TIME MANAGEMENT, ACTIVITY SELECTION AND SALES PERFORMANCE:

A NEW WAY TO REPOSITION THE ROLE OF MANAGEMENT AND SALESPEOPLE.

INTRODUCTION

When considering the roles of management and salespeople at the strategic level of analysis or at the operational level of analysis, we note that often there is no agreement between the objectives determined by management and results obtained by the sales force. To resolve this disparity, we propose to shed light on a major gap that exists in traditional management. This gap deals with the way salespeople perform their role. To date, no previous research has investigated the extent to which the role assigned by management has been modified into the role taken by the salesperson. We propose that when salespeople make choices about their role, distance exists between the role assigned by management and the roles actually performed.

Time is a familiar problem which provides a new explanation for the existence of the differences in roles set forth in this gap. We propose that an individual's perspective of time (i.e., monochronic vs. polychronic) explains their time management choices, their activity preferences, and the performance of sales personnel. A better understanding of this concept and its integration into management would reduce the gap between the roles assigned by management and the roles taken by members of the sales force.

To begin, we define concepts like prescribed role or exerted role and present how these are used in a major sales organization. Next, we precisely define the notions of time management and time orientation, and how they influence the activities of salespeople. These issues will be investigated in a research project that should have implications for every sales organization. A study in the French banking industry has already started. This investigation will provide tangible results addressing the issues raised here.

THE CONCEPT OF ROLE -FROM PRESCRIBED ROLE TO EXERCISED ROLE

THE CONCEPT OF PROFESSIONAL ROLE

The concept of role comes first from theatre or philosophy, and has received its modern interpretation from psycho-sociological works, before being used in management. The social and relational context, in which it is inserted, indeed, has a very strong impact, likewise the structural position to which it is correlated. Role theory, and a lot of works on this topic [START_REF] Durand | Sociologie contemporaine[END_REF][START_REF] Goffman | La mise en scène de la vie quotidienne, tome 1 : la présentation de soi[END_REF][START_REF] Grawitz | Lexique des sciences sociales[END_REF]Loubès, 1998;Fogarty and alii, 2000;Wils and alii, 2000;etc.), provides numerous definitions of the role. From our point of view, the individual's professional role is defined as the set of coherent acts and behaviours expected from his part, due to his specific position and status in the firm. But it is a very global vision, of which we may deduce with difficulty planned or exercised activities. As an example, the French Association for Normalization [START_REF] Afnor | Les fonctions de l'entreprise[END_REF] defines a business consultant as a person "in charge to accomplish an act of advice that may be invoiced, and after which he's led to sell products and services". Therefore the role is very often reduced to the standard mission which expresses its purpose, but it does not point out the way to exercise it, the tasks that must be realized, or the priorities that may command the realization of theses tasks. Consequently, we might be afraid by this phenomenon: managers develop a specific conception of the role they want their employees to take onthe prescribed role. When they get the role across to their collaborators, these might understand it with a personal perceptionthe perceived role. But employees have previously elaborated their own conception of the role they would like to exertthe wished role. Finally, what will they do daily? The exerted role is this fourth representation implemented by professionals, and which results unequally from the other three. It is possible to explain such differences between managers' and employees' perceptions, about roles in a firm. At least two different approaches of the notion of role coexist. Most of the time managers follow a functionalist vision, in which the role is an instrument of behaviour normalization and forecast [START_REF] Crozier | L'acteur et le système[END_REF]. It allows the firm to impose upon employees the prescribed role, and constrains employees to take it at face value. In this meaning the role is coercive and must be applied the same way it is defined to contribute to the organizational goals. It is intimately linked to the status allocated by the company to the role holder, and formalizes individual's place and social position in the organization, conferring prerogatives, obligations and very often explicit position norms.

In this framework, the firm is a system made with harmonious and complementary roles, created to achieve organizational goals [START_REF] Touraine | Production de la société[END_REF]. That is why a company tries to control its agents practices, and wants to convey values and behaviour "excellence" models, that allows for example to define what is a "good" manager or a "good" salesman. Hierarchy transmits and reinforces the impact of such role models, which may be respected by anyone that wants to be considered worthy of holding one's position. Meanwhile behind a certain doctrine of performance [START_REF] Thévenet | Impliquer les personnes dans l'entreprise[END_REF], more and more contradictions, ambiguities and weaknesses come to light, producing gaps between the ideal represented by the prescribed role and the reality of the exerted role. To the contrary, employees develop an interactionist vision, which allows them to adapt their role to the circumstances that they meet everyday. Consequently, we have tried to verify this observation in a previous study.

ROLES OBSERVED WITHIN A SALESFORCE

We carried out from 1997 to 2000 a research task applied to the case of a company, which led us to study the role of its middle managers at the first level of the hierarchy. The principal objective was to check that there was a significant difference between the roles, such as it is prescribed by the management of the firm and such as it is exerted by the executives. By adapting the model of the role episode of [START_REF] Katz | The Social Psychology of Organizations[END_REF][START_REF] Katz | The Social Psychology of Organizations[END_REF][START_REF] Katz | The Social Psychology of Organizations[END_REF], Figure 1), we built a tool of investigation intended at the same time for the middle managers and the leaders. Indeed, the Role theory regards the role defined by the company as a means of anticipating the probable behaviour of its agents, one realizes that, in practice, the roles are built with the wire of time by their holders, who interact between them with this intention [START_REF] Berger | The Social Construction of Reality[END_REF]. Interpretations appear then necessarily, between the role such as it is defined a priori, and what it is really in the daily exercise of the profession. The model of the role episode offers reading this type of evolution of the role, explaining how one can pass from expectations of the company to the role actually exerted by its employees. Role stress (conflict, ambiguity and role overload) can be born from the gaps existing between the roles. We developed a model integrating the social representations of the role, on the basis of the model of Katz and Kahn. Thanks to the concept of representation, the gaps in question can be explained and analyzed according to whether they appear fundamental or secondary. If the elements of role causing of the divergences belong to the core of two representations of the role, for example, then the gaps have an important impact on the exercise of the role. Conversely, if they constitute the periphery of the representations concerned, the influence will be less. 1The central topic of the study which was used to us as a basis of construction for this model is the role of middle managers in a salesforce. It is composed of 24 tasks defined during successive stages of research, that is to say six tasks on average for the functions Leadership, Sales, Administration and Supervision. The various representations of the role are those referred to above: the role prescribed by the top managers of the company, the role perceived by the middle managers (the role prescribed such as they interpret it), the wished role (that which they want ideally to exert), the role exerted finally (what they estimate to carry out daily). Our perceptual role model is presented in Figure 2.

The measuring instruments used are shown completely reliable (Coefficient α over 0.75). They made it possible to reveal three types of complementary gaps: the number of tasks considered as priority on all the others, the average value allocated to each task, finally the place conceded to the tasks in each function. Table 1 synthesizes this information. On a basic scale 100, the tasks which obtain a score ranging between 70 and 100 are regarded as very priority by the people interviewed. That relates to 14 tasks for the wished role by the middle managers, 11 tasks for the prescribed role, but only 6 in the case of the perceived role, and 5 for the exerted role.

In other words, the priority disperses between the tasks composing the role: if the top managers consider that about half of the activities of the middle management is essential, this message is not perceived by the executives concerned. However, those estimate that 58% of their tasks have priority, while at the same time they judge to be able of attaching importance only to 1/6e of them in the facts.

The second criterion, which is the average score of each task, is degraded while passing from a representation of role to the other, modifying the hierarchy of the priorities. Thus, "to show the example" obtains a row of priority of 79.20 in the wished role but only of 72 in the prescribed role.

