robot motions was higher in this case.
B. Frequency Analysis of Interaction Forces
The averaged spectral power extracted from FFT for
the two co-manipulation conditions are shown in Fig. 5.
Since the averaged interaction force was higher in the high-
damping (see Fig. 4b), a vertical shift is present between
the two spectral powers in Fig. 5a. To acquire a better
insight for comparison, the FFT magnitude of frequency
components for the low-damping are scaled based on the
ratio of DC magnitudes (Pf(0)) between the two conditions.
The result is shown in Fig 5b and the presence of high
frequency components in the interaction forces with the low-
damping is clear. Based on the results of averaged spectral
powers, an ωmvalue of 10 Hz was chosen to calculate the
instability index IR. However, an optimal ωcwas found to
be subject-dependent and variations in ωcaffected the IR
distribution for each subject, signiﬁcantly. This is mainly due
to the individual differences in terms of arm impedance and
motor control characteristics. For instance, the differences
between subject 8 and 11 in terms of interaction forces in
the frequency domain are shown in the ﬁrst row of Fig. 6.
To address this issue, a statistical approach is proposed
to ﬁnd an individualized ωc. For each subject, the index IR
is calculated for a range of ωcfrom 0.5 to 4 Hz with a
Fig. 6. Spectral powers in the ﬁrst row represent the individual differences
in terms of interaction forces and motor control in high- and low-damping
conditions. Second row shows the F-statistic values obtained from ANOVA
on the distributions of IRfor different ωcvalues. Vertical Blue lines on the
graphs denote the selected ωcfor each of the subjects.
0.25 Hz step size. Then, at each ωc, the degree of difference
between the IRdistribution of high- and low-damping are
estimated using F-statistics obtained from analysis of vari-
ance (ANOVA). The frequency at which F-statistic reached
its maximum is considered as the optimum ωc. As an
example, the F-statistic curves for subject 8 and 11 and
their maximums are shown in the second row of Fig. 6. The
results of the proposed procedure for the subjects are listed
in Table I. Note that this approach requires the existence of
a signiﬁcant difference between the low- and high-damping
which is already considered in the experimental design and
veriﬁed based on the behavioral and subjective assessment.
RESULTS OF INDIVIDUALIZED CROSS-FREQUENCY (ωc).
Subject 1 2 3 4 5 6 7 8 9 10 11 Ave
ωc(Hz) 3.25 2 2.25 2.5 1.75 2 1 2 3.5 1.5 3.25 2.27
Although calculating IRusing a personalized ωccan pro-
vide a better estimate of motor control difﬁculty, this imposed
individual differences in the IRdistribution such that a
subject with larger ωchad smaller values of IRand shifted
distribution toward zero. In other words, individualized ωc
values are suitable for within-subjects analysis, however, for
our between-subjects regression analysis which combined
the IRindices of all the subjects, consistent responses were
required. To address this issue, the averaged ωcindex (2.27
Hz) was used to calculate IRfor all the subjects.
According to the performance and subjective assessment,
we expected higher IRvalues for the LD than HD condition.
A paired-sample t-test was performed on the averaged IR
indices of the subjects for comparison purposes. Statistical
analysis revealed a strong difference (t(10)=−15.1,p<1e−
7) indicating that IRwas higher in the low-damping than
high-damping. This conﬁrms the validity of the proposed
index for the quantiﬁcation of motor control difﬁculty.
C. Results of Regression Analysis
The SWMLR yielded a signiﬁcant result (p<.001,
adj = 0.51) and 29 dominant EEG measures (13 co-
herences and 16 spectral powers) were identiﬁed as the
best predictors. Fig. 7 depicts selected EEG measures using
topographic scalp maps. A single linear model is constructed
using the selected measures of all the subjects and its estima-
tion results for the ﬁrst 8 subjects are shown in Fig. 8. Despite
the existing differences between actual and estimated IR
indices from brain activity, the linear model demonstrates an
overall reliable performance, especially in the discrimination
between low and high motor workload conditions.
