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In this paper the performance of a sensor system, which has been developed to estimate hip and knee angles and the beginning of the gait phase, have been investigated. The sensor system consists of accelerometers and gyroscopes. A new algorithm was developed in order to avoid the error accumulation due to the gyroscopes drift and vibrations due to the ground contact at the beginning of the stance phase. The proposed algorithm have been tested and compared to some existing algorithms on over-ground walking trials with a commercial device for assisted gait. The results have shown the good accuracy of the angles estimation, also in high angle rate movement.

Gait analysis can be very important to support the rehabilitation of patients with a motor impairment and the monitoring of the patient's healing progress. Indeed, gait analysis can provide a quantitative description of the gait cycle and then improve the standard observational analysis. In the rehabilitation of motor function, the physiotherapist normally evaluates the improvement of the patient and his motor learning just by the visual information of the movements or by measurement of the time for a task; on the other hand, quantitative evaluation of movements, with a measurement system, are commonly used in research works. Gait analysis has attracted an increasing amount of attention from researchers and clinicians since the 1970s. Using video cameras, gait analysis based on highly accurate computer-based force plates was established in the 1980s and was applied in specialized motion laboratories. An optical 3D motion analysis system with a camera was used in [

In order to mitigate these problems, alternative gait analysis methods based on wearable sensors were studied and have shown great perspectives in the past two decades. Indeed, the term wearable implies that such a system is portable, lightweight and safe. In order for such a device to be accessible for home use, additional requirements are that the wearable sensor systems have to be cheaper and easy to operate.

In recent years, wearable sensors, such as accelerometers and gyroscopes, have been used in the measurement of human motion and in gait analysis; these inertial sensors have the properties of lower cost, small size robustness, easiness of setting and a number of efficient algorithms that exists, providing the estimation of gait parameters. Therefore, they are suitable for clinical application. Placed on foot segments, inertial sensors can be used for gait parameter estimation [

Another method to estimate joint angles from measured accelerations is the estimation of angles between sensors and the vertical direction. These methods could became less accurate if the segment accelerations are as large as the gravity [

The accurate estimation of joint angles and the beginning of the stance phase allows the detection of the gait phases. Indeed, a normal walking gait cycle is divided into eight different gait phases, including initial contact, loading response, mid-stance, terminal stance, pre-swing, initial swing, mid-swing and terminal swing, and each phase is determined by the joint angles and gyros measurement [

A different approach was presented in [

In many applications, the offset drift is solved by means of the Kalman filter. Cikajlo

Popovic

An interesting method was proposed by Watanabe

A strategy to estimate hip and knee joint angles has been recently proposed in [

In order to solve these issues in this paper, two methods are proposed to estimate gait parameters based on the complementary filter method [

In the Section 2, we provide the methods for the hip and knee angles estimation and the complementary filter method used for the results comparison, whereas in Section 3, we present the sensor system. Furthermore, some experimental findings are shown in Section 4, and Section 5 deals with some conclusions.

In this section, the acceleration propagation-based method originally proposed in [

A significant problem for the measurement of joint angles with gyroscopes is the error accumulation in the integral value, due to the pronounced drift. In order to avoid this drawback, the following second order kinematic model between two consecutive leg segment can be considered.

First, let us consider the kinematic relation expressing the position of the knee accelerometer, _{1}, with reference to that of the hip, _{0}:
_{1} is the position of the knee accelerometer (with respect to the coordinate Frame 0), and the rotation matrix is defined as
_{1}, _{1}, _{1}, the direction vectors. Indeed,
_{1} is the measure from the knee gyroscope.

As the measure from the _{0} on both sides, becomes:
_{0,mx}, _{0,my} and

Multiplying _{1} and _{1}. Then, obtaining the hip angle is straightforward.

In the same way for the second link, the position between the hip and ankle accelerometer is expressed by:
_{01} is the position of the origin, _{1} (with respect to coordinate Frame 0), _{2}

The two successive time differentiation of _{1} + _{2}

As in the case of the first link, multiplying _{12} and _{12} are the cosine and the sine of the angle (_{1} + _{2}). With some algebraic manipolation, _{2}_{2}

Considering the kinematic relation _{2} and _{2}, therefore allowing one to estimate the knee angle, _{2}.

The kinematic relations _{1} — _{01}), namely the distance between the knee accelerometer and the origin of Frame 1. Therefore, if the knee accelerometer is put as _{1} = _{01}, the system will become more robust, and the joint angle computation is a simple propagation of the same formula.

