Sophie Jacquot
email: sophiejacquot@ifrance.com

Cornelia Woll
email: woll@mpi-fg-koeln.mpg.de

Usage of European Integration -Europeanisation from a Sociological Perspective

Keywords: Europeanisation, integration theory, multi-level governance, policy-coordination, polity-building, participation, political opportunity structure, European public space, structuration theory, sociology Europäische Integrationstheorien sind geprägt von Institutionenforschung. Besonders in der Europäisierungsdebatte dominieren Annahmen über Zwänge, die aus struktureller Inkompatibilität zwischen dem europäischen und den nationalen Ebenen entstehen können. Oft wird dabei den Handlungsträgern, den politischen Akteuren, nur zweitrangige Bedeutung zugemessen. Mit den analytischen Mitteln der politischen Soziologie untersucht dieses Projekt die Bedeutung der Einzelhandlungen politischer Akteure im Integrationsprozess. Hierbei wird vor allem auf die Anpassungsdynamiken der nationalen Ebene Integration auf die nationalen Systeme, so unsere These, ergibt sich aus dem Gebrauch, den politische Akteure von Elementen der europäischen Integration machen. Die Idee eines "Gebrauchs" dient einerseits der Analyse strategischer Interaktionen zwischen Akteuren und Institutionen und anderseits dem Verstehen der diffusen Konsequenzen

The effect of European integration on its member states constitutes the new research agenda within the study of European integration. Marked by the "the institutionalist turn" of Anglo-Saxon political sciences, the most dominant theories on europeanisation focus on structural arrangements. Institutional incompatibility between the European and the national level, so the hypothesis, creates pressures for change. Actors are often only considered as mediators of these pressures. Consequentially, few approaches try to explain adaptational change initiated by policy actors in the absence of institutional pressures. Using a political sociology approach, the central concern of this paper is to insist on the political discretion of national actors in translation of European requirements. We believe that understanding not only "adaptation to" but also "usage of" the process of European integration is important to understanding the transformation of European member states. By insisting on usage, we aim at analysing both the strategic interaction of rational actors with the European institutions and the more sociological effect of "usage" -as "daily practice" -on the interest and identities of the actors.

Contents:

1.

Theorizing about European Integration

What can be the interest of regarding European integration from a sociological perspective? In our eyes, the answer resides in the evolution of theorizing about European integration. Early theories had the objective of explaining a regime, a form of international cooperation. Consequently, the most dominant theories came from the field of international relations. For a long time, theorizing was divided between neo-functionalist explanations [START_REF] Haas | The Uniting of Europe: Political, Social and Economic Forces, 1950-1957[END_REF][START_REF] Lindberg | Europe's Would-Be Polity: Patterns of Change in the European Community[END_REF]Sandholtz and Stone Sweet 1998) and the realist critique of liberal intergovernmentalism [START_REF] Moravcsik | Preferences and Power in the European Community: A Liberal Governmentalist Approach[END_REF][START_REF] Moravcsik | The choice for Europe : social purpose and state power from Messina to Maastricht, Cornell studies in political economy[END_REF]. For both camps, the ambition was to explain the creation and stability of a case of interstate cooperation and the public policies that were consequentially produced at the supranational level. National politics came into play as a factor determining the choices made at the supranational level, but in-depth research of national public policy developed in relative isolation from European studies.

While US theories on European integration became somewhat trapped between the opposition of neo-functionalism and liberal intergovernmentalism [START_REF] Lequesne | Union europeenne et science politique: ou en est le debat theorique? In[END_REF], European integration research reoriented during the 1990s. Faced with the "European Union", with a completed single market and ambitious new projects, European scholars tackled a new issue: explaining the complexity of the European construction. Research on policy networks [START_REF] Jachtenfuchs | Regieren im dynamischen Mehrebenensystem[END_REF] and the interaction of the different levels of policy making (Marks, et al. 1996) flourished and developed into theories of multi-level governance [START_REF] Kohler-Koch | The Transformation of Governance in the European Union[END_REF][START_REF] Marks | Multilevel Governance and European Integration[END_REF]. Still, the study of supranational politics, policies and their implementation remained the principal objective of EU research.

Meanwhile, the increasing complexity of European politics drew comparativists towards this research object. There was a sense that the EU had developed into a full-grown policy realm whose analysis could gain from the tools of classical public policy theory [START_REF] Majone | Regulating Europe[END_REF][START_REF] Muller | Un espace européen de politiques publiques[END_REF][START_REF] Streeck | From National Corporatism to Transnational Pluralism: Organized Interests in the Single European Market[END_REF][START_REF] Hassenteufel | Des politiques publiques comme les autres? Construction de l'objet et outils d'analyse des politiques européennes[END_REF]. Likewise, the EU became an important factor for the analysis of national policy development, so that comparativists increasingly incorporated the European variable into their research [START_REF] Mény | Adjusting to Europe : the impact of the European Union on national institutions and policies[END_REF]. The "institutional turn" of political science, which marked especially Anglo-Saxon literature (Aspinwall and Schneider 2001;[START_REF] Jupille | Institutionalism and the European Union: Beyond International Relations and Comparative Politics[END_REF], helped to bridge the study of European integration by scholars of international relations and comparative public policy. While international relations research started analysing institutional dynamics [START_REF] March | The Institutional Dynamics of International Political Orders[END_REF] and the pressures the international system imposed on domestic politics (Keohane and Milner 1996), comparativists tried to understand the effects of European integration on the politics of the Member States.

Research on Europeanisation

The question of these effects is at the heart of the research which focuses on the Europeanisation of national political systems, a research agenda with has flourished in recent years. European integration becomes the independent variable with influences the politics of the Member States -a perspective that is exactly the inverse of traditional integration research. Essentially, the term "Europeanisation" is used to signify the transformation of a variable at the national level which adapts to a European model, logic or constraint.(1) Since most authors use the term only as a vague concept guiding their empirical investigation, a recurring discussion revolves around the ambiguous utilisation of the meaning of "Europeanisation" and the great diversity of studies which all claim to deal with the topic [START_REF] Radaelli | Wither Europeanization? Concept Stretching and Substantive Change[END_REF][START_REF] Olsen | The Many Faces of Europeanization[END_REF]).

One can nonetheless distinguish studies of Europeanisation according to the object which is supposed to go through the process of adaptation. Sidney [START_REF] Tarrow | The Europeanisation of Conflict: Reflections from a Social Movement Perspective[END_REF] or Gary Marks and Marco Steenbergen (2004) examine a possible relocation of the political struggle -politics -towards the European level. Klaus Goetz and Simon Hix (2001) or Jeffery [START_REF] Anderson | Europeanization and the Transformation of the Democratic Polity, 1945-2000[END_REF] analyse the evolving constellation of political institutions -the polity. Pierre [START_REF] Muller | L'Europeanization des Politiques Publiques[END_REF] or Christophe Knill and Dirk Lehmkuhl (2002) focus on the transformation of public policies. Again others analyse the whole or a part of these objects for one country in particular [START_REF] Cole | The Europeanization of the French polity: continuity, change and adaptation[END_REF][START_REF] Ladrech | Europeanization of Domestic Politics and Institutions: the case of France[END_REF][START_REF] Falkner | The Europeanisation of Autria: Misfit, Adaptation and Controversies[END_REF][START_REF] Lavdas | The Europeanization of Greece[END_REF].

Because of this diversity, the attempt to establish a general theory or explanatory models has most influenced the study of europeanisation [START_REF] Börzel | When Europe Hits Home: Europeanization and Domestic Change[END_REF]Caporaso, et al. 2001). The central element of these works, which try to clarify the mechanisms of europeanisation, has been called the misfit model.(2) The occurrence of divergence or convergence of the level of adaptation between different Member States is explained by the degree of compatibility between the national and European conditions. Incompatibility -misfit -between the two levels create adaptational pressures, which are then transmitted by mediating institutions. « The lower the compatibility (fit) between European institutions and national institutions, the higher the adaptational pressure, » (Caporaso, et al. 2001: 7). At the heart of this model is an assumption taken from historical institutionalism which underlines the rigidity of institutional arrangements (cf. [START_REF] Pierson | Increasing Returns, Path Dependence, and the Study of Politics[END_REF]Steinmo, et al. 1992).

Critical assessment

As in the studies of Europeanisation, the object which we would like to focus on is -very generally speaking -the effect of European integration. Contrary to the dominant strand of literature, however, we would like to insist on two dimensions in particular: the role of actors in the concrete translation of these effects and the motives of action that can be identified. These two aspects seem so far underdeveloped in the current discussions, which have a tendency to focus on structural elements and institutional pressures with less attention to the mechanisms through which these induce change.

