1
The Spatial Spectrum Of Tangential Skin
Displacement Can Encode Tactual Texture
Michael Wiertlewski, Jos
´
e Lozada, and Vincent Hayward Fellow, IEEE
Abstract—The tactual scanning of five naturalistic textures was
recorded with an apparatus capable of measuring the tangential
interaction force with a high degree of temporal and spatial
resolution. The resulting signal showed that the transformation
from the geometry of a surface to the force of traction, and
hence to the skin deformation experienced by a finger is a
highly nonlinear process. Participants were asked to identify
simulated textures reproduced by stimulating their fingers with
rapid, imposed lateral skin displacements as a function of net
position. They performed the identification task with a high
degree of success, yet not perfectly. The fact that the experimental
conditions eliminated many aspects of the interaction, including
low-frequency finger deformation, distributed information, as
well as normal skin movements, shows that the nervous system is
able to rely on only two cues: amplitude and spectral information.
The examination of the “spatial spectrograms” of the imposed
lateral skin displacement revealed that texture could be repre-
sented spatially despite being sensed through time and that these
spectrograms were distinctively organized into what could be
called “spatial formants”. This finding led us to speculate that the
mechanical properties of the finger enables spatial information
to be used for perceptual purposes in humans without any
distributed sensing, a principle that could be applied to robots.
I. INTRODUCTION
T
EXTURE — the organized deviation from smoothness
of the surface of objects — typically is first apprehended
visually but once contact is made with the hand, touch must
take charge. Katz, in 1925, noted that there are two ways in
which organisms can become tactually aware of the texture
of objects [1]. One way is to determine directly the relevant
spatial features of the geometry of a touched surface. To
illustrate how this could be done, consider a deeply grooved
grating, such as a knurled knob. Under reasonable normal
static loading, the skin interacts with such a surface through
a collection of minute contact surfaces. Assuming that the
sensory apparatus is able to detect these individual contact sur-
faces, then presumably a coarse notion of the surface geometry
can be acquired. If such surface has any degree of fineness,
however, the individual contacts become so numerous that
such strategy becomes highly implausible. Most psychologists
and neurophysiologists agree with Katz that the experience of
surface texture must result from mechanical signals brought
about by finger sliding that change through time, in addition
to mechanical signals that vary through space.
M. Wiertlewski and J. Lozada are with CEA LIST, Sensory and
Ambient Interfaces Laboratory, Fontenay-Aux-Roses, France. E-mail:
michael.wiertlewski@cea.fr, jose.lozada@cea.fr. V. Hayward is with UPMC
Univ Paris 06, UMR 7222, Institut des Syst
`
emes Intelligents et de Robotique,
Paris, France. E-mail: vincent.hayward@isir.fr.
Vol. 27, No. 3, pp. 461–472. doi 10.1109/TRO.2011.2132830
To the haptics engineer interested in devices and transducers
able reproduce tactile and haptic sensations, these observations
are very significant since the overriding objective is to extract
from the complexity of the ambient physics those aspects that
are the most significant to the perceiver and to discard the
others in the name of technical feasibility.
Of course, tactual texture is an ill-defined notion. In a
single sentence, it is hard to discuss the sensations caused
by rough burlap, those resulting from finely machined bronze,
or those derived from the velvety skin of an apricot. To make
things worse, from a physical view point, and even restricting
attention to hard materials, texture and roughness can be
characterized in many different ways that also depend on the
method used to measure it [2], [3]. With soft materials the
situation is even more inextricable.
The many studies in the psychophysics of texture and
roughness perception unfortunately contribute little insight to
the haptics engineer because these studies rarely speak of the
same quantities, although there is a general agreement that
roughness has perceptual significance [4], [5], [6], [7], [8],
[9], [10], [11], [12], [13], [14], even if it is nearly impossible
to define it unambiguously from the physical characteristics
of the touched object [15].
