The original publication is available www.springer.com.
DOI: 10.1007/s10055-011-0192-z
Noname manuscript No.
(will be inserted by the editor)

Discriminability-Based Evaluation of Transmission
Capability of Tactile Transmission Systems
Shogo Okamoto · Masashi Konyo · Satoshi Tadokoro

Received: date / Accepted: date

Abstract Tactile transmission systems deliver tactile
information such as texture roughness to operators ofrobotic systems. Such systems are typically composedof tactile sensors that sense the physical characteristics of textures and tactile displays that present tactile
stimuli to operators. One problem associated with tactile transmission systems is that when the system has abottleneck, it is diﬃcult to identify whether the tactile
sensor, tactile display, or perceptual ability of the user isthe cause because they have diﬀerent performance criteria. To solve this problem, this study established anevaluation method that uses the discriminability index
as an evaluation criterion. The method lets tactile sensors, displays, and human tactile perception be assessedin terms of the ability to transmit physical quantities;
the same criterion is used for all three possible causes sothat their abilities can be directly compared. The developed method was applied to a tactile-roughness transmission system (Okamoto et al. 2009), and its tactile
sensor was identiﬁed as the bottleneck of the system.
Keywords Assessment of man-machine system ·Discriminability index · Performance measurement ·Tactile display · Tactile sensor
1 Introduction
A large number of tele-operation or telecommunication
systems provide sensory feedback to users; these can inS. Okamoto
The Graduate School of Engineering, Nagoya University, Furocho, Chikusa-ku, Nagoya, Japan
E-mail: okamoto-shogo@mech.nagoya-u.ac.jp
M. Konyo and S. Tadokoro
The Graduate School of Information Sciences, Tohoku University,
6-6-1, Aramaki Aza Aoba, Sendai, Japan

Fig. 1 Image of Master-Slave-Type Tactile Transmission System

clude force, tactile, or visual sensations. Sensory feedback is useful for improving the operability and validityof such systems. Quantitatively evaluating the components of sensory-feedback systems and identifying thecomponents that cause deterioration in the system performance will be useful for enhancing sensory feedback.
This study focuses on tactile transmission systems,
which are a type of sensory feedback system. Tactile
transmission systems deal with cutaneous sensations
such as the texture sensations of rough or smooth surfaces and the sense of contact with objects. Several tactile transmission systems have been developed thus far.
Most of these systems consist of tactile sensors and displays. For instance, consider the transmission of texture
sensations in systems using master-slave-type robots(Fig. 1). In such systems, tactile sensors and displays
are installed in slave and master robots, respectively.
The sensation of the textures touched by the slave robot
is transmitted to the operator by means of tactile displays (Yamauchi et al. 2010; Yamamoto et al. 2006). In
palpation systems used for minimally invasive surgery,tactile sensors have been installed on the tip of probes.
The probes are pressed onto the body tissues of patients. Tactile displays equipped on the other side of theprobe provide physicians with information on the pressure distribution on the tactile sensor (Ottermo 2006;

2

Howe et al. 1995). For prostheses, information on contact locations or the intensity of force applied to artiﬁcial limbs is delivered to the wearers (Fan et al. 2008;
Warwick et al. 2003).
Problems The accuracy of the tactile sensations delivered to the operators or users depends on the tactile
sensor’s ability to sense texture or contact information,
tactile display’s ability to present tactile stimuli to theoperators, and operator’s perceptual ability. If the performance of the developed tactile transmission systems
is found to be worse than what is required or expected,
the bottleneck in the system causing the deteriorationin performance must be identiﬁed and corrected. However, no method has yet been established that quantitatively compares the performance of the tactile display,sensor, and human perception individually and holistically and then correctly identiﬁes the factors causing
the deterioration.
If tactile sensors with sensing abilities considerably
better than those of humans are available, and if tactile
displays are capable of presenting stimuli with resolutions better than what a human can distinguish, quantitatively comparing the abilities of the display, sensor,
and human tactile perception would be unnecessary. Insuch cases, the human perceptual capability would limit
the performance of the entire system. However, humantactile perception has good resolution and a wide sensible range both spatially and temporally. For example, ahuman ﬁnger can detect vibratory stimuli with an amplitude of smaller than 1 μm and a weight of less than
0.1 g to the pain level of a few kilograms, discriminate
two-point stimuli with a gap of approximately 2 mm,
and respond to vibrations of 1 kHz (Jones et al. 2006).
Of course, some devices partially surpass these sensitivity levels. For example, Motoo et al. (2007) developed atactile sensor with a sensitivity range that changes fromthe level of a few Pascals to 10 kPa. Summers et al.
(2002) developed a tactile pin matrix display with 100
independently drivable pins in an area of 1 cm2 . Killebrew et al. (2007) devised a dense matrix with 400
pins/cm2 for neurophysiological purposes. However, ingeneral, it is technically diﬃcult to develop tactile sensors and displays with abilities that surpass human tactile perception. Further, manufacturers of commercial
products usually do not prefer systems in which somecomponents perform considerably better than others.
Therefore, in most tactile transmission systems, tactile sensors and displays whose abilities more or lessmatch humans tactile perception are used. These components of a tactile transmission system must be quantitatively compared in order to identify the bottleneck
among them.

