Necessary spatial resolution for realistic tactile feeling display

Abstract

In this paper, we show a hypothesis on the sensing mechanism in the human tactile organ and its resolution. The hypothesis is that human skin cannot resolve any finer pattern than the resolution suggested by the two-point-discrimination test, but that variety created by four kinds of signals from four kinds of mechano-receptors makes it possible to detect fine feature of texture. This means if we control stimulus to four kinds of mechanoreceptors individually, the realistic contact-feeling display will not need higher spatial resolution than suggested by the two-point discrimination threshold. We examine this hypothesis through psychophysical experiments.

Full text

Necessary Spatial Resolution for Realistic Tactile Feeling Display
Naoya ASAMURA, Tomoyuki SHINOHARA, Yoshiharu TOJO, Nobuyoshi KOSHIDA
and Hiroyuki SHINODA
Department of electrical and Electronic Engineering,
Tokyo University of Agriculture and Technology
2-24-16 Koganei, Tokyo 184-8588 Japan
asamura@cc.tuat.ac.jp (N. Asamura) shino@alab.t.u-tokyo.ac.jp (H. Shinoda)
Abstract
In this paper, we show a hypothesis on the sensing
mechanism in the human tactile organ and its resolution.
The hypothesis is that human skin cannot resolve any
finer pattern than the resolution suggested by the
two-point-discrimination test, but that variety created
by four kinds of signals from four kinds of
mechano-receptors makes it possible to detect fine
feature of texture. This means if we control stimulus to
four kinds of mechanoreceptors individually, the
realistic contact-feeling display will not need higher
spatial resolution than suggested by the two-point
discrimination threshold. We examine this hypothesis
through psychophysical experiments.
Keywords; virtual reality, haptic interface, tactile
feeling display, spatial resolution, two-point
discrimination, teletaction
1. Introduction
The recent development of the Internet is motivating
a cutaneous display that makes people feel realistic
tactile feeling, for on-line shopping or amusements
[1,2]. For such a display not aiming some manipulation
tasks [ 3,4 ,5, 6,7,8 ,9], the display area should not
necessarily be focused on the finger tip having the
highest receptor density. Instead, high-fidelity of tactile
feeling becomes crucial.
In this paper, we discuss the minimum requirement
for the special resolution of such a tactile feeling
display. Our target area in this study is the palm
because it seems sufficiently sensitive for tactile feeling
transmission and also dull enough for technological
realization.
The two-pint discrimination threshold (TPDT) is one
classical and popular measure of the skin resolution.
This TPDT is the minimum distance with which we can
identify 2 points given in a simultaneous
two-point-contact. The TPDTs on a fingertip and a
palm are 2~3 mm and about 10 mm respectively [
10].
However, the evaluation of the tactile resolution
includes some complex problems. Humans can identify
a very fine feature of objects less than the TPDT. For
example, our palms easily distinguish between the top
and the bottom of a pen though the both sizes are
smaller than the TPDT. Our skin is so sensitive that it
hardly feel the motion of pins arrayed on a device
create a realistic feeling of a cotton towel or a leather
bag.
In order to understand this paradoxical problem and
realize the realistic tactile display, we have to consider
both spatial resolution and skin receptor’s selective
sensitivity in parallel. In this paper, we propose a
hypothesis on the cutaneous sensing mechanism. The
scientific proof of the hypothesis will need other
researches including neurophysiological approaches
beyond the research in this paper. However, the
hypothesis suggests a base to understand the human
skin perception. In the following, we describe the
psychophysical experiments to examine the hypothesis,
and show that we can control various tactile feeling to
the palm by a low-resolution display device.
Fig. 1: Spatial resolution for displaying realistic tactile
feeling on the palm.
Proceedings of the 2001 IEEE
International Conference on Robotics & Automation
Seoul, Korea • May 21-26, 2001
0-7803-6475-9/01/$10.00© 2001 IEEE
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TPDT
Distribution
x
y
2
σ
σσ
σ
1
σ
σσ
σ
2
σ
σσ
σ
3
σ
σσ
σ
4
Fig. 2: Candidates for the four static stress bases in
hypothesis 2. The arrows represent the direction of the
applied force. The stress by σ
σσ
σ
4
does not reach the deep
part of the skin.
2. A Hypothesis on human tactile
perception
It is widely accepted that human glabrous skin has
four kinds of mechanical receptors. Though thermal
stimuli is also important for touch feeling [
11], we omit
that argument here. It is relatively easy to add thermal
controller to a mechanical stimulator because high
resolution and quick response are unnecessary.
The hypothesis we should examine here is:
Hypothesis
A half of TPDT is the sufficient resolution (interval of
stimulation) for displaying any fine tactile feeling if we
individually control stimulus to the four kinds of hand
mechanoreceptors.
