Eric Charmes

Max Rousseau

The Geopolitics of Urban Green Belts Between Exclusionary Zoning and the Militarization of Urban Space Maryame Amarouche

Introduction

This paper aims to combine French and English approaches to urban geopolitics, a discipline that means different things to French and English scholars (see the part "an introduction to urban geopolitics and la géopolitique urbaine"). In the French-speaking sphere, geopolitics developed a specifically urban dimension in the 1990s, when it became known as la géopolitique urbaine, hereafter called GU [START_REF] Hulbert | L'espace politique de la ville : plaidoyer pour une géopolitique urbaine[END_REF][START_REF] Subra | The tale of ethno-political and spatial claims in a contested city: the Muhajir community in Karachi[END_REF]. It focuses on the territorial dimensions of power struggles in cities. By contrast, in English-speaking scholarship, the concept commonly refers to an approach, which emerged in the 2000s and was geared to analysing the militarization of urban space in relation to new forms of international conflict (Graham 2004a). Later, this school of urban geopolitics (hereafter, called UG) gradually included other issues, such as postcolonial power relations, inter-ethnic relations [START_REF] Rokem | Urban geopolitics rethinking planning in contested cities[END_REF], formal and informal planning and numerous studies on phenomena relating to everyday life, which [START_REF] Fregonese | Urban geopolitics 8 years on. hybrid sovereignties, the everyday, and geographies of peace[END_REF] calls geographies of peace. As the French academic sphere has long been (and still is overall) quite separate from the English-speaking academic sphere [START_REF] Boudreau | Conversation avec Julie-Anne Boudreau autour des études urbaines et de leurs revues[END_REF], both schools developed independently, with little discussion between them apart from a promising attempt by Lopes de Souza (2016) through the analysis of urban eco-geopolitics in the case of Rio de Janeiro. Lopes de Souza however decided to side with UG. This paper aims to go another way by proposing a combination between the two schools, between GU and UG. To do so, this paper builds on the recent evolution of UG, taking better account of the territorial dimension of conflicts (Cociña and López-Morales 2018; [START_REF] Ortiz | The medellín's shifting geopolitics of informality. the encircled garden as a dispositive of civil disenfranchisement? in Urban geopolitics rethinking planning in contested cities[END_REF]Sultan Khan et al. 2018).

As this paper explains, the two schools have many differences (see the part "the main differences between urban geopolitics and la géopolitique urbaine"). For example, UG develops a critique of geopolitics (Graham 2004), whereas GU uses geopolitics as a method for criticism [START_REF] Lacoste | La géographie, ça sert, d'abord, à faire la guerre[END_REF]. While both approaches recognize that geopolitical stakes are multi-scalar, UG has largely focused on national and international stakes, until recently at least [START_REF] Fregonese | Urban geopolitics 8 years on. hybrid sovereignties, the everyday, and geographies of peace[END_REF]. In contrast, GU does not put a premium on national and international scales [START_REF] Subra | The tale of ethno-political and spatial claims in a contested city: the Muhajir community in Karachi[END_REF]. Despite these differences and the misinterpretations that arise when the same words are used to refer to different paradigms, this paper discusses the theoretical possibility of combining both schools of urban geopolitics (see the part "building a bridge between the two approaches") and shows how both approaches can be usefully combined.

To establish the empirical potential of this combination, the paper examines two case studies that analyse policies designed to preserve non-built open spaces. Combining the UG framework, which regards urbanism as ideologically charged policies, and the GU method, which emphasizes the territorial dimension of power relations, we compare two similar environmental policies set in two different contexts and involving different stakeholders. One case study is located in the Global North (Lyon, France, presented in the part "West Lyon's green belt: the local government's deceptive implementation of a national policy") and the other in the Global South (Rabat, Morocco, presented in the part "South Rabat's green belt: militarizing urban planning").

With this North/South comparison [START_REF] Rokem | Urban geopolitics rethinking planning in contested cities[END_REF], this paper aims to make a contribution to comparative research built on the richness of differences [START_REF] Rokem | Urban geopolitics rethinking planning in contested cities[END_REF][START_REF] Purenne | Towards cities of informers? community based surveillance in France and Canada[END_REF]. Indeed, while urban policies have been circulating globally for several decades [START_REF] Mccann | Urban policy mobilities and global circuits of knowledge: toward a research agenda[END_REF], urban research did not take global comparisons seriously until the 2000s [START_REF] Robinson | Cities in a world of cities: the comparative gesture: cities in a world of cities compared[END_REF]). To overcome this, several researchers have tackled methodological and theoretical issues head on [START_REF] Brenner | World city theory, globalization and the comparative-historical method-Reflections on Janet Abu-Lughod's interpretation of contemporary urban restructuring[END_REF][START_REF] Roy | The 21st-century metropolis: new geographies of theory[END_REF][START_REF] Schmid | Towards a new vocabulary of urbanisation processes: a comparative approach[END_REF], in order to go beyond particularism and incommensurability. Postcolonial urban studies (Robinson 2016a;[START_REF] Roy | Worlding the South: toward a post-colonial urban theory[END_REF]) emphasize the importance of global comparison in terms of urban theory through taking local specificities seriously [START_REF] Robinson | Cities in a world of cities: the comparative gesture: cities in a world of cities compared[END_REF][START_REF] Robinson | Debate on global urbanisms and the nature of urban theory[END_REF]Robinson 2016bRobinson , 2016a;;[START_REF] Schmid | Towards a new vocabulary of urbanisation processes: a comparative approach[END_REF]. Indeed, as this paper will demonstrate, comparing cities in contexts as different as France and Morocco, helps to understand how approaches like GU and UG may be heuristically combined.

The cases of Rabat and Lyon were chosen partly because the authors of this article have connections in both cities. Despite the contextual difference between a burgeoning city in the South and a city in the North, which is more concerned about improving the quality of life, the choice can also be explained by the fact that Rabat and Lyon are fairly similar in size. There are 2.3 million people in Lyon's metropolitan area and 1.9 million in Rabat. The comparison of a French and Moroccan metropolis should also be considered in the light of the long history of policy transfers between the two countries. In the early 20 th century, the French protectorate used its colonies in the Maghreb as a laboratory for new town planning techniques. Some were later applied in France, in particular with the villes nouvelles ("satellite towns") (Picard 1994). The marks of colonial town planning are still visible in Rabat's policies today. The satellite towns developed by the central state on the periphery of the city demonstrate this clearly [START_REF] Wagner | Rabat retrospective: colonial heritage in a Moroccan urban laboratory[END_REF]X et al. 2016;Harroud and X 2019).

The green belt is one of the planning tools that are used all over the world (Gant et al. 2011). Rabat and Lyon are no exception. However, as we will see, given the situational and historical differences between the two cities, protections from urbanization offered by green belts have very different political implications. They provide an interesting subject for geopolitical analysis, from an allied perspective of la géopolitique urbaine and urban geopolitics [START_REF] Webster | Property rights and the public realm: gates, green belts, and gemeinschaft[END_REF][START_REF] Blinnikov | Gated communities of the Moscow green belt: newly segregated landscapes and the suburban Russian environment[END_REF]. From the GU viewpoint, green belts are the result of bitter struggles between actors to control a territory. This control, as the case of Lyon confirms, generally benefits the better off. From the UG viewpoint, green belts outline buffer zones, which can play a role in international conflicts to separate two opposing groups, as confirmed by the case of Rabat. Therefore, depending on the context, UG may provide a very pertinent analytical framework, whereas GU may be a better choice in a different context. As the paper will show, the two approaches can be complementary in a given situation. In Lyon, for example, the issues that are key to UG, particularly the militarization of control methods, are present.

It is important to specify that this paper partly results from a process involving serendipity (Merton and Barber 2004). It stems from a collective research project funded by the French National Research Agency (ANR). The project developed within the Frenchspeaking academic sphere and initially applied the French geopolitical approach to compare anti-sprawl and growth control policies in France and Morocco 1 . To start with, green belts were considered as a tool for controlling urban sprawl in a research framework, and following on from Philippe Subra's work (2007), the aim was to identify how local stakeholders were affected by anti-sprawl and growth control policies decided on a broader national scale. The research was thus embedded within GU perspective. We started to focus on UG with the idea of presenting our research findings at international conferences. In particular, we wanted to present them at a RC21 conference dedicated to UG, organized in Leeds in 2016 by the editors of this special issue, Jonathan Rokem and Camillo Boano. This paper is in large part the result of a discussion we had during the conference, which we pursued with the editors of the special issue and later with anonymous reviewers.