If roughness, and more generally, if tactual texture is
hard to discuss directly from the physics of an object, then
perhaps a more productive approach from the view point of
interface design would be to focus on the characteristics of the
mechanical interaction of the skin with an object, although the
prospects for identifying simple signals are rather bleak at first
sight. The finger is a soft, highly deformable object which,
besides its complex detailed geometry, exhibits several types
of nonlinearities that are manifest at different length scales
of interaction with surfaces [16], [17], [18], [19], [20]. Even
under the extremely simplified assumption of linear visco-
elasticity and perfectly clean contacts free of foreign bodies
and liquids, the contact of deformable bodies with rough
surfaces gives rise to theories of considerable complexity that
are unlikely to yield simple interaction models [21]. These
observations justify the measurement-reproduction approach
adopted in this study.
II. ROUGHNESS AND TEXTURE IN
MANUFACTURING AND VIRTUAL REALITY
Numerous industrial processes, from mirrors to roads, de-
pend on the measurement of roughness. It is achieved using
profilometers based on slow mechanical scanning with a sharp
stylus (the tip radius can be as small as a few nanometers) or
2
by optical methods (confocal microscopy, laser triangulation,
interferometry). Reporting roughness is mostly a function
of the intended application. In part machining, for instance,
roughness is traditionally characterized in terms of the relative
heights of a set of asperities specifying their standardized
moments: 0
th
, 1
st
, 2
nd
, 3
rd
. Interestingly, the latter measures
report zero roughness for any regular grating and therefore
cannot be applied to perceptual studies. Other measures report
the statistics of the peak-to-valley distances of sets of asperities
which makes them more relevant. Some measures consider
autocorrelation, some account for spatial wavelength or for
extrema density. Some others take into consideration the
magnitude of the slopes of asperities, and yet others their
curvature. The later measure is probably one of the most
relevant to tactual roughness of these different approaches.
The measurement process is typically slow (minutes, hours)
and provides details that are not necessarily relevant to tactual
sensing. On the other hand, it is an everyday experience that
the roughness of a surface can be felt, or that two textured
surfaces can be discriminated, or even that a wood grain can
be identified in a fraction of a second by the scanning finger.
These observations have let researchers in virtual reality
to adopt the more expeditious method used by humans to
sense texture, rather than to rely on industrial-type methods.
Examples of this approach can be found in [22] where the
scanning interaction force is measured, in [23] where the
scanning acceleration of a stylus is measured, or in [24] where
the scanning velocity is measured. The reader is referred
to a recent survey where 50 articles on the subject are
commented [25].
For texture reproduction, the most widely adopted approach
is the force-feedback device with a position-dependent tex-
tured virtual wall, also extensively surveyed in [25]. A more
recently introduced technique is to modulate the friction force
between the finger and a mechanically grounded active surface.
The friction force modulation can be achieved, for instance,
by electrostatic fields [26], ultrasonic amplitude modulation
[27], surface acoustic waves [28] or with the squeezed film
effect [29], [30].
III. DESIGN MOTIVATION FOR A TEXTURE TRANSDUCER
The above considerations led us to engineer a new de-
vice capable of accurate measurement and reproduction of a
surface-finger interaction, having a bandwidth and a dynamic
range able to do justice to the biomechanics and sensory
performance of the human finger. This device is already briefly
described in reference [31] where is was shown that it was
able to provide perceptually equivalent sensations of roughness
between a virtual and a real surface. The surface used in these
preliminary experiments was a “simple” triangular grating of
spatial period 1.0 mm with groove depth 0.1 mm. Although
the surface was periodic, the force of interaction during
sliding turned out to be a complex, broadband signal having
a complicated harmonic signature which can be appreciated
by consulting Fig. 1 and caption. The transformation from
geometry to signal is highly nonlinear, a fact that is hardly
surprising considering that friction is the primary phenomenon
involved [32].
02
0 5 10 15 20 25 30
nger position (mm)
interaction
force (mN)
−40
40
0
0.1
10
1
4
Speed = −21.0 mm/s
Normal Force = 1.5N
0
1.4
spat. freq. (1/mm)
ampl. (mN)
ampl. (mN)
Figure 1. Spatial spectrogram produced by sliding a finger on a perfectly
periodic triangular grating. The methods used to construct such plots are
described in detail later in this article. For now, it can be appreciated
that the transformation from a triangular profile to a force signal is far
from straightforward. A triangular wave has only odd harmonics. While the
fundamental “formant”, or spectral peak, at 1 mm
−1
is present, it is actually
weaker than the first even-harmonic spectral peak. Notice also the present of
energy in the sub-harmonic frequencies. These are the hallmarks of a nonlinear
transformation.
