PhD student, MINES Helen Micheaux
email: helen.micheaux@mines-paristech.fr

professor, Franck Aggeri
email: franck.aggeri@mines-paristech.fr

THE EMERGENCE OF HYBRID CO-REGULATION: EMPIRICAL EVIDENCE AND RATIONALE IN THE FIELD OF E-WASTE MANAGEMENT

Sub-theme 32: the privatization of regulation However, the practice of hybrid regulation is constantly growing and often actively promoted.

How is it implemented in practice? What are their rationale, effects, limits and conditions of exercise?

.

. The implementation of such logic does not exclusively focus on incentive mechanisms but also on hybrid regulations within sectorial negotiated approaches.

The case of waste management in Europe illustrate this logic of negotiated accountability through the concept of extended producer responsibility (EPR), which is implemented in all European countries since the 90's.

In order to disclose the logic of hybrid regulation, the article will be developed as follows.

The next paragraph will expose the theoretical framework and research gap that conduce to the problematization at stake. In the second part, the concept of hybrid regulation will be analyzed through a practical case, which is the electrical waste sector. The empirical findings will lead to the authors' contributions and open to discussion.

Theoretical framework and research gap

. These modes of regulation suppose also that the object to regulate is well known and that social behaviors are predictable. However, in complex situations these

Introduction

According to Michel Foucault, neoliberal governmentality is closely linked to the issue of making individuals responsible [START_REF] Foucault | The birth of biopolitics: Lectures at the Collège de France, 1978-1979[END_REF][START_REF] Hache | La responsabilité, une technique de gouvernement néolibérale?[END_REF]. In this perspective, unilateral public action (command and control) is considered not only inefficient but also illegitimate, and shall be replaced by different government techniques and governance methods aiming at making them responsible (accountable) and equip them with new capabilities (empowerment). Thus, the State does not give up its regulation power but make it change towards more negotiated forms of governance, based on flexible and incentive instruments. This phenomenon has been labeled hybrid regulation to capture the idea that complementary forms of public and private regulations coexist in transnational governance [START_REF] Levi-Faur | Regulation and regulatory governance[END_REF][START_REF] Djelic | A world of governance -the rise of transnational regulation[END_REF]. However, under this label, heterogeneous practices have developed, with different degree of hybridization [START_REF] Cafaggi | Public and private regulation mapping the labyrinth[END_REF], ranging from forms of loose co-shaping between private and public regulations to stronger co-regulation where explicit governance structures are purposefully set to organize role-plays and subsidiarity rules between the different parties. This paper addresses the latter form of hybrid regulation. Despite numerous experiments, hybrid co-regulation has received little attention and is under theorized, especially in law and economics. classical modes can become insufficient. Bleischwitz et al. discuss the market and the hierarchy failures to bring about sustainability improvements [START_REF] Bleischwitz | Sustainable development and collective learning: theory and a European case study[END_REF].

Market-based economists advocate profit-oriented instruments that are incompatible with public interest services and conflicting with long-term approaches. Likewise, public instruments tend to fail because of Governments' lack of resources and knowledge of the object to regulate. In the standard law theory, the tropism toward individual responsibility is also visible, emphasizing regulation mechanisms (property rights, sanctions, regulations) aiming at enhancing accountability and liability [START_REF] Ackerman | Reforming environmental law[END_REF][START_REF] Sachs | Planning the funeral at the birth: Extended Producer Responsibility in the European Union and the United States[END_REF].

It is in the institutional and governance theories about regulation that authors have identified the transformations of the international regulation. Some authors have analyzed such transformation as a consequence of the rise of transnational activities, which led to a "profound re-ordering of our world" [START_REF] Djelic | A world of governance -the rise of transnational regulation[END_REF]Ewert and Maggetti, 2016). The rise of privatization, deregulation and liberalization logics led to the explosion of rule-making in organizations and in society. At the same time, "a decline in trust" accompanied the liberal movement, which led to the expansion of public and private monitoring and auditing activities in order to assure transparency [START_REF] Moran | Understanding the regulatory state[END_REF]. In fact, theories of governance do not suggest a retreat of the State but rather a change in the role of governments, e.g. "the new governance" and the "new regulatory states" [START_REF] Moran | Understanding the regulatory state[END_REF]. Not only are new organizations emerging to issue rules but, at the same time, they also participate in the elaboration and implementation of the rules, which creates novel highly complex interactions between public and private actors.

A rich literature exists revealing the re-ordering trend of the world through transnational regulations [START_REF] Djelic | A world of governance -the rise of transnational regulation[END_REF]. These papers focus on the rise and diffusion of non-state actors in public regulation activities [START_REF] Levi-Faur | The global diffusion of regulatory capitalism[END_REF][START_REF] Djelic | A world of governance -the rise of transnational regulation[END_REF], the complex relations between private and public actors that the co-activity creates and the emergence of third parties [START_REF] Levi-Faur | Transnational politics and policy: from two-way to three-way interactions[END_REF], as well as the level of hybridization between these actors (Ewert and Maggetti, 2016). Others propose hybrid regulation taxonomies based on the nature of the participants [START_REF] Levi-Faur | Regulation and regulatory governance[END_REF] or their role in the policy process [START_REF] Cafaggi | Public and private regulation mapping the labyrinth[END_REF]. However, very little research has been conducted analyzing hybrid regulation as a policy principle in the service of the State [START_REF] Cafaggi | Public and private regulation mapping the labyrinth[END_REF]. Indeed, most of the time public policy-makers have to make with private governance ineluctable emergence and create monitoring and auditing activities ex post facto. However, in some cases, in particular in the field of the environment, other forms of hybrid regulation exist, such as "enforced self-regulation" and "meta-regulation", where the regulator compels the regulatee to participate to governance activities [START_REF] Levi-Faur | Regulation and regulatory governance[END_REF].

Such policy can create very effective and flexible regulatory hybrid systems. In that optic more research should focus on the synergetic dynamics of hybrid regulations. Indeed, most of the studies focus on the nature of the actors and neglect "reciprocal influence and interaction" and "the transformation and reinvention that is likely to follow regular interaction" and the "win-win" game potential to increase each regulatory power [START_REF] Djelic | A world of governance -the rise of transnational regulation[END_REF]. Thus, hybrid regulation can be used as a solution rather than a problem [START_REF] Cafaggi | Public and private regulation mapping the labyrinth[END_REF].

Still, complex organizations that empower private actors must keep in mind the threat of opportunistic behaviors, as it has happened in the case of the financial crisis [START_REF] Cafaggi | Public and private regulation mapping the labyrinth[END_REF]. The issue for public authorities is then to maintain control over the system while reviving constantly private actors' motivation and engagement to the "common purpose". Thus, implementing such regulation is not an easy task for policy makers, especially as the concept is rather eluded by traditional theories. In order to render hybrid regulation legitimate and comprehensible to all actors and controllable by public authorities, a focus on a practical case is essential to reveal the potentials and logics of such a regulation mode as well as its limits.

Our observation of the waste sector and its management highlight the importance of the notion of responsibility, and, more precisely, the complexity and evasiveness of the concept of collective responsibility in shaping hybrid regulation. Indeed, even though responsibility is rather a common and historic principle, with the industrialization and the growing number of industrial accidents, it has undergone profound mutations [START_REF] Neuberg | Responsabilité élargie des producteurs. Manuel à l'intention des pouvoirs publics[END_REF]. Indeed, up to the 19 th century, the notion of responsibility was based on the logic of accountability that focused on the culprit and its crime. Whereas at the beginning of the last century, a more socialized version emerged progressively replacing the focus on the fishing out of the guilty parties and the most appropriate sanctions by assurance and compensation mechanisms [START_REF] Ewald | L'expérience de la responsabilité. Qu'est-ce qu'être responsable?[END_REF]. More recently, the complexity and the extent of environmental crises, made identifying a guilty party a tremendous challenge for authorities. The "polluter-pays" principle that was created in the 70s enabled to tackle various environmental wrongful cases, however as it is based on an individual responsibility it has its limits, particularly when dealing with the waste issue. Indeed, beyond financial compensation, a waste reduction policy also implies prevention incentives. But, prevention measures cannot be based on individualistic mechanisms targeting individuals responsible of a crime, as no crime has occurred yet. Only a collective approach of the notion of responsibility can overcome the dilution of liability that characterizes environmental damages. However in both standard economic and legal approaches, issues and mechanisms of collective responsibility are understudied and under-theorized. Indeed, to delegate individually is rather simple, the difficulty is to delegate to a group of actors and make sure that they will organize themselves in the interest of the common good.

In institutional theory, different scholars, including the Nobel Prize Elinor Ostrom, have highlighted the importance of collective responsibility when the governance of commons is engaged, i.e. situations characterized by strong interdependencies and/or the preservation of pooled resources [START_REF] Ostrom | Governing the commons: The evolution of institutions for collective action[END_REF]. In Ostrom's perspective, collective responsibility does not always require State intervention. She analyzes situations in which collective forms of selfregulation are put in place by communities to govern common resources. The underlying assumption is that communities do already exist and commons are clearly identifiable. In this approach, regulations are implemented and controlled by private actors. For certain scholars or actors from the civil society, such practices of negotiated regulation run the risk of regulatory capture and should be avoided [START_REF] Laffont | A theory of incentives in procurement and regulation[END_REF].