An Introduction to Urban Geopolitics and la Géopolitique Urbaine

English-speaking researchers commonly understand UG as an approach designed to study "the telescoping between transnational geopolitical transformations and highly localized acts of violence against urban sites" (Graham 2004b,191). This approach developed in the wake of 9/11, with a focus on several very specific case studies (former Yugoslavia, Palestine, Lebanon). It analyses the growing importance of the local scale for restructuring the governance of security issues [START_REF] Fregonese | Urban geopolitics 8 years on. hybrid sovereignties, the everyday, and geographies of peace[END_REF]. Indeed, since the end of the Cold War and especially in the last two decades, international conflicts, which may be violent, have been rescaled: old state wars have given way to new forms of conflict, involving state and non-state actors, like cartels, militias or terrorist organizations [START_REF] Kaldor | Mary. new and old wars: organised violence in a global era[END_REF]. This shift has come with a change of scale: the state scale lost its primacy as the main target of violent operations. As more than 50% of the world's population lives in cities, cities have become the perfect setting for war and now crystallize global conflicts [START_REF] Rokem | Urban geopolitics rethinking planning in contested cities[END_REF][START_REF] Bhavnani | Group segregation and urban violence[END_REF]. Conflicts increasingly target and kill urban dwellers, destroy urban sites, block access to cities or prevent them from operating. This "urbanization of violence' may even go as far as "urbicide", i.e. "the deliberate denial, or murder, of the city" (Graham 2004a, 25). The term urbicide was coined by the critical urban research conducted in the 1960s. Initially, it was used to criticize the American federal state's urban policy, before being adopted by urban geopolitics in various works, such as those compiled by Graham (2004a) in the 2000s. It has been applied to diverse cases, ranging from urban planning during the Cold War [START_REF] Farish | Another anxious urbanism: simulating defence and disaster in cold war america[END_REF] to the militarization of Western cities in response to the proliferation of anti-globalization movements [START_REF] Warren | City streetsthe war zones of globalization: democracy and military operations on urban terrain in the early twenty-first century[END_REF]). Within UG, violence appears to be increasingly channelled towards urban sites. This "new military urbanism" is a major concern [START_REF] Graham | Cities as battlespace: the new military urbanism[END_REF]. One of its most striking features is the way it abolishes the divisions between war and peace. A sort of "diffuse war" emerges [START_REF] Gregory | The everywhere war[END_REF], characterized by a set of discourses and practices, such as prevention, security, surveillance and resilience [START_REF] Coaffee | Towards next-generation urban resilience in planning practice: from securitization to integrated place making[END_REF]. The internationalization of the new military urbanism, through war policy transfers, constitutes a further topic of urban geopolitics. For example, the construction of new settlements can be analysed as an important feature of Israeli geopolitics [START_REF] Weizman | Strategic points, flexible lines, tense surfaces, and political volumes: ariel sharon and the geometry of occupation[END_REF]) and the destruction of Palestinian housing appears as an equally central tactic [START_REF] Graham | Cities under siege: the new military urbanism[END_REF]. A similar tactic was later adopted by the United States as part of their "War on Terror" programme (Graham 2004a). This "new military urbanism" is strongly criticized because of its impact on segregation, discrimination and civil liberties. UG, however, is subject to some criticism. For example, [START_REF] Hills | Future war in cities: rethinking a liberal dilemma[END_REF] calls into question one of the main assumptions of urban geopolitics, by indicating that urban warfare has hardly changed since the Second World War. Many critics also argue that the hypothesis of a "rescaling" of war is somewhat simplistic. For instance, Flint (2006, 217) questions how today's car bomb attacks differ from those of the IRA in the 1970s and "why we are heading towards an urban geopolitics and what that may be when we arrive, and how it will be different from an undefined initial geopolitics".

Those critics aside, the main features of UG can be summarized in five points:

(1) Geopolitics is approached from a critical perspective and is, thus, considered as a framework (2) The rescaling of geopolitics at the urban level is a key aspect (3) States are key (but not exclusive) actors (4) Nation states' borders lose their importance, since they are blurred by the rise of new forms of conflicts territorialisation (5) The most pressing questions are about military or police control.

By contrast, French geographers use the term la géopolitique urbaine (GU) to refer to a research stream that has little in common with UG. GU emerged in the 1980's with the publication of Hulbert's works on Québec (1989). Hulbert demonstrates how the municipal reforms in Eastern Canada, which were implemented to adapt local government and governance to extensive urbanization, are also used by municipal actors to equilibrate negotiations between urban centres and peripheries. Hulbert's work was deeply influenced by Yves Lacoste's pioneering work. Lacoste, a then-Marxist geographer was known for his 1976 publication, which had a major influence on the French-speaking academy: La géographie, ça sert d'abord à faire la guerre ("Geography is used primarily to wage war"). Lacoste's argument was simply that geography is not a neutral, purely descriptive science applied to the analysis of population distribution or to the spatial distribution of natural resources. The year his book was published, Lacoste and a group of other scholars launched a new journal, Hérodote. The journal's subtitle was "Ideologies, geographies, strategies". The cover of the first issue showed the bombing of rice fields in North Vietnam. It also included an interview with Michel Foucault on territorial control. With Hérodote, Lacoste developed his initial argument by calling for a precise account of local conflicts to improve our understanding of the evolution of what was then called the "Third World".

Initially, in the context of the Cold War, the questions raised by Lacoste were quite similar to those subsequently developed in UG. In the 1970s, geographers were very wary of the notion of geopolitics because the concept was instrumentalized by colonial powers, the Nazis, in particular [START_REF] Giblin | Hérodote, une géographie géopolitique[END_REF]. Thus, geopolitics itself was initially a subject of criticism. However, geographers that came together around Hérodote gradually reconsidered the meaning of geopolitics and shifted away from the normative vision of classical geopolitics. Over time, geopolitics came to be used as a method for the critical analysis of the political issues involved in territorial rivalries and conflicts. In the light of this evolution, Hérodote's subtitle was eventually changed in 1982 to the Revue de géographie et de géopolitique (Journal of geography and geopolitics). Shortly afterwards, following the French decentralization reforms of 1982, the geopolitical approach was applied to the study of intranational power relations and the analysis of multi-scalar governance. Béatrice Giblin, who will later become director of Hérodote, carefully applied the geopolitical approach in her analysis of the French regions (régions) that had just gained democratic legitimacy, by focusing on the territorial actors' different interests, as well as their rivalries, conflicts and negotiations [START_REF] Giblin | Région, territoires politiques[END_REF].

Together with Hulbert's research, this pioneering work paved the way for GU and a new French-speaking geopolitical approach to territories and their actors. Over the years, the French school has diversified its range of topics and developed new works on local and urban geopolitics [START_REF] Douzet | Pour une démarche nouvelle de géopolitique urbaine à partir du cas d'Oakland (Californie)[END_REF][START_REF] Subra | The tale of ethno-political and spatial claims in a contested city: the Muhajir community in Karachi[END_REF][START_REF] Hulbert | L'espace politique de la ville : plaidoyer pour une géopolitique urbaine[END_REF]. As it gave more room to urban issues, francophone geopolitical analysis came to share many features with North American research on urban governance, especially issues relating to the role of territorial boundaries and the spatial dimension of power conflicts (see, for example, [START_REF] Keil | Governance restructuring in Los Angeles and Toronto: amalgamation or secession?[END_REF][START_REF] Boudreau | Making new political spaces: mobilizing spatial imaginaries, instrumentalizing spatial practices, and strategically using spatial Tool[END_REF]). As Douzet (2001,67) explains:

Urban geopolitics concerns an urban territory, which according to the issue at stake may have various boundaries. These may include conflicts between cities, rivalries between cities and suburbs, or even conflicts within the same city between rival forces with conflicting interests, struggling for political, economic or social control of the same territory, or seeking to attract to their own territory a share of the resources of an entire city.

Compared with the five main features of UG listed above, the main features of GU can be summarized as follow:

(1) Geopolitics is considered as a methodological resource for analysing conflicts (2) Access to urban resources through territorial control is a key issue (3) Many actors are considered and special attention is paid to their networks, coalitions and convergences of interest (see below). (4) Territories and their limits (both state and municipal or territories claimed by occupy movements) are a key focus (5) The rule of law is considered as a resource, even if access to it is unequal (see below).

The Main Differences between Urban Geopolitics and la Géopolitique Urbaine

There are many differences between the two approaches. A key feature of UG is its attention to other scales than that of the nation state. The latter remains relevant, but UG also emphasizes the need to work at scales that differ from those classically considered within geopolitics. It underlines the need to work at various scales, airports for example relocating border control within metropolis. Overall, however, UG's main focus remains directly linked to international or transnational relations. It gives less importance to political conflicts that arise at the urban scale. Indeed, the city is often reduced to a passive scene for conflicts that originate beyond its perimeter. On the contrary, GU does not prioritize international dimensions. The French-speaking approach to geopolitics also sees the state as merely one player among many. Indeed, it considers that urban actors play a vital role and, in some cases, are the main or sole actors. In GU, conflicts, tensions or compromises linked to the control of territories are examined at all scales, including cities or neighbourhoods. As Subra (2012, 53) wrote about the Basque conflict:

The Basque conflict, for example, is mainly a matter of […] an "internal state conflict" because its main issue is the birth or not of a Basque state on a territory that until now was part of another state, Spain (and incidentally on territories, the "Northern Basque Country" in the Etarra vocabulary, which are currently French). But it also obviously has a local, secondary dimension, because it takes the form of a series of local conflicts between supporters of ETA 2 and other parties in the provinces, municipalities and Basque districts, with issues that are local (control of a town hall or the executive of a province, control of the street). Just as it also has, in a way that is also secondary, an external or international dimension insofar as it involves the French State and Franco-Spanish relations. Analysing this type of conflict therefore implies dealing with it at all the scales where it occurs, taking into account the specific context, the issues and the actors involved at each of these scales.

