FR3142246A1 - Method for estimating the evolution of a speed of a measuring point - Google Patents

Abstract

This method (1320) for estimating the evolution of a speed of a measurement point during a movement interval comprises the downstream integration (1322) of movement parameters of the measurement point acquired by an inertial device during the interval. movement interval, taking as initial value of the speed a value of the speed at the start of the movement interval, the upstream integration (1324) of the movement parameters, taking as initial value of the speed a value of the speed at the end of the movement interval, and calculating (1326) the estimated speed by merging the upstream and downstream integrations. Figure for abstract: Fig. 7

Description

Method for estimating the evolution of a speed of a measurement point Field of invention

The present invention relates to the field of estimating the evolution of the linear speed of a point from measurements carried out using an inertial device.

The invention also relates to the estimation of the trajectory of a point of interest belonging to a limb of a person from measurements carried out by means of an inertial device, and the use of such an estimation to evaluate and analyze an effort exerted by said limb, in particular when this limb is an upper limb.

Technological background

For a person, moving their upper limbs depends on the use and coordination of several muscles. The analysis of an individual's movements can therefore be used to characterize their physical fitness, and in particular the muscular strength that the latter is capable of developing. This muscular strength is likely to vary according to many factors such as the individual's fitness, their age, their physical training, or the taking of a treatment affecting their muscular efficiency.

The evolution of an individual's movements over time can be representative of the evolution of their physical fitness, particularly in the case of an individual suffering from a neuromuscular or neurodegenerative disease. These diseases, such as Duchenne Muscular Dystrophy (DMD), result in a reduction in the individual's muscular capacities as the disease progresses. This leads to a loss of motor skills in the affected patients.

WO 2019/243609 discloses a method for analyzing the stride of a walking pedestrian, intended to characterize the evolution of his fitness, from measurements taken using an inertial device attached to the pedestrian's ankle. Such a method, which is minimally invasive, finds a very particular application in the monitoring of neuromuscular or neurodegenerative diseases. However, it is only suitable for monitoring such diseases as long as the individual retains sufficient motor skills in his lower limbs. When the individual is no longer able to walk, typically because the disease is at an advanced stage, an alternative method is necessary to allow the disease to be monitored.

A consensus has thus emerged in the scientific community on the need to be able to precisely quantify the motor function of the upper limbs of individuals suffering from neuromuscular or neurodegenerative diseases. This consensus has led to the emergence of several methods for evaluating this motor function.

• l’échelle de Brooke (Brooke, M H et al. “Clinical investigation in Duchenne dystrophy: 2. Determination of the "power" of therapeutic trials based on the natural history.”Muscle & nervevol. 6,2 (1983): 91-103. doi:10.10002/mus.880060204),
• l’échelle révisée des membres supérieurs (mieux connue sous l’acronyme RULM, de l’anglais « Revised Upper Limb Module ») (Mazzone, Elena S et al. “Revised upper limb module for spinal muscular atrophy: Development of a new module.”Muscle & nervevol. 55,6 (2017): 869-874. doi:10.10002/mus.25430), et
• l’échelle de performance des membres supérieurs (mieux connue sous l’acronyme PULM, de l’anglais « Performance of Upper Limb Module ») (Mayhew, Anna G et al. “Performance of Upper Limb module for Duchenne muscular dystrophy.”Developmental medicine and child neurologyvol. 62,5 (2020): 633-639. doi:10.1111/dmcn.14361).

The vast majority of these assessment methods consist of traditional methods based on functional scales assessed by professional clinicians in controlled environments. The individual is typically invited to a hospital setting where they are asked to perform certain movements and, based on the success or failure of these movements, the clinician assigns a motor score. These methods include, for example:

• the Brooke scale (Brooke, MH et al. “Clinical investigation in Duchenne dystrophy: 2. Determination of the “power” of therapeutic trials based on the natural history.” Muscle & nerve vol. 6,2 (1983): 91-103. doi:10.10002/mus.880060204),
• the revised upper limb module (RULM) scale (Mazzone, Elena S et al. “Revised upper limb module for spinal muscular atrophy: Development of a new module.” Muscle & nerve vol. 55,6 (2017): 869-874. doi:10.10002/mus.25430), and
• the Performance of Upper Limb Module (PULM) scale (Mayhew, Anna G et al. “Performance of Upper Limb module for Duchenne muscular dystrophy.” Developmental medicine and child neurology vol. 62,5 (2020): 633-639. doi:10.1111/dmcn.14361).

However, these methods have several drawbacks: they are restrictive for the patient, requiring them to travel to a hospital, and their results may vary depending on the patient's state of health on the day of the assessment and the assessor.

Recently, other methods have emerged, based on the use of information technologies. Most use the analysis of data recorded in a controlled environment, typically in a hospital setting, using an optical capture system under the control of a health professional, as described for example in Han, JJ et al. “Reachable workspace and performance of upper limb (PUL) in duchenne muscular dystrophy.” Muscle & nerve vol. 53 (2016): 545-554. doi:10.10002/mus.24894. However, these methods suffer from most of the drawbacks already identified for traditional methods, in particular because they are restrictive for the patient and produce results that vary depending on the patient's fitness level on the day of the assessment.

To solve these problems, solutions have been sought to enable the assessment of the motor function of the upper limbs over long acquisition times, in the daily lives of patients, most often by means of measurements carried out by inertial devices attached to the upper limbs. These inertial devices must meet particularly demanding constraints of weight, size and autonomy to allow their portability, they are composed of MEMS type sensors. However, such sensors have a significant time drift which greatly complicates the monitoring of movements using the measurements returned by these sensors.

To circumvent this difficulty, it was proposed in WO 2017/129890 to assess the motor function of the upper limbs only for very specific movements, when the elbow is placed motionless on a surface and the movement of the wrist, to which the inertial device is attached, follows an arc of a circle centered on the elbow. However, this solution is not entirely satisfactory, since many movements of the upper limbs are not taken into account in this assessment of motor function.

It has also been proposed in El-Gohary, Mahmoud, and James McNames. “Shoulder and elbow joint angle tracking with inertial sensors.” IEEE transactions on bio-medical engineering vol. 59,9 (2012): 2635-41. doi:10.11009/TBME.2012.2208750 to combine a kinematic model of the upper limb with measurements acquired by two inertial devices positioned one on the arm, the other on the forearm, to compensate for sensor drift. This solution, which uses several inertial devices, is however poorly suited to daily use, because it is too invasive.

Finally, it was proposed in Villeneuve, Emma et al. “Reconstruction of Angular Kinematics From Wrist-Worn Inertial Sensor Data for Smart Home Healthcare.” IEEE Access , 5 (2017): 2351-2363. doi:10.11009/access.2016.2640559 to estimate the kinematics of a person's wrist from measurements provided by simple accelerometers worn at the wrist, using a particle filter and imposing constraints related to the respect of a biomechanical model of the person's upper limb. However, if this method allows to estimate the kinematics of the wrist without using a gyrometer, it does not solve the problem of the temporal drift of the sensors.

Other difficulties encountered in assessing upper limb motor function using inertial devices are that upper limb movements are much more varied and difficult to recognize than lower limb movements and that, unlike the latter, upper limb movements are often related not only to their own muscular activity, but also to muscular activity in other parts of the body, particularly the trunk or lower limbs.

One objective of the invention is to enable the monitoring of an individual's physical fitness over time. Another objective is to enable a good estimation, in an uncontrolled environment and over a long period, of the physical efforts made by an upper limb of a person for various movements. Other objectives are to minimize the invasive nature of the devices used to perform this estimation, and to improve the quality of the estimates deduced from the measurements of an inertial device.

• détermination d’une vitesse initiale et d’une vitesse finale du point de mesure respectivement au début et à la fin de l’intervalle de déplacement,
• estimation de l’évolution d’une vitesse du point de mesure durant l’intervalle de déplacement, ladite estimation comprenant :
  • l’intégration aval de paramètres de déplacement du point de mesure acquis par un dispositif inertiel durant l’intervalle de déplacement, en prenant comme valeur initiale de la vitesse la valeur de la vitesse initiale,
  • l’intégration amont des paramètres de déplacement, en prenant comme valeur initiale de la vitesse la valeur de la vitesse finale, et
  • le calcul de la vitesse estimée par fusion des intégrations amont et aval.

For this purpose, the invention relates, according to a first aspect, to a method for estimating the evolution of a linear speed of a measurement point during a movement interval, the method being implemented by a data processing unit and comprising the following steps:

• determination of an initial speed and a final speed of the measuring point respectively at the beginning and at the end of the movement interval,
• estimation of the evolution of a speed of the measurement point during the displacement interval, said estimation comprising:
  • downstream integration of displacement parameters of the measurement point acquired by an inertial device during the displacement interval, taking as the initial value of the speed the value of the initial speed,
  • the upstream integration of the displacement parameters, taking as the initial value of the speed the value of the final speed, and
  • the calculation of the estimated speed by merging the upstream and downstream integrations.

• estimation de l’évolution, durant l’intervalle de déplacement, d’une vitesse d’un point de mesure solidaire du point d’intérêt au moyen d’un procédé selon le premier aspect,
• estimation de l’évolution d’une orientation du point de mesure durant l’intervalle de déplacement, et
• estimation de la trajectoire du point d’intérêt durant l’intervalle de déplacement à partir de la vitesse et de l’orientation du point de mesure estimées,

The invention also relates, according to a second aspect, to a method for estimating a trajectory, over a movement interval, of a point of interest belonging to a limb of a person, the method being implemented by a data processing unit and comprising the following steps:

• estimation of the evolution, during the movement interval, of a speed of a measurement point integral with the point of interest by means of a method according to the first aspect,
• estimation of the evolution of an orientation of the measurement point during the displacement interval, and
• estimation of the trajectory of the point of interest during the movement interval from the estimated speed and orientation of the measurement point,

the point of interest preferably being chosen from a point on a forearm of the person and a point on a leg of the person.