A set of 29 EEG spectral measures was appeared as the
most dominant predictors of motor control difﬁculty based
on an SWMLR method. Most of these measures belonged to
the high frequency bands (beta and gamma). EEG activity
in these bands is mainly correlated with localized sensory
integration and sensory processing demand  and it ele-
vates as sensorimotor demand increases. For instance, EEG
Fig. 7. Selected EEG measures from a stepwise multiple linear regression
analysis. Each topographic map corresponds to a certain frequency-band.
t-statistic is used to determine the signiﬁcance of each measure using a
color-map for the spectral power and line-thickness for the coherence.
( IR )
( IR )
S1 S2 S3 S4
S5 S6 S7 S8
Fig. 8. Results of regression prediction for the ﬁrst 8 subjects (S1-S8).
Red and green box-plots denote high- and low-damping, respectively. The
left two box-plots represent the actual distributions of the difﬁculty index,
whereas, the right plots show the predictions from EEG measures.
beta and gamma power in temporal, parietal and occipital
region have been found to be signiﬁcantly affected by only
increasing motor difﬁculty aspects of a cognitive-motor task
when the cognitive difﬁculty was maintained constant .
Among selected EEG measures, the coherence of Fz
with T3 (left-temporal) and T4 (right-temporal) have strong
relationships with “psychomotor efﬁciency” hypothesis in
psycho-physiology. This hypothesis indicates that an adaptive
cortical activity and efﬁcient networking (especially reduced
Fz-T3) identiﬁes skilled performance of experts in sports like
golf and riﬂe shooting , . Fz-T3 coherence is associ-
ated with verbal-analytical processes (self-instructing) and is
essential for early stages of motor learning, whereas, Fz-T4
connectivity becomes dominant when movements are highly
learned. It can be assumed that our subjects continuously
attempted to learn the coupled human-robot dynamics to
increase their performance. However, contrary to the learning
of free arm movements, the rate of learning dynamics in the
pHRI with unstable controllers (LD condition) becomes very
slow. Thus, such EEG indices can indicate motor control
difﬁculty in pHRI, particularly when the interaction is not
intuitive/well-designed and instability is likely to occur.
The linear regression model demonstrated an overall reli-
able estimation performance, however, the quality of estima-
tion varied between subjects. There are at least two factors
contributing to these variations. First, functional differences
in how participants perform the motor control task which
inﬂuences their cortical activity. This issue can be potentially
overcame by using a set of benchmark experiments to
personalize a general model (e.g., ). Second, individual
differences in terms of motor control characteristics as ob-
served in the calculation of ωcin section III.B.
EEG correlates of motor control difﬁculty in human-robot
co-manipulation is investigated. Participants performed a ﬁne
manipulation task in which controller intrinsic dynamics is
used to manipulate motor control difﬁculty (decreasing the
damping and making the precise guidance more challenging).
Based on the frequency domain analysis of the interaction
force, an index is deﬁned to distinguish between the low
frequency human voluntary force inputs and unintended
high frequency motions of the robot due to the improper
admittance. This index is used as an indirect measure of
motor control difﬁculty and validated through statistical
analysis and comparison with performance and subjective
assessments. An optimal selection of the parameters for the
proposed index (ωmand ωc) requires knowledge about the
robot dynamics as well as human arm impedance and motor
control characteristics. The effects of individual differences
on the spectral power of interaction forces are discussed and
a statistical approach is proposed to ﬁnd an individualized
ωc. Although the average of ωcis used for the between-
subjects analysis of this study, such personalization can be
used for within-subject analysis and designs.
A stepwise multiple linear regression method is used to
identify the most correlated EEG measures to motor control
difﬁculty and the results are used to construct a linear model
to predict the proposed index. The relationship of the selected
measures with visuospatial processing and psychomotor ef-
ﬁciency as well as obtained prediction performance support
the validity of the procedure. This model can potentially be
used as a real-time adaptation strategy to adjust task difﬁculty
in robot assistance of motor learning and rehabilitation.
This material is based upon work supported by the Na-
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