Tactile texture rendering for electrostatic friction displays:
Incorporation of low-frequency friction modeland high-frequency textural model
Kazuya Otake1 , Shogo Okamoto1,2 , Yasuhiro Akiyama1 and Yoji Yamada1

Abstract— Tactile texture presentation on touch panels enhances their usability and realizes immersive user interfaces.
This study develops a tactile texture rendering method forelectrostatic friction displays. The method combines two rendering models for material textures compared with previous
studies which focused on either of these two models. One ofthese models is a physical model that simulates low-frequency
frictional signals depending on the exploratory ﬁnger velocities
and contact loads. The other is an autoregression-based datadriven model for high-frequency textural friction. For user
studies, we compared combining the two models with using only
the physical model for the four types of materials. Although theeffectiveness varied across the materials, the subjectively judged
realism and identiﬁcation of the materials were improved forthe combined condition. The new method combining highfrequency textural information and low-frequency physicalmodel-based friction is expected to provide realistic tactile
textures for electrostatic surface tactile displays.

I. I NTRODUCTION
Touch panels have been a major human–computer interface, and tactile feedback techniques for them, i.e., surface
tactile displays, have been studied intensively by many
researchers [1]. Methods needed to render tactile textures areamong the core techniques. Along with vibrotactile displays,
friction-variable tactile displays are suitable for providing
tactile feedback to ﬁngers on touch panels. Electrostatic
friction displays that generate friction variations on the panel
are a type of friction-variable display. Ultrasonic displays
constitute another type used to reduce surface friction. Datadriven methods are becoming a popular approach to circumvent the establishment of physical models for contact
between ﬁngers and ﬁne textures. These methods were also
introduced in the cases of electrostatic friction displays.
Accelerations [2] and frictional forces [3] caused by sliding
ﬁngers or contactors on material surfaces are typically used
to build data-driven models. For example, in [3], a touch
pen scanned several types of materials, such as cloths, tocollect information on contact forces, based on which neuralnetwork models were constructed for individual materials toThis study was in part supported by MEXT Kakenhi (20H04263,
21H05819).
1 Kazuya Otake, Shogo Okamoto, Yasuhiro Akiyama, and Yoji Yamada
are with the Department of Mechanical Systems Engineering, Nagoya
University, Furocho, Chikusaku, Nagoya 464–8603, Japan
2 Shogo Okamoto is also with the Department of Computer Sciences,
Tokyo Metropolitan University, 6-6, Asahigaoka, Hino, Tokyo, Japanokamotos@tmu.ac.jp
This study was approved by the Institutional Review Board of the Schoolof Engineering, Nagoya University (#20-8).

Fig. 1. Schematic of the measurement instrument for the contact force
and ﬁnger motion. Normal and shear forces were measured by three crystal
load cells, and the ﬁnger velocity was measured by a pair of encoders.

retain the frequency characteristics of friction signals. The
models were evaluated by user studies that focused on thesubjective similarities between the actual and virtual material
textures.
Earlier studies on data-driven methods [2], [3], [4], [5],[6] focused on surface textures and excluded low-frequency
components (e.g., less than 5–10 Hz) for their texture models.
This may be partly because some studies used miniature accelerometers that did not properly respond to signals smaller
than ∼10 Hz to record vibratory information generated ininstances in which a ﬁnger slid on textured surfaces. Further,
researchers tend to study high-frequency textural stimuli
separately from low-frequency stimuli rendered by physicalmodels. For example, in [6], a vibrotactile actuator andforce display device were adopted to present high-frequency
textural and friction components, respectively.
In this study, we used two types of models concurrently.
One is a physical model used to present low-frequency friction forces. The other is a data-driven or frequency-responsemodel that retains the high-frequency frictional properties oftextures. No previous study incorporated such two models
to cover a wide frequency range for electrostatic surface
displays except our earlier work [7]. We adopted previously
the simplest Coulomb frictional model to represent lowfrequency frictional forces; however, it was ineffective formodeling the ﬁnger-material frictions [7]. Furthermore, thehigh-frequency textural model in [7] did not depend on theﬁnger speed sliding on the touch panel. In the present study,
we adopted a physical model for low-frequency signals andan autoregressive model [2], [4], [5] for high-frequency tex-

