IEEE SENSORS JOURNAL, VOL. 9, NO. 9, SEPTEMBER 2009
1103
A Small and Low-Cost 3-D Tactile Sensor for a
Wearable Force Plate
Tao Liu, Member, IEEE, Yoshio Inoue, and Kyoko Shibata
Abstract—In this paper, a new 3-D tactile sensor is proposed for
measuring triaxial ground reaction force (GRF) distribution. A
pressure-sensitive electric conductive rubber (PSECR) and compact pectinate circuits were used to design the sensing cells of the
sensor, making it possible to implement a low-cost and compact
system without a complex 3-D structure. Moreover, to tailor the application for measuring human GRF, we adopted the use of elastic
rubber as the contact interface of the sensor in order to realize a
comfortable human–sensor interface. Calibration and test experiments were conducted to characterize the developed sensor, and a
small triaxial force sensor (Tec Gihan, Japan) as well as a six-axial
force sensor (Nitta Corporation, Japan) were used as verification
measurement devices. Coupling effect tests were performed to calculate cross-sensitivity of the sensor. The experimental results of
repeatability, nonlinearity, hysteresis, and dynamic tests indicate
that the sensor is feasible for implementing 3-D tactile measurement.
Index Terms—Conductive rubber, force plate, ground reaction
force, tactile sensor.
I. INTRODUCTION
T
he use of a force plate has been successfully employed to
measure ground reaction force (GRF) during gait in the
laboratory environment [1], [2]. However, this device requires
a sizeable operating space and expensive signal processing devices, and moreover, not more than one stride at a time can be
measured during a trial. Therefore, it is difficult to apply it to
measurements in real life human environments, which require
the device to be small, noninvasive, reliable, easy to use, and
low-cost. Winter has pointed out that “A suitably instrumented
lightweight ‘force-plate shoe’ is needed to give us the ground reaction forces step by step” [3]. Goran et al. state that the existing
methods do not accurately reflect individual physical activity
levels, and that further methodological development of physical
activity tools should be a high priority for research [4].
Recently, many wearable sensor systems have been developed for the applications of GRF measurements as an alternative to the traditional force plate. Pressure sensors have been
used to estimate the distributed normal forces in [5]–[7], but
Manuscript received April 02, 2009; accepted June 09, 2009. Current version published August 14, 2009. This paper was presented at the Seventh IEEE
Sensors Conference and was published in its proceedings. The Associate Editor
coordinating the review of this paper and approving it for publication was Prof.
Gerald Gerlach.
The authors are with the Department of Intelligent Mechanical Systems Engineering, Kochi University of Technology, Kochi 782-8502, Japan
(e-mail: [email protected]; [email protected]; [email protected]).
Color versions of one or more of the figures in this paper are available online
at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/JSEN.2009.2026509
Fig. 1. Research background about wearable force sensors.
the transverse or frictional force could not be measured. Some
flexible force sensors designed by using new materials such as
silicon or polyimide and polydimethyl-siloxane have been proposed to measure the normal and transverse forces [8], [9], but
force levels of these sensors using these expensive materials
were limited to the measurements of small forces (about 50 N).
By placing two universal six-axial force sensors at the front
and rear boards of a special shoe, researchers have developed
some wearable sensor systems for ambulatory GRF measurement during uninterrupted walking in trials [10], [11], but the
increased height of the instrumented shoes necessarily affects
normal human gait. A method was introduced to estimate the
complete GRF by using pressure insoles during walking [12], in
which a complex pressure insole measurement system with 99
pressure sensors was constructed and the ensuing data were fed
into regression models. By measuring the human body’s center
of gravity and foot pressure, Miyawaki et al. proposed an indirect measurement method to estimate the GRF vector [13].
However, high-precision measurement of the human center of
gravity is difficult.
As shown in Fig. 1, we are presently concentrating on developing and applying some wearable force sensors to measure
GRF during gait, and our research on sensors has been divided
into four phases. In the first phase, the flexi-tactile sensor system
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IEEE SENSORS JOURNAL, VOL. 9, NO. 9, SEPTEMBER 2009
Fig. 2. Three-dimensional ground reaction force measurement system.
