Joëlle Forest

Joelle Forest
email: joelle.forest@insa-lyon.fr

FOR AN ARTIFICIALIST WAY OF THINKING ORGANIZATION

Keywords: artefact, artificialism, empiricism, organization, science of design

This work originates from the statement that the design of organizations was not considered in a systematic way by the theorist or the expert of the field. The word design is not mentioned, or if it is, it is generally assimilated to the choice of a structure in a constraint environment.

We will however show in the present contribution that organizations can really be regard as artifact and by this way that it is possible to develop a science of organization design. To this end we will first present what science of design and Artificialism are.

Then it will be possible to consider the multiples implications of the aforesaid point of view for the theory of the firm and to whom such a work can be useful.

Introduction

The literature devoted to the firm is particularly flourishing. Paradoxically, many authors and experts draw up a mitigated evaluation of it, considering that various theories can hardly be said to be theories of the way the firm really are. The consequences of such a situation is that, on the one hand, the building of theories of the firm looks like a "cacophony of speech" [Brechet, 1999] and, on the other hand, that the firm remain a "terra incognita" for a majority of economists [START_REF] Dréan | L'entreprise et la théorie économique[END_REF].

At the same time, and although the first research program relating to the science of the design was launched more than thirty years ago by famous theorists like H. Simon, we cannot help but notice that this science remains neglected by the theorists of the firm.

More precisely, the design of organization was not considered in a systematic way by the theorist or the expert of the field. The word design is not mentioned, and if it is, it is generally assimilated to the choice of a structure in a constraint environment. The design is then comparable with a simple choice : for this environment, choosethat type of organization [Lawrence, Lorsch, 1969].

The question of the design of organizations is thus apprehended from the organizational structure point of view and not from that of process [START_REF] Aoki | Horizontal vs. Vertical information structure of the firm[END_REF][START_REF] Sah | The architecture of economic systems : hierarchies and polyarchies[END_REF][START_REF] Radner | Bounded rationality, indeterminacy and the theory of the firm[END_REF], which in other words corresponds more to the design of the decision than to the design of the organization [START_REF] Roux | Design des organisations et dynamiques des réseaux pour innover : explorations théoriques et empiriques[END_REF]. Is it necessary to conclude that we had better not develop researche towards a science of design ? Certainly not !

In the present contribution we wish to show how the artificialist approach to organization, which systematizes H. Simon's point of view, opens new prospects for the theory for the firm. But before going further in the presentation of such prospects, it is advisable to first present what the science of the design is. Then it will be possible to appreciate if firms can be considered as artifacts and by doing this to question the implications of the aforesaid sciences for the theory of the firm.

WHAT IS SCIENCES OF DESIGN ABOUT?

Whereas the world is filled with artificial objects, i.e. entities, tangible or not, which have been conceived intentionally in order to meet needs, one can only note that science was primarily focused, throughout the 19th century, on natural objects. Does this fact mean that artificial objects are not worthy of interest? That they are not understandable, and finally that they could not be teached? Obviously not! As early as 1969 with his work The Science of the Artificial, H. Simon showed that sciences of designor what he called sciences of the artificial or sciences of engineering -are sciences as fundamental as usual sciences of analysis.

According to Simon, objectives and singularities of sciences of design may be expressed as follows: « whereas the sciences of nature aim at showing that the marvellous is not incomprehensible, to show how it can be understood,the sciences of design seek to explain how the multiple artifacts which characterize the human societies are designed » [Simon, 1991].

This reversing of perspectives brought forward by the sciences of design may seem trivial but is in fact of paramount importance. It leads to seeing the world of the artificial as the result of the way man apprehends his external environment so as to act on its components in order to satisfy his needs [START_REF] Simon | The Sciences of the Artificial[END_REF].

Adopting such a point of view lead us to note that the object of knowledge of such a science is not the object as such -i.e. the artifact in its existential reality -but the process of design: « one possible definition of design as a scientific discipline would be a study of the thought process comprising the creation of an artifact in a given (social, technical, economical, etc.) environment. » [START_REF] Kryssanov | Understanding design fundamentals : how synthesis and analysis drive creativity, resulting in emergence[END_REF].

In other words, sciences of design postulate the non-existence of a metaphysics of the artifact, that is to say a theory which would explain its raison d'être outside the conscience and the actions of man. As such, it allows us to consider the major difference from naturalism because sciences of design place design at the heart of man's actions. Adopting such a point of view saves theorists from making some hypothetical speculations on artifacts origin « transformism, evolutionism, genetic, natural selection, divine creationism » [Le Moigne, 1995: 157].

One is also led to consider that the stake of a science of design is not only operational and turned towards the instituted designers [Forest, Mehier, Micaelli, 2005]. It is also an epistemological stake.

During a long time, design was considered only in terms of a problem-solving process. However, design can no longer be reduced to this.

By making it possible to account for novelty [START_REF] Kryssanov | Understanding design fundamentals : how synthesis and analysis drive creativity, resulting in emergence[END_REF][START_REF] Hatchuel | La théorie C-K, Fondements et usages d'une théorie unifiée de la conception[END_REF]Lester & Piore, 2005], the analysis of the process of design implies that creativity can no longer be considered as belonging to the field of the unexplainable [START_REF] Faucheux | Expliquer l'inexplicable : Sciences de la conception et créativité , Diogène[END_REF]. It allows the questioning of possible worlds instead of real world [START_REF] Roozenburg | A Theory is not a Thing, A Methodological Comparison of Design and Research[END_REF], the exceeding of the probable one [START_REF] Jong | Distinguish Environmental Design from Empirical Research[END_REF], and thus the founding of an epistemology of invention, that is, of what one conceives and what does not yet exist [START_REF] Schmid | Science de la conception, une épistémologie originale[END_REF].

Taking into account such a point of view leads us to consider the science of design as the science of " ingenuity ", the science of creative thought and not simply expertise turned towards the application of already learned models.

By doing this, we are brought closer to the concept of ingenium theorized by J.B. Vico, which refers to a type of transversal rationality. The ingenium being this faculty to connect, to establish a correlation between phenomena distant from one another , is opposed to the academic, analytical reason which is the source of the current knowledge cartography «because the analytical method harms ingenium (or ingeniousness) and ingenium was given to man to understand, i.e. to make » [Vico, 1710[Vico, , 1981]].

More precisely, the ingenium concept, which seems to refer to the Greek mètis and to the thought of Ulysses, is the inventiveness thought [START_REF] Faucheux | Expliquer l'inexplicable : Sciences de la conception et créativité , Diogène[END_REF]], opposed to Cartesian reason which has been, according to J.B. Vico, at the origins of none of the great technical inventions of his time [START_REF] Pons | De l'invention chez Vico[END_REF]. Finally, we can infer from the above presentation, that the sciences of design are about the elaboration of a science of creativeness.

The object of a science of design having been presented the question is whether it is possible to regard organizations as artifacts.

To this end we will now, and without claiming exhaustiveness, give an outline of the various meanings of the organization as artifact.

ORGANIZATION AS ARTIFICIAL ENTITY: AN OLD POINT OF VIEW

J.P Micaelli underlines that « if one is to consider a technical object as an artifactthat is to say to search in its initial design the causes of its existence and in its successive redesign those of its dynamicsdoes not seem to pose problem, one can nevertheless note that to recognize organization as artifact and then to imagine a science which is dedicated to it, causes the reserve of the theorist or the expert, or at best leaves them doubtful » [Micaelli, 2006].

More precisely we will show in the present section that while regarding organizations as artificial entities is not new, H Simon introduced a major break with traditional views by claiming that organizations are artifacts.

We will then see how the change of emphasis suggested by H. Simonfrom the organization as artificial entity to the organization as artifactopens with new directions of research.

EARLY BEGINNINGS OF THE ARTIFICIAL POINT OF VIEW

As we have suggested before, while the concept of artificiality applied to organization is not recent, one should note that it was first employed in the sense of non-natural or fictitious According to D. Gindis in "Some building blocks for a theory of a firm as a real entity" [START_REF] Gindis | Some building blocks for a theory of a firm as a real entity[END_REF], two representations of the firm exist at the end of the 19th century, each of them carrying direct implications for current debates on how firms should be run.

The first one considers the firm as a fiction. This view is as old as Roman law, and refers to an artificial construct under the law which is merely used for convenience. This view is far from being forgotten, since it is according to the author the basis of the modern nexus of contracts theory of the firm.

The second one, the real entity theory, goes in the opposite direction and stresses that firms are natural entities: « a corporation is an entitynot imaginary or fictitious, but real, not artificial but natural [Machen, 1911] » [START_REF] Gindis | Some building blocks for a theory of a firm as a real entity[END_REF].

The question we are interested in here is whether it is (or not) in the nature of the firm to be a natural object. The artificial qualifier is usually used in its most immediate sense: that which is artificial is not natural. From our perspective, and as we will see later on, this representation is relatively poor insofar as the question of the design of the firm is missing.

WHAT ABOUT THE AUSTRIAN PERSPECTIVE?

One finds roughly the same situation within the Austrian tradition, and in particular in Hayek's thought due to the distinction which he introduces between order (i.e. the spontaneous result of the individual actions and not the intentional result of a plan) and organization (i.e. intentionally created construction in which each individual works towards a common end (purposeful construct)).