Fig. 2. Coefﬁcient of friction (CoF) when the denim was traced by a ﬁnger at a reference velocity of 75 mm/s. (a) CoF recorded when a ﬁnger slides
over the denim. (b) Low-frequency (< 3.5 Hz) components of CoF. (c) High-frequency (≥ 3.5 Hz) components of CoF. When the CoF is close to zero,
the ﬁnger does not touch the material.

tural frictions for several ﬁnger velocity levels. The method isthen evaluated in terms of two viewpoints: subjective realism
and texture identiﬁcation performance based on user tests.
II. DATA COLLECTION FOR COEFFICIENT OF FRICTION
The instrument shown in Fig. 1 was used to measure
the two axial forces to derive the coefﬁcient of friction(CoF) and scanning velocity. A similar device was used in
our previous study [8]. Two load cells (9313AA2, Kistler,
Switzerland, dynamic resolution = 0.01 N) and a highprecision load cell (9217A, Kistler, Switzerland, dynamic
resolution < 0.001 N) were used to measure the normal andshear forces, respectively. The interference of the two axial
forces was mitigated by the leaf springs ﬁxed to the sidesof the instrument. The outputs of the force sensors were
ampliﬁed by charge ampliﬁers (5073A and 5015, Kistler,
Switzerland for the normal and shear forces, respectively)
and transmitted to the computer at 2 kHz. The ﬁnger position
was measured using a pair of encoders based on a string
rewinder mechanism (MTL-12, Microtech Laboratory Inc.,
Japan). The string attached to the shaft of the encoder was
ﬁxed to the ﬁrst joint of the ﬁnger, and the movement of
the ﬁnger was linked to the rotation of the encoder. Forces
to rewind the strings connected to the two encoders weredirected opposite to each other and cancelled with each other.
Furthermore, the strings were horizontally aligned with theﬁnger, and they did not produce any rewinding forces along
the normal direction. These setups hardly interfered with thenatural motions and forces of the ﬁngers.
We measured the two-axial forces generated when participants repeatedly traced materials ﬁxed on the upper surfaceof the measurement apparatus in one direction, that is, left toright in Fig. 1, with the index ﬁnger of their dominant hand.
Six men in their 20s participated in the measurements after
providing written informed consents. The average normal
and friction forces of each participant were 0.26–0.96 N and
0.14–0.47 N, respectively. In addition, they adjusted theirhand motions to achieve scanning velocities close to 50, 75,
100, 125, and 150 mm/s with feedback displayed on thecomputer screen. For later data analysis, continuous regionsof 100 ms or longer were spliced, wherein the actual velocity
was within ± 20 mm/s for each of these reference velocities.
The size of the materials was 100 mm × 40 mm. For these

Leather

Cork

Denim

Wood

Fig. 3. Four types of materials used in the experiments: leather, cork,
denim, and wood.

specimens, the forces could be continuously measured forapproximately 1 s or less. Hence, the sliding motions wererepeated multiple times during a single trial lasting 20 s.
For each reference velocity, 10 trials were conducted byindividuals. Regarding the normal force, no instructions were
given to them. The four types of materials shown in Fig. 3,that is, leather, cork, denim, and wood, were used for datacollection. These materials are familiar in our daily lives
and exhibit fairly different CoF and surface properties. In ourprevious study [7], we used a drawing paper; however, it was
highly smooth and exhibited minimal textural information.
Hence, we replaced the drawing paper with wood in thepresent study.
The CoF at an instant was calculated as the ratio of theshearing force to the normal force. Only the instants at which
the shearing and normal forces were greater than 0.05 N
were used. These coefﬁcients of friction were separated into
low- and high-frequency components using a Butterworth
ﬁlter with a cutoff frequency of 3.5 Hz. The cutoff frequency
was determined by considering that the natural exploratory
hand motion frequencies are only a few Hz [9]. This cutoff frequency was determined such that the coefﬁcient ofdetermination became greatest for the friction model of lowfrequency CoF components. As an example, Fig. 2 shows
the CoF before and after separation when tracing a denim
sheet at a reference velocity of 75 mm/s.
III. R ENDERING METHOD
A. Quasistatic friction model
Herein, a quasistatic friction model was introduced torepresent the low-frequency (< 3.5 Hz) components of the
CoF between the ﬁngers and materials. The CoF between

TABLE I
M EANS AND STANDARD ERRORS OF QUASI - STATIC FRICTION MODELPARAMETERS .