The middle managers think that one asks them to be strongly mindful (74.40) while at the same time they place this act of management at the bottom of the list of the priority tasks (70.40). Within sight of the third criterion, which is the total weight of each function of the role, it is noted that the hierarchy of priorities of a representation of a role to the other are strongly disturbed. Thus, the sales tasks disappear from the principal concerns in the exerted role, which leaves perplexed in the case of sales managers. The most stable tasks are "to give instructions" and "to supervise the objectives", which they themselves call tasks of "micro manager". Consequently several questions arise. One is of knowing how the sales managers define their priorities: if they really implement only half of the activities which are required of them, how can they guarantee the expected results which rise of these activities? In addition, whereas they aim at the prototype of the "charismatic entrepreneur" who leads his team with dynamism, they have the feeling that one especially asks them to supervise the salesforce and to push them to obtain good results. In the same time, they finally think of acting as "firemen" in many emergencies, without being able to work for the long-term performance. Using complementary tools, we raised a significant professional dissatisfaction in the middle managers, dependent on role ambiguity and on role conflicts due to the situations which they live because of these role gaps. Daily, the hierarchy of the priorities in their role necessarily leads, because of its variability between the prescribed role and that exerted, with notable gaps in the management of their time. Indeed, a priority activity will be in particular one of those which the professional will carry through before others, in the chronology of the role which he exerts, and which he will be inclined to devote to it a significant part of his time. Consequently, it appears probable that the estimated diary of a manager will not be in conformity with that which will materialize finally. By way of illustration, we collected the following information. The sales managers of the network studied have 217-days annual timetable. However, time that they indicate to devote specifically to the leading tasks in their sales team varies from 40 to 120 days. This means gaps exist, from 1 to 3 according to the manager, and indicates necessarily dysfunctions in the allowance of time that they realize indeed. Brought back to the unit of time allocated to each commercial by his manager (11 days per year and per team on average), a salesman sees his manager between one day per month and one day per quarter, according to the team in whom he works. Can one imagine that a customer is visited three times less than it is envisaged? In front of this type of dysfunction, it appeared essential to us to cross these two variables: the role such as it is prescribed or such as it is exerted, and time, according to the way in which it is employed in the role.

THE CONCEPT OF TIME -FROM TIME ALLOCATION TO TIME PERCEPTION

THE CONCEPT OF TIME MANAGEMENT

Time, as a fundamental variable of individual and group activity, has been examined not only into numerous disciplines (economy, sociology, anthropology, literature, philosophy, theology, linguistics, mathematics, physics, communication, etc.), but already in terms of orientations (past, present and future), of activity levels (monochronism and polychronism) and even in terms of possible uses (incomes, obligations, etc.) [START_REF] Denton | The Dynamism of Personal Timestyle: How We Do More in Less Time[END_REF]. The research on this concept has in fact been organised successively around two dimensions.

The objective dimension, or activities time allocation, caught the attention of the majority of researchers till the middle of the eighties [START_REF] Hendrix | The Allocation of Time by Consumers[END_REF][START_REF] Feldman | The Use of Time: An Integrated Conceptual Model[END_REF][START_REF] Holman | The Imagination of the Future: A Hidden Concept in the Study of Consumer Decision Making[END_REF][START_REF] Menefee | The Demand for Consumption Time: A Longitudinal Perspective[END_REF]etc.). They observed how individuals share their time among different activities, resulting in the development of several models of time allocation. This dimension is built on a mathematical and segmentable time, which can be counted and added. It is only from the eighties and especially during the following decade, that the second dimension of time aroused interest: it is the subjective dimension also called time perception. A lot of works focused on how individuals' time experience interfere in their purchasing decision, their consumption decision, their waiting decision, etc. [START_REF] Usunier | Négociation commerciale internationale et perceptions culturelles du temps[END_REF][START_REF] Usunier | Businesstime Perceptions and National Cultures: A Comparative Survey[END_REF]Bergadaà, 1990;Kaufman, Lane et Lindquist, 1991;Ko et Gentry, 1991;[START_REF] Poole | On Time: Contributions from the Social Sciences[END_REF]etc.). It is now admitted that time perception is a determining factor in the understanding of customer's behavior [START_REF] Feinberg | Misperceptions of Time in the Sales Transaction[END_REF].

Even if Grönmo argued that "the concepts of time are complementary rather than mutually exclusive or completely independent one from another", these two research currents have had no link between them during a lot of time. Even today, few interdisciplinary works exist [START_REF] Gentry | Measures of Personal Time Orientation, 7 th John-Labatt Marketing Research Seminar[END_REF][START_REF] Moreau-Durrande | Temps objectif, temps subjectif : vers une mesure de la pénibilité de l'attente ?[END_REF]etc.). Yet, when an individual buys a product, the time he spends researching and buying it is particularly important, but the perception he has about this time is even more decisive. In fact, if he considers that the time dedicated to buying a product is too important compared to the use of this product, he can give up doing his purchase. We think that such a logic can be implemented in a professional context. Actually, when an individual is given a lot of tasks to be done in a specific lapse of time, first he organises them, and then he allocates a sum of time to realise them according to what he judges necessary, it means according to his time perception.

Literature revealed two components of time perception: its orientation and its management. The temporal orientation is defined as someone's preference or predisposition to visualise one of the three temporal areas (past, present, future) when he makes a decision [START_REF] Moinier | Comportement du consommateur et orientation temporelle : proposition d'une mesure opérationnelle[END_REF][START_REF] Poole | On Time: Contributions from the Social Sciences[END_REF]. The management of time refers to "the attitude of every one toward time, the way everybody thinks of time and the impact of this perspective on their behaviour" (Pailler, 1997). Among the numerous ways to deal with and to perceive time, the anthropologist [START_REF] Hall | La danse de la vie, temps culturel, temps vécu[END_REF] brought out two opposite concepts, called monochronism and polychronism, upon which our research is based. Briefly, we can remember that in a monochronic system, individuals prefer to commit themselves in one activity at the same time and that they are tied to programming activities. On the contrary, in a polychronic system, individuals enhance the value of committing themselves in many activities at the same time and they give greater importance to social relations rather than to the adherence to an established program.

Considering the case of salespeople and their manager, it means for example that a polychronic salesman is able to do many activities during a single segment of time, like receiving a client, answering the telephone and giving information to a colleague. The monochronic salesman is more prone to realise the same activities one after the other; for example, he would not answer the telephone when he is with a client. It partly explains why two professionals doing the same job do not achieve the same results, as they do not manage to do them in the same way. This temporal interpretation of activities forming a given role might explain the gaps observed, in particular, between the role assigned by management and the role actually performed by salespeople. In other words, it means first that monochronic and polychronic salespeople have a high propensity to not allocate time to the same tasks, and that second in the binomial manager-salesman they also risk to not conceive their respective role in the same way. Finally, what the superior wants is not interpreted in the right way by the salesman, whereas the expectations of the latter in terms of management might be translated back by the manager in other needs than those expected by the salesman.

In order to illustrate how salespeople's management of time can really influence their activity and the results they achieve, it seems convenient to present, in the next point, the foundations of the qualitative study that will be realised in the banking area, which is the starting point of a bigger research project on this subject.

THE MANAGEMENT OF TIME OF COMMERCIAL BANKERS

Banking and financial sector has undergone massive changes for the past two decades. The insertion of new actors in the market (insurance companies, direct selling, mass marketing, etc.), the exaggerated competition (reduction of offers) and the evolution of customers behaviour have had great consequences upon the strategy of banks. Sales team is in the centre of this new problematic and the job of commercial bankers has been redefined. As he represents the firm, the counsellor is in charge of initiating, developing and perpetuating the relation with clients. He actually is responsible for a client's portfolio and he must manage its financial situation. He can no longer content himself with being reactive; from now on, he must try to be proactive, that is to answer first to the expectations of his clients [START_REF] Cledy | L'impact de l'utilisation des applicatifs informatiques sur le travail et les performances commerciales du conseiller clientèle[END_REF]. Thus, he has to make contact with them "at the right time", he has to propose them offers adapted to their situation, hence the strategic importance of his choice. The use of a diary, often an electronic calendar, is now recommended in the activity of salespeople. This tool gives the opportunity to answer to major objectives. For example, it helps the commercial bankers organising his time in order to optimise the commercial one.

The role of commercial bankers is becoming more and more structured, in order to permit the appropriateness among the different distribution channels, which are all in the service of clients. Parallel to the office, today there are a set of externalised distribution channels2 , which allow clients to realise simple operations that have no real added value for the bank.