• l’estimation de la trajectoire comprend les étapes suivantes :
  • calcul de plusieurs trajectoires candidates par application de la vitesse et de l’orientation estimées à différentes paires de configurations de départ et d’arrivée d’un modèle biomécanique du membre,
  • évaluation d’une compatibilité de chaque trajectoire candidate avec le modèle biomécanique, et
  • sélection de la trajectoire candidate présentant la meilleure compatibilité ;
• le point d’intérêt est un point d’un avant-bras appartenant à un membre supérieur de la personne, chaque configuration de départ du modèle biomécanique du membre étant définie par une paire d’angles de départ formée d’un premier angle de départ entre l’avant-bras et la verticale et d’un deuxième angle de départ entre le bras et la verticale et chaque configuration d’arrivée du modèle biomécanique du membre étant définie par une paire d’angles d’arrivée formée d’un premier angle d’arrivée entre l’avant-bras et la verticale et d’un deuxième angle d’arrivée entre le bras et la verticale ;
• pour chaque configuration de départ ou d’arrivée du modèle biomécanique du membre :
  • le premier angle de départ, respectivement d’arrivée, est déduit de l’orientation du point de mesure au début, respectivement à la fin, de l’intervalle de déplacement, et
  • le deuxième angle de départ, respectivement d’arrivée, est inférieur au premier angle de départ, respectivement d’arrivée ;
• il existe, pour chaque valeur de deuxième angle de départ inférieure au premier angle de départ et chaque valeur de deuxième angle d’arrivée comprise dans un intervalle prédéterminé, une paire de configurations de départ et d’arrivée pour laquelle une trajectoire candidate est calculée ;
• l’intervalle prédéterminé est constitué par un intervalle compris entre 0° et la valeur du premier angle d’arrivée, ou par un intervalle angulaire autour d’un angle β_tvérifiant la relation suivante :

According to particular embodiments of the invention, the trajectory estimation method also has one or more of the following characteristics, taken in isolation or in any technically possible combination(s):

• trajectory estimation includes the following steps:
  • calculation of multiple candidate trajectories by applying the estimated speed and orientation to different pairs of starting and finishing configurations of a biomechanical model of the limb,
  • assessment of the compatibility of each candidate trajectory with the biomechanical model, and
  • selection of the candidate trajectory presenting the best compatibility;
• the point of interest is a point on a forearm belonging to an upper limb of the person, each starting configuration of the biomechanical model of the limb being defined by a pair of starting angles formed by a first starting angle between the forearm and the vertical and a second starting angle between the arm and the vertical and each arrival configuration of the biomechanical model of the limb being defined by a pair of arrival angles formed by a first arrival angle between the forearm and the vertical and a second arrival angle between the arm and the vertical;
• for each starting or finishing configuration of the biomechanical model of the limb:
  • the first starting angle, respectively arrival angle, is deduced from the orientation of the measuring point at the beginning, respectively at the end, of the displacement interval, and
  • the second angle of departure, respectively of arrival, is less than the first angle of departure, respectively of arrival;
• there exists, for each second departure angle value less than the first departure angle and each second arrival angle value within a predetermined interval, a pair of departure and arrival configurations for which a candidate trajectory is calculated;
• the predetermined interval is constituted by an interval between 0° and the value of the first angle of arrival, or by an angular interval around an angle β _t verifying the following relation:

• L est la longueur du bras du membre supérieur,
• β_iest la valeur du deuxième angle de départ dans la configuration de départ appartenant à la même paire que la configuration d’arrivée,
• t_iest l’instant de début de l’intervalle de déplacement,
• t_fest l’instant de fin de l’intervalle de déplacement,
• est le vecteur vitesse du point de mesure à chaque instant t de l’intervalle de déplacement,
• l est la distance entre le coude du membre supérieur et le point de mesure,
• est un vecteur unitaire donnant l’orientation d’un axe principal de l’avant-bras à la fin de l’intervalle de déplacement,
• est un vecteur unitaire donnant l’orientation de l’axe principal de l’avant-bras au début de l’intervalle de déplacement,
• est un vecteur unitaire donnant l’orientation verticale,

in which:

• L is the length of the arm of the upper limb,
• β _i is the value of the second departure angle in the departure configuration belonging to the same pair as the arrival configuration,
• t _i is the start time of the displacement interval,
• t _f is the end time of the movement interval,
• is the velocity vector of the measuring point at each instant t of the displacement interval,
• l is the distance between the elbow of the upper limb and the measuring point,
• is a unit vector giving the orientation of a principal axis of the forearm at the end of the displacement interval,
• is a unit vector giving the orientation of the principal axis of the forearm at the start of the displacement interval,
• is a unit vector giving the vertical orientation,

• l’intervalle angulaire s’étend sur moins de 20°, de préférence sur moins de 15°, par exemple sur sensiblement 10° ; et
• le calcul de chaque trajectoire candidate comprend les étapes suivantes :
  • intégration aval de la vitesse estimée, en prenant comme position initiale la position du point de mesure dans la configuration de départ,
  • intégration amont de la vitesse estimée, en prenant comme position initiale la position du point de mesure dans la configuration d’arrivée, et
  • calcul de la trajectoire candidate par fusion des intégrations amont et aval ;

vectors , , And being expressed in the same inertial frame;

• the angular interval extends over less than 20°, preferably over less than 15°, for example over substantially 10°; and
• The calculation of each candidate trajectory includes the following steps:
  • downstream integration of the estimated speed, taking as initial position the position of the measuring point in the starting configuration,
  • upstream integration of the estimated speed, taking as initial position the position of the measurement point in the arrival configuration, and
  • calculation of the candidate trajectory by merging the upstream and downstream integrations;

• estimation d’une trajectoire d’un point d’intérêt appartenant au membre sur au moins un intervalle de déplacement primaire au moyen d’un procédé selon le deuxième aspect,
• évaluation, à partir de la trajectoire et de l’évolution de vitesse estimées, d’un effort primaire exercé par le membre durant le ou chaque intervalle de déplacement primaire.

The invention also relates, according to a third aspect, to a method for evaluating an effort exerted by a limb of a person, the method being implemented by a data processing unit and comprising the following steps:

• estimating a trajectory of a point of interest belonging to the member over at least one primary displacement interval by means of a method according to the second aspect,
• evaluation, from the estimated trajectory and speed evolution, of a primary effort exerted by the member during the or each primary movement interval.

• le procédé comprend les étapes supplémentaires suivantes :
  • déduction, à partir des paramètres de déplacement acquis durant l’intervalle de déplacement primaire, d’une composante rotationnelle d’une énergie cinétique primaire acquise par au moins une portion du membre durant l’intervalle de déplacement primaire, l’effort primaire étant fonction de ladite composante rotationnelle de l’énergie cinétique primaire,
  • détermination d’une relation entre l’effort primaire et la composante rotationnelle de l’énergie cinétique primaire,
  • estimation de l’évolution d’une orientation d’un point de mesure solidaire du point d’intérêt durant au moins un intervalle de déplacement secondaire,
  • déduction, à partir de paramètres de déplacement acquis par le dispositif inertiel durant un intervalle de déplacement secondaire, d’une composante rotationnelle d’une énergie cinétique secondaire acquise par ladite au moins une portion du membre durant l’intervalle de déplacement secondaire,
  • évaluation, à partir de la relation déterminée et de la composante rotationnelle de l’énergie cinétique secondaire, d’un effort secondaire exercé par le membre durant le ou chaque intervalle de déplacement secondaire ; et
• le procédé comprend, pour chacun des intervalles de déplacement primaire(s) et secondaire(s) :
  • l’estimation de l’évolution, durant l’intervalle de déplacement primaire ou secondaire, d’une vitesse d’un point de mesure solidaire du point d’intérêt au moyen d’un procédé selon le premier aspect,
  • le calcul de plusieurs trajectoires candidates par application de la vitesse et de l’orientation estimées à différentes paires de configurations de départ et d’arrivée d’un modèle biomécanique du membre,
  • l’évaluation d’une compatibilité de chaque trajectoire candidate avec le modèle biomécanique, et
  • la vérification, pour chaque intervalle de déplacement primaire ou secondaire, du caractère acceptable de la compatibilité d’au moins une trajectoire candidate,

According to particular embodiments of the invention, the effort evaluation method also has one or more of the following characteristics, taken in isolation or in any technically possible combination(s):

• The method includes the following additional steps:
  • deduction, from the displacement parameters acquired during the primary displacement interval, of a rotational component of a primary kinetic energy acquired by at least a portion of the member during the primary displacement interval, the primary force being a function of said rotational component of the primary kinetic energy,
  • determination of a relationship between the primary effort and the rotational component of the primary kinetic energy,
  • estimation of the evolution of an orientation of a measurement point attached to the point of interest during at least one secondary displacement interval,
  • deduction, from displacement parameters acquired by the inertial device during a secondary displacement interval, of a rotational component of a secondary kinetic energy acquired by said at least one portion of the member during the secondary displacement interval,
  • evaluation, from the determined relationship and the rotational component of the secondary kinetic energy, of a secondary effort exerted by the member during the or each secondary displacement interval; and
• the method comprises, for each of the primary and secondary displacement intervals:
  • estimating the evolution, during the primary or secondary displacement interval, of a speed of a measurement point integral with the point of interest by means of a method according to the first aspect,
  • the calculation of several candidate trajectories by applying the estimated speed and orientation to different pairs of starting and finishing configurations of a biomechanical model of the limb,
  • the evaluation of the compatibility of each candidate trajectory with the biomechanical model, and
  • the verification, for each primary or secondary displacement interval, of the acceptable nature of the compatibility of at least one candidate trajectory,

the trajectory of the point of interest being estimated only when at least one candidate trajectory has acceptable compatibility.

• a) estimation, pour plusieurs intervalles de déplacement d’un point d’intérêt du membre survenus au cours d’une période prédéterminée, d’un effort exercé par ledit membre au moyen d’un procédé selon le troisième aspect,
• b) détermination de la valeur d’au moins une grandeur statistique, calculée sur l’ensemble formé par les efforts estimés, représentative d’un état de forme de la personne.

The invention also relates, according to a fourth aspect, to a method for analyzing an effort exerted by a limb of a person, the method being implemented by a data processing unit and comprising the following steps:

• (a) estimating, for several intervals of displacement of a point of interest of the member occurring during a predetermined period, a force exerted by said member by means of a method according to the third aspect,
• b) determination of the value of at least one statistical quantity, calculated on the set formed by the estimated efforts, representative of a state of fitness of the person.

• le procédé comprend la répétition des étapes a) et b) pour plusieurs périodes prédéterminées et l’observation de l’évolution de la ou chaque grandeur statistique à travers les différentes périodes prédéterminées.

According to a particular embodiment of the invention, the effort analysis method also has the following characteristic:

• the method comprises repeating steps a) and b) for several predetermined periods and observing the evolution of the or each statistical quantity across the different predetermined periods.

The invention also relates, according to a fifth aspect, to a method for monitoring the fitness level of a person, comprising the analysis of an effort exerted by a limb of the person by means of an analysis method according to the fourth aspect and the deduction of a fitness level of the person from said analysis.

• le procédé comprend l’administration d’un traitement à la personne, et l’évaluation d’une efficacité du traitement à partir de l’état de forme déduit.

According to a particular embodiment of the invention, the tracking method also has the following characteristic:

• the method comprises administering a treatment to the person, and evaluating an effectiveness of the treatment from the deduced fitness state.

• un équipement comprenant un dispositif inertiel pour l’acquisition de paramètres de déplacement d’un point de mesure durant au moins un intervalle de déplacement, et une unité de traitement de données configurée pour estimer, à partir des paramètres de déplacement acquis par le dispositif inertiel, par la mise en œuvre d’un procédé selon l’un quelconque des premier, deuxième et troisième aspects, au moins l’un de : l’évolution d’une vitesse du point de mesure durant l’intervalle de déplacement, une trajectoire, sur l’intervalle de déplacement, d’un point d’intérêt solidaire du point de mesure, et un effort exercé par un membre d’une personne auquel appartient le point d’intérêt ;
• un produit programme d’ordinateur comprenant des instructions de code pour la mise en œuvre d’un procédé selon l’un quelconque des premier, deuxième, troisième, quatrième et cinquième aspects lorsque ledit programme est exécuté par un ordinateur ; et
• un moyen de stockage lisible par un équipement informatique sur lequel est stocké un produit programme d’ordinateur comprenant des instructions de code pour la mise en œuvre d’un procédé selon l’un quelconque des premier, deuxième et troisième aspects lorsque ledit programme est exécuté par un ordinateur.