Thus, Ostrom's framework does not encompass all possible situations of commons governance. As we discussed, public authorities can comply private actors to engage in a public issue and, in that sense, commons may result from purposeful public initiatives. In Europe, setting a framework for waste management is negotiated with economic actors and stakeholders. For specific waste streams, declaring that producers are made responsible of waste treatment and valuation, de facto creates a common purpose where producers are collectively in charge of addressing the waste treatment and valuation issue. Commons may also be unclear from the beginning due to important uncertainties about the actions to be taken and strong interdependencies. Finally, structured ecosystems or communities may not exist and shall be the purpose of collective action. In such a context, hybrid regulation, we argue, has a potential value to address these complex and evolving issues. The question remains how to perform hybrid regulation in practice. Ostrom has proposed principles for the governance of natural resources in the shadow of the State. The issue is to adapt this framework for the analysis of hybrid regulation in waste management.

Instead of traditional approaches focused on ostensive arguments (how regulation should work in principle), we will adopt a performative approach, where the objective is to give account of regulation practices and their dynamic effects [START_REF] Latour | The powers of association[END_REF][START_REF] Feldman | Reconceptualizing organizational routines as a source of flexibility and change[END_REF]. Indeed, not without pointing at Latour's performative definition when analyzing organizations and society, "it is impossible in principle to define the list of properties that would be typical of" hybrid regulation, as the concept has emerged out of classical frameworks, "although in practice it is possible to do so". The concept of hybrid regulation cannot be theorized by an ostensive approach, as it has no pre-defined assumptions, but is rather the consequence of the collective action. Thus, in order to identify the founding principles of hybrid regulation, an empirical analysis is needed. For that purpose, we analyze, through the e-waste case, the historical emergence of this form of hybrid regulation, the underlying rationale provided by actors, the experiments and organizations put in place, the regulation practices invented along the way and their effects on collective learning. Analyzing hybrid regulation in practice will enable us to propose founding principles.

Hybrid co-regulation process in the electrical waste sector

Methodology

In order to better understand the dynamics of hybrid regulation in practice, we have conducted an empirical analysis. The case chosen is the materialization of the Extended Producer Responsibility (EPR) in the electrical waste (e-waste) sector. EPR is a new concept put in place since the late 90's in Europe and aiming at making producers responsible for the sound treatment and prevention of waste they generate. Its significance and implementation has constantly evolved since then. In order to capture such dynamics, the methodology adopted is based on a longitudinal research methodology (Pettigrew, 1990) that was used to fully capture the emergence and evolution of hybrid regulation guiding the waste management system. Different materials have been considered: regulation documents (European directives and laws), reports concerning the EPR principle (OECD, 1999) and previous literature on the history of waste. The empirical analysis relies on more than thirty interviews of producers and recyclers of the e-waste sector, some of whom have been operating in the sector since the beginning.

Waste management and regulation: a brief genealogy

Waste management is an old issue but its purposes, stakes and forms of regulations have profoundly evolved over the last decades. We can identify three representative periods that we will briefly outline, based on the French case. The periodization chosen reflects the transformation of waste perception over time and the evolution of the relation between regulators and regulated that this change produces.

i. Waste, from ancient times to urbanization

In ancient times, the concept of waste did not exist, consequently, neither waste management.

In France, it was probably introduced in the 15th century deriving from the verb to wane, « déchoir » in French, from which the term « déchet » (waste) is derived [START_REF] Dagognet | Des détritus, des déchets, de l'abject : Une philosophie écologique[END_REF].

Everything was reused by the intermediary of scrap merchants (the private sector) or left to natural putrefaction. It was probably in the Antiquity in influential cities that the society started to be concerned about their leftovers. In Athens, toilets were invented in order to take away the sludge. In Rome, they added pits out of the city for animal bones. Indeed, since the Middle Ages, cities have gotten bigger and the quantity of filth has increased and was becoming detrimental to social life. People would leave their litter in the streets and in nearby rivers, where they would also draw the water from. They would also reuse crafts waste (metal, used paper, old rags).

As urbanization increased, the cycle of nature was breached. The more people would live in cities, the more congested the streets would get with organic filth and sewage. Cities became more and more unbearable to live in. As streets started to smell heavily measures were implemented. First, streets were cobbled. In France, Philippe Auguste cobbled the street in 1185 and created septic tanks in main areas of Paris. People would be given some hygiene advice and would be asked to bring their waste in specified spots. However, no one would care much. Thus, epidemic arose, the most harmful one being the black plague in 1347. At that time, it was believed that the smell was responsible of the diseases. Despite of few decrees to oblige inhabitants to get rid of their waste in a proper way, they would still mostly through their garbage out of the window. In that context, the ragman activity emerged.

Ragmen would practice door-to-door collection and gather old items of clothing, rags, animal bones and all sorts of things that could be reused. It is only in the 17th century that order is starting to become the norm because of dissuasive taxes. However, major policies were not taken before the 19th century.

One important factor that changed people perception of waste was Louis Pasteur's discoveries. Louis Pasteur, a French scientist, was the one bringing to light the link between hygiene and health in 1870. At that point, sanitary issues became a political preoccupation. In France the emblematic prefect Eugène Poubelle compelled Parisians to put their house wastes in « boxes » that would be collected by municipal service. His name was given to a new artifact the « poubelle », which means bin in French. This new phase categorized waste as a contaminant substance causing diseases. In 1896, Paris implemented its first treatment centers and in 1907 its first incinerator. These centers would use grinding and incineration techniques. Thus, waste management was ruled by the public sector. Ragmen, originally free merchants, had to comply with the new regulation. First, in 1828 they had to wear medals with their identification, but unwilling to comply with legislative formalities the obligation was revoked in 1873. However, the up scaling sanitary policy of the beginning of the 19th century was too strong for ragmen to thwart any of it and they were proposed municipal employments as official refuse collectors. From then on, the waste management became more and more institutionalized.

ii. The setting of a public agenda Even if communal waste collection started gradually to develop itself it remained an urban privilege. In rural areas initiatives were very scarce. No general law existed at that point. In France, it is the out-line law of 1975 that officially defined waste in legal terms and made municipalities responsible for the management of domestic waste. Treatment choices strongly depended on the degree of knowledge. At one point, incineration was preferred because of its ability to generate energy and to heat up cities. However, later in time, incineration revealed to be more costly than what it could produce and revealed to be a major source of pollution.

Around landfilling and incineration, the so-called "Not In My Back Yard (NIMBY) syndrome" emerged. This syndrome is characterized by the mobilization of local residents that protest against the implementation of incinerators or landfills near their homes.

Since then, waste treatments became a source of numerous conflicts, particularly as waste composition became more and more complex with the emergence of novel technologies (mobile phones, computers, etc.) and integrated harmful pollutants (plastics, heavy metals, etc.). This complexification of waste, as well as its continuous growth, made landfilling and incineration problematic and controversial solutions. Public policy remained strongly based on classical instruments such as landfilling taxation (TGAP) or regulation (for incineration) rather than on making producers responsible. But these measures revealed to be ineffective. Indeed, as the amount of waste still continued to grow even more rapidly, as municipalities became incurred increasing costs of collection and treatment and as illegal landfilling has become major issue, a new policy orientation became urgent.

To sum up, the first problematization of waste focused on hygienic issues and the first actions put in place were to organize communal services to bring out of site the litter that was dumped on the street that were proved to be a precursor of diseases. The invention and diffusion of the bin artifact (poubelle) and the development of landfilling in France in the XIXth Century associated to educational programs and public support, illustrate the rise of a hygienic rationale where waste had to be contained and stored in specific places. Secondly, the simultaneous development of urbanization and the consumer society skyrocketed the amount of waste that was no longer manageable by municipalities alone, obliging public authorities to take stronger measures to address this pollution issue. However, classic regulations revealed to be insufficient and alternatives proved to be necessary.

iii. Innovation and responsabilization of producers (1990-now)

At the European level discussions begun in order to find an alternative to finance waste management and encourage prevention and cleaner production. Thomas Lindhqvist proposed, on behalf of the Swedish Ministry, the concept of Extended Producer Responsibility (EPR) based on the « polluter-pays » principle [START_REF] Lindhqvist | Extended producer responsability in cleaner production policy principle to promote environmental improvements of product systems[END_REF]. The concept was formally introduced in EU directives related to waste management, first concerning used batteries (1991) and then packaging (1994). The purpose was to internalize the cost of waste disposal into the cost of the product, theoretically meaning that the producers will improve the waste profile of their products, thus decreasing waste and increasing possibilities for reuse and recycling. Parallel to the cost internalization, recycling targets were implemented for the first time at the European level.