The misfit explanation is a good example of the lack of interest for the elements that we would like to develop further. Let us look at both of them in turn. First of all, the strong concentration of the literature on institutional dynamics leads to an underestimation of the discretion and role of political actors in the adaptation process. In a perspective which emphasises the macro level where national institutions are confronted with European policies, the adjustment process of national politics seems to be driven by adaptive pressures alone. National actors only come into play as "intermediary variable". To be sure, the authors of the misfit model insist that adaptation pressures can simply have no effect if actors refuse to react to them (Caporaso, et al. 2001: 2). Yet this means only that actors have the discretion to potentially block the translation of specific pressures. However, an actor cannot initiate adaptation independent of the pressures coming for institutional misfit.

This assumption runs counter to several empirical studies. In his study of the implementation of European directives in several Member States, Oliver [START_REF] Treib | Europäische Vorgaben, nationaler Anpassungsbedarf und seine politische Verarbeitung[END_REF] shows that more than one third of the directives have been implemented in the absence of institutional misfit. Similarly, Christoph Knill and Dirk Lehmkuhl (1999a) demonstrate that the European policy of road haulage has had an important effect on French road haulage policy, even though there has been a perfect fit between the two levels prior to the reform.(3) Secondly, the qualification of different motifs for actions seems to be dealt with only as an afterthought. In their collective work, [START_REF] Caporaso | Transforming Europe: Europeanization and Domestic Change[END_REF] suppose that both rational calculation -based on veto points and available resources -and the transformation of actors' identities -through organisation culture or social learning -can influence the mediation undertaken by actors. Drawing on March and Olson, Börzel and Risse (2000;2002) extend this reflection by distinguishing between two logics of action: one taken from rational institutionalism and another one from sociological institutionalism. This distinction is very helpful, but remains trapped between misfit pressure and institutional change. It only aims to answer the question, "How does the actor chose to react?" We believe that it is necessary to consider a political actor who can "choose" and "learn" outside of institutional pressures. On the contrary, we maintain that one should begin by analysing the actions of individuals in order to be able to evaluation the dynamics of change. As cognitive theory emphasizes, any social action requires an understanding of the environment, in this case the political context [START_REF] Christiansen | The Social Construction of Europe[END_REF][START_REF] Surel | L'intégration européenne vue par l'approche cognitive et normative des politiques publiques[END_REF]. In order to be able to act, actors need to interpret European institutions as well as the pressures that are supposed to emanate from them. This cognitive effort, as well as a number of other behavioural elements, constitutes the essence of the political work that lies at the heart of the European integration process.

A Comprehensive Sociology of European Integration

In an article on the analysis of public policy, Pierre Muller (2000:2) wrote that one of the greatest merits of the cognitive approach was to "sociologise" the political science vision of the State. He underlines that "instead of taking the State from the top and as a whole, it allows us to observe the bottom and to pay attention to the details." With respect to European studies, our approach is comparable. Our intention to "sociologise" integration studies implies emphasizing the role of actors in social interactions as well as the recognition that their mediation is a fundamental part of the integration process. To adopt a sociological perspective also means rethinking mechanisms of structural determination in order to show that these can only operate through continued interactions. As Georg Simmel has suggested almost a century ago, the complexity of networks of social interaction do not produce uniform effect, "only contradictory and conflicting effects."(4) If one accepts this proposition, one has to accept a very high degree of causal complexity when analysing the micro level of social interaction. Paying attention to the role of actors therefore implies studying the mechanisms of appropriation, re-appropriation, engagement and disengagement of the process of European integration. Of course, our intention is not to ignore the importance of other explanatory variables. Actors clearly evolve "within the framework of 'global' structures upon which they do not have the possibility to act," (Muller 2000: 193). Still, our approach necessitates the consideration of the actors' place, choices and strategies. Again, following [START_REF] Simmel | Das Gebiet der Soziologie ?[END_REF][START_REF] Simmel | Das Gebiet der Soziologie ?[END_REF]: 42), the specificity of a sociological analysis is not to determine a new research object, but to provide "an approach, a method of science," which focuses on the forms of interaction between individuals. In this perspective, an actor is faced with institutions who frame his behaviour, who open a "realm of possibilities", but who do not determine his behaviour entirely.

By defining what one could call a "sociology of the usage of European integration", we would like to insist two specific elements of the process of European political transformations: the central role of individual actors and the interaction between the micro-level of the actor and the macro-level of the political institutions. The perspective is sociological because it aims to understand how the actor and his behaviour are constructed and how the institutions evolve dialectically with individual behaviour.( 5) For us, these individual actions constitute the dynamic of national adaptation to the European level, hence the dynamics of Europeanisation.

The following section proceeds in three steps. First, we present the concept of "usage", the central element of our approach. Second, we try to place the concept in a categorisation of analytical perspectives focusing on the transformations triggered by European integration. In conclusion, we try to insist on the heuristic benefits of the analysis of usages.

The concept of usage

The word usage has two dictionary definitions: 1) "the action of using something or the fact of being used" and 2) "habitual or customary practice".( 6) By insisting on the term, we wish to cover both the strategic interaction of rational actors with the European institutions and the more sociological effect of usage -as "daily practice" -on the interest and identities of the actors. The concept thus ties political changes and transformations to the utilisation an actor is able to make of the European integration process and the less conscious, habitual practice that might evolve out of this utilisation. In our analysis, the term usage covers, more precisely, practices and political interactions which adjust and redefine themselves by seizing the European Union as a set of opportunities, be they institutional, ideological, political or organisational.

These practices and political interactions happen as the actors go back and forth between the European level and the national, local, sectoral or institutional level on which they act (or wish to act), creating a context of reciprocal influence.

Concentrating on practices, and thus on usage, allows us to translate the notion of political action or political work. Our intention is to focus on the substance of political relations. Through the concept of usage, it becomes possible to study the nature of the political work of different actors. How does their political role materialize? How do they translate their social position (their institutional situation, their interests, their visions) into practices who are in turn framed by specific political settings?

A usage is guided by a complex set of strategies whose objective is to obtain a particular goal. However, we maintain that the objective can be both "more or less explicit and more or less constructed," (Muller and Surel 1998: 31). A conscious and rational action does not require that the goal that motivated the action in the beginning be identical to the objective followed later, nor that the final effect are completely known or manageable [START_REF] Merton | The unanticipated consequences of social action[END_REF][START_REF] Boudon | Effet pervers et ordre social[END_REF].

Political opportunities, i.e. resources and constraints, provided by the European system provide the necessary conditions for the practices we wish to analyse, but they should not be confused with these practices. Usage implies an intention at work and can therefore not be defined by opportunities alone. Whatever might be the nature of a specific opportunity (e.g. political, financial, institutional or symbolic), actors need to seize them in order to transform them into political practices. The whole process of transforming resources or constraints into political practices constitutes a usage. Opportunities are a necessary but not sufficient condition of usage: they are the contextual element that usage is based on.

A categorisation of different analytical approaches

Our proposed approach is thus a sociological one that focuses on the micro-level of individual interactions between the European and the national level. In order to place this perspective in the larger context of European studies, we propose to categorise the literature on the impact of European integration along two axes. A first axes goes from the macro level of the institutional structure to the micro level of the political actor. A second axes distinguishes analyses based on assumption of rational choice theory from analyses in a more sociological tradition. Let us consider these two dimensions in turn.

It seems to be useful to distinguish studies focusing on large institutional structures from studies concentrating on actors, even though a strict dichotomy between the two and an exclusive focus on either one is clearly outdated (Mayntz and Scharpf 1995;[START_REF] Scharpf | Interaktionsformen: Akteurszentrierter Institutionalismus in der Politikforschung[END_REF]. In Europeanisation studies, for example, there is a consensus that "national institutions and actors matter, in the sense that they have a profound, if not determining, effect on how European integration as a force of polity and politics change plays out in the domestic context," (Goetz and Hix 2001: 20). When it comes to more concrete models or explanations, however, the hierarchy established between the two levels of analysis varies considerably. The authors of the misfit theory as well as [START_REF] Duina | National-States amd Common Markets: The Institutional Conditions for Acceptance[END_REF] or [START_REF] Pollack | The New Institutionalism and EC Governance: The Promise and Limits of Institutional Analysis[END_REF] place a definition emphasis on institutional structures and only turn to the question of political actors in a case of divergence between countries. Dyson et Featherstone [START_REF] Dyson | Italy and the EMU as a "Vincolo Esterno": Empowering the Technocrats, Transforming the State[END_REF][START_REF] Dyson | The Road to Maastricht: Negotiating Economic and Monetary Union[END_REF], by contrast, focus on the strategic action and interaction of individuals placed in specific institutional configurations.