Indeed, Hayek, faithful to the research program relating to the spontaneous order tradition initiated in Scotland in the 18th century with authors such as A. Smith and A. Ferguson in particular, attempted to understand how institutions can be the unintentional result of human action or, to use the terms of A. Ferguson, « the products of human action but not human design », or those of C. Menger « How can it be that institutions which serve the common welfare and are extremely significant for its development come into being without a common will directed toward establishing them ? » [Menger 1985(1883):146 in Horwitz 2001].

By doing this, Hayek concentrated his research on market analysis neglecting in fact the organizations' functioning. It seems that this is the reason why there is not a theory of the firm among Austrians: « More specifically, as [START_REF] Loasby | The minds and methods of economists[END_REF], [START_REF] Langlois | Orders and Organizations : Towards an Austrian theory of social institutions[END_REF] and Foss [1994,1996] have noted, Austrian economists have never attempted to produce an Austrian theory of the firm » [START_REF] Ioannides | Towards an Austrian perspective on the firm[END_REF]].

From the preceding, one will nevertheless retain that while the Austrians, and in particular Hayek, did not analyze the question of the design of organizations in return they do not refuse the idea that organizations can be designed.

J.R. COMMONS' ARTIFICIALISM

The situation is about the same among old institutionnalists. If the process of conflict resolution is, according to J.R. Commons, the instigator of institutional evolution, on the other hand his point of view is very different from which of T. Veblen because he stresses that one should take into account the short term and claims that the aforementioned process cannot only be conceived as undergone and escaping from human will and action.

By considering the role of intentions on the one hand and the negotiated character of the decisions on the other hand, J.R. Commons adopts a position contrary to that of Hayek.

As underlined by L. Bazzoli, "social order is an order built by collective action, and not a spontaneous order such as it was defined by the Scottish philosophers". Such a statement leads the author to conclude that "this social system representation that one could describe as "artificialist" implies that the organized individuals, if they are determined by the institutions in which they intervene, have in return a certain amount of power over them" [Bazzoli 1995: 38-39].

Nevertheless, while the rupture introduced by J.R. Commons is far from negligible, and led some authors to underline the artificial character of a histheoretical framework, one can only consider it regrettable that the process of design is not specified.

From our perspective, this is the reason why it is difficult to regard J.R. Commons as an artificialist author.

BUILDINGS BLOCKS FOR A THEORY OF THE FIRM AS AN ARTIFACT

A. Demailly and J.L. Moigne, in the introduction of their work Sciences of the Intelligence, Sciences of artificial, underline H. Simon's audacity "claiming in 1943 at twenty seven years a thesis whose central argument was: social organizations are not given, they are designed" [START_REF] Demailly | [END_REF].

Since this date Simon was always interested in the « artificialist » nature of organizations. He claimed in his book Administrative Behavior written in 1947 that the design of organization is not different from an architectural one. He therefore strongly believed in 1969 in his work The Sciences of the Artificial that there was no reason for limiting the word "artifact" to simple technical objects.

According to him the project of understanding the genesis and/or the evolution of an organization consists in answering the following questions: Who designs? What are the designer's goals ? What is the process followed?, How does one arrive at such a decision? These questions seek to make design the central process of the dynamics of organizations but also introduces, without any doubt, a serious amount of historical relativism.

Unfortunately, although H. Simon is recognized as a theorist of organization, it should be observed that the arguments which refer to the artificial nature of organizations are disseminated throughout his work. This is perhapsthe reason why his theory of design, which from our perspective seems an important contribution, is less well known by economists.

Systematizing this work, the artificialism approach [Micaelli, Forest, 2003] sees the organization as an object having artificial properties and identifies its designer, that is, the manager in the case of the large modern company.

IS IT LÉGITIMITATE TO CONSIDER ORGANIZATIONS AS ARTIFACTS?

Artificialism is a theoretical framework of the origin and dynamic of artifacts. It relies on five key propositions constituting its core:

Proposition 1 -Artifacts are « universal » (the universality is not seen here in terms of time and space but in terms of objects). Proposition 2 -The existence and the dynamics of artifacts result from the design process. Proposition 3 -Design is submitted to a time constraint. Design is creative (i.e. its result and its process cannot be predicted). Design is proactive (it is not possible to design without any intermediate artifacts). Design is evaluative (designing implies evaluating the performances of that which is being designed and of how it is being designed). Finally, design is complex (different views are required in the design process). Proposition 4 -Design can be empirically and experimentally observed and therefore theorized at different and complementary levels (macro, meso, and micro).

Proposition 5 -Design being both universal and creative, the dynamics of a system of artifacts (the succession of artifacts made by man) is not gradual. There can qualitative, unforeseeable, important and fast leaps in the dynamics of artifacts [Micaelli, Forest, 2003]. As is shown in these five propositions, artificialism is partial. It does not cover the whole field of human actions. It cannot explain the reason why any given value, conflict (social or not), macroactor (professional, political, social, etc. group) appear at a given time in a given place. However artificialism can explain how the above groups design alternative artifacts (fashion, propaganda, lobbying, etc.) from the needs induced by those values.

Artificialism centers on the tactical dimension of actions, that is to say on the process responsible for the transition from the formulation of a need to the realization of a satisficing solution in a given time interval.

Following artificialism, an artifact can be regarded as such, if and only if, it has been designed by man in order to satisfy a need. Thus, applied to organizations, the first line of demonstration relates to the existence of goals, while the second to that of a design process. What does exactly?

RELEVANCE OF ARTIFICIALISM KEY PROPOSITIONS FOR ORGANIZATIONS

While for H. Simon there is no doubt that « similar lists of desiderata that must be attended to could be drawn up for designing organizations » [Simon 1995: 251], one can note that there seems to exist a relatively broad consensus: « Organizations are social inventions, that is, they are created by people for specific purposes at a particular time in history (...). The structure of an organization reflects the objectives it sought to accomplish» [Davis, 1982: 213]. Moreover, A. Martinet and A. Silem underline that dealing with firm performances without stating the goals, the objectives, and the strategies pursued does not make any sense.

Integrating goals and objectives leads us to consider organizations as artifacts in the same way as any technical object and more generally any material or immaterial objects designed by man. This is not just an intellectual point of view. Based on a comparison of organizational models of different car manufacturers, P. Milgrom and J. Roberts, in their work Economics, organization and management show, right from chapter one, that success (or indeed failure) of an organizational model is linked to its relevance (or irrelevance) with regard to the goals and very objectives of the organization.

If the first proposition of artificialism were to be accepted, does this mean the same thing for the second proposition? Can we really speak of organization design?

Here again it seems that the answer is affirmative as noted by D. Muster and W. Weekes:"Engineering and organizational design deal with differententities but the process is the same » [Muster, Weekes, 1985: 137] ; or by L. Davis: « design process (…) [is] the process of inventing or creating or forming an organization within which the efforts of many people are combined and coordinated to achieve the goals crucial to the organization's survival and success » [Davis, 1982 :211].

In addition, many works converge to present the organizations design process as a multi stages problem resolution process [START_REF] Muster | Towards concepts of organisation design in the systems age[END_REF][START_REF] Perrin | Définition de "l'approche artefact" et application de l'approche artefact aux structures organisationnelles[END_REF]] that makes possible the emergence of a satisficing concept of solution [START_REF] Simon | The Sciences of the Artificial[END_REF][START_REF] Simon | Problem Forming, Problem Finding and Problem Solving in Design[END_REF].

, As H. Simon underlined it, citing the example of the Congress initiated post-war Marshall plan design that was operated by the Economic Cooperation Administration (ECA): « The goal of the legislation was to provide the European nations with funds and goods that would enable them to revive their own productive capacities. But there were different ways in which an organization could have been structured to do that. The ECA could have been an organization for processing European shopping lists, validating them, and aiding procurement. That was one model. Another conceiving the ECA as an extension of the State Department, organized to engage in bilateral negotiations with individual nations to fix the terms on which aid would be offered. A third model -the one followed -conceived the organization as a nucleus around which economic cooperation among the European states could develop, so that they would be led toward a European economy very different from the fragmentation of the pre-War era. » [Simon, 1995: 256 ].

Thus artificialism breaks radically away from theories that recognize any optimal organizational structure. At best, an organizational structure can be said to be satisficing. Artificialism, most probably because it cannot be and does not claim to be predictive, therefore appears more robust than previous theories. Quite obviously, the « one best way » idea, applied to organizations, does not make sense. The adopted solution is contextualised with regards to the objectives of the organization as defined at a given time with given values but also to the way production is thought out. Therefore, transposing a successful solution from a given organization to another is characteristic of a total misunderstanding of the genesis process of firms and their dynamics.

This example also shows that not only do alternatives emerge in the design process, the problem also does. By designing we learn what we want.

Building on H. Simon's example of oil painting, J.L Lemoigne explains that the design process is the process through which an ongoing system defines new intermediate goals which in turn trigger the identification of new means («Means-Ends analysis»). These new means may then suggest new goals: « When using oil paint, each brush stroke creates a new kind of organisation which yields a source of new ideas for the painter. Painting is a cyclical interactive process between the painter and the painting in which ends lead to new brush strokes while the gradually changing organization of the painting suggests new goals » [Simon in LEMOIGNE 2002: 4].