First EPR experiences emerged in the 90s. The original example is the DSD German System, followed by the French Eco-Emballage setting. Producers could comply with the EPR legislation by becoming a member of these organizations. In that case, they had to pay a license fee according to the volume of product they put on the market. In exchange, these organizations (DSD GmbH and Eco-Emaballage) had to invest the total of fees in the development of collection and treatment schemes. In 2001, the Organization for Economic Cooperation and Development (OECD) formally introduced the EPR concept (OECD, 2001), clearly referring to a neoliberalism approach. In this document, the EPR principle is based on an economic rationale and associated to an individual responsibility. The report recognizes that other options are possible such as setting shared responsibility organizations as it had been experimented in the DSD or Eco-Emballages systems. However, it shall be noticed that shared responsibility was not really theorized.

In France, the first EPR system was implemented for waste packaging. Collective organizations, called « Producer Responsibility Organizations » (PRO), managed by producers were created in order to fulfill producers' responsibility (Eco-Emballage and Adelphe, 1993). In all EPR policies, producers have to choose between joining a PRO or fulfilling their responsibility individually. For economies of scale motives in collection and treatment activities, in most cases producers opted to share their responsibility by joining a PRO. Practices of collective organizations and shared responsibility have not been fully theorized yet. American scholars, for whom responsibility shall be based on individual mechanisms in order to avoid any free-riding behaviors, have expressed their skepticism about this collective settings [START_REF] Sachs | Planning the funeral at the birth: Extended Producer Responsibility in the European Union and the United States[END_REF].

iv. Waste value and regulation modes

This brief history of waste emergence highlights that waste perception has fluctuated during time and led to very different regulation systems. When wastes are considered as "bads" (i.e. pollutants) public management is more likely to intervene (hygiene measures, treatments policies, etc.). On the contrary, as soon as waste also appears as a source of "goods" (e.g. precious metals contained in electronic waste), market regulation prevails (e.g. scrap merchants).

Today, the aim is to reduce waste negative out of "bads" value and to increase economic value out of "goods" by identifying and creating shared value out of it to the benefit of all.

One example is the logic of reuse that can reduce raw material utilization and at the same time can treat waste in a sound way, which avoids added pollution by landfilling or incineration.

The idea is to consider waste as "goods", or potential commons for collective action, referring to Elinor Ostrom's work. Yet, the major difference with Ostrom's approach on natural commons is that wastes composition and value are highly dependent on the rapid change of technologies. In other words, waste considered as a source of "goods" is non-stationary and depends on innovations both on products and treatment processes (to extract the value from waste).

In this new problematization, "command and control" regulation is difficult to set and implement to the extent that the list of "bads" and "goods" is constantly evolving with innovation and technological progress. Furthermore, the valuation of goods requires other instruments than banning or setting emissions targets. In this perspective, the European commission introduced a new public policy based on a new driving principle: making producers responsible (the responsibilization), i.e. involving them in a kind of hybrid or joint regulation. Implicating private actors can prove effectiveness for many reasons such as proximity with the industry being regulated, flexibility reducing administrative constraints, greater compliance and greater potential to mobilize resources [START_REF] Coglianese | The Role of Government in Corporate Governance[END_REF]). As profit oriented actors it was assumed that producers would try their best to comply with environmental laws while creating value out of waste. "In such partnership, the private sector's dynamism is combined with the public sector's custodianship of public interest" [START_REF] Ahmed | People as partners: Facilitating people's participation in public-private partnerships for solid waste management[END_REF]. By combining public legitimacy and legislative power control with private responsiveness and efficiency, hybrid regulation can face unpredictable environments.

Indeed, this combination permits wide exploration of various possible configurations of solutions. In this new logic, public authorities develop a new rationale: the issue is not so much to ban or to regulate but rather to direct, to frame and to adapt to dynamic situations. "These modes are thought to have specific advantages: They evade the lengthy, unwieldy, and cumbersome process of legislative decision-making. […] At the substantive level the advantages are seen in the greater flexibility of the policy measures and the greater adaptability of those measures to a rapidly changing social, economic, and technological environment" [START_REF] Héritier | New modes of governance in Europe: Policy-making without legislating?[END_REF].

In principle, hybrid regulation seems well adapted to tackle environmental issues where uncertainties are strong and control difficult to implement. However, its implementation in practice is not that obvious. Risks of implicating private actors include "conflicts of interest, inadequate enforcement and accountability, and insufficient monitoring of compliance" [START_REF] Cafaggi | Public and private regulation mapping the labyrinth[END_REF]). Héritier has noticed how complex it could be to implement hybrid regulation and which conditions are needed. "The new modes of governance would have to rely on an entire infrastructure aimed at establishing the following conditions: the right incentives for those bearing the costs of regulation; the right participatory structure for shaping the instruments so that all those affected have a voice in shaping them; the guarantee of legal certainty; and the possibility to hold actors accountable for the consequences of particular actions. Hence, as easy as the new modes of governance may seem at first glance, when they are analyzed in detail it becomes clear that they are more demanding than expected" [START_REF] Héritier | New modes of governance in Europe: Policy-making without legislating?[END_REF]. In order to give account of hybrid co-regulation practices and their dynamic effect, we analyze through the e-waste case, the historical emergence of this form of regulation, the underlying rationale provided by actors, the experiments and organizations put in place, the regulation practices invented along the way and their effects on collective learning.

The hybrid regulation process of e-waste in France

i. First experiments E-waste have the particularity to be highly complex used products containing at the same time valuable metals (goods) and hazardous substances (bads). This growing complexity and dangerousness led producers of electrical products, on behalf of the French Ministry of environment, to experiment collectively an EPR system in a specific geographical area before setting a general national framework. Producers conducted a two-years experiment in the Nantes area supported by the French environmental agency (ADEME). Its aim was to put in place an operational system that would collect and orientate waste to treatment facilities.

During these two years specific measures were carried out that enabled producers to address technical, logistical, economical and environmental issues concerning the implementation of a full-scaled e-waste operational system. One of the major lessons learnt from the experiment for the stakeholders was to consider that an engineering and organizational support was lacking in order to facilitate the emergence of an industry, of a nexus of contracts and an endof-life economy. As a consequence, the choice was made in France to introduce an operational function (design and implement a new collection and recycling industry architecture with contracts, templates and specifications consistent with policy targets) beside the traditional financial role (subsidize costly operations such as collection and waste treatment)1 in the mission statement of e-waste PRO's. This experimentation had a considerable impact on the choices that led to the current structure of the e-waste stream, and even on the other EPR systems that followed in France. It enabled to conduct a collective learning based on returns on experiments.

ii. Organization and governance

After the experiment in Nantes four PROs were created on the approval of the Ministry. In addition, an EPR coordinator for the e-waste sector was created at the demand of the collectivities in order to facilitate their relations with the different PROs. PROs are organizations with a specific legal status and governance: they are non-profit private companies with a public mission statement and a multi-stakeholder governance.

Their missions are defined through legal specifications for a period of six years. Their role is to assume their members EPR principle and to achieve the targets negotiated with the State.

Besides recycling targets, the State defines the rules that will guide PROs' action after a participative decision-making process involving different stakeholders (NGO's, consumer associations, producer and recycling organizations, public authorities). Indeed, specifications are negotiated and discussed every six years in an accreditation commission before the State's final decision. The mission statement establishes and defines the relations that PROs have to engage during their six years of authorization with collectivities, operators of the waste sector (collection points, transportation, treatment), actors from the social economy, the e-waste EPR coordinator, public authorities and with their members. These relations are subjected to contracts, some of which are based on public and/or private terms of Contract Law. These distinctions are summarized in table 1. One major originality is that co-contractors cannot negotiate the terms of contracts. For example, members of PROs cannot negotiate their member fees, as the law imposes that fees must be proportionately equal to all members of a same PRO.

Table 1: Private and public terms of Contract Law in the e--waste sector

This hybrid status is highly original and difficult to conceive for lawyers and judges and can lead to various litigations [START_REF] Gossement | La réforme des éco-organismes dans le cadre du projet de loi relatif à l'économie sociale et solidaire[END_REF]. One common issue is to identify which judge, the civil or administrative court, is in capacity to rule on a conflict involving PROs that are private actors with a public utility mission (Gossement, 2016a).

In this perspective, regulation is clearly hybrid, associating public and private actors through tailor-made governance and organizational mechanisms and reciprocal commitments. Figure 1 shows the contract outline in the e-waste sector. All the stakeholders are represented in the agreement commission and discuss PROs' specifications. The approval can be removed at the end of the authorization or during the mandate if the dynamic and results are not satisfactory, as it was the case for one of the e-waste PRO that have not been renewed. Public authorities can also introduce additional targets and specifications and introduce different incentives or regulations if specific problems are encountered, which we will develop more, later in the paper. Therefore, the EPR model is highly dynamic as the system is periodically revised according to its performances (Figure 2). Proposals of revisions can emanate from any stakeholders, even from producers themselves.

Thus, the responsibility principle gives relative autonomy to PROs that can conduct on-going experimentations in order to comply with their specifications.

Findings: on-going experimentations and pitfalls of the hybrid regulation process

i.

On-going experimentations

As a collective organization crystallizing the shared responsibility principle, PROs are key actors. During their six-years mandate they are enticed to experiment innovative solutions.