The second axis distinguishes between the rational or sociological nature of the underlying assumptions. In the case of Europeanisation studies, these two assumptions are taken up by studies in the tradition of economic institutionalism [START_REF] North | Instititutions, Institutional Change and Economic Performance[END_REF]) and studies in the tradition of sociological institutionalism [START_REF] March | Rediscovering institutions: the organizational basis of politics[END_REF]. The principal difference between the two perspectives resides in the continuity of preferences. In a rational economical analysis, actors' preferences are both exogenous and stable and therefore essential to explaining a certain phenomenon such as institutional change. For sociological analyses, preferences are endogenous to the institutional setting that the individual needs to act in. Consequently, they often become the primary object of a sociological study, which aims at understanding their transformations. However, the focus is essentially on the relationship between institutions and individuals rather than the individuals' interactions among each other. For the case of Europeanisation, the interest of a comprehensive sociology is to combine these two analytical dimensions: the sociology of cognitive change and the evolution of preferences with an analysis of strategic interaction. Only few studies have analysed these questions from a consistently sociological perspective [START_REF] Bach | Die Europäisierung nationaler Gesellschaften[END_REF], even though our approach reflects a trend in recent political science literature to start analysing the dynamics of strategic and cognitive interactions (Fallend Grabner and Lenschow 2003;[START_REF] Trondal | Why Europeanisation Happens : The Transformative Power of EU Committees[END_REF][START_REF] Schimmelfenig | Theorizing EU enlargement: research focus, hypotheses, and the state of research[END_REF].

Other research has furthermore studied elements of these interactions, such as discourse [START_REF] Diez | Speaking "Europe": the politics of integration discourse[END_REF][START_REF] Hay | Globalisation, European Integration and the Discursive Construction of Economic Imperatives[END_REF][START_REF] Schmidt | Discourse and (dis)integration in Europe: the cases of France, Germany, and Great Britian[END_REF], cognitive framing [START_REF] Marcussen | Central-Bankers, the Ideational Life Cycle and the Social Construction of EMU[END_REF][START_REF] Muller | Entre l'Europe et le local: la crise du modèle française des politiques publiques[END_REF], or on the role of European institutions as a normative entrepreneur [START_REF] Jabko | In the name of the Market: how the European Commission paved the way for monetary union[END_REF][START_REF] Wendon | The Commission as image-venue entrepreneur in EU social policy[END_REF]).

On a side-note, we should mention that we do not deal with historical institutionalism, because it seems to be different from economical or sociological institutionalism only in its diachronic optic, not in its presuppositions. According to Hall and Taylor (1996: 939), « historical institutionalisms tend […] to conceptualise relations between institutions and individual behaviour in relatively large terms.» Indeed, depending on the author, historical institutionalism can be based either on rational assumptions [START_REF] Pierson | Increasing Returns, Path Dependence, and the Study of Politics[END_REF] or on sociological ones [START_REF] Mahoney | Path dependence in historical sociology[END_REF].

We suggest crossing the two dimensions we have just identified in order to better isolate the focus of different approaches.

Table 1 In quadrant I, institutions and preferences are given. Studies in this perspective focus above all on the compatibility or conflict of national and European structures, and how these situations might affect the interests of a national actor in a very general sense. In quadrant II, a given institutional opportunity structure provides the context for an analysis of the strategic behaviour of an actor who decides to react strategically in order to maximize his benefits. In quadrant III, the central interest lies in the constitutive relations between institutions and actors. The analysis combines a definition of actors in terms of identity and interests with the procedures of legitimation employed by the European institutions. Quadrant IV finally allows analysing the adaptation of actors' preferences. The focus will therefore be on the general and reciprocal process of interaction and transformation of actors and institutions, with a central interest on the changing resources, opportunities, legitimacy and identity of national or transnational political actors.

By proposing a comprehensive sociology of usage, we intent to put into light the interaction of actors with the realities of European integration and the consequences of this interaction. According to this approach, usage of the EU, as strategic as it might be in the first place, will through repetition lead to cognitive and/or normative adaptations, which in turn change the behaviour of the actor or his or her social positioning. Our primary interest is thus in both the second and the fourth quadrant: the analysis of an actor faced with a world where her preferences and the institutional constraints transform due to her behaviour and the behaviour of others like her. The advantage of such a perspective is to draw attention to this succession of adaptations.

However, as all approaches that one could cite under the label « structuration » [START_REF] Giddens | The Constitution of Society: Outline of the Theory of Structuration[END_REF], this approach suffers from the fact that both actors' preferences as well as the shape of the institutions are endogenous to the process in question. The action chosen has an impact on the institution which likewise impacts on the interests and the learning potential of that actor, and so on. Despite it conceptual value, the approach entails thus explicative and methodological difficulties. At which moment should an analysis of a particular situation start? If institutions are not stable, but can also not be explained out of one particular set of actions, is it useful to concentrate on the actions of specific actors or does one need to begin with the institutions?

In order to avoid some of these difficulties, it therefore seems heuristically necessary to analyse any given case study by distinguishing actors and institutions. We suggest dividing empirical investigations into a part where the actor adapt (strategically or cognitively) to specific institutional realities and another part where the European institutions contribute to the formation of the actors' interests and representations. Thus, a short term analysis by means of usage would need to focus on both strategic mobilisations and cognitive adaptation. For a long term analysis, it becomes necessary to understand how the resulting interactions generate dynamics that affect the construction or transformation of identities and interests.

Actors and European transformations -no impact without usage

The prime concern of our perspective is thus to underline the central role of actors and the effects of their behaviour at the heart of the European integration process.( 7) Too often actors only enter an analysis as secondary or intermediary variable. Frequently, they become a facilitating or blocking part of the transmission of political adaptation, while their role in the evolution of institutional structures is ignored.

To summarize our propositions, political usage describes the mediation done by an actor to transform a material or immaterial resource provided by the European institutions into a political action. At the same time, the word usage implies the repetition of such actions, which make them customary -usage then describes a habitual act, which has become much less conscious than at its first use. Contrary to analyses focusing on institutions only, our central hypothesis is that political usage is necessary for any impact of the European integration process on national political systems. More generally speaking, a measure cannot have an impact if no actor seizes it and transmits it to the national level.

Several conceptual merits of the approach seem to be worth underlining. By insisting on the discretional action of individuals, it permits to understand Europeanisation as a dynamic process, which is much less linear and automatic than in the dominant conception. Furthermore, the approach provides a means of studying how the adaptation of public policy is carried out by individuals.

Concerning the application of this concept, we would like to point out that both constraining and non-constraining processes can benefit from a study of political usage. While it seems relatively evident that usage applies to the study of soft law procedures, it also comes into play in the context of hard measures. Soft law measures, like the method of open coordination, provide actors with a general, yet sufficiently vague framework, which they can interpret to increase their political discretion. To cite an example, the Service des droits des femmes et de l'égalité français, a French ministerial service, has in this way been able to benefit both from the fact that a fourth pillar of gender equality was inserted in the European Employment Strategy and from the overall objective of gender mainstreaming within the EU. These two measures allowed the service department to participate in the elaboration of the National Action Plans for Employment in France, which meant that it had taken a formerly inaccessible position in national policy making. Yet, even constraining procedures, such as directives or court rulings, can benefit from a usage analysis. Even if it is to a lesser degree, the mediation of political actors is not absent and the impact of a constraining measure not automatic. The often differential procedure of parliamentary transposition [START_REF] Treib | Die Umsetzung von EU-Richtlinien im Zeichen der Parteipolitik: Eine akteurzentrierte Antwort auf die Misfit-These[END_REF] or judiciary strategies of specific interest groups [START_REF] Caporaso | The europeanization of gender equality policy and domestic structural change[END_REF]) are examples of the mediation necessary for the transposition of hard elements of European integration. Without usage, there is no impact. Still, it is important to note that usage does not necessarily imply impact. Usage does not imply automatic results -their failures are always possible and need to be considered. The concept of usage is a constitutive mechanism: it is part of a process, not necessarily its cause. To be more precise, usage is a necessary condition for impact, but not always a sufficient one.

A Typology of Usage

Since our primary objective is working on actors, an immediate intuition would be to organise a typology according to categories of actors. At a first glance, public officials or politicians, for example, seem to utilise different elements of the EU than non-governmental organisations. However, a typology structured according to actors seems to run the risk of confusing the motivation of specific behaviour with their results. This is why we have chosen to classify usage according to their functionality.

Three types of usage Strategic usage

As the term « strategic » implies, this usage describes the transformation of resources in political practices with the intention of pursuing a specific goal. The goal is clearly defined and consciously pursued, be it in order to influence a particular policy decision, increase one's capacity of action, one's access to the political process or the number of political tools available.

Strategic usage seems to be the most common of all usages. With the extension of competencies of the EU, it is open to a large and increasing number of actors. It can therefore apply to actors found at the supranational level, the national level or the transnational level, in the form of both governmental and non-governmental actors.