F-scan (Nitta Corporation, Japan), which can measure only the
distribution of normal force, was integrated into an insole to estimate the normal components of GRF. In our second phase,
we developed a multiaxial force sensor to measure the triaxial
GRF and coordinates of the center of pressure when fixed under
a specially designed shoe [14]. However, its hard interface and
the weight load on the foot affected the normal human gait according to our experimental test. In the last two phases, we want
to develop a thin and light force plate based on 3-D tactile sensors and using lower cost materials. A sensor matrix will be constructed to directly perform 3-D force measurement [15], which
also can be integrated into a flexible material, so this sensor
system will be able to measure the 3-D GRF via what is a comfortable interface for the human body (see Fig. 2). A new design
for a low-cost 3-D tactile sensor that can be easily constructed
and miniaturized is presented in this paper.
II. MATERIALS AND METHODS
Fig. 3. Material test. (a) Test platform. (b) Test results.
A. Sensing Material
The sensing cell in the sensor was designed using pressuresensitive electric conductive rubber (PSECR) provided by the
Pongpara Codan Rubber (PCR) Technology Company, Japan
[16]. The PSECR is a composite of an elastomer and specially
treated carbon particles, and is available in gray–black flexible
sheet form, 0.5 mm in thickness. The PSECR can be glued onto
the surface of pectinate electrodes to make a resistor, and the
PSECR can be covered with hard-wearing rubber as a protective coat. When a normal force is applied to the surface of a
PSECR film, the resistance in the pectinate circuit will decrease.
As shown in Fig. 3(a), we made a sensing cell prototype (size:
10 mm 10 mm), and designed a test platform to carry out
repeatability, nonlinearity, and hysteresis tests of the sensing
cell. The imposed normal loading ranged from 0 to 100 N, and
could be accurately measured using a reference force sensor
IFS-67M25A50-L40 (Nitta Corporation). The resistance of the
pectinate circuit were measured using a multimeter. When the
sensing cell was tested under the two conditions of increasing
load from 0 to 100 N and decreasing load from 100 to 0 N, we
calculated its characteristic parameters, which included: sensitivity of 3.2 k /N, repeatability of 1.5% rate output (R.O.),
nonlinearity of 2.7% R.O., and hysteresis of 2.4% R.O. A representative result of the hysteresis test experiments is given in
Fig. 3(b).
copper-film substrate, because electrode lead lines could be
constructed on the same substrate. We designed a 3-D tactile
sensor by integrating four sensing cells, each composed of a
PSECR film and a fan-shaped pectinate circuit. A PSECR film
was glued to the pectinate electrodes, and then, an elastic dome
as a spherical interface was glued to the PSECR film. The basic
mechanism of the 3-D sensor is that changes in the normal
distribution and the amount of force measured on the four
separated pressure sensors are used to estimate tridirectional
forces imposed on the sensor. As shown in Fig. 4(a), the
and axes of the sensor cell were defined along the transverse
direction, and the axis was chosen as the vertical axis. A point
force vector exerted on the spherical interface of the sensor can
,
be decomposed into tridirectional components including
, and
. The measurements of four sensing cells were used
to estimate the normal component force ( ) and coordinates
( , and ) of the center of pressure (COP) on the – plane
defined by the two transverse axes ( axis and axis) using the
following equations:
(1)
(2)
(3)
B. Structure and Mechanism of Sensor
The pectinate electrodes made it possible that multiple
sensing cells made of PSECR could be constructed on a
, and
are the normal forces measured
where
using the four sensing cells. We can estimate the four normal
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LIU et al.: A SMALL AND LOW-COST 3-D TACTILE SENSOR FOR A WEARABLE FORCE PLATE
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Fig. 4. Mechanism of the sensor.
forces from the voltage signal outputs
of the four sensing
cells, so (1)–(3) could be given as new forms as
(4)
is defined as a
When the constant coefficient
and the subscript indicates the label
single parameter
of the sensing cells, in order to estimate the tridirectional
components of the force vector, we can rewrite (4), (7), and (8)
as follows:
(5)
(9)
(10)
(11)
(6)
, and
are the calibration coefficients for the
where
four sensing cells in the 3-D sensor, and the subscripts (1, 2,
3, and 4) indicating the label of the sensing cells are shown in
Fig. 4(d).
As shown in Fig. 4(a), the force vector’s orientation can be
estimated by the coordinates of the COP, and the two transverse
and
) can be calculated by the vector
force components (
orientation and the normal component ( ) of the force vector.