For example, since the second agreement in 2009, PROs are asked to modulate producers' financial contribution according to specific criterions. The criterions are established through a participative decision-making process involving all the stakeholders. First criterions that were established concerned pollutants. For example, if a producer would use more than 25 grams of brominated flame retardant, he would pay 20% more than if he did not. The aim is to entice producers to use fewer pollutants in their products. For that purpose, PROs had to inform their members and develop teaching skills in order to make them understand each criterion. As these criterions became systematic, in the last agreement in 2014, more criterions were added that had been also discussed between all the stakeholders. Most of these new criterions concern prevention and product usage extension. For example, producers of washing machines, dishwashers, coffee machines, etc. can benefit from a 20% discount if they are able to provide for spare parts for at least 11 years. Other criterions are: provision of technical documentations concerning the product to be given to repairers, the use of secondary plastic in the product, etc. These criterions are more complex than the first ones that concerned only pollutants. In this second phase of the modulation experimentation, PROs have to develop even greater instruction skills. In order to help producers to embark on ecodesign and comply with these criterions, one of the PROs has conceived for its members an online calculator that evaluates the re-usability, recyclability and recoverability of e-products and gives advice to improve eco-design.

Our observations highlight that PROs main activity is to conduct on-going experiments and collective learning processes (Callon & Muniesa, 2008) by means of different regulation mechanisms and through incremental approaches and iterative learning. Charles Lindblom introduced the former in 1959 as "the science of muddling through". He believed that "it is not possible to come to a comprehensive analysis of governance or government systems because complex societal problems can never be grasped entirely" [START_REF] Bachus | Inclusive governance or incrementalism? The choice of a sustainable development governance model for Flanders[END_REF]. Therefore, it is of no use to apply strict long-term planning in politics as "one has to adapt constantly to reality". Change can only be "step by step". Along an incremental approach, iterative learning can lead to innovative solutions. "Iterative processes are about learning from experience and making adjustments on the way -a process also described as the observe-plan-do-check-adjust circle" (Layman, 2014). Indeed, iterative learning processes have the particularity to be somewhat open-ended as both goals and approaches may change on the way. In fact, not only is the objective pursued to rationalize the treatment of waste considered as a "bad", but it is also to exploit the waste value potential as a good by developing new markets and technologies. Recently, a new focus was made on the recycling of strategic metals (precious metals, rare earth elements, critical metals, etc.) of which their value is being more and more recognized and stimulates new experimentations. In this innovation perspective, technologies and organizations do not preexist: they have to be discovered and constantly revised. As a matter of fact, technological changes in the e-sector and changes in commodity prices can have a great impact on the EPR organization. For example, an international successful French Rare Earth Elements (REE) recycler decided to shut down two REE recycling sites at the end of 2016 because of a substitution of technology (from fluorescent lamps to light-emitting diode bulb) and because of China's competing industry [START_REF] Leoty | La Rochelle: Fermeture de l'atelier de recyclage des terres rares de Solvay d'ici fin 2016[END_REF]. Generally, because of the current drop in the price of raw materials the recycling sector is being tremendously challenged. In truth, the price of secondary materials are indexed with commodity prices, and, at the same time, their production generates fixed cost. Therefore, recyclers have great difficulty to align secondary materials prices with the low price of raw materials. These challenges lead to reorganization and new experimentations. For instance, recyclers tend to overcome the commodity price competition by specializing their activity and investing niche markets. Some recyclers have invested in high innovative start-ups enabling them to develop new recycling solutions [START_REF] Theunissen | Recyclage: Et si la crise des matières premières était une opportunité pour les acteurs du secteur?[END_REF]. Moreover, in order to support the plastic recycling industry, one of the e-waste PROs launched end of 2015 with public organizations and a consulting firm a feasibility study for incentives mechanisms to secure the business model of the sector in France (2ACR, 2015).

Therefore, different regulation mechanisms are required that go far beyond financial support or setting specifications. In recent years, the variety of regulation mechanisms put in place by these private actors has considerably spread (contracts, specifications, guidelines, R&D supports, individual responsibilization for ecodesign, financial participation) and used to support or expand pioneering experiments or avoid certain practices. This on-going experimentation process can be affected by various events or lead to contentious drifts. That is why a continuous regulation production process supports and guides the collective action.

ii.

On-going production of public regulations

This on-going experimentation process is affected by various events such as the impact of new political priorities (promoting ecodesign). Also, the shared responsibility principle led to a few drifts that public authorities tackled by reinforcing public control and supervision.

These events influence constantly the outcome of EPR organizations.

For example, following a financial scandal concerning the transfer by a PRO's of funds in a fiscal paradise, public authorities decided to impose a State censor that would verify PROs' financial movements (CGEFI, download 2016; Article 46, Law n° 2009-967, 08/03/2009).

This measure was implemented to all PROs in every EPR waste schemes, not only in the ewaste sector. Also, since 2014, PROs are systematically subjected to periodic inspections by independent authorities (Article L541-10 modified by the Law n°2014-856, 07/31/2014) in order to verify if they respect the clauses of their mission statement. Recently, a non-renewal agreement of an e-waste PRO has generated many debates (ERP, 2015). This event has led to a decree proposal last April [START_REF] Gossement | Déchets : un projet de décret pour préciser les conditions d'agrément et de gouvernance des éco-organismes[END_REF]. This decree specifies the rules for a PRO's accreditation in an EPR system, rules which have never been really clarified before. Besides, the proposal specifies the condition of a non-renewal or rejection of a PRO accreditation demand.

The production of new regulations can also come from the initiative of producers themselves.

For example, in order to fight against illegal waste traffic, French PROs advocated a ban on cash transactions in the scrap metal trade. This measure has had a great impact on the illegal struggle. In fact, the two-years European project (the Countering WEEE Illegal Trade (CWIT)) gave its final restitution in July 2015 and strongly recommended an EU-wide ban cash (UNU, 2015). Also, the French decree proposal of last April contains an obligation to all e-waste operators to contract with either a PRO or an individual EPR system [START_REF] Gossement | Déchets : un projet de décret pour préciser les conditions d'agrément et de gouvernance des éco-organismes[END_REF]. The aim of this measure is to oblige all waste operators to hand their wastes over to the EPR scheme and limit illegal trades.

The production of new regulations can also emanate from the political agenda. For instance, since the Grenelle Environment Round Table in 2007, a new political priority was made on ecodesign that had a significant impact on PROs' mission statement, since it was acknowledged that this environmental objective was left aside. Indeed, this political shift was operationalized in the second PROs' agreement in 2009 with the expansion of the mission statement in which criterions for financial modulations were introduced. Other specifications were also added concerning the need for more research on recycling treatments, for developing new collection channels, for engaging more with the social economy, etc. Since the first mission statement, the amount of specifications for PROs' activity has tremendously increased. In truth, the first mission statement document published in 2005 contained three pages against 47 in the last one in 2014. This significant amplification highlights the complexity of EPR schemes and the constant need for more clarifications in order to reflect to the exactness of the collective action changes and progress.

Not only do the production of regulations concern the e-waste sector but it also impacts every EPR schemes (used packages, used cars, paper waste, etc.). In fact, the various mission statements of the different EPR schemes influence one another. For example, the creation of a PRO coordinator, as we can see in the e-waste sector, has been put forward in the decree proposal to become systematic in all EPR schemes when the situation of multiple PROs in a unique waste sector occurs [START_REF] Gossement | Déchets : un projet de décret pour préciser les conditions d'agrément et de gouvernance des éco-organismes[END_REF]. More generally, after having created more than twenty EPR schemes over the last decade, public authorities decided to focus on an overall harmonization and rationalization phase. As a matter of fact, last December a horizontal commission has been created in order to harmonize the various waste schemes and the numerous accreditation commissions (Decree 2015(Decree -1826(Decree , 12/30/2015)). The aim is to favor mission statements standardization and mutual progress between waste sectors.

Thus, in this process, regulation is a dynamic and hybrid activity that is aimed at reducing uncertainties, reducing treatment costs and promoting innovation. In this perspective of possible unpredictable and unsettling internal changes or externalities, a crucial issue for PROs is to maintain their members commitment to the common purpose that materializes the shared responsibility principle.

iii. Maintaining and revising the common purpose

Shared responsibility is a fragile principle that can be threatened by free-riding strategies and conflicts. Indeed, in a collective scheme it is common to observe passive actors that do not contribute to the collective effort but still benefit from it. Making sure that a collective strategy is acceptable for the main stakeholders and suitable with policy targets is a constant purpose for PROs because it is their license to operate that is at stake. In theory, their accreditation to operate can be revoked at any time (even if it has never happened before, except for a non-renewal). Also, producers can change their membership to another PRO if they are not satisfied with the service provided. For example, a producer could choose to change PRO because of an increase of the financial contribution.