Leather
Cork
Denim
Wood

a
.51 ± .12.35 ± .04
.30 ± .07
.30 ± .05b
.36 ± .13.39 ± .01
.53 ± .08
.32 ± .08c
.02 ± .00
.02 ± .01
.03 ± .01
.14 ± .08d
.11 ± .04
.18 ± .08
.21 ± .07
.29 ± .11q
.89 ± .05
.08 ± .13.77 ± .06
.87 ± .07

the ﬁngers and materials is proportional to the power of thenormal force fn [10], [11], as follows,µp (fn ) = afnb

(1)

where a and b are constants. Furthermore, the CoF is known
as a function of the relative velocity [12],µp (v) = e

1 + dv q
1 + cv(2)where v is the scanning velocity, and c, d, e, and q are
constant coefﬁcients. We combined these two models andused
1 + dv qµp (fn , v) = afnb
(3)
1 + cv
to approximate the motion-dependent CoF. c and d arezero or positive values, and q ranges from zero to one.
As an example, Fig. S1 in Supplemental material presents
a comparison of the observed and modeled low-frequency
components of CoF.
The model parameters (a–q) were computed using theleast-squares method for individual participants and materials. The means and standard errors of the R2 values forthe modeling were 0.38 ± 0.06, 0.52 ± 0.11, 0.47 ± 0.09, and0.22 ± 0.04 for leather, cork, denim, and wood, respectively.
Therefore, in this friction model, 20–50% of the measured
CoF could be rendered. Inclusion of dynamic hand motions,such as acceleration in the model, may improve the modelingaccuracy. Although this study did not focus on the development of a model of the CoF, it should be updated to a bettermodel in the future.
Table I lists the means and standard errors of the model
parameters. In general, the magnitudes of CoF were thehighest for the leather, followed by the cork, denim, andwood, whereas the CoF values varied with the hand force
and velocity. The mean value of each parameter was used
to determine the voltage output of the electrostatic friction
display, as described later.
B. Textural friction model above 3.5 Hz
The autoregressive model [4], [5] was used to simulate
the frequency response of the textural components above
3.5 Hz in the CoF1 . As mentioned above, the components(higher than 3.5 Hz) of the CoF collected in Section II wereused for this purpose. The model was established for each
1 The components above 3.5 Hz include frictional vibrations, such asa stick-slip vibration. Hence, the name “textural components” may be
misleading. However, for convenience, we refer to the components greaterthan 3.5 Hz as textural components.

combination of the ﬁve levels of the reference velocity (50,75, 100, 125, and 150 mm/s) and four types of materials.
To model the average frequency characteristics of the CoF
among the six participants, we computed ﬁrst the fast Fouriertransformation of the time series of CoF. The spectra of
the six participants were then averaged for each pair ofmaterials and reference velocity. The average spectrum wasthen inversely converted in the time-series of CoF. Thesetime-series of CoF were used to establish autoregressivemodels. The autoregressive model was deﬁned byµt (k∆t) =p∑aj µt ((k − j)∆t) + w(k∆t)

(4)

j=1

where µt denotes the high-frequency textural component of
the CoF at time k∆t. ∆t is the sampling period: 0.5 ms.
The aj are the coefﬁcients obtained by the Yule–Walker
method. w represents the white noise. The textural component µt (k∆t) was determined at a certain point in timeby a linear combination of past p CoF. p is the order of themodel, and was determined based on the Akaike Information
Criteria (See the last paragraph of Section V).
We evaluated the similarity between the measured andmodeled CoF using a similarity index originally introduced
in [5], [13]. According to this index, the mean CoF waswell represented although there existed substantial individual
differences. The details are summarized in Supplemental
material 2.
The frequency responses obtained by the autoregressivemodel for the four types of materials are shown in Fig. 4.
For all materials, the amplitudes at 100, 125, and 150 mm/s
were relatively larger than those at 50 and 75 mm/s, and theamplitudes increased as a function of velocity. Findings arecomparable to those reported by [14].
IV. E XPERIMENT
A. Apparatus: Electrostatic friction surface display
The electrostatic friction display changes the frictional
force by controlling the electrostatic attraction by applying a
voltage between the ﬁnger pad and panel, as shown in Fig. 5.
An insulator exists between the ﬁnger pad and panel, and nocurrent ﬂows through the skin. The frictional force varies
with the magnitude of the applied voltage and promotes
deformation of the ﬁnger pad in the shear direction when
the ﬁnger slides on the panel. Therefore, electrostatic friction
stimuli are effective for presenting surfaces in which thefrictional force is dominant.
In the experiment, the electrostatic friction display shownin Fig. 6 was used. The electrostatic friction stimuli were
presented by applying a voltage between the indium tin oxide(ITO) panel to which an insulating ﬁlm of 8 µm (kimotect
PA8X, Kimoto Co. Ltd., Japan) was attached and the ﬁnger
pad. Participants experienced stimuli by touching the panel
while they holded a stainless steel rod connected to theground. The applied voltage was ampliﬁed by a voltage
ampliﬁer (HJOPS-1B20, Matsusada Precision Inc., Japan,
maximum output: ±1 kV, response: 75 kHz).