Since the positions of the COP projected on the two transverse
axes ( axis axis) are connected with the direction of the imposed force vector [see Fig. 4(b) and (c)], we can estimate the
and
) of the force vector extwo transverse components (
erted on the dome by the following equations:
where is the calibration coefficients for estimating the normal
component ( ) of the applied force vector. Since the manufacturing and assembling of the three parts including the pectinate electrodes, PSECR film, and elastic dome can change the
boundary condition of each sensing cell in the sensor, we esti, and ) by
mate the calibration coefficients (
an experimental calibration method.
As shown in Fig. 5, four pectinate circuits and condition circuits for the sensing cells were constructed on a copper-film substrate, and a prototype of the 3-D sensor (diameter height: 10
mm 10 mm, weight: 10 g) was developed for our experimental
test. When a force vector is applied to the sensor, the changes
in resistance of the PSECR film are converted into four voltage
outputs using the pectinate circuits and operation amplifiers.
III. EXPERIMENTAL STUDY
(7)
(8)
A. Static Calibration of Sensor
To calibrate the developed sensor, a calibration experiment
system composed of a small triaxial force sensor USL06-H5500N-C (Tec Gihan, Japan) and a 3-D stage (Micro Mill) were
constructed to provide triaxial reference forces (see Fig. 6). For
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IEEE SENSORS JOURNAL, VOL. 9, NO. 9, SEPTEMBER 2009
Fig. 7. Experimental results of sensor calibration. (a) x axial reference load.
(b) Output signals of sensing cells.
Fig. 5. Three-dimensional tactile sensor prototype.
Fig. 6. Calibration experiment system.
the first step, we needed to obtain calibration coefficients for
the two transverse directions referred to as and axes. In
the static calibration experiment, a low-pass filter (cutoff frequency: 10 Hz) was applied on the small triaxial force sensor
for measuring input forces. As shown in Figs. 7 and 8, we applied, respectively, the two directional transverse forces ( and
axes) to the sensor and the imposed forces were measured using
the small triaxial force sensor. A group of results including the
four sensing cells’ voltage outputs and the imposed two directional reference forces ( axis: 0, 6.1, 11.8, 18.1, 24.3, 30.1,
,
,
,
, and
N; axis: 0, 6.0, 12.1,
,
,
,
, and
N)
18.3, 23.9, 30.0,
were obtained. This calibration experiment provided estimates
, and
of the calibration coefficients including
in (9) and (10). We completed the multiple regression analysis
of the sampled sensor data using a statistical software package
Statistical Package for the Social Sciences (SPSS) 11.0 J. The
Fig. 8. Experimental results of sensor calibration. (a) y axial reference load.
(b) Output signals of sensing cells.
TABLE I
RESULTS OF THE MULTIPLE REGRESSION ANALYSIS
results of the multiple regression analysis are given in Table I,
column of calibration coefficients were used for the
and the
next step of the vertical direction force (z-axial force) calibration experiment.
By substituting the results of the first step of the calibration of
the transverse forces into (11), a linear regression analysis was
used for obtaining the calibration coefficient ( ) and calculating
the axial force. Fig. 9 presents the graphs of the data, which
were imported into the linear regression analysis in SPSS 11.0 J.
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LIU et al.: A SMALL AND LOW-COST 3-D TACTILE SENSOR FOR A WEARABLE FORCE PLATE
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Fig. 9. Experimental results of sensor calibration. (a) z axial vertical reference
load. (b) Output signals of four pressure sensing cells.
The results of the linear regression analysis show a low standard
.
error of 0.09 for
B. Characterization of Sensor
Based on the calibration experiment system, we completed
repeatability, nonlinearity, hysteresis tests, and a load range
evaluation of the developed sensor. According to the PSECR
material test results, the maximal normal load capacity of the
sensor was limited to 100 N, and we calculated that the maximal
static friction force or transverse force on the sensor surface
was limited to 35 N when the 100-N normal load was imposed.
N for
Therefore, load ranges of the sensor are rated as
and axes, and 100 N for axis. To analyze repeatability of
the sensor on the three axes, we applied -directional reference
forces (0, 10, 20, and 30 N), -directional reference forces
(0, 10, 20, and 30 N), and -directional reference forces (0,
30, 60, and 90 N), respectively. We repeated loading on the
three directions five times, and repeatability of the sensor in
measuring -, -, and -directional forces is 3.2%, 3.5%, and
2.1% R.O., respectively. By using the measurement results of
the sensor outputs in the repeatability test, we could calculate
the nonlinearity of the sensor, and the nonlinearity in measuring
-, -, and -directional forces was 5.4%, 4.3%, and 5.0% R.O.,
respectively. In the hysteresis test, the sensor was tested for the
three directions under two conditions; first, of increasing load
from zero to rate load, and second, of decreasing load from rate
load to zero load. The hysteresis of the sensor in the -, -, and
-directions was 5.2%, 5.0%, and 4.1% R.O., respectively.