As a matter of fact, one of the e-waste PROs is at the point of increasing its membership fees because of the recycling sector struggle. For that purpose, the PRO launched a quantitative and qualitative study in order to evaluate how much should be the increase and to find the best way to communicate and justify it to its members. Also, it has developed guiding and support tools for better eco-design performances exclusive to its members in order to compensate a possible fee increase and to foster individual responsibility. Indeed, it is acknowledged that the collective EPR system enables tremendous reduction in logistics and treatment costs because of significant scale effects. However, a collective organization has a reverse side that is responsibility dilution and limit individual action [START_REF] Olson | Collective Action. Public goods and the theory of groups[END_REF]. That is why public authorities and PROs struggle to encourage producers to promote eco-design, as eco-design can only emanate from an individual action [START_REF] Mayers | Implementing Individual Producer Responsibility for Waste Electrical and Electronic Equipment through Improved Financing[END_REF]. Indeed, the producer is the only one able to influence its production design in order to decrease the environmental footprint. Encouraging members to go beyond the mere obligation of contributing financially to the e-waste scheme and to fully engage in the common purpose is a great challenge for PROs.

More generally, this same PRO had always been very cautious about how to define and communicate its strategy to its members. At each approval periods the PRO has carefully defined the common purpose that would appeal its main stakeholders and suit policy targets.

At the creation of the e-waste scheme, between 2005 and 2010, the focus was on the reduction of collection and treatment costs. Their strategy was to "comply with the collect and treatments obligations at the lowest cost, while developing a high-quality sector and while integrating the social economy". After the Grenelle Environment Round Table in 2007, the PRO focused more on eco-design and its strategy between 2010 and 2013 was to "contribute to the optimization of the environmental footprint of e-products in the respect of the members interests". Today, with the economic struggle, the aim is to create more value out of waste. Thus, the current strategy of this PRO is to "foster the emergence of operational recycling solutions at high environmental, social, and economic performance for the benefit of the general interest" (translated from French from confidential documents).

By maintaining and revising a common purpose suitable at the same time to stakeholders and policy targets, PROs embody the armed wing of public authorities. Indeed, by integrating new regulations in their strategies and by informing producers of these complex regulation changes, PROs enable waste Law interpretation. In that sense, the EPR principle is an original political tool that appears to be relevant and useful to give meaning to waste regulation and to federate producers to act in favor of the common purpose.

In this perspective, a dynamic and vivid governance is all the most important since intense collective learning takes place and leads to different strategic options (resumed in Table 2). If the e-waste regulation setting in France has promising characteristics, we also argue that certain issues has still received little attention (such as prevention, reuse or the lengthening of the product life) to the extent that they may contradict the producers' traditional business models. As these issues may prove to have great value, we plead for a stronger public In this communication, we have proposed to consider hybrid regulation as a performative practice rather than from a traditional ostensive viewpoint [START_REF] Latour | The powers of association[END_REF]. In other words, the value of hybrid regulation shall not be considered in principle but in practice, through the careful examination of its dynamic effects. For standard economists or lawyers, hybrid regulation is difficult to explain and justify in theory.

As we have shown in earlier sections, considering the practices of hybrid regulation in the ewaste sector in France provides a very different picture of the underlying dynamics. In particular, it appears as an adaptive and revisable model well suited to complex and uncertain issues for which direct public intervention is difficult to design, implement, control and provide sanction.

However, as we shall argue, the performativity of this model depends on the capacity of private regulatees to build, beyond individual responsibility mechanisms, a collective waste management framework, based on a common purpose, aimed at reducing "bads" and valuing "goods". This empowerment of private actors can be achieved through hybrid regulation. The practical case gave insight of how hybrid regulation can be performed in practice. Based on this pragmatic approach we aim at proposing a model of hybrid co-regulation. As said, Ostrom has proposed principles for the governance of natural resources. However, at the light of the e-sector major differences can be identified between natural resources governance and e-waste hybrid regulation. First, the "common purpose" in the waste sector is created by the State as the common interest is not directly identifiable. Secondly, waste and the issues surrounding their management are continuously evolving and changes are highly unpredictable. Thus, the "common purpose" must be maintained and revised. These assumptions enable us to propose a more dynamic model of hybrid co-regulation that can be discussed. We propose that such a model shall have six main characteristics:

-Based on a specific scope and purpose, different actors are designated collectively as responsible of a public issue; -A shared responsibility principle is defined, materialized in a mission statement which define targets and reciprocal commitments; -The pursuit of this mission can be delegated for a period of time to a collective organization who acts on behalf of its members and is dedicated to the pursuit and actualization of the common purpose; -The mission-driven organization has a governance structure, composed of different stakeholders, who have the power to revise the mission of the organization; impacts and the value creation generated (economic, environmental and societal value). Indeed, we assume that EPR systems should be compared not only through direct quantitative indicators (e.g. collection rate, valorization rate), but also through more global indicators reflecting the multiple value creation such as e-waste employment rate, number of masters' degree dealing with economy, etc. Furthermore, qualitative indicators could be created to evaluate the link between a system performativity and its level of hybridization.

In this perspective, we aim to contribute to the present debates about regulation dynamics of capitalism in a transnational world [START_REF] Djelic | A world of governance -the rise of transnational regulation[END_REF] by providing a dynamic model of hybrid co-regulation and discussing its performativity, which remains under-theorized although practices and experiments are strong. We believe the value of such a model expands far beyond waste issues and is worth for issues with similar characteristics.

  Operational regulation is led to private actors, particularly PRO's who has a crucial role of coordination. Public authorities have a supervision and framing role and can activate different levers. PRO's activity is officially approved for a period of time of six years and is scrutinized by public bodies. They also have a strong consultative power that can influence the mission statement's conditions. As to date, three agreements period took place: 2005, 2009 and 2014.

  Figure 1: Contracts outline in the e--waste sector

Figure

  Figure 2: The EPR model, a dynamic model enabling revisions

Table 2 : On--going experimentations of the hybrid regulation process Discussion and contributions: towards a dynamic model of hybrid co-regulation

 2

	regulation at the European level since certain activities (eco-design and product strategies for
	instance) should be dealt at a transnational level to have stronger effects on worldwide
	producers.

Eco--Emballages, the PRO dedicated to package management, has only a financial function.

-Targets and mission given to this organization are revisable, depending on results and problems observed in the field and new public objectives; -Public intervention may be required to correct the failures of self-regulation: if the mission has not been achieved or needs to be revised, when free-riding behaviors threaten collective action. These characteristics can be summarized according to three main ideas (Table 2). The first one is the political impulse to create a collective action that will have to endorse a public issue. The second idea is the possibility for the collective to claim for representatives' organizations to embody the armed wing of public authorities. The last and main point is the right to revise and strengthen the whole system through a participative-decision making process.

Collective action created by public authorities

Actors are designated collectively

Definition of a mission statement

Possibility of key actors as armed wing of public authorities

The mission can be delegated to a collective organization The governance structure gives power to the organization

Possibility to revise and strengthen the system

Targets and missions are revisable

Public intervention accepted in case of failures

Tableau 3: Three main ideas of hybrid--regulation and six characteristics

We argue that such a model may avoid the pitfalls of neoliberal individual responsibility or command-and-control approaches in evolving contexts characterized by uncertainty, interdependence, ambiguity and innovation. Is it a transitory regime of regulation? As long as issues remain complex and progressive, it is highly consistent with setting a dynamic agenda.

But if the context stabilizes, one can imagine a progressive privatization. On the contrary, if important drifts and insufficient results are observed, stronger public intervention might be legitimate.

In a next step, it should be highly enlightening to expose PROs and public actors to the proposed model. Moreover, an international comparison is planned in order to understand, in view of these novel principles, the various implementations of the EPR principle, their


Fernando Garrido
email: fernando.garrido-carpio@inria.fr

David González

Vicente Milanés
email: vicente.milanes@inria.fr

Joshué Pérez
email: joshue.perez@tecnalia.com

Fawzi Nashashibi
email: fawzi.nashashibi@inria.fr

Real-time planning for adjacent consecutive intersections

Real-time path planning constitutes one of the hot topics when developing automated driving. Different path planning techniques have been studied in both the robotics and automated vehicles fields trying to improve the trajectory generation and its tracking. In this paper, a novel local path planning algorithm combining both off-line and real-time generation for automated vehicles in urban environments is presented. It takes advantage of an off-line planning strategy to achieve a smooth and continuous trajectory generation with adjacent consecutive intersections. Therefore, this approach allows a smooth and continuous trajectory by means of planning consecutive curves concurrently, i.e., it will plan the upcoming curve and the following one in advance, taking into account the constraints of the infrastructure and the physical limitations of the vehicle. The real-time planning algorithm has been tested in simulation based on the INRIA-RITS vehicles architecture. The results obtained show an improvement in the smoothness, continuity and comfort of the generated paths.

