Sergio Dario Magnani

Véronique Ancey

Bernard Hubert

"(Dis)Ordered intensification?" Techno-political models, resource access and pastoralist / agrobusiness relations in the Middle Valley of the Senegal River

Keywords: Intensification, Techno-political models of development, Pastoralism, Agrobusiness, Middle Valley of the Senegal River

published or not. The documents may come

'(Dis)ordered intensification?' Techno-political models, resource access and pastoralist/agribusiness relations in the Middle Valley of the Senegal River

Introduction

From the colonial era to the end of the 1990s, the technoscientific model of intensification of livestock production served as an explicit reference for interventions in pastoral development in semi-arid climates in Africa [START_REF] Landais | Sur les doctrines des vétérinaires coloniaux français en Afrique noire[END_REF]Scoones, 1994). Its rational approach posits the need to artificialise livestock conditions by limiting their interactions with the environment, in order to secure and increase pastoral production. The model rests on the assumption that it is possible and desirable to overcome the major climatic variability of semi-arid habitats, which is considered to be a risk factor and a constraint, by stabilising pastoralists and their herds and promoting access to water and the use of feed inputs.

Between the 1990s and 2010, a considerable volume of scientific literature showed that this model was not workable because it fails to take into account the ecology of semi-arid climates [START_REF] Ellis | Stability of African pastoral ecosystems: Alternate paradigms and implications for development[END_REF][START_REF] Behnke | Rethinking range ecology: implications for rangeland management in Africa[END_REF][START_REF] Homewood | Ecology of African Pastoralist Societies[END_REF] and the characteristics of pastoral systems [START_REF] Krätli | Cows who choose domestication. Generation and management of domestic animal diversity[END_REF][START_REF] Krätli | Time to outbreed animal science? A cattle-breeding system exploiting structural unpredictability: the Wodaabe herders in Niger[END_REF][START_REF] Krätli | Living off uncertainty: The intelligent Animal Production of Dryland Pastoralists[END_REF]. These critiques have led to a change in rhetoric evident in certain policy texts in the sector and political agreements at continental (Union Africaine, 2013), regional (Déclaration de N'Djamena, 2013) and national levels (Government of Kenya, 2012). However, a major discrepancy remains between this growing formal recognition of pastoral systems and their characteristics, and the persistence of conceptual and methodological foundations reflecting the old paradigm [START_REF] Krätli | Valuing variability: New Perspectives on climