ThP01-28
Proceedings of the 2005 IEEE
9th International Conference on Rehabilitation Robotics
June 28 - July 1, 2005, Chicago, IL, USA
Foot and ground measurement using portable sensors
Wolfgang Svensson and Ulf Holmberg
Abstract— A portable gait measurement system for foot dynamic analysis is proposed. Portable cheap sensors are suitable
in active control rehabilitation equipments such as prostheses
and orthoses. A system of one gyroscope and two accelerometers
was used to measure the foot movement in the sagital plane.
Both ground inclination during stance and foot angle relative to
ground during swing are estimated. This enables fast detection
of changing environments such as hills and stairs.
I. INTRODUCTION
Gait measurement is of interest for both orthopaedists
and biomechanical engineers. It is useful for analysis of
gait disorders and in design of orthotic and prosthetic devices. Commonly used vision based systems are restricted
to laboratory environments where only a few stance phases
are practically observable. This also limits the number of
possible case studies to treadmill and shorter stair walking. Moreover, the marker positioning is fundamental but
not elementary. In recent years portable sensors have been
studied as a complement, see e.g. [5]. They have been used
to measure both the kinematics of gait such as accelerations
and angles as well as kinetics such as torques and forces. The
main contribution of using portable sensors is the possibility
of long time measurement of daily life situations.
But the technique has also been included in active control
of foot for rehabilitation. The research has mainly been focusing on the area of drop foot control. These approaches are
orthotic control [1] or functional electrical stimulation(FES),
see e.g. [12] [6]. While the former still has to be designed
with a realistic transducer the latter has been used by patients.
FES activates the dorsiflexion muscles in the back ankle with
electricity. The objective is to provoke foot lifting just in
time for swing phase. Therefore the step has been divided
into heel-off, stance, swing and heel strike. These phases
were estimated in real time using gyros and force sensitive
resistors (FSR).
In kinematical analysis several studies have been focused
on estimating the angles between calf and thigh or thigh and
hip. With several accelerometers placed apart the difference
due to the distance can be used in estimating the angle.
Willemsen et al. [13] positioned two accelerometers on a
rigid bar, on each leg part. They could estimate the calf angle
with a standard deviation error of 4 degrees. This was further
improved by Mayagoita et al. [3] who added a gyroscope
(gyro) to each pair achieving a mean accuracy of 3 degrees
and a standard deviation of 3 degrees, which is similar to
School of Information Science
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and Computer and Electrical
301 18, Sweden, Emails :
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(W.Svensson)
and
[email protected] (U.Holmberg)
0-7803-9003-2/05/$20.00 ©2005 IEEE
a visual system. Gyroscopes include a drift which can be
compensated by resetting the angle at midstance. Tong and
Granat [10] assumed that the angle was constant and this
phase could be detected using four FSR’s resulting in an
angle estimation with 4 degrees error.
Veltink et al. [12] used the same approach and showed that
using only one 3D-accelerometer and one 3D-gyro, the 3D
movement could be estimated. Thus the gyro signal estimated
the angle which was used to withdraw the gravitational
component from accelerometers. By integrating these signals
twice the position could be found. They found that the system
gave 3 percent distance accuracy in the walking direction.
However, they noticed though that the system did not work
so well on uneven ground or in stairs.
Current systems, based on gyros and accelerometers, can
under special conditions measure the angular movement just
as accurate as visual systems. The angle between foot and
ground can be estimated by integrating the gyro signal.
But due to internal noise and temperature sensitivity the
estimation tends to drift. Sabatini et al. [9] used that foot
blade is stationary during the stance phase and the drift
was calibrated by measurement of ground inclination using
accelerometers. The stance was found by dividing the step
into the four phases and from the gyro signal the phase
transitions could be estimated. From this they determined
several gait parameters i.e. walking speed, stride time,
relative stance, inclination etc. However, only consecutive
transitions between gait phases where considered making the
approach less suited for analysis of gait disorders and stairs.
In [8] a switching technique between 3 gyros and 3
accelerometers was proposed for attitude estimation of pitch
and roll angles of a walking robot.
This approach is modified in this paper to suit estimation
of one foot angle in the sagital plane, independent on
gait phase transitions. Only two accelerometers are needed
for calibration during stance and one gyro is used during
swing. A smooth sensor fusion between stance and swing
estimations makes tuning simple. Also, the sensor placement
at the front of the foot avoids the need for heel strike for
stance transition. Stair walking can therefor be studied.
II. ANGLE ESTIMATION
The angle foot-to-ground was estimated by mounting three
sensors close the toe as shown in Fig. 1. The placement
guarantees that the sensors are stationary during stance
for all possible gait situations, even in stairs. The sensor
system consists of one gyroscope measuring the angular
velocity, ω and two accelerometers measuring a1 and a2 .
In the stationary case when the foot is at inclination φ the
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the correction from stance estimation. The function uses the
filtered |ω| since during change of rotational direction the
filtered ω would be zero without being in stance.