The consequence of such an assessment on the dynamics of the design process is that reducing design to a situation of choice is a misunderstanding of the reality of design. Choice is only a minor part (for which time and resources spent are a unit) of the designer's activity: « I do not wish to dwell upon the choice aspect of design, for it is not the aspect on which designers spend most of their time and energy. Most design resources go into discovering or generating alternatives, and not into choosing among them » [Simon 1995: 247].

In other words designing is not only a matter of choosing among pre-existing alternatives. It is from the combination of hypotheses that alternatives and therefore creation emerge. And it is impossible to consider the result ex ante [START_REF] Simon | Problem Forming, Problem Finding and Problem Solving in Design[END_REF]].

ARTIFICIALISM: A UNIVERSAL THEORETICAL FRAMEWORK?

The above arguments lead us to consider organizations as artifacts, like any technical objects and more generally like all the material or immaterial objects designed by man. However, is there really no difference with a simple technical object? Some, opposing ontological arguments, related to the essence and irreducible singularities of organization, will undoubtedly claim that our conclusion is a little hasty on this point. That it is not in the nature of the organization to be an artifact [Micaelli, Forest, 2003].

Nevertheless one must note that this type of argument stresses more the singularities of the organization than an impossibility of regarding it as an artifact.

Others will stress that there are notorious differences between the design process of an organization and that of a technical object. This point of view is undeniable.

Arguably, in addition to the fact that one is dealing with designers who are unaware of themselves, in the majority of cases there is no set of conditions allowing one to test (i.e. to simulate) the alternative organizational concepts ex ante, unlike a mechanical system for example.

Indeed, the impossibility of simulation for the design of organizations is reinforced by that of correctly identifying the representations of its future members and anticipating the induced effects. This problem is even more complex if one considers that the system is itself a representation (a design) of those who observes it [Le Moigne, 1985;Genelot, 1992;[START_REF] Perrin | Définir les performances et concevoir les organisations[END_REF] Do these differences, which by no means exhaust the argument, preclude us from regarding organizations as artifacts? Undoubtedly not! There is effectively no more difference between the design process of an organization and that of a vehicle, than between the design process of a software and that of a public space or between the design process of a landing gear of a plane and that of the brake of a child's scooter.

Moreover, it should be stressed that claiming that mechanisms can be different from one artifact to another is, here again, more a matter of stressing the singularities of the organization than to underline the impossibility of regarding it as an artifact.

In other words, it is necessary to understand that the concepts and key propositions of artificialism have not been theorized and developed to account for only simple technical objects and that the social sciences can potentially adopt them.

Artificialism, indeed, was not developed to serve a unique discipline (mechanical design, urban space design...) or group of disciplines: the engineering sciences for example. Artificialism acts as a generic (universal) theoretical framework of the emergence and dynamics of artifacts that mechanics, computer science, biology, economics, and other disciplines can each mobilize without questioning their specificity.

In addition, it is necessary to underline that the will to restrict the space of artificialism to engineering sciences only is the result in the majority of cases of a real ignorance of the way technical objects are designed.

It is precisely the case of F. Hayek when he rejects socialist planning on the basis of the limits of human rationality on the one hand, and on that of our capacity to design top-down solutions for social problems on the other hand: « There is nothing in the ideal of the Enlightenment that commits one to applying inappropriately the methods of science, which are so powerful and productive in their own arena, to the social world. The mindset of the scientist or the engineer is inappropriate for solving human problems » [START_REF] Horwitz | From Smith to Menger to Hayek : Liberalism in the spontaneous Order Tradition[END_REF].

Hayek's refusal to make use of scientific methods resulting from the engineering sciences for social problems is indeed founded on a double error of judgement. The first is to believe that all can be known. The second is that when we design a technical object we know ex ante what will emerge. However, whoever has been in a situation of design knows that this postulate is unfortunately false.

From what precedes one will retain that claiming that there are differences in the way the need emerges for example not only does not question the generics of the artificialism framework, but on the contrary, leads us to thorough research in order to better understand the design process of the different classes of artifact [START_REF] Forest | Sciences de la conception : fondements, méthodes, pratiques[END_REF].

WHY TODEVELOP ORGANIZATION RESEARCH TOWARDS A SCIENCE OF DESIGN?

To consider organizations from the point of view of the design sciences is useful to three types of actors: the manager as the designer of organizations, the teacher who trains the aforementioned managers and the researcher.

CONTRIBUTION TO MANAGERS

A priori, managers seem to be the first concerned by the development of organization research towards a science of design.

Why? Because this research should be able to help them to understand and exercise their professional activity.

Stating that organizations are designed and elaborated artifacts leads us to focus on the analysis of organization design process. Today there is a severe lack of knowledge on the choices made, on the dynamics of the process. The very few existing publications come from business literature and, if we take a closer look, do not deal with « organization » or « organizational design » as one might expect but with what may better be termed « organization re-design ». The question is: can we do without research on organization design ? This seems all the more paradoxical than for the past few years creating new businesses is at the forefront of French economic policies.

What is at stake is thus the development of knowledge on organizations design process. More precisely, the aim is to establish a scholarship backed up by history through a reflection on the ways the science of design can take into account organizational problems.

However, it is less interesting to describe the external aspects of organizations or to compare their « design ». What matters is the analysis of the design process of their structure [START_REF] Perrin | Définition de "l'approche artefact" et application de l'approche artefact aux structures organisationnelles[END_REF]. Recognizing that organizations are the result of a design process implies trying to unveil the content of design stages and more particularly their « conceptual design » and « embodiment design » stages. In fact, we believe that this is the condition for an explanation of what really occurs and for an understanding of why protean entities can coexist.

The stake is resolutely practical here. The objective is to gain knowledge which enables managers to better understand in a reflexive way their activity and their position in the process in order to improve their location. This knowledge can take the form of concepts or models of the process. From a more operational point of view this knowledge can be valorized through the production of guides, methods and tools, dedicated to the improvement of their activity.

Indeed, we hypothesize that any improvement in our understanding of the design process should have positive effects on organizations by identifying key factors for example. We hypothesize that such work could help us appreciate the possibility of deploying methods developed to assist the design of technical objects for the organizations too.

CONTRIBUTION TO TEACHERS

To consider organizations from the point of view of the design sciences is also useful for teachers who train the aforementioned managers.

According to H. Simon, whoever imagines some provisions in order to change an existing situation into a preferred one is a designer [Simon, 1991]. He thus concludes that it is design which makes the difference between sciences and professions and that engineering, architecture, management schools as well as the faculty of medecine or the institutes which train teachers, are all concerned by the process of design. This is not an isolated point of view. C. Schmitt and M. Bayad, basing their research on that of A. Martinet and that of R. Teulier-Bourgine, underline that many tasks in organizations are tasks of design [Schmitt & Bayad, 2004].

One is thus led to a shift from the vision of the manager/decision maker to that of the manager/designer.

Considering managers as designers leads, however, to wondering about what their competencies really are. This is precisely the problem.

Building on the work of R. Hayes and W. Abernathy and on that of T. Peters and R. Waterman, D. Musters and W. Weekes stress the vacuity of our education system to in terms of managerial training: « Without doubt, our education system has been successful in training analysts (…). However, we appear to have virtually ignored the training of inventors, creative designers, synthesists and generalists » [START_REF] Muster | Towards concepts of organisation design in the systems age[END_REF].

The work Made in America, published in 1990 by M. Dertouzos, R. Lester and R. Solow, as well as the National Research Council report Improving engineering design: designing for competitive advantage, also arrive at the same conclusions. This is why we think that by developing the science of design we also contribute to the building of a "science of organization design" that we are persuaded is necessary for the training of managers, too strongly embedded in the traditional representation of the firm based on the emblematic figure of the super calculating and optimizingr decision maker and insufficiently on that of the ingenious and creative decision maker.

Thus, the major contribution of a science of design to teachers is to give them the possibility to effectively train designers through a new representation and understanding of real managerial activity.

CONTRIBUTION TO RESEARCHERS

One must add to the practical and institutional stake of developing organization research oriented towards a science of design an epistemological one.

Why? Because developing such a point of view is, for a community of researchers, a necessary way of examining the nature of the knowledge produced but also about the methodologies used in its produce .

To dispose of a research methodology (or some methodologies) is indeed important for recognition in the scientific space of research. To this end, we believe that empiricism is an alternative research methodology, adequate for the founding of a realistic theory of the firm and of its evolution.

Following the artificialism point of view, an artifact can be defined in an empirical way. The association of an object to a designer and to a process of design or a process of redesign -synonym of rationalization -is sufficient to define it as an artifact. It is useless to have an unspecified talent or revelation in order to carry out this process. Curiosity, a sense of observation, the will to find and reconstitute the traces of its design, are sufficient [Micaelli, Forest 2003].

The situation is the same for the design process. It can also be observed empirically. It is then possible to identify its actors, it object, from that one design? How does the creativity appear? And so on.