Objective The objective of this study is to establish
an evaluation method that can assess tactile sensors,
displays, and human tactile perception using the same
criterion and thus identify the bottlenecks in a tactile transmission system. As an example, the proposed
method is applied to a roughness transmission system.
2 Related Studies
This section describes the manner in which tactile transmission systems were evaluated in related studies. The
tactile sensor and tactile display are chosen or developed before the development of the transmission system. In previous studies, tactile sensors were designedon the basis of certain criteria such as spatial resolution, maximal and minimal sensible pressure, and refresh rate (Ottermo 2006; Pawluk et al. 1998). Similarly, tactile displays were designed on the basis of spatial density, maximal output force or displacement, andfrequency response characteristics of tactors (Goethals
et al. 2008; Peine et al. 1997; Yao & Hayward 2005).
For completely developed and ready systems, theperformance of the entire system was evaluated in previous studies in terms of how operators actually use thesystems and perform tasks. For example, when evaluating texture transmission systems, operators select the
textures that they feel are closest to those perceived
through the system (Yamamoto et al. 2006). In somestudies, the performance of palpation systems with tactile transmissions was evaluated by performing tasks
to distinguish the size and stiﬀness of tumor-like objects (Ottermo 2006) or to localize them (Howe et al.
1995). The performance of prostheses with tactile feedback was evaluated through tasks in which the wearers
discriminate the intensity or pattern of pressure stimuli
that are presented to the limbs (Fan et al. 2008). For
teleoperation systems with tactile feedback, one study
rated the performance of the systems on the basis of thecompletion time of given tasks, such as putting a peg
into a hole (Kontarinis & Howe 1995). Subjective ratings in accordance with the Likert scale or quality of service have also been employed to evaluate the validity of
sensory feedback systems (Dev et al. 2002; Hikichi et al.
2006). Some of these subjective assessments come fromthe standards devised by the International Telecommunication Union for assessing pictures and sounds (ITUR 2004; ITU-R 2009).
When tactile transmission systems are developed,
the sensor and display are designed ﬁrst; the system isthen constructed from the components. Finally, the performance of the entire system is comprehensively evaluated through experimental tasks. However, the primaryobjective of the abovementioned studies was to test the

3eﬀectiveness of the developed tactile transmission systems and not to achieve a quantitative comparison of
the components for identifying bottlenecks in the system.

3 Proposed Method
Three conditions were considered for evaluation in the
proposed method. First, the same criteria must be applied to the tactile sensor, tactile display, human perception, and the entire system. Second, the method
must evaluate the transmission capabilities for physical quantities because many tactile transmission systems sense physical quantities and represent them tothe users. Finally, considering the noise in sensory outputs and the variations in human responses to a stimulus, the evaluation method should be applicable to systems with probabilistic responses.
This paper proposes the adoption of discriminability
indices for physical quantities as the evaluation criteria;these are applied to the tactile sensor, tactile display,human tactile perception, and the entire system. The
discriminability index is an index that is used in signal detection theory to indicate how readily a humancan detect stimuli (Green & Swets 1966).The indices
are calculated by observing the variations in human responses toward physical stimuli. Because the discriminability index assumes that the responses toward thestimuli follow probabilistic distribution, it can be used
for both human perception as well as tactile sensory
systems. The index allows us to evaluate and compare
each component of tactile transmission systems using
the same criteria.
The method evaluates the system based on the accuracy when transferring a unique physical quantity.
Therefore, the proposed method is not eﬀective for tactile information involving multiple physical quantities.
For instance, the recognition of textures, i.e., clothes, isaﬀected by the various physical properties of textures.
Hence, the proposed method cannot evaluate how accurately the texture sensations are transferred. However, it can be applied to each of the physical properties that are related to texture sensations, such as
surface roughness or friction coeﬃcient. In this case,the method can be eﬀectively applied to those physicalquantities that predominately contribute to the texture
sensations. These physical quantities have been identiﬁed to some extent (e.g., Shirado et al. 2005; Yoshioka et al. 2007).