The estimator is then constructed as
φ̂k+1 = φ̂k + ωh + σk (ŷk − φ̂k )
The stance phase is characterised by the conditions
⎧
⎨ σk1 −1 < k = k1 , . . . , k2
σk > ⎩
σk2 +1 < Fig. 1. The sensors are mounted at the fifth metatarsal measuring angular
velocity ω and accelerations a1 and a2 . The angle foot-to-ground φ is
defined positive in the counterclockwise direction.
accelerometer measures are:
a2
a1 = −g cos φ
→ φ = − arctan
a2 = g sin φ
a1
(2)
(3)
A weighting function σ(ω) is chosen for trade off between
stance and swing estimation. It is defined as
σk = βe−αxk
xk+1 = dxk + (1 − d)|ωk |
with accuracy estimated by the standard deviation
k2
std[φg ] = N1 k=k
(ŷ − φg )2
1
(8)
III. MEASUREMENT RESULTS
A. Sensor system
A complete algorithm should be able to switch between
stance estimation (1) and swing estimation (2). One switching function was proposed by Rebinder and Hu [8]. That
approach exploited that the size of the acceleration is approximately g during stance. This needed to be fulfilled over
a certain time interval in order to reduce noise effects.
Here we propose to use a simpler and intuitive algorithm
with a smooth transition between swing and stance. First,
noise influence is reduced by low pass filtering of (1)
according to
yk = − arctan aa21 (k)
(k)
ŷk+1 = cŷk + (1 − c)yk
(6)
with a duration of N = k2 − k1 + 1 samples and using
a threshold . The placement of the sensors guarantees that
N > 1 since the toe is likely to be in contact with the ground
for all walking situations (even in stairs and running). An
average ground angle can be estimated as
k2
(7)
ŷk
φg = N1 k=k
1
(1)
respectively and where g is the gravitational constant. Thus,
the foot to ground angle is defined positive for foot dorsiflexion. Since the foot is stationary during stance the angle φ
can be estimated using the accelerometers according to (1).
During swing, however, the accelerometers do not only
measure the gravitational acceleration but also the acceleration of the foot. Therefore, (1) cannot be used for estimation
of φ during swing. Instead, integration of the gyro signal
ω = φ̇ can be used as an estimate. In discrete time with a
sampling period h, such an estimation φ̂ of φ would be
φ̂k+1 = φ̂k + ωk h
(5)
(4)
where α > 0 and 0 < β < 1. These parameters trade off
small noise sensitivity versus speed. The parameter α is used
to distinguish between stance and swing while β quantifies
One Murata 03JB gyro and one ADXL 311 (a two directional accelerometer) were mounted on a shoe at the fifth
metatarsal bone. The motivations of choosing this position
were two: 1) Shoe mounting reduced the effect of skin
movement and internal bone movement. Thus, the sensor
during stance phase is not affected by the calf rotation. 2)
Robustness to different stance conditions since the frontal
position is almost always stationary. The signals were sampled and logged using a portable Texas DSP system at 1kHz.
The signals were converted using a 14 bit AD-converter and
each experiment was 20 seconds long. The standard deviation
of ω-noise was 0.16 degree/sec and each acceleration-noise
0.014g per s2 .
B. Experiments
The measurements were done on one healthy male wearing
normal shoes. Three typical gait situations where studied:
horizontal walking, ascending and descending stairs and
walking when the ground is inclining and declining. These
situations have been useful in gait analysis [7], [4], comparing and designing prosthetic feet [2], [11]. The horizontal
walking was done at different speeds which did not significantly influence the algorithm performance, see Fig. 2. It
shows typical signals for one “start step” followed by 1.2
m/s horizontal walking. When walking at constant speed
there are insignificant differences in angle trajectories from
step to step. The estimated angle is averaged over 15 number
of steps shown in Fig. 3. There is, however, a significant
difference between horizontal walking, stair ascending and
descending. From the angle estimation it can be observed that
the angle reaches its minimum when the heel lift phase is
completed. This is followed by a calf pendulum movement
forward in the swing phase which ends when the angle is
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3) Inclination of the ground: The ground inclination was
measured by walking on horizontal ground followed by
ascending a hill and finally the same hill was descended. The
angle could be updated each step according to (7). The hill
had two 4 degrees inclinations and was a wooden ramp into
a post office entrance designed for wheelchairs. The results
show, as can be seen in Fig. 4, an estimated angle within
one degree accuracy both for horizontal and hill walking.
IV. CONCLUSIONS
Fig. 2. a) Sensor signals, b) weighting function σ, and c) estimated angle
φk when walking on a horizontal surface.
A simple and robust foot-to-ground angle estimation algorithm was proposed. It is robust in the sense of being
insensitive to walking situations e.g. speed, inclinations or
stairs. The position of the sensors was crucial to get a robust
algorithm performance. Shoe mounting reduced the effect of
skin movement and internal bone movement and the frontal
position is almost always stationary during stance.
Furthermore, this algorithm can be used to estimate the
foot angle during the swing phase. The measurements show
that during normal conditions the estimation accuracy is
within a few degrees. Distinct differences between ground
walking, stair ascending and descending can be seen in the
angle estimation.
V. ACKNOWLEDGMENTS
This work was funded by the KK-foundation and is a part
of the PRODEA research group.
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Fig. 3. Averaged gait angle for: horizontal walking(dashed), stair ascending(solid) and stair descending(dotted).
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