An example which is quite typical of this type of usage would be a national interest group transforming itself into an EUrelevant interest group in order to benefit from the funding scheme provided by the European Commission. This transformation furthermore permits the interest group to participate in EU-specific policy discussions, which opens the possibility of playing a "two-level game" with the government of its home country.

Cognitive usage

Cognitive usage is most common in the contexts of policy interpretation and persuasion. Any social fact requires interpretation before it can be used in a political debate. Cognitive usage covers, first of all, the understanding and interpretation of a political subject. Secondly, it applies to the diffusion of specific ideas which provide a framework for understanding and deliberating over a certain subject. Eventually, cognitive usage provides the vectors for persuasion within a policy discussion.( 8)

Cognitive usage applies to supranational actors, national and transnational actors once they enter into a deliberative context. Through policy discussions, evaluations, and the importation or rejection of new policy concepts, actors advance the issue at stake, be they policy or hierarchy decisions, policy interpretations, or definitions of sectors, professions or others. Typical examples for ideas diffused in the EU context are, for instance, the principal of subsidiary, social cohesion or the knowledge economy.

Legitimising usage

This last type is a very specific type of usage that includes a mix of both strategy and cognitive framing. Since it is quite central to the political process, we would nonetheless like to single it out as a separate type of usage.

Patrick Hassenteufel and Yves Surel (Hassenteufel and Surel 2000: 19) have described this form of usage "the reference to Europe as a way of legitimising national public policies." The function of this type of usage is to increase or renew the public acceptance of a policy decision at the national level (see [START_REF] Jobert | France : la consécration républicaine du néo-libéralisme[END_REF]. It is most commonly employed by governmental actors who try to appeal to the public opinion of their country and relies heavily on rhetorical figures such as "European interest" or "European constraints". This "European rhetoric" corresponds to what Eric [START_REF] Fassin | Good cop, Bad cop. Modèle et contre-modèle américains dans le discours libéral français depuis les années 1980[END_REF] has described as the "rhétorique de l'Amérique" used in the early 1980s in France in order to justify the oxymoron "French liberalism". By interrogating what this rhetoric seeks to describe and achieve, one will find that a situation presented as scientific might actually be exclusively political [START_REF] Hay | Globalisation, European Integration and the Discursive Construction of Economic Imperatives[END_REF].

Even though this legitimation seems to be founded on "empty" discourse, we would like to insist that even discourse might have an effect. "Ideas do not float freely" as Thomas Risse reminds us, and rhetoric is never completely neutral, because it conveys associations and images that then circulate and transform national references.

Figure 1 Figure 1 aligns the three types of usage identified with the type of political stake it applies to most. It seems most helpful to crudely distinguish between three moments in a political process: 1. the moment in which issues are problematised, ideas are defined and alternatives are suggested; 2. the very general procedure of decision-making, which entails both the conflict around the decision itself, the mode of decision-making and the struggle of actors to participate in the decision-making process; and 3. the justification of a given political action or decision on the political stage in front of an audience.

The definitions which we have just elaborated upon are of quite abstract nature. In order to make them more concrete, we suggest putting them in a context of further elements that are connected to the different types of usage. We will later use the elements spelled out below to give some further indications about the variety of motifs that triggered a specific act.

Elements used

Usage depends upon specific elements or tools that actors can seize. Most generally, these elements can be divided into two categories: immaterial and material elements. In the first category, we have identified discursive references, ideas and the use of the European public sphere; in the second, European institutions, policy instruments and funding.

Immaterial elements:

Discursive references, as pointed out above, are rhetoric figures aiming at invoking a positive or negative association.

Ideas are more complex than discursive references. In policy analysis, ideas are used as a label to assemble all forms of thought constructs: perceptions, believes, values and norms as well as more complex frameworks such as paradigms. It might be useful to divide ideas into three subcategories: cognitive interpretations, causal ideas and normative believes.( 9) Cognitive interpretations allow an actor to grasp an event, to transform it into a reality that is understandable, analysable and utilisable. Causal ideas are believes about cause-and-effect relationships and therefore contain prescriptions for action. Normative believes are value judgements: what is assumed to be good or bad for the political objective in question. Causal and normative believes are most often inserted in a complex form, a cognitive framework.

The public sphere or the European public space is a concept elaborated initially by Jürgen [START_REF] Habermas | Strukturwandel der Öffentlichkeit[END_REF][START_REF] Habermas | Strukturwandel der Öffentlichkeit[END_REF]) and later taken up again by scholars working on participatory and deliberative politics. The public sphere refers to the discursive space independent from governmental institutions which allows for the exchange of ideas on collective problems or action. In the European context, the public sphere is most relevant for non-governmental organisations, which can increase their political salience by linking themselves to like-minded organisations from other Member States. One can also imagine protest movements or political discussions of socio-economical elites from across Europe, who seize the new public space in order to draw attention to an issue they present as collective and European.

Material elements:

More concrete elements or tools provided by the EU are, above all, the European institutions themselves. Access to these institutions, by means of the Commission's comitology, for example, implies access to the political deliberation, the problematisation of policy issues. By acquiring the status of experts, non-governmental organisations can thus gain political legitimacy or simply obtain important policy information that would have otherwise been outside of their reach. But even public officials might find it useful employ a formerly unused mechanism of institutional cooperation with other Member States.

Policy instruments, as mentioned above, can be either constraining (directives, court judgments) or non-constraining (resolutions, recommendations, communications, the open method of coordination, "benchmarking", "mainstreaming" or others). Non-constraining instruments leave by definition a larger discretion to the political actor, but constraining policy instrument also require interpretation and transposition to the national level.

Financing or funding very directly covers financial allocations for the use of a particular political project distributed through a call for tender from the European Commission. It is important to note that the use should be political not individual, as in the case of Erasmus stipends. A typical example would be the Commission's funding scheme for nongovernmental organisations.

Concerning the different types of actors, it useful to distinguish between the different levels of the European system:(10) supranational, national and transnational. One could cite governments, political parties, interest groups, political movements, as well as more vague groups such as political, administrative or socio-economical elites.

Even though exception are possible, the most reoccurring associations between the different elements used and the actors we have elaborated upon and the three types of usage identified earlier seems to be the following:

Logics of action

Finally, in order to develop a set of declinations of possible usage situations, we would like to consider the different logics motivating action. One of the benefits of the approach of political usage is to draw our attention to these motivations, as most usage is premeditated and needs to be incited by a specific desire. By crossing the elements used with the effects that an actor intents to pursue, it becomes possible to distinguish different logics of action.

Seite 8 von 14 EIoP: Text 2003-012: Full Text 30.12.2003 http://eiop.or.at/eiop/texte/2003-012.htm 9 However, a special caveat is necessary concerning the intended effects. Any action will have consequences that the actor tries to evaluate and intents to cause. Yet intended effects should not be confused with actual effects. Since a great variety of factors intervene before the final consequence plays out, we can only consider here the consequences the actor has actually aimed for. Only his intention is a part of the motifs of his action. In the political domain, we distinguish between short term effects, long term effects and an absence of effects. Absence of effects means that there are no consequences for the direct political issue that the individual tries to act upon. A variety of factors can explain the gap between a determined action and the unattained goal. One could imagine, for instance, that the action was only a pretence: while it looked like the actor was trying to influence a political decision, he might just have wanted to increase his reputation or social positioning or defend his standing.

Table 3 The logics that motivate and orient action vary as a function of the result that actor intended as well as the element the actor employed. Three specific groups of situations seem to exist, which can be regrouped under the following labels: influence logic, positioning logic and justification logic.( 11)

Influence logic: The goal is to act on the content or orientation of a political issue, more generally speaking, to weigh on a political stake. As the name indicates, wanting to gain political influence is the specific goal aimed at through strategic or cognitive means.

Positioning logic: Here, the goal is to position oneself more advantageously in the political process. In the context of political groups wishing to reinforce their access to the political game, or more precisely in the political network that develops around a political issue, this logic is very common. When applying to groups, the positioning logic contains the "logic of membership", which we borrow from [START_REF] Schmitter | The Organisation of Business Interests : Studying the Associative Action of Business in Advanced Industrial Societies[END_REF]. According to this notion the important goal is not to influence the decision-making process, but to please the members of the political group by claiming a presence on the European stage. The group might undertake a lot of actions in the European policy context, which eventually yield very few results. Membership logic reminds us that the issue here might have been to gain in reputation or credibility, which is part of the social positioning of the political actor.

Justification logic: This last motif is specific and relates exclusively to cases where the political decision has already been taken and needs to be justified. Justification logic is most often tied to the political objective of gaining support for a political choice that has already been made. In an often very obvious way, actors try to justify their choices through means of European symbolism, which often has more positive associations than national symbols, or to promote a specific position in the European public sphere.