The nation state-city binary are the two key points of reference in UG. In contrast, the GU method takes into account the interests pertaining to various scales. Therefore, investigating micro-local conflicts (for example, over land use rights), negotiations, coalitions and networks between multi-scalar stakeholders is central for grasping the issue at stake [START_REF] Subra | The tale of ethno-political and spatial claims in a contested city: the Muhajir community in Karachi[END_REF]. Until recently (see below), this approach was rare in UG. Again, although the UG approach recognizes the need to consider several scales (as the airport case shows), the dominant geopolitical issue in UG remains directly linked to international relations (see de Souza 2016 for a discussion on the issue).

Another important difference is that, even though UG and GU both focus on struggles and conflicts, their primary concerns differ. GU is less concerned with police or military control than UG. The latter places particular emphasis on armed conflicts or the militarization of police operations because of the obvious link with the central role played by states, which have the monopoly of legitimate violence. In contrast, GU focuses on unarmed conflicts, which generally have less national or international media coverage. These very different views on the nature of geopolitical conflicts determine the methods used by the two approaches.

On the basis of this brief comparison, we can conclude that applying UG seems more appropriate in urban situations where citizens' basic democratic rights are being violated. By contrast, GU methods are more relevant when the rule of law is relatively well established [START_REF] Subra | The tale of ethno-political and spatial claims in a contested city: the Muhajir community in Karachi[END_REF], i.e. in a context where conflicts can be mitigated without systematic repression. However, these differences are not irreconcilable when it comes to the theoretical and empirical dimensions. In the case of the latter, as parts 4 and 5 demonstrate, the rule of law has some scope in most situations, while certain citizens are almost always denied rights (this will be discussed in the conclusion). As far as the theoretical dimension is concerned, the next part will show that combining the two approaches can be useful: UG can be applied to conduct a critical analysis of the broad context and issues at stake, while GU can be of heuristic importance to consider the territorial dimensions of local conflicts.

Building a Bridge between the two Approaches

While there are many differences between UG and GU, the two schools are complementary. A bridge can even be built between them for analysing specific sets of local urban policies. Indeed, several proponents of one approach made a move towards the other. Recently, GU began to move towards UG regarding international conflicts, the militarization of urban space and conflicts involving state power intervention, issues that are important to UG (Fuentes-Carrera and Subra 2018; Robine 2016; Douzet and Robine 2013). From UG perspective, the possibility to combine GU and UG was recently discussed by Lopez de Souza (2016) in the Brazilian context. He raised important theoretical questions. After developing one of the few critical discussions comparing UG and GU, he demonstrates the value of a geopolitical approach, not only for analysing security issues, but also for understanding other policiesurban environmental policies, in his case. Lopez de Souza's (2016) key argument is that environmental protection policies in Rio de Janeiro are implemented in a socially selective manner: the more affluent families are, the better their quality of life is protected. In the case of Tijuca National Park, the poorest families who live in the nature reserve are evicted to 'protect' the site, while the richest families are allowed to stay and enjoy the protected natural area.

We concur with Lopes de Souza's idea that local environmental policies are particularly suitable for an analysis that combines the two geopolitical approaches. Indeed, urban environmental policies involve different scales of government, where the state usually plays an important (yet not exclusive) role. Urban environmental policies are also frequently shaped by major conflicts, particularly between different social or ethnic groups fighting for territorial control. The social and ethnic conflicts underlying environmental policies may well be confined to a symbolic and discursive level. However, they sometimes take a quasimilitary turn, as the case of Morocco demonstrates. Lastly, environmental policies question the notion of boundariesboth symbolic and physical -within metropolitan regions.

Nevertheless, Lopez de Souza sides with the UG approach, by simply proposing that its scope can be extended to environmental issues. While he acknowledges the importance of GU, he ultimately considers that geopolitics should remain the subject of normative critics. This is an important point, which makes resorting to UG incompatible with GU according to de Souza. He argues that one cannot criticize geopolitics and use it as a tool for criticism at the same time. He also maintains that focusing attention on state actors and the national level is consubstantial to a geopolitical analysis. Consequently, the emphasis that GU puts on the role of local actors (i.e. local elected officials, but also various decentralized state services, residents, non-profit organisations and economic actors) is inappropriate in the framework of a geopolitical analysis. These arguments are strong, but they are debatable. If one carefully circumscribes validity domains for both the GU and UG approaches, one does not have to choose between them. The theoretical contradictions identified by de Souza no longer prevent analysis because, on the one side, the focus is on issues determined by geopolitics as a framework, while on the other side, geopolitics is used as a method to examine the territorial dimension of power relations. The main problem here is that the term geopolitics has two different meanings. We will come back to it in the conclusion. Before that, we get round this problem by using two different acronyms to distinguish UG et GU.

In any case, de Souza's findings would have clearly benefited if he had given more consideration to GU. For example, in the empirical analysis he proposes, GU would have helped identify how the middle-classes, who settled in preserved natural areas, were able to defend their interests. De Souza suggests that the interests of the middle-classes are in line with those defended by state policies. However, he only establishes a correlation and fails to provide sufficient empirical evidence to show how state and middle-class interests were aligned. An examination of the convergence of interest, coalitions and networks of actors involved in protecting Tijuca National Park, as GU proposes, would have helped fill this gap. It would have revealed details of the negotiations, which ultimately ensured that middle class interests were supported by the state. As the case of Lyon will show, the state does not fully control urban planning tools. They are largely in the hands of local elected officials. The future of Lyon's peri-urban rings depends on where local policies can find common ground with national policies to protect natural spaces and reduce urban sprawl.

By building on these links between UG and GU approaches, we will try to demonstrate their complementary features empirically. As the rest of the paper will show, combining UG and GU is particularly useful for comparing environmental policies. We compare a similar set of anti-sprawl and growth control policies, the so-called 'green belts' or 'green ring' in Lyon and Rabat, while focusing on the political, social and territorial issues at stake. One of the rationales for combining UG and GU here is that the relevance of each approach very much depends on the context. As we will see, the selective use of UG and GU enhances the comparison between Lyon and Rabat and our analysis of the social and spatial effects of anti-sprawl policies. In the case of Lyon and Rabat, using the two approaches helps identify the power relations and social inequalities behind the consensus regarding sustainable development policies. It is a way to politicize the debate.

West Lyon's Green Belt: The Local Government's Deceptive Implementation of a National Policy

As a consequence of the decentralization laws passed in the 1980s, French municipalities have become key players in urban planning and development. Since the end of the 1990s, decentralization has been tempered by the promotion of intercommunal governments, which are gradually becoming more and more integrated (Le [START_REF] Galès | Les deux moteurs de la décentralisation: concurrences politiques et restructuration de l'état jacobin[END_REF]). Yet even within the most integrated metropolitan governments, mayors still have considerable weight [START_REF] Desage | La démocratisation de l'intercommunalité n'aura pas lieu[END_REF]. In this context, GU is particularly relevant for understanding the negotiations and coalitions established at the local level [START_REF] Béhar | Un objet local mal identifié : l'action territoriale en réseau[END_REF][START_REF] Estèbe | Gouverner la ville mobile : intercommunalité et démocratie locale[END_REF]. In fact, anti-sprawl policies promoted at national level must be implemented by municipalities. While the state still plays an important role in France, the decentralization laws enacted in the 1980s changed the balance of power at the municipal level, as well as the interests at stake in territorial policies. In the case of urban sprawl, the process of local appropriation is by no means neutral. As demonstrated below, the fight against urban sprawl may even be reversed, i.e. it may become a vector of urban sprawl (X 2014).

This paradox is particularly visible in the affluent suburban and peri-urban municipalities located in the Western part of the Lyon metropolitan region (hereafter West Lyon), where the local actors (especially the mayors) carefully negotiate anti-sprawl measures with the state. The state acts primarily through a planning document: the territorial directive for the development (DTA) of the Lyon metropolitan region, approved in 2007. This document imposes limited demographic growth in the West Lyon metropolitan region. Urban development is concentred within the heart of the metropolis, as well as more low-income eastern suburbs. An elected representative of a West Lyon municipality summarized the role of the DTA as follows (see Figure 1):

[The challenge] is to control population growth. We have (…) strong land pressure now.

(…) In central areas, each time an individual house went down, there are thirty homes that are built. (…) So we went to review the planning documents, to find tools, to try to control [this pressure] as much as possible. (…) The DTA met well ahead the role of Brignais as a buffer, precisely, between the urban sprawl of the Lyon metropolitan area and all the stake of green belt and the green pole beyond with the Monts du Lyonnais. So, the stake is to achieve this balance with the preservation of natural and agricultural areas. (…) When you look at all the local planning documents of West Lyon municipalities, there is nothing that opens to urbanization as it was usual before (Interview, May 2018) Within the logic of the DTA, West Lyon municipalities should be limiting constructions in order to densify area, which is well served by public transport. In West Lyon, several areas have been classified for natural protection, through various land-use regulations. This general protection ultimately led to the creation of a 'couronne verte' ('green ring'). The term designates an area that the state wishes to sanctify because of its greenery, mainly for landscape purposes. Therefore, the West Lyon area was designated to preserve the 'quality of life' in the metropolitan region (X and X 2014). The green ring was imposed by the state to concentrate the housing supply within the metropolitan core and reduce urban sprawl. At first, local officials in West Lyon protested against the constraints imposed upon their territory by the state. However, they gradually worked out how to take advantage of the DTA and related measures for curbing new urban extensions. Indeed, anti-sprawl regulations were reinterpreted locally as Malthusian land-use tools. They were applied to preserve the villagelike character of the municipalities (most have less than 3,500 inhabitants).