In the present article, we describe this device in greater
detail and we employ it in a experiment where it is used to re-
produce various textures. We show that the textural recording-
reproduction obtained with this device is of sufficient quality
to enable several participants to correctly match a virtual
surface with a real surface included in a set of five. The
mechanical consequences of net friction were eliminated by
the transduction process and so was distributed skin deforma-
tion within the finger contact area. As a result, the apparatus
reproduced accurately the oscillatory components of the skin
tangential displacement at the exclusion of other mechanical
consequences of sliding a finger over a rough surface.
A particular feature of our device is that the same mechan-
ical structure was used in the sensor and actuator modes. It is
based on the piezoelectric effect which, as is well known, is
reversible. In sensor mode it operates like a high-quality, stiff
force sensor. In actuator mode it provides accurate isometric
stimulation to the skin. The questions regarding the reciprocal
signal causalities are discussed in [31].
A. Performance Considerations
The device should be orders of magnitude stiffer than the
fingertip to provide unambiguous measurement and stimula-
tion, noting that the converse possibility is considerably harder
to achieve due to the difficulties met in reducing the effects
of inertia to sub-threshold levels [33].
Other design considerations include the level at which
interaction forces should be resolved. In absence of knowledge
on the smallest dynamic forces able to stimulate the skin, an
estimate can be obtained by considering that the elasticity of
the fingertip is roughly of the order of 10
3
N·m
−1
and that a
detectable skin displacement is of the order of 10
−7
m. One
could infer that the sensor should resolve 10
−4
N, which is far
beyond the reach of commercial strain-gauge force sensors. In
terms of actuator displacement, similar considerations indicate
that 10
−4
m would be needed to create the 10
−1
N peak-to-
peak force oscillations that can be encountered when stroking
3
texture as can be seen from Fig. 1. This requirement has been,
in hindsight, the hardest to meet and, due to saturation, has
somewhat limited the scope of our investigations. Finally, it
is commonly accepted that a 500 Hz bandwidth is needed
to represent tactile interactions. Interestingly, this figure was
actually proposed by Katz almost a century ago [1].
B. Description
The main components, shown in Figure 2a, comprise a
multilayer, 40 mm piezoelectric disk-bender (CMBR07, Noliac
Group A/S, Kvistgaard, Denmark) connected to a 20 mm-
wide tray that can hold a sample. The bender is clamped
vertically by two epoxy ridges of semi-circular section that
apply uniform pressure on the bender. A treaded rod connected
to the hollow center of the bender transmits motion to the tray
which is linearly guided by a flexure made of two leaf springs.
Connection to the bender is realized by two Delrin
c
washers
that can tolerate ± 0.5
o
of misalignment. The texture samples
are bonded to the tray using double-sided adhesive tape.
During sensor operation, the interaction forces induce flexu-
ral deformations of the blade along x and in the piezoelectric
element, as indicated in Fig. 2b. Through the piezoelectric
effect, the deformation of the ceramic causes charges to appear
on the electrodes that are picked up by an instrumentation am-
plifier. Conversely, when applying a voltage to the electrodes
of the bender, the piezoelectric effect causes the transducer to
operate as an actuator. In this case, displacements of the tray
impose deformations in the fingertip resting on it.
leaf springs
tray 20 x 45 mm
bender
clamp
base
a b
y
x
z
Figure 2. a. Transducer schematic. b. Cross section of the system at rest
(solid lines) and during deformation (dashed lines).
C. Transducer Modeling
Since the mechanical constitution of the transducer is com-
mon to the sensor and to the stimulator, their models include
the same lumped parameters. They differ only by the electron-
ics. In sensor mode, a high gain, low noise instrumentation
amplifier collects charges and convert it into readable voltage,
whereas in actuator mode, a high voltage amplifier, with a low
output impedance is used to drives voltage on the electrodes of
the piezoelectric bender and therefore the tray’s displacement.
