Emerging Technologies

Vision-Based
Sensor for RealTime Measuring ofSurface Traction
FieldsT

he desire to reproduce and expand thehuman senses drives innovations in sensor technology. Conversely, human-interface researchaims to allow people to interact with machines as if they
were natural objects in a cybernetic, human-oriented
way. We wish to unite the two paradigms with a haptic
sensor as versatile as the sense of
touch and developed for a dual purpose: to improve the robotic capaBy measuring a surface
bility to interact with the physicalworld, and to improve the humantraction field, the GelForcecapability to interact with the virtual world for emerging applicatactile sensor can represent
tions with a heightened sense of
the magnitude and direction presence.
When force is applied to the skin’s
surface, the human sense of touchof force applied to the skin’s
detects not only magnitude but also
direction of force distributed over a
surface.
surface. We obtain rich tactile information with a robustness that is difficult to emulate
through technology. The difﬁculty lies in obtaining vector information with both high speed and high density.
We’re developing a type of tactile sensor that uses computer vision to achieve this goal. We designed a sensor,
dubbed GelForce, that acts as a practical tool in both conventional and novel desktop applications using common
consumer hardware.

Surface traction field measurement
The spatial characteristics of objects in contact are
encoded in the human somatosensory system by a dense
population of subcutaneous mechanoreceptors. Neural activity is triggered by deformation, and is sensitive todirection and orientation of applied stimuli. Generally
speaking, we perceive a traction ﬁeld, or a 3D force ﬁeld
deﬁned over a 2D surface. Measuring such a ﬁeld is acentral concern for endowing a human-like sense of
touch to mechanical devices.

68

January/February 2005

Kazuto Kamiyama, Kevin Vlack, Terukazu Mizota,
Hiroyuki Kajimoto, Naoki Kawakami, andSusumu Tachi
University of Tokyo

Elastostatic theory
The principles of our sensor are rooted in elasticity
theory (see Hetnarski and Ignaczak1 for an excellent discourse on the subject). We adopt a standard Cartesian
coordinate system in ℜ3, where the set of vectors {ei} ={e1, e2, e3}and origin 0 represent an orthonormal basis,
with xi = x ⋅ ei giving the coordinates for points x in ℜ3
By convention, we deﬁne an elastic body B with boundary ∂B as a set of elements x with a one-to-one correspondence with points in physical space. We deﬁne a
deformation of B as a uniquely invertible map κ of B onto
κ(B). A vector field u(x, t) representing the displacement of B to a new conﬁguration describes the motion,
which we deﬁne asu(x, t) = κ(x, t) − x(1)where κ(x, t) is the point occupied by x at time t. We.
associate velocity with u and acceleration with ü. For atime-independent equilibrium state where ü(x,t ) =ü(x) = 0, elastostatic theory dictates admissibility conditions for u(x) and a 3 × 3 stress tensor ﬁeld S(x) for all
points x ∈ B.
For practical problems with speciﬁed boundary conditions in B, the remaining effort is obtaining continuous and self-equilibriated solutions for [u, S] in B. An
example naturally arising in haptics is to solve for u(B)given a surface traction field s(∂B) or a stress vector
ﬁeld s(x) = S(x)n(x) for all points x ∈ ∂B, where n(x)is the outward normal vector at x. Figure 1 shows anexample traction field on a plane with n(x) =(0, 0, 1).
Finding the corresponding solution [u, S] is laborious in general. To simplify the problem, we assume theelastic medium is linear, isotropic, and homogeneous.
These are common assumptions because they closely
approximate the actual properties of many engineering
materials, and an analytical solution is often intractablewithout them.

Published by the IEEE Computer Society0272-1716/05/$20.00 © 2005 IEEE

Transparent
elastic body

Two layers of
spherical markers

Acrylic board

CCD
camera2 Basic schematic of proposed sensor.
When we apply force to the topmost planar surface∂B, the camera measures the markers’ displacement.
The rubber has low hysteresis (energy loss) and quickly relaxes to its original configuration when force isreleased. Thus, we can effectively treat the body as a static inﬁnite semispace with only a modest accuracy loss.