With the goal of either influence or positioning, an actor can proceed both by cognitive or strategic means. To illustrate, the use of a policy instrument such as benchmarking might represent a strategic usage aimed at a short term goal. A public official could for example seize this new method in order to extend the field of competencies of his department who would be in charge of the evaluation. In a long-term perspective, the usage of this instrument will weigh upon the cognitive structure of the organisation or the policy sector and will provide new cognitive and normative references. With the long term in mind, the use of benchmarking is therefore a cognitive usage. Table 3 does not indicate this set of possibilities for reasons of clarity. The variation of different situations in the table illustrates the multiplicity of actions imaginable.

The objective of this section has been to clarify the tools that can be derived from an analytical approach focusing on political usage. We have distinguished three types of usage (strategic, cognitive and legitimising) and have shown how they are inserted in the political process. In order to make this typology more operational, we have identified a series of constitutive elements of each type. Since the elements used are a good indicator of the motifs of action, we have finally provided examples of the objectives of different actors, which has allowed us to isolate three different logics.

Conclusion

Our intention is not to open up a fundamentally different research agenda, but to multiply the angles of analysis of the impact of European integration. By relying on the method approach of sociology, it becomes possible to put the micro level of social interactions into light and to understand its importance for the study of a highly complex political system. The goal is not to make a conceptual innovation, but to provide a new analytical instrument that has been forged from existing sociological concepts.

An interrogation about usage poses the question of interactions between national or transnational actors with European ones. The repetition of these exchanges produces reciprocal transformations, of which Europeanisation is one. By relating different studies through the concentration on similar forms of interaction, our objective is to arrive at a more global vision of the transformations at work. It seems to us that individual actions have so far been ignored in the study of large European transformations. Despite the difficulties that arise when one tries to deal with them systematically, we would like to insist on bringing them back in. (1) As a dictionary entry in the French Petit Robert (Edition 2000), "européanization" dates back to 1906 and describes the result of "européaniser", a word recorded since the time of Napoleon in 1807, meaning "to give a European character to something."

(2) One should note that the authors of the misfit model use the term "Europeanisation" with the following definition: "the emergence and development at the European level of distinct structures of governance," (Caporaso, et al. 2001: 3). This definition has been criticized because it confuses Europeanization with European integration [START_REF] Bulmer | New Perspectives on EU-Member State Relationships[END_REF]. However, the poor definition does not disturb the clarity of the model, where they describe the adaptation process at the national level as "Europeanisation and domestic structural change." In the following text, we will use the term "Europeanisation" in order to describe the adaptation process of within the Member States, even when we cite the misfit model specifically.

(3) This actually became a point of contention in an interesting exchange between the authors and Thomas Risse. See [START_REF] Knill | How Europe matters: three Europeanization mechanisms[END_REF].

(4) Richard Münch (1994) summarizes Simmel's conclusion in the following way: "… in the distinction to the causal laws studied by the natural sciences, the laws of forms of sociation are always laws of interaction, which have to take into account the relationship of at least two parts to one another and the effects of their interaction on each of them and on different aspects and subparts of them. Because of this complicated web of interactions, there is no uniform effect, only contradictory and conflicting effects."

(5) Attention to the socialisation effect of European integration is not new. Neo-functionalists such as Ernest Haas have underlined the development of European identities or "supranational loyalties" which emerge through the integration process, for example.

(6) The Concise Oxford Dictionary, 10 th edition.

(7) By insisting on the centrality of actors in institutional dynamics of European integration, we apply several notions from the actor-centred institutionalism of Renate Mayntz and Fritz Scharpf to the study of Europeanisation.

(8) This last element makes cognitive usage somewhat strategic as well. Since the primary objective is to frame and understand a topic, even if this eventually leads to the pursuit of a specific goal, we nonetheless propose to distinguish between the two. As all typologies, the forms of usage are but ideal types and occur most often in a somewhat mixed way.

(9) Goldstein et Keohane (1993) add a fourth category, world visions. We have decided to omit these in our analysis, because they seem to be merely a sophisticated combination of the other three categories.

(10) We use the term "European system" in a large sense here, covering both the actors engaged in it, the policy arenas and politic policies that constitute as well as the European public sphere.

(11) As the different types of usage, these logics of action are ideal types and can only be separated analytically. In reality, trying to achieve a better positioning in the political process is always attractive because it promises greater influence in the long run. But the ambition of influence is often very vague and quite far in the future, so that it seems useful to distinguish the two.

©2003 by Jacquot/Woll formated and tagged by MN, 18.12.2003

  This paper presents the theoretical framework of a Ph.D. student conference held at the Institut d'Etudes Politiques in Paris in February 2003. Alongside some of the contributions to this conferences, it will be published in French in 2004 as "Usages de l'Europe: acteurs et transformations européennes," Paris: l'Harmattan, in the collection "Logiques politiques". The English version has been presented at the General Conference in Marburg in September 2003 at the panel 16.5. on "Theories of Europeanisation" chaired by Gerda Falkner. The authors would like to thank Richard Balme, Bruno Palier, Frédéric Merand, Olivier Rozenberg, Dirk Lehmkuhl and two very helpful anonymous referees for their comments and suggestions.

  Theorizing about European Integration 1.1. Research on Europeanisation 1.2. Critical assessment 2. A Comprehensive Sociology of European Integration 2.1. The concept of usage 2.2.

A categorisation of different analytical approaches 2.3. Actors and European transformations -no impact without usage 3. A Typology of Usage 3.1. Three types of usage 3.2. Elements used 3.3. Logics of action 4. Conclusion References 1

Table 2

 2

Usage and political stakes ©2003 by Jacquot/Woll formated and tagged by MN, 18.12.2003


Teresa Vidal

Cyrille Berger

Joan Sola

Simon Lacroix

Environment modeling for cooperative aerial/ground robotic systems

This paper addresses the cooperative localization and visual mapping problem for multiple aerial and ground robots. We propose the use of heterogeneous visual landmarks, points and line segments. A large-scale SLAM algorithm is generalized to manage multiple robots, in which a global graph maintains the topological relationships between a series of local sub-maps built by the different robots. Only single camera setups are considered: in order to achieve undelayed initialization, we present a novel parametrization for lines based on anchored Plücker coordinates, to which we add extensible endpoints to enhance their representativeness. The built maps combine such lines with 3D points parametrized in inverse-depth. The overall approach is evaluated with real-data taken with a helicopter and a ground rover in an abandoned village.

Introduction

In a aerial / ground multi-robot context, as in any multi-robot context, the ability to build and share environment models among the robots is an essential pre-requisite to the development of cooperation schemes. Be it for exploration, surveillance or intervention missions, environment models are indeed necessary to plan and coordinate paths, but also to determine the utility of vantage points, to assess whether robots will be able to communicate or not, and to localize the robots in a common frame. In particular, 3D information on the environment is required: not only the robots evolve in the three dimensions, but the determination of vantage points calls for visibility computations in the 3D space. Also, vision is here the primary en-vironment sensor to build environment representations: besides the fact that images carry a lot of information on the environment, vision is passive, it has the main advantage to perceive features that are arbitrarily far away, and it is the only sensor that can be exploited on-board micro-drones -that have undoubtedly a promising future.

Approach. Our aerial / ground context requires the resolution of the two following issues: on the one hand the mapping approach must be distributed so as to cope with the communications constraints, and on the other hand the map structure must allow data association and fusion, coping with the fact that the sensors or viewpoints can be very different among the different robots. The contribution of this paper is therefore twofold.

We first propose a distributed mapping approach in which robots build series of sub-maps using a classical EKF-based SLAM paradigm. The overall spatial consistency of the maps among the robots is ensured by an optimization process, that takes into account various inter-robot and absolute localization estimates. This work stems from the work on hierarchical SLAM proposed by Estrada et al in [START_REF] Estrada | Hierarchical SLAM: Real-time accurate mapping of large environments[END_REF], which relies on a hierarchical representation of the map: the global level is an adjacency graph, where nodes are local maps (or "sub-maps"), and edges are relative locations between local maps. In a multi-robot context, various events can trigger loop closures and later map merging, namely rendezvous between robots, landmark correspondences ("map matching") and absolute localizations provided by GPS fixes or by matches with an a priori existing map. These events exhibit a cycle on the graph of the map poses, and thus define constraints that allows the system to refine the estimates of the sub-maps origins.