The invention finally has as its object, according to respectively a fifth, a sixth and a seventh aspects of the invention:

• equipment comprising an inertial device for acquiring movement parameters of a measurement point during at least one movement interval, and a data processing unit configured to estimate, from the movement parameters acquired by the inertial device, by implementing a method according to any one of the first, second and third aspects, at least one of: the evolution of a speed of the measurement point during the movement interval, a trajectory, over the movement interval, of a point of interest integral with the measurement point, and a force exerted by a limb of a person to which the point of interest belongs;
• a computer program product comprising code instructions for implementing a method according to any of the first, second, third, fourth and fifth aspects when said program is executed by a computer; and
• a storage medium readable by computer equipment on which is stored a computer program product comprising code instructions for implementing a method according to any one of the first, second and third aspects when said program is executed by a computer.

Brief description of the Figures

• la est un schéma d’un équipement selon un exemple de réalisation de l’invention,
• la est un schéma d’un dispositif de mesure de l’équipement de la ,
• la est un schéma d’un capteur de mouvement de l’équipement de la ,
• la est un diagramme illustrant un procédé d’analyse d’effort mis en œuvre par l’équipement de la ,
• la est un diagramme détaillant une étape du procédé de la ,
• la est un diagramme détaillant une première sous-étape de l’étape de la ,
• la est un diagramme détaillant une deuxième sous-étape de l’étape de la ,
• la est un diagramme détaillant une troisième sous-étape de l’étape de la ,
• la est un schéma d’un modèle biomécanique d’un membre supérieur utilisé pour la mise en œuvre du procédé de la , et
• la est un schéma présentant une paire de configurations de départ et d’arrivée du modèle biomécanique de la .

Other characteristics and advantages of the invention will appear on reading the description which follows, given solely by way of example and made with reference to the appended drawings, in which:

• there is a diagram of equipment according to an exemplary embodiment of the invention,
• there is a diagram of a measuring device of the equipment of the ,
• there is a schematic of a motion sensor of the equipment of the ,
• there is a diagram illustrating a stress analysis process implemented by the equipment of the ,
• there is a diagram detailing a step in the process of the ,
• there is a diagram detailing a first sub-step of the step of the ,
• there is a diagram detailing a second sub-step of the step of the ,
• there is a diagram detailing a third sub-step of the step of the ,
• there is a diagram of a biomechanical model of an upper limb used for the implementation of the method of the , And
• there is a diagram showing a pair of starting and ending configurations of the biomechanical model of the .

Detailed description of an example of realization

Equipment 10 shown in the is intended for the evaluation and analysis of the efforts exerted by the muscles of an upper limb 12 of a person 14. For this purpose, the equipment 10 comprises a measuring device 20 attached to a forearm 22 of the upper limb 12. In the example shown, it also comprises a motion sensor 24 intended to capture the movement of at least one lower limb of the person 14.

It is recalled here that, anatomically, an upper limb such as the upper limb 12 is made up of three segments: the arm 25, articulated to the trunk 26 by the shoulder 27, the forearm 22, articulated to the arm 25 by the elbow 28, and the hand 29, articulated to the forearm 22 by the wrist 30. Here and hereinafter, it is in this sense that these terms are used, the term “arm” being in particular used to designate only the segment of the upper limb between the elbow and the shoulder and not, as in common language, the entire upper limb.

The measuring device 20 is secured to the forearm 22 of the upper limb 12, that is to say that it presents, in the terrestrial frame of reference, a movement substantially identical to that of the forearm 12. It is in particular placed between the elbow 28 (excluded) and the wrist 30 (included), for example, as shown, substantially on the wrist 30.

In reference to the , the measuring device 20 comprises a support 31 and an attachment member 32 for attaching the support 31 to the forearm 22. It also comprises an inertial device 33 and a data processing unit 34 mounted on the support 31. In the example shown, it further comprises a communication system 36, typically a wireless communication system, mounted on the support 31 for communication of the measuring device 20 with the second measuring device 24 and/or an external device such as a mobile terminal (not shown), for example a multifunction mobile, or a remote server (not shown). Optionally, it further comprises a storage module 38 mounted on the support 31.

The support 31 is typically constituted by a housing.

The attachment member 32 is here constituted by a bracelet, for example with self-gripping strip, adapted to encircle the forearm 22 and allow the integral connection. Alternatively (not shown), the attachment member 32 is constituted by any element allowing an integral connection with the forearm 22.

The inertial device 33 comprises a gyrometer 40 for measuring an angular speed of the measuring device 20 according to a system of three orthogonal axes defining a moving frame (R _m ) integral with the measuring device 20, i.e. measuring the three components of an angular speed vector in said moving frame (R _m ). It is thus understood that the gyrometer 40 is typically made up of a set of three gyrometers each associated with one of the three axes, in particular in tri-axis (i.e. each capable of measuring one of the three components of the angular speed vector).

• un axe U colinéaire à l’avant-bras 22 et orienté vers la main 29,
• un axe V orthogonal à l’axe à l’axe U, et
• un axe W orthogonal aux axes U et V.

Preferably, the mobile reference frame (R _m ) is chosen so that one of its axes is colinear with the forearm 22 when the measuring device 20 is worn. Here and in the following, the mobile reference frame (R _m ) is defined as being a direct orthogonal reference frame formed by a triplet of axes, shown in the , including:

• a U axis collinear with the forearm 22 and oriented towards the hand 29,
• a V axis orthogonal to the U axis, and
• a W axis orthogonal to the U and V axes.

The inertial device 33 also comprises an accelerometer 42 for measuring an acceleration of the measuring device 20 according to a system of three orthogonal axes defining a mobile reference frame integral with the measuring device 20, which is advantageously the same as the mobile reference frame (R _m ) of the gyrometer 40. In other words, the accelerometer is capable of measuring the three components of an acceleration vector in said mobile reference frame. It is thus understood that the accelerometer 42 is typically made up of a set of three accelerometers each associated with one of the three axes, in particular in tri-axis (i.e. each capable of measuring one of the three components of the acceleration vector). These accelerometers are sensitive to external forces, including gravitational forces, applied to the inertial device 33, and make it possible to measure a specific acceleration.

The data processing unit 34 is configured to deduce from the measurements of the inertial device 33 an orientation, a linear speed and a position of a measurement point integral with the measurement device 20, for example constituted by the origin of the mobile reference frame (R _m ) of the gyrometer 40 and the accelerometer 42. It is also configured to estimate a linear speed and a position of the center of gravity of the forearm 22. It is further configured to evaluate and analyze the efforts of the muscles of the upper limb 12.

For this purpose, the data processing unit 34 is, in the example shown, constituted by a programmable machine, such as a DSP (“ Digital Signal Processor ” in English) or a microcontroller. It comprises a processor or CPU (“ Central Processing Unit ” in English) 44 and a memory 46 of the RAM (“ Random Access Memory ” in English) and/or ROM (“ Read Only Memory ” in English) type. The processor 44 is configured to execute instructions loaded into the memory 46. When the measuring device 20 is powered up, the processor 44 is capable of reading instructions from the memory 46 and executing them. These instructions form a computer program causing the implementation, by the processor 44, of certain steps of a method 1000 ( ) which will be detailed below.

Alternatively (not shown), the data processing unit 34 is constituted by a machine or a dedicated component, such as an FPGA (“ Field-Programmable Gate Array ”) or an ASIC (“ Application-Specific Integrated Circuit ”).

The data processing unit 34 further comprises a buffer memory 48 for the temporary storage of information necessary for the implementation of the method 1000.

The communication system 36 is configured to implement short-range wireless communication, for example Bluetooth or Wi-Fi (in particular in the example shown with the motion sensor 24) and/or to connect to a mobile network (typically UMTS/LTE/5G) for long-distance communication. Alternatively (not shown), the communication system 36 is, for example, a wired connection (typically USB) to transfer data from the storage module 38 to another storage module, typically a server (not shown).

For example, the communication system 36 is configured to receive from the motion sensor 24 movement data of at least one lower limb of the person 14 and/or to transmit the analysis data to an external device for presentation to a human operator, typically for display on a screen.

Optionally, the measuring device 20 also comprises a network of magnetometers (not shown) linked to the support 31, that is to say that they each have a movement substantially identical to that of the support 31 in the terrestrial frame of reference, and spatially spaced from each other. Each magnetometer is a three-axis magnetometer capable of measuring a magnetic field along three axes. For this purpose, each magnetometer is typically constituted by three single-axis magnetometers (not shown) oriented along axes substantially perpendicular to each other. These axes are preferably the same as those of the system of three orthogonal axes of the gyrometer 40 and/or the accelerometer 42.

The network of magnetometers is suitable, due to its particular geometry, for allowing the determination, at each measurement time of the magnetometers, of a spatial gradient of the measured magnetic field, in particular of the coefficients of this gradient along each of the axes U, V, W of the moving frame (R _m ) linked to the support 31. Each coefficient of said gradient is for example determined by a method using the vector measurements of the magnetic field carried out by the magnetometers, associated with optimization methods of the least square or median filter type or associated with the intrinsic properties of the magnetic field described by Maxwell's equations. However, any other conventional method adapted to calculate the coefficients of the spatial gradient of the magnetic field is suitable.

The data processing unit 34 is then typically configured to determine the linear speed of the measuring point, over certain displacement phases, by implementing the method described in EP 2 541 199.

In the example described above, the processing unit 34 of the measuring device 20 is mounted on the support 31. Alternatively (not shown), at least part of the data processing unit 34 is remote, for example in a mobile terminal (not shown) and/or in a remote server (not shown). In other words, at least part of the steps of the method 1000 is performed by a mobile terminal and/or a remote server. The communication system 36 is then configured to send to the mobile terminal and/or the remote server the data from the inertial device 33 and, where appropriate, from the magnetometer network of the first measuring device 20.

Back to the , the motion sensor 24 is here secured to a lower limb 50 of the person 14.

It is recalled here that, anatomically, a lower limb such as the lower limb 50 is made up of three segments: the thigh 51, articulated to the trunk 26 by the hip 52, the leg 53, articulated to the thigh 51 by the knee 54, and the foot 55, articulated to the leg 53 by the ankle 56. Here and hereinafter, it is in this sense that these terms are used, the term “leg” being in particular used to designate only the segment of the upper limb between the knee and the ankle and not, as in common language, the entire lower limb.

The motion sensor 24 is in particular secured to the leg 53 of the lower limb 50, that is to say that it presents, in the terrestrial frame of reference, a movement substantially identical to that of the leg 53. It is in particular placed between the knee 54 (excluded) and the ankle 56 (included), for example, as shown, substantially on the ankle 56.

Alternatively, the motion sensor 24 is attached to a wheelchair 58 in which the person 14 is seated.

In reference to the , the motion sensor 24 here comprises a support 61 and an attachment member 62 for attaching the support 61 to the leg 53. It also comprises a gyrometer 63 and a data processing unit 64 mounted on the support 61. In the example shown, it further comprises a communication system 66, typically a wireless communication system, mounted on the support 61 for communication of the motion sensor 24 with the measuring device 20 and/or an external device such as a mobile terminal (not shown), for example a multifunction mobile, or a remote server (not shown). Optionally, it further comprises a storage module 68 mounted on the support 61.