Elastic semispace problem
1 Traction fields measured in real time.
System design
The body B of our sensor, illustrated in Figure 2, is a 10
× 10 × 4-cm rectangular block of transparent silicone rubber ﬁxed by an acrylic board. We printed a collection ofcolored markers, 0.6 mm in diameter, inside the elastic
body at approximately 3-mm intervals. We mounted acolor charge-coupled device (CCD) camera 15 cm below
the markers, pointed upward. To control the lighting conditions, we placed an opaque black layer of identical elastic material over the body’s surface and illuminated the
body’s interior with white light-emitting diodes (LEDs).

Consider the linear elastic state in a homogeneous
isotropic semispace B deﬁned by the inequalities x1< ∞, x2 < ∞, and 0 < x3 < ∞, subject to a traction ﬁeld
s(x) on boundary ∂B = {x : x3 = 0}, with the x3 axis
defined perpendicular to the surface and directed
toward its interior. We seek an admissible solution for[u, S] that is continuous over B. We ﬁrst consider twoelemental cases of the Green’s functions for a point force
applied at origin 0. The proofs are extensive and thus
omitted for brevity (see Hetnarski and Ignaczak1 for arigorous discussion).
The ﬁrst case is a normal point force fN = (0, 0, f3),
as shown in Figure 3a. We obtain the resulting displacement vector ﬁeld uN(x) for internal points x ∈ Bfrom the Boussinesq solution

fN = (0, 0, f3)
fT = (f1, 0, 0)
x1

x2

x2

x3

x3

(a)

x1

0

0

(b)

3 Two cases of point force: (a) Boussinesq problem of normal point force; (b) Cerruti problem of tangential point
force.

IEEE Computer Graphics and Applications

69

Emerging Technologies

(

)

(

)

x x
1 − 2v x 1  1 3 −
 R2
R + x3 u 
1+ v  x x
1 − 2v x 2 
 1
2 3
=
u
f
−


3
 2
2π ER  R 2
R + x3  u 
3 N

 x2
3


+ 2 − 2v

 R2



(

)

(

which can be chosen freely. Equation 4 then takes the
form
n

(2)

)

is the distance of x from 0.
The ﬁrst elasticity constant in Equation 2 is Young’s
modulus E > 0 with units in Pascals, characterizing stiffness. The elastic material we use is a stiff silicone rubberwith a high E value, so for a wide range of applied force,
any elastic displacement is small relative to the body’s
total size.
The second constant is Poisson’s ratio −1 ≤ v ≤ 1/2,
characterizing compressibility. Very compressible materials such as cork have a value close to 0, and nearly
incompressible elastomers, such as silicone, have a ratio
close to 1/2. Some synthetic materials have molecularlattices that effectively expand under tension, granting
a negative value.
The second case is a tangential point force fT1 = (f1, 0,0), as Figure 3b shows. Here, we obtain the resulting displacement vector ﬁeld uT1(x) from the Cerruti solution
 R2 + x 2
R 2 + Rx 3 + x 12 1
+ 1 − 2v
2
 R2
R + x3


u 

1+v 
x 1x 2x 1x 2 1
− 1 − 2v
 u2  = f1 2π ER 2R2
 u 
+
R
R
x
3


3 T1


x 1x 3x1+ 1 − 2v

R2
R2 R + x3

(

)

(

)

(

) (

(

)

(

)

)

(3)
where R is deﬁned as it is in Equation 2. Clearly, we mightalso ﬁnd uT2 for a tangential force fT2 = (0, f2, 0) by interchanging x1 and x2 as well as u1 and u2 in Equation 3.
Because we assume the elastic medium is linear, given
an arbitrary point force f = (f1, f2, f3), by superposition
we can gather the solutions for uT1, uT2, and uN into
matrix form u(x) = H(x)f, where H(x) is a 3 × 3 tensor
ﬁeld dependent entirely on the position x. We obtain a
traction vector ﬁeld by parameterizing stress vectors s(v,w) over a domain boundary map Ω: Ω × ℜ2 → ∂B andcompute the displacement ﬁeld for any interior point x∈ B from the formulau(x) = ∫ΩH(x − Ω(v, w))s(v, w)dvdw(4)

To formulate the extended semispace problem’s discrete solution, we deﬁne a discrete traction ﬁeld Φ = [{f1,f2, …, fn}, {ξ1, ξ2, …, ξn}] as a set of n distinct impulsive
point forces fi and their respective positions ξi ∈ ∂B,