Among the three possibilities to close loops in the overall graph of maps, map matching is the most difficult to achieve when maps have been built by heterogeneous robots, i.e. with different kinds of sensors or vantage points. To be able to match maps, we need to represent in maps characteristics of the environment that are invariant with respect to large viewpoint changes. For this purpose, we exploit line segments detected in the images in order to build 3D wireframe maps that can be matched among the robots. This calls for a dedicated implementation of the EKF-based SLAM approach, which relies on the undelayed initialization of anchored Plücker 3D lines.

Outline. Sections 2 and 3 present the localization and mapping approach to deal with multiple robots. The approach is based on the scalable SLAM approaches, known as hybrid or hierarchical, that consider sub-maps and graph levels. Section 4 is devoted to the building of a 3D wireframe model on the basis of line segments detected in monocular imagery. It introduces the anchored Plücker line parametrization to use segments as landmarks in a monocular EKF SLAM approach. Finally, Section 5 present results obtained with data gathered by a helicopter and a ground rover.

Hierarchical SLAM

The multiple robot localization and mapping problem is formulated using sub-maps in a similar manner to hierarchical SLAM in [START_REF] Estrada | Hierarchical SLAM: Real-time accurate mapping of large environments[END_REF] or hybrid metrictopological SLAM in [START_REF] Blanco | Subjective local maps for hybrid metric-topological SLAM[END_REF], where there are two levels: metric (local sub-maps), and topological (global graph).

The topological (global) level represents the relationships s j i between local maps i and j. The metric level contains the local maps, composed of the set of landmarks m i and the current robot pose x i . Each local map stores information in its own lrf. At a certain point a new local map is generated with the robot pose acting as the new local reference frame (lrf ). Thus the robot pose x i truly represents the relation between the previous map and the new one, and one can set s i+1 i = x i . Other non-correlative relations s j i may be established between maps as we will see. Based on simple frame compositions, information in the world reference frame (wrf) is also available for the origins S i of each map, and for the map itself M i if it is required.

Metric Level. The local or metric level contains the feature-based locally referred stochastic maps, built with the standard EKF-SLAM. The i-th local map is defined by

x i m = x i m i , (1)
where x i is the current pose of the robot, and

m i = [l i 1 . . . li m ]
⊤ is the set of m mapped landmarks, both with respect to the i-th lrf. EKF-SLAM keeps a Gaussian estimate

x i m ∼ N {x i m , P i m } of this map, namely xi m = xi mi , P i m = P xixi P ximi (P ximi ) ⊤ P mimi . (2)
The maps are built sequentially as mentioned above. Once a threshold is passed, either in number of landmarks or in robot's uncertainty, a new map is created. Let us consider for now that no information is shared between these sub-maps, thus the new map starts in a lrf with robot's pose and error covariance equal to zero.

Topological Level. The global or topological level is represented as an adjacency graph in which origins of local maps S i in wrf are nodes, and the links between them are the relative transformations s i+1 i . Let us define the global level as the Gaussian state s ∼ N {ŝ; P s } of relative transformations between local maps, namely:

ŝ =    ŝ1 0 . . . ŝi+1 i    , P s =   P s 1 0 0 0 0 . 0 0 0 P s i+1 i   . (3)
The global origins of the maps in the wrf are computed as the compounding of the previous global origin with the relative transformation between sub-maps, S i+1 = S i ⊕ s i+1 i . The current position of the robot in wrf is computed as X i = S i ⊕ x i . Also, the global map can be obtained through,

M i = S i ⊕ m i . (4)
Mean and covariances of the Gaussian estimates are obtained by regular linear-Gaussian propagation using the Jacobians of ⊕ and ⊖.

Considering the relative transformations between local maps as past robot poses, we note that the global level can be viewed as a sparse delayed-state pose-SLAM [START_REF] Eustice | Exactly sparse delayed-state filters for view-based SLAM[END_REF], where local maps are like landmarks hanging from robot poses in wrf. The main difference is associated to the fact that the statespace in our case contains relative poses x i , instead of absolute poses S i .

Loop Closure. At the global level, a loop closure corresponds to a cycle in the graph, that appears for instance when a relative position estimate between non-consecutive sub-maps is established by a map matching process. Such a cycle defines a constraint between a series of relative transformations:

h(s) = s 1 0 ⊕ s 2 1 • • • ⊕ s 0 i = 0 (5) = S i ⊕ s 0 i = 0 . (6)
Given that h(s) is not linear due to the angular terms, the enforcement of this constraint can be formulated as a nonlinear constrained optimization problem. A solution for instance could be based on the Iterative EKF [START_REF] Estrada | Hierarchical SLAM: Real-time accurate mapping of large environments[END_REF]: the part of the state involved in the loop closure at global level then becomes correlated, resulting in a non-sparse covariance matrix P s .

Note that for a single robot, local maps are obtained sequentially, hence the relative transformation between the local maps is given by the last robot pose in the current lrf, s i+1 i = x i .

Multiple robots

A hierarchical/hybrid SLAM approach in the multi-robot case seems a priori straightforward: each robot manages a set of sub-maps and a global graph of poses. But the interests of multi-robot mapping arise of course when the robots exchange mapping or position information, which allows to enhance the spatial consistency and to build up a multi-robot global graph of map poses (origins of local sub-maps).

In general when multiple robots are exploring the same area, they meet sooner or later or their maps partially overlap: these events will allow the system to establish connections between robot locations [START_REF] Vidal-Calleja | Even-driven loop closure in multi-robot mapping[END_REF]. The events we or feature matches with an existing environment model. The latter is not exactly a multi-robot loop closure, it provides a link between a lrf and a global geo-referenced frame: this yields the possibility to establish a link with another robot that has already been absolutely localized once.

All these events create a link between the robots' global levels. Whereas in a single robot case a loop closure only occurs when the robot revisits a previously mapped place, in a multi-robot case these events trigger loop closures: any cycle that appears in the overall graph defined by the concatenation of each robot graph (the multi-robot graph) is a loop closure. The compounding of all relative transformations that define a cycle is equal to zero as in Eq. 5, and a batch optimization over the transformations can be performed. Note that to obtain a cycle in the graph defined by the concatenation of two robots global levels, at least two events between these robots are required.

The main advantage to exploit a hierarchical map structure in multi-robot mapping is the low communication bandwidth required among the robots: only the individual graphs need to be exchanged to update the multi-robot graph. We will however see that in the map-matching case, the sub-maps that match must also be communicated: but they have naturally already been exchanged to establish the matches. Most importantly is that in the general case, only marginal distributions of each node has to be communicated, as opposed to the full joint distributions of the graph. As we will see later, each robot performs its own optimization based on the minimal cycle.

Robot Rendezvous. The event occurs when a robot observes another robot (partial rendezvous) or when both robots observe each other (full rendezvous). We will focus on the case when the relative transformation between two robots it is fully recovered, from the information obtained through a partial or full rendezvous.

New local maps are created in the instant of the rendezvous, then the current robot poses are promoted to the global level. In this way, the observed transformation z naturally produces a link between the maps' origins S i and S j on the global level, thus z = s i j .

Matching common information. There exist at least two different ways to match common information. For example, using information completely independent to the SLAM, e.g. image's descriptors matching (SIFT, SURF), image indexing techniques or scan matching (ICP). A common way to produce a map of poses [START_REF] Eustice | Exactly sparse delayed-state filters for view-based SLAM[END_REF] is to find the rotation and translation between two robot poses using one of these techniques, as opposed to tracking features. A second way to match common information is using the available information of the maps (position and uncertainty in global level). This is usually done using the current position of the robot or robots in the wrf.

• The "image to image" association produces a link directly between images, that are associated to certain poses S i and S j . Note, the robot poses have to be part of the global graph when this event occurs. This is a simple, but effective manner to obtain the relationship between two robots, or even to close a loop with a single robot. Note that the observations are independent from the previous mapped information. As in the rendezvous case, this event produces the missing link z = s i j . In practical terms, image to image matching is equivalently to rendezvous.

• The "map to map" kind of data association requires both local maps to be transformed to a common frame, e.g. promoted to the global level as M i and M j using Eq. 4. In other words, the matching process happens in a common frame, being the wrf or one of the lrf. The disadvantage of this method is that in the worst case the absolute position of the two maps must be computed. Moreover, once the maps are matched, they have to be fused into a single one, otherwise it could lead into inconsistencies when merging all the maps.

Absolute Localization. In an aerial/ground context, it is reasonable to assume that both kind of robots receive GPS fixes from time to time. The relative transformation provided by a GPS fix for vehicle i is simply s G i , where G is the geo-referenced frame. Such information provides a link between a lrf and a global geo-referenced frame, and generates a loop at the graph level for an individual robot.