The support 61 is typically constituted by a housing.

The attachment member 62 is here constituted by a bracelet, for example with self-gripping strip, adapted to enclose the leg 53 and allow the integral connection. Alternatively (not shown), the attachment member 62 is constituted by any element allowing an integral connection with the leg 53.

The gyrometer 63 is capable of measuring an angular speed of the motion sensor 24 according to a system of three orthogonal axes defining a mobile reference frame integral with the motion sensor 24, i.e. measuring the three components of an angular speed vector in said mobile reference frame. It is thus understood that the gyrometer 63 is typically made up of a set of three gyrometers each associated with one of the three axes, in particular in tri-axis (i.e. each capable of measuring one of the three components of the angular speed vector).

The data processing unit 64 is configured to deduce from the measurements of the gyrometer 63 the movement phases and the immobility phases of the motion sensor 24. For this purpose, the data processing unit 64 is typically configured to compare the norm of the angular speed measured by the gyrometer 63 with a threshold, and to define the phases during which this norm is lower than the threshold as being immobility phases and the phases during which this norm is lower than the threshold as being movement phases.

The data processing unit 64 is, in the example shown, constituted by a programmable machine, such as a DSP ( Digital Signal Processor ) or a microcontroller. It comprises a processor or CPU ( Central Processing Unit ) 74 and a memory 76 of the RAM ( Random Access Memory ) and/or ROM ( Read Only Memory ) type. The processor 74 is configured to execute instructions loaded into the memory 76. When the motion sensor 24 is powered up, the processor 74 is capable of reading instructions from the memory 76 and executing them. These instructions form a computer program causing the processor 74 to implement a method for detecting a movement of the motion sensor 24.

Alternatively (not shown), the data processing unit 64 is constituted by a machine or a dedicated component, such as an FPGA (“ Field-Programmable Gate Array ”) or an ASIC (“ Application-Specific Integrated Circuit ”).

The data processing unit 64 further comprises a buffer memory 78 for the temporary storage of information necessary for detecting the movement of the motion sensor 24.

The communication system 66 is configured to implement short-range wireless communication, for example Bluetooth or Wi-Fi (in particular in the example shown with the measuring device 20) and/or to connect to a mobile network (typically UMTS/LTE/5G) for long-distance communication. Alternatively (not shown), the communication system 66 is, for example, a wired connection (typically USB) to transfer data from the storage module 68 to another storage module, typically a server (not shown).

For example, the communication system 66 is configured to transmit the start and end times of the immobility phases to the measuring device 20 and/or to an external device, typically a mobile telephone or a server.

A method 1000 implemented by the equipment 10 will now be described, with reference to Figures 4 to 8.

As visible in Figure 4, the method 1000 begins with a step 1002 of acquiring displacement parameters of the measurement point. During this step, the inertial device 33 acquires the acceleration (t _k ) and the rotation speed (t _k ) of the measurement point at each of a plurality of sampling times t _k . Note that the acceleration (t _k ) and the rotation speed (t _k ) are here vectors each having three components along each of the axes U, V, W of the moving frame (R _m ) attached to the support 31 of the measuring device 20. The sampling times t _k are spaced from each other by a time dt which is very small compared to the characteristic time of the movements of the person 14, this time dt being for example substantially equal to 10 ms.

Step 1002 follows a start-up of the measuring device 20 and typically lasts until a shutdown of the measuring device 20.

The method 1000 further comprises, following step 1002 or, more precisely, following the acquisition of acceleration vectors (t _k ) and rotation speed (t _k ) for enough sampling instants t _k , a step 1004 of determining an orientation of the measuring point relative to the forearm 22. This step makes it possible to know the orientation of the mobile reference mark (R _m ) attached to the support 31 of the measuring device 20 relative to the forearm 22. Indeed, if the orientation of said mobile reference mark (R _m ) relative to the support 31 is known, two positions of the support 31 relative to the forearm 22 are possible, depending on the direction in which the attachment member 32 is mounted on the forearm 22: a position in which the axis U of the mobile reference mark (R _m ) colinear with the forearm 22 points towards the hand 29 and a position in which said axis points towards the elbow 28.

For example, step 1004 comprises the detection, by the processing unit 34, of immobility phases of the measuring device 20, followed by the measurement of the acceleration during said immobility phases. The detection of the immobility phases is typically carried out by comparison of the rotation speed standard (t _k ) with a threshold, a phase of immobility being detected when, for several successive sampling instants t _k , the norm of the rotation speed (t _k ) is less than said threshold. The measurement of the acceleration during these phases of immobility gives the orientation of the gravitational acceleration in the moving frame (R _m ), from which the processing unit 34 deduces the orientation of the measurement point relative to the forearm 22.

If it follows from this deduction that the U axis points towards hand 29, then the moving frame (R _m ) is maintained. If, on the contrary, the U axis points towards elbow 28, then the moving frame (R _m ) is reoriented (it is typically rotated 180° around its V axis or its W axis) so that the U axis points towards hand 29.

In parallel with steps 1002 and 1004, the method 1000 also comprises a step 1006 of detecting phases of immobility of the lower limbs of the person 14, followed by a step 1008 of transmitting the start and end times of these phases of immobility to the measuring device 20.

In step 1006, the processing unit 64 of the motion sensor 24 typically compares the rotation speed standard measured by the gyrometer 63 with a threshold, and determines the immobility phases as being the periods during which said standard is lower than the threshold.

Then, during step 1008, the motion sensor 24 transmits to the measuring device 20, via the communication systems 66, 36, the start and end times of the immobility phases thus detected.

Steps 1004 and 1008 are followed by a step 1100 of selecting periods of interest of the acquired parameters. During this step 1100, the processing unit 34 of the measuring device 20 identifies the periods between the start and end times of the immobility phases of the lower limbs as forming periods of interest of the acquired parameters and selects these periods. The accelerations (t _k ) and rotation speeds (t _k ) acquired outside of these periods are then discarded.

Then, for each period of interest, the method 1000 comprises a step 1200 of determining a linear speed of the measurement point at various times of the period of interest. During this step 1200, the processing unit 34 determines the linear speed of the measurement point during certain phases.

Said phases are for example phases of immobility of the measuring device 20 that the processing unit 34 detects and for which it determines a zero linear speed of the measuring point during these phases. These immobility phases are typically detected by comparison of the rotation speed standard (t _k ) with a threshold, a phase of immobility being detected when, for several successive sampling instants t _k , the norm of the rotation speed (t _k ) is lower than said threshold.

Preferably, said phases also include phases of immobility of the elbow 28, which the processing unit 34 detects when the movement of the measuring point is a pure rotation of radius equal to the distance between the measuring point and the elbow 28. The linear speed of the measuring point is then easily determined, in a manner known to those skilled in the art.

Advantageously, said phases also include phases during which the linear speed of the measurement point is determined by means of data other than that provided by the inertial device 33. These other data consist, for example, of magnetic field gradient measurement data provided by the magnetometer network. The phases during which the linear speed of the measurement point is determined then include phases of stationarity of the ambient magnetic field, the processing unit 34 then implementing the method described in WO 2019/016474 to determine the linear speed of the measurement point during these phases.

The phases during which the linear speed of the measurement point is determined are spaced from each other by time intervals during which the linear speed of the measurement point is not a priori known. The method 1000 comprises, for each of these intervals, a step 1300 of estimating an effort exerted by the muscles of the upper limb during this interval.

This step 1300 is implemented by the processing unit 34.

• un axe Z confondu avec la verticale,
• un axe X horizontal, et
• un axe Y horizontal formant avec les axes X et Z un repère orthogonal X, Y, Z direct.

With reference to Figure 5, step 1300 comprises a first sub-step 1310 of estimating the evolution of an orientation of the measurement point during the interval. By “orientation of the measurement point”, here and hereinafter is meant an orientation of the mobile reference frame (R _m ) in a terrestrial inertial reference frame (R _i ) having an axis coincident with the vertical, such that the angular velocity (t _k ) is equal to the rotation speed of the moving frame (R _m ) relative to said inertial frame (R _i ). Here and in the following, we define the inertial frame (R _i ) as being a direct orthogonal frame formed by a triplet of axes, represented on the , including:

• a Z axis coincident with the vertical,
• a horizontal X axis, and
• a horizontal Y axis forming with the X and Z axes a direct orthogonal X, Y, Z reference frame.

The orientation of the measurement point can be given by a rotation matrix (denoted R), an orientation quaternion (denoted Q), or Euler angles (roll φ, pitch θ, yaw ψ). These three notations being equivalent, they are used interchangeably in this document.

We know in particular that the formula giving the transition matrix from the inertial frame (R _i ) to the mobile frame (R _m ) from the Euler angles is written:

In reference to the , sub-step 1310 comprises a first sub-step 1312 of determining an initial orientation of the measurement point at an initial instant t _i of the start of the interval.

In this sub-step 1312, the processing unit 34 first determines a starting orientation of the measuring point at a starting time t ₀ at which the forearm 22 and therefore the measuring device 20 is considered to be stationary. This determination is typically carried out from the acceleration measurements, the measured acceleration (t ₀ ) being equal to the opposite of the gravitational field: (t ₀ ) = - . The rotation matrix at the starting time t ₀ is then such that it solves the following equation:

• est le vecteur unitaire vertical du repère inertiel (R_i),
• est l’accélération mesurée par l’accéléromètre 42 à l’instant de départ t₀, exprimée dans le repère mobile (R_m), et
• est la norme de l’accélération mesurée à l’instant t₀.

in which:

• is the vertical unit vector of the inertial frame (R _i ),
• is the acceleration measured by the accelerometer 42 at the starting time t ₀ , expressed in the moving frame (R _m ), and
• is the norm of the measured acceleration at time t ₀ .

Note that this equation is not fully deterministic and leaves degrees of freedom on some components of the rotation matrix R(t ₀ ). This is because the yaw angle ψ(t ₀ ) at the starting time t ₀ is of little importance for the rest of the calculations and the X axis can therefore be set arbitrarily. For example, the X axis is chosen so that the yaw angle ψ(t ₀ ) at the starting time t ₀ is zero, i.e. so that the rotation matrix at the starting time t ₀ solves the following additional equation:

• est le vecteur unitaire du repère inertiel (R_i) correspondant à l’axe Y,
• est le vecteur unitaire du repère mobile (R_m) correspondant à l’axe U,
• est l’accélération mesurée par l’accéléromètre 42 à l’instant de départ t₀, exprimée dans le repère mobile (R_m),
• est la norme de l’accélération mesurée à l’instant t₀, et
• ∧ est l’opérateur produit vectoriel.

in which:

• is the unit vector of the inertial frame (R _i ) corresponding to the Y axis,
• is the unit vector of the moving frame (R _m ) corresponding to the U axis,
• is the acceleration measured by the accelerometer 42 at the starting time t ₀ , expressed in the moving frame (R _m ),
• is the norm of the measured acceleration at time t ₀ , and
• ∧ is the vector product operator.

Preferably, the starting time t ₀ is equal to the initial time t _i ; the initial orientation is then equal to the starting orientation. Alternatively, the starting time t ₀ is prior to the initial time t _i , the initial orientation then being deduced from the starting orientation by downstream integration of the measurements provided by the gyrometer 40. By “downstream integration” is meant here and hereinafter that the integration is carried out in positive time, with an initial value chosen in the past.