By this way we are close to the old institutionalist tradition according to which the realism of an organization theory must be based on the realism of its assumptions: "empirical success relates first to the need for founding empirically its assumptions. For social sciences it means to elaborate theories on relevant cognitive and behavioral assumptions from the observation point of view" [Bazzoli, Kirat, 2002:23].

One is led to note that considering organizations from the science of design perspective invites us to question the epistemological bases of economic knowledge which holds, according to L. Bazzoli and T. Kirat, that the deductive method is the only scientific method that can be extended to the knowledge of institutional phenomena [START_REF] Bazzoli | Règles juridiques et coordination économique en dynamique : une confrontation entre l'institutionnalisme réaliste et la théorie des coûts de transaction sur les contrats comme institutions[END_REF].

SOME CONCLUSIONS

The present contribution allowed us to note that while the concept of artificiality applied to organizations is not new, very few works employ it in the sense of designed artifact, neglecting the analysis of their design process.

One might believe that such a situation implies an absence of interest to develop such a science of design. We nevertheless underlined the practical, institutional and epistemological issues at stake in such a development.

Finally, from our perspective, what is at stake is the rehabilitation of the science of design which has been all to often neglected.

We believe that this science of design (science of ingenium) can offer the social sciences, and particularly economics, a better understanding of the way organizations really work on the one hand and a new theoretical framework of firm evolution on the other.

Vanberg V. 1994 "Hayek's legacy and the future of liberal thought : rational liberalism versus evolutionary agnosticism". The Cato Journal, vol 14, n°2, fall 1994.


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Antoine Ferreira

Vision-Based Force Sensing of a Magnetic Microrobot in a Viscous Flow

This paper has presented a new vision-based force-sensing framework that allows to characterize the forces applied on a magnetic microrobot in an endovascular-like environment. Especially, unlike common approaches used with optical microscopy where orthographic projection model are used, we consider in this paper the weak-perspective model. The proposed vision-based force characterization allows to retrieve the three dimensional (3D) translational velocities and accelerations of a microrobot viewed from a digital microscope. Hence, thanks to the dynamic model the external forces are estimated on-line. The framework was applied and validated for a magnetic microrobot navigating in a viscous flow. Experimental results in two different environments illustrate the efficiency of the proposed method.

I. INTRODUCTION

Untethered microrobots can significantly improve many aspects of medicine and bioengineering by navigating through the cardiovascular networks to perform targeted diagnosis and therapy [START_REF] Cavalcanti | Nanorobot for Brain Aneurysm[END_REF], [START_REF] Nelson | Microrobots for minimally invasive medicine[END_REF]. In particular, the use of magnetic fields is till now the most considered approach, and different designs have been proposed in the literature [START_REF] Nelson | Microrobots for minimally invasive medicine[END_REF], [START_REF] Abbott | How should microrobots swim?[END_REF]. A first solution is to mimic microorganisms behavior using helical tail [START_REF] Zhang | Artificial bacterial flagella for micromanipulation[END_REF], [START_REF] Peyer | Bio-inspired magnetic swimming microrobots for biomedical applications[END_REF] or elastic flagella [START_REF] Evans | Propulsion by passive filaments and active flagella near boundaries[END_REF] for bio-inspired magnetic swimming design. It has been shown that such designs are suitable in small vessels such as arterioles or capillaries, whereas in larger vessel (as arteries) bead pulling scheme is more efficient [START_REF] Arcèse | Endovascular Magnetically-Guided Robots: Navigation Modeling and Optimization[END_REF]. Indeed, bead pulling were successfully applied in the carotid artery of a living swine [START_REF] Martel | Automatic navigation of an untethered device in the artery of a living animal using a conventional clinical magnetic resonance imaging system[END_REF]. Thus, in this work we consider a spherical neodymium magnet as microrobot body (termed microrobot throughout the text). Nevertheless, whatever the propulsion scheme used, all contributions point out the problem of navigation controllability of microrobots in a viscous flow. Especially, all magnetic microrobot designs have to face important constraints related to the system dynamics. To improve the magnetic navigation strategy against the biological laws governing patient body, a characterization of the magnetic microrobot behavior within a microfluidic environment is mandatory.

Our motivation in this work is to characterize and validate the system's dynamic model of a magnetic microrobot navigating in a microfluidic viscous environment. To do so, the forces acting on the microrobot must be measured. Force measurements could be achieved using capacitive force sensors [START_REF] Sun | Characterizing fruit fly flight behavior using a microforce sensor with a new comb-drive configuration[END_REF], atomic force microscope (AFM) [START_REF] Ducker | Measurement of forces in liquids using a force microscope[END_REF], piezoresistive cantilevers [START_REF] Fauver | Microfabricated cantilevers for measurement of subcellular and molecular forces[END_REF], or magnetic bead [START_REF] Fass | Tensile force-dependent neurite elicitation via anti-1 integrin antibody-coated magnetic beads[END_REF]. But David FOLIO (Email: david.folio@insa-cvl.fr) such approaches are intrusive, and it is troublesome to use them with the microrobot in endovascular-like environments. A non-intrusive solution is to consider vision-based forcesensing [START_REF] Wang | Vision-based sensing of forces in elastic objects[END_REF], [START_REF] Greminger | Vision-based force measurement[END_REF]. Proposed methods usually rely on the measurement of the displacement or deformation retrieved from an imaging sensor. In our context, to ensure efficient navigation control of magnetic microrobot its location is determined from medical imaging such as magnetic resonance imaging (MRI) [START_REF] Felfoul | In vivo mrtracking based on magnetic signature selective excitation[END_REF], or digital microscopy [START_REF] Bergeles | Singlecamera focus-based localization of intraocular devices[END_REF], [START_REF] Belharet | Control of a magnetic microrobot navigating in microfluidic arterial bifurcations through pulsatile and viscous flow[END_REF]. Hence, no additional sensing modalities are required, and the vision sensor is a priori able to provide the force feedback [START_REF] Greminger | Vision-based force measurement[END_REF]. Nevertheless, most vision-based force measurement techniques rely on elastically deformable objects properties. As in our case the considered object is a hard material in a viscous flow, such solutions seems limited.

The main contribution of the paper is to define a mapping between the system dynamics and sensory data acquired from an imaging system to characterize the endovascular like interaction forces applied on the magnetic microrobot. Classically, when dealing with an optical microscope the orthographic perspective model is considered, that is a scaling of the observed scene. However, pure orthographic projection is usually unrealistic, and methods that use orthographic projection are only valid in a limited domain where the distance and position effects can be neglected [START_REF] Xu | Epipolar geometry in stereo, motion and object recognition: a unified approach[END_REF]. Therefore, we propose here to consider the weak-perspective model that is closer to the full perspective model, and allows to improve the knowledge of the external forces.

In the remainder of this paper, we first present in Sect. II a new vision-based force characterization based on the vision-based model. Then in Sect. III we apply the proposed approach to a magnetic microrobot navigating in a viscous flow. Sect. IV presents different experiments that illustrate the efficiency and robustness of the proposed framework, before to conclude in Sect. V.

II. VISION-BASED FORCE MEASUREMENT

The proposed vision-based force-sensing relies on the observation of the microrobot motion from an imaging sensor. To do so, we use the mapping between the system dynamics and the image data provided by the sensor-based model.

A. The Sensor-Based Model

We consider a fixed vision system observing a moving device (here the microrobot), and assuming that only the device motion imply a sensor signal variation, the sensorbased model is expressed as follows [START_REF] Chaumette | Visual servo control, part I: Basic approaches[END_REF]:

ṡ = J ξ (s) v 0 ( 1
)
where ṡ is the observed microrobot motion vector in the image acquired from the vision sensor, and v 0 is the device velocity screw in the 3D Euclidean space expressed in the reference frame F 0 = (O, -→ x 0 , -→ y 0 , -→ z 0 ) (see Fig. 1). The term J ξ (s) is the Jacobian matrix, often referred as image Jacobian [START_REF] Hutchinson | A tutorial on visual servo control[END_REF]. The subscript ξ denotes that J ξ (s) is generally a function of the extrinsic ξ Ex and intrinsic ξ In parameters of the sensor, and the tracked sensor features s. Indeed, the image Jacobian matrix could be decomposed as follows:

J ξ (s) = L(ξ In , s) • c W 0 (ξ Ex ) (2)
where L(ξ In , s) is often referred as the interaction matrix [START_REF] Chaumette | Visual servo control, part I: Basic approaches[END_REF], and the matrix c W 0 (ξ Ex ) allows to transform the motion v 0 of the device between here the sensor frame F c and the reference frame F 0 , as illustrated in Fig. 1. Let us assume that the image Jacobian matrix J ξ (s) is a full rank matrix, and then define J + ξ = (J ⊺ ξ J ξ ) -1 J ⊺ ξ its Moore-Penrose pseudo-inverse. Thus, the previous visionbased model equation ( 1) could be re-written as follow:

v s F c F 0 c W 0 z c x c
v 0 = J + ξ ṡ (3)
This relation allows to characterize the microrobot motion in the 3D Euclidean space using vision data.