Yet, these restrictive land-use policies pushed young households further away in search of low-density areas and new detached houses. The process accelerated sprawl and the extension of peri-urban areas to the west. In addition, it increased the average length of commuting trips (X, X and X 2020). These policies also reinforced segregation on the metropolitan scale. Access to the inner peri-urban ring was earmarked for the affluent households, excluding more modest homebuyers. The latter had to move to remote rural areas and deal with higher petrol costs, which fuelled the growing discontent and played an important role in the recent Gilets Jaunes ("Yellow Vests") movement [START_REF] Depraz | La géographie est-elle une science engagée ? Fracture(s) territoriale(s) et gilets jaunes. Historiens et géographes[END_REF][START_REF] Genestier | Les gilets jaunes: une question d'autonomie autant que d'automobile[END_REF]).

The case briefly presented here shows the analytical potential of GU in terms of understanding how zoning rules, territorial policies and land-use regulations may be transformed through the negotiation process involving various stakeholders at different scales. In the case of West Lyon, the environmental policy promoted by the state was reinterpreted locally by the village-like municipalities to match their preoccupations, namely, to preserve social exclusiveness under an environmental label. The Lyon green ring became an exclusionary zoning tool (see Figure 1). This example demonstrates that the state is not the only major player in urban geopolitics in France. The municipalities' political projects also have considerable weight. Municipalities can make their interests prevail when negotiating with central and metropolitan governments. GU is particularly relevant for analysing this phenomenon.

Nonetheless, GU is not the only relevant approach for examining the case of Lyon. Mobilizing the UG approach reveals another important aspect of the local preservation of West Lyon, i.e. the urban riots, which have been a regular feature of the working-class, lowincome eastern suburbs of Lyon. They received considerable media coverage and political attention both locally and nationally. The riots are often referred to in terms of ethnicity by the right-wing media and have even been described as the first signs of a coming 'civil war' in France (Dikec 2011). The riots reshaped the political landscape in the Lyon metropolis and go some way to explaining why urban development is so much feared in West Lyon (X,X and X, 2020). Notes :where agriculture and nature preservation prevent peri-urban villages with small detached family homes (like Orliénas in the centre) from expanding and becoming part of the metropolitan core suburbs (the edge of which corresponds to the limits of Brignais, the suburban town on the right).

Source: IGN-Geoportail.gouv.fr)

South Rabat's Green Belt: Militarizing Urban Planning

Unlike France, Morocco's urban planning is still highly centralized. The reigning King, Mohammed VI, firmly promotes urban development [START_REF] Barthel | Casablanca-marina : un nouvel urbanisme marocain des grands projets[END_REF][START_REF] Bogaert | Globalized authoritarianism[END_REF]) and several megaprojects have gradually given major cities the role of showcasing the country's success and openness. Yet, despite this change, the central government still monitors Moroccan cities closely and oversees various development and strategic plans. Although a recent 'communal charter' provides the municipalities with new capabilities, human and financial resources are very limited. Consequently, local decision makers lack the means to become prominent actors in urban development.

Therefore, the changes introduced by Mohammed VI failed to reverse the centralization of power established under King Hassan II, who reigned from 1959 to 1999. The latter's power was based on rural areas and their politico-administrative structures [START_REF] Leveau | Le fellah marocain: défenseur du trône[END_REF]. This power base was reinforced by the urban riots and the two military coups in 1971 and 1972, which generated a strong anti-urban bias in the Moroccan regime. The state's repression of left-wing movements and its increasing oppression of slum dwellers are remembered as the 'Years of Lead'. This period was characterized by a climate of 'diffuse war' [START_REF] Daoud | Maroc : les années de plomb, 1958-1988 : chroniques d'une résistance[END_REF]. State repression worsened in the early 1980s, which were marked by 'bread riots'. Poor people from the slums rioted in the wealthy neighbourhoods in Morocco's main cities to denounce the liberalization of the price of basic goods, a policy implemented under pressure from the IMF and the World Bank. The central state used punitive measures to quell the urban uprising. There was impressive militarization of Rabat and Casablanca (the political and economic capitals of Morocco). But the militarization took different forms.

In Casablanca, where the most violent riots took place, demonstrators and slum dwellers were evicted from the city centre and forced out through slum clearance [START_REF] Rachik | Casablanca : l'urbanisme de l'urgence[END_REF]. In parallel, the Ministry of the Interior implemented policies to promote the gentrification of the city centre, modelled on the Haussmann boulevards in Paris. Consequently, the poor flocked to the suburbs. The latter were separated from the city centre with the construction of a coastal highway in the early 1980s [START_REF] Berry-Chikhaoui | Les compétences des citadins : enjeux et illustrations à propos du monde arabe[END_REF]. Those move generated numerous new tensions, and tough measures were taken to control the impoverished suburbs. In the case of Lahraouiyine, a booming suburban shantytown separated from Casablanca by the coastal highway, the police enforced an embargo on concrete materials in the 1980s in order to block self-construction in what was perceived as an insurgent town (Belarbi and X 2019). The Ministry of the Interior also set up an urban agency with the clear aim to prevent unrest through urban projects. This ministerial supervision demonstrates how urban planning can be designed and used by an authoritarian state to maintain the social order [START_REF] Rachik | Casablanca : l'urbanisme de l'urgence[END_REF][START_REF] Bogaert | Globalized authoritarianism[END_REF].

In Rabat, the kingdom's capital, the main response to the "bread riots" was the creation of a green belt as part of the 1981 masterplan (see Figure 2). Under the guise of environmental preservation, Rabat's green belt was as much a military tool as Casablanca's coastal highway. Covering 61 hectares, the green belt was officially designed to contain the spread of Rabat and separate the capital city from the municipality of Témara. At the time, Témara was an expanding peripheral municipality dotted with slums, which welcomed poor populations from rural areas. As an agent of the Ministry of the Interior stated:

In the beginning it was for that, to control the urban space and to separate Rabat from Témara… The agglomeration was booming, it was generating problems of management and security. (…). The objective was to delimit Rabat and Témara. The two cities don't have the same identity. There was no border between Rabat and Témara. Therefore, the urban pressure was generating enormous tension regarding the management of the flux between both cities. (Interview, technician from the Ministry of the Interior, May 2017)

The design and management of the green belt was deeply influenced by military concerns. Indeed, King Hassan II entrusted the project to his right-hand man, Driss Basri, the minister of the Interior. He was in charge of the regime's security programme during the 'Years of Lead'. He had 'enormous means' at his disposal to create the green belt between Rabat and Témara (interview, Ministry of the Interior 2017). The belt was totally surrounded by fences and fifty agents were deployed to guard it. Several watchtowers (see Figures 3 and4)were built in the forest inside the belt, officially to prevent fires. However, as an agent of the Ministry of the Interior admitted, it was above all 'to watch (…) whoever would cross the forest'. Although the green belt is now marketed in the brochures on Rabat's green spaces as proof of its claim to be 'Africa's greenest capital', its conception clearly confirms that growth control policies in Morocco were implemented, first and foremost, for purposes of security and urban control.

In contrast with Lyon, the case of Rabat shows the analytical potential of UG in terms of understanding how Morocco's recent history of urban violence and repression shaped an environmental policy, such as South Rabat's green belt. Conversely, the GU approach seems less relevant since the green belt was always conceived and managed at the central level. Notwithstanding these important differences, both green belts hide a similar political dimension of social control and separation behind a seemingly neutral and technical feature.

As with the Lyon case study, although UG appears to be the most relevant approach for analysing how sprawl is managed in Morocco, GU also provides important elements of understanding. Indeed, urban sprawl is not controlled solely by the central state. It is also shaped by local actors, such as municipalities. Despite the fact that they are still politically weak overall, they have been empowered by the recent decentralization reform and, above all, by owners of large unbuilt areas of land. These landowners take advantage of the pressure on land for informal urbanization due to the influx of poor rural populations [START_REF] Abouhani | Gouverner les périphéries urbaines : de la gestion notabilaire à la gouvernance urbaine au Maroc[END_REF]. This process allows landowners to gain political support from the poor newcomers. In turn, it increases their influence and boosts their bargaining power with local authorities and central administrations. They use this power to enhance their control of peripheral urban growth and increase their profits from developing their land.

GU also provides new insights into Rabat's green belt policies. Eventually, local authorities rather cynically realized that the green belt could be used to their advantage: today Rabat's urban forest is a marketing tool used to enhance Rabat's image as 'Africa's capital of sustainable development'. The green belt is also used by the well-off population in Rabat's southern neighbourhoods. It prevents the city from expanding, creating artificial scarcity on the housing market. Consequently, the houses located on the 'good' side of the green belt, inside Rabat, are now worth twice as much as identical houses in Témara on the 'bad side'. Therefore, it is not surprising that three decades after it was created by the Ministry of the Interior, the green belt is strongly supported by the well-off. They even founded an association to protect the forest, officially in the name of 'preserving the green lung of Rabat' (interview, leader of the environmental association), unofficially to prevent slum dwellers from squatting there. This example shows how GU complements UG and sheds light on the rationale of anti-sprawl and growth control policies in Morocco. This approach helps to analyse the green belt, not only as a tool for population control used by an authoritarian state, but also as a justified anti-sprawl policy. GU also permits to consider a larger convergence of interests i.e middle-class pressure groups, planning agencies and institutional representatives. This convergence explains why Rabat's green belt was immutable and highly respected, despite strong pressure for urban development. Notes: an impenetrable forest that prevents the junction between the unplanned, high density, fast growing suburban town of Témara (left and bottom) and the capital's well-planned, low density neighbourhoods (top of picture).