Facing such a notable evolution of the profession, we wonder if all the present and future salespeople will be able to follow these changes. The introduction of a segmentation of salespeople based on their time management can particularly be relevant in this new context of work in a banking office. A monochronic individual is in the habit of structuring time; consequently, using a diary and respecting a program should be relatively easy for him. On the contrary, for a polychronic individual, this new situation may be uncomfortable, as he does not perceive the necessity of structuring his time. We make the supposition that these different ways to deal with time will have consequences on the results of these two types of salespeople. Forcing a polychronic salesman to use a diary should have contradictory effects than those expected; it would entail some losses of efficiency in the exercise of his role and it would conduct to deterioration in his commercial performance. The adjustment is only possible at the level of the office. We can imagine this situation: the team manager would identify the temporal profile of his colleagues; then he should be able to determine which ones need to be supervised or even trained to the use of time management tools. He could also take the temporal nature of each salesman into account when he fixes their objectives (of product sales, of programmed or spontaneous interviews realisation, etc.). Such a study can even be conducted for the manager. Anyway, considering the diversity of tasks he has to do, the unexpected prompting he has and his degree of responsibility, he is highly incited to adopt a polychronic management of his role.

All these reflections justify the elaboration of a research project, in order to establish their accuracy.

OUR RESEARCH PROJECT IN THE BANKING AREA

THE INTEREST OF SUCH A RESEARCH

The object of our research can be synthesised with these words: Is time management of salespeople and managers an explicative factor for the gap observed between the role assigned by the firm and the role they take on?

The problematic of time has been the subject of only few research works in organisational marketing.

The major questions raised dealt with the way temporal aspects could be integrated into strategic choices [START_REF] George | The Role of Time in Theory and Theory Building[END_REF][START_REF] Mosakowski | A Selective Review of Time Assumptions in Strategy Research[END_REF], with the effect of temporal perspective on work motivation [START_REF] Seijts | The Importance of Future Time Perspective in Theories of Work Motivation[END_REF], or even with the influences of an individual management and perspective of time on his perception of terms. Considering time management, Bluedorn, [START_REF] Bluedorn | How Many Things Do You Like to Do at Once? An Introduction to Monochronic and Polychronic Time[END_REF] made an interesting contribution to the area of management. From studies conducted on the use of polychronic time, these researchers showed that, on a managerial plane, the distinction between the concepts of polychronism and monochronism has important implications upon behaviour and action at three levels.

First, at the level of personal management of time, asking a polychronic individual to focus his attention on a single activity is more difficult than it is for a monochronic individual. Consequently, these personal differences must be taken into account to manage people and to help them organise their time efficiently. At the level of supervision and coordination, we wonder which the best combination is in a sales team, when there are monochronic and polychronic individuals, or even the best binomial to do between a salesman and his manager. For example, with the concept of "time urgency", Waller and alii (2001) showed that inside a team, monochronic and polychronic individuals do not consider terms in the same way, so that it causes tensions, it perverts perceptions of the work capacity of colleagues, and other forms of dysfunction.

Finally, at the level of cultural diversity, it is necessary to understand temporal concepts like monochronic or polychronic orientation, as they are understood by differently cultural groups, in order to avoid misunderstandings and conflicts. Using monochronic or polychronic time is one of the major distinctive factors among cultures. If salespeople from diverse cultures and traditions understand these differences or even understand that they exist, then the conflicts linked to polychronicity and other temporal differences could be managed more efficiently by the manager.

We have seen that the problematic of role has even been the subject of diverse works, on the basis of Katz and Kahn's role model, and that a form of duality of role perception appears between company managers, focused on the organisational structure functioning, and their employees, who try to satisfy their numerous expectations. Important role stress may result from such a situation. For a lot of professionals, the exercise of their role in the firm is not as obvious as it seems to be. Between the standing arbitration among his aspirations and the constraints he meets, which priorities has to adopt a salaried employee in order to act? While a lot of people around them express expectations that are easily contradictory to their, individuals finally try to translate their role into behaviours and into activities that are compatible with their self perception of what must be a daily capable and efficient professional. Nevertheless, concerning managers or salespeople, we observe that the role they exercise takes more after a multitude of unexpected tasks, which follow one another often in emergency, than after a real anticipation of the role to be taken (Rizzo and alii, 1970;Churchill and alii, 1976;[START_REF] Teas | Supervisory Behavior, Role Stress, and the Job Satisfaction in Industrial Salespeople[END_REF][START_REF] Mintzberg | Le manager au quotidien ; les dix rôles du cadre[END_REF][START_REF] Hales | What Do Managers Do? A Critical Review of the Evidence[END_REF][START_REF] Rich | The Sales Manager as a Role Model: Effects on Trust, Job Satisfaction, and Performance of Salespeople[END_REF][START_REF] Courpasson | Transformation des identités managériales dans le secteur bancaire, Le devenir de l'encadrement intermédiaire[END_REF][START_REF] Dumoulin | Rôles managériaux et contrôle. Explicitation des rôles dans la ligne hiérarchique du réseau d'une entreprise de service[END_REF]etc.).

To date, no previous research tried to integrate these two concepts of time and role, and to see how the attitude of salespeople or managers toward time influences their way of imagining and of playing their role. It is the study we propose to conduct, based on the sales human resources of banking networks.

THE RESEARCH METHODOLOGY

The work unit of our research is the bank office, which is the commercial team composed of the director, the commercial bankers and possibly other colleagues. On the one hand, the study should allow identifying and measuring the gaps that exist between the prescribed role, assigned by managers, and the role exercised by commercial bankers. We will carry out the same analysis with their managers. On the other hand, we aim at defining the temporal profile (i.e. monochronic vs. polychronic) of salespeople and of managers. Then, we should be able to bring out the more significant deviations of role, as the links they have with weakness in commercial performance.

Thanks to the study, we will show to which extent temporal profile is an explanatory factor of such gaps in role and in performance. For example, is the distance of role higher when a manager and a salesman have different temporal profiles?

Two major measuring scales will be used in the research; the first one will evaluate the actors' time perception and the second will evaluate their perception of role. The scale of time perception is the aggregation of different items related to each dimension of the concept. The items are often stemming from studies conducted on one or more dimensions of time. In the research, we will use the "time styles" scale of [START_REF] Usunier | Construction d'une échelle de perception du temps : résultats préliminaires, 7 ème Séminaire John-Labatt de Recherche en Marketing[END_REF]. Since the beginning, this tool has been developed in a transcultural perspective. It presents two major advantages in relation to other multidimensional scales, which make it interdisciplinary and give it a relatively good validity. First, the scale of Usunier and Valette-Florence emphasises the perception of temporal dimensions described at once by anthropologists and by psychologists in an experimental way (Kluckhohn and Strodtbeck, 1961;[START_REF] Calabresi | Personality and Time Attitudes[END_REF]Hall, 1961[START_REF] Hall | La dimension cachée[END_REF][START_REF] Hall | La danse de la vie, temps culturel, temps vécu[END_REF]. Second, this measuring tool was constructed from many scales with different national origins (American, Australian, French, Brazilian, Swedish and Arab). In fact, the research was initiated from five major studies and a 180 items base. The scale of Usunier and Valette-Florence is now considered by a lot of authors like one of the most complete ones. It has been used many times [START_REF] Djlassi | Test d'une échelle de mesure de la perception du temps (Usunier et Valette-Florence 1991[END_REF]Durrande-Moreau, 1994;[START_REF] Valette-Florence | Comparaison des systèmes de valeurs et des styles de temps : une étude exploratoire[END_REF], so that it relativizes one of its major limits stated by the authors themselves: the fact it lies on a single sample.

As we have not found an instrument adapted to our problematic and to the professions we study, the scale that will be used to measure salespeople role perceptions is based on that one we have developed in our previous works on sales managers' role. It makes an inventory of a selection of tasks considered to be essential for the exercise of this role, succeeding a detailed work of qualitative research. We are at the moment constructing the same type of instrument for commercial bankers, which constitute our major studied population.

In the first part of the study, focused on commercial bankers, we will initially interview a set of experts from many banks: salespeople, offices managers, sales directors, etc. Then, we will constitute a sample of about 400 salespeople, divided up among the main existing banks. Thanks to this process, we will have a global perspective of the developed problematic and of the answers collected.

IMPLICATIONS OF THE RESEARCH FOR NETWORK BANKS

If the research we undertake establishes the existence of a link between managers and salespeople temporal profile and the gaps of role observed, it will have implications at two levels of the financial institution: at the level of the commercial team composition and at the level of management. The final objective of our research is to improve the constitution of successful teams in bank offices, because these ones are the main places for meeting clients. For example, if we observe that a monochronic manager works better with commercial bankers who have the same temporal profile, perhaps would it be a good idea to reorganise the offices commercial team according to this criteria. It would be all the easier since banks regularly organise a "rotation" of their salespeople.