I. INTRODUCTION

Vehicle automation is gaining more and more attraction within the intelligent transportation research field. As a matter of fact, significant demonstrations of automated capabilities have been shown in the last years. Specifically, one of the most relevance was the Bertha Benz memorial route carried out by the Karlsruher Institut für Technologie (KIT) [START_REF] Ziegler | Trajectory planning for Bertha -A local, continuous method[END_REF]. They emulated the first trip did by a Mercedes car but on a fully automated way on German roads, presenting some advances on perception, localization and motion planning. In 2010, the VisLab Intercontinental Autonomous Challenge was conceived as an extreme test of automated vehicles [START_REF] Broggi | The VisLab Intercontinental Autonomous Challenge: an extensive test for a platoon of intelligent vehicles[END_REF], where two driverless vehicles made a 16,000 kilometers trip from Parma (Italy) to Shanghai (China). Some important demonstrations have been celebrated last year, such as the ones related to the CityMobil-2 project and the 22nd ITS World Congress in Bordeaux, where automated vehicles were tested in urban areas in order to enhance the vehicleinfrastructure communication and that way the cooperation among them, pursuing the objective of building an efficient public transport system in dedicated areas [START_REF] Parent | Automated vehicles: autonomous or connected?[END_REF]. Recently, several teams participated in the 2016 Grand Cooperative Driving Challenge (GCDC) 1 . It was focused on cooperative driving, where some important advances were made in sensor fusion, vehicle-to-vehicle communication and cooperative control. Finally, some promising results have been achieved in urban roads, handling a variety of dynamic scenarios while respecting the traffic rules [START_REF] Li | Real-Time Trajectory Planning for Autonomous Urban Driving: Framework, Algorithms, and Verifications[END_REF]. Although these are very promising results, there is still a long way to go before having fully automated vehicles driving on public roads.

In the automated vehicles control field, the planning of the route plays a key role in order to improve transport efficiency and safety [START_REF] Gu | On-Road Motion Planning for Autonomous Vehicles[END_REF], increasing the driving stability [START_REF] Fu | Path Planning and Decision Making for Autonomous Vehicle in Urban Environment[END_REF]. For open spaces, such as the urban areas where automated vehicles deal with the different road actors (pedestrians, cyclists, etc), it has to determine the best feasible and collisionfree path. Based on the team's vehicle architecture described in [START_REF] González | Control architecture for Cybernetic Transportation Systems in urban environments[END_REF], path planning composes the decision stage of the architecture. This is divided in two sub-stages: global and local planning. The first one uses the information of the environment to create a path of way-points that describe a route itinerary. Meanwhile, the local planner ensures a real time, safe and comfortable trajectory throughout the path, smoothing the raw path by considering the kinematics of the vehicle and the road constraints.

Current planning systems consider a short term path planning, that is, with a short planning horizon. As examples, an horizon of 10 seconds was considered by the KIT institute in the Bertha Benz Memorial Path [START_REF] Ziegler | Trajectory planning for Bertha -A local, continuous method[END_REF], whereas an horizon of 30 meters was considered by the Vislab team of Parma University in the Public Road Urban Driverless car test (PROUD) of 2013 [START_REF] Broggi | PROUD-Public road urban driverless test: Architecture and results[END_REF] and the same distance was considered in the Boss car of Carnegie Mellon University (CMU) during the 2007 Darpa Urban Challege [START_REF] Gu | On-Road Trajectory Planning for General Autonomous Driving with Enhanced Tunability[END_REF].

Digital maps and global planners are getting more and more precise, being able to provide information beforehand about the environment where the vehicle has to drive. That is, the way-points that define the intersections on the route are known in advance (both the distances to reach the intersections, their angles and their turning directions). That way, the optimal trajectory for each isolated curve [START_REF] Garrido | Optimized trajectory planning for Cybernetic Transportation Systems[END_REF] is already registered in databases. Using this previous knowledge, a path planning algorithm that optimizes the two following curves generating a smoother and continuous path is presented.

The rest of the paper is structured as follows. Section II presents a path planning techniques overview. The path planning algorithm for interpolated curves is explained in section III. This is the basis of the optimized path planning algorithm for consecutive curves, presented in section IV. Simulation results are included in Section V. Finally, some concluding remarks and future work are given in Section VI.

II. PATH PLANNING TECHNIQUES OVERVIEW

There exist several path generation techniques that can be used in the planning stage. The most common ones in the automated navigation field can be classified in the following categories [START_REF] González | A Review of Motion Planning Techniques for Automated Vehicles[END_REF]:

Graph search based planners: Describe the environment as a grid or lattice of different states. They provide the states the vehicle would visit to achieve the destination. Then, these algorithms give a solution in the case of having a sequence of valid states, but this could not be the optimal one. Some examples are: 1) the A * algorithm that is described as an extension of the Dijkstra's algorithm [START_REF] Delling | Algorithmics of Large and Complex Networks[END_REF]. It was used in the 2007 DARPA Urban Challange [START_REF] Kammel | Team AnnieWAY's autonomous system for the 2007 DARPA Urban Challenge[END_REF]; 2) The State Lattice that searches the discretization of the vehicle state space represented as a direct graph to find a motion plan that satisfies the constraints [START_REF] Pivtoraiko | Differentially constrained mobile robot motion planning in state lattices[END_REF]. This method has been used in the generation of trajectories to be followed at high-speed running with real time performance [START_REF] Ziegler | Spatiotemporal state lattices for fast trajectory planning in dynamic on-road driving scenarios[END_REF], or to compute highly optimized paths between destinations [START_REF] Andreasson | Autonomous Transport Vehicles: Where We Are and What Is Missing[END_REF].

Sampling based planners randomly sample the space looking for connectivity and fulfilling with timing constraints. As an example, the Rapidly-exploring Random Tree (RRT) method, which builds an incremental tree for searching in high-dimensional spaces. There exist an enhancement of this algorithm, called Enhanced RRT or RRT * . It quickly finds a feasible motion plan, but unlike RRT, RRT * almost surely converges to an optimal solution thanks to the asymptotic optimality property [START_REF] Karaman | Anytime Motion Planning using the RRT*[END_REF].

Interpolating Curve Planners: These methods generate a smooth path from a set of way-points that describe the road. Below the most significant methods are described.

Clothoids: These are curves whose curvature changes linearly with its curve length. Since they are defined in terms of Fresnel integrals that cannot be solved analytically, using them in real-time applications is a difficult issue in comparison with non-linear curvature curves that are easier to compute [START_REF] Brezak | Real-time Approximation of Clothoids With Bounded Error for Path Planning Applications[END_REF]. Clothoids are used in road design because they provide a constant change on the curvature, allowing a smooth change from linear to circular stretches and viceversa.

Polynomial curves: These are curves defined by polynomial equations. They are used to fit a series of data points, possibly subject to constraints, where either interpolation or smoothing is involved.

Splines: These are piecewise differentiable curves defined by polynomials. These can be parametric equations or Bsplines, i.e., a generalization of Bézier curves. Their knots or polynomial joints pose a high degree of smoothness.

Bézier curves: These are polynomial curves that use information of checkpoints, called control points, to be generated. The basis of these curves are the Bernstein poynomials.

A. Bézier curves: definition and properties

Among the different path planning techniques, we use Bézier curves because of their simplicity and low computational load which make it more suitable than the other path generation techniques [START_REF] Han | Bézier curve based path planning for autonomous vehicle in urban environment[END_REF], allowing a fast trajectory computation. This is a needed feature that has to be fulfilled by the proposed local planner in order to generate the selected trajectory from the database and send it to the controller stage. Thanks to be defined by a set of control points, the curves generated are malleable. That way, it is easier to join curves preserving the curvature continuity.

The generation of a n-degree Bézier curve is mathematically defined by Equation 1.

B(t) = n i=0 n i (1 -t) n-i t i P i t ∈ [0, 1] (1)
where n is the degree of the polynomial equation and P i are the control points that define the curve.

In [START_REF] Han | Bézier curve based path planning for autonomous vehicle in urban environment[END_REF] some features of the Bézier curves are described. The most relevant for the work done are explained below.

• Bézier curves always start on the first control point P 0 and they end at the last control point P n . • The direction vector that defines the beginning of the curve is described by ---→ P 0 P 1 and the direction vector that defines the end of the curve is described by -----→ P n-1 P n . • The curves are fully symmetric, i.e., if the control points are reversed, we get the same curve.

• The curves will be always framed within the convex hull defined by the control points, i.e., the one formed by the outermost control points. • The behaviour of the curve concavity is consistent with the concavity formed by the control points. Thus, we will test our trajectory generation approach in urban scenarios where different kind of curves can be found. The results obtained will be compared with the previous works developed in the framework of INRIA RITS team for intersection scenarios [START_REF] Rastelli | Dynamic trajectory generation using continuous-curvature algorithms for door to door assistance vehicles[END_REF].

III. VEHICLE PATH PLANNING FOR INTERPOLATED

CURVES

Urban areas usually present several consecutive intersections in a short period of time, with a limited space between them. Our approach proposes a strategy to generate a smoother real-time path planning. Considering the information of the route (coming from the global map), the road layout and the physical limitations of the vehicle, the optimal curve for each intersection can be load to generate a continuous and smoother path optimizing consecutive curves.

The proposed planning strategy tries to emulate the human behaviour when driving. Thus, when a human driver is driving on a well-known environment, he will take advantage of the road to adjust his trajectory depending on the road layout. Similary for the local planner, when several zig-zag curves are presented, the system will keep the vehicle in the internal side of the road, that is, not opening its trajectory followed, like a human driver does. By contrast, when several consecutive curves with the same direction of rotation are presented, it will open the trajectory followed by the vehicle in the turn, without returning to the centre of the road. This provides to the planning system a naturalistic driving style.