Source: Zoom Earth Figures 3 and4. The urban forest as a military tool.

Notes: the fence surrounding the green belt (left) and a watchtower in the forest (right) Credits: Max Rousseau.

Conclusion

The two cases described in this paper illustrate the interest of combining the anglophone and francophone geopolitical schools. Several recent studies (De Souza 2016; Ortiz and Boano 2018) discuss the merit of both approaches. However, despite their potential complementarity, to our knowledge, there has been no attempt to combine them so far. UG defines a framework for the issues to be studied and GU provides methodological tools to analyse the specific role played by territories, borders and frontiers. As illustrated here, the combination of UG and GU demonstrates that the gap between English and French academic scholarships is not insurmountable, despite their different conceptual views of urban geopolitics. In reality, the hurdle is not theoretical, but nominalist. The main problem that the combination of the two approaches comes up against, is knowing what to call it.

At the moment, combining the two approaches means using two different normative definitions of geopolitics: it is a critical object in one case and a critical tool in the other [START_REF] De Souza | Urban eco-geopolitics[END_REF]. In this paper, we overcame the problem by using two different acronyms to identify the two. However, this device falls short of providing an integrated theoretical framework that can draw on the notion of geopolitics. Choosing between UG and GU appears to be necessary. If we stay within the framework of anglophone discussions, which is the case here for our contribution to the special issue of Geopolitics, the most relevant choice is undoubtedly the one that several authors have already made (De Souza 2016; Rokem and Boano 2018), i.e. start with the theoretical framework of urban geopolitics and extend the scope of its relevance and analytical field. However, we maintain that even the extended framework of UG does not do justice to the intuition that GU stems from, i.e. local actors can be considered as territorialized actors that have geopolitical relationships with each other. In fact, if we have to find a research field that is homologous to GU outside French-speaking circles, we should probably look at the work that has been conducted on urban governance. From that perspective, the main merit of GU is to draw attention to the importance of the territorial dimension.

If we put this nominalist problem aside, UG and GU can be combined. By doing just that, this paper discusses the politics behind green belts and the discourse on environmental preservation (which is common practice for UG). Simultaneously, it demonstrates how and why green belts may be diverted from their stated purpose, by opening the black box that reveals how local actors and stakeholders interact (as proposed by GU). This line of research is promising, but additional research is required on different issues and in different contexts to further demonstrate the potential of the combined approach.

Lastly, this paper contributes to the recent attempts in UG [START_REF] Rokem | Ordinary urban geopolitics: contrasting Jerusalem and Stockholm in Urban Geopolitics Rethinking Planning in Contested Cities[END_REF]Boano 2018, Subra 2018) to bridge the gap between urban research on both sides of the North/South divide. The comparison reveals the differences, by focusing on the local idiosyncrasies (fostered by GU). It also reveals the similarities, by focusing on the broader picture (fostered by UG). As we have shown, this type of comparative analysis is valuable for studying apparently similar environmental urban policies in very different contexts. The combined approach sheds light on how anti-sprawl policies may serve certain interests, i.e. already advantaged populations. It reveals how a policy, which is presented as an effective tool for preserving the natural environment on the fringes of large cities, actually has major negative environmental and social consequences. On the one hand, the pressure due to urban sprawl is transferred further afield and on the other hand, commuting is longer and harder for those who are excluded from the privilege of living in the metropolitan cores. As the two examples clearly show, this phenomenon occurs in the Global North and in the Global South and is obviously not limited to Lyon and Rabat. Various case studies on garden planning (Dooling 2009), residential areas in green belts [START_REF] Webster | Property rights and the public realm: gates, green belts, and gemeinschaft[END_REF][START_REF] Blinnikov | Gated communities of the Moscow green belt: newly segregated landscapes and the suburban Russian environment[END_REF] or national parks (De Souza 2016) have revealed a similar pattern across the North/South divide.

Figure 1 .

 1 Figure 1. West Lyon's green ring;

Figure 2 .

 2 Figure 2. South Rabat's green belt.

The data used to analyse the case studies was drawn from 70 interviews with the different actors, who helped shape and reshape the peripheries of Lyon and Casablanca (e.g. elected representatives, civil servants at different levels, associations, residents and farmers).2 Euskadi ta askatasuna, "Basque country and freedom", is a party calling for the independence of the Basque region.


Emeline Simonetti

Elena Bergamini
email: elena.bergamini@uniroma4.it

Joseph Bascou
email: joseph.bascou@invalides.fr

Giuseppe Vannozzi
email: giuseppe.vannozzi@uniroma4.it

Hélène Pillet
email: helene.pillet@ensam.eu

Three-dimensional acceleration of the body center of mass in people with transfemoral amputation: Identification of a minimal body segment network

Keywords:

Background: The analysis of biomechanical parameters derived from the body center of mass (BCoM) 3D motion allows for the characterization of gait impairments in people with lower-limb amputation, assisting in their rehabilitation. In this context, magneto-inertial measurement units are promising as they allow to measure the motion of body segments, and therefore potentially of the BCoM, directly in the field. Finding a compromise between the accuracy of computed parameters and the number of required sensors is paramount to transfer this technology in clinical routine. Research question: Is there a reduced subset of instrumented segments (BSN) allowing a reliable and accurate estimation of the 3D BCoM acceleration transfemoral amputees? Methods: The contribution of each body segment to the BCoM acceleration was quantified in terms of weight and similarity in ten people with transfemoral amputation. First, body segments and BCoM accelerations were ob-tained using an optoelectronic system and a full-body inertial model. Based on these findings, different scenarios were explored where the use of one sensor at pelvis/trunk level and of different networks of segment-mounted sensors for the BCoM acceleration estimation was simulated and assessed against force plate-based reference acceleration. Results: Trunk, pelvis and lower-limb segments are the main contributors to the BCoM acceleration in trans-femoral amputees. The trunk and shanks BSN allows for an accurate estimation of the sagittal BCoM acceleration (Normalized RMSE ≤ 13.1 %, Pearson's correlations r ≥ 0.86), while five segments are necessary when the 3D BCoM acceleration is targeted (Normalized RMSE ≤ 13.2 %, Pearson's correlations r ≥ 0.91). Significance: A network of three-to-five segments (trunk and lower limbs) allows for an accurate estimation of 2D and 3D BCoM accelerations. The use of a single pelvis-or trunk-mounted sensor does not seem advisable. Future studies should be performed to confirm these results where inertial sensor measured accelerations are considered.

Introduction

The study of biomechanical parameters derived from the body center of mass (BCoM) motion may reveal crucial information about gait impairment [START_REF] Minetti | The mathematical description of the body centre of mass 3D path in human and animal locomotion[END_REF][START_REF] Pavei | On the estimation accuracy of the 3D body center of mass trajectory during human locomotion: inverse vs. forward dynamics[END_REF][START_REF] Tesio | The motion of body center of mass during walking: a review oriented to clinical applications[END_REF], especially in people with lower-limb amputation [START_REF] Tesio | The motion of body center of mass during walking: a review oriented to clinical applications[END_REF][START_REF] Bonnet | Mechanical work performed by individual limbs of transfemoral amputees during step-to-step transitions: effect of walking velocity[END_REF][START_REF] Askew | Energy cost of ambulation in trans-tibial amputees using a dynamic-response foot with hydraulic versus rigid "ankle": insights from body centre of mass dynamics[END_REF]. Indeed, 3D BCoM acceleration, velocity and displacement allow to describe the kinematics of the body as a whole [START_REF] Pavei | Body center of mass trajectory and mechanical energy using inertial sensors: a feasible stride?[END_REF] and have been shown to provide insights on dynamic stability [START_REF] Hof | The condition for dynamic stability[END_REF][START_REF] Al Abiad | A mechanical descriptor of instability in human locomotion: experimental findings in control subjects and people with transfemoral amputation[END_REF], gait efficiency [START_REF] Askew | Energy cost of ambulation in trans-tibial amputees using a dynamic-response foot with hydraulic versus rigid "ankle": insights from body centre of mass dynamics[END_REF][START_REF] Pillet | APSIC: training and fitting amputees during situations of daily living[END_REF], and gait asymmetries [START_REF] Minetti | The mathematical description of the body centre of mass 3D path in human and animal locomotion[END_REF][START_REF] Tesio | The motion of body center of mass during walking: a review oriented to clinical applications[END_REF] both in the able-bodied population and in lower-limb amputees. Although 3D BCoM motion is of particular interest to describe pathological gait, it is scarcely studied in clinical routine [START_REF] Tesio | The motion of body center of mass during walking: a review oriented to clinical applications[END_REF], partly due to the high cost and complexity of laboratory-based systems generally required for its investigation.