1) Mechanical Flexure: The flexure acts like a mass-spring-
damper system with stiffness k
r
according to Fig. 3a. Damping
due to internal and external friction is by and large dominated
by losses in the bender. It arises mostly from hysteresis in
the piezoelectric material. As further discussed later, it is
reasonable to represent it by viscous damping. The inertial
term corresponds to the equivalent moving masses of the tray
and of the bender. The actuator force is shown as an external
force, f
p
, acting in the opposite direction of x. Another
external force, f
d
, models the finger interaction through its
contact with the sample.
a b
y
x
z
f
d
k
r
b
r
x(t
)
f
p
f
p
˙q
−
˙q
p
˙q
+
v
−
v
+
m
Figure 3. a. The plate, the sample and the bender are modeled by a mass
m. It is suspended by a spring of stiffness k
r
connected to a damper b
r
.
Forces f
p
and f
d
represent the piezoelectric actuator and finger interaction
forces, respectively. b. The piezoelectric effect causes charges to appear on
the electrodes as a result of displacement.
Applying Newton’s second law and converting to the
Laplace domain gives
(ms
2
+ b
r
s + k
r
)X(s) = −F
p
(s) + F
d
(s), (1)
where X(s), F
p
(s) and F
d
(s) represent the Laplace transform
of the variables x(t), f
p
(t) and f
d
(t).
2) Static Constitutive relationships: The Y-poled bimorph
piezoelectric element has two external electrodes plus one cen-
tral electrode located in the neutral fiber. Bending deformation
results in the compression of one layer and traction of the
other. Layers are polarized which creates charges q
+
, q
p
and
q
−
through the piezoelectric effect. Operating as an actuator,
imposed voltages v
+
and v
−
push the charges on the armatures
to induce axial deformation as a result of the radial strain.
The linear, static constitutive relationships can be expressed
in matrix form as follows [34],
x
q
+
q
−
=
1/k
p
β β
β C
p
0
β 0 C
p
f
p
v
+
v
−
, (2)
where β = δ
max
/2v
max
is the ratio of the largest unloaded
deflection to the total maximum operating voltage applied to
one layer, k
p
is the flexural stiffness in open circuit and C
p
is the capacitance of one piezoelectric layer when no stress is
applied. In this model, the dynamic parameters like mass and
damping are not taken into account.
3) Transfer function in sensor mode: Only one layer is
used. The voltage generated by an external force can be written
from (2) by summing the piezoelectric induced voltage, v
p
,
with the voltage due to the circulation of charges,
v
+
=
q
0
+
R
˙q
+
dt
C
p
−
β
C
p
f
p
=
q
+
C
p
+ v
p
.
The transducer acts electrically like a voltage generator in
series with a capacitor C
p
. The generated voltage, v
+
, is
amplified by a high input impedance (10
12
Ω) instrumentation
amplifier (LT1789, Linear Technology Corp., Milpitas, CA,
USA), see Fig. 4. Load resistances, R
s
, combined with the
4
capacitor form a first-order high-pass filter which can be
expressed in the Laplace domain by
V
+
= −
2βR
s
s
1 + 2R
s
C
p
s
F
p
=
2R
s
C
p
s
1 + 2R
s
C
p
s
V
p
. (3)
piezo
G
s
R
s
R
s
C
p
v
p
v
s
Figure 4. Schematic of the sensor circuit. The electrode of the upper layer is
connected to an instrumentation amplifier. Resistors create a high-pass filter.
Neglecting the contribution of v
p
to the mechanical behav-
ior, the mechanical constitutive equation is x(t) = 1/k
p
f
p
(t).
Combining it with (3), V
s
(s) = G
s
V
+
(s) gives the output
voltage, V
s
(s), as a function of the displacement X(s) :
V
s
(s) = −G
s
βk
p
2R
s
s
1 + 2R
s
C
p
s
X(s)
Using (1), the transfer function of the sensor, H
s
(s), becomes
H
s
(s) =
V
s
(s)
F
d
(s)
=
−2G
s
R
s
k
p
β s
(1 + 2R
s
C
p
s)(ms
2
+ b
r
s + k
r
+ k
p
)
4) Transfer function in actuator mode: The bender is con-
nected to a power source (PA86U, Cirrus Logic Inc., Austin,
TX, USA) which drives the central electrode as in Fig. 5. The
amplifier is connected voltage-mode with a gain G
a
= 20.