Fig. 2 Human Probabilistic Response toward Physical Stimuli

3.1 Discriminability Index
In signal detection theory, d is used as the discriminability index and is calculated from the distributionsof a human’s response toward physical stimuli. Fig. 2
shows the distributions of internal responses of a human to three physical stimuli S1 , S2 , and S3 . Thesephysical stimuli have diﬀerent magnitudes. The human
responses to these stimuli follow the normal distributions with averages of μ1 , μ2 , and μ3 , respectively, andthe standard deviations of σ. The deﬁnition for d isdetermined by the distance between the centers of two
internal responses and the uncertainty σ, which is givenbyμi − μj.
(1)dij =σA large d value indicates that it is easy to detect thediﬀerence between Si and Sj . When perceptual unidimensionality can be expected,d13 = d12 + d23

(2)

holds (Macmillan & Creelman 2005). d13 is also givenbyμ1 − μ3.
(3)
σHowever, for real experimental data, the cumulative d13
determined by (2) is not always equal to the one derivedby (3). Hence, in this study, we use the estimated ddetermined by the least square method (Gulliksen 1956)
using the d values of (2) and (3).
Let dij be d between Si and Sj (i, j = 1, ..., n). d0i
is the estimated d between Si and an arbitrary originof the internal response. The observed dij is describedby the estimated d0i and d0j :d13 =

dij = −d0i + d0j .

(4)

Therefore,nj=1dij = −(n − 1) · d0i +

n

j=1

d0j

i = j.

(5)

4

Because we have (5) for each i, we get⎡ n⎡⎤⎡  ⎤
 ⎤−(n − 1) · · ·1d01
j=1 d1j
⎥ ⎢
⎢
⎥
⎢
..
. ⎥
.
.
.
..
..
..
⎦=⎣
⎣
⎦ ⎣ .. ⎦ . (6)
.
n

d0n
1
· · · −(n − 1)
j=1 dnj
We describe (6) as
Dobs = A · Dest .

(7)

However, because of the lack of degrees of freedom, A−1
does not exist. To solve this, we need to use a submatrixof A. We assign zero to d01 , which means that we set theorigin on d01 . Then, the ﬁrst column of A is eliminated,and (6) is transformed to⎡⎡ n⎤⎡  ⎤
 ⎤
1 ···
1
d02
j=1 d1j⎥ ⎢ .. . .
⎢⎥ ⎢ .. ⎥..
.
.
(8)⎦=⎣. .
⎣⎦⎣ . ⎦.
.
.
n


d0n
1 · · · −(n − 1)
j=1 dnj
We describe (8) as
Dobs = B · Eest .

(9)

The estimated d values are given by
Eest = (B T B)−1 B T Dobs .

(10)