January/February 2005

iu(xj) =Ηi,jfi
where Ηi,j = H(xj − ξi)

R = x 12 + x 22 + x 32 > 0

70

i

i =1

For a set of m distinct sample points {x1, x2, …, xm},
where xi ∈ B, convoluting over x and ξ lets us represent
the tensor ﬁeld H(x) by a constant 3m × 3n block matrixΗ such that

where

( )

( ) ∑H(x -ξ )f

u x =

(5)

Because we can only measure u(x) with a camera, weseek the inverse problem—namely, to derive a discrete
traction ﬁeld f(x) given a displacement ﬁeld u(x). So,
for m ≥ n, we obtain the 3n × 3m block pseudoinverse
matrix Q through a standard linear squares scheme,
such as the normal equations method:( )HT u = HT H f
(HT H )− 1 HT  u = f


Qu=f

The matrixΗ is constant, and well conditioned forappropriate choices of x and ξ. Moreover, we can accurately compute the constant Q using a Cholesky factorization in a precomputation phase and then apply it
online at every frame to compute a discrete traction ﬁeld
with a single matrix-vector multiplication.

Measuring displacement information
Researchers have developed a wide variety of methods for acquiring force information as a distribution.
Examples include the strain gauge and recent devices
based on piezoelectric elements (see the “RelatedWork” sidebar). To circumvent circuitry-related complications for large-scale, high-density sensing, we
adopted an approach based on computer vision, which
has grown increasingly popular in robotics as the costand size of high-quality imaging systems has decreased.
Issues concerning linear perspective and lens distortion2
are discussed in detail elsewhere, and for now we shallassume they are properly accounted for.
Single marker displacement. We use a fast and simple approach to measure the planar movement of thecircular markers described earlier. Figure 4 shows animage captured by the CCD camera and sent directly toa PC. The captured area’s size is 100 × 75 mm, so one
pixel of the 640 × 480 image roughly corresponds to a0.15-mm square. To reduce background noise effects,
we applied a threshold to the image’s color channels toaccentuate the marker arrangement topology. This isanalogous to raising the water level to segment a hilly
landscape into a chain of islands.
To measure marker displacement within the captured
image, we decompose the image into small independent
cells. We initially detect each marker’s location througha windowed autocorrelation technique and then create
a bounding box Mi large enough to contain the marker

Related Work
Nearly all existing force sensors belong to one of two categories.1,2
The ﬁrst measures a force vector at a single point; the second measuresa distribution of forces, but only the forces’ magnitude, not their direction. Few sensors can measure force as a vector distribution, or traction
ﬁeld. Most current sensors use a sensing unit in which mechanical pressure causes variances in electric resistance or capacitance.1,3,4 Thesesensors require complex wiring and a large sensor unit to measuredense traction ﬁelds. This is especially problematic when the sensors
are integrated into a compact mechanism such as a robotic hand or adesktop accessory.
An alternative force-sensing method uses optics. Optical sensors
require much less circuitry and allow dense measurement at low cost.
However, few reported optical sensors measure traction ﬁelds. Ohoka
et al. developed a sensor using an elastic sheet and a collection of pyramidal projections arranged in a transparent board parallel to thesheet.5 The sensor measures a traction ﬁeld by monitoring the projections, but for it to properly measure force, the projections must be
adjusted precisely.
Ferrier and Brockett proposed a shape sensor, coincidentally with asystem design similar to ours, that tracks dots on an elastic material tocompute the 3D conﬁguration of a ﬁngertip-shaped elastic membrane.2
Their measurement approach is robust and reportedly performed at interactive refresh rates for problem domains with dozens of vector elements.

4 CCD camera image of interior elastic body.

zBlue marker
Red marker

Force

z
Deformedby force

Side viewyxyx

Top view

References

Markermovementyy

5 Representing depth information through color.
for all of its expected displacement range. Because therubber is stiff and the deformation is mostly reversible,
this amounts to only a few pixels in each direction, evenfor a wide range of applied force. To compute the position xi in Mi, we apply a standard discrete center of masscalculation over all pixels p∑ pη(p)X =∑ η(p)