B. Linking Vision-based Sensing to System Dynamics

Now let us differentiate the vision-based model (1) to expose the sensor features dynamics:

s = J ξ (s) v0 + v 0 • H ξ (s) • v 0 (4)
where H ξ (s) is the image Hessian, defined as:

H ξ (s) = ∂J ξ (s) ∂s J ξ (s) = G(s) J ξ (s) (5)
Substituting equation ( 3) into (4) yields:

v0 = J + ξ s -G(s) ṡ J + ξ ṡ (6)
This relation allows to characterize the microrobot acceleration v0 in the 3D Euclidean space, using the image feature s provided by the vision sensor. Finally, thanks to the Newton's second law one can relate the microrobot acceleration v0 to the forces acting on it:

m v0 = f ( 7
)
where m is the microrobot mass, and f is the net force expressed in the reference frame F 0 .

III. APPLICATION TO A MAGNETIC MICROROBOT NAVIGATING IN A VISCOUS FLOW

A. Dynamics Modeling

The considered microrobot body immersed in a microfluidic environment is modeled by a magnetic microsphere as illustrated on Fig. 2. The microrobot environment is modeled by a 3D Euclidean space, and we denote by F 0 its fixed reference frame. Actuated by external magnetic gradients ∇b in a microfluidic environment, the microrobot will mainly experience the steering magnetic (f m ), apparent weight (f g ), contact (f c ), electrostatic (f e ), van der Waals (f v ) and hydrodynamic drag (f d ) microforces that affect the microrobot's motion. The effects of these forces are explained in detail in [START_REF] Arcèse | Endovascular Magnetically-Guided Robots: Navigation Modeling and Optimization[END_REF]. Hence, the translational motion of the ferromagnetic microsphere is formulated as follows :

m v0 = f = f m + f d + f g + f v + f e + f c fVasc ( 8
)
where v 0 is the translational velocity of the microrobot and m its mass.

w a ll R δ v f d f g f m f e +f v ∇b x ∇b y ∇b z v f d f g f m y 0 x 0 z 0 Fig. 2.
Forces applied on a microrobot navigating in microfluidic environment: (left) in an infinite extend and (right) in cylindrical channel.

In the remainder of this paper, we assume that the orientation of the magnetic microrobot does not change due to the magnetic torque which tends to align the magnetization of the robot along the magnetic field. Hence, no angular motion is considered and the microrobot's velocity screw is reduced to its sole translational velocity: v 0 = (v x , v y , v z ) ⊺ . Moreover, we also assume that the microrobot is never in contact with the walls of the environment, namely f c = 0. Actually, in case of wall contact, the vision-based force-sensing could be achieved using elastically deformable objects properties as in [START_REF] Wang | Vision-based sensing of forces in elastic objects[END_REF], [START_REF] Greminger | Vision-based force measurement[END_REF].

B. Digital Microscope Projection Model

In this work, the magnetic microrobot motion is observed from a fixed digital microscope, and its position in the image plane is retrieved from image processing. As illustrated in Fig. 3, classically a 3D point of coordinates x = (X, Y, Z) ⊺ in the microscope frame F c is projected into a 2D point with coordinates s p = (x p , y p ) ⊺ in the image plane with a pinhole perspective projection, and yields:

x p = f X Z , y p = f Y Z ( 9
)
where f is the focal length. If we denote (u, v) the position of the corresponding pixel in the digitized image, this position is related to the 2D point s by:

u = u 0 + α u x p v = v 0 + α v y p ( 10
)
where α u and α v are the ratio between the focal length and the size of a pixel, and (u 0 v 0 ) is the principal point coordinate in pixel. Then, these four parameters define the digital microscope intrinsic parameters: ξ In = {α u , α v , u 0 , v 0 }, and are calibrated off-line [START_REF] Tsai | A versatile camera calibration technique for high-accuracy 3D machine vision metrology using off-the-shelf tv cameras and lenses[END_REF], [START_REF] Bouguet | Camera calibration toolbox for matlab[END_REF].

1) Orthographic perspective model: Generally, when a digital microscope is used, due to the size of the objects of interest wrt. the focal length f and the vision system distance, the orthographic projection model is considered, that is:

x orth = k x X, y orth = k y Y (11)
where k x and k y scale the observed scene. As one can see, in orthographic projection, the depth Z of the point x does not affect its image formation. However, in neglecting the depth information, the orthographic projection models image formation incorrectly and solves for (approximately) known parameters as if they were unknowns. It is given the freedom to reconstruct wrong values for these artificial unknowns, which in turn can corrupt the recovery of the true unknowns. Therefore, methods that use orthographic projection are only valid in a limited domain where the distance and position effects can be neglected. Nevertheless, the full perspective projection model (9) requires a model or an estimation of the depth Z of the considered 3D point x. Several approaches may be used to determine it. The most obvious solution is to measure it using dedicated sensors such as telemeters or stereoscopic systems. However, if the system setup is not equipped with such sensors, it is possible to use structure from motion (SFM) techniques [START_REF] Oliensis | A critique of structure-from-motion algorithms[END_REF], signal processing methods [START_REF] Matthies | Kalman filter-based algorithms for estimating depth in image sequences[END_REF], or even pose relative estimation [START_REF] Thrun | Robust mote-carlo localization for mobile robots[END_REF]. Moreover, knowing an initial guess Z(t 0 ), in [START_REF] Folio | Dealing with visual features loss during a vision-based task for a mobile robot[END_REF] the authors propose to use the sensor-based model to estimate the Z-depth.

2) Weak perspective model: A suitable approximation is to use the so-called weak-perspective (or scaled orthographic) projection model, defined by:

x wp = f X Z 0 , y wp = f Y Z 0 ( 12
)
where Z 0 is an average depth plane, as depicted in Fig. 3.

The weak-perspective model is valid when the field of view is small and the average variation of the depth of the object (∆Z) along the line of sight is small wrt. Z 0 , i.e. |∆Z| ≪ Z 0 . Especially, the weak-perspective is seen as a zero-order approximation of the full perspective projection [START_REF] Sun | Characterizing fruit fly flight behavior using a microforce sensor with a new comb-drive configuration[END_REF]. More precisely, for a point x of depth Z = Z 0 + ∆Z, the error is:

s err = s p -s wp = - f Z 0 ∆Z Z X Y (13)
This error shows that a small focal length (f ), small field of view (X/Z 0 and Y /Z 0 ) and small depth variation ∆Z contribute to the validity of this model.

3) The interaction matrix: We have to use the interaction matrix L(ξ In , s) that map visual feature motion ṡ to the microrobot velocity v 0 (1). This matrix can be derived for many visual features, such as lines, circle, image moments, etc. [START_REF] Chaumette | Visual servo control, part I: Basic approaches[END_REF]. In the case of a feature point s = (x, y) ⊺ , the interaction matrix could be easily derived from the full projection model ( 9), and for a pure translational motion is given by:

L(ξ In , s) =    f Z 0 - x Z 0 f Z - y Z    (14)
Using the weak-perspective, the above interaction matrix is then evaluated for the average plane Z 0 . In this context the intrinsic parameters are defined by: ξ In = {α u , α v , u 0 , v 0 , Z 0 }.

4) The transformation matrix:

The transformation matrix c W 0 (ξ Ex ) allows to transform the velocity screw from the camera frame F c to the reference frame F 0 . In the case of a pure translational motion, this matrix is simply defined by:

c W 0 (ξ Ex ) = c R 0 ( 15
)
where c R 0 ∈ SO(3) (special orthogonal group of transformations of R 3 ) is the rotation matrix between F c and F 0 . As for intrinsic parameters ξ In , the transformation matrix parameters ξ Ex are calibrated off-line [START_REF] Tsai | A versatile camera calibration technique for high-accuracy 3D machine vision metrology using off-the-shelf tv cameras and lenses[END_REF], [START_REF] Bouguet | Camera calibration toolbox for matlab[END_REF].

IV. EXPERIMENTAL VALIDATION

A. Electromagnetic Actuation Testbed

The motion control of the untethered microrobot in a microfluidic environment relies upon magnetic gradients ∇b. To this aim, an electromagnetic actuation (EMA) testbed has been developed specifically by Aeon-Scientific™ to generate the 3D controlled magnetic fields. The setup is illustrated in Fig. 4. The EMA setup consists of three nested sets of Maxwell coils and one nested set of Helmholtz coils. These coils set are combined coaxially such that the magnetic field and magnetic gradient fields can be controlled in the center of the workspace [START_REF] Belharet | Control of a magnetic microrobot navigating in microfluidic arterial bifurcations through pulsatile and viscous flow[END_REF]. Hence, the magnetic gradient fields generated by the EMA system are controlled through the electrical currents circulating in the coil set.

Finally, the magnetic setup is equipped with a CCD high-resolution miniature microscope camera (TIMM 400, Nanosensor™) that is rigidly linked to the EMA setup. A robust tracking algorithm measure, with a sub-micrometer resolution, the location of the magnetic microrobot by realtime images processing. Finally, after a calibration procedure, the extrinsic parameters are fully characterized such as the frame F 0 and F c are collinear.