Substep 1312 is followed by a substep 1313 of downstream integration of the measured orientation on the basis of the initial orientation.

During this sub-step 1313, the processing unit 34 produces a first estimate R _f of the orientation of the measurement point at each sampling instant t _k of the interval by integrating the rotation speed measurements prior to the instant t _k , taking as initial value the initial orientation at the instant t _i .

Preferably, this determination comprises the implementation of a linear state estimator filter (Luenberger filter, Kalman filter, etc.) or non-linear (extended Kalman filter, invariant observer, etc.). In the present description, the implementation of an extended Kalman filter is described, but those skilled in the art will be able to transpose to other filters.

The implementation of said extended Kalman filter firstly comprises a prediction step, during which the processing unit 34 uses the following formula:

where t _k-1 is the sampling time immediately preceding sampling time t _k , and is the time derivative of the rotation matrix of the moving frame (R _m ) in the inertial frame (R _i ), given by the following differential equation:

Noting matrix estimation after n sample steps, the estimation of the matrix for each measure East :

The equation is given here for a rotation matrix but an equivalent differential equation exists between attitude quaternion and angular velocity.

In parallel, the processing unit 34 modifies, by linearization of the differential equation, a covariance matrix estimating the covariance between each state of the filter.

The prediction step is followed by an update step.

This update step uses the fact that acceleration measured by accelerometer 42 is equal to the sum of the gravity field and acceleration linked to the movements of the measuring device 20:

We also know that acceleration is on average zero (we understand that the upper limb 12 regularly returns to its starting position and that the movements in one direction or the other statistically compensate for each other). We deduce that the measured acceleration expressed in the terrestrial inertial frame (R _i ) is equal on average to .

From the rotation matrix and measurements of the accelerometer in the moving frame (R _m ), we can express the measured acceleration in the inertial frame (R _i ):

The difference between the estimated gravity field and the actual Earth gravity field is then written as:

This difference, which must be zero on average, is used for orientation recalibration during the update step.

Furthermore, by linearizing this formula, we can calculate the Kalman gain and consequently update the state and the covariance matrix. The update of the covariance matrix is based on the assumption that the errors due to the sensors and the approximations are modeled as Gaussian distribution noise. The variance is estimated by measuring the noise of the sensors at rest and from assumptions on the movements made by the forearm 22.

We thus obtain a first estimate of the orientation of the measurement point at each sampling instant t _k of the interval.

Substep 1313 is followed by a substep 1314 of determining a final orientation of the measurement point at a final time t _f at the end of the interval.

In this sub-step 1314, the processing unit 34 first determines a reference orientation of the measurement point at a reference time t _r at which the forearm 22 and therefore the measuring device 20 is considered immobile. This determination is typically carried out from the acceleration measurements, the measured acceleration γ(t _r ) being equal to the opposite of the gravitational field: (t _r ) = - . The rotation matrix at the reference time t _r is then such that it solves the following equation:

• est le vecteur unitaire vertical du repère inertiel (R_i),
• est l’accélération mesurée par l’accéléromètre 42 à l’instant de référence t_r, exprimée dans le repère mobile (R_m), et
• est la norme de l’accélération mesurée à l’instant t_r.

in which:

• is the vertical unit vector of the inertial frame (R _i ),
• is the acceleration measured by the accelerometer 42 at the reference instant t _r , expressed in the moving frame (R _m ), and
• is the norm of the measured acceleration at time t _r .

This equation allows us to obtain the roll and pitch at the reference instant t _r , which are given by the following formulas:

in which is the component of the measured acceleration along the U axis, is the component of the measured acceleration along the V axis and is the component of the measured acceleration along the W axis.

The yaw angle ψ(t _r ) is set so as to be equal to the yaw angle obtained by downstream integration of the rotation speed measurements from the starting time t ₀ to the reference time t _r .

Preferably, the reference time t_ris equal to the final time t_f ; the final orientation is then equal to the reference orientation. Alternatively, the reference time t_ris after the final time t_f, the final orientation then being deduced from the reference orientation by backward integration of the measurements provided by the gyrometer 40. By “backward integration” we mean here and hereinafter that the integration is carried out in negative time, with an initial value chosen in the future.

Substep 1314 is followed by a substep 1315 of upstream integration of the measured orientation on the basis of the final orientation.

During this sub-step 1315, the processing unit 34 produces a second estimate R _b of the orientation of the measurement point at each sampling instant t _k of the interval by integrating the rotation speed measurements subsequent to the instant t _k , taking as initial value the final orientation at the instant t _f .

Preferably, this determination comprises the implementation of a linear state estimator filter (Luenberger filter, Kalman filter, etc.) or non-linear (extended Kalman filter, invariant observer, etc.). In the present description, the implementation of an extended Kalman filter is described, but those skilled in the art will be able to transpose to other filters.

• la formule utilisée dans l’étape de prédiction est la suivante :

This implementation is substantially identical to that of the downstream integration step 1313 described above, with the following differences:

• the formula used in the prediction step is:

• l’équation différentielle donnant la matrice de rotation instantanée du repère mobile (R_m) dans le repère inertiel (R_i) est exprimée de la manière suivante :

where t _k+1 is the sampling time immediately following sampling time t _k , and

• the differential equation giving the matrix instantaneous rotation of the moving frame (R _m ) in the inertial frame (R _i ) is expressed as follows:

In essence, these differences can be summarized as follows: while forward integration uses prior estimates for the prediction step of the extended Kalman filter, backward integration uses posterior estimates.

We thus obtain a second estimate of the orientation of the measurement point at each sampling instant t _k of the interval.

Sub-step 1310 concludes with a sub-step 1316 of merging the upstream and downstream integrations, during which a final estimate of the orientation of the measurement point at each sampling instant t _k of the interval is calculated by linear-spherical interpolation of the first and second estimates:

• est la première estimation de l’orientation obtenue lors de la sous-étape 1313 par intégration aval,
• est la deuxième estimation de l’orientation obtenue lors de la sous-étape 1315 par intégration amont, et
• est donné par la formule suivante :

Or :

• is the first estimate of the orientation obtained during sub-step 1313 by downstream integration,
• is the second estimate of the orientation obtained during sub-step 1315 by backward integration, and
• is given by the following formula:

Back to the , step 1300 comprises, in parallel with step 1310, a step 1320 of estimating a linear speed of the measurement point during the interval.

In reference to the , this sub-step 1320 comprises a first sub-step 1322 of downstream integration of the displacement parameters on the basis of the linear speed at the start of the interval.

During this sub-step 1322, the processing unit 34 produces a first estimate V _f of the linear speed of the measurement point at each sampling instant t _k of the interval by integrating the acceleration and rotation speed measurements prior to the instant t _k , taking as an initial value an initial speed at the instant t _i . This initial speed is equal to the linear speed of the measurement point at the end of a phase for which the linear speed was determined during the step 1200 and which immediately precedes the interval.

The first estimate of the linear velocity of the measurement point is estimated iteratively at each sampling time t _k , starting from the oldest, using the following formula:

in which is the first estimate of the linear velocity at sampling time t _k , is the first estimate of the linear velocity at a sampling time t _k-1 immediately preceding the sampling time t _k (and therefore estimated at the previous iteration), and is the acceleration at the sampling time t _k , given by the following formula:

• est l’accélération mesurée par l’accéléromètre 42 à l’instant t_k, exprimée dans le repère mobile (R_m),
• est la matrice de rotation donnant l’orientation du point de mesure dans le repère inertiel, ladite matrice de rotation étant soit égale à la première estimation R_b(t_k) de l’orientation à l’instant d’échantillonnage t_kestimée lors de la sous-étape 1313, soit égale à l’estimation finale R(t_k) de l’orientation à l’instant d’échantillonnage t_kestimée lors de la sous-étape 1316,
• est le champ gravitationnel exprimé dans le repère inertiel (R_i),
• est la vitesse de rotation mesurée par le gyromètre 40 à l’instant t_k-1, exprimée dans le repère mobile (R_m), et
• est l’opérateur produit vectoriel.

Or :

• is the acceleration measured by the accelerometer 42 at time t _k , expressed in the moving frame (R _m ),
• is the rotation matrix giving the orientation of the measurement point in the inertial frame, said rotation matrix being either equal to the first estimate R _b (t _k ) of the orientation at the sampling time t _k estimated during sub-step 1313, or equal to the final estimate R(t _k ) of the orientation at the sampling time t _k estimated during sub-step 1316,
• is the gravitational field expressed in the inertial frame (R _i ),
• is the rotation speed measured by the gyrometer 40 at time t _k-1 , expressed in the moving frame (R _m ), and
• is the vector product operator.

This gives a first estimate of the linear speed of the measuring point during the interval.

Substep 1322 is followed by a substep 1324 of backward integration of the displacement parameters based on the linear speed at the end of the interval.

During this sub-step 1324, the processing unit 34 produces a second estimate V _b of the linear speed of the measurement point at each sampling time t _k of the interval by integrating the acceleration and rotation speed measurements subsequent to the time t _k , taking as an initial value a final speed at the time t _f . This final speed is equal to the linear speed of the measurement point at the start of a phase for which the linear speed was determined during the step 1200 and which immediately follows the interval.

The second estimate of the linear velocity of the measurement point is estimated iteratively at each sampling time t _k , starting from the most recent, using the following formula:

in which is the second estimate of the linear velocity at sampling time t _k , is the second estimate of the linear velocity at a sampling time t _k+1 immediately following the sampling time t _k (and therefore estimated at the previous iteration), and is the acceleration at the sampling time t _k , given by the following formula:

• est l’accélération mesurée par l’accéléromètre 42 à l’instant t_k, exprimée dans le repère mobile (R_m),
• est la matrice de rotation donnant l’orientation du point de mesure dans le repère inertiel, ladite matrice de rotation étant soit égale à la deuxième estimation R_b(t_k) de l’orientation à l’instant d’échantillonnage t_kestimée lors de la sous-étape 1315, soit égale à l’estimation finale R(t_k) de l’orientation à l’instant d’échantillonnage t_kestimée lors de la sous-étape 1316,
• est le champ gravitationnel exprimé dans le repère inertiel (R_i), et
• est la vitesse de rotation mesurée par le gyromètre 40 à l’instant t_k+1, exprimée dans le repère mobile (R_m), et
• est l’opérateur produit vectoriel.

Or :

• is the acceleration measured by the accelerometer 42 at time t _k , expressed in the moving frame (R _m ),
• is the rotation matrix giving the orientation of the measurement point in the inertial frame, said rotation matrix being either equal to the second estimate R _b (t _k ) of the orientation at the sampling time t _k estimated during sub-step 1315, or equal to the final estimate R(t _k ) of the orientation at the sampling time t _k estimated during sub-step 1316,
• is the gravitational field expressed in the inertial frame (R _i ), and
• is the rotation speed measured by the gyrometer 40 at time t _k+1 , expressed in the moving frame (R _m ), and
• is the vector product operator.

This gives a second estimate of the linear speed of the measurement point during the interval.