1. R.S. Fearing, “Using a Cylindrical Tactile Sensor for Determining Curvature,” IEEE Trans. Robotics and Automation, vol. 7, no. 6, 1991, pp. 806-817.
2. N.J. Ferrier and R.W. Brockett, “Reconstructing the Shape of a Deformable
Membrane from Image Data,” Int’l J. Robotics Research, vol. 19, no. 9, 2000,
pp. 795-816.
3. J.G. Silva, A.A. Carvalho, and D.D. Silva, “A Strain Gauge Tactile Sensor for
Finger-Mounted Applications,” IEEE Trans. Instrumentation and Measurement, vol. 51, no. 1, 1991, pp. 18-22.
4. D.T.V. Pawluk et al., “Distributed Pressure Sensor for Biomechanical Measurements,” J. Biomechanical Eng., Trans. ASME, vol. 120, no. 2, 1998, pp.
302-305.
5. M. Ohoka et al., “Data Conversion Capability of Optical Tactile Sensor Featuring an Array of Pyramidal Projections,” Proc. IEEE Conf. Multisensor Fusion
and Integration for Intelligent Systems, IEEE Press, 1996, pp. 573-580.

p∈M i

i

p∈M i

where η(p) denotes the image intensity at pixel p in thecorresponding color channel. During a calibration stage
when no force is applied, we store the initial marker positions x. Applying force deforms the positions to κ(x), andwe compute the displacement u(x) using Equation 1.
We’ve found empirically that we can calculate the position to a precision of less than 0.1 pixels, which corresponds to approximately 15 microns in the xy-plane.
Depth information through color. Clearly, the third
component of u in Equation 1 is unobtainable because
a pixel p has only two components, corresponding to
row and column. However, elastic boundary value
problems are generally invertible as long as there areat least as many independent equations as there areunknown variables.3 No definitive correspondence
between markers and force vectors exists, so eventhough we obtain only 2D displacement information,
we can still solve the discrete semispace problem for n
3D force vectors as long as the number of sample points
m is at least 3n/2.
Although the elastostatic theory guarantees invertibility, no such assurance regarding the problem’s stability exists when complete displacement information is
unknown. Indeed, as we show in the next section, ourmethod’s accuracy experiences a marked degradation
when there is no depth information in the measured displacement. We therefore use two layers of markers at separate depths, interspersing them to avoid occlusion, as
Figure 5 illustrates. We distinguish the layers by color, in
this case red and blue, so by separating the color chan-IEEE Computer Graphics and Applications

71

Emerging Technologies

1.1
Difference
Fz
Fx
Fy

Normalized difference

1.0
0.9
0.8
0.7
0.6
0.5
0.4

0.3
One
0
1
2
3
4
5
6
8
13
layer Double
Distance between blue and red layers (mm)density

6 Simulated errors versus layer separation distance. Fx, Fy, and Fz depict
the errors for each measured force component.
nels in an RGB stream, we obtain two planar displacement distributions in each image. In Figure 5, the blue
marker layer is at x3 = 6.0 mm, and the red layer is at x3= 8.0 mm. It follows from Equations 2 and 3 that for apoint force at the origin, the displacement of internal
points diminishes on the order of o(R-1). At small depths
the difference is substantial. This added information cancompensate for the dimension lost using a single camera.

Evaluation experiments
Measuring traction ﬁelds optically is a relatively new
concept, and there are concerns about the accuracy andeffectiveness of the method. In contrast to most conventional mechanical sensors, there is no obvious inputoutput relationship between the captured image andthe computed force ﬁeld. We therefore assess the performance of our optical traction ﬁeld sensor with a few
evaluation experiments.

Force vector evaluation
We ﬁrst evaluated the effectiveness of the two layersof markers and the inﬂuence of distance between theblue and red layers using a simulated model of the sensor with the same speciﬁcations as the actual system.
We chose a discrete computed traction ﬁeld Φ as an n =24 × 24 square grid of force vectors centered at the origin. We then simulated an applied discrete traction ﬁeldΦ̂ on the surface with 100 force vectors arranged in asquare given by()

fˆ = 0, 50,100 ij
: i , j = − 5, − 4,..., 3, 4 

,
,
i
j
ξ
3
3
0
=
 ij


(

)

{

}

with units properly scaled to the image size.
We investigated the effect of the two layers by comparing Φ and Φ̂. Iterating the simulation let us systematically change the given distance between the two