3.2 Procedures of Proposed Evaluation Method
In the evaluation procedure, the performances of thetactile sensor, tactile display, human tactile perception,and the entire system are evaluated by conducting experiments. For each experiment, discriminability indices
are computed from the responses of human observers orof tactile sensors. For the tactile display, its outputs forgiven commands are assessed for computing the indices.
First, the evaluation for the tactile sensor is described. Here, the sensory outputs against the inputsof physical stimuli are recorded; this is a standard assessment procedure for sensors. For example, for signal
detection tasks, we record the ratios at which the sensor
successfully detects the physical stimuli. The discriminability index is then calculated based on the signal
detection ratios. For example, for signal discrimination
tasks, sensory outputs with an input of physical stimulus are recorded, and the mean and standard deviations
for the outputs of each input are recorded. By applying the law of comparative judgment (Thurstone 1927),
which is elaborated upon in section 5.1, to the measuredmeans and standard deviations, the discriminability indices are calculated.
Second, with respect to the evaluation of tactile displays, the display is used repeatedly, and its outputs arerecorded. This is a common assessment process for tactile displays. The discriminability indices are computedfrom the output means and deviations.
To evaluate the human ability for tactile perception,
the tactile display is not used, and the physical stimulus
is directly applied to the ﬁnger of the experiment participants, who may also explore the stimuli using theirbare ﬁngers. Because, data on the sensitivity of tactile
perception are available in literature in many cases, additional experiments may not be needed.
When real stimulus samples can be used to evaluate human tactile perception or when the usage of suchstimuli is appropriate, an evaluation involving real samples is recommended as a straightforward method. For
some tactile displays, however, stimuli from tactile displays qualitatively diﬀer from those from the real samples. For example, a plane composed of a pin matrix is
diﬀerent from the continuous surfaces of real samples.
In such cases, a comparison between human tactile perception of the stimuli presented by the tactile display
and that of real samples is invalid. Therefore, in casessuch as the example in section 5, the ability of humantactile perception is evaluated against the stimuli applied by the tactile display. It should be noted that theabilities of human and tactile displays cannot be separately assessed in these cases. In this method, the human responses against physical stimuli presented by atactile display are recorded. Similarly to for the tactile
sensor, both signal detection and discrimination tasks
are possible. Signal detection tasks are based on thesignal detection ratios, while discrimination tasks are
based on the correct discrimination ratios of the task;
in both cases, the discriminability index is calculated
by taking these factors into consideration.
Finally, to evaluate the entire system, the index is
calculated in the same manner as that for the humanperception mentioned above. However, in this procedure, the experiments are conducted by using the entire
system connecting the tactile sensor and tactile display.
As described above, the discriminability index is calculated separately for each of the tactile sensor, tactile
display, entire system, and human perception. Finally,
by comparing these indices, the bottleneck in the system can be identiﬁed.

4 Outline of Roughness Transmission System
The proposed evaluation method is applied to a tactileroughness transmission system (Okamoto et al. 2009),
which is outlined here. The roughness transmission system consists of a master-slave-type robot, as shown in
Fig. 3. The motion of the slave arm is synchronized with

5

that of the master arm. A tactile sensor is installed on
the slave arm. The roughness sensation of a texture
scanned by the tactile sensor is transferred to the operator on the master side by using a tactile display. The
system can transfer the perceived roughness of gratings
with a surface wavelength varying 0.8–2.0 mm in increments of 0.2 mm.
To deliver the sensation of roughness to a systemuser, the system transfers vibrotactile stimuli to the ﬁnger pad of the user while s/he explores a rough texture
using the master-slave system. The vibratory frequency
and amplitude of the stimuli are controlled. While scanning the texture, the displacement applied to the ﬁnger
pad is determined byy(t) = A(t) sin (2π

x(t)
)
λ(t)

Fig. 3 Master-Slave-type Roughness-transmission System(11)

where x(t) and λ(t) denote the position of the user’s ﬁnger on the texture along the X-axis and surface wavelength of the texture, respectively. The vibrotactile frequency is determined by f (t) = |v(t)|/λ(t), where v(t)is the exploring velocity of the user’s ﬁnger. The frequency changes according to the hand speed and onlineestimated surface wavelength. The tactile sensor estimates λ(t), and transfers it to the master side of thesystem. The amplitude of the vibratory stimuli is givenby A(t), which is determined by the magnitude of thesensory outputs of the tactile sensor in real-time. A(t)is not used in this study since the evaluation method
is applied to λ(t) (see sections 5 (ﬁrst paragraph) and5.3.2).

4.1 Tactile Display and Master System
Fig. 4 shows the tactile display used in the system. The
display adopts a piezo-stack actuator (NEC/TOKIN,
ASB510C801P0, Japan) as a stimulator. The stimulator is installed on a linear slider. The user of the system places his/her right middle ﬁnger on the stimulator and then moves his/her hand along the linear guide(X-axis), as shown in Fig. 3. The position of the linear slider is measured by a linear encoder and sent to acontrol computer for producing the tactile stimuli. The
computer outputs the voltage supplies to the stimulator based on x(t), λ(t), and A(t), which are determinedusing (11). As a result, the stimulator produces a displacement along its longitudinal direction (Z-axis). The
control frequency for the tactile display is 3 kHz. The
participants agreed that the stimuli perceived by theequipment were similar to those perceived when they
explored rough textures such as gratings by using astylus with a blunt tip.