Recently, the use of magneto-inertial measurement units (MIMUs) has been proposed as an alternative to gold standard instrumentations for the estimation of BCoM-derived parameters [START_REF] Pavei | Body center of mass trajectory and mechanical energy using inertial sensors: a feasible stride?[END_REF][START_REF] Shahabpoor | Real-life measurement of tri-axial walking ground reaction forces using optimal network of wearable inertial measurement units[END_REF][START_REF] Ancillao | Indirect measurement of ground reaction forces and moments by means of wearable inertial sensors: a systematic review[END_REF]. MIMUs are indeed small, light, and low-cost wearable sensors, embedding orthogonally mounted 3D accelerometers, gyroscopes and magnetometers. The information provided by these sensors can be fused to estimate the orientation of the inertial frame defined by the MIMU case relative to an Earth-fixed frame [START_REF] Bergamini | Estimating orientation using magnetic and inertial sensors and different sensor fusion approaches: accuracy assessment in manual and locomotion tasks[END_REF]. Therefore, provided MIMUs are securely attached to their respective underlying segments with a known relative orientation [START_REF] Pacher | Sensor-to-segment calibration methodologies for lower -body kinematic analysis with inertial sensors: a systematic review[END_REF], they can be used to estimate segmental orientation and motion, and ultimately the 3D motion of each segment's center of mass (SCoM) and of the whole body [START_REF] Pavei | Body center of mass trajectory and mechanical energy using inertial sensors: a feasible stride?[END_REF].

For the sake of simplicity, most wearable protocols developed for BCoM motion tracking involve a single sensor at pelvis level [START_REF] Ancillao | Indirect measurement of ground reaction forces and moments by means of wearable inertial sensors: a systematic review[END_REF][START_REF] Meichtry | Criterion validity of 3D trunk accelerations to assess external work and power in able-bodied gait[END_REF]. Yet, several works evidenced that the single-sensor paradigm tends to overestimate the 3D trajectory of the BCoM [START_REF] Pavei | On the estimation accuracy of the 3D body center of mass trajectory during human locomotion: inverse vs. forward dynamics[END_REF][START_REF] Meichtry | Criterion validity of 3D trunk accelerations to assess external work and power in able-bodied gait[END_REF][START_REF] Jeong | Comparison of segmental analysis and sacral marker methods for determining the center of mass during level and slope walking[END_REF]. In particular, the mediolateral [START_REF] Jeong | Comparison of segmental analysis and sacral marker methods for determining the center of mass during level and slope walking[END_REF][START_REF] Mohamed Refai | Portable gait lab: estimating 3D GRF using a pelvis IMU in a foot IMU defined frame[END_REF] and anteroposterior [START_REF] Meichtry | Criterion validity of 3D trunk accelerations to assess external work and power in able-bodied gait[END_REF] components of BCoM position and acceleration were shown not to be accurately captured with this method, especially when participants exhibited an asymmetrical gait pattern or dynamical upper body motions, as it is the case in people with a lower-limb amputation [START_REF] Goujon-Pillet | Three-dimensional motions of trunk and pelvis during transfemoral amputee gait[END_REF]. Consequently, multi-segment methods, including 11-17 MIMUs, have been proposed [START_REF] Pavei | Body center of mass trajectory and mechanical energy using inertial sensors: a feasible stride?[END_REF][START_REF] Karatsidis | Estimation of ground reaction forces and moments during gait using only inertial motion capture[END_REF][START_REF] Fasel | An inertial sensor-based method for estimating the athlete's relative joint center positions and center of mass kinematics in alpine ski racing[END_REF].

If single-sensor approaches may not be accurate enough, especially for pathological gait, finding a balance between the number of MIMUs and the accuracy of BCoM-related parameters is essential to effectively allow the use of wearable protocols in clinical routine [START_REF] Ancillao | Indirect measurement of ground reaction forces and moments by means of wearable inertial sensors: a systematic review[END_REF][START_REF] Jeong | Comparison of segmental analysis and sacral marker methods for determining the center of mass during level and slope walking[END_REF]. In this perspective, Shahabpoor and coworkers recently proposed a method to select a reduced number of MIMU-bearing segments (called an "optimal network of [sensors]") for the estimation of 3D BCoM acceleration in able-bodied individuals using optoelectronic system data [START_REF] Shahabpoor | Real-life measurement of tri-axial walking ground reaction forces using optimal network of wearable inertial measurement units[END_REF]. While the identified optimal segment configurationincluding the trunk, pelvis and one thighachieved a satisfying accuracy in the vertical direction, only moderate accuracy was achieved in the mediolateral and anteroposterior directions (Normalized Root Mean Square Error = 7 % versus > 16 %) [START_REF] Shahabpoor | Real-life measurement of tri-axial walking ground reaction forces using optimal network of wearable inertial measurement units[END_REF]. Although the adopted configuration may not suit transfemoral amputee gait due to differences in inertial parameters and overall gait pattern, the proposed method appears promising and could be adapted to this population in order to identify the location and minimal number of sensors required for an accurate monitoring of the BCoM acceleration of transfemoral amputee patients. On a longer-term perspective, such a methodology could be considered in-the-field to characterize clinically-relevant parameters derived from the BCoM acceleration such as the distribution of ground reaction forces between the prosthetic and sound leg [START_REF] Cutti | Reference values for gait temporal and loading symmetry of lower-limb amputees can help in refocusing rehabilitation targets[END_REF] or the symmetry of external work production [START_REF] Agrawal | Symmetry in external work (SEW): a novel method of quantifying gait differences between prosthetic feet[END_REF] which could benefit the rehabilitation by providing clinicians with quantitative data to monitor patients' progression or prescribe adapted prosthetic components.

The aim of the present study was therefore to identify potential optimal sensor networks, that is, subsets of segments to be instrumented with inertial sensors offering a good compromise between accuracy and number of sensors for the estimation of 3D BCoM acceleration in people with transfemoral amputation ambulating on level ground. First, segmental contributions to the BCoM acceleration were investigated using optoelectronic system data and a full body inertial model. This step allowed the identification of the most contributing segments to the BCoM acceleration. Based on these results, the BCoM acceleration was estimated from various combinations of the identified segments also called "body segment networks".

Methods

Participants

The study was designed according to the Declaration of Helsinki and was granted ethical approval (Comité de Protection des Personnes CPP NX06036). Ten people with traumatic transfemoral amputation (age: 41.5 ± 11.3 years; mass: 68.8 ± 15.2 kg; height: 1.73 ± 0.07 m; 8 males) gave written informed consent to participate in the study (Table 1). Inclusion criteria were adults with non-vascular transfemoral unilateral amputation, fitted with a definitive prosthesis and able to walk without any assistance. Participants walked with their usual passive microprocessor-controlled knee with an energy storing and return foot, the alignment of which was controlled by a prosthetist prior to data collection.

Measurement protocol

Each participant was equipped with a full-body marker set [START_REF] Al Abiad | A mechanical descriptor of instability in human locomotion: experimental findings in control subjects and people with transfemoral amputation[END_REF] (Fig. 1). An optoelectronic system (VICON, Oxford, UK, 200 Hz) recorded marker 3D positions while the participant kept a static standing posture and two photographs (front, profile) were taken. Following this static calibration, each participant walked at self-selected speed along an 8 m pathway, with 3 ground-embedded force plates (AMTI, MA, USA, 1000 Hz) in the middle. Only trials with three successive foot contacts on the force plates (i.e. a complete stride) were considered for further analysis.

Data processing

The markers positions were used to build a 15-segment hybrid inertial model, following [START_REF] Pillet | Evaluation of force plate-less estimation of the trajectory of the centre of pressure during gait. Comparison of two anthropometric models[END_REF] with the addition of hand segments [START_REF] Dumas | body segment inertial parameters[END_REF], thus allowing to obtain body segmental inertial parameters (mass, inertial matrices and center of mass of each segment). Prosthetic limbs were represented by a concentrated mass estimated from the manufacturers' manuals similarly to [START_REF] Al Abiad | A mechanical descriptor of instability in human locomotion: experimental findings in control subjects and people with transfemoral amputation[END_REF] and located below the prosthetic knee joint and at the junction of the prosthetic foot and knee components. Markers and force plate data were filtered using a zero-phase fourth order Butterworth low-pass filter, with a cut-off frequency of 5 Hz. The acceleration of each segment center of mass (SCoM) and of the inertial-model-based BCoM were computed from differentiation of the marker-based signals, each differentiation step being preceded by the abovementioned low-pass filtering of the signals. Additionally, reference BCoM acceleration (a BCoM, ref ) was derived from ground reaction force time-series (GRF) (Eq. ( 1), with m body , the participant's body mass and g the gravitational acceleration). All acceleration data were time-normalized to percent of the gait cycle, identified using a 20 N threshold on force plates data.

m body a BCoM,ref = GRF + m body g (1)

Segmental contributions

Segmental contributions to the BCoM accelerations were defined according to two criteria following [START_REF] Shahabpoor | Real-life measurement of tri-axial walking ground reaction forces using optimal network of wearable inertial measurement units[END_REF]: the relative weight of SCoM accelerations in BCoM acceleration and the similarity between SCoM and BCoM acceleration patterns.

The weight of the contribution of each segment (Contrib seg i ) in BCoM acceleration was defined as the SCoM acceleration (a SCoMi ) weighted by the relative mass of the segment in the body (Eq. ( 2), m segi for the i th segment). Segmental contribution weights were normalized by peak-topeak BCoM acceleration for each gait cycle.

Contrib seg i = m segi m body a SCoMi (2)
Regarding the similarity of SCoM accelerations, the average Pearson's correlation coefficients between each SCoM acceleration and the inertial-model-based BCoM acceleration were computed for each participant.

The contribution weights and correlations were averaged over all participants and used to identify the most contributing segments to BCoM acceleration.

