Experimental Evaluation of
the Gyroscope Sensor used in a New Gait Phase Detection System
Ion P. I. Pappas, Thierry
Keller,
Automatic Control
Laboratory, ETHZ, ETL-I, 8092 Zürich
Abstract
This paper
focuses on the experimental evaluation of a gyroscope sensor used in a new gait
phase detection system, which has previously been presented in [1]. The system distinguishes four phases during walking (stance,
heel-off, swing and heel-strike) and consists of three force sensitive
resistors, a gyroscope and a processing unit. The system has been successfully
tested by subjects with normal and pathological gait styles. Further, it has
been verified that the system works with very high reliability even on
irregular ground surfaces and varying ground inclinations. The contribution of this paper lies in the
in-depth analysis of the processing of the gyroscope signal. Miniaturized
gyroscopes have recently been used also in other biomedical applications, for
which the presented results are of particular interest.
Introduction
|
Figure 1
Placement of the force sensitive resistors (FSR) and the gyroscope used for
the gait phase detection system. |
In a previous paper [1] we presented a new gait phase detection system which
distinguishes four phases during gait: stance, heel-off, swing, heel-strike.
The system, as shown in Figure
1, consists of three force sensitive
resistors (FSR), which measure the applied weight pressure in three areas of
the sole and a piezoelectric gyroscope which is inserted in the shoe heel and
which measures the rotational velocity of the foot (about the y-axis) with
respect to an inertial system. In previous publications [1], [2] we have claimed that the combined use of the FSRs and
the gyroscope together with a intelligent rule based detection algorithm leads
to a very robust gait phase detection system. The performance of the system has
been validated by healthy and walking-impaired subjects on irregular and
inclined ground surfaces and even on stairs. A key role for this highly
reliable performance is played by the gyroscope sensor which provides information
about the foot’s momentary angular velocity, which the FSRs can not provide.
Based on this information we are able to estimate in real-time the angular
inclination of the foot 
with respect to the
ground and thus distinguish between a true heel-off event and a simple
unloading of the foot (for instance due to weight shifting from one leg to the
other during stance without and actual lifting of the heel). The gyroscope is
also used to detect the beginning of the swing phase, which is characterized by
a change of the foot rotation from clockwise direction to counter-clockwise
(viewed from the right hand lateral side). The gait phase detection system
shall be used to trigger the onset of stimulation sequences in functional
electrical stimulation (
In the last years, miniaturized gyroscopes have been
used for several purposes in the field of biomedicine and rehabilitation. J. R.
Henty [3], for example, placed a gyroscope on the foot above
the metatarsals in order to distinguish two phases in the gait cycle, the swing
phase and the stance phase. Further, he calculated the hip, knee and ankle
flexion angles during the gait cycle by placing a gyroscope at the thigh, at
the shank and at the foot and by integrating the differences of the gyroscope
signals. In another application, Thomas Fuhr in [4] placed a gyroscope on the thigh of his subjects in
order to estimate the angular velocity of the knee flexion during the
standing-up phase. In spite of the above mentioned works and the multiple use
of the same gyroscope device[1],
no detailed analysis of the gyroscope signal has been reported yet. Therefore,
in the following, we present results obtained from the experimental analysis of
the gyroscope sensor and discuss the consequences for the gait phase detection
application. The analysis does not include the FSR sensors, because they are
used as simple switches, i.e. they determine whether weight is applied to the
respective area of the foot sole or not.
Theoretical Aspects of
Gyroscope Signal Analysis
|
Figure 2 Illustrates Equation 3 for a=3.8mV/deg/sec, T=10ms, sv=10mV |
During rotations the gyroscope senses the mechanical
deformation of an internal vibratory prism caused by the coriolis force. It
delivers an output voltage 
which is proportional to the rotational velocity 
, as expressed by Equation 1. The parameters 
and 
are the gain and
offset values and 
is the measurement
noise which includes round-off errors and disturbances. The angular excursion 
can be estimated by
integrating the gyroscope signal, according to Equation 2.
The estimation error committed by the integration of the noisy gyroscope signal
is given by 
. Under the
assumption that the measurement noise is random, white and
zero mean with standard deviation 
, the standard deviation 
of the estimation
error 
increases with time
according to a random walk law, see Equation
3 and Figure 2.
However, this is a conservative estimate, since in reality the measurement
noise may not be white or zero-mean. For time critical systems (such as the
gait phase detection system), the following question is of interest: How
accurately can the time point 
be determined at which
the angular excursion reaches a given threshold value 
? Given the
uncertainty in the estimation of (standard deviation 
), the standard deviation 
on the estimation of is given by Equation
4.
Experiments
In order to validate the theoretical predictions of
the error committed by the
integration of the gyroscope’s signal the following experiment was performed.
The gyroscope was mounted on an articulated arm which was rotated repetitively
by 45 degrees. The average rotational velocity was approximately 
(very slow for walking
purposes, taken as worst case). Figure
3a shows recordings of the
gyroscope signal during the first 4 trials.