Fig. 4 Tactile Display

Fig. 5 Grating

4.2 Tactile Sensor and Slave System
The slave system is mainly comprised of a slave armand tactile sensor. The tactile sensor is installed on thearm, as shown in Fig. 3. The sensor consists of silicone
rubber with a Young’s modulus that is similar to thatof a human ﬁnger (Mukaibo et al. 2005). The dimensions of the sensor are three times as large as those of
the average human middle ﬁnger. Strain gauges are embedded inside the sensor as transducers. When the arm
moves and the sensor scans the texture surfaces, thedeformation of the tactile sensor is sensed by the strain
gauges. The outputs of the strain gauges are sampled
at 1 kHz.
The tactile sensor estimates the surface wavelength
λ(t) of rough textures. λ(t) is estimated using the relationship λ(t) = |v(t)|/f (t), where f (t) denotes thevibratory frequency of the sensory outputs at t. f (t)is acquired by computing the short-time Fourier transformation (STFT) of the sensory outputs. The estimation algorithm is described in detail in the literature(Okamoto et al. 2009).
Fig. 5 shows the grating scanned by the tactile sensor. The grating has alternating machined grooves andridges on its surface. Its surface wavelength is characterized by the sum of the groove and ridge widths. In
our study, the ratio of the groove width to the ridge
width was 1, i.e., the groove width is equal to the ridge
width.

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5 Application of Proposed Method to
Roughness Transmission System
As an example, the proposed evaluation method wasapplied to a roughness transmission system; the performance is described here. The evaluation was conductedfollowing the procedures described in section 3.2. As described in section 3, the proposed method assesses thetransmission capability of a unique physical quantity.
The roughness transmission system functions by transferring two types of physical quantities: λ(t) and A(t).
The proposed method was applied to λ(t); therefore,
A(t) was not transferred in the experiments. In normal
usage, A(t) determines the amplitude of the vibrotactile
stimuli in proportion to the magnitude of the sensory
outputs of tactile sensor in real-time. However, insteadof using A(t), the amplitude of the vibrotactile stimuli
was determined here by an equal sensation curve of thevibrotactile stimuli such that the amplitude does not
aﬀect the participants’ perception. This is elaborated
upon in section 5.3.2. Since λ is more appropriate fordiscrimination rather than signal detection tasks, thetasks in the experiments were designed to be the former.

Fig. 6 Surface Wavelengths of Gratings Estimated by Tactile
SensorTable 1 Tactile sensor: d between two gratings

λ2

Table 2 Tactile sensor: Estimated d between two gratings

5.1 Evaluation of Tactile Sensor
An experiment was conducted to estimate λ of gratings
using the tactile sensor. In the experiments, the sensor
scanned the gratings, and STFT was computed fromthe sensory outputs acquired there. The scanning velocity was sinusoidal with a frequency of 1.07 Hz and maximum speed of 197.0 mm/s; the speed and frequency
were determined by the average measured data in literature (Okamoto et al. 2009), in which thirteen people
explored a virtual texture with the same tactile display
used in this study. The computation for the estimation
was conducted at 1 kHz and was based on the data forﬁve cycles, i.e., 4.665 s. Fig. 6 shows the experimental results as the average and standard deviation of theestimated λ(t).
The data shown in Fig. 6 can be used to obtain d byapplying the law of comparative judgment (Thurstone
1927). The concept is as follows. We have two probabilistic variables X1 and X2 that are subject to thenormal distributions N (μ1 , σ12 ) and N (μ2 , σ22 ), respectively. We want to calculate probability P (X1 > X2 )in which X1 becomes larger than X2 . P (X1 > X2 ) isequal to P (X1 − X2 > 0). The diﬀerence between thetwo variables, X12 = X1 − X2 is also subject to the normal distribution N (μ1 − μ2 , σ12 − 2γ12 σ1 σ2 + σ22 ), where
γ12 is a correlation coeﬃcient between X1 and X2 , and
γ12 = 0 in this case. d between these two distributions

Surface wavelength of sample: λ1
1.0 mm 1.5 mm 2.0 mm
0.5 mm
1.31
3.06
5.20
1.0 mm1.32
3.17
1.5 mm2.35

d(0.5,0.5)d(0.5,1.0)d(0.5,1.5)d(0.5,2.0)

0

1.60

2.90

5.07

is given byd12 =

μ1 − μ2
σ12 + σ22.

