C. Quaternion calculation from accelerometer and ... - Hal

Il s'agit ici de vérifier s'il existe un changement notable sur l'évolution du taux de
croissance du PIB entre la période d'avant ..... d'Afrique sub-saharienne pour ce
qui est des IDE entrants, soit 1431 M USD contre 323 en 2002. ...... R carré
corrigé ...... 2) le report sur les résultats des 5 exercices suivants, du déficit
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A Complementary Sliding Mode Observer Approach for Motions Human Body
Segments Capturing by Means of Wearable Inertial and Magnetic MEMS Sensors
Hassen Fourati, Student, IEEE, Noureddine Manamanni*, Member, IEEE, Lissan
Afilal, Yves Handrich

Abstract-The aim of the paper is to develop and to validate an estimation
approach of human body segments motion (also known as attitude). The
challenge of the proposed approach is that it uses only a wearable Inertial
Measurement Unit (IMU) and without resorting to GPS data. This unit
consists of Micro-Electro-Mechanical-Systems (MEMS) sensors as a 3-axis
accelerometer, a 3-axis magnetometer and a 3-axis gyroscope. Based on these
sensors, the final objective is to design a low-cost and lightweight
prototype and easy to use by persons. The prototype can then be used in
many applications as ambulatory monitoring of human body motion in order to
evaluate the corresponding mechanical work. To reach this goal, a
quaternion-based Complementary Sliding Mode Observer (CSMO) is designed
with a multiplicative quaternion correction technique. This algorithm will
continuously correct the quaternion estimates obtained by integration of
the angular velocity. The correction is performed using a quaternion
obtained from the accelerometer and the magnetometer data fusion based on
the Levenberg Marquardt Algorithm (LMA). The efficiency of the CSMO is
illustrated through simulation tests using a theoretical example. Moreover,
a set of experiments is performed on a robot and human limbs motion through
sensor measurements provided by an IMU.

Index Terms-Motion capturing, human limbs motion sensing, Complementary
Sliding Mode Observer, Inertial Unit, wearable inertial/magnetic MEMS
sensors, quaternion, rehabilitation.