For many reasons, in a rural zone for example, such a commercial reorganisation would be difficult to set. In this case, it will be advisable to act at the level of human management; for example, it could consist of constructing training programs intended for offices managers to help them manage monochronic and polychronic individuals. Moreover, management tools may be adapted, in order to take into account the colleague's dominant style, in terms of time management and of commercial actions.

CONCLUSION

The traditional job of commercial bankers has drastically changed with the passing years, in particular because of the introduction of externalised channels in the banking distribution (ATM, call centres, the Internet, etc.). If the number of contacts between banks and clients has increased due to the use of these new technological possibilities, the number of contacts made in the office has decreased. Yet, the role of the office and of the commercial counsellor remains essential when it is to deal with complicated questions, like the subscription of a life assurance or of a loan. Experts announce that in next years we should witness a grouping of the different channels round the office activity; they will be complementary rather than a substitute for work done by counsellors. The office manager will have a position of conductor, repositioned in the centre of the relation with clients. Consequently, it is essential to improve the performance of sales teams. According to us, this implies the reduction of gaps that exist at the moment both in salespeople' and managers' roles. The research we are going to undertake in the banking area will not only bring to the fore such gaps, but also role stress and decreases in performance, resulting from that.

At this level, we postulate that taking into account time management of professionals from sales forces would allow handling this problem. Our more completed objective is to contribute constituting more successful sales teams in bank offices.

For developments, cf. Brassier P., AGRH,

These externalised distribution channels are, for example, ATM (Automatic Teller Machines), the Internet, call centres, mobile phones, etc.

Each task is classified according to its hierarchy of priority, measured by its average score compared with a base 100. The closer the note is to 100, the more the task is important. They are also classified in four management functions, Leadership (L), Sales (S), Administration (A) and Supervision (Su).

Graphs and Tables


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R Dumas

IMU-based Sensor-to-Segment Multiple Calibration for Upper Limb Joint Angle Measurement -A proof of concept

Keywords: Joint angle, IMU measurement, Posture, Calibration, Soft-tissue artifact

A lot of attention has been paid to wearable inertial sensors regarded as an alternative solution for outdoor human motion tracking. Relevant joint angles can only be calculated from anatomical orientations, but they are negatively impacted by soft tissue artifact (STA) defined as skin motion with respect to the underlying bone; the accuracy of measured joint angle during movement, is affected by the ongoing misalignment of the sensor. In this work, a new sensor-to-segment calibration using IMUs is proposed. Inspired by the multiple calibration for a cluster of skin markers, it consists in performing first multiple static postures of the upper limb in all anatomical planes. The movements that affect sensors alignment are identified then alignment differences between sensors and segment frames are calculated for each posture and linearly interpoled. Experimental measurements were carried out on a mechanical model and on a subject who performed different movements of right elbow and shoulder.

Multiple calibration showed significant improvement in joint angle measurement on the mechanical model as well as on human joint angle comparing to those obtained from attached sensors after technical calibration. During shoulder internal-external rotation, the maximal error value decreased more than 50% after correction.

Nomenclature

: Segment i orientation at neutral posture 0 : Sensor i frame orientation at neutral posture 0 : Rotation of IMU1 at posture 0 to align with gravity : Segment i orientation at posture j : Sensor i orientation at Posture j : 90°-rotation about a given axis of the segment i at posture j : Alignment difference between and

, : Mean value of all alignment differences j i q ~calculated for each segment i at all postures j resulting either from the rotation of the joint angle =0° or 90° about the axis u and presenting the same segment frame orientation.

: Alignment correction during movement and obtained by linear interpolation Several non-invasive technologies can be used to assess human joint angles such as electrogoniometers [START_REF] Rowe | Validation of flexible electrogoniometry as a measure of joint kinematics[END_REF], inertial measurement units IMUs [START_REF] Alvarez | Upper limb joint angle measurement in occupational health[END_REF][START_REF] Robert-Lachaine | Validation of inertial measurement units with an optoelectronic system for whole-body motion analysis[END_REF][START_REF] Bouvier | Upper Limb Kinecmatics Using Inertial and Magnetic Sensors: Comparaison of Sensor-to-Segment Calibrations[END_REF][START_REF] Bolink | Validity of an inertial measurement unit to assess pelvic orientation angles during gait, sit-stand transfers, and step-up transfers: Comparison with an optoelectronic motion capture system[END_REF] and optical motion capture system (OMCS) system [START_REF] Cappozzo | Human movement analysis using stereophotogrammetry Part1 : theorical background[END_REF][START_REF] Cappello | Multiple anatomical landmark calibration for optimal bone pose estimation[END_REF] considered as gold-standard. From a practical point of view, OMCS system cannot be easily used for daily rehabilitation activities because of the cumbersome protocol and calibration procedure, limited working space, and so on. OMCS system is typically used in the laboratory to evaluate the accuracy of other (ambulatory) measurement systems [START_REF] Robert-Lachaine | Validation of inertial measurement units with an optoelectronic system for whole-body motion analysis[END_REF][START_REF] Bolink | Validity of an inertial measurement unit to assess pelvic orientation angles during gait, sit-stand transfers, and step-up transfers: Comparison with an optoelectronic motion capture system[END_REF].