(12)

We regarded λ(t) estimated by the sensor as probabilistic variables that are subject to the normal distribution. The mean and standard deviation of the distributions were determined from the data shown in Fig. 6.
For instance, when λ = 1.5 mm, the mean and standard
deviation of the estimated values were 1.361 ± 0.169
mm. Furthermore, when λ = 1.0 mm, they were 0.956±
0.255 mm. Thus, X1 and X2 were regarded as subject
to N (1.361, 0.1692) and N (0.956, 0.2552), respectively.
X12 is subject to N (0.405, 0.3062). d12 between X1 andX2 is 0.405/0.306 = 1.32. For the other pairs of gratings, d were computed the same way and are shown in
Table 1. By applying the least square method describedin section 3.1 on the data of this table, we get the estimated d as shown in Table 2. d(0.5,0.5) in the table
is meaningless. This variable was merely yielded during
the computation of the least square method.

7

5.2 Evaluation of Tactile Display
The tactile display was evaluated in terms of its ability to accurately present the vibratory frequency. The
frequency characteristic of the piezo stimulator reached−3 dB at 310 Hz. The command refresh rate for the
stimulator was 3 kHz. The maximum vibrotactile frequency used in the latter experiments was approximately
170 Hz with a supposed maximum hand speed of 200
mm/s and minimum surface wavelength of 1.2 mm.
Within the frequency band used in the experiments(up to 170 Hz), in terms of the accuracy of the frequency, the ability for the tactile display exceeds thatfor human perception, for which the diﬀerential limenof vibrotactile frequencies is approximately 20 % overa wide frequency range (Goﬀ 1967; Rothenberg 1977).
Thus, we omitted the assessment of the tactile display.

1.4 mm), (1.2mm, 1.6 mm), (1.4 mm, 1.6 mm), (1.4mm, 1.8 mm), and (1.6 mm, 1.8 mm). The pair of (1.2mm, 1.8 mm) was excluded since the participants of thepreliminary experiments could correctly discriminate it
at a rate of approximately 100%. Each participant performed ten trials per pair for a total of 50 trials. The
order of comparison pairs presented to the participants
was random. Exps. A and B took approximately 20 and
40 min, respectively, to complete.

5.3 Evaluation of Human Perception and Entire
SystemParticipants Eight paid students from Tohoku University in their twenties participated in both Exps. A andB. Four of the eight participants performed ﬁrst Exp. A
and then Exp. B, while the other participants went in
the opposite order. The participants practiced for approximately 5–10 min until they felt familiar with theprocedures of the task. The participants wore a headphone and listened to pink noise during the experiments
in order to block the sounds produced by the vibrator.
Since they had to know the position of the linear slider
on the guide, they were not blindfolded.

5.3.1 Experimental Methods

5.3.2 Vibrotactile Stimuli

Tasks In order to evaluate the transmission capabilityof the human perception and the entire system, Exps.
A and B were conducted. In Exp. A, the participants
discriminated pairs of λ by using the tactile display
only. λ was given to the control computer of the tactile display instead of being estimated by the slave-sidesystem. Thus, the performance of the tactile sensor did
not aﬀect Exp. A. In Exp. B, the participants discriminated pairs of λ using the master-slave system. λ wasestimated by the tactile sensor and sent online to thetactile display system.
The experiments were a paired comparison. As shownin Fig. 3, two gratings of diﬀerent λ were arranged on
the left and right side of the linear slider or slave arm as
the stimuli. After hearing a beeping sound as a cue, theparticipants explored both the stimuli for 20 s in total;they then reported the λ that they felt was larger. The
task was a two-alternative forced choice. At the beginning of the experiments, the linear guide and slave arm
were positioned at the center of their moving range by
the experimenters.