The determination of moving objects orientation is involved in several
fields: among them, of interest here, ambulatory human motion tracking and
analysis [1]. Moreover, the current information of orientation still one of
the central assessment tools in many related application as stroke
rehabilitation to help patients to restore motor functions of the affected
limbs [2], gait analysis [3], monitoring of daily living [4], and
measurement of neurological disorders in medicine [5].
A literature survey shows that there are currently several fundamental
technologies embedded within human movement tracking systems, which
consistently update spatio-temporal information with regard to human
motion. These technologies can contain mechanical tracking, electromagnetic
tracking, acoustic tracking, optical tracking, and inertial/magnetic
tracking [1]. Among these techniques, inertial/magnetic tracking technology
has currently attracted many interests since such method is free of most of
the problems occurring with the other technologies. An inertial/magnetic
tracking system uses a combination of accelerometers, rate gyros, and
magnetic sensors and is suitable for ambulatory measurement of human body
segments orientation without restrictions [6]. There is no inherent latency
associated with inertial/magnetic sensing and all delays are due to data
transmission and processing. Another benefit with inertial/magnetic sensing
is its sourceless, whereas electromagnetic, acoustic, and optic devices
require emissions from source to track objects.
Nowadays, due to the recent technological advances of MEMS, inertial and
magnetic sensors have become generally available with a low cost, small
size, light weight and low energy consumption. Consequently, human motion
estimation can be tracked continuously outside of a laboratory with quite
smaller and ambulatory measurement system. Each of these sensors has
different advantages and disadvantages. Accelerometers measure acceleration
and gravity [7] and can be used as an inclinometer for movements in which
the acceleration can be neglected with respect to the gravity [8]. However,
this way to do leads to unacceptable errors in dynamic human motion.
Gyroscopes measure angular velocity and can be used to estimate a change in
orientation. The drawback of gyroscopes is that the estimation of
orientation change is prone to integration drift [9]. Magnetometers are
used to measure the local earth magnetic field vector. This provides
additional information about orientation [10].
Several advanced signal processing fusion approaches for integrating the
sensors described above to estimate human segments orientation have been
proposed in order to overcome the drawbacks of the separate sensors and to
improve the performance of existing sensing hardware. The basic idea behind
complementary filtering is that orientation drift errors resulting from
gyro output errors can be bounded by aiding the gyros with additional
sensors, the information from which allows correcting the gyro orientation
solution. In [11], the authors combined sensors such as 3-axis
accelerometer and 3-axis magnetometer to measure the body orientation. A 3-
axis gyroscope and 3-axis accelerometer were applied by [12] and the
proposed works are developed based on a Kalman filter for measuring
orientation. The main idea in [3] concerns the use of the cyclical nature
of human gait to provide attitude estimation based on angular velocity rate
and acceleration measurements. The change in orientation obtained using
gyroscopes was fused with the inclination measured by the accelerometers,
yielding an inclination estimate that was sufficiently accurate even in the
presence of accelerations.
The main purpose in [13] deals with the addition of magnetometers to
gyroscopes and accelerometers to overcome this problem. A linear Kalman
Filter was designed to process the sensor signals to estimate desired
sensing variables of gravity and magnetic field, and further yields
orientation of the body segment. Heading errors due to magnetic field
disturbance can be effectively rejected by an adequate model-based sensor
fusion [14]. This triad of sensors is used also in [15], [16] to develop an
Extended Kalman Filter (EKF). Another method to obtain kinematics between 2
body segments is to estimate the orientations of each segment using a
multiple sensor system and to use anatomical constraints to link the
different segments [2], [3].
Quaternion has been the subject of studies in many attitude and motion
capturing systems using various filtering theories. Due to the
unconventional nature of quaternion kinematics, filter models have been
synthesized in two different ways related to the objectives, the
formulation of the measurement error vector and the update of the state
estimates. The first way is based on additive quaternion correction [15],
[17]. This approach is easy to implement but it is considered as localized
approximation since it is valid only for small attitude changes. The second
way uses multiplicative quaternion correction [18], [19] and can be applied
for larger attitude maneuvers.
In this paper, an alternative sensing method for the human limbs motion
estimation is developed then validated. This approach is based on a fusion
technique of inertial and magnetic sensors. The main goal is to use the
obtained results to monitor human movements during rehabilitation
exercises. One of the interests of this work is also to look for the
ambulatory monitoring of the elderly movements. Hence, we propose a robust
method recovering the full attitude represented by a quaternion and which
represents the rigid body motion. The main idea is to use a Complementary
Sliding Mode Observer (CSMO) instead of Extended Kalman Filter that
presents some drawbacks such as the difficulty to guarantee the global
convergence of the filter due to the linear approximation of the nonlinear
process model [20].
The proposed CSMO exploits the multiplicative quaternion correction
technique to recover the full rigid body orientation. The designed observer
is fed with inertial and magnetic measurements and takes into account the
complementary spectra of the signals. In fact, the estimation algorithm
idea uses 3-axis gyroscope measurements to derive the attitude (strap-down
system). The correction was performed using a quaternion continuously
derived from a 3-axis accelerometer and a 3-axis magnetometer data fusion
method that is based on Levenberg Marquardt Algorithm (LMA). This reduces
the integration drift that originates from the angular velocity.
This paper is organized as follows: section II describes the problem
statement and our motivations. Section III presents the physical system
including the rigid body kinematic equation and the design model. Section
IV details the structure of the proposed CSMO for motion estimation. In
section V, some simulation tests are presented to illustrate the
performance of the proposed approach. Experimental trials are designed on a
robot and a human subject in section VI to demonstrate the efficiency of
the developed filtering technique. Finally some conclusions are given in
section VII.

Motivation and problem definition

The main contribution of the performed work in this paper is to propose
available approach to estimate the movement patterns (attitude or
orientation) of human body segments. Each segment can be represented by a
rigid body. Generally, the body attitude is an essential quantity t