B. Experimentation Protocol

In the experiments, a neodymium magnet (NdFeB N35) microsphere with a radius r = 250 µm was used as microrobot body. To characterize the force net f and validate the proposed vision-based force-sensing, experiments within different environments have been conducted (see Fig. 5). In particular, each experiment is realized within static viscous fluid made of a mixture of water and 80% of glycerol which is close to blood flow viscosity (η f = 60 mPa/s). Each perspective model is calibrated twice: before the first experiments in i) free and ii) microfluidic channel environments. To facilitate the external force calibration a constant magnetic gradient is applied in the x-axis direction, and in the z-axis direction to compensate the gravitational force, leading to a straight line motion as depicted in Fig. 5.

C. Results in Free Extend

First, experiments in a viscous fluid with "no walls" are performed to calibrate the velocity and the interaction forces without wall effects, as described in Fig. 5(a). Hence, DLVO forces (that is van der Waals and electrostatic forces) could be effectively neglected, and mainly the magnetic, the hydrodynamic and the gravitational forces could be considered in the interaction force expression [START_REF] Martel | Automatic navigation of an untethered device in the artery of a living animal using a conventional clinical magnetic resonance imaging system[END_REF]. Within this free extend the average depth of the weak-perspective model is calibrated at Z 0 = 67.67 mm. Then, experiments are conducted with different magnetic gradients applied along the x-axis. Fig. 6 illustrates the velocities and accelerations using the orthographic projection and the weak-perspective models with different magnetic gradients. As expected the velocities and accelerations decrease with the magnetic gradient amplitude. Furthermore, as the orthographic projection is less reliable, it tends to underestimate the velocity, implying a poor acceleration estimation. In particular, as the orthographic projection consider only the aspect ratio, only the 2D components (v x , v y ) of the microrobot's motion v 0 could be directly estimated. Although the sole midplane Z 0 is considered, the weak-projection is able to provide an approximation of the full 3D motions. Actually, here the interaction matrix ( 14) is evaluated with the average plane Z 0 .

Thus, knowing the microrobot motion in the free extend, the dynamics model introduced in Sect. III-A is computed (see [START_REF] Arcèse | Endovascular Magnetically-Guided Robots: Navigation Modeling and Optimization[END_REF] for detailed forces model). For instance, Fig. 7(a) shows the forces using the orthographic perspective and Fig. 7(b) using the weak-perspective model with a constant magnetic gradient ∇b x = 208.7 mT/m along the x-axis. Using a top view digital microscope, the orthographic model is capable to consider only the x -y plane and through a scaling retrieved only the 2D components of the magnetic and hydrodynamic drag forces. Especially, by not explicitly considering some depth information, the orthographic projection models image formation incorrectly and mis-estimates the unknown parameters. In contrast, the weak-projection allows us to estimate the full 3D motions and dynamics. Therefore, thanks to our proposed framework we are able to consider the gravitational forces f g , and improve the force balance model [START_REF] Martel | Automatic navigation of an untethered device in the artery of a living animal using a conventional clinical magnetic resonance imaging system[END_REF]. Hence, Fig. 8 presents the difference between the logarithmic error between the force net f computed using the model referred in [START_REF] Arcèse | Endovascular Magnetically-Guided Robots: Navigation Modeling and Optimization[END_REF] and the microrobot acceleration computed from vision-based measurements, that is: log f -log m v0 , with different magnetic gradient amplitudes. As one can see, our framework seems to validate the proposed system's dynamic model. Furthermore, the use of weak perspective model allows to improve the knowledge of microrobot velocities and accelerations.

D. Results within a microfluidic channel

Secondly, experiments in a viscous fluid within a channel of radius R = 500 µm are realized, as shown in Fig. 5(b). The average depth is here calibrated at Z 0 = 85.26 mm, and the distance to the wall is in average of δ = 0.256 mm. In such microfluidic environment, van der Waals forces remain negligible (as it was in the order of 10 -14 mN) whereas the electrostatic forces become significant, as illustrated on Fig. 9. Especially, Fig. 9(a) and 9(b) represent the forces computed from the orthographic perspective and the weak perspective, respectively. The results consider a constant magnetic gradient ∇b x = 208.7 mT/m along the x-axis. Once again, the orthographic projection is able to deal only with the 2D components of the force balance (8) in the x -y plane, and does not allow to consider explicitly the gravitational forces along the z-axis.

Fig. 10 shows the logarithmic error between the force balance model [START_REF] Martel | Automatic navigation of an untethered device in the artery of a living animal using a conventional clinical magnetic resonance imaging system[END_REF] and the microrobot acceleration computed using our proposed approach based on the weak-perspective model. In particular the dashed line represents the logarithmic error when no electrostatic forces are considered, in opposition to the solid line. As one can see, adding the electrostatic forces knowledge may help to improve the dynamic model of the microrobot.

E. Discussion

The experimental results show that the proposed framework permits to characterize the external forces applied on a microrobot navigating in an endovascular-like environment from imaging data. Based only on scaling considerations, the orthographic model is not directly and explicitly able to deal with the 3D components of the motions nor dynamics. To get access to the 3D motions some knowledge on the Zdepth is mandatory. A first step is to use the average depth Z 0 , and thus the weak perspective projection. This model allows to estimate the full 3D motion of the microrobot, and significantly improve the approximation of the microrobot motion. However, results also exhibit that the use of the third component increases the variance on the recovered 3D motion, and then, on the experimental forces. This behavior is due to the fact that the weak-perspective is based on the use of the average plane Z 0 instead of the true Z-depth of the microrobot. This issue could be overcame by using a second lateral digital microscope for instance, and thus consider the full perspective model.

V. CONCLUSIONS

This paper presented a new framework to characterize forces applied to a magnetic robot through the use of the vision-based and weak perspective models. To this aim a mapping between the vision-based data and the system's dynamic model is expressed. More precisely, unlike classical approach that uses an orthographic projection model when a microscope is considered, we have proposed here to deal with the weak-perspective model. In particular, the weakperspective is known to be closer to the full perspective. Hence, the proposed vision-based force sensing formalism allows to recover the full three dimensional motion and dynamics of the magnetic microrobot in order to characterize experimentally the external forces acting on the microrobot's body. Thus, the external forces could easily be characterized on-line from the images acquired by the digital microscope. The proposed method has been applied and experimentally validated for a magnetic microrobot navigating in a viscous flow. Finally, the experimental results illustrate the efficiency of the proposed framework, and validate the dynamics modeling of the swimming microrobot evolving in a free extend and in a microchannel. In both cases, the influence of the DLVO forces are demonstrated improving significantly the estimation of the force net.

Fig. 1 .

 1 Fig. 1. Sensor-based modeling.

Fig. 3 .

 3 Fig. 3. Projection model: (a) 3D representation of image formation, and (b) full perspective (sp), weak-perspective (swp) and orthographic perspective (s orth ) projection model comparisons.

Fig. 4 .

 4 Fig. 4. Experimental testbed composed of four sets of EMA coils and a digital microscope.

Fig. 5 .

 5 Fig. 5. Experiments in (a) free extend and (b) in a microchannel of radius R = 500 µm.

Fig. 6 .

 6 Fig. 6. Comparison of (a) the velocity v 0 and (b) the acceleration v0 of the orthographic perspective and the weak-perspective.

Fig. 7 .Fig. 8 .

 78 Fig. 7. Force model and magnetic microrobot's dynamics using (a) the orthographic perspective and (b) the weak-perspective models with ∇bx = 208.7 mT/m.

Fig. 9 .

 9 Fig. 9. Force model and magnetic microrobot's dynamics using (a) the orthographic perspective and (b) the weak-perspective models with ∇bx = 208.7 mT/m.

Fig. 10 .

 10 Fig. 10. Comparison between the force balance model and the microrobot dynamics in a microchannel: log f -log m v0 . Dashed-line without electrostatic forces, solid line with electrostatic forces.

K. Belharet is with Hautes Études d'Ingénieur campus Centre, PRISME EA 4229, Châteauroux, France.

D.Folio and A. Ferreira are with INSA Centre Val de Loire, Université d'Orléans, PRISME EA 4229, Bourges, France. Corresponding author:


Nabil Amari

David Folio

Antoine Ferreira

Robust Tracking of a Two-Fingered Micromanipulation System Working Through the Focus of an Optical Beam

This paper reports a control strategy of two AFM gripper for manipulation on analysis Beam, using dual micro/nano manipulators in order to grippe a micro spherical ball and tacking-maintain on the focus of laser beam. The main idea is to control and drive AFM gripper to expose micro samples in the laser beam by localization of the maximum intensity laser beam given by a four-quadrant photodiode. The focalization of analysis Beam used for microhandling is few micrometer that making the intensity measurement sensitive at the externals variations and positioning of the four-quadrant photodiode affecting the control of the gripper and position the sample far of the focalization of laser beam. To overcome this problem, the Particle Filter (PF) algorithm is used to estimate the position of laser beam.The dual manipulators is controlled by combine different performance dynamics (micro manipulator and nano manipulator) to track a laser beam with high precision.