As mentioned in the ﬁrst paragraph of section 5, thetransmission system did not transfer the amplitude of
the vibrotactile stimuli A(t) in the experiments, while
the system usually transfers both A(t) and λ(t) in realtime. The amplitude of the stimuli was set to have aconstant sensation level such that the amplitude would
not aﬀect the judgment of λ(t). Hence, the participants judged λ(t) solely from the vibratory frequencyof the stimuli. The amplitude was determined by obtaining a curve of equal sensation magnitude for vibrotactile stimuli. Before the main experiments, the curveof the equal sensation magnitude for vibrotactile stimuli was identiﬁed by a preliminary experiment involving
six participants. The preliminary experiment was conducted by the method of adjustment using the same
setup used in this study. Fig. 7 shows the identiﬁed
curve. The vertical axis in the ﬁgure is half of the peakto-peak amplitude of the applied voltage. The error bar
in the ﬁgure shows the maximum and minimum valuesof the participants’ answers. The corresponding peakto-peak displacements of vibrations are shown in parentheses in micrometers. The curve was U-shaped with alocal minimum around 200–300 Hz. These characteristics are identical to those of the curve of equal sensation
magnitude reported in other studies (Goﬀ 1967; Verrillo1969).The curve is an approximation of the reported
values (R2 = 0.998), and it is⎧⎨ log10 a(f ) = 3.07e−5 f 2 − 1.65e−2f + 2.386
if f ≥ 35.1(13)⎩a(f ) = 70
otherwise,

Stimuli Four stimuli with λ of 1.2, 1.4, 1.6, and 1.8 mm
were used. The interval of each stimulus’s λ was set to
0.2 mm. Using the data of preliminary experiments,
the interval was determined such that the paired comparison tasks would not become too diﬃcult or easy.
The ﬁve comparison pairs were obtained by excluding
a pair (1.2 mm, 1.8 mm) from the six comparison pairs
formed by the four stimuli. The pairs were (1.2 mm,

8
Table 6 Result of Experiment B (entire system): Discrimination
ratio for surface wavelengths

λ2Surface wavelength of samples: λ1
1.4 mm
1.6 mm
1.8 mm
1.2 mm 0.76 ± 0.13
0.84 ± 0.17
1.4 mm0.74 ± 0.24
0.86 ± 0.09
1.6 mm0.79 ± 0.12

Table 7 d for Experiment B (entire system)

λ2

Fig. 7 Amplitude of voltage applied to vibrator based on equal
sensation curve. Values in parentheses are the corresponding
peak-to-peak output displacement in micrometers.

Surface wavelength of samples: λ1
1.4 mm 1.6 mm 1.8 mm
1.2 mm0.71
0.98
1.4 mm0.64
1.09
1.6 mm0.80

Table 8 Estimated d for Experiment B (entire system)d(1.2,1.2)
0d(1.2,1.4)
0.57

d(1.2,1.6)
1.15

d(1.2,1.8)
1.72

Table 3 Result of Experiment A (human + tactile display): discrimination ratio for surface wavelengths

λ2Surface wavelength of samples: λ1
1.4 mm
1.6 mm
1.8 mm
1.2 mm0.82 ± 0.14
0.94 ± 0.05
1.4 mm0.81 ± 0.18
0.90 ± 0.10
1.6 mm0.77 ± 0.16

Table 4 d for Experiment A (human + tactile display)
Surface wavelength of samples: λ1
1.4 mm 1.6 mm 1.8 mm
1.2 mm0.93
1.55
1.4 mm0.89
1.29
1.6 mm0.72

λ2

Table 6 shows the discrimination ratios acquired byExp. B. The corresponding d values and estimated d
values by the least square method are presented in Tables 7 and 8, respectively.

Table 5 Estimated d for Experiment A (human + tactile display)d(1.2,1.2)

d(1.2,1.4)

d(1.2,1.6)

d(1.2,1.8)

0

0.75

1.50

2.25

where f is the frequency of vibrotactile stimuli. Basedon the identiﬁed curve, the amplitude of the voltage
supply to the vibrator was determined. Hence, in theexperiments, the amplitude of the voltage supply was
E(t) = a(f (t)) sin (2π

x(t)
)
λ(t)

sponded to the pairs of (λ1 , λ2 ). The ratios are the averages and standard deviations for the responses of theeight participants. Table 4 presents d values computedby the averages of the discrimination ratios in Table 3.
These d values were computed into estimated d values by using the least square method. The estimated d
values are in Table 5.