Substep 1320 concludes with a substep 1326 of merging the upstream and downstream integrations, during which a final estimate of the linear speed of the measurement point at each sampling time t _k of the interval is calculated by linear interpolation of the first and second estimates:

• est la première estimation de la vitesse linéaire obtenue lors de la sous-étape 1322 par intégration aval,
• est la deuxième estimation de la vitesse linéaire obtenue lors de la sous-étape 1324 par intégration amont, et
• est donné par la formule suivante : .

Or :

• is the first estimate of the linear speed obtained during sub-step 1322 by downstream integration,
• is the second estimate of the linear speed obtained during sub-step 1324 by backward integration, and
• is given by the following formula: .

This gives an estimate of the change in orientation and an estimate of the change in linear speed of the measurement point during the interval.

Back to the , sub-steps 1310 and 1320 are followed by a sub-step 1330 of defining an inertial calculation frame.

• un premier axe Z confondu avec la verticale,
• un deuxième axe X, horizontal, orienté suivant la direction dans laquelle pointait l’axe du repère mobile (R_m) colinéaire à l’avant-bras 22 lorsque ledit axe a présenté l’orientation la plus horizontale de l’intervalle, et
• un troisième axe Y, horizontal, formant avec les premier et deuxième axes un repère orthogonal X, Y, Z direct.

This calculation inertial reference frame is for example the same as the inertial reference frame (R _i ) used for estimating orientation and linear speed. Alternatively, this calculation inertial reference frame is any other inertial reference frame and preferably a reference frame having:

• a first Z axis coincident with the vertical,
• a second X axis, horizontal, oriented in the direction in which the axis of the mobile reference frame (R _m ) collinear with the forearm 22 pointed when said axis presented the most horizontal orientation of the interval, and
• a third Y axis, horizontal, forming with the first and second axes a direct orthogonal X, Y, Z reference frame.

The orientations R(t _k ) and the speeds previously estimated are then recalculated to be expressed in said inertial calculation frame, by means of a simple change of reference well known to those skilled in the art.

Sub-step 1330 is itself followed by a sub-step 1340 of calculating candidate trajectories for the center of gravity of the forearm 22.

This calculation is based on a biomechanical model 100 of the upper limb 12, shown in the .

As visible in this Figure, the biomechanical model 100 comprises a first segment 102 having a free end 104. It also comprises a second segment 106 articulated by a first 108 of its ends 108, 110, via a first ball joint 112, to a proximal end 114 of the first segment 102 opposite the free end 104, and articulated by its second end 110, via a second ball joint 1116, to a fixed point.

The first segment 102 models the forearm 22 of the upper limb 12. It is constituted by a cylinder having a radius r and a length l equal to the distance between the measuring device 20 and the elbow 28. It forms with the vertical Z a first primary angle α modeling an angle of the forearm 22 with the vertical, and with the plane (X, Z) a first secondary angle ζ (not shown) modeling an angle of the forearm 22 with said plane.

The second segment 106 models the arm 25 of the upper limb 12. It is constituted by a cylinder having a length L equal to the length of said arm 25. It forms with the vertical a second primary angle β modeling an angle of the arm 25 with the vertical, and with the plane (X, Z) a second secondary angle η (not shown) modeling an angle of the arm 25 with said plane.

Each of the segments 102, 106 is rigid, i.e. it is not bendable. Preferably, at least one of the segments 102, 106 is extensible. If both segments 102, 106 are extensible, these extensions are advantageously constrained so as to be equal to each other.

The center of gravity C _G of the forearm 22 is placed on the first segment 102, at a distance from the joint 112 substantially equal to half the length of the forearm 22.

The biomechanical model 100 thus has a plurality of possible configurations, each defined by the values of the first primary α and secondary ζ angles and the values of the second primary β and secondary η angles.

In substep 1340, a candidate trajectory is calculated for each of a plurality of pairs of starting and ending configurations 130, 132 of the biomechanical model 100, shown in the , respectively modeling the configuration of the upper limb 12 at the start and end of the interval. By hypothesis, the first secondary angle ζ is defined in each of these configurations as being equal to the heading ψ of the measurement point, and the second secondary angle η is set equal to the first secondary angle ζ. Each of the starting and finishing configurations of the biomechanical model 100 is therefore directly defined by the first and second primary angles α, β.

In reference to the , sub-step 1340 thus begins, for the purposes of defining the starting and finishing configurations, with a sub-step 1342 of deducing an initial value α _i ( ) of the first primary angle α and a sub-step 1344 of deducing a value on arrival α _f ( ) of the first primary angle α.

In sub-step 1342, the first primary angle at the start α _i is deduced from the orientation of the measurement point at the initial time t _i , using the following formula:

in which is the vertical unit vector of the inertial frame (R _i ) and is the unit vector defining the direction of the forearm 22 in the inertial frame (R _i ) at the initial instant t _i , said vector given by the following formula:

where R ^t (t _i ) is the transpose of the rotation matrix at the initial time t _i and is the unit vector of the moving frame (R _m ) corresponding to the U axis.

In substep 1344, the first primary angle on arrival α _f is deduced from the orientation of the measuring point at the final time t _f , using the following formula:

in which is the unit vector defined above and is the unit vector defining the direction of the forearm 22 in the inertial frame (R _i ) at the final instant t _f , said vector given by the following formula:

where R ^t (t _f ) is the transpose of the rotation matrix at the final time t _f and is the unit vector of the moving frame (R _m ) corresponding to the U axis.

These sub-steps 1342, 1344 are shown as being implemented one after the other. Alternatively, they are implemented in parallel with each other.

Sub-steps 1342, 1344 are followed by a sub-step 1346 of calculating a displacement of the elbow 28. Alternatively, they are implemented in parallel with this sub-step 1346.

In sub-step 1346, the processing unit 34 calculates a displacement of the elbow 28 between the initial instant t _i and the final instant t _f , from the speeds and orientations estimated during the sub-steps 1310, 1320. This displacement is given by the following formula:

Or is the linear velocity vector estimated at a time t of the interval and And are the unit vectors defined above.

Sub-step 1340 also comprises, following sub-step 1342, a sub-step 1348 for determining a range of starting values of the second primary angle β compatible with the starting value α _i of the first primary angle α.

• la comparaison de la norme du déplacement avec la longueur L du bras 25, et
• la comparaison avec la valeur 1 de la différence entre le cosinus de la valeur au départ α_idu premier angle primaire α et le rapport de la norme du déplacement sur la longueur L du bras 25 ( ).

Preferably, this substep 1348 comprises:

• the comparison of the displacement norm with the length L of the arm 25, and
• the comparison with the value 1 of the difference between the cosine of the initial value α _i of the first primary angle α and the ratio of the displacement norm on the length L of the arm 25 ( ).

• si a norme du déplacement est inférieure ou égale au double de la longueur L et la différence entre le cosinus de la valeur au départ α_idu premier angle primaire α et le rapport de la norme du déplacement sur la longueur L du bras 25 est inférieure ou égale à 1, alors la plage de valeurs de départ compatibles est déterminée comme étant égale à la plage [0, α_i] ;
• si la norme du déplacement est strictement supérieure au double de la longueur L ou la différence entre le cosinus de la valeur au départ α_idu premier angle primaire α et le rapport de la norme du déplacement sur la longueur L du bras 25 est strictement supérieure à 1, alors la plage de valeurs de départ compatibles est déterminée comme étant égale à la plage [0, α_i+δ], où δ est un petit angle de valeur prédéterminée, typiquement compris entre 20° et 40° et par exemple sensiblement égal à 30°.

We then have different scenarios:

• if the displacement standard is less than or equal to twice the length L and the difference between the cosine of the initial value α _i of the first primary angle α and the ratio of the displacement norm on the length L of the arm 25 is less than or equal to 1, then the range of compatible starting values is determined to be equal to the range [0, α _i ];
• if the displacement standard is strictly greater than twice the length L or the difference between the cosine of the initial value α _i of the first primary angle α and the ratio of the displacement norm on the length L of the arm 25 is strictly greater than 1, then the range of compatible starting values is determined as being equal to the range [0, α _i +δ], where δ is a small angle of predetermined value, typically between 20° and 40° and for example substantially equal to 30°.

Alternatively, substep 1348 comprises only one of these comparisons, the choice of the range [0, α _i ] or [0, α _i + δ] then depending on the result of this single comparison. Alternatively, substep 1348 does not comprise any comparison and the range of compatible starting values is directly determined as being equal to the range [0, α _i ].

Substep 1348 is followed by a substep 1350 of constructing a starting configuration of the biomechanical model 100.

This sub-step 1350 comprises the selection 1352 of a starting value β _i of the second primary angle β within the range of compatible starting values.

To construct the starting configuration of the biomechanical model 100, the first primary angle α is thus assigned the starting value α _i and the second primary angle β is assigned the starting value β _i .

Substep 1350 is followed by a substep 1354 of downstream integration of the estimated linear speed V on the basis of the initial configuration.

During this sub-step 1354, the processing unit 34 produces a first estimate P _f (t _k ) of the position of the measurement point at each sampling instant t _k of the interval by integrating the estimates of the linear speed V of the measurement point prior to the instant t _k , taking as initial value an initial position P _i of the measurement point at the instant t _i . This initial position is given by the following formula:

• L est la longueur du bras 25,
• l est la distance entre le dispositif de mesure 20 et le coude 28,
• est le vecteur unitaire définissant la direction de l’avant-bras 22 dans le repère inertiel (R_i) à l’instant initial t_i,
• Q_iest une matrice de rotation correspondant à une rotation autour de l’axe vertical Z convertissant le vecteur unitaire en la projection horizontale du vecteur .

in which:

• L is the length of the arm 25,
• l is the distance between the measuring device 20 and the elbow 28,
• is the unit vector defining the direction of the forearm 22 in the inertial frame (R _i ) at the initial instant t _i ,
• Q _i is a rotation matrix corresponding to a rotation around the vertical Z axis converting the unit vector in the horizontal projection of the vector .

The first estimate of the position of the measuring point is estimated at each sampling time t _k using the following formula:

This gives us a first estimate of the trajectory of the measurement point during the interval.

In parallel with this sub-step 1354, the sub-step 1340 comprises a sub-step 1355 of determining a range of arrival values of the second primary angle β compatible with the starting value β _i of said angle β and/or with the arrival value α _f of the first primary angle α.

• la comparaison de la norme du déplacement avec la longueur L du bras 25, et
• la comparaison avec la valeur 1 de la somme entre le cosinus de la valeur à l’arrivée α_fdu premier angle primaire α et le rapport de la norme du déplacement sur la longueur L du bras 25 ( ).

Preferably, this substep 1355 comprises:

• the comparison of the displacement norm with the length L of the arm 25, and
• the comparison with the value 1 of the sum between the cosine of the arrival value α _f of the first primary angle α and the ratio of the displacement norm on the length L of the arm 25 ( ).