A resistor, R
a
, in series with the output tunes the frequency
response since a low pass filter is formed with the capacitance
of the piezoelectric element.
v
+
v
p
v
−
˙q
p
˙q
−
˙q
+
R
a
G
a
v
a
−v
max
+v
max
Figure 5. Circuit in actuator mode. Upper and lower electrodes are connected
to fixed voltages ±v
max
. The power amplifier drives the central electrode
voltage, v
p
.
By application of Kirchhoff’s law at the output node,
˙q
+
+ ˙q
p
= ˙q
−
, (4)
with ˙q
+
= C
p
˙v
+
, ˙q
p
= (1/R
a
) (G
a
v
a
−v
p
) and ˙q
−
= C
p
˙v
−
.
Using these values in (4) and substituting v
+
= v
max
−v
p
and
v
−
= v
p
+ v
max
yields in the Laplace domain,
1
R
a
(G
a
V
a
− V
p
) = C
p
(V
p
+ V
max
) s − C
p
(V
max
− V
p
) s,
finally giving,
V
p
=
G
a
1 + 2R
a
C
p
s
V
a
. (5)
The power stage acts as an amplifier of gain G
a
with a first-
order low-pass filter of cutoff frequency ν
cut
= 1/(4πR
a
C
p
).
The first line of (2) combined with (1) gives
(ms
2
+ b
r
s + k
r
+ k
p
)X(s) = 2βk
p
V
p
(s) + F
d
(s). (6)
The two last lines of (2) can be simplified since the voltage
driver supplies and draws charges as necessary such that (2)
becomes
q
+
= C
f
V
+
and q
−
= C
f
V
−
.
The transfer function of the unloaded stimulator is found by
combining (5) with (6),
H
a
(s) =
X(s)
V
a
(s)
=
G
a
k
p
β
(1 + 2R
a
C
p
s)(ms
2
+ b
r
s + k
r
+ k
p
)
.
D. Identification
The model parameters could be initially estimated from the
data provided by manufacturers, as well as from the design
of the leafs and of the tray. Parameter identification was then
performed to obtain a better model and to take into account
nonlinearities and parameter deviations from their manufac-
turing specification. Because the mechanical parameters are
common to the sensor and the actuator, it is more convenient
to identify the system first in actuator mode.
1) Actuator mode: The frequency response was determined
using a frequency sweep from 10 Hz to 1000 Hz, applying
4 Vpp voltage signal, v
a
, (using a digital-to-analog converter
PCI-6229, National Instruments Corp., Austin, TX, USA).
Output displacement was measured using a laser telemeter
(LT2100 with LC2210, Keyence Corp., Osaka, Japan). At
each frequency, amplitude and phase were measured after a
200 ms pause to let the transients subside. The response was
determined under the following conditions: unloaded, with a
finger resting on the tray (normal force ≈ 0.5 N) and with
a finger pushing down the plate (normal force ≈ 1 N). The
result is shown in Fig. 6. The system exhibits the intended
natural resonance at 500 Hz followed by a small un-modeled
resonance at 800 Hz.
10 100 1000
frequency (Hz)
0
24
18
12
6
0
-90
-180
-270
(µ m/V)
phase (°)
amplitude
unloaded
0.5 N
1.0 N
model
10 100 1000
Figure 6. Frequency response of the actuator. Measurement are in grey dot
and the model in plain black.
Since the actuator is two order of magnitude stiffer than the
finger, finger loading has a negligible impact on response in
a 10–400 Hz band. At resonance, however, damping due the
5
fingertip causes a 3 dB attenuation of the resonant peak. In
the experiments, caution was taken to roll-off the signal with
3 dB attenuation at 500 Hz, flattening the response. The effects
of the finger damping as well as of the second resonance
can therefore be neglected. Least-square fitting (R
2
= 0.85)
provided the parameters shown in Table I. As can be seen from
the figure, the model and the uncorrected system responses are
graphically indistinguishable up to 500 Hz.
Table I
ELECTRO-MECHANICAL PARAMETERS.