Fig. 10. Test experiment system. (a) Schematics of drag equipment. We
adopted this mechanism to produce vertical and horizontal reference forces.
(b) Experimental equipments picture.
Fig. 11. Dynamic sensitivity of the sensor.
C. Dynamic Test of the Sensor
When the developed sensor is used for dynamic measurements, errors of dynamic response can occur because of the different frequency ranges of the load imposed on the sensor. The
dynamic sensitivity (DS) of the force sensor could be calculated
, in which is the sensor output based on the
using
denotes the
static calibration of the developed sensor and
imposed dynamic force detected accurately using the reference
sensor IFS-67M25A50-L40 (Nitta Corporation). As shown in
Fig. 10, a special test system was developed based on the static
calibration and the test system to investigate the dynamic behavior of the sensor. Using a DSP control system (DS1104 controller, dsPACE), we controlled a dc motor using a gear system
and a rotational encoder (3863H012C-2016-IE2-512, Koshin
Denki Kogoyo Company, Ltd.) to produce a sinusoidal load
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IEEE SENSORS JOURNAL, VOL. 9, NO. 9, SEPTEMBER 2009
TABLE II
RESULTS OF THE COUPLING EFFECT TEST
Fig. 13. Verification experiment in a triaxial force measurement.
Fig. 12. Loading response of the four sensing cells. (a) z axial force input. (b)
x axial force input. (c) y axial force input.
on the normal and transverse directions. Fig. 11 shows the frequency characteristics of the normal force
for the developed
and
. The
sensor, and the DS of the transverse forces
sensor shows acceptable frequency characteristics up to 100 Hz
in all the tridirectional tests. This operational frequency range
can meet the requirements of human dynamics analysis for measuring GRF during gait [17].
D. Coupling Effect Test
After obtaining the calibration parameters, we can calculate
triaxial force from the normal force measurements on the four
sensing cells, but the coupling effect, which is a common
problem in the design of multiaxial sensors, should be addressed. Coupling effect tests were performed to calculate the
cross-sensitivity of the sensor using equipment specifically developed for the purpose. The cross-sensitivity can be expressed
as the forces measured on the sensors, which are normal to
the testing direction loading force [18]. The four sensing cells’
outputs, in terms of voltage change versus loading force, in
responding to loads in three different directions were plotted
in Fig. 12. The coupling effect of the sensor was evaluated
according to the results of the cross-sensitivity test. To produce
a transverse force on the interface of the developed sensor when
testing the - and -directional loads, a constant pressure load
(
N) was applied to the sensor. When the sensor was
tested in the -direction, the cross-sensitivity for the - and
-directions was calculated as 5.10% and 2.33%, respectively.
While the tests were being carried out in the - and -directions,
the cross-sensitivity was calculated as 3.33% and 3.13%, and
1.45% and 1.21%, respectively (Table II).
E. Verification Experiments of Triaxial Force Measurement
In order to evaluate the precision of the sensor in measuring
GRF, 3-D measurement tests were performed using the developed sensor test system composed of a triaxial force sensor and a
3-D stage. Since the transverse components of GRF are less than
10% of the normal component of GRF during gait, we produced
a dynamic load with a large normal component to stimulate
human GRF in walking. The correlation coefficient was used
as a measure of the association between two results of the two
sensor systems, and the correlation coefficient ( ) is defined
as
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LIU et al.: A SMALL AND LOW-COST 3-D TACTILE SENSOR FOR A WEARABLE FORCE PLATE
, where is the force measured by the developed
is the force measured by the reference sensor, and
sensor,
denotes the number of the sample data [19]. Moreover, the root
of the mean of the square differences (rms) was used to compare the closeness in amplitude of the two sensor measurement
results. The percent error (PE) was calculated as the ratio between the rms errors and the average peak-to-peak amplitude
of the measurements of the reference force sensor. As shown
in Fig. 13, when the developed sensor and the reference sensor
simultaneously measured the input force vector, data from the
two sensors were sampled at the same frequency (100 Hz), and
were compared with the tridirectional reference loads. The correlation coefficients for the vertical force ( axis) and two-axial
transverse force ( and axes) were 0.92, 0.98, and 0.93, respectively. In the measurement experiment, the PEs of , , and
axial outputs were 1.2%, 2.0%, and 4.5%, respectively.