Fig. 4.

Spectral density of CoF for four types of materials at ﬁve velocity levels. Estimated by autoregressive models.

Finger movement
Load
Friction force----

Insulator
Conductor++ ++Attractive force
Electric charge

Fig. 5. Principles of electrostatic friction stimuli. The frictional force variedby controlling the electrostatic attraction force that was generated between
the ﬁngertip and the panel. The frictional force caused deformation of the
ﬁngertip in the shear direction. Adapted from [7].

10 cm

17 cm

Fig. 6. Tactile texture display used in the experiments. Force sensors placedat the four corners measured the ﬁnger loads to estimate their positions.

Four force sensors (USLG25, Tec Gihan Co. Ltd., Japan)
were placed under the ITO panel, and the normal force wasmeasured in real time. The position of the ﬁnger pad wasestimated from the proportion of the outputs of the four
sensors. The voltage ampliﬁer and force sensors were connected to a DAQ board (PEX-361216, Interface Corporation,
Japan). The sampling frequencies were 87 Hz and 2 kHz forthe force sensors and voltage outputs to the friction display,respectively.
B. Tasks
The following two tasks were conducted to compare
the condition in which only the physical model for lowfrequency CoF was adopted, and the condition in which
the two models were adopted in conjunction. Note that thecondition in which only the high-frequency textural model
was adopted is not implementable because the electrostatic
friction cannot lead to a negative CoF or decrease the CoF of
the ITO top panel. Adjusting the base friction level [15] is notsuitable for resolving this problem, because it increases theaverage friction level, which makes the comparison among
the conditions difﬁcult.
In Task 1, the realism of the two stimulus conditions wascompared. The participants experienced the two stimulus
conditions for each of the four types of materials that were
presented in a randomized order. They then selected theconditions in which the virtual materials felt more realistic.
Once all the materials were tested, they evaluated them again
after a break of several minutes. Hence, each material wastested twice by individual participants. For the latter analysis,
the mean proportions of two trials were used. During theexperiment, they were able to touch natural materials andvirtual stimuli as many times as they wanted, and no time
limit was set.
In Task 2, the identiﬁcation performance of the materials
was investigated at the two stimulus conditions. The task was
designed to ensure correspondence between the four typesof virtual materials to the four types of actual materials foreach of the two stimulus conditions. Participants could freely
touch the four types of actual materials during the task. Each
type of material was tested twice, and eight virtual materials
were presented in a randomized order per participant at eachof the two stimulus conditions. After the participants werebriefed on the task, they spent a few minutes in a training
session with feedback.
During Tasks 1 and 2, participants were able to movetheir ﬁngers freely with no instructions on ﬁnger force andspeed. Furthermore, they wore headphones and listened topink noise.
C. Participants
Fourteen university students (males in their 20s) participated in each task after they provided written informed
content. All participants were unaware of the purpose of theexperiment.
D. Electrostatic friction stimuli
The relationship between the frictional force fs (t) and theapplied voltage Ve (t) was modeled asfs (t) = µ{fn (t) + kVe (t)2 }(5)

TABLE II
M EAN PROPORTIONS , 95% CONFIDENCE INTERVALS , z VALUES , AND p

TABLE IIIR ESULTS OF TASK 2, IDENTIFICATION OF FOUR TYPES OF MATERIALS .