Random
Errors: The random measurement noise
amounts to 
and the signal to
noise ratio at these slow rotational velocities is at an approximate level of @30dB. Figure
3b shows estimates of the angular
excursions obtained by the
integration of the gyroscope signal. The deviation of the final angle estimate
amounts to 
and is due to the
integration of the random measurement noise. This measured error is in good
agreement with the theoretical standard deviation of 
calculated by Equation 3 (with 
, 
). The uncertainty with which we can determine the time point
at which crosses the threshold
of e.g. 
is given by Equation 4 and amounts approximately to: 
. A large portion of the measurement noise is due to
disturbances in the signal transmission through the long wires and to the
round-off errors of the employed 10bit resolution A/D converter. In order to
reduce the relative importance of the measurement noise shielded wires were
employed and the gyroscope signal was amplified using the circuit displayed in Figure 4b (amplification factor = 3.3).
Offset
Drift: The Figure
3c and 3d, show the integration
results for the same experiment as above carried out at different temperatures
(18.7°, 20.4°C). The integrated signals exhibit a significant systematic error which is due to an
offset drift caused by the temperature variations. This systematic error can be
eliminated by re-calibrating the gyroscope signal before each trial. The Figure 3e and 3f show the same data as the Figure 3c and 3d but with a software offset
correction.
Figure 3
The
experiment shown in this figure consisted of repetitive rotations of the
gyroscope of 45 degrees. (a) shows the gyroscope signals for the first set of 4
trials. (b) shows the angular excursion 
obtained by integration of the gyroscope signals
shown in (a). The final integration error is eq=1.5
degrees, which is due to the integration of the random measurement noise. (c)
and (d) show integration results of the same experiment repeated at different
temperatures. The large error is due to a temperature drift. In (e) and (f) the same data as in (c)
and (d) are shown, but with a software offset correction.
To evaluate the influence of the temperature on the
offset drift of the gyroscope signal the above experiment was repeated at
different temperatures ranging from 5 to 50°C. In Figure 4c the measured offset values are shown
as function of the temperature. In the same temperature range, the gain factor 
varied within a range of ±5%, which results in a less important error
as compared to the offset drift.
Figure 4 (a)
shows the gyroscope connections and (b) the amplifying circuit used in the
experiments. (c)Shows the offset drift of the measured gyroscope signal as a function of the temperature. The offset
at 20°C
is set to zero and the deviations are scaled to equivalent [deg/sec]
units.
Discussion
The main conclusion from the above experiments is
that the gyroscope sensor can provide very valuable information if its signal
is processed appropriately. First, a compensation of the gyroscope’s
temperature drift is absolutely necessary in order to obtain quantitative
measurements. If the drift is (computationally) compensated the gyroscope
signal can be used to measure rotational velocity or angular excursions (by
integration of the gyroscope signal). Integration of the gyroscope signal
should be limited to short time periods (depending on the required precision),
in order to maintain an approximately constant temperature and in order to
avoid the integration error which increases with the number of integrated
samples according to Equation
3 and Figure
2. In the case of the gait phase
detection system the signal offset is re-calibrated once in every walking cycle
during the stance phase (rotational velocity 
). However, at fast walking speeds (>7km/h) the stance
phase becomes shorter and shorter and does not satisfy the condition of
rotational velocity anymore, because the
foot rolls from heel-strike to heel-off continuously on the ground without a
pause. Thus at these speeds, it is impossible to compensate for the temperature
drift. We have shown that the timing uncertainty in the detection of the gait
phases is affected by the errors in the estimation of the angular inclination.
Based on the presented (worst case) experiments this error should be smaller
than 26ms, which is sufficiently
accurate for a FES walking application. Finally, in a future design it would be
desirable to develop for the gyroscope a temperature compensating electronic
circuit or to actively regulate the temperature of the gyroscope to a constant
value.
References
[1] I. Pappas, “A Novel Gait Phase Detection System” presented at AUTOMED'99, Darmstadt, Germany, 1999.
[2] M. R. Popovic, T. Keller, S. Ibrahim, G. v. Bueren, and M. Morari, “Gait Identification and Recognition Sensor” presented at 6th Vienna International Workshop in Functional Electrostimulation, Vienna, Austria, 1998.
[3] J. R. Henty and D. J. Ewins, “Applications of gyroscopic angular velocity sensors in FES systems” presented at 6th International Workshop on Functional Electrostimulation, Vienna, Austria, 1998.
[4] T. Fuhr and G. Schmidt, “Autokalibrierungsverfahren für ein patientenfixiertes Goniometer-Gyroskop-System zur Bewegungsmessung” presented at AUTOMED '99, Darmstadt, 1999.
NOTES:
Figures 1-4 where edited in the files final figs.ppt
Figure 2 was generated by the files:
Y:\3feslab\ionshome\conferences\ifess99\intgvar.m
Figure 3 was generated by the files:
Y:\3feslab\measdata\GyroTemp2\mgy45_T02.m
Figure 4 was generated based on the file:
Y:\3feslab\measdata\GyroTemp2\mgy45T01.m