To achieve a real-time smooth and continuous path generation, the proposed algorithm is based on an off-line planning

Trajectory Starting point Ending point Blue A A Red A B Green B A Black B B
strategy presented in [START_REF] Garrido | Optimized trajectory planning for Cybernetic Transportation Systems[END_REF]. Since the real-time computational cost for the path planning can be too high, an off-line evaluation has been applied in this module. It consists on the generation of a database of the best curves that a vehicle can follow on an interpolated intersection scenario, considering a big set of possible intersection scenarios while changing the angle of the curve and the length of the segments. The curve for each kind of intersection is chosen by means of the cost function Q described in Equation 2, which tries to minimize both the curvature (k) of the path and its derivative ( k), trying to remove abrupt changes on it.

Q = n i=0 w ki |k i | + w ki ki (2)
As the maximum speed of the experimental vehicles (cybercars) is 40 kph [START_REF]CityMobil2 Vehicle Technical Specifications -Selection of offers for the city demonstrations[END_REF], at this low-speed the vehicle behaviour is not significantly affected by vehicle dynamics and the planning is mainly affected by vehicle's kinematics and physical road constraints [START_REF]CityMobil2 Vehicle Technical Specifications -Selection of offers for the city demonstrations[END_REF]. To that end, as every vehicle has a maximum steering angle, all the curves evaluated have to present a curvature less than or equal to the maximum curvature feasible by the vehicle. Furthermore, the curve is generated into the road limits by placing the control points into the polygon formed by an internal separation of the vehicle width with respect to the road limits, according to the 4th Bézier property, as explained in [START_REF] Garrido | Optimized trajectory planning for Cybernetic Transportation Systems[END_REF].

Table I explains the combination of all possible scenarios that can be found. The starting/ending points for generating the trajectory can be either center in the lane (represented by A) or slightly moved to the side of the lane (represented by B) according to a more naturalistic driving. Fig. 1 summarizes the possible consecutive intersection scenarios that can be found in an urban scenario in terms of

G n-2 G n-1 2 G n G n+1 G n+2 1 1 < 2 2 > 3

IV. OPTIMIZED PLANNING FOR CONSECUTIVE CURVES

The main contribution of this work is the generation of a safe and smooth path planning with an extended planning horizon of two curves for urban scenarios, assuming a reliable information of the route coming from the global planner. A real-time planning is generated in order to decide which path is the optimal one. As it is computationally expensive analyzing all the possible paths that a vehicle could track, the local planner loads from the off-line generated database the isolated curves generated for each intersection according to the urban scenario.

Urban scenarios may present consecutive intersections with a limited space between them. Then, a planning strategy is needed to find the best joint point between consecutive curves to generate a continuous path. Fig. 2 is an example of several consecutive intersections handled with three joined Bézier curves: C 1 (in orange), C 2 (in green) and C 3 (in red).

Different adjacent intersections have been handled in previous works [START_REF] González | Continuous curvature planning with obstacle avoidance capabilities in urban scenarios[END_REF]. However, they considered the previous (G n-1 ) and the next (G n+1 ) intersection points if the space between curves was lower than 20 meters. Doing this, the global control points maximum distance was fixed to the half of the distance of the minor shared segment, as it generated symmetrical curves.

Meanwhile, in the proposed real-time planner the location of the joint point is changed taking into account the There are two segments that are shared between the curves (see Fig. 2): seg 2 between the curves C 1 and C 2 , whereas seg 3 is the segment between the curves C 2 and C 3 . The principle that has been applied to divide the shared segments is to give more space to the more closed curve (i.e. the one with the least angle). According to the intersection angles, the more closed curve, the more segment stretch will be used for that curve.

In the example of Fig. 2, as the angle of the first intersection is smaller than the angle of the second intersection (α 1 < α 2 ), for the first curve will be considered all the possible curves changing the external control point distance from the midpoint of the segment to the point G n . The maximum value of this margin is limited by the maximum required spaces for performing the next curve in a proper way. In the same way, as the angle of the second intersection is greater than the angle of the third intersection (α 2 > α 3 ), for the second curve will be considered the curves generated changing the external control point distance from the midpoint of the segment to the point G n . If the point G n+1 were the path end, it would be considered the whole length of the segment (G n , G n+1 ), i.e., from 0 to 1.

The different curves changing the external control point distances are analyzed in order to optimize both the current and the following curve. In the example would be the curves C 1 in orange and C 2 in green for planning the first intersection, and the curves C 2 and C 3 for the second one.

Fig. 3 present all the cases that have to be evaluated, where the section of shared segment considered for placing the external control points in the curves is represented with an interval as a fraction of unity.

The algorithm developed to make the real-time planning is introduced in Algorithm 1. This algorithm plans the path of the current curve and the next in advance. Therefore, the way-points that define it are read (line 1, Algorithm 1). This Algorithm 1 Real-time path planning algorithm 1: Read route way-points from the global planner 2: Estimate direction of rotation and angles of upcoming and two following intersections 3: Calculate intervals for the intersections shared segments 4: Estimate piece of the 1 st segment used for the curve 5: Check first, last or intermediate intersection 6: for the different 1 st curves moving the joint point on the 2 nd segment interval do 7:

Calculate the piece of the 2 nd segment that can be used for the curve 8:

Estimate the direction of rotation of the previous and following curve to load the curve from the right database 9:

for the different 2 nd curves moving the joint point on the 2 nd segment interval do 10:

Estimate the piece of the 3 rd segment that can be used to plan the 2nd curve 11:

Estimate direction of rotation of previous and following curve to load the proper database 12:

Check if both planned curves improve the optimal path 13: Generate the optimal upcoming curve allows to calculate the direction of rotation and the angles of the upcoming intersections and the following two ones (line 2, Algorithm 1) planned in advance.

The intervals where the curves can be moved on the shared segments are calculated (line 3, Algorithm 1), following the criterion described before in Fig. 3. That way, the interval of segment where the consecutive curves can be joined is defined. This will allow to generate the different curves modifying the curve's beginning and ending points in order to find the optimal trajectory. Line 4 describes the calculus of the piece of segment that can be considered for the upcoming curve. It considers whether it is the first curve (where the whole segment is used) or not (where it is used the rest of the segment that didn't use the previous curve). Since the database cannot consider neither all the possible angles nor all the possible distances for the segments, these values have to be approximated to the lower ones existing to load the nearest curve.

Line 5, the current intersection position (first, last or an intermediate one) is checked in order to generate the path for each curve loading the proper database for isolated intersections.

Later on, the location of the joint point of both upcoming and next curves is changed in the interval set before (line 4) to generate the different curves while moving its last point (line 6).

Once it is determined the piece of the second segment that is assigned to the upcoming curve (making the fitting as with the 1st segment, line 7), the direction of rotation of the following curves is analyzed in order to plan the upcoming curve (line 8).

In the same way as with the second segment, it is de-termined the piece of the segment that can be considered to generate the different curves to plan in advance the following (second) one (line 9). As with the other segment, it is needed a fitting in order to load from the database the nearest curve (line 11). Previously is checked if there exist a third curve and its direction of rotation. Once both upcoming (first) and next (second) curves are planned, it is checked if the path generated with both consecutive curves is the optimal one. This occurs when the sum of its finesses is lower than the local optimum (line 12). If so, the configuration of the curve is saved (longitudinal and lateral distances to the control points). Once it has finished the evaluation of all the different curves, the optimal one is generated for the upcoming intersection (line 13).

V. RESULTS

This section presents the results to validate the realtime planner presented in comparison with the used in the team defined at [START_REF] González | Continuous curvature planning with obstacle avoidance capabilities in urban scenarios[END_REF]. To that end, the planning module has been developed in RTMaps 2 , and the generated component has been tested with Pro-Sivic simulator 3 . This software simulates complex scenarios such as urban environments, allowing us to use the perception information and the models of the vehicles.

The experiments have been carried out on urban scenarios of multiple consecutive intersections, including ones with the same direction of rotation and others with the opposite. Fig. 4 represents the tested scenario. There, a lane road defined by squared intersections is assumed, where the lane width is 3 meters to fit with real scenarios. It is composed of two right turns and two left turns. Path planning considering pairs of curves was tested, taking into account a higher horizon of vision that considers the following curve and its respective turning angles and their direction of rotation. Upper part of Fig. 4 shows both the planned and tracked path with the previous team's implementation [START_REF] González | Continuous curvature planning with obstacle avoidance capabilities in urban scenarios[END_REF] and the proposed one. Whereas, in the lower part the curvature and its derivative are presented.

In the paths sub-figure the red continuous line shows the path generated with the previous team's implementation, detailed in [START_REF] González | Continuous curvature planning with obstacle avoidance capabilities in urban scenarios[END_REF], while the blue continuous line represents the one generated with the proposed planning system. The dotted lines represent the paths tracked by the vehicle during the simulation. The planned paths have been generated with 4th degree Bézier curves. This is the minimum degree in order to generate continuous enough paths to be joined for several curves. Meanwhile, in the lower sub-figure, the red and blue continuous lines represent the curvatures for both planning algorithms, the dashed lines represent their curvature derivative respectively.