Body segment networks

Following the contribution analysis, different body segment networks (BSNs) were proposed for the estimation of BCoM acceleration. The BSN-based BCoM acceleration was computed as the sum of the segmental contributions for the N included segments (Eq. ( 3)):

a BCoM, BSN = ∑ N i=1 Contrib seg i = ∑ N i=1 m segi ∑ N j=1 m segj a SCoMi (3)
The inertial-model and BSN-based BCoM accelerations were compared to the reference BCoM acceleration over the central prosthetic gait cycle of each trial using Pearson's correlation coefficients (with an alpha-level of 0.05) as well as peak-to-peak normalized root-mean square errors (NRMSE, defined following [START_REF] Ren | Whole body inverse dynamics over a complete gait cycle based only on measured kinematics[END_REF]), subsequently averaged over all patients. The results achieved when including a single segment, namely the pelvis or the trunk, are also provided as an indication of the performance of the single-segment paradigm. Given the low number of available strides, only descriptive statistics were provided.

Results

A total of 25 complete prosthetic gait cycles were retrieved for the analysis, with an average of 3 gait cycles per participant (range 1-6).

Segmental contributions

Absolute and relative contribution weights are represented as stacked bar plots (Fig. 2) in order to observe both the weight of individual segments and between-segments compensations. For instance, contributions from the right and left upper limbs are shown to compensate each other in the anteroposterior direction (Fig. 2a.) and to account for less than 20 % of the 3D BCoM acceleration (Fig. 2d.-f.).

Similarities between SCoM and BCoM accelerations along the prosthetic gait cycle are reported in Fig. 3.

Overall, the trunk, pelvis and both thighs appear to be the main contributors of the BCoM acceleration in all three directions, both in terms of similarity and weight. Shank and foot segments being also significant contributors of the BCoM acceleration during the contralateral stance phase (Fig. 2d.,f.), the trunk, pelvis, and segments from both lower limb segments seem promising sensor locations for BCoM acceleration estimation.

Body segment networks

Several networks combining from three to six segment locations were considered for further analysis and compared to the reference BCoM acceleration along with the single-segment paradigm (Table 2). It should be noted that the inertial-model-based BCoM acceleration achieved mean errors of 9.9 ± 1.8 %, 10.7 ± 2.4 % and 10.6 ± 2.4 % in the anteroposterior, mediolateral and vertical directions respectively. The five-segment model including the trunk, thighs and feet exhibited the higher agreement with reference BCoM acceleration while the threesegment models including the trunk and either shanks or thighs represented the best compromises for 2D BCoM acceleration estimation in the sagittal and frontal plane, respectively. The estimated BCoM acceleration with the pelvis paradigm, and the BSN models including either the trunk and shanks or the trunk, thighs and feet are represented in Fig. 4 against the reference BCoM acceleration.

Discussion

Segmental contributions

The first objective of the study was to quantify the segmental contributions to BCoM acceleration in people with transfemoral amputation.

Similarly as in able-bodied gait [START_REF] Gillet | Contribution of accelerated body masses to able-bodied gait[END_REF], the trunk was found to be the major contributor to BCoM acceleration in the vertical and mediolateral directions while the thighs were the prime acceleration generator in the direction of progression. They were indeed found to explain more than 53 % of the BCoM acceleration, which might be due to their being the heaviest three segments of the body.

The analysis of trunk and pelvis contributions to BCoM acceleration is of particular interest as they are often used in the literature as proxy measures of BCoM motion [START_REF] Pavei | On the estimation accuracy of the 3D body center of mass trajectory during human locomotion: inverse vs. forward dynamics[END_REF][START_REF] Gard | Comparison of kinematic and kinetic methods for computing the vertical motion of the body center of mass during walking[END_REF]. Stronger correlations were found in the vertical direction (r = 0.92) than in the anteroposterior and mediolateral directions (r ≥ 0.74 and r ≤ 0.65 for the trunk and pelvis, respectively). This corroborates previous findings regarding the single-segment paradigm: it might be accurate enough for the study of vertical BCoM motion [START_REF] Gard | Comparison of kinematic and kinetic methods for computing the vertical motion of the body center of mass during walking[END_REF] while unsuited for 3D BCoM motion tracking [START_REF] Meichtry | Criterion validity of 3D trunk accelerations to assess external work and power in able-bodied gait[END_REF][START_REF] Jeong | Comparison of segmental analysis and sacral marker methods for determining the center of mass during level and slope walking[END_REF].

Interestingly, contrary to what was observed in able-bodied subjects [START_REF] Shahabpoor | Real-life measurement of tri-axial walking ground reaction forces using optimal network of wearable inertial measurement units[END_REF], segmental contributions were not observed to be near-constant during the prosthetic stance phase in the vertical direction (Fig. 2f.). An increased weight of the contribution of the sound leg accelerations is indeed observed at the beginning of the prosthetic cycle. This might result from sound-side ankle plantarflexion at push-off, which was shown to be a major determinant of vertical BCoM motion [START_REF] Hayot | Contribution of the six major gait determinants on the vertical center of mass trajectory and the vertical ground reaction force[END_REF]. In the anteroposterior direction, the lower limbs were found to constitute the primary contributor to BCoM acceleration, with the sound limb accounting for almost half of the total BCoM acceleration. The asymmetry in the contribution weight might be partly explained by the lower mass of the prosthetic limb compared to the contralateral limb. Additionally, gait compensations involving the hip and ankle joints of the sound limb are frequent in this population [START_REF] Bonnet | Mechanical work performed by individual limbs of transfemoral amputees during step-to-step transitions: effect of walking velocity[END_REF][START_REF] Drevelle | Vaulting quantification during level walking of transfemoral amputees[END_REF] and may have led to increased accelerations of the contralateral thigh, shank and foot segments.

In light of these results, the inclusion of either shank or foot sensors in addition to that of the thighs seems relevant for BCoM acceleration estimation. This is also supported by the fact that shank sagittal angles were previously shown to predict BCoM displacement along with thigh and upper body segments in the asymptomatic population [START_REF] Revi | Indirect measurement of anterior-posterior ground reaction forces using a minimal set of wearable inertial sensors: from healthy to hemiparetic walking[END_REF][START_REF] Mohan Varma | Segmental contributions to the center of mass movement in normal gait[END_REF].

Similarly to [START_REF] Shahabpoor | Real-life measurement of tri-axial walking ground reaction forces using optimal network of wearable inertial measurement units[END_REF], the head and upper limbs were discarded from the list of potential sensor locations for the wearable estimation of BCoM acceleration during straight level walking. Indeed, while an important contributor to BCoM mediolateral acceleration, head motion can often be uncorrelated from the whole-body motion [START_REF] Shahabpoor | Real-life measurement of tri-axial walking ground reaction forces using optimal network of wearable inertial measurement units[END_REF]. Regarding the upper limbs, their minor contribution weight (< 10 % for each limb) was found to be near-constant along the gait cycle, possibly due to their reduced mass relative to the body's or to their limited range of motion during straight walking. However, the upper limbs may play a more important Results are provided as mean (standard deviation). NRMSE = Normalized root mean square error; AP = Anteroposterior; ML = Mediolateral; V = Vertical.

role in other ambulation situations, especially when mitigating disturbances to avoid falling [31], and should therefore not be systematically discarded.

Body segment networks

Following the identification of the major contributors to BCoM acceleration, different BSNs were devised including from three to six segments with the aim of finding a compromise between accuracy and number of segments to be considered. The higher weight and agreement of trunk acceleration with the BCoM acceleration compared to the pelvis one (Figs. 2 and3) favored the investigation of three and five-sensor models involving the trunk and lower-limb segments. Relevance of this choice was confirmed by the achieved results: poorer accuracy was achieved when using the pelvis in a single-segment paradigm compared to when using the trunk and adding the pelvis to a trunk-based BSN model improved the NRMSE by less than 0.5 % (Table 2). Thus, our results advocate for the inclusion of the trunk segment when tracking BCoM motion in people with transfemoral amputation during straight walking. This is in agreement to previous literature reporting significant trunk 3D motion and pelvis rotations in this population [START_REF] Goujon-Pillet | Three-dimensional motions of trunk and pelvis during transfemoral amputee gait[END_REF].

The added-value of including several segments compared to the trunk-only or pelvis-only models for the anteroposterior and mediolateral components of BCoM acceleration is demonstrated in Table 2 and Fig. 4. Our results strengthen previous findings showing the unsuitability of the single-sensor paradigm for accurate capture of the 3D BCoM motion in asymmetrical gait [START_REF] Pavei | On the estimation accuracy of the 3D body center of mass trajectory during human locomotion: inverse vs. forward dynamics[END_REF][START_REF] Meichtry | Criterion validity of 3D trunk accelerations to assess external work and power in able-bodied gait[END_REF][START_REF] Jeong | Comparison of segmental analysis and sacral marker methods for determining the center of mass during level and slope walking[END_REF][START_REF] Mohamed Refai | Portable gait lab: estimating 3D GRF using a pelvis IMU in a foot IMU defined frame[END_REF][START_REF] Gard | Comparison of kinematic and kinetic methods for computing the vertical motion of the body center of mass during walking[END_REF]. In particular, the limited agreement and higher excursions of the BCoM acceleration estimated with a single segment compared to the reference BCoM acceleration in the anteroposterior direction might be due to an increased range of motion of the upper body in people with transfemoral amputation [START_REF] Goujon-Pillet | Three-dimensional motions of trunk and pelvis during transfemoral amputee gait[END_REF].