Impact on the sub-maps. From the point of view of a hierarchical SLAM formulation, the hierarchical nature of this model manifests itself in the ability to apply a loop-consistency constraint to a subset of local transformations (e.g. a single loop) without taking into account the local sub-maps. Particularly, when no information is shared between sub-maps, which is the case between sub-maps built by different robots, but an approximation for the sub-maps that are built by the same robot, the origin of the local sub-map is the only state that changes after the constraint is applied. It can be easily shown that m i-1 ⊥ m i | x i-1 , i.e., given the relative transformations, the consecutive local sub-maps are independent. Notice that the global poses S are d-separated of all possible paths between any pair of sub-maps m or even M. Note that the approximation can be palliated using conditionally independent local maps as proposed in [START_REF] Piniés | Scalable slam building conditionally independent local maps[END_REF].

Also, in the multi-robot case it can happen that two different events create a link on the same node, i.e. if a map-matching is established after a rendezvous. To avoid this problem, new sub-maps are started after an event occurs. In the case of receiving GPS fixes once in a while, the fact of starting a new local map at the time t when the fix is received, removes the dynamics aspects of the internal local maps setting a fix pose at global level.

Similarly, to avoid counting information twice if one eventually wants to merge all the sub-maps, after a map-matching event both sub-maps should be fused into a single sub map. This has the disadvantage that the sub-maps must be shared among the two robots, but on the one hand this is a prerequisite for at least one robot to establish the matches, and on the other hand such events will occur when the robots are within communication range.

Line segments for monocular EKF-SLAM

We explore the possibility of using linear landmarks or line segments, which provide an improved semantic over points: lines inherently contain the notions of connectivity and boundary, which open the door to potential automatic interpretations of the environment, both at the metrical and topological levels. A 3D model based on lines, akin to a wireframe model, can further allow the possibility to build higher level entities (planes, closed regions, objects).

Plucker lines (PL). Plücker lines have been used in major vision works with straight 3D lines [START_REF] Bartoli | The 3D line motion matrix and alilgnment of line reconstructions[END_REF][START_REF] Kamgar | Algorithms for matching 3D line sets[END_REF]. These works, and other ones referenced therein, are based on Structure From Motion approaches. We showed in [START_REF] Solà | Undelayed initialization of line segments in monocular SLAM[END_REF], drawing on previous work in [START_REF] Lemaire | Monocular-vision based SLAM using line segments[END_REF], the way to employ Plücker lines to achieve undelayed initialization of lines in monocular SLAM.

The Plücker coordinates for a line consist of a homogeneous 6-vector in projective space, L ∈ P 5 . In this vector, one can identify two sub-vectors1 , L = (n : v), with {n, v} ∈ R 3 , with which an intuitive geometrical interpretation of the line in 3D Euclidean space is possible (Fig. 2):

• The sub-vector n is a vector normal to the plane π supporting the line L and the origin O. • The sub-vector v is a director vector of the line.

d = n v π n v L O Q P2 P1
Fig. 2 Geometrical representation of the Plücker coordinates and sub-vectors n and v.

The line L and the origin O define the support plane π. The line's sub-vector n ∈ R 3 is orthogonal to π. The sub-vector v ∈ R 3 is a director vector of the line, and lies on π. This implies

n ⊥ v. The closest point to O is Q = (v × n : v ⊤ v) ∈ P 3 . The distance from L to O is d = n / v ,
showing that v acts as the homogeneous part of L, thus exhibiting inverse-depth properties.

• The distance from the line to the origin is given by d = n / v .

The two most remarkable properties of the Plücker line are its linear transformation and projection equations and the inverse-depth behavior of the sub-vector v, something that will allow us to design appropriate initialization methods for EKF. For details on the use of Plücker lines in monocular EKF-SLAM see [START_REF] Solà | Undelayed initialization of line segments in monocular SLAM[END_REF].

Anchored Plücker lines (APL). Now, we add an anchor to the parametrization to improve linearity, as it is done for points in the inversedepth parametrization [START_REF] Civera | Inverse depth parametrization for monocular SLAM[END_REF]. Anchoring the Plücker line means referring it to a point p 0 in 3D space different from the origin (Fig. 3). The anchor point p 0 is chosen to be the optical center at initialization time. The effect of such anchoring is that, on subsequent EKF updates, only the accumulated errors from the anchor p 0 to the current camera position T are considered, in contrast with regular Plücker lines where the error accounts for the absolute motion of the sensor from the origin of coordinates.

The anchored Plücker line (APL, Fig. 3) is then the 9-vector:

Λ =   p 0 n v   ∈ R 9 (7)
Transformation and projection expressions are as follows:

Frame transformation: Given a (camera) reference frame C specified by a rotation R and a translation T, an anchored Plücker line Λ in global frame is obtained from a line Λ C in frame C with the affine transformation

= p 0 + (v × n)/(v ⊤ v) n v π Λ !"#$%&'"($ )!)*!"#$%&'"($ p 0 T T
Observability conditions. The line is 3Dobservable if and only if the motion vector (Tp 0 ) does not lie on the line's support plane π.

Fig. 3 The anchored Plücker line.

Λ =   R 0 0 0 R 0 0 0 R   •Λ C +   T 0 0   . ( 8
)
The inverse transformation is performed with

Λ C =   R 0 0 0 R 0 0 0 R   ⊤ • Λ -   T 0 0   . (9)
Un-anchoring: given an anchored Plücker line Λ = (p 0 , n : v), its corresponding (un-anchored) Plücker line L is computed with

L = n + p 0 × v v (10)
Pin-hole projection: Projection is better expressed for regular Plücker lines. Given a perspective camera defined by the intrinsic parameters k = (u 0 , v 0 , α u , α v ), a Plücker line L C = (n C : v C ), expressed in the camera's coordinate system, projects into a homogeneous line l ∈ P 2 in the image plane with the linear expression [START_REF] Bartoli | The 3D line motion matrix and alilgnment of line reconstructions[END_REF][START_REF] Solà | Fusing monocular information in multi-camera SLAM[END_REF]

l = K•n C αv 0 0 0 αu 0 -αvu 0 -αuv 0 αuαv •n C ∈ P 2 . ( 11
)
where K is called the Plücker intrinsic matrix.

Transformation and projection: Transformation and projection are accomplished with a transformation to the camera frame ( 9), un-anchoring [START_REF] Civera | Inverse depth parametrization for monocular SLAM[END_REF], and projection [START_REF] Solà | Fusing monocular information in multi-camera SLAM[END_REF]. This can be composed in one single expression with:

l = K•R ⊤ •(n -(T -p 0 ) × v) ∈ P 2 , ( 12
)
in which we will notice:

• The linear behavior with respect to n.

• For accurate estimates of the camera motion (Tp 0 ), which is true for observations shortly after initialization, the linear behavior with respect to v, which additionally exhibits inverse-depth behavior.

Expression [START_REF] Fabiani | Autonomous flight and navigation of vtol uavs: from autonomy demonstrations to outof-sight flights[END_REF] gives us the means to analyze line observability as a function of the camera motion (Fig. 3(b)). Let (T -0 ) be the camera motion since initialization time. Because the projected line l is expressed in projective space, any vector l ′ = αl, with α ∈ R, represents the same line and the line sub-vector v is only observable if the vector (Tp 0 ) × v is not proportional to n. If we remind the Plücker constraint stating that v ⊥ n, this resumes to a motion (Tp 0 ) that does not belong to the plane π. As the anchor p 0 belongs to this plane, we conclude that the new camera position T must escape the plane π in order to fully observe the line.

Segment endpoints. The line's endpoints in 3D space are maintained out of the filter via two abscissas defined in the local 1D reference frame of the line, whose origin is at the point q = p 0 + v×n v ⊤ v , the closest point to the anchor (see Fig. 3(a)). Given the line Λ = (p 0 , n : v) and abscissas {t 1 , t 2 }, the 3D Euclidean endpoints are obtained with

p i = q + t i • v v ∈ E 3 , i ∈ {1, 2}. (13)
Back-projection of an APL. APL back-projection consists in defining a Plücker line L from a segment observation l, and anchoring it at the camera position T to obtain an APL Λ. These operations are detailed below.

Back-projection of a Plücker line: In the camera frame, the Plücker subvector n C resulting from the observation l is simply

n C = K -1 l. (14)
The sub-vector v C is not measured and must be obtained by injecting prior information. We give here the formulation and refer the reader to [START_REF] Solà | Undelayed initialization of line segments in monocular SLAM[END_REF] where full explanations and justifications are provided. The sub-vector v C is obtained with

v C = Eβ, (15)
where E ∈ R 3×2 is a matrix transforming vectors β ∈ R 2 in the Cartesian plane into the plane in R 3 supporting the line, defined by the optical center and n C . It is constructed as a base spanning the plane orthogonal to n C , i.e., the two non-measured DOFs,

E = e 1 e 2 , n C ⊥ e 1 ⊥ e 2 ⊥ n C , (16)
the base vectors e i being chosen so that e 1 is parallel to the image plane,

e 1 = n C 2 -n C 1 0 ⊤ (n C 1 ) 2 + (n C 2 ) 2 and e 2 = n C n C ×e 1 . (17)
The vector β = (β 1 , β 2 ) must be provided as prior. To help selecting an appropriate one, we give here some intuitive notions about β:

• A vector β = (1, 0) is a line parallel to the image plane at a distance d = n C from the optical center. • A vector β = (0, 1) is a line perpendicular to the detected segment l in the image. • The distance from the optical center to the line is given by d = n C / β .