Note that a similar approach is proposed in [

The complementary filter is one of the most powerful and simple methods for the data fusion of different sources of information, which are complementary in a frequency domain [

For every signal,

If _{low}_{high}

In many applications, the high frequency approximation of the signal can be obtained by the integration of a velocity signal, which shows a low frequency drift phenomena. Then,

The most simple implementation of the CF can be obtained starting from the low-pass filter:

In this application, the estimation of the position is based on measurements provided by accelerometers (_{low}_{high}

The classical implementation of the CF requires the use of the accelerometer as an inclinometer,

To solve this problem, a new complementary filter method has been introduced:
_{APB}_{gyro}

The APB algorithm, as well as the complementary filter method, as is shown in the next section, have an accurate performance in the walking tests, where there are not considerable fast variations of joint angles nor contacts of the foot with the ground, the latter bringing to oscillations of the position estimation for a short time interval due to the second order characteristic of the accelerometer. The proposed intelligent complementary filter (ICF) tries to solve this problem by using complementary filters with a rate limiter and the integrated signal from gyros blended together.

The general idea of the method proposed in this section is based on the fact that during oscillations, due to the contact, the integrated gyroscope signal is accurate enough. Then, the accelerometer signal, bringing oscillations in the time interval right after the contact of the foot with the ground, should not be considered in this circumstance, and the integrated gyroscope signal will be considered instead.

The scheme of the ICF estimation method is shown in the

The sensor system consists of accelerometers and gyroscopes put near the knee and the ankle (see

The experimental equipment is comprised of:

LPY510Al (ST), an analog, low-power dual-axis micro-machined gyroscope, capable of measuring the angular rate along pitch and yaw axes. It provides excellent temperature stability and high resolution. The gyroscope allows band limiting of the output rate response through the integrated low-pass filter.

MMA7361L (FreeScale), a capacitive low power, three-axis accelerometer, integrating a voltage regulator and a low-pass filter.

ARDUINO DUE, a microcontroller board based on the Atmel SAM3X8E ARM Cortex-M3 CPU, providing 54 digital input/output pins, 12 analog inputs (12 bits of resolution), an 84-MHz clock, 96 KBytes of SRAM, 512 KBytes of Flash memory for code.

AS5045 contactless magnetic rotary sensor for accurate angular measurement over a full turn. It is a system-on-chip, combining integrated hall elements, an analog front end and digital signal processing in a single device.

The proposed algorithm has been tested on angle measurements of the hip and knee of a commercial device for assisted gait: the NF-Walker [

The experiments performed have the main purpose of comparing the different ways of estimating hip and knee angles with direct angular measurement from encoders.

In addition, these algorithms are evaluated on an over-grounded walking trial. However, due to the limited laboratory size (therefore, the limited walking distance), this kind of measurement was restricted to only a few steps.

This experiment is performed to evaluate the performance of the mixed complementary filter-APB (CF-APB) algorithm on an over-ground walking trial.

In the

From this figure, it is pointed out that the APB algorithm, as well as the complementary filter method show good accuracy for the angle estimation, save for a time interval after the contact, where there are vibrations.

Finally, in

This experiment is performed to evaluate the performance of the intelligent complementary filter (ICF) algorithm on an over-ground walking trial.

As already said, both the CF and ICF methods get information from a position signal obtained from the accelerometer and a second piece of position information obtained from the integral of the gyros. In

In the

Finally, in

In this paper, a low-cost sensor system, based on accelerometer and gyroscope measurements, has been studied in order to estimate hip and knee angles during the rehabilitation and monitoring of patients.

The main purpose of the work is to avoid the significant problem of the error accumulation due to the offset drift caused by gyroscopes and the oscillations related to the time interval right after the contact of the foot with the ground, caused by the accelerometer.

In order to solve these problems, some algorithms have been proposed and experimentally evaluated and compared, estimating hip and knee angles during gait. In particular, as we can see from the experimental results, the acceleration propagation-based method (APB) and the complementary filter (CF) method have good performance, save for the time interval where the contact of the foot with the ground occurred. These problems were solved with the mixed complementary filter-ABP method (CF-APB) and the intelligent complementary filter method (ICF).

In addition, it is possible to use the trigger signals of accelerometers in order to detect the beginning of the stance phase, namely the initial contact of the foot with the ground.

The estimated gait parameters could be used in order to detect accurately gait phases, as is shown in [

Future developments of this algorithm will be the development of a mechanistic system for the walking assistance of motor-impaired child. In particular, hip and knee angle estimations, with both angular velocity and acceleration measurements and the detection of the beginning of stance phase will be shortly used to detect gait phase in a totally wearable system and, afterwards, to develop a proper control law to activate pneumatic muscles, put on the ortheses, in order to support the rehabilitation gait patterns.

This work was supported by the Italian Ministry of Education, University and Research, Research Project of National Interest: Robotics Collaborative and Cooperative (Ro.Co.Co.), 2011–2013.

The authors declare no conflicts of interest.

Kinematic scheme of a leg.

Schematic structure of the intelligent complementary filter (ICF) method.

(

(

Statistic comparison between APB, CF and both bound together (CF-APB).

The integrated gyroscope signal and the accelerometer-based position estimation: (

Estimation of the angles by means of the CF method vs. encoder measurement: (

Comparison between the APB, CF and intelligent complementary filter (ICF) methods vs. encoder measurement: (