Significant attention has been paid to IMUs regarded as alternative tools for human motion tracking which can provide low-cost ambulatory measurements and easy set up compared to OMCS. When using these motion tracking technologies to estimate human joint angles, two sources of errors can appear and affect measurement correctness. The first one is related to the measurement system itself [START_REF] Qureshi | An algorithm for the in field calibration of a MEMS IMU[END_REF][START_REF] Kopacik | Systematic Error Elimination Using Additive Measurements and Combination of Two Low Cost[END_REF] while the other results from the sensors misalignment with respect to human segments [START_REF] Bouvier | Upper Limb Kinecmatics Using Inertial and Magnetic Sensors: Comparaison of Sensor-to-Segment Calibrations[END_REF][START_REF] Cutti | Ambulatory measurement of shoulder and elbow kinematics through inertial and magnetic sensors[END_REF][START_REF] Vargas-Valencia | An IMU-to-Body Alignment Method Applied to Human Gait Analysis[END_REF][START_REF] De Vries | Functionally interpretable local coordinate systems for the upper extremity using inertial & magnetic measurement systems[END_REF][START_REF] Robert-Lachaine | Accuracy and repeatability of single-pose calibration of inertial measurement units for whole-body motion[END_REF][START_REF] Lach | Evaluation of Automatic Calibration Method for Motion Tracking Using Magnetic and Inertial Sensors[END_REF]. What is more, the sensor misalignment is changing during the movement due to soft tissue artifact (STA) [START_REF] Cappello | Multiple anatomical landmark calibration for optimal bone pose estimation[END_REF][START_REF] Camomilla | A model of the soft tissue artefact rigid component[END_REF][START_REF] Blache | Main component of soft tissue artifact of the upper-limbs with respect to different functional, daily life and sports movements[END_REF][START_REF] Cutti | In vivo validation of a new technique that compensates for soft tissue artefact in the upper-arm: Preleminary results[END_REF][START_REF] Cutti | Soft tissue artefact assessment in humeral axial rotation[END_REF][START_REF] Cappello | Soft Tissue Artifact Compensation in Knee Kinematics by Double Anatomical Landmark Calibration: Performance of a Novel Method During Selected Motor Tasks[END_REF]. STA is defined in the literature as the skin motion relative to the underlying bone [START_REF] Cappello | Multiple anatomical landmark calibration for optimal bone pose estimation[END_REF][START_REF] Meng | Accuracy Improvement on the Measurement of Human-Joint Angles[END_REF] and is regarded as a major source of error that disrupts the estimation of joint angles when non-invasive measurement systems are used [START_REF] Camomilla | Human movement analysis: The soft tissue artefact issue[END_REF]. In OMCS measurements, STA results in markers cluster shape deformation as well as, predominantly, maker-cluster rotation and translation with respect to the underlying bone. Several papers have been reported in the literature on how to compensate STA effects to improve the accuracy of joint angles measurements. A multiple calibration procedure was proposed to model OMCS marker-cluster deformation between a set of calibration postures in knee flexion/extension [START_REF] Cappello | Multiple anatomical landmark calibration for optimal bone pose estimation[END_REF][START_REF] Cappello | Soft Tissue Artifact Compensation in Knee Kinematics by Double Anatomical Landmark Calibration: Performance of a Novel Method During Selected Motor Tasks[END_REF] or scapular movement [START_REF] Brochard | Double calibration: An accurate, reliable and easy-to-use method for 3D scapular motion analysis[END_REF]. Typically, in double calibration, the alignment difference is assessed for two calibration postures. A linear interpolation in time is implemented on the position of anatomical landmarks in the technical frame [START_REF] Cappello | Multiple anatomical landmark calibration for optimal bone pose estimation[END_REF][START_REF] Brochard | Double calibration: An accurate, reliable and easy-to-use method for 3D scapular motion analysis[END_REF]. STA was defined in [START_REF] Camomilla | A model of the soft tissue artefact rigid component[END_REF] as a series of rigid geometrical transformations and a dynamic calibration based on an ad hoc model was applied. The compensation of STA effects related to skin-mounted markers placed on upper or lower limb has been extensively studied in the literature, and some efficiency has been proved when using multiple calibration of the clusters of markers [START_REF] Cappello | Multiple anatomical landmark calibration for optimal bone pose estimation[END_REF][START_REF] Cutti | In vivo validation of a new technique that compensates for soft tissue artefact in the upper-arm: Preleminary results[END_REF][START_REF] Cappello | Soft Tissue Artifact Compensation in Knee Kinematics by Double Anatomical Landmark Calibration: Performance of a Novel Method During Selected Motor Tasks[END_REF][START_REF] Brochard | Double calibration: An accurate, reliable and easy-to-use method for 3D scapular motion analysis[END_REF]. As for OMCS, IMU calibration procedure consists in establishing a relation between the sensor frame and the segment frame related to the underlying bone [2-4, 20, 23-30]. This procedure named "sensor-to-segment calibration" can either be one-axis [START_REF] Ligorio | A novel functional calibration method for real-time elbow joint angles estimation with magnetic-inertial sensors[END_REF] or three-axis calibration [START_REF] Alvarez | Upper limb joint angle measurement in occupational health[END_REF][START_REF] Robert-Lachaine | Validation of inertial measurement units with an optoelectronic system for whole-body motion analysis[END_REF][START_REF] Bouvier | Upper Limb Kinecmatics Using Inertial and Magnetic Sensors: Comparaison of Sensor-to-Segment Calibrations[END_REF][START_REF] Cutti | Ambulatory measurement of shoulder and elbow kinematics through inertial and magnetic sensors[END_REF]. Generally, static calibration is performed by asking the subject to maintain postures in order to establish the relation between the sensor and the segment frames. In the case of IMU-calibration, the alignment difference between the sensor frame and the segment frame was supposed constant in time. This is a classical assumption made in most studies on sensor-to-segment calibration. In the case of joint angle measurement by IMUs, two adjustments based on the mean misalignment were proposed by Meng et al. [START_REF] Meng | Accuracy Improvement on the Measurement of Human-Joint Angles[END_REF] with multiple static postures related to five active movements such that only one angle was varied per movement. It is important to keep in mind that they combined both IMU and OMCS to get a statistics of the alignment difference. The latter was not modeled individually but in average using a linear regression of data collected from fifteen participants including the body fat percentage. They obtained values less than 1° for mean error, RMSE and SD after adjustments. A multiple calibration method that do not refer to OMCS is yet to be developed for IMUs.

In this paper, an IMU-based sensor-to-segment calibration referred to as multiple calibration for upper limb joint angle measurement is proposed to take into account the variation of the misalignment between sensor and segment. It consists in performing multiple static postures during the calibration session. The movements that affect IMUs alignment (i.e. sensor frame orientation vs. segment frame orientation) are identified by calculating the alignment differences at the two joint angles (0° and 90°)

for each joint axis of movement. Then, linear or bilinear interpolation is applied between this two alignment differences to assess this difference during the movement. To the author's knowledge, such a method of misalignment compensation has not been reported in the literature. In the following, Section 2 introduces first the calibration postures and the method of calculation and correction of the misalignment between segment and IMU orientations. Section 3 presents the results of the tests performed on mechanical model and on human right upper limb. A discussion of the achieved results is provided in Section 4. Finally, Section 5 draws conclusions.

Materials and Methods

Four IMUs are placed on the right upper limb and the thorax as shown in Fig. 1. A so-called technical calibration [START_REF] Bouvier | Upper Limb Kinecmatics Using Inertial and Magnetic Sensors: Comparaison of Sensor-to-Segment Calibrations[END_REF] is first performed by adjusting manually IMUs positions in order to visually align their local frames with the associated segment anatomical frames. Then, static calibration is achieved at several predefined static postures.

Calibration postures

Twenty-one static predefined postures were selected in the proposed multiple calibration procedure.

Starting from the anatomical posture presented in Fig. 1, the subject has to perform the other twenty static postures illustrated in Fig. 2. These postures were selected in order to cover simple anatomical upper limb joints movements such as flexion/extension (FE), adduction/abduction (AA), and internal/external rotation (IER) in the three anatomical planes or any combination of them.

FIGURE 1 HERE FIGURE 2 HERE

The calibration postures illustrated in Fig. 2 are the results of either 0°-rotation or 90°-rotation of distal segment with respect to a proximal segment of the right upper limb. It is much easier for a subject to perform rotations of 0 or 90 degrees than any other prescribed joint angles values. In this work, the joint angles are supposed to remain 0° or vary by 90°, and the calibration postures are only be considered at these two rotation angle values during the calibration session.

Initial alignment and Alignment differences

Both segment and IMUs frame orientations must be defined at each one of the proposed calibration postures of Fig. 2. In this paper, quaternion representation was used to describe the orientations.

The IMUs frames as well as segment frames of the upper limb and the thorax in neutral posture are shown in Fig. 3a andb. In this work, the quaternions q and p are related to the IMUs frames orientations and segment frames orientations, respectively. In a first stage, considering the technical calibration [START_REF] Bouvier | Upper Limb Kinecmatics Using Inertial and Magnetic Sensors: Comparaison of Sensor-to-Segment Calibrations[END_REF] established during the neutral posture 0, the orientations of both sensors and segments frames are assumed to be aligned, except for the thorax. For this segment, the gravity axis is used to re-aligne the vertical axis of the sensor:

0 i 0 i q p 
for i=2,3,4 and

0 1 0 1 0 1 q q p  for i = 1 (1)
with 0 i p (i from 1 to 4 for thorax to hand) the segment frame orientation and 0 1 q the sensor frame orientation in posture 0. The quaternion 0 1 q ~ represents rotation of IMU1 at posture 0 illustrated in Fig. 3a that transforms the IMU1 frame orientation so that it coincides with the thorax frame in Fig. 3b.

In the posture 0, after this calibration, all the segment definitions are expected to follow, at best, ISB recommendations [START_REF] Wu | ISB recommendation on definitions of joint coordinate systems of various joints for the reporting of human joint motion-Part II: shoulder, elbow, wrist and hand[END_REF]. The right-arm and thorax segment frames have their X, Y and Z axes pointing forward, upward and to the right, respectively. .

0 1 j i j i p p p  (2)
The subscript i (from 2 to 4) corresponds to upper limb segments while the superscript j represents the different calibration postures (from 1 to 21).The segment orientations corresponding to all the calibration postures are obtained using a similar procedure. At the end of the calibration session, two kinds of upper limb segment frame orientations are gotten, i.e., the calibrated orientations j i p deduced from thorax frame orientation and the directly measured orientations j i q estimated from the IMUs.

Due to STA, the calibrated and directly measured orientation are not identical, so the alignment difference j i q ~between j i q and j i p can be calculated for each segment involved in a calibration posture. The alignment difference j i q ~ related to a given calibration posture j is defined by

j i * j i j i q p q  ~ (3) with j i * q
is the quaternion conjugate of the quaternion .

j i q 2.3.