VALUES OF TASK 1 WHERE TWO STIMULUS CONDITIONS WEREM EAN ANSWER PROPORTIONS AND 95% CONFIDENCE INTERVALS FOR
THE TWO STIMULUS CONDITIONS .

COMPARED REGARDING THE REALISM .

Leather
Cork
Denim
Friction + Texture .54 ± .16.96 ± .07
.89 ± .15
Friction only
.46 ± .16.04 ± .07
.11 ± .15
z
.35
6.84
3.93
−16
p
1.00
4.0 × 10
2.5 × 10−7Wood
.54 ± .16
.46 ± .16
.35
1.00

from the law of electrostatic force and Coulomb friction2 . µ
and k are the CoF and constant related to the electrostaticforce of the panel, respectively. Therefore, the applied voltage to the touch panel Ve (t) was given by√
Ve (t) = ±α {µp (fn , v) + βµt (t)}fn (t).
(6)µp is the CoF of the low-frequency friction model in (3).
µt (t) is the textural component of the CoF depending on
the ﬁnger’s planar velocity on the touch panel v(t) and thetype of material. As previously mentioned, the models ofµt (t) were established for each of the ﬁve reference velocity
levels, and the model for the reference velocity closest to
the user’s actual ﬁnger velocity was selected during thetask. α and β represent the gains, and the authors adjusted
them a priori. Furthermore, as the perception of electrostatic
friction varies among individuals, the gain was adjusted forindividuals near the preset values. These values were reduced
when participants felt the frictions were unnaturally strongor painful, and increased when they could not perceive thefrictional changes. Approximate ratios (friction component: textural component) of the applied voltages were (10:3),(10:6), (10:6), and (10:4) for leather, cork, denim, and wood,
respectively. For safety reasons, stimuli above 250 V were
not used. To increase the effect of electrostatic friction [17],the polarity of the applied voltages was switched at a carrier
frequency of 2 kHz.
E. Results
Table II lists the results of Task 1, i.e., the mean proportions and 95% conﬁdence intervals for the two-alternative
task to select realistic stimulus condition for each of thefour materials. For the leather, cork, denim, and wood,
respectively, the combined low-frequency friction and highfrequency textural conditions were selected at 0.54 ± 0.16,
0.96 ± 0.07, 0.89 ± 0.15, and 0.54 ± 0.16. The table also
shows the results of the z-tests to investigate whether the
proportions were greater than the chance level, that is, 0.5,
with p values with Bonferroni correction. For cork anddenim, the combined stimulus condition was preferred. In
contrast, there was no signiﬁcant difference between the two
stimulus conditions for the leather and wood.
Table III shows the mean proportions and 95% conﬁdence
intervals for Task 2, i.e., the material identiﬁcation task, in
2 This formula may not be correct in principle; however, it formalizes thephenomenon that the frictional force is proportional to the square of theapplied voltage [1], [16].

(a) Friction model + textural model

Leather
ActualCorkmaterials Denim
Wood

Leather.71 ± .16
.07 ± .09
.14 ± .12.07 ± .09

Virtual materials
Cork
Denim
.00 ± .00 .18 ± .16.75 ± .16 .11 ± .11.21 ± .13 .68 ± .16.04 ± .07 .04 ± .07

Wood.11 ± .11.00 ± .00
.07 ± .09
.82 ± .16

Leather.39 ± .18
.46 ± .23
.11 ± .11.04 ± .07

Virtual materials
Cork
Denim
.14 ± .12 .36 ± .18.43 ± .19 .04 ± .07.36 ± .18 .46 ± .21.07 ± .09 .14 ± .15

Wood.11 ± .11.04 ± .07
.14 ± .05
.71 ± .21(b) Friction model

Leather
ActualCorkmaterials Denim
Wood

TABLE IV
M EAN PROPORTIONS , 95% CONFIDENCE INTERVAL , z VALUES , AND p
VALUES OF TASK 2 WHERE TWO STIMULUS CONDITIONS WERECOMPARED REGARDING THE IDENTIFICATION .