IV. DISCUSSION AND CONCLUSION
PSECR and pectinate circuits were used to design sensing
cells in a 3-D tactile sensor, making it possible to implement a
low-cost, compact, and light sensor system without a complex
3-D structure. We constructed an experimental test system using
a triaxial force sensor to measure reference loads, and a calibration experimental test of the sensor was completed through the
application of arbitrary forces with known magnitude and direction. The verification experiment results indicate that the sensor
can measure the triaxial force with high precision. Coupling effect tests were performed to examine the cross-sensitivity of the
sensor, and we found that the change of vertical load may affect the precision in measuring the transverse forces because
of the deformation of the elastic interface under a high pressure force. For the next step of the application, if abundant sensors are constructed under a plate (see Fig. 2), it is desired that
the distributed pressure may produce less effect on the elastic
interface; whereas, if a single sensor is used to measure large
normal force (over 100 N) and transverse force, a hard interface
is necessary.
N for and
Load ranges of the sensor were rated as
axes (transverse direction), and 100 N for axis (the normal
direction); so, it follows that if we integrate more than eight
sensors, a wearable force plate can be implemented for GRF
measurement during gait of a normal human subject. Moreover,
the small size (diameter height: 10 mm 10 mm) and light
weight (10 g) of the sensor mean that it can be easily fixed beneath shoes with a low impact on the weight and height of the
shoes, so the sensor will correspond with the need for a method
of ambulatory gait assessment in clinical applications, a setting
where GRF measurement is required in daily life.
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Tao Liu (M’08) received the B.Eng. and M. Eng.
degrees in mechanical engineering from the Harbin
University of Science and Technology, Harbin,
China, in 2003 and the Doctorate degree in engineering from Kochi University of Technology,
Kochi, Japan, in 2006.
From 2003 to 2006, he was a Research Assistant
at the Kochi University of Technology, where during
2007, he was a Postdoctoral Fellow in the Department
of intelligent Mechanical Systems Engineering. He
has been an Assistant Professor in the Department of
Intelligent Mechanical Systems Engineering, since 2008. His current research
interests include wearable sensor systems, multiaxial force sensors, human motion analysis, and rehabilitation robots.
Dr. Liu is a member of the Japan Society of Mechanical Engineers.
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IEEE SENSORS JOURNAL, VOL. 9, NO. 9, SEPTEMBER 2009
Yoshio Inoue received the B.Eng. degree in mechanical engineering, the M.Eng. degree in precision engineering, and the Doctorate degree in engineering
from Kyoto University, Kyoto, Japan, in 1970, 1972,
and 1993, respectively.
From 1989 to 1996, he was the Head of the
Vibration and Sound Laboratory, Kobe Steel, Ltd.,
Kobe, Japan. During 2007, he was a Special Director
with Kobe Steel, Ltd. He is currently a Professor in
the Department of Intelligent Mechanical Systems
Engineering, Kochi University of Technology,
Kochi, Japan. His current research interests include vibration analysis, human
dynamics, and robotics.
Dr. Inoue is a member of the Robotics Society of Japan, the Society of Automotive Engineers of Japan, the Society of Instrument and Control Engineers,
the Japan Society for Design Engineering, and the Sports Engineering, Editorial Board, and a Fellow of the Japan Society of Mechanical Engineers. He is a
recipient of the merit commendation of the 110th Japan Society of Mechanical
Engineers Anniversary in 2008 and the Director-General Prize of the Science
and Technology Agency of Japan government in 1984.
Kyoko Shibata received the B.Eng. degree in measurement engineering, the M.Eng. degree in measurement engineering, and the Doctorate degree in engineering from Seikei University, Tokyo, Japan, in
1994, 1996, and 2001, respectively.
In 1996, she joined Sony System Design, Ltd.,
Japan. From 1998 to 2002, she was a Research
Associate in the Department of Measurement Engineering, Seikei University. During 2003, she was an
Assistant Professor in the Department of Intelligent
Mechanical Systems Engineering, Kochi University
of Technology, Kochi, Japan, where she is currently an Associate Professor.
Her current research interests include medical and welfare robots and human
friendly robotics.
Dr. Shibata is a member of the Japan Society of Mechanical Engineers, the
Japan Society for Precision Engineering, the Society of Instrument and Control
Engineers, the Institute of Electrical Engineers, and the Institute of Electronics,
Information and Communication Engineers.
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