72

January/February 2005

layers. We simulated m = 576 red + 576 blue internalmarkers with positions Ψ obtained from an actual CCD
camera image. Given applied traction ﬁeld Φ̂, we used
Equation 5 to calculate the theoretical displacement vector ﬁeld u(Ψ) for the markers and mapped it to accountfor linear perspective. We multiplied the result by the
2m × 3n pseudoinverse matrix Q to obtain Φ.
Figure 6 shows the mean difference between the individual vectors fi in Φ and f̂i in Φ̂ for each component. On
the horizontal axis, from left to right, the mean values arefor only the blue layer, the blue and red marker layers at
the same depth, then each case with an interlayer distance between 1 and 6 mm, then 8 and 13 mm. Having
the blue and red layers located at the same depth is equivalent to doubling the density of sampling points at only
one layer. Because we scale the computed ﬁeld Φ arbitrarily, results are normalized with respect to the absolute
error obtained by a single layer of blue markers. Although
the average of the difference is almost the same in theﬁrst two cases, as the layers separate, the mean difference
decreases. However, this trend bottoms out, and the meandifference increases with additional separation. This conclusion suggests that the proposed method is most accurate when the difference between the two marker layers
is 2 or 3 mm, the distance adopted in our prototype.
We then evaluated the resolution of force magnitude
and direction. We applied an actual traction ﬁeld using
a probe with a 5-mm diameter hemispherical contact
site. Summating each force vector in the computed Φ
gives us a total computed force f. By comparing f withthe total applied force f̂ measured by a separate 6-axis
force sensor controlled by an xyz-stage, we examine theresolution and linearity of the measurement Φ.
First, we investigated the magnitude of the computed force f. We increased the applied normal force f̂ from0 to 750 gram force (gf) by 50 gf increments and recorded the computed force over 10 trials. Figure 7a shows
the result. The straight plot indicates that the sensor can
sufﬁciently measure the force linearly with a magnituderesolution of about 30 gf. We expect that using a less
stiff material might further improve the result.
Next, we estimated the force’s angle resolution. Using
the same hemispherical probe, we ﬁxed the magnitudeof the applied force f̂ at 400 gf and applied the force ata variable angle with respect to the surface normal,changing from 0 to 45 by 5-degree increments. The
probe’s base plane remains parallel to the xy-plane. Figure 7b shows the result. As the ﬁgure shows, the proposed force sensor measures the angle of force precisely
and linearly. The graph’s data spread shows that themeasured force’s angle resolution is about 5 degrees.
The proposed force sensor calculates force using a
pseudoinverse matrix, so the computed result at eachpoint includes an error that is distributed around its
neighbors. We investigated this error’s effects on spatial
resolution. For simplicity, for each force vector we considered only the normal component fN and tangential
component fT. The evaluation used an applied traction
ﬁeld from force applied at a certain point on the surface.
However, because the sampling interval isn’t fineenough to estimate the distributed error, we adopted
the following procedure. We selected two adjacent mea-

1.0
Normalized force (Fz)Measured force (gf)

800

600

400

0
0
(a)

Angle of measured force (degrees)(11.1, 8.9)
(11.8, 8.9)
(12.2, 8.9)
(12.6, 8.9)
(13.0, 8.9)
(13.3, 8.9)

0.6
0.4
0.2
0.0

200
−0.2
−10 −8 −6 −4 −2 0

Measured value
x=y

200
400
600
Applied force (gram force [gf])(measured by 6-axis force sensor)

800

40
Magnitude of applied force
is fixed at 400 gf
30

2

4

6

8 10 12Distance from force-applied point x (mm)8 Normal component of measured force at high-density sampling when we apply point force.

Table 1 summarizes the prototype’s speciﬁcations andexecution times.

Applications
As computing hardware improves, many applications
are emerging that induce a heightened sense of presence for the user. Accordingly, we can expect anincreased demand for input and control devices withhigh bandwidth and rich geometrical structure.