(14)

where f (t) = |v(t)|/λ(t). The amplitude was set to a
constant value when f (t) was smaller than 35.1 Hz sothat the voltage supply did not exceed the voltage capacity of the vibrator.
5.4 Results and Estimated d
The results of Exp. A is given in Table 3. The tableshows the ratios at which the participants correctly re-Fig. 8 shows the estimated d of Tables 2, 5 and 8.
The estimated d were approximated by a linear equation. In order for the three lines to have the same origin
for visual clarity, the scores were shifted such that they-intercept of each line became zero. The higher theslopes of the lines, the higher is the system’s ability todiscriminate λ.

5.5 Comparison of System’s Transmission Capability
Table 9 summarizes the slopes of the approximatedlines. The highest slope was for the human perception
plus tactile display at 3.75. The second-highest slope
was for the tactile sensor at 3.31. The slope of the entire system was 2.86, which is lower than that of eachcomponent. Therefore, the capability of the entire system was limited by the tactile sensor’s ability to estimate λ. The results indicate that in order to improvethe capability of the entire system, the tactile sensor orits sensing algorithm should be improved ﬁrst.

9determined by
ds+h = Fig. 8 Graphs of d vs. Surface Wavelengths of Roughness Samples

11
1
d2s + d2h

= 

1
1
1
3.312 + 3.752= 2.48(15)

where, ds and dh are the slopes of discriminability indices for the tactile sensor and tactile display, respectively. However, the slope of the entire system was 2.86
in the experiment, which showed a better performance
than the slope of 2.48. Although the reason of this discrepancy is unclear, we suggest that this increase in theperformance was due to the imbalanced eﬀects of ds anddh on the human perceptual process. For example, in(15), it would be necessary to weight ds and dh in someway for better estimation of the entire system’s performance than that expected based on the propagation oferrors.

Table 9 Slope of d for Each System
SystemSlope

Human + Display(Exp. A)
3.75

Sensor
3.31

Entire(Exp. B)
2.86

5.6 Discussion
In the comparison, the performance of the entire system
was worse than that of the tactile sensor and tactile display. Intuitively, the performance of the entire systemshould be as bad as the component with the worst performance in the system. Here, we discuss why the entire
system performed worse than its components due to the
propagation of errors.
In the tactile transmission system, the tactile sensor
estimates a physical quantity and transmits it to themaster-side system with the error. In the master-sidesystem, the tactile display presents the physical quantity to the users of the system. The internal response of
the users toward the physical quantity presented by thetactile display includes uncertainty or probabilistic error. Thus, the error of the tactile sensor is additionallyimposed onto the perceptual process of the users. Suppose, the tactile sensor estimates the physical quantitywith the standard deviation of σs . The uncertainty of
the human internal response toward the input of physical quantity is expressed as σh . The uncertainty of thehuman response toward the physical quantity estimated1by the tactile sensor is (σs2 + σh2 ) 2 , which is larger thanσs or σh . Therefore, the entire system’s ability to discriminate the physical quantity is worse than that of
the tactile sensor or tactile display.
According to this concept, the discriminability index of the entire system per unit surface wavelength is

6 Conclusions
In this study, a method for identifying the bottleneck intactile transmission systems was developed. Such evaluation methods have not been proposed thus far partly
because the tactile sensor, tactile display, and perceptual ability of humans have diﬀerent performance criteria, and their performances cannot be directly compared. This problem was solved by using the discriminability indices as the evaluation criteria. The probabilistic outputs of tactile sensors and humans probabilistic responses in signal detection or stimuli discrimination tasks can be converted into discriminability indices. Hence, the evaluation method that we developed
allows us to quantitatively compare the tactile sensor,
tactile display, and human perceptual abilities in termsof the transmission capability of physical stimuli. The
developed method was applied to a tactile-roughnesstransmission system, and its ability to transfer the surface wavelength of rough textures was evaluated. The
results from the application of the method indicate thatthe performance of the entire system was limited by
the tactile sensor’s ability to estimate the surface wavelength.
Acknowledgements This work was supported by grants fromMIC SCOPE (082102006,) and MEXT Kakenhi (19360120) and(07J01804).

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