I. INTRODUCTION

The Beam analysis(laser beam, synchrotron radiation) represent a great tool for comprehension physic phenomena with small focalization. In biology it is became possible to detects different pathologies with precision by micro cellular samples diagnostics in the infrared. The difficulty is how to maintain a micro sample in the focus of the laser beam that depends of the focal localization precision. The micro manipulation systems can answer for this request by nano gripper driven with high-precision positioner[]. The Fig. 1 shows a protocol manipulation using two gripper to achieve sequential micro griping of micro sample and transport it to focus of laser Beam. In such a system involves dual manipulators system contain different dynamics and used piezoelectric-stack actuated nanomanipulators, various control design architectures and methodologies have been developed for dual-stage servo control designs to deal with uncertainties (modeling errors, sensor limitations) and environment noise. They can be largely classified into two categories: those based on decoupled or sequential single-inputsingle-output (SISO) designs, and those based on modern optimal design methodologies, such as LQG, LQG/LTR, Hinfinity, and -synthesis, in which the dual-stage controllers are obtained simultaneously[][].

To maintain the micro sample in the focus of laser beam, in addition to the handling system, also depends on the position of the laser beam a local search of the maximum laser beam position is needed to control the micro handling system, N. Amari, D. Folio and A. Ferreira are with the Laboratoire PRISME EA 4229; Ecole Nationale Suprieure d'Ingnieurs de Bourges, 88 boulevard Lahitolle, 18020 Bourges, France. Corresponding author: Antoine Ferreira (Email:antoine.ferreira@ensi-bourges.fr, Tel: +33 2 4848 4079) usually the photodiode sensor device(PSD) is used for this task.

We design a control system that guaranteed microhandling tasks of micro samples in analysis beam. The purpose of this control system is to coordinate two AFM gripper mounted on a 6 dof dual-alignment system for maintain micro spherical ball on maximum laser beam intensity sensed by fixed four-quadrant PSD. The laser beam tracking processus by automated control a AFM gripper depends on real-time of laser beam maximum intensity positioning, where the Particle Filter (PF) algorithm is used to estimate the position of the laser beam in real-time, transmitted at each precision dual alignment system . A Control strategy is adopted to drive each dual alignment system composed by different dynamics by a single laser beam estimation feedback.

The paper is divided into five sections. Section 2 describes the experimental setup. Section 3 describes the dynamics which is involved in the control. Section 4 describes the different control step of a Two-Fingered. Section 5 presents experimental results for the performance of the beam laser beam tracking.

II. EXPERIMENTAL SETUP

The control scheme of the beam pointing and tracking is shown in Fig. 2. composed of: i) Handling device comprises two fingered (Kleindiek FMT-400: 400 m force sensors) mounted in each compact computer-controllable XYZ alignment and positioning systems combining the advantages of ultra-high-resolution piezo drives(to 120×120 × 120µm) i.e., x-y-z closed-loop nanostage (P-611.3S NanoCube from Physics Instruments,characterized by high bandwidth) with the long travel range of motorized stages (to 15 × 15 × 15 cm) i.e., X-Y-Z closed-loop microstage (F-130 DC from Physics Instruments). ii)Optical device placed in side view of the handling device, integrate a 635nm laser diode(Red) Lightshow for producing laser beam, where the laser beam position is measured by the image laser beam formed on a four-quadrant position sensing device(PSD). iii)Imaging device for top-view (top optical microscope -Mituyo ×50) and side-view (TIMM × 400) used for localization and guidance.

Fig. 3 shows the overall control scheme for power, laser beam tracking and fingered control . The control strategy of two fingered for microrobotic manipulation tasks and maintain a spherical ball on maximum laser beam intensity by tracking laser beam motion (Brownian or stochastic trajectory) are processed in real-time using MATLABs xPC software. For laser beam intensity maximum detection and beam tracking a highspeed data acquisition (DAQ) (NI 6289) card is used to register photodiode voltage output, generated when the PSD is illuminated. A multi-thread structure is developed to independently control and coordination of fingered for parallel manipulation, object/Beam detection, handling and tracking laser Beam motion.

III. DYNAMICS MODELING

This section reviews the different model dynamics of the different system components.

A. Dynamics of Piezoelectric and Magnetic Actuators

The micro manipulation processus and the high precision laser beam tracking detected by PSD need a cooperative control of two fingered, i.e, control and combine the different dynamic of the micro/nano stage for drive each fingered in x-y-z direction. For controller synthesis adopted in strategy control, and because we have no parametric information on drivers we need to set up dynamic modeling of dual micro/nano stages. The dynamic model of the Piezoelectric and Magnetic actuators are obtained by experiment estimated transfer functions based on responses of each actuator using random input signal. The dynamics models of the micro and nano are done by the following third-order approximation reduced order for each x-y-z direction respectively :

G micro(x,y,z) (z) = b0+b1z -1 +b2z -2 +b3z -3 1+a1z -1 +a2z -2 +a3z -3 G nano(x,y,z) (z) = b1z -1 +b2z -2 +b3z -3 1+a1z -1 +a2z -2 +a3z -3 (1)
B. Dynamics of Four Quadrant Detector and Laser Beam in our optical device the Photo Sensitive Detector(PSD) used consists of 4 photosensing parts separated by a small gap. Usually, The laser beam is pointed towards the dead center between the 4 quadrants and the beam diameter is selected to fit inside of the total quadrant area. When light falls on all four quadrants, they will generate current for each quadrant according to the light intensity and then amplified into voltage signals V1-V4 respectively.

The difference between the left and right quadrants (Vx) and top and bottom quadrants (Vy) can be used to indicate the offsets of the spot and be adjusted to zero by centering the beam, whereas the sum quadrants voltages corresponding at intensity laser beam (Vs) is at a maximum

V x = (V 1 + V 4 ) -(V 2 + V 3 ) V y = (V 1 + V 2 ) -(V 3 + V 4 ) V s = V 1 + V 2 + V 3 + V 4 . (2)
In Fig. 4) that demonstrate the voltage signal Vx(Vy is similar at Vx) thereby become very sensitive to slight deviations in the position of the beam from this initial centered setting. Than V x and V y channel outputs are directly related to the energy of the laser beam that falls in each quadrant while V s is the sum voltage. It is assume that the light intensity on the laser's beam cross section obeys Gaussian distribution. The current generated by each sensing element can be described as given in:

I = k 1 2E l π 2 r e 2(x 2 1 +y 2 1 ) r 2 dx 1 dy 1 ( 3
)
where I is the current, r the radius of the laser light spot, E t is the energy of the laser beam, (x 1 ,y 1 ) is the coordinate of a point on the light spot in a coordinates system located at the center of the light spot, and k 1 is a coefficient. As shown in Fig. 4) -AFM, The Vs can be used to measure changes in the beam intensity, so this can be used to correct the X and Y output values for voltage changes that are due to intensity fluctuations rather than actual beam deviations by filtering. As we can see in Fig. 5, the experimental intensity sensed by the PSD can be fitted with a gaussian distribution as calculated by the theoretical equation ( 4).

The maximum Gaussian intensity variation by the motion of the laser beam in x direction showing the position of the beam on the dial can be represented by Brownien seconde order variation given by:

d 2 x(t) dt 2 + β x dx(t) dt = W x (4)
were β x coefficient of friction and W x is zero-mean Gaussian random variable with variance δ 2

x . The y-axis can be modeled in the same manner as the x-axis, though with different dynamics. The discrete state space of eq5 laser beam is represented by: Fig. 6. Master-slaver controller with decoupling structure for maximum light tracking.

X k = AX k-1 + BW k ( 5
)
Y k = CX k-1 (6)
where

[x k y k ẋk ẏk ] T (7)
(x k , y k ) and ( ẋk , ẏk ) are the source potion in the plane x-y and velocity respectively.

IV. CONTROL SCHEME OF A TWO-FINGERED AND LASER BEAM TRACKING

The focusing of micro spherical ball handled by Two-Fingered on maximum intensity laser beam and maintain it for several minutes without fingered loose the micro spherical ball during beam tracking, requires a robust control motion of each dual micro/nano manipulator(characterized by two independent control output micro controller and nano controller) and friability localization of laser beam position. Figure 7 presents the control scheme. The detection and estimation of the position of maximum laser beam intensity to drive fingered implies to anticipates the intensity variation caused by the dynamic of the beam laser by estimationprediction filters, transmitted for each dual micro/nano manipulator. The coordination the separated performance of the micro stage and nano stage are important to tack laser beam by only position feedback signal available and maintain the micro sphere ball.