20

10
Measured value
x=y

0
0

(b)

Force-applied
point (mm)(x, y)

0.8

10
20
30
40
Angle of applied force (degrees)(measured by 6-axis force sensor)

7 Relation between applied and measured force for(a) z-direction and (b) angle from the surface.
surement points, (fi, xi) and (fj, xj), from the computed
traction ﬁeld Φ, subdivided the distance between theminto n points, and applied a given perpendicular forcef̂N at each point. Then, we computed force vectors fN at
each point, regarding each point as the origin. We
repeated this procedure as we increased the density ofsampling points in Φ and then derived the spatial resolution of Φ from the obtained force distribution’s width.
Figure 8 shows the result, with the horizontal axis
representing the distance from each origin, and the vertical axis representing the normal component of themeasured force vector f. We normalize the vertical axis
value using the maximum value among the acquired
data. The magnitude of normal applied force f̂N is ﬁxed
at 200 gf and the adjacent measurement points are at
the center of the area in which we acquire force distribution. The actual measurement interval is 2.2 mm, andwe subdivide adjacent points into 0.37-mm intervals.
Half of the width, in effect the spatial resolution of forcesin Φ, is about 4 mm.

Performance evaluation
The core motivation of GelForce is to measure a largescale and high-density surface traction ﬁeld in real time,
so a few words regarding performance are in order.

Interactive digital art
Because the GelForce sensor measures dense traction
ﬁelds in real time, it shows promise for novel interactive
digital artwork. To assess the computed ﬁeld’s geometrical structure, we implemented several visualizationsin an application called GelVis using various graphics
hardware acceleration techniques to visualize vectorﬁelds, contour plots, and spline surfaces. Applying force
to the surface let us easily achieve sophisticated visual
effects, such as those in Figure 9.
We conﬁrmed many of the force vector distribution
interface’s novel capabilities through visualization. For
example, when we slid a ﬁnger along the sensor’s surface, the force vector field followed the movementsmoothly, with the distribution’s leading end correctly
pointing parallel to the surface. When we applied torqueto the sensor’s surface, the traction ﬁeld indicated a curling distribution. Pressing on the elastic body with various intensities, ranging from a gentle tap to afull-strength press, causes the displayed arrows to scalecorrectly along the complete range of applied force.

Universal computer interface
The developed sensor is inexpensive to manufactureand easy to use. With the continual improvement of CPU
and GPU technology, novel uses for high-bandwidth
traction ﬁeld sensing in image processing, animation,
virtual reality, music, and computer entertainment willsoon become mainstream.
Most conventional interfaces, such as the keyboard
or pointer device, rely on applied force sensors. Force
input devices can be classiﬁed by measured value andmeasured region dimensions. For example, a standard
joystick measures a 2D force vector at a 0D point, and aIEEE Computer Graphics and Applications73

Emerging Technologies

Table 1. Prototype system speciﬁcations and execution times.
FeatureDescription

Size
Elastic body

10 × 10 × 15 cm
Silicone rubber, 10 × 10 × 4 cm
(Young’s modulus E ≈ 1.8 × 104 Pa, Poisson’s ratio n ≈ 0.49)
Two 24 × 24 grids at 3-mm intervals
Depth: (blue) 6 mm, (red) 8 mm
24 × 24 regular grid of 3D vectors
Magnitude: 30 gf
Direction: 5 degrees
Spatial: 4 mm
Point Grey Research Streaming Dragonfly(640 × 480 RGB, 30 frames per second)Intel Pentium 4 HT, 2.6 GHzIntel C/C++ Compiler 8.0
Intel Math Kernel Library 6.1
Normal equations to compute 1,728 × 2,304 pseudoinverse: 8.5 seconds
Marker tracking: 1.07 ms
Traction computation: 11.5 ms
Frame rate restricted by camera

Markers
Traction field
Resolution

CameraCPU
Implementation
Precomputation
Time per frame

analysis,4 are useful for accurately extracting criticalpoints, such as concentrated forces or vortices, that canbe used for familiar tasks such as point-based control,
afﬁne transformations, and text input.

Robotic sense of touch

(a)

(b)

A traction ﬁeld sensor can endow a robotic ﬁngertip
with a lifelike sense of touch. Simple tasks, such as picking up an egg, depend on feeling the weight of an object
not only by muscle contraction but also by force parallelto the skin. Adjusting the proportion of perpendicularand parallel force lets humans grasp fragile objects safely. Similarly, to operate dexterously, robots must sense
both the grasping and the friction force on the ﬁngertip.
With appropriate Green’s functions, we can use the principles behind the GelForce sensor to measure traction
ﬁelds for an arbitrary shape, such as a ﬁngertip, so it caneasily be mounted on a robot hand. Figure 10 shows therobotic ﬁngertip in development at our laboratory.