Following a similar procedure for the selection of segments in able bodies, Shahabpoor and coworkers developed an BSN model including the trunk, the pelvis and a thigh while accounting for the masses of all the body segments [START_REF] Shahabpoor | Real-life measurement of tri-axial walking ground reaction forces using optimal network of wearable inertial measurement units[END_REF]. Their method required the computation of accelerations cross-correlation matrices for each participant. In the present study, one 3-segment and both 5-segment BSN models achieved similar or improved accuracy compared to that reported by [START_REF] Shahabpoor | Real-life measurement of tri-axial walking ground reaction forces using optimal network of wearable inertial measurement units[END_REF] with subject-specific matrices, without requiring the computation of subject-specific cross-correlation matrices. This is an important outcome, as it suggests that the 17-MIMU calibration procedure to obtain subject-specific cross-correlation matrix may not be necessary. The number of sensors included can be further reduced to three MIMUs on the trunk and shanks when aiming at capturing only the BCoM acceleration in the sagittal plane (Table 2). In order to further improve the compromise between accuracy and number of required sensors, an interesting track of research could be to propose kinematic models for groups of segments.

Limitations and sources of errors

The contribution analysis presented in this study was performed by comparing individual SCoM accelerations to that of the BCoM using the inertial model developed in [START_REF] Pillet | Evaluation of force plate-less estimation of the trajectory of the centre of pressure during gait. Comparison of two anthropometric models[END_REF]. Since inertial models were shown to influence the retrieved BCoM motion [START_REF] Pavei | On the estimation accuracy of the 3D body center of mass trajectory during human locomotion: inverse vs. forward dynamics[END_REF][START_REF] Catena | Does the anthropometric model influence whole-body center of mass calculations in gait?[END_REF], alternative models could have led to different results. Nevertheless, the present analysis provided the same major contributors of BCoM acceleration as in the literature on able-bodied individuals [START_REF] Shahabpoor | Real-life measurement of tri-axial walking ground reaction forces using optimal network of wearable inertial measurement units[END_REF][START_REF] Gillet | Contribution of accelerated body masses to able-bodied gait[END_REF], with specificities that are presumably related to the specific gait pattern of people with transfemoral amputation. It should be noted that the inertial model used achieved mean NRMSE of about 10 % in all directions with respect to force plate-based reference acceleration, which may explain why no further improvement in accuracy was achieved by the different BSN model-based estimations when adding segments, mainly in the vertical direction.

BSN models presented within this study were developed and validated with data derived from optical motion capture rather than wearable sensors. Therefore, their validity should be verified when using MIMUs. The latter provide raw acceleration and angular velocity measured at the origin and along the axes of the MIMU local frame, as well as orientation data in a global reference frame. To transfer the measured accelerations at the SCoM, the position of each MIMU relative to the underlying SCoM must be obtained and angular velocity differentiated. These processes may introduce errors which could jeopardize the accuracy of BCoM estimates [START_REF] Karatsidis | Estimation of ground reaction forces and moments during gait using only inertial motion capture[END_REF] while the direct measurement of acceleration may reduce the errors due to the double differentiation of position data when using optoelectronic systems. Therefore, the investigation of the impact of MIMUs positioning relative to the underlying SCoM and the development of wearable methods allowing the identification of these relative positions represent research tracks of interest for the future. Furthermore, the orientation outputs estimated from MIMU signals have been shown to be affected by ferromagnetic perturbations [START_REF] Picerno | A spot check for assessing static orientation consistency of inertial and magnetic sensing units[END_REF], which may result from the ground within buildings or prosthetic components. In such conditions, different MIMUs may sense different Earth-fixed frames [START_REF] Picerno | A spot check for assessing static orientation consistency of inertial and magnetic sensing units[END_REF], which could introduce new errors when computing BCoM acceleration from a weighted average of estimated SCoM acceleration. However, similar accuracy levels achieved with a full body instrumentation using either MIMUs or optoelectronic systems in [START_REF] Karatsidis | Estimation of ground reaction forces and moments during gait using only inertial motion capture[END_REF] is promising and suggests that transferring the BSN models developed within this study in a wearable framework might be feasible.

Finally, the suitability of the proposed BSN models to accurately capture the BCoM 3D velocity and displacement, which are relevant parameters for motion analysis in people with transfemoral amputation, should also be investigated in the future.

Conclusions

This study investigated the feasibility of estimating BCoM acceleration in people with transfemoral amputation from the acceleration of a limited number of segments during straight level walking. Including a minimum of five segments provides an accurate estimation of 3D BCoM acceleration compared to the literature, while only three segments are necessary for the estimation of 2D acceleration. The trunk segment was shown to be crucial for the estimation of 3D BCoM acceleration and should be instrumented along with a minimum of two lower-limb segments.

The promising results achieved in this study may benefit the rehabilitation field by allowing the development of a wearable-sensors based framework for the obtention of BCoM-derived parameters for in-thefield patients monitoring.

  BMI, body mass index; F, female; M, male; TF, Transfemoral amputation; KD, Knee disarticulation, SD, standard deviation. The prosthetic devices are from Ottobock (C-Leg, Triton, and 1C40) from Ossür (Rheo Knee, Mauch SNS, Total knee TK200, Variflex, Elation and Pro-Flex) and from Freedom Innovation (Silhouette).

Fig. 1 .

 1 Fig. 1. A participant during the static standing posture. The 59-marker set can be appreciated on the front and back photographs.

Fig. 2 .

 2 Fig. 2. Segmental contributions to the whole body center of mass (BCoM) acceleration compared to inertial-model based acceleration and reference acceleration (GRF) and total contributions in the anteroposterior [AP] direction (a. and d.), mediolateral [ML] direction (b. and e.) and in the vertical [V] direction (c. and f.) every 2% of the prosthetic gait cycle. (a.-c.) Segmental contribution weights normalized per axial BCoM peak-to-peak acceleration; (d.-f.) Segmental contributions weights expressed as percent of total absolute contribution. (For a better interpretation of the figure, the reader is referred to the coloured web version of this article).

Fig. 3 .

 3 Fig. 3. Average correlation coefficients between each body segment centers of mass (SCoM) accelerations and inertial model-based body center of mass acceleration (BCoM) along the prosthetic gait cycle in the anteroposterior (AP), mediolateral (ML), and vertical (V) directions. Crossed correlations indicate that the correlation was non-significant (p-value > 0.05). The darker and bigger the circle, the stronger the correlation (blue tones: positive correlation, red tone: negative correlations). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article).

Fig. 4 .

 4 Fig. 4. Average acceleration (acc) of the body center of mass (BCoM) as estimated with the single-sensor paradigm (pelvis, blue dotted line), the body segment network (BSN) including the trunk and shanks segments (yellow dashed line), the BSN model including the trunk, thighs and feet segments (purple dotted line) compared to the reference force platesbased BCoM acceleration (gray straight line) in the anteroposterior (AP), mediolateral (ML) and vertical (CC) directions. Shaded regions represent the interval [mean--standard deviation, mean + standard deviation] for each estimate of the BCoM acceleration. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article).

Table 1

 1 Participants' characteristics.

	Participant	Gender	Age (years)	Height (m)	Mass (Kg)	BMI	Amputation delay (years)	Amputation level	Prosthetic knee	Prosthetic foot
	TF1	M	58	1,8	68	21,9	31	TF	Mauch SNS	Variflex
	TF2	M	48	1,8	64	19,7	1	TF	C-leg	Triton
	TF3	M	54	1,8	85	25,9	7	TF	C-leg	1C40
	TF4	M	43	1,6	72	26,7	3	KD	Rheo knee	Variflex
	TF5	F	49	1,7	53	19,4	25	KD	Total Knee	Elation
	TF6	M	44	1,7	47	16,6	18	TF	C-leg	Silhouette
	TF7	F	26	1,7	65	23,9	2,5	Gritti	Rheo knee	Elation
	TF8	M	26	1,8	56	17,3	1,5	TF	C-leg	Pro-Flex
	TF9	M	32	1,8	95	29,3	7	TF	Rheo knee XC	Pro-Flex
	TF10	M	35	1,7	83	29,1	9,5	KD	C-leg	Triton
	Mean		41,5	1,73	68,8	23,0	10,5
	SD		11,3	0,07	15,2	4,7	10,6

Table 2

 2 Comparison of body center of mass (BCoM) acceleration derived from various body segment network (BSN) models to the reference acceleration from force plates.

	Number of segments	Included segments	NRMSE (%) AP ML	V	Pearson's AP	ML	V
	1	Pelvis	25.3	26.1	11.1	0.65	0.60	0.91
			(2.5)	(8.1)	(1.9)	(0.07)	(0.28)	(0.05)
	1	Trunk	20.0

Acknowledgments

Research reported in this publication was supported by grants from the Fédération des Amputés de Guerre de France and the Université Franco-Italienne [Call VINCI 2018 -C2-881, attributed to E. Simonetti]. Study sponsors did not have a role in the study design, collection, analysis and interpretation of data, writing of the manuscript or the decision to submit the manuscript for publication.

The authors would like to thank Dr Facione (HIA Percy), Xavier Bonnet, Laura Valdes (Institut de Biomécanique Humaine Georges Charpak) and Coralie Villa (INI/CERAH) for their help in the data acquisition.

Declaration of Competing Interest

The authors report no declarations of interest.