Table II summarizes the results obtained. First, an improvement on the curvature is appreciated, being this clearly manifested in lower peak curvature values: 0.4295 m -1 is the maximum curvature with the previous team algorithm, 2 www.intempora.com 3 www.civitec.com whereas 0.2891 m -1 is the curvature with the proposed one. It means an improvement of a 32%. Furthermore, it can be also appreciated an improvement on the curvature derivative, being manifested in both peak and mean values. These improvements rely on the generation of smoother planned paths, allowing the vehicle to track more comfortable trajectories. This behaviour can be noticed on Fig. 4, where the path is better tracked by the vehicle in our approach based on the controller developed in [START_REF] Rastelli | Dynamic trajectory generation using continuous-curvature algorithms for door to door assistance vehicles[END_REF].

VI. CONCLUSIONS AND FUTURE WORKS

In this work, a new real-time path planning algorithm has been presented for CTS in urban scenarios. Considering several intersections in a short period of time, an optimization in the path generation is developed considering an extended planning horizon: it plans the upcoming curve and the following one in advance for each intersection, trying to optimize both of them. Furthermore, an analysis of the division of the shared segment between two consecutive intersections has been done in order to evaluate the different curves moving the joint point between curves through the segment to generate a smoother and more continuous curvature on the path. The results obtained show a clear improvement in the path generation in terms of continuity, taking into account the path's curvature and its derivative. This let automated vehicles tracking smoother and more comfortable trajectories.

As future work, a comparison with other interpolating planning methods will be carried out. In addition, dynamic environments will be handled by introducing an algorithm to avoid obstacles in the path by considering the maneuver risk evaluating the obstacle's surrounding. Ordinates axis [m] [START_REF] González | Continuous curvature planning with obstacle avoidance capabilities in urban scenarios[END_REF] planned path Proposed approach planned path [START_REF] González | Continuous curvature planning with obstacle avoidance capabilities in urban scenarios[END_REF] tracked path Proposed approach tracked path

Fig. 1 :

 1 Fig. 1: Paths databases for consecutive intersections scenarios

Fig. 2 :

 2 Fig. 2: Adjacent consecutive intersections planning strategy

ForFig. 3 :

 3 Fig. 3: Segmentation process of the consecutive intersections shared segment

Fig. 4 :

 4 Fig. 4: Path planning over the tested urban scenario

TABLE II :

 II Experiments summary

	Algorithm	Measurements |µ k | (1/m) |kmax| (1/m) µ k (1/m 2 )	k max (1/m 2 )
	González et al., 2014	0.0929	0.4295	0.4286	1.9522
	Proposed approach	0.0657	0.2891	0.2916	1.2554

http://www.gcdc.net

ACKNOWLEDGMENTS

The authors want to thank the ANR-COCOVEA and ANR-VALET french projects for its support in the development of this work.

This work was supported by the VeDeCoM institute


André Loescher
email: andre.loescher@ifsw.uni-stuttgart.de

Jan-Philipp Negel

Thomas Graf

Wolfgang Pallmann

Bojan Resan

Igor Martial

Julien Didierjean

Fabien Lesparre

Jean-Thomas Gomes

Xavier Délen

Frederic Druon

Francois Balembois

Patrick Georges

Marwan Abdou

A 265W and 782 fs amplified radially polarized beam emitted by a thin-disk multipass amplifier

Keywords:

The amplification of a high-power radially polarized beam in a thin-disk multipass amplifier is presented. Up to 265W output power at a pulse duration of 782 fs and a high degree of radial polarization is achieved.

Introduction

The benefit of beams with radial polarization for many applications has often been reported in the last decades. However, at high outputpower the main interest is material processing [1]. Besides cutting of metal sheets, drilling applications using radial or azimuthal polarization states can benefit from such beams in order to increase the process efficiency when compared to standard (linear or circular) polarization states. Furthermore, ultrafast laser systems have gained a tremendous interest in various micro-processing applications like drilling, surface structuring, etc… In this paper, we present -to the best of our knowledge-the highest average output power of beams with radial polarization at sub-1ps pulse duration. A thin-disk multipass amplifier with similar architecture of the one in [START_REF] Negel | 1.1 kW average output power from a thin-disk multipass amplifier for ultrashort laser pulses[END_REF] s used to achieve up to 265 W of amplified donut LG01 beam with radial polarization and at a pulse duration of 782 fs.

Design and implementation of the thin-disk multipass amplifier for radially polarized beams

Figure 1 represents schematically the amplifier system presented in this paper and developed by the IFSW of the University of Stuttgart. A mode-locked oscillator (provided by JDSU) combined to multi-stage single-crystal-fiber amplifiers (provided by CNRS and Fibercryst) [START_REF] Lesparre | High-power Yb:YAG single-crystal fiber amplifiers for femtosecond lasers in cylindrical polarization[END_REF] is used as seed laser for the multipass amplifier. This seed laser delivers a linearly polarized beam with up to 60 W (M² < 1.2) of power at a pulse duration of 727 fs and a repetition rate of 20 MHz. In a sub-sequent step, the linear polarization of the seed laser is converted to radial by means of a linear to radial/azimuthal polarization converter (LRAC) composed of 8 half-wave segments [START_REF] Ahmed | A 1-kW radially polarized thin-disk laser[END_REF]. After the LRAC a radially polarized beam with 50W of output power is obtained. Figure 2 shows the recorded intensity distribution of the converted beam without and with polarization analyzer at different orientation confirming the radial polarization behavior of the transmitted laser beam.

The multipass amplifier is similar to the one reported in [1] but it uses an mirror array of 60 individually adjustable mirrors instead of 40 as previously reported [1], since the amplifier is operated in a single pass configuration due to the cylindrical polarization.. An Yb:YAG thin-disk with a diameter of 15 mm, a radius of curvature of around 20 m, a thickness of approximately 115 μm and 11% doping concentration was mounted on a diamond heat sink at the IFSW and is used as amplifier medium. The disk is pumped at 969 nm wavelength (with stabilized laser diode provided by DILAS) by a multi-pass cavity with 24 passes (standard "G1-module" as commonly provided by IFSW). The pumped spot has a diameter of approximately 5.2 mm. The radially polarized seed beam is collimated with a beam radius of 2.2 mm . Radally polarized laser beams are very sensitive to phase-shifts which can be introduced by the optical components composing the multipass amplifier (especially the 45° folding mirrors). In a multipass amplifier this effect is accumulating due to the high-number of passes through these components. Therefore, the polarization of the propagated beam through the multipass amplifier was first analyzed without amplification process. As expected, a strong degradation of the radial polarization purity can be seen in figure 3-a. Sub-sequent simulation and experimental implementation allowed us to compensate for the accumulated phase-shift by using a precompensation device at the entry of the multipass amplifier. By a proper adjustement of this pre-compensation device, one could almost completely recover the high radial polarization quality as shown in the qualitative polarization analysis of figure 3-b.

Experimental results

Figure 4 shows the extracted output power versus the incident pump power at a seed power of 50 W. As can be seen up to 265 W of average output power (at a pump power of 750 W) could be extracted in a single pass configuration. This corresponds to a gain of 5.3 and a slope efficiency of 38.3%.

The qualitative polarization analysis of the extracted beam at an output power of 250W is shown in figure 4-b. As can be seen, the radial polarization is preserved thanks to the pre-compensation approach. The measured optical spectra before and after the multipass amplifier are shown in figure 5a) and the pulse duration after the multipass is shown in figure 5 b). Assuming a sech² temporal shape, a pulse duration of 727 fs was measured at the entrance of the multipass amplifier and 782 fs at the output of the multipass amplifier. In conclusion, we have demonstrated an efficient amplification of beams with radial polarization in a thin-disk multipass amplifier. Up to 265 W of average output power could be generated at a pulse duration of 782 fs and a repetition rate of 20 MHz. To the best of our knowledge, this is the highest average output power of amplified beam with radial polarization in a sub-ps regime. Furthermore, a method to compensate for phase-shifting, which can occur during propagation through all optical components, has been demonstrated to be satisfactory to maintain a high degree of radial polarization and will be discussed in more details during the talk.

Figure 1 :

 1 Figure 1: Schematic representation of the thin-disk multipass amplifier (left). A Photograph of the mirror array is shownon the right side.

Figure 2 :

 2 Figure 2: Seed beam (left) converted to radial polarization which is confirmed by rotating a polarizer in front of a camera (right). White arrows indicate the transmission axis of the polarizer.

Figure 3 :

 3 Figure 3: Polarization analysis at the exit of the multipass amplifier (without amplification process) without (a) and with the precompensation (b). Balck arrows indicate the transmission axis of the polarizer.

Figure 4 :

 4 Figure 4: a) Extracted power versus pump power for 30 reflections over the disk with a 50 W radially polarized seed beamand b) polarization analysis of the output beam at 250W of extracted power. Balck arrows indicate the transmission axis of the polarizer.

Figure 5

 5 Figure 5: a) Spectra and b) autocorrelator trace of the output beam.

Acknowledgement: This work is supported by the Ultrafast_RAZipol project funded by the European Union's Seventh Framework Program for research, technological development, and demonstration under grant agreement no. 619237.