The hypothesis is based on an analogy of the human
visual system. It says we do not need much finer
resolution than the TPDT even if we should display
very fine texture, as long as we stimulate the four kinds
of the mechanoreceptors selectively. It is well known
that human skin can distinguish very fine features of
the texture [12,13]. The hypothesis insists that the
human skin should perceive these fine features from the
4-D vector detected by the four kinds of receptors with
sampling intervals 1/2
× TPDT. If the four kinds have
different spatial responses, they can detect such features,
just as our three kinds of RGB visual receptors identify
colors.
On the palm, it is said that the density of innervation
of each types of receptors is 10~30 units/cm
2
[14].
Among the four types, the two kinds of the superficial
receptors (Meissner corpuscle and Merkel cell) are
located more densely than the others, and their densities
are especially high on the fingertip [15]. The other two
receptors (Rufini ending and Pacinian corpuscle) are
located in the deep part of the skin. The temporal and
spatial responses are various among the four types [16],
but there is a certain temporal frequency range in which
all the types respond well.
6 mm
5 mm
1 mm
Acrylic resin
board
S1
0.5 mm
in diameter
S2
Skin
Fig. 3: Selective stimulator to a human palm. The S1
applies uniform normal stress (σ
σσ
σ
3
) while the S2 applies
concentrated normal stress (σ
σσ
σ
4
approximately).
3. Examination of the hypothesis
Let (x,y) be the spatial coordinate system on a hand.
Suppose stress distribution given on the hand is written
as σ
σσ
σ(x,y,t) = (σ
x
(x,y,t),σ
y
(x,y,t),σ
z
(x,y,t)). Next we
describe the subjective feeling to a stress distribution σ
σσ
σ
as p(σ
σσ
σ). A equation p(σ
σσ
σ
1
) = p(σ
σσ
σ
2
) means that the
tactile feeling to σ
σσ
σ
1
is identical to (indistinguishable
from) that to σ
σσ
σ
2
.
For a point Q(a,b) on the hand, we define Φ(Q) as a
subspace of stress distribution in which the stress is
zero outside the circle round the center Q with a radius
of TPDT/2. That is
Φ(Q (a,b))
= {σ
σσ
σ; σ
σσ
σ(x,y,t) = 0 where |(x-a, y-b)| > TPDT/2}.
Here we rewrite the hypothesis in a different manner.
Hypothesis 2
We can find four static stress bases σ
σσ
σ
1
,σ
σσ
σ
2
,σ
σσ
σ
3
, and σ
σσ
σ
4
in
Φ(Q) that realize P’ = P where
P = {p(σ
σσ
σ); σ
σ σ
σ
∈ Φ(Q)}
P’ = {p(σ
σσ
σ); σ
σ σ
σ = α
1
(t)σ
σσ
σ
1
+
α
2
(t)σ
σσ
σ
2
+
α
3
(t)σ
σσ
σ
3
+
α
4
(t)σ
σσ
σ
4
}.
This hypothesis means we can find four basic
components of stress pattern whose summation can
display any tactile feeling caused by any stress
distribution given around Q. If it is true, an array of the
stimulators giving the four bases with intervals of
TPDT/2 will be able to produce any tactile feeling.
The equivalence of the hypothesis 2 to the original
hypothesis is not very obvious. But from now we
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examine the hypothesis 2 instead of the original one
that was a hint to come up with the second one.
The candidates we imagine now for the four bases
are 1) smooth distribution (around Q) of x-directional
stress, 2) y-directional stress, 3) z-directional stress
(vertical to the skin), and 4) concentrated vertical stress
that does not reach the deep part of the skin [17]. See
Fig. 2. These candidates were obtained by the
following logic. First, since the skin can discriminate
among σ
σσ
σ
1
,σ
σσ
σ
2
, and σ
σσ
σ
3
, the bases should include them.
And because the human skin has an excellent ability to
detect sharp edge, we added one more basis σ
σσ
σ
4
to them.
We guess the σ
σσ
σ
4
is detected by the combination of
Meissner corpuscle and Merkel cell [18].
In this paper we report results of examining
hypothesis 2 for a subspace Φ
n
(Q) included in Φ(Q)
where Φ
n
(Q) consists of stress distributions having no
lateral components (no shearing stress). Then the two
bases σ
σσ
σ
3
and σ
σσ
σ
4
in Fig. 2 should display any tactile
feeling for any σ
σσ
σ in Φ
n
(Q). In order to examine this, we
prepared an apparatus as shown in Fig. 3 that stimulates
the skin with S1 and S2.