• si la norme du déplacement est inférieure ou égale au double de la longueur L et la somme entre le cosinus de la valeur à l’arrivée α_fdu premier angle primaire α et le rapport de la norme du déplacement sur la longueur L du bras 25 est inférieure ou égale à 1, alors la plage de valeurs d’arrivée compatibles est déterminée comme étant égale à un intervalle angulaire s’étendant sur moins de 20°, de préférence sur moins de 15°, par exemple sur sensiblement 10°, centré sur un angle β_tvérifiant la relation suivante :

We then have different scenarios:

• if the displacement standard is less than or equal to twice the length L and the sum between the cosine of the arrival value α _f of the first primary angle α and the ratio of the displacement norm on the length L of the arm 25 is less than or equal to 1, then the range of compatible arrival values is determined as being equal to an angular interval extending over less than 20°, preferably over less than 15°, for example over substantially 10°, centered on an angle β _t verifying the following relationship:

• if the displacement standard is strictly greater than twice the length L or the sum between the cosine of the arrival value α _f of the first primary angle α and the ratio of the displacement norm on the length L of the arm 25 is strictly greater than 1, then the range of compatible arrival values is determined as being equal to the range [0, α _f +ε], where ε is a small angle of predetermined value, typically between 0° and 40°, preferably between 20° and 40° and for example substantially equal to 30°.

Alternatively, substep 1355 comprises only one of these comparisons, the choice of the angular interval centered on the angle β _t or the range [0, α _i + ε] then depending on the result of this single comparison. Alternatively again, substep 1355 does not comprise any comparison and the range of compatible starting values is directly determined as being equal to the angular interval centered on the angle β _t .

Substep 1355 is followed by a substep 1356 of constructing an arrival configuration of the biomechanical model 100.

This substep 1356 comprises the selection 1357 of an arrival value β _f of the second primary angle β within the range of compatible arrival values.

To construct the arrival configuration of the biomechanical model 100, the arrival value α _f is thus assigned to the first primary angle α and the arrival value β _f is assigned to the second primary angle β.

Substep 1356 is followed by a substep 1358 of upstream integration of the estimated linear speed V on the basis of the arrival configuration.

During this sub-step 1358, the processing unit 34 produces a second estimate P _b (t _k ) of the position of the measurement point at each sampling instant t _k of the interval by integrating the estimates of the linear speed V of the measurement point subsequent to the instant t _k , taking as initial value a final position P _f of the measurement point at the final instant t _f . This initial position is given by the following formula:

• L est la longueur du bras 25,
• l est la distance entre le dispositif de mesure 20 et le coude 28,
• est le vecteur unitaire définissant la direction de l’avant-bras 22 dans le repère inertiel (R_i) à l’instant final t_f,
• Q_fest une matrice de rotation correspondant à une rotation autour de l’axe vertical Z convertissant le vecteur unitaire en la projection horizontale du vecteur .

in which:

• L is the length of the arm 25,
• l is the distance between the measuring device 20 and the elbow 28,
• is the unit vector defining the direction of the forearm 22 in the inertial frame (R _i ) at the final instant t _f ,
• Q _f is a rotation matrix corresponding to a rotation around the vertical Z axis converting the unit vector in the horizontal projection of the vector .

The second estimate of the position of the measuring point is estimated at each sampling time t _k using the following formula:

This gives a second estimate of the trajectory of the measurement point during the interval.

Sub-step 1340 concludes with a sub-step 1359 of merging the upstream and downstream integrations, during which a final estimate of the position of the measurement point at each sampling instant t _k of the interval is calculated by linear interpolation of the first and second estimates:

• est la première estimation de la position obtenue lors de la sous-étape 1354 par intégration aval,
• est la deuxième estimation de la position obtenue lors de la sous-étape 1356 par intégration amont, et
• est donné par la formule suivante : .

Or :

• is the first estimate of the position obtained during sub-step 1354 by downstream integration,
• is the second estimate of the position obtained during sub-step 1356 by backward integration, and
• is given by the following formula: .

This gives a final estimate of the trajectory of the measurement point during the interval for the pair of departure and arrival configurations.

From this final estimate of the trajectory of the measurement point, the processing unit 34 easily deduces a candidate trajectory of the center of gravity C _G , this trajectory being composed of a set of candidate positions at time t _k deduced from the final estimates of the positions of the measurement point by means of the following formula:

where d is the distance from the center of gravity C _G to the measurement point and is a unit vector defining the direction of the forearm 22 in the inertial frame (R _i ) at time t _k , said vector given by the following formula:

where R ^t (t _k ) is the transpose of the rotation matrix at sampling time t _k and is the unit vector of the moving frame (R _m ) corresponding to the U axis.

Substeps 1356, 1358 and 1359 are repeated for each arrival value β _f included in the range of compatible values determined during substep 1355 and substeps 1350, 1354, 1355, 1356, 1358 and 1359 are repeated for each departure value β _i included in the range of compatible values determined during substep 1348. It will be noted that, by “each value included in the range”, is meant a set of discrete values spaced from each other by a predetermined step, for example substantially equal to 0.1°.

Thus, for each starting value β _i included in the range of compatible values determined during substep 1348 and for each arrival value β _f included in the range of compatible values determined during substep 1355, there exists a pair of starting and arrival configurations for which a candidate trajectory of the center of gravity C _G is calculated.

Back to the , sub-step 1340 is followed by a sub-step 1360 of evaluating the compatibility of each candidate trajectory with the biomechanical model 100.

During this sub-step 1360, the processing unit 34 evaluates a compatibility of each candidate trajectory with the biomechanical model 100. This compatibility is typically evaluated by means of a cost function which is a function of the deformations that the tracking of the candidate trajectory imposes on the biomechanical model 100. Typically, the compatibility is inversely proportional to the result of the cost function: for example, in the case where the segment 106 (which corresponds to the arm 25) is extensible, the cost function can be the difference between the maximum extension of the segment 106 and the length L, the compatibility being inversely proportional to said difference. Alternatively, the cost function is constructed in such a way that the compatibility increases with the result of the cost function.

Substep 1360 is followed by a substep 1365 of selecting the candidate trajectory presenting the best compatibility.

During this sub-step 1365, the processing unit 34 selects the candidate trajectory whose result of the cost function reflects the best compatibility, that is to say whose result is the lowest (when the compatibility is inversely proportional to the result of the cost function) or the highest (when the compatibility increases with the result of the cost function).

Substep 1365 is followed by a substep 1370 of verifying the acceptable nature of the compatibility of the selected trajectory.

In this sub-step 1370, the processing unit 34 compares the result of the cost function of the selected trajectory with a predetermined threshold, said threshold being chosen such that the comparison of the result of the cost function of the selected trajectory with said threshold reflects the acceptable or unacceptable nature of the compatibility of the selected trajectory. Typically, said threshold is chosen such that the compatibility of the selected trajectory is considered acceptable if and only if the result of the cost function is lower than the threshold (when the compatibility is inversely proportional to the result of the cost function) or higher than the threshold (when the compatibility increases with the result of the cost function).

For each interval, which we will call in the following "primary interval", for which the compatibility of the selected trajectory is acceptable, the sub-step 1370 is followed by a sub-step 1372 of validation of the selected trajectory. The selected trajectory therefore constitutes a validated estimate of the trajectory of the center of gravity C _G during said primary interval.

Substep 1372 is followed by a substep 1374 of deducing a rotational component of the kinetic energy of the forearm 22 during the primary interval.

During this sub-step 1374, the processing unit 34 deduces from the rotational speed measurements during the primary interval a rotational component E _k,r of a mass kinetic energy acquired by the forearm 22 during the primary interval. This rotational component is typically obtained by means of the following formula:

• est le tenseur d’inertie massique de l’avant-bras 22, c’est-à-dire indépendant de la masse de l’avant-bras 22, exprimé dans le repère mobile (R_m),
• est la vitesse de rotation du point de mesure à un instant t, exprimée dans le repère mobile (R_m) et typiquement fournie par le gyroscope 40, et
• est l’accélération rotationnelle du point de mesure à un instant t, exprimée dans le repère mobile (R_m) et typiquement déduite des mesures du gyroscope 40 par calcul de la différence entre deux mesures de vitesse consécutives.

in which:

• is the mass inertia tensor of the forearm 22, i.e. independent of the mass of the forearm 22, expressed in the moving frame (R _m ),
• is the rotation speed of the measurement point at a time t, expressed in the moving frame (R _m ) and typically provided by the gyroscope 40, and
• is the rotational acceleration of the measurement point at a time t, expressed in the moving frame (R _m ) and typically deduced from the measurements of the gyroscope 40 by calculating the difference between two consecutive speed measurements.

Substep 1374 is followed by a substep 1376 of evaluating a primary force W _p exerted by the upper limb 12 during the primary interval.

During this step, the processing unit 34 evaluates said primary force W _p from the estimated trajectory and linear speed evolution, typically using the following formula:

• E_k,rest la composante rotationnelle de l’énergie cinétique massique acquise par l’avant-bras 22 durant l’intervalle primaire mentionnée plus haut,
• E_k,test une composante translationnelle de l’énergie cinétique massique acquise par l’avant-bras 22 durant l’intervalle primaire, donnée par la formule suivante :

in which:

• E _k,r is the rotational component of the mass kinetic energy acquired by the forearm 22 during the primary interval mentioned above,
• E _k,t is a translational component of the mass kinetic energy acquired by the forearm 22 during the primary interval, given by the following formula:

• est la vitesse linéaire de déplacement du centre de gravité C_Gà un instant t, exprimée dans le repère inertiel (R_i) et déduite de la vitesse linéaire estimée du point de mesure à l’instant t,
• est l’accélération du centre de gravité C_Gà un instant t, exprimée dans le repère inertiel (R_i) et typiquement déduite de la vitesse linéaire de déplacement du centre de gravité C_Gpar calcul de la différence entre les valeurs de ladite vitesse linéaire à deux instants consécutifs.
• E_pest une énergie potentielle massique acquise par l’avant-bras 22 durant l’intervalle primaire, donnée par la formule suivante :

in which:

• is the linear speed of movement of the center of gravity C _G at a time t, expressed in the inertial frame (R _i ) and deduced from the estimated linear speed of the measurement point at time t,
• is the acceleration of the center of gravity C _G at a time t, expressed in the inertial frame (R _i ) and typically deduced from the linear speed of movement of the center of gravity C _G by calculating the difference between the values of said linear speed at two consecutive times.
• E _p is a mass potential energy acquired by the forearm 22 during the primary interval, given by the following formula:

• g est la norme du champ gravitationnel
• z(t_f) est la coordonnée verticale du centre de gravité C_Gà la fin de l’intervalle primaire, et
• z(t_i) est la coordonnée verticale du centre de gravité C_Gau début de l’intervalle primaire.

in which:

• g is the norm of the gravitational field
• z(t _f ) is the vertical coordinate of the center of gravity C _G at the end of the primary interval, and
• z(t _i ) is the vertical coordinate of the center of gravity C _G at the beginning of the primary interval.

Substep 1376 is further followed by a substep 1378 of determining a relationship f between primary force W _p and rotational component E _k,r of the kinetic energy acquired by the forearm 22 during each primary interval. This relationship f is typically determined by regression, preferably a linear regression, on all the couples (primary force W _p , rotational component of the kinetic energy E _k,r ) obtained for the different primary intervals.

For each interval, which we will call in the following "secondary interval", for which the compatibility of the selected trajectory is not acceptable, the sub-step 1370 is followed by a sub-step 1382 of rejection of the candidate trajectories. None of the candidate trajectories is then considered as a valid estimate of the trajectory of the center of gravity C _G during said secondary interval.

Substep 1382 is followed by a substep 1384 of deducing a rotational component of the kinetic energy of the forearm 22 during the secondary interval.