Correction of IMU frame orientation

For a given segment i, the same segment frame orientation j i p may be present in more than one posture j, so the alignment difference related to that specific segment will be the mean value of all alignment differences j i q ~calculated at all postures presenting the same segment frame orientation.

n q n j j i   1 , i q ~ u (4)
with n the number of postures presenting the same segment frame orientation. These postures result from either = 0° or = 90° rotation about one axis of the thorax frame. Thus, for each joint rotation axis u, and each of these rotations, a mean alignment difference is computed. Moreover, for each movement about a joint axis u, 0 , i u q and 0 9 , i u q correspond to the average alignment difference values calculated when joint angle  is equal to 0° and 90°, respectively. For example, in elbow FE movement about the axis u = Z aU , the alignment difference value 0 , i u q for the elbow fully extended ( = 0°) is taken as the mean value of the alignment difference values related to the five postures 1, 2, 3, 20 and 21 shown in Fig. 2 and obtained using Eq. ( 4). In the same way, the alignment difference value Linear interpolation is applied between 0 , i u q and 0 9 , i u q and the alignment difference value u ~i q ( ) during the movement is given by

  . ) ( ~u, u, u, u 90 0 90 0 i i i i q q q q    (5)
Therefore, the segment frame orientation i p of the segment i is computed from the IMU frame orientation i q corrected by the alignment difference

) ( ~u  i q
obtained from the proposed multiple calibration. The corrected segment frame orientation i p is related to i q according to the Eq. ( 6).

i i i q q p ) ( ~ u  (6)
with  the joint angle obtained about axis u after technical calibration (i.e., computed from i q ).

The joint angles were finally computed following the ISB convention [START_REF] Wu | ISB recommendation on definitions of joint coordinate systems of various joints for the reporting of human joint motion-Part II: shoulder, elbow, wrist and hand[END_REF] considering the relative movement of the distal segment with respect to the proximal segment. The YZY sequence is used to estimate shoulder joint angles while the ZXY sequence is used for elbow. In other words, shoulder IER corresponds to u = Y aU and elbow FE and PS correspond to u = Z aU and u = Y aF , respectively.

In case the alignment difference u ~i q depends on the variation of both two joint angles  1 and  2 , bilinear instead of linear interpolation is applied; the related alignment difference is expressed by:

, θ , θ , , , , , , . θ , , , , , , . θ , , , , , , , , , , , , . . θ . θ
, , ,

2.4.

Validation of the multiple calibration method

To test the multiple calibration method, four wireless sensor nodes SN have been designed to measure the right upper limb joint angles. Each SN is composed of a System in Package BNO055 from Bosch company integrating an IMU consisted of a triaxial 14-bit accelerometer with ranges switchable from ±2g to ±16g, a triaxial 16-bit gyroscope with ranges switchable from ±125°/s to ±2000°/s and a triaxial geomagnetic sensor which can detect ±1300µT in X and Y axes while up to ±2500µT in Z axis with a magnetic resolution around 0.3µT. A 32-bit microcontroller running the sensor fusion software is also integrated. The circuit BNO055 was configured in the fusion mode such that it provided absolute orientation, i.e., sensor orientation with respect to earth coordinate system. Compared to two other typical consumer-grade attitude and heading reference systems (AHRS) (MPU-9150 from InvenSense, X-NUCLEO-1KS01A1 from STMicroelectronics), it displayed the best static and dynamic performances. Attitude measurement obtained from BNO055 showed accuracy of 1.4°, 0.8° and 4.6°

for roll, pitch and yaw, respectively [START_REF] Lin | An Experimental Performance Evaluation of the Orientation Accuracy of Four Nine-Axis MEMS Motion Sensors[END_REF].

An ATmega328 controller was also used first to acquire data from sensors through the I 2 C serial bus then to communicate with an NRF2401 wireless transmission module. The emitting nodes share the same receiving node which ensures data transmission to PC (See Fig. 4). Another possibility consists in using a System on Chip SoC which integrates in the same module the microcontroller and the wireless transceiver, e.g., ESP32s series from Espressif Inc. (single or dual-core module with Wi-Fi & dual-mode Blutooth).

FIGURE 4 HERE

As a proof-of-concept, an upper limb mechanical model composed of three adjacent rigid body segments was designed to test the proposed method under controlled conditions. The upper arm segment is linked to a fixed body through a 3-DoF joint (shoulder) at one end and to the forearm segment through a 2-DoF joint (elbow) at the other end. Elbow FE is obtained by means of a hinge joint whereas two pipes (white and grey on Fig. 5a) with two different diameters were used in the forearm segment to ensure the second DoF movement (pronation-supination PS). Another hinge joint (wrist) is used to link the forearm and the hand segments. A magnetic rotary encoder (0.08° resolution), taken as a reference, was also placed at the elbow joint to measure elbow FE angle and transmit wirelessly the data via an NRF2401 module.

FIGURE 5 HERE

Three sensor nodes SN1, SN3 and SN4 were attached with a double-sided tape to the upper arm, forearm and hand segments axes respectively as illustrated in fig 5b. They were placed so as their long axes were parallel to the segments axes. The fourth one, i.e., SN2 was also attached with a double-sided tape to a 5 mL plastic syringe whose one extremity was attached to the upper arm and the other extremity to the forearm segment via a rod. Initially, when the elbow is fully extended, the piston is parallel to the upper arm segment, so SN2 is aligned with SN1. As soon as the elbow is flexed, the piston induces a misalignment of SN2 (See Fig. 5b) that increases gradually with respect to SN1 till elbow joint reaches 90°. The piston ensures a controlled and repeatable misalignment of SN2 with respect to the upper arm segment. The proposed calibration method was applied to elbow FE between 0° and 90°. SN1 was used during the calibration session to get the upper arm segment orientation without misalignment. The joint angle was obtained from SN2 and SN3 data. Once the calibration postures achieved, the alignment differences j i q ~were calculated between SN1 and SN2 orientations for each posture presented in Fig. 2.

Since elbow flexion disturbed only the SN2 alignment with respect to the upper arm segment, a linear interpolation was applied to correct the orientation of the upper arm segment.

Right upper limb joint angle measures

For a more realistic evaluation of the method, experimental measures have been carried out on a healthy male subject (age: 27 years, height: 175cm, mass: 65 kg). Four SNs were attached on the right upper limb segments as illustrated on the photograph of Fig. 6.

FIGURE 6 HERE

One sensor node was attached on the subject torso and three others on the right upper limb using elastic bracelets. SN placements shown in Fig. 6 are the same as the IMU sensors used in [START_REF] Bouvier | Upper Limb Kinecmatics Using Inertial and Magnetic Sensors: Comparaison of Sensor-to-Segment Calibrations[END_REF]. SN1 was placed on the flat part of the sternum, and SN2 and SN3 were respectively attached to the outer side of the arm and near to the wrist on the forearm. SN4 was fixed dorsally on the hand. The technical calibration was performed by adjusting manually SNs positions in order to visually align their local frames with the associated segment anatomical frames. The subject was asked to successively perform the 21 calibration postures in the same way as presented in Fig. 2. The correctness of each posture is checked by an operator before executing to the next one. The subject remained static during several seconds and a calibration session duration did not exceed five minutes. OMCS system based on four Bonita infrared cameras from Vicon was used as a reference system; this system can provide precision down to 0.5mm of translation and 0.5° of rotation using 9mm markers. Reflective markers were placed on anatomical landmarks according to the methodology of Cooper et al. [START_REF] Cooper | Glenohumeral joint kinematics and kinetics for three coordinate system representing during wheelchair propulsion[END_REF]. Both of SNs and video systems were synchronized and operated at a sampling rate of 50Hz. The subject in the neutral position was instructed to achieve three different movements not fastly (average angular speed around 60°/s): (i) forearm PS when elbow is 90° flexed in the sagittal plane; (ii) maximum elbow FE in the sagittal plane; (iii) Shoulder internal external-rotation IER in the horizontal plane when the elbow is 90° flexed in the sagittal plane.

Results

Three-linked rigid segment body

Several elbow FE movements have been carried out on the three-linked rigid segment body representing the upper arm, the forearm and the hand. Elbow FE angle versus time before and after calibration is depicted in Fig. 7. The reference angle from the magnetic encoder is also represented on the same figure in black dashed line. The bottom curves plotted in red dashed and blue solid lines refer to the error value between the angles deduced from SNs and those gotten from the encoder before and after calibration, respectively. Initially, the three SNs were aligned with the body's segments, so the joint angles values from IMUs and the reference system were the same and equal to zero. As the elbow flexion angle value increases, the alignment error raises gradually to reach a maximal value of 20.7° when the elbow is 90° flexed with a root mean square error RMSE equal to 8.3°. After correction, both the maximal error value and RMSE decreased to 6.1°and 2.2° respectively.