S1) Smooth normal stress distribution (σ
σσ
σ
3
) by a moving
cylinder with a diameter of 1/2
× TPDT.
S2) Concentrated normal stress distribution (σ
σσ
σ
4
approximately) by a needle through the S1 cylinder.
The stimulator S1 represents an object with very
small curvature, while the S2 very large curvature. We
examine whether the combination of the S1 and S2 can
create tactile feeling of an intermediate curvature of an
object, and whether the curvature can be controlled
continuously from a sharp tip to a smooth surface.
If this is true, the hypothesis 2 for the subspace
Φ
n
(Q) sounds very reasonable because the contact in
general can be assumed as a combination of multiple
contacts with various curvature surfaces.
Fig. 4 shows the apparatus for experiments. The
diameter of S1 is 5 mm, a half of TPDT 10 mm on palm,
while the inside diameter of S1 is 1 mm. The S2 is a pin
with diameter of 0.5mm. Each stimulator moves
independently in vertical direction. Subjects put the
hand on a flat panel, and we apply the S1 and S2
through a hole in the panel. The examined part is the
thenar for the easiness of the experiment.
The S1 and S2 are actuated by ultrasonic motors with
displacement-resolution 0.002 mm/pulse.
(a)
(b) (c)
Fig. 4: Photographs of the apparatus. (a): The structure.
(b): The stimulators S1 and S2. (c): A view of the
experiment stimulating a thenar.
0
400
800
200
600
1000
0
0.5
1.0
Time(ms)
D
i
s
p
l
a
c
e
m
e
n
t
(
m
m
)
S2
S1
Fig. 5: Experiment I. Displacement patterns of the
stimulator S1 and S2.
Display surface
Skin (palm)
Steel s
p
here
Diameter :1mm
3mm
5mm
S2
S1
Fig. 6: Tactile feeling comparison between synthesized
stimuli and real sphere surfaces.
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4. Experiment I
When the S1 and S2 were driven by a signal pattern
as shown in Fig. 5 (they are at the same level at the
beginning), the subjects did not feel a projection on a
flat surface but an intermediate curvature surface. Then
we examined if we could produce tactile feeling
identical to a round object with an intermediate
curvature by using S1 and S2. The hand is fixed and
passive to stimuli.
Stimuli
We prepare the best driving pattern to create the
feeling of the sphere 3 mm in diameter. In that best
signal, the maximum displacements of S1 and S2 are
0.8 mm and 1.2 mm, respectively. We name this
stimulus “Virtual.” Another stimulus is a contact with a
real 3 mm-diameter sphere moving in the S2 pattern in
Fig. 5. We name this “Real.” In addition to these, we
prepare one more similar stimulus “V2” for a reference,
in which S1 does not move (displacement zero) while
S2 follows the S2 pattern in Fig. 5. Using these signals,
we test if the subject can discriminate between the
synthesized feeling by S1 and S2 and the real spherical
object.
Procedure
We give the subject two stimuli sequentially at a 4
second interval. The one stimulus is the “Real” arising
twice at a 1 second interval. The other is one of three
kinds of stimuli “Virtual,” “Real,” and “V2” that also
arise twice at a 1 second interval. Then the subject
replies either “yes” or “no” to the question “Is the
second stimulation (after the 4 second interval)
identical with the first one?” See Fig. 6. The choice of
the stimulus combination and the order are random, and
each subject answers fifteen times to a series of trials.
The subjects were six males in their twenties with
eye-masks and headphones.
Results
Fig. 7 shows the percentage that the subjects
answered “identical” in response to the sequentially
given 2 stimuli. “Real-Real” means the case the tester
touched the identical sphere twice, and “Real-Virtual”
means stimulus “Real” and “Virtual” were given
sequentially.
Even for “Real-Real,” the subjects sometimes felt
they were not identical. The result shows the stimulus
“Virtual” felt so similar to the “Real” that they missed
the difference once in twice even if they concentrated
on that.
0
10
20
30
40
50
60
70
80
90
100
Real-Real Real-V2 Real-Virtual
Stimulus pair
Percentage of yes [%]
0 %
Fig. 7: Results of discrimination test. Percentage that
the six subjects answered that the two stimuli given
sequentially felt identical. The“Real-Virtual” means the
case the stimulus “Real” and “Virtual” were given
sequentially.
5. Experiment II
In this experiment we examine how the perceived
curvature changes when we change the maximum
displacement of S1 in Fig. 5.