Anchoring: This step is trivial as we have interest in making the anchor p 0 coincide with the current camera position, which is the origin when we are in camera frame,

Λ C =   0 n C v C   . (18)
Back-projection and transformation: The operations above plus the transformation to the global frame (8) can be composed and written as a singlestep function of R, T, l and β,

Λ =   p 0 n v   =   T RK -1 l REβ   . (19)
ALP initialization and update in EKF-SLAM. We now have expressed all the basic relations to deal with APL, that are useful to exploit them in an EKF framework. The line initialization and update equations are not depicted here, details can be found in [START_REF] Solà | Undelayed initialization of line segments in monocular SLAM[END_REF].

Experimental results

The environment is "semi-structured", in the sense that it does not contain as many buildings as an urban area -and the building themselves do not contain many straight lines or perfect planar areas, see Figures 4.

The ground robot Dala is an iRobot's ATRV platform, equipped with a calibrated stereo-vision bench made of two 1024×768 cameras with a baseline of 0.35m. The helicopter Ressac is controlled by algorithms developed at Onera [START_REF] Fabiani | Autonomous flight and navigation of vtol uavs: from autonomy demonstrations to outof-sight flights[END_REF], and is also equipped with a calibrated stereo vision bench made of two 1024 × 768 cameras, with a 0.9m baseline (Figure 5). Involved processes. Unfortunately, because of engineering issues encountered during the data collection, no inertial or odometric motion estimates are available2 . As a consequence, we use a visual odometry approach based on stereo vision for the motion prediction steps of the EKF SLAM algorithms -all the results presented hereafter have therefore been obtained using exclusively visual data.

The SLAM algorithms integrate two types of observations from only one camera; image points ( parametrized as inverse-depth points) and image line segments (parametrized as anchored Plücker line segments). At each image acquisition, point observations are firstly processed: the resulting updated motion estimate is exploited by the line segment tracker, and line landmarks observations are then processed. A heuristic is used to select the points that will be used as landmarks: the image is regularly partitioned in 3 × 3 regions, in which one ensures that at least 2 landmarks are being tracked. As for the lines, all the ones whose length is grater than 60 pixels are retained as landmarks.

Point landmarks are Harris interest points, that are matched from one view to the other with the group based matching procedure described in [START_REF] Lemaire | Vision-based slam: Stereo and monocular approaches[END_REF]. We use different initialization parameters for inverse depth point parametrization with Dala and Ressac. Dala's parameters are ρ init = 0.1 m -1 and σ ρ = 0.2 m -1 , while Ressac's parameters are ρ init = 0.025 m -1 and σ ρ = 0.0125 m -1 (the points are initialized at 40m, which is its the helicopter average elevation over the terrain.

We use the algorithms presented in [START_REF] Berger | DSeg: Direct line segments detection[END_REF] to detect and track segments. For the estimation part, the a priori parameters used in the experiment for the APL are β = (0.025, 0), σ β1 = 0.025 and σ β2 = 0.0375 for both robots. The prediction of the line segment position in the image, required for the segment tracker, is done using the projection of the 3D line segment into the image frame.

New local maps are created when 100 landmarks (combining points and line segments) are in the map. Immediately after, the current robot's pose is the new relative transformation in the global graph.

Enforcing loop closures. In the experiments, we have two types of events: rendezvous and image to image matching.

• The rendezvous is emulated using matches of interest points perceived by the two robots using their current image frames. The 3D coordinates of the points in each robot frame are obtained by stereo vision: as a result, the point matches yields an estimate of the relative robot position. • The image matching event recovers the relative transformation between the current robot's pose and a past pose from a different robot (origin of a local sub-map), using also matches of interest points between their respective frames.

Figure 7 shows results obtained by the integration of events between Dala and Ressac. Dala starts at the entry of the north-west group of buildings, with no uncertainty in its local map, but also in the wrf : the first Dala sub-map is the origin of the world. Ressac starts above Dala, and heads towards southeast. A first rendezvous event occurs immediately after start, and Ressac is localized in Dala's reference frame.

A second event occurs after Ressac comes back from the south-east village, passing above a place previously visited by Dala. The effects of the image to image matching event are shown in Figure 6. The figure also shows the image frames that were evaluated for the matching: new local maps are initiated afterward for both robots. Note that Ressac's uncertainty in height is pretty large, especially before the second event: the visual motion estimates are indeed not very precise in the vertical direction, because Ressac stereo baseline is small with respect to the depth of the perceived points -and the integration of points and lines in the sub-maps does not reduces much the elevation estimates. However, after the image to image matching event, the elevation of Ressac and the origins of all the built maps are strongly corrected.

Conclusion

We have explored the use of a multiple local maps technique for multi-robots according to a hierarchical SLAM approach, in which loop closures are integrated through an optimization process (an Iterative EKF). Loop closures are triggered using multi-or single-robot events such as finding information correspondences between unconnected local maps, rendezvous between two robots or GPS fixes. Therefore, the mapping problem is relegated within the local sub-maps, and is decorrelated from the global localization problem, making our approach akin to a cooperative localization approach. The approach is distributed, and the graph level is the sole information that must be exchanged between the robots. It is well suited to a multi-robot context, and it can in particular handle all the possible localization means, from odometry to absolute localization with respect to an initial model.

In order to build more meaningful landmark maps and to be able to match data acquired from very different vantage points (or even different sensors), we have proposed to use line segments to build a wireframe model. An important contribution of this paper is the new line segment parametrization for undelayed initialization. We add an anchor to our previously proposed parametrization [START_REF] Solà | Undelayed initialization of line segments in monocular SLAM[END_REF] to improve the linearity, exactly as it is done with inversedepth points. Thanks to the cross-correlations stored in the EKF, the anchor allows the filter to account for accumulated errors only from the anchor to the current position, not from the origin of coordinates. Ongoing work is a more detailed analysis of different line parametrization in view of their linearity behavior.

Heterogeneous visual landmarks are proposed to map semi-structured environments. We combine inverse-depth points and anchored Plücker line seg-ments. Our experiments show that inverse-depth points, that are numerous in the scene but not very robust to large viewpoint variations, play a crucial role for robot localization, while Plücker line segments, that are seldom in semi-structured environments but allow detection and matching from disparate viewpoints, are well suited to build a 3D model that exhibit some of the environment structure.

Fig. 1

 1 Fig.1Loop-closing events for multiple robots.

  have identified are: (i) robots rendezvous (Figure 1(a)), (ii) common information match within sub-maps (Figure 1(b)), and (iii) receiving external information that provide absolute localizations (e.g. a GPS fix (Figure 1(c)),

  Geometrical interpretation of anchor p 0 and sub-vectors n and v. The closest point to the anchor is q

Fig. 4

 4 Fig. 4 Aerial view of the experiment area (obtained on www.geoportail.fr). The robot Dala evolves in the north-west group of buildings, while the helicopter Ressac is flying along a swathing pattern oriented diagonally between the north-west and south-east groups of buildings, at an elevation of about 40m. The red rectangle approximately represents the field of view of the image acquired by Ressac shown on top-right of the figure. On this latter image, the red angular sector shows approximately the field of view of Dala when taking the bottom-right image.

Fig. 5

 5 Fig. 5 Ground and aerial robots used for the experimental validation.

  Fig. 6 Top: Image frames from both robots before the event. Green squares represent interest point currently considered as landmarks, yellow squares represent interest points just initialized as landmarks. The line segments are in blue, with endpoints in red. Yellow ellipses are the uncertainty in the image view. Bottom: Event effect in the global map, the sub maps origins expressed in the wrf are the large ellipsoids -only 3D line segments landmarks are shown here.

Fig. 7

 7 Fig. 7 Comparative trajectory plots: visual odometry in dash-dot line, open loop run in dashed line and cooperative run for Dala (left) and Ressac (right).

We use a colon (:) to separate the non-homogeneous and homogeneous parts in projective space.

GPS ground truth could neither be recorded.

Acknowledgments. This work has been partially founded by the Action project (action.onera.fr). Cyrille Berger is founded by a Cifre contract with Thales Optronics. We would like to especially thank the Onera "Ressac team" for all their help for the experiments.