Correction of the forearm pronation-supination movement

The subject performed several forearm PS when the elbow is 90°-flexed with SNs placed as illustrated in Fig. 6. Fig. 9 shows elbow joint angle during forearm PS as a function of time from both SNs and optical systems. Black dashed line curve is obtained from OMCS system while the red dashed line curve corresponds to angle data from SN3 with respect to SN2. It can be noticed that SN3 joint angle is almost the same as the reference angle from OMCS system with a mean error value equal to 1.0° and max error value of 2°. Still, the correction of the forearm PS can be useful if another placement of the SN is adopted (see Supplementary Material). Whatever the placement of the SN on the forearm, it can be noticed that the errors at the beginning and ending of the movement are tending to zero demonstrating initially aligned IMUs in the upper arm and forearm segments.

FIGURE 9 HERE

Correction of the maximum elbow FE movement

The subject was asked to perform successive cycles of maximum right elbow FE (range of motion equal to 140°) and FE angle was measured simultaneously with SNs and the optical reference system.

FIGURE 11 HERE

Error up to 30° was obtained before correction with a mean value of 8° (SD=11°). After correction, the error was reduced to less than 15° with a mean value equal to 3° (SD=7°). Again, it can be noticed that the errors at the beginning and ending of the movement are tending to zero demonstrating initially aligned IMUs in the thorax and upper arm segments.

Discussion

The proposed compensation method is based on a multiple sensor-to-segment calibration. It is assumed that the alignment between sensor and segment is impacted by the joint movement. Twenty-one predefined static postures are necessary to study the misalignment -non constant in time-for the all of the shoulder, elbow and wrist joints movements with a calibration session not exceeding five minutes.

This number of static predefined postures could be cumbersome in a clinical context. If only one joint is studied at the time, the number of postures can be highly reduced (to two) as it was the case for the application on the mechanical model (see Fig. 5). The purpose of displaying the 21 postures is to allow the reader to pick the ones of interest for its own research.

Concerning the alignment differences during the multiple calibration, the IMUs placed on the upper limb are not impacted in the same way according to the different joint orientations. SN4 alignment is significantly modified by wrist FE, SN3 by elbow FE or forearm PS, and SN2 by elbow FE as well as shoulder IER. The impact of the elbow FE and shoulder IER on the movement of skin markers was already reported in the literature [START_REF] Cutti | Soft tissue artefact assessment in humeral axial rotation[END_REF][START_REF] Cao | Compensation for the Effect of Soft Tissue Artefact on Humeral Axial Rotation Angle[END_REF]. This observation justifies the use of an interpolation based on joint angles for the correction of the IMU frame orientation. Few studies have quantified the STA on the upper limb using bone pins or fluoroscopy [START_REF] Cereatti | Standardization proposal of soft tissue artefact description for data sharing in human motion measurements[END_REF]. Skin markers placed on the humerus can undergo a displacement up to 4 cm with respect to the bone during arm abduction. The main movement pattern of the marker displacement is also a rotation of the marker cluster [START_REF] Blache | Main component of soft tissue artifact of the upper-limbs with respect to different functional, daily life and sports movements[END_REF] which implicates potential large errors when IMUs are used. As a matter of fact, in the present study, the differences of IMU alignment reached 53° for the upper arm.

Concerning the correction of the IMU frame orientation, the tests performed on the upper limb mechanical model confirmed the feasibility and efficiency of the proposed method to compensate for an ongoing misalignment when IMUs were initially aligned.

The graphs corresponding to the subject movements of forearm PS, elbow FE and shoulder IER revealed two results relative to the IMUs. First, a good initial alignment has been achieved with the technical calibration during the calibration session as reported in the literature [START_REF] Bouvier | Upper Limb Kinecmatics Using Inertial and Magnetic Sensors: Comparaison of Sensor-to-Segment Calibrations[END_REF][START_REF] Cutti | Ambulatory measurement of shoulder and elbow kinematics through inertial and magnetic sensors[END_REF]. However, other types of calibration such as anatomical calibration may be considered [START_REF] Cappello | Soft Tissue Artifact Compensation in Knee Kinematics by Double Anatomical Landmark Calibration: Performance of a Novel Method During Selected Motor Tasks[END_REF][START_REF] Donati | Enhanced anatomical calibration in human movement analysis[END_REF][START_REF] Picerno | Joint kinematics estimate using wearable inertial and magnetic sensing modules[END_REF]. Second, a correct placement of SN3 on the forearm is important as this sensor can provide an accurate elbow PS measurement without correction. However, with SN3 placed far from the wrist, when compared to the data obtained from the optical OMCS system, maximal alignment error values up to 30° are reached during the forearm PS. Elbow FE angle has been measured on the mechanical upper arm as well as on a subject.

FE angle values obtained from the multiple calibration are somehow underestimated in the former case while they are slightly overestimated in the second case. These effects may be due to an error associated with the segment placement at 0° or 90° during the calibration session. Results accuracy estimated as RMSE for elbow FE and PS were found to be equal to 4°. This value is significantly lower than those reported in the literature from static calibration with misalignment constant in time (11° RMSE  24°) [START_REF] Bouvier | Upper Limb Kinecmatics Using Inertial and Magnetic Sensors: Comparaison of Sensor-to-Segment Calibrations[END_REF].The maximal error value for shoulder IER initially equal to 30° confirms that this movement is the most affected by STA. Such a result is consistent with the value of the parameter K defined by Cutti et al. [START_REF] Cutti | Soft tissue artefact assessment in humeral axial rotation[END_REF] to measure STA effect on humeral internal/external rotation. This error decreased more than 50% (SD=7°) after correction. For the three movements studied, the errors were then reduced to less than 15° in maximum (less than 5° in average) for both elbow and shoulder joints after correction. The mean error value of 5° could be considered as a good result especially for shoulder's movements compared to those already reported in the literature [START_REF] Robert-Lachaine | Validation of inertial measurement units with an optoelectronic system for whole-body motion analysis[END_REF][START_REF] Bouvier | Upper Limb Kinecmatics Using Inertial and Magnetic Sensors: Comparaison of Sensor-to-Segment Calibrations[END_REF]. Low-cost consumer-grade motion sensors with quite good performances were used in this study. Better results would have been expected if industrial-grade motion sensors such as MTi-300 from Xsens Inc. which shows better orientation accuracy [START_REF] Lin | An Experimental Performance Evaluation of the Orientation Accuracy of Four Nine-Axis MEMS Motion Sensors[END_REF].

It is worth noticing that the definition of the segment axes from the OMCS system in the present work follows the methodology of Cooper et al. [START_REF] Cooper | Glenohumeral joint kinematics and kinetics for three coordinate system representing during wheelchair propulsion[END_REF] This choice was made in order to limit the number of skin marker and avoid occlusion (i.e., typically the medial epicondyle) in the different postures. It seems that with this definition of the segment axes, the technical calibration of the IMUs provides better results than previously reported in the literature [START_REF] Robert-Lachaine | Validation of inertial measurement units with an optoelectronic system for whole-body motion analysis[END_REF][START_REF] Bouvier | Upper Limb Kinecmatics Using Inertial and Magnetic Sensors: Comparaison of Sensor-to-Segment Calibrations[END_REF], as demonstrated by the limited errors values (close to zero) at the beginning and ending of the studied movements whereas RMSE was found to vary between 15.8° and 18.7° for elbow FE and PS, and up to 23.4° for shoulder IER in [START_REF] Bouvier | Upper Limb Kinecmatics Using Inertial and Magnetic Sensors: Comparaison of Sensor-to-Segment Calibrations[END_REF].