Stimuli
Also in this experiment, the S2 is driven in the S2
pattern in Fig. 5. And the Subjects are given seven
types of stimuli in which the S1 reaches the maximum
displacement in seven manners. The times to reach the
top and to start going down are common while the top
displacements are (A) 1.2mm, (B) 1.1 mm, (C) 1.0 mm,
(D) 0.9 mm, (E) 0.8 mm, (F) 0.7 mm, and (G) 0.6 mm,
respectively. In stimulus (A) the subjects felt a smooth
surface because the top displacements of S1 was equal
to that of S2. In stimulus (G) they felt a sharp object
because the projection of S2 was large.
The subjects answer the perceived curvature
comparing with reference objects of metal sphere with
diameters of 1, 3, and 5 mm, moving in the S2 pattern
in Fig. 5.
Procedure
A subject receives one pattern of seven kinds of
stimuli A, B, - - F, and G from the S1-S2 stimulator,
and memorize the feeling especially paying attention to
the curvature. Next, the subjects touch the three
reference objects coming sequentially at constant
intervals of 1 second, and they answer the comparison
of the curvature between the S1-S2 stimulus and the
reference objects. The answers are classified into the
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seven categories and give those categories points from
0 to 6 as shown in Tabl e 1. For instance, if it felt as the
same as the sphere with diameter of 3 mm, we give it 3
points. (Though feeling of the S1-S2 stimulator was not
always identical with that of reference objects,
comparison was possible.)
The experiment was done 3 times for each signal.
During the experiment, the subjects wore headphones
and eye-masks not to obtain any cues from the sound
and sight. The subjects were five males in their twenties
with eye-masks and headphones.
Tabl e 1 : Assigning points to the perceived curvature
categories by S1-S2 stimulus.
Perceived
diameter
of sphere
x [mm]
I
x < 1
1
II
1 < x < 3
3
III
3 < x < 5
5
IV
x > 5
Point 0 1 2 3 4 5 6
Fig. 8: Histogram of perceived curvature for various
intensities of S1-S2. The maximum displacements of
S1 were (A) 1.2, (B) 1.1, (C) 1.0, (D) 0.9, (E) 0.8, (F)
0.7 and (G) 0.6 mm, while S2 always moved in the S2
pattern in Fig. 5.
Results
Tabl e 2 and Fig. 8 show the perceived curvature versus
stimulus A, B, - - F, and G. Fig. 8 is a histogram of the
perceived diameter classified following Table 1. The
perceived curvature changed by the maximum
displacement of S1. When maximum displacement of
S1 decreased, subjects felt higher curvature. The
average points for the stimulus A, B, - - F, and G are
summarized in Table 2. And its graphical plots are
shown in Fig. 9. For stimuli B - G, subjects felt finer
object than the cylinder of S1 though the surface of S1
always touched the skin. The results showing
continuous change of perceived curvature along the S2
projection change, is consistent with our hypothesis.
Tabl e 2 : Subjective curvature versus the maximum
displacements of S1. The averaged points defined in
Table 1 are shown.
Stimulus A B C D E F G
Average
point
5.4 4.7 4.1 3.4 3.0 2.1 1.3
1
1.5
2
2.5
3
3.5
4
4.5
5
5.5
6
0.6 0.8 1 1.2
Maximum displacement of S1 [mm]
Perceived diameter [mm]
Fig. 9: Plots of Table 2. The perceived diameter is the
average point in Table 2.
6. Summary and discussions
We proposed a hypothesis on realistic tactile display
and its spatial resolution. It suggests that 4-D
stimulators arrayed at intervals of TPDT/2 can produce
any tactile feeling. The 4-D stimulator means a
stimulator to the skin applying four bases of local stress
distribution and their summation. And we showed the
explicit forms of the four bases.
In experiments, we examined the hypothesis for a
subspace Φ
n
of tactile stimulation in which the stress
has no lateral components. In this case the hypothesis
tells us that the number of the bases to span all tactile
feelings becomes two from four. Then one of the two
bases is a local but smooth normal-stress distribution
S1, and the other is a concentrated distribution S2.
In Experiment I, we examined whether the
combination of the S1 and S2 can create tactile feeling
of an intermediate curvature of an object. And we
obtained a driving pattern of S1 and S2 in which the
subjects felt once in twice that the stimulus was
identical to that of an intermediate curvature of an
object.
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In Experiment II we confirmed the perceived
curvature could be controlled continuously from a
sharp tip to a smooth surface.
These results for the subspace Φ
n
supported the
hypothesis because the contact in general can be
assumed as a combination of multiple contacts with
various curvature surfaces.
However, we have to add a remark that it is not
straightforward to display wide range of tactile feeling
with a simple array of the cylinders and pins as is
shown in Fig. 3 because we easily feel the shapes of the
cylinder and the pin by an active movement of the hand.
In the experiments of this paper, the thenar was fixed
and stimulated through a hole to obtain perfect
passiveness.
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