During this sub-step 1384, the processing unit 34 deduces from the rotation speed measurements during the secondary interval a rotational component E _k,r of the kinetic energy acquired by the forearm 22 during the secondary interval. This rotational component is typically obtained by means of the formula already mentioned for step 1374.

Substep 1384 is followed by a substep 1386 of evaluating a secondary force W _s exerted by the upper limb 12 during the secondary interval.

During this step, the processing unit 34 evaluates said primary force W _s from the rotational component E _k,r of the kinetic energy acquired by the forearm 22 during the secondary interval and from the relationship f between primary force W _p and rotational component E _k,r of the kinetic energy acquired by the forearm 22 determined during sub-step 1378. Typically, the processing unit 34 evaluates the primary force W _s by means of the following formula:

Step 1300 is repeated for each time interval of the period of interest during which the linear speed of the measurement point is not a priori known and which is between two phases for which the linear speed of the measurement point was determined during step 1200.

Steps 1200 and 1300 are repeated for each period of interest included in a predetermined period. This predetermined period typically has a duration greater than one week and, advantageously, less than three months.

Following this repetition of steps 1200, 1300, the method 1000 comprises a step 1400 of determining the value of a statistical quantity, calculated on the set formed by the primary efforts W _p and/or secondary efforts W _s evaluated for the various time intervals included in the predetermined period, representative of a state of form of the person 14 over said predetermined period.

During this step 1400, the processing unit 34 performs a statistical calculation on the set formed by the primary efforts W _p and/or secondary efforts W _s evaluated for the various time intervals included in the predetermined period. Typically, the processing unit 34 calculates an average and/or a percentile of these efforts, relative to all of the efforts evaluated for the predetermined period. For example, the processing unit 34 calculates the ^50th percentile, which corresponds to the median, the ^80th percentile, the ^95th percentile, the ^99th percentile, or any other percentile value of the efforts evaluated for the predetermined period.

Preferably, the processing unit 34 selects the statistical quantity from a predetermined percentile range, in particular a high percentile range, i.e. percentiles greater than the ^70th percentile. Indeed, these high percentiles are representative of the maximum effort and the maximum muscular power that the person 14 is capable of developing, because they reflect the fastest and/or longest movements of an individual, the speed and duration of the movements of the upper limbs being constrained by the state of muscular strength. These high percentiles are therefore particularly sensitive to the state of fitness of the person 14.

Advantageously, the statistical quantity is constituted by the ^99th percentile of the efforts evaluated for the predetermined period.

Optionally, step 1400 comprises the selection of at least one other statistical quantity representative of a state of fitness of the person 14 over the predetermined period.

Steps 1002 to 1400 are repeated for several predetermined periods. The processing unit 34 thus produces a set of values of the statistical quantity representative of the fitness state of the person 14 over several predetermined periods.

Following this repetition of steps 1002 to 1400, the method 1000 comprises a step 1500 of observing the evolution of the statistical quantity across the different predetermined periods. The fitness level of the person 14 can thus be monitored.

Advantageously, this monitoring of the fitness level of the person 14 is used to determine the effectiveness of a treatment administered to the person 14.

Thanks to the example of implementation described above, it is thus possible to monitor over time the physical fitness of an individual who cannot use his lower limbs, with few constraints for the individual. This monitoring is particularly made possible in an uncontrolled environment and over long periods, which allows for faithful monitoring of the individual's actual fitness level.

The embodiment also allows a good estimation, in an uncontrolled environment and over a long period, of the physical efforts made by an upper limb of a person for various movements. It further allows the quality of the estimations to be improved, in particular of linear speed and position, deduced from the measurements of an inertial device, in particular when this inertial device is attached to a limb of an individual.

It will be noted that, although the above description focuses on an exemplary embodiment in which the measuring device 20 is attached to an upper limb 12 of a person 14, the efforts evaluated being those of this upper limb 12, the invention also extends to a method for evaluating the efforts of a lower limb of an individual, the measuring device 20 then being attached to the leg of this lower limb. Those skilled in the art will easily be able to make the necessary adaptations.

Claims (15)

Method for estimating the evolution of a speed of a measurement point during a movement interval, the method being implemented by a data processing unit (34) and comprising the following steps:

• determining (1200) an initial speed and a final speed of the measuring point respectively at the start and at the end of the displacement interval,
• estimation (1320) of the evolution of a speed of the measurement point during the displacement interval, said estimation comprising:
  • downstream integration (1322) of displacement parameters of the measurement point acquired by an inertial device (32) during the displacement interval, taking as initial value of the speed the value of the initial speed,
  • the upstream integration (1324) of the displacement parameters, taking as the initial value of the speed the value of the final speed, and
  • the calculation (1326) of the speed estimated by merging the upstream and downstream integrations.

Method for estimating a trajectory, over a movement interval, of a point of interest belonging to a limb (12) of a person (14), the method being implemented by a data processing unit (34) and comprising the following steps:

• estimation (1320) of the evolution, during the movement interval, of a speed of a measurement point integral with the point of interest by means of a method according to claim 1,
• estimation (1310) of the evolution of an orientation of the measurement point during the displacement interval, and
• estimation of the trajectory of the point of interest during the movement interval from the estimated speed and orientation of the measurement point,

the point of interest being preferably chosen from a point on a forearm (22) of the person (14) and a point on a leg of the person. The method of claim 2, wherein estimating the trajectory comprises the following steps:

• calculating (1340) several candidate trajectories by applying the estimated speed and orientation to different pairs of starting and finishing configurations (130, 132) of a biomechanical model (100) of the limb (12),
• evaluation (1360) of the compatibility of each candidate trajectory with the biomechanical model, and
• selection (1365) of the candidate trajectory presenting the best compatibility.

Method according to claim 3, wherein the point of interest is a point of a forearm (22) belonging to an upper limb of the person (14), each starting configuration (130) of the biomechanical model (100) of the limb (12) being defined by a pair of starting angles formed by a first starting angle (α _i ) between the forearm (22) and the vertical and a second starting angle (β _i ) between the arm (25) and the vertical and each arrival configuration (132) of the biomechanical model (100) of the limb (12) being defined by a pair of arrival angles formed by a first arrival angle (α _f ) between the forearm (22) and the vertical and a second arrival angle (β _f ) between the arm (25) and the vertical. Method (1300) according to claim 4, in which, for each starting (130) or arrival (132) configuration of the biomechanical model (100) of the limb (12):

• the first starting angle (α _i ), respectively arrival angle (α _f ), is deduced from the orientation of the measuring point at the beginning, respectively at the end, of the displacement interval, and
• the second starting angle (β _i ), respectively arrival angle (β _f ), is less than the first starting angle (α _i ), respectively arrival angle (α _f ).

A method according to claim 4 or 5, wherein there exists, for each second departure angle value (β _i ) less than the first departure angle (α _i ) and each second arrival angle value (β _f ) within a predetermined interval, a pair of departure and arrival configurations (130, 132) for which a candidate trajectory is calculated. A method according to claim 6, wherein the predetermined interval is constituted by an interval between 0° and the value of the first angle of arrival (α_f), or by an angular interval around an angle β_tverifying the following relationship:

in which:

• L is the length of the arm (25) of the upper limb,
• β _i is the value of the second departure angle (β _i ) in the departure configuration (130) belonging to the same pair as the arrival configuration (132),
• t _i is the start time of the displacement interval,
• t _f is the end time of the movement interval,
• is the velocity vector of the measuring point at each instant t of the displacement interval,
• l is the distance between the elbow (28) of the upper limb and the measuring point,
• is a unit vector giving the orientation of a principal axis of the forearm (22) at the end of the displacement interval,
• is a unit vector giving the orientation of the principal axis of the forearm (22) at the beginning of the displacement interval,
• is a unit vector giving the vertical orientation,

vectors , , And being expressed in the same inertial frame. A method according to any one of claims 3 to 7, wherein the calculation (1340) of each candidate trajectory comprises the following steps:

• downstream integration (1354) of the estimated speed, taking as initial position the position of the measuring point in the starting configuration (130),
• upstream integration (1358) of the estimated speed, taking as initial position the position of the measurement point in the arrival configuration (132), and
• calculation (1359) of the candidate trajectory by merging the upstream and downstream integrations.

Method (1300) for evaluating an effort exerted by a limb (12) of a person (14), the method being implemented by a data processing unit (34) and comprising the following steps:

• estimating a trajectory of a point of interest belonging to the member (12) over at least one primary displacement interval by means of a method according to any one of claims 2 to 8,
• evaluation (1376), from the estimated trajectory and speed evolution, of a primary force exerted by the member (12) during the or each primary displacement interval.

The method (1300) of claim 9, comprising the following additional steps:

• deduction (1374), from the displacement parameters acquired during the primary displacement interval, of a rotational component of a primary kinetic energy acquired by at least a portion of the member (12) during the primary displacement interval, the primary force being a function of said rotational component of the primary kinetic energy,
• determination (1378) of a relationship between the primary effort and the rotational component of the primary kinetic energy,
• estimation (1310) of the evolution of an orientation of a measurement point attached to the point of interest during at least one secondary displacement interval,
• deducing, from displacement parameters acquired by the inertial device (32) during a secondary displacement interval, a rotational component of a secondary kinetic energy acquired by said at least one portion of the member (12) during the secondary displacement interval,
• evaluation, from the determined relationship and the rotational component of the secondary kinetic energy, of a secondary force exerted by the member (12) during the or each secondary displacement interval.

Method (1300) according to claim 10 comprising, for each of the primary and secondary displacement intervals:

• estimating (1320) the evolution, during the primary or secondary displacement interval, of a speed of a measurement point integral with the point of interest by means of a method according to claim 1,

• calculating (1340) several candidate trajectories by applying the estimated speed and orientation to different pairs of starting and finishing configurations (130, 132) of a biomechanical model (100) of the limb (12),

• the evaluation (1360) of a compatibility of each candidate trajectory with the biomechanical model (100), and
• the verification (1370), for each primary or secondary displacement interval, of the acceptable nature of the compatibility of at least one candidate trajectory,

the trajectory of the point of interest being estimated only when at least one candidate trajectory has acceptable compatibility. Method (1000) for analyzing an effort exerted by a limb (12) of a person (14), the method being implemented by a data processing unit (34) and comprising the following steps:

• a) estimation, for several intervals of displacement of a point of interest of the member (12) occurring during a predetermined period, of a force exerted by said member (12) by means of a method (1300) according to any one of claims 9 to 11,
• b) determination (1400) of the value of at least one statistical quantity, calculated on the set formed by the estimated efforts, representative of a state of fitness of the person (14).

Method (1000) according to claim 12, comprising repeating steps a) and b) for several predetermined periods and observing (1500) the evolution of the or each statistical quantity across the different predetermined periods. Equipment (10) comprising an inertial device (32) for acquiring movement parameters of a measurement point during at least one movement interval, and a data processing unit (34) configured to estimate, from the movement parameters acquired by the inertial device (32), by implementing a method according to any one of claims 1 to 11, at least one of: the evolution of a speed of the measurement point during the movement interval, a trajectory, over the movement interval, of a point of interest integral with the measurement point, and a force exerted by a limb (12) of a person (14) to which the point of interest belongs. Computer program product comprising code instructions for implementing a method according to any one of claims 1 to 13 when said program is executed by a computer.