Though the misalignment correction was based on interpolation between alignment differences related to 0° and 90° joint angles, this method showed good results for intermediate values of joint angles in 0-90° range. Even if the joint angle exceeds 90° as in the maximal elbow FE, the proposed multiple calibration revealed good results by extrapolation. Quaternions rather than rotation matrices or Euler angles are more suitable for interpolation. Moreover, the interpolation is based on joint angles and it has been established that STA effect is correlated to the joint angles [START_REF] Picerno | Joint kinematics estimate using wearable inertial and magnetic sensing modules[END_REF][START_REF] Cappozzo | Position and orientation in space of bones during movement: experimental artefacts[END_REF]. In the present work, the misalignment due to STA is assumed to behave linearly during the multiple calibration. Similar assumption was proposed in a multiple anatomical landmark calibration for optimal bone pose estimation for lower limbs [START_REF] Cappello | Multiple anatomical landmark calibration for optimal bone pose estimation[END_REF]. STA behavior was fairly described by a linear model as function of the joint angles on pin-marker data and skin-marker data from lower limbs [START_REF] Camomilla | A model of the soft tissue artefact rigid component[END_REF][START_REF] Barre | Assessment of the lower limb soft tissue artefact at marker-cluster level with a high-density marker set during walking[END_REF][START_REF] Andersen | A linear soft tissue artefact model for human movement analysis: Proof of concept using in vivo data[END_REF][START_REF] Bonci | A soft tissue aretefact model driven by proximal and distal joint kinematics[END_REF]. In real time, STA is depending on the movement of the whole limb. The choice of considering only one joint angle was driven by the number of postures needed to calibrate the model. If a multi-linear model is used, more than 21 postures are required. Moreover, multi-linear STA models based on three to four joint angles for the lower limb have been proposed in the literature, but they necessitate calibration with bone pin data in order to identify the model parameters [START_REF] Camomilla | A model of the soft tissue artefact rigid component[END_REF][START_REF] Bonci | A soft tissue aretefact model driven by proximal and distal joint kinematics[END_REF]. In the method presented in this work, only linear or bi-linear interpolation is considered and the calibration is performed non-invasively with 21 postures during the calibration session. Interpolation of higher order would have necessitated additional postures.

Another possibility to compensate for the STA, yet more rarely applied to IMUs, is to introduce joint constraints and to perform a multibody kinematics optimization [START_REF] Begon | Multibody kinematics optimization for the estimation of upper and lower limb human joint kinematics[END_REF].

The present study shows some limitations: (i) the measurements were carried out on an upper limb mechanical model taken as a proof-of-concept and only on one healthy subject knowing that STA is subject and task specific [START_REF] Camomilla | Soft tissue displacement over pelvic anatomical landmarks during 3-D hip movements[END_REF]. However, it has been demonstrated that a same STA model (a linear function of the joint angle) can be calibrated on different subjects [START_REF] Camomilla | A model of the soft tissue artefact rigid component[END_REF][START_REF] Bonnet | Joint kinematics estimation using a multi-body kinematics optimisation and an extended Kalman filter, and embedding a soft tissue artefact model[END_REF]; (ii) the performance of the proposed multiple calibration has been investigated on three active movements of the upper limb during which only one angle varies. These movements are performed at low velocities which may tend to minimize the STA; (iii) the shoulder complex is simplified and the scapula movement has not been considered in this work; (iv) the STA were not measured (i.e. using bone pins or fluoroscopy) but indirectly estimated. Using the OMCS as the reference implicitly assumes that STA effects are weaker on the markers placed on the anatomical landmarks than on the IMUs orientations. This remains to be demonstrated. The differences in the IMU alignment during the calibration step rely on the postures which are assumed to represent ideal 0° or 90° joint angles. The joint angle values obtained from IMUs are then compared to those from OMCS considered as a reference. This is a standard procedure [3-5, 10, 25, 27] but the true joint angles remain unknown.

Conclusion

The multiple calibration proposed in this work is an IMU based sensor-to-segment calibration method which can be considered as an extension of the double calibration: it is applied to IMUs orientation rather than marker cluster deformation and considers two joint angles rather than only one. The proposed procedure allows for the identification of the sensor frame misalignment and of the joint axes of movement that cause it. Once identified, the sensor frame misalignments can be corrected during the movement with promising results showed in this proof-of-concept study. In future work, another study shall be undertaken on the multiple calibration of IMUs which takes into account the scapula movement and consider more complex movements performed by several subjects.

:

  Alignment correction during movement and obtained by bilinear interpolation : corrected segment frame orientation 1. Introduction

FIGURE 3 HERE

 3 FIGURE 3 HEREDuring all the calibration session, the thorax remains static and all upper limb movements are performed with respect to the thorax segment frame considered as a reference. The movements from the neutral posture (posture 0) to the postures adopted for the calibration are then interpreted as known rotation noted j i p ~ (90° about a given axis) of the segment frames with respect to the thorax. For instance, the

  elbow flexed is obtained from the mean value of the alignment difference values associated with postures 4 to 19 of the same figure.

3. 2 .

 2 Human joint angle estimation3.2.1. Alignment differences during the calibrationThe impact of each movement about the upper limb joint DoFs considered during the calibration session is investigated by computing the median, quartiles, and range of the alignment differences j i q ~ for all postures. The SN4 alignment difference varies between 4.8° and 43.5° with a mean value equal to 18°.A closer analysis revealed that the alignment difference is mainly associated with wrist FE. SN3 alignment difference varies between 4.3° and 32.5° with a mean value equal to 15.5°. The alignment difference is mostly associated with elbow FE and forearm PS. The most affected sensor node is the SN2 as presented in Fig8where alignment difference ranges from the smallest variation 3.9° to 53.8° with a mean value equal to 23.6°. The alignment difference is predominantly related to elbow FE and shoulder IER.

FIGURE 8 HERE

 8 FIGURE 8 HERE

FIGURE 10 HERE

 10 FIGURE 10 HERE

3. 2 . 4 .

 24 Correction of the Shoulder internal -external rotation movement The right shoulder IER movement was performed in the horizontal plane when the elbow joint is 90°flexed. The red dashed line curve in Fig.11 corresponding to shoulder IER angle before correction diverge a lot when comparing to the reference angles plotted in black dashed line. The results obtained from SNs after correction (blue solid line) are still different but improved when compared to before correction (red dashed line).

Figure 1 -

 1 Figure 1 -IMUs and reflective markers placement on the thorax and the right upper limb: (a) Frontal view; (b) Side view; (c) Rear view.

Figure 2 -

 2 Figure 2 -Proposed calibration postures in the calibration session.

Figure 3 -

 3 Figure 3 -(a) IMUs' frames (Xi j ,Yi j , Zi j ) j=1 to 4 , associated with IMUi (i=1 to 4); anatomical frames (Xa k ,Ya k , Za k ) related to the neutral posture (b) and to the right shoulder adduction (c) correspondingto posture 3 in Fig.2; the subscripts T, U, F and H stand for the thorax, the upper arm, the forearm and the hand, respectively.

Figure 4 -

 4 Figure 4 -Block diagram of a wireless sensor node SN (left); Schematics of BNO055with I2C interface (right) [33].

Figure 5 -

 5 Figure 5 -Three-linked rigid segment body with attached plastic syringe without (a) or with a wireless sensors nodes SNs mounted on the three segments.

Figure 6 -

 6 Figure 6 -Sensor nodes and reflective markers placement on right upper limb and thorax.

Figure 7 -Figure 8 -

 78 Figure 7 -Upper-limb-mechanical-model elbow FE angle (top) and error (bottom) versus time before calibration (red dashed line) and after calibration (blue solid line); from encoder (black dashed line), Figure 8 -Alignment difference variation during calibration postures for each attached sensor node.

Figure 9 -

 9 Figure 9 -Right elbow PS angle (top) and error (bottom) versus time without correction (red dashed line); from OMCS (black dashed line).

Figure 10 -

 10 Figure 10 -Maximum right elbow FE angle (top) and error (bottom) versus time before correction (red dashed line) and after correction (blue solid line); from OMCS (black dashed line).

Figure 11 -

 11 Figure 11 -Right shoulder IER joint angle (top) and error (bottom) versus time from SNs before correction (red dashed line) and after correction (blue solid line); from OMCS (black dashed line).

Figure 1 Figure 2 Figure 3

 123 Figure 1

Figure 4 Figure 5

 45 Figure 4

Figure 6

 6 Figure 6

Figure 8 Figure 9

 89 Figure 7

Figure 10

 10 Figure 10

Figure 11

 11 Figure 11

Authors' Biography