Mechanical Electrical
δ = 82.35 µm C
p
= 818 nF
k
p
= 76.47 × 10
3
N·m
−1
v
max
= 100 V
m = 6.8 g G
s
= 100
b
r
= 4.49 N·mm
−1
·s
−1
R
s
= 12 kΩ
k
r
= 4.05 × 10
−3
N · m
−1
G
a
= 20
R
a
= 680 Ω
It is known that piezoelectric ceramic transducers have
significant hysteresis which affects the quasi-static and the
dynamic responses. Fig. 7 plots the response of the trans-
ducer to 0.1 Hz sinusoidal 10 V peak-to-peak amplitude
signal showing a 16% hysteresis. The hysteresis introduced
by piezoelectric ceramics is of non-saturating type and hence
introduces small amplitude distortion of no consequence in
our experiments, since the minor loops are very small. It does
introduce constant phase lag of 8
◦
which, at a given frequency,
can be represented as linear damping [35]. It is the actuator
hysteresis that accounts for the nicely damped resonance of
the system at 500 Hz but is neglected in the low frequences.
In summary, the actuator is capable of a maximum peak-to-
peak displacement of 200 µm, with a quasi-static gain of 20
µm/V in the range from DC to 500 Hz.
measurement
voltage (V)
-5 -4 -3 -2 -1 0 1 2 3 4 5
-100
100
50
-50
0
displacement (µm)
linear t
8° phaser t
Figure 7. Quasi-static measurement of the actuator response (gray circles).
Data show a non saturating hysteresis that can be approximate by a 8
◦
ideal
phaser (black line).
2) Sensor mode: A known external force, calibrated using
a conventional force sensor (Nano 17, ATI Industrial Automa-
tion, Apex, NC, USA), was applied to the sensor. This force was
used as an input for the model described earlier. Fig. 8 the fit of
the model with the measurement (R
2
= 0.91). The simulated
output is 10 times more noisy than the actual measurement
from the sensor because of the noisy input measurements from
the strain-gauge force sensor.
The model predicts a sensitivity of 26 V·N
−1
for a gain
of G
s
= 100 in the bandwidth 10–500 Hz with the resistor
input
measured
simulated
0.60.50.40.30.20.10
0
-4
-2
4
2
Output Voltage (V)
Time (s)
Figure 8. Fit of the sensor model with actual measurements.
R
s
set to 12 kΩ. Like in the actuator mode, the sensor has
a natural resonance at 500 Hz. The signal is acquired with
the data acquisition board already mentioned. With 16 bits
of resolution, the force signal can be measured with 10
−5
N
resolution. The experimentally measured noise floor is as low
as 25 µN/
√
Hz.
IV. EXPERIMENT 1 : TEXTURE IDENTIFICATION
As described in [31], the transducer was used in a causal-
ity inversion process: recording force and stimulating with
displacement, but instead of asking participants to simply
compare the roughness of a virtual surface with that of a
real one, we asked them to identify different textures, thereby
showing that they could discriminate textured surfaces in the
complete absence of stimulation distributed in space. The
principle of the experiment was to first record interaction with
five different texture samples. A group of participants were
then asked to identify three of these virtual samples among the
five real samples, and another group of participants to match
three of the real samples with the five real samples, leaving
much possibility for confusion. We expected participants to
be able to identify the real or the virtual textures with an
equivalent level of performance. We also expected that a
learning effect would be made apparent from the order of
testing.
A. Methods and Materials
1) Design: We used a 5-alternative forced-choice matching
procedure during which the participants were asked to identify
a comparison stimulus with the five five standard textures.
With the first group of five participants, in a first session, the
comparison stimulus was a real surface picked randomly in a
set of three and the standard stimuli were the five real textures.
They were then tested in a second session with a simulated
surface picked randomly among the same set of three as the
comparison stimulus and the standard stimuli were also the
five real textures. A different group of five participants was
also tested, but with the simulated stimuli first, and then with
real comparisons. The two missing textures in the comparison
set served as ‘catch samples’ to test the participants’ ability
to detect non matching textures. They also acted as distractors
since the participants were looking for them.
2) Sensing apparatus: The transducer was used to measure
the interaction force of the author’s finger sliding on a textured
surface as in Fig. 9. The samples were placed on the tray of the