Leather
Friction + Texture .71 ± .16
Friction only
.39 ± .18
z
2.58
p
.04

Cork
.75 ± .16
.43 ± .19
2.58
.04

Denim
.68 ± .16
.46 ± .21
1.95
.20

Wood
.82 ± .16
.71 ± .21
1.29
.77

the two stimulus conditions. In the combined condition, as
shown in Table III (a), the mean correct answer proportions
were 0.71±0.16, 0.75±0.16, 0.68±0.16, and 0.82±0.16 forthe leather, cork, denim, and wood, respectively. Considering
the conﬁdence intervals, all materials exceeded the chance(0.25) and were correctly identiﬁed at 68–82%. As shownin Table III (b), when only the low-frequency friction stimuli
were presented, the mean correct response proportions were0.39 ± 0.18, 0.43 ± 0.19, 0.46 ± 0.21, and 0.71 ± 0.21 forthe leather, cork, denim, and wood, respectively. Considering
the 95% conﬁdence interval, denim and wood were identiﬁed
at proportions above the chance, but the proportions for theleather and cork were not greater than the chance level. The
four types of materials were correctly identiﬁed in the rangeof 39–71%.
The mean correct response proportion and 95% conﬁdence
interval for all materials were 0.74 ± 0.13 for the combined
condition and 0.50±0.16 for the low-frequency friction condition. The identiﬁcation performance was better in the caseof the combined condition. Table IV summarizes the p-values
when the mean correct answer proportions between the two
stimulus conditions are compared with Bonferroni correction.
For the leather and cork, the combined condition barely
signiﬁcantly improved the identiﬁcation performances. Refer
to Supplemental material 3 for the analyses of incorrect
answer proportions.

V. D ISCUSSION
The present study found that the effects of the combinedmodel depended on the type of materials whereas our previous study [7] showed that the virtual materials could be more
discriminable from each other by using the combined model.
The materials can be divided in three groups based on the
results of Tasks 1 and 2. The ﬁrst group comprises the cork
and denim. By using the combined model, both the realism
and identiﬁcation accuracies were improved, although the
improvement for the identiﬁcation accuracy for denim was
not statistically signiﬁcant. For these materials with roughsurfaces, the textural model is thought to be necessary,and the combined stimuli were effective. The second group
comprised the leather. By using the combined stimuli, therealism of the leather did not change, whereas the leather
exhibited the highest friction forces and was easily separated
from other materials. According to the introspective reports
from the participants, the virtual leather was not realistic
because of the lack of the typical softness of leather. The
third group comprised wood for which the combined stimuli
did not improve the realism and identiﬁcation performance.
Its surface was largely smooth, and its tactile feelings were
mostly determined by its frictional properties. Hence, thepresence or absence of the textural model did not make asigniﬁcant difference to the performance of the two tasks.
In Task 2, participants could identify the wood with highprobability even at friction-only model potentially because
its exponential power b was the lowest among the four typesof materials and the friction force rarely depended on thenormal force.
There exist some issues and limitations which need to besolved in the future. Our friction model in Section III-A does
not capture the changes in the measured low-frequency CoF
with high precision partly because the effects of dynamic
ﬁnger motions, such as acceleration, were not considered.
The friction model may need to embrace the effects ofstatic friction, whereas only the kinetic friction was modeledin this study. In addition, we determined the order of AR
models on the basis of Akaike Information Criteria. Thisapproach might not have accurately produced low-frequency
components. The method to determine the order for tactile
texture rendering remains to be studied. Although it is unclear which of these factors is the most important for texture
perception, it may improve the quality of surface texture
displays. Furthermore, it is interesting to compare the resultsof the present study and our past study [7] underlining thepresent rendering methods. However, the direct comparison
is difﬁcult because of the inherent differences in the user
experiments in the two studies.
VI. C ONCLUSION
We developed a texture rendering method for electrostatic
friction surface displays. The method combined a physicalmodel for low-frequency frictional components (0–3.5 Hz)
and a data-driven textural model for high-frequency frictional
components (> 3.5 Hz). Many earlier data-driven methods
did not aim at covering such a wide frequency range forthese types of texture displays. We tested the efﬁcacy of the
combined rendering method by comparing it with a methodthat adopted only low-frequency frictional components. Twouser studies revealed that the developed method increased
the perceived realism and identiﬁcation rates for material
textures, and was especially effective for non-soft textured
surfaces, such as cork and denim. This method is expected
to improve the quality of material textures for use in electrostatic surface displays.
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