A. Particle filter approach

The first step is to guarantied a real time maximum intensity position estimation sensitive at the laser beam motion. The particle filter is used for this Tasks, that implements the Bayesian filter by modeling the tracking problem as estimating the posterior distribution using the importance sampling of Monte Carlo methods, which approximates the real distribution by generating a set N samples x i k distributed according to the posterior distribution of the Markov state process given the observations,p(x t |y t ), and their associate a normalized importance weights. The estimates calculation of the posterior distribution of the whole process by importance sampling method give:

p(x k |y 1:k ) ≈ N i=1 w i k δ(x k -x i k ) (8)
w i k ∝ w i k-1 p(y k |x (i) k ) (9)
were normalized weights

w(i) k = w (i) k / N j=1 w (j)
k i = 1....N . The particle filter is generally called the Sequential Importance Sampling (SIS) algorithm, which is limited by the degeneracy phenomenon [START_REF] Xie | High-Efficiency Automated Nanomanipulation with Parallel Imaging/Manipulation Force Microscopy[END_REF]. The Sampling Importance Resampling (SIR) By adaptive multinomial resampling based on bootstrap method [START_REF] Pawel | Optimal Disturbance Rejection by LTI Feedback Control in a Laser Beam Steering System[END_REF] is used to estimate and predicate laser beam positions and overcome the degeneracy problem of the original Particle Filter. At every k th step each of the particles is propagated according to dynamical model as the importance distribution p(x i k |y 1:k ) = p(x i K |x i K-1 ), can be generated by first generating a process noise sample

v i k-1 ∼ p v (v k-1 and setting x i k = f (x i k-1 , v i k-1
). The particles are then resampled according to their new importance weights to ensure a uniform weight distribution i.e. x i k-1 = 1/N and so

w i k ∝ p(y k |x (i) k ).
Resample cycle is as follow : N sorted random numbers uniformly distributed in [0,1] are selected. From the cumulative sums of the particle weights calculated, the number of the sorted random numbers that appear in each interval of the cumulative sum represents the number of copiers of this particular particle which are going to be propagated to the next generation. Intuitively, if a particle has a large weight then many random numbers are going to survive. SIR particle filter approach:

• Generates N samples {x i 0 } N i=1 form the initial distribution • Calculate the weights w i k αp(y k |x i k ), i = 1, ...., N and normalize

w(i) k = w (i) k / N j=1 w (j)
k .

• Generate a new set {x i * k } N i=1 by performing resampling. • Predict new particles,x i k+1 = f (x i * k , v k ) ie using different noise realization for the particles.

• Compute the output of the SIR filter by:x

N k = N i=1 w i k x i k
In order to evaluate the performance of Particle Filter used to estimate position of laser beam we give to the laser beam a synthetic trajectory generated randomly without working zone. For particle filtering the particle number needed is determined so that the computational remained suitable for real time application, and assuring high performances , we have done several experiments to determine the appropriate number of particles used in the estimation step. The number of the particles ,thus choused N=80. The results of laser beam motion prediction using Particle Filter are presented in fig. 7. At first glance, the filter succeed to fellow the true trajectories very closely. Another performances test are realized by comparing performance with a classical filter changing the velocity actuator of the laser beam motion and maintaining the initial parameters of the filter. the curve of the square error ε(n) is represented in figure .8. As can be illustrate the performances of the particle filter are better that those of the classical filter in terms of precision were particle filter converge to the real position of the laser beam with a minimal error. As can be seen in fig. 9 the particle filter commits less error than classical filter. The MIMO H ∞ standard problem is used, because it have been successfully used in a wide variety of applications and it proved its efficiency in coping with model uncertainty. The H ∞ concept is to represent system with the block diagram shown in fig. 10 where W i are a weighting function. The H ∞ standard problem consists to find a controller K which stabilizes system and determine a positive number γ 0 to satisfy:

T (s) ∞ < γ(γ ≥ γ 0 ) (10)
Where T (s) closed loop transfer function of the system represented in fig. 10, given by: Fig. 10. H∞ structure

T zw = W 1 S W 1 SGW 3 W 2 KS W 2 KSGW 3 (11)
S is the sensivity function S = (I + G(s)K(s)) -1 . For Solving H ∞ standard problem and obtain a good controller depends on appropriate choice of a structure weighting function with optimal parameters which reflect the robust stability and performance requirements. Since the axis coupling of the fine stage is negligible and the the 3 axis of nano stage have different dynamics, which lets us to choose:

W i = diag(w i1 , w i2 , w i3 ) with i = 1 : 3 (12)
and

w 1i = a1ip+a2i p+b1i w 3i = p+a3i b2ip+b3i w 2i = const i (13)
The inverse of w 1i and w 3i are an upper bound on the desired sensitivity loop shape and complementary sensitivity function T (s), the inverse w 2i will effectively limit the controller u [START_REF] Lee | Temperature Measurement of Visible Light-Emitting Diodes Using Nematic Liquid Crystal Thermography With Laser Illumination[END_REF].

C. Parameters optimization

The GA approach [START_REF] Evans | Piezoelectric microactuator for dual-stage control[END_REF] is used to compute the parameters weighting function namely: a 1i , a 2i , a 3i , b 1i , b 2i , b 3i and const i , and to obtain a optimal H ∞ controller. The concept is to generate a values population of chromosomes representing the parameters to optimize, and subjected to check whether it satisfies the performance index or not. If any the chromosomes does not satisfy the performance index a new chromosome is generated repeatedly until satisfied. Assuming the parameters weighting function to be a binary bits of chromosomes X k . Each of parameters is encoded using N b binary bits, and all the binary bits of these parameters are cascaded to generate a binary chromosome of length N *N b , were N is the number of target parameters considered for optimization and N b necessary number of bits for one parameter binary coding. A population of N p chromosomes can be represented as:

X k = [x k 0 x k 1 ...x k j ] 0 ≤ k ≤ N p -1, 0 ≤ j ≤ N -1 (14)
The x k j is the j th coded parameter in the k th chromosome. The chromosome will be constituted with the cascaded parameters weighting function for each axis. However, the chromosome of parameters weighting is generated within their corresponding minimum and maximum intervals. As W 1 should be low-pass filter and W 3 should be high-pass filter the parameters for optimization will have the same maximum and minimum limitation i.e : After the encoding of the chromosomes has been developed, the controller synthesize is realized with the following computing procedure form : Initialization:

• a 1i The optimized discrete transfer function K(z) is given by: K x (z) = 1.186z 4 -4.01z 3 +5.623z 2 -3.953z+1.154 z 4 -3.25z 3 +4.405z 2 -3.06z+0.9044 then,we obtain u x (k).

q(r) = [max(r) -min(r)]/2 N -1 1 ≤ r ≤ N
and corresponding H ∞ norm = 1.010. The fig. 11 represents the fitness evolution for each chromosome of the population by generation, as can be seen from fig. 11(a) a rapid convergence of the fitness.the chromosome population having a maximum fitness for each generation are selected and represented in the fig. 11(b) as can be seen again the convergence of fitness to a optimal value γ opt = 1.01, which assumes many solution of parameters are envisaged.As GA exhibits an excellent characteristic of global search and selection technic, the chromosomes optimal converge to a same optimal value.For illustrates the parameters optimization convergence, the fig. 12 represents the W 31 parameters optimization evolution.

V. EXPERIMENTS

The control strategy exposed in section 4 to control each AFM tip piloted by dual micro/nano actuators is implemented in our experimental platform.

Fig. 1 .

 1 Fig. 1. High-precision position measurement based on laser beam transmission are commonly used in nanomanipulation applications.

Fig. 2 .Fig. 3 .

 23 Fig. 2. Experimental setup.

Fig. 4 .

 4 Fig. 4. Output voltage curve Vx with a zoom in the block area near zero on an four-quadrant PSD.

Fig. 5 .

 5 Fig. 5. Light intensity on the laser's beam cross section: (left) theoretical and (right) experimental intensity obeying to Gaussian distribution.

Fig. 7 .

 7 Fig. 7. Position estimation with particule filter: (a) Motion estimation on x direction, (b) 2D motion

Fig. 9 .

 9 Fig. 9. mean quadratic error

[0 1 ]

 1 , a 2i [10 100], a 3i [0 1], b 1i [0.001 0.01] b 2i [0 1], b 3i [0 1], const i [0.01 1] • Number of parameters N =21. • Number of generations G n =100. • Bits number N b =5. • Chromosomes number N p =7. • Population size P z = (N p , N * N b ).• Crossover rates=0.75 and mutation rates=0.3. 1-Generate randomly the initial binary population of weights parameters. 2-Repeat for each generation : 2.1-Convert binary population to a decimal population by quantum :

2. 2 -

 2 Evaluate the individual fitness function of all individuals by f i = T (s) ∞ (i = 1, N p ). 2.3-Apply the Elitism selection technique to select the best-fit individuals for reproduction: • compute the total fitness:F = Np i=1 f i . • compute the means fitness:F m = fi F . • for each chromosome, compute :e j = fj Fm (where f i =array of fitness function of chromosomes) the chromosome i is reproduced integer part of e j . 2.4-Breed new individuals through crossover and aleatory mutation operations of genes to obtain new chromosomes. 2.5-Replace least-fit population with new individuals. 3-After obtain optimal weights, use Riccati approach to synthesize H ∞ controller. 4-Use a reduction method based on singular values to reduce the controller order . For displacement on x axis direction the computing procedure allows to obtain the following weighting function: W 11 = s+1 s+0.9258 W 31 = s+0.005935 0.913s+0.9032 W 21 = 0.7097

  Fig. 11. Fitness evolution: (a): Population fitness computed for each generation, (b): Optimal fitness

Fig. 13 .

 13 Fig. 13. Microhandling task of a 20 µm spherical bead using a dualnanomanipulation system: (a) detection of the AFM tip1 by the laser beam, (b) approach of the AFM tip1 and AFM tip2 close to the microobject and (c) stable and reliable handling of the microobject.