Conclusion

(c)

(d)

9 GelVis snapshots: (a) deformed surface with multiple contact points,(b) overhead projection onto sensor surface, (c) contour plot of measured
force magnitude, and (d) complex traction field with a curved object.
pressure-pad3 measures 1D force magnitude over a 2D
surface. Generally speaking, sensors with higher dimensions of either measured value or region are more universal. That is, any device that can measure a 3D vector
can obviously measure a 2D vector or a 1D scalar, andlikewise for measurement region.
As such, we wish to exploit the universality of traction ﬁelds to support existing applications as well. Standard techniques, such as spline interpolation and ﬂow

74

January/February 2005

It wouldn’t be an exaggeration to say that every scientific technology is based on sensors. For example,
audio recording couldn’t exist without the measurementof sound, and television broadcasts would be impossible
without catching radio waves as picture signals. Like thehuman tactile sense, the technology of the developed
sensor allows the real-time measurement of complete
information about force—that is, direction, magnitude,
and distribution. This versatile ability plays a crucial rolein our daily lives, even our own identities in space, and
we look forward to ﬁnding use for high-bandwidth traction sensation in ways yet to be discovered.
■

References
1. R.B. Hetnarski and J. Ignaczak, Mathematical Theory of
Elasticity, Taylor and Francis, 2004.

2. K. Kamiyama et al., “A Vision-Based Tactile Sensor,” Proc.
11th Int’l Conf. Artiﬁcial Reality and Telexistence, 2001, pp.
127-134.
3. W. Menke, Geophysical Data Analysis: Discrete Inverse Theory, Academic Press, 1989.
4. K. Polthier and E. Preu, “Identifying Vector Field Singularities Using a Discrete Hodge Decomposition,” Visualizationand Mathematics 3, Springer-Verlag, 2003, pp. 113-134.

Kazuto Kamiyama is a doctoral
student in the Graduate School ofInformation Science and Technology
at the University of Tokyo. His
research interests include tactile sensors and virtual reality. Kamiyama
received an MS in information science and technology from the University of Tokyo. Contact
him at kazuto@star.t.u-tokyo.ac.jp.

Kevin Vlack is a master’s student in
the Graduate School of Interdisciplinary Information Studies at the University of Tokyo. His research interests
include signal processing, computer
graphics, and virtual reality. Vlack
received a BS in computer sciencefrom the College of Engineering at the University of Illinois
in Urbana-Champaign. Contact him at vlack@star.t.utokyo.ac.jp.

Camera unit
Light source

Base ofelastic body
Transparent elastic bodyand markers(a)10 Traction
field measurement on a
robotic finger:(a) basic system
schematic,(b) prototype
with mounted
camera, and(c) fingershaped elastic
body withinternal markers.
(b)

Terukazu Mizota is a researcher
in the Department of Information
Physics and Computing at the University of Tokyo. His research interests
include tactile sensors and virtual
reality. Mizota received a BS in general engineering from Tokushima Bunri
University. Contact him at mizota@star.t.u-tokyo.ac.jp.

Hiroyuki Kajimoto is a research
associate in the Department of Information Physics and Computing at
the University of Tokyo. His researchinterests include tactile displays, tactile sensors, and virtual reality.
Hiroyuki received an MS in mathematical engineering and information physics from the University of Tokyo. Contact him at kaji@star.t.u-tokyo.ac.jp.

Naoki Kawakami is a lecturer inthe Department of Information
Physics and Computing at the University of Tokyo. His research interests
include virtual reality. Kawakami
received a PhD in advanced interdisciplinary studies from the Universityof Tokyo. Contact him at kawakami@star.t.u-tokyo.ac.jp.

(c)Susumu Tachi is a professor in the
Department of Information Physics
and Computing at the University ofTokyo. His research interests include
virtual reality, psychophysics, andtelerobotics. Tachi has a doctoral
degree in mechanical engineeringfrom the University of Tokyo. He is a founding director of
the Robotics Society of Japan (RSJ), a Fellow of the Society of Instrument and Control Engineers (SICE), and is thefounding president of the Virtual Reality Society of Japan(VRSJ). Contact him at tachi@star.t.u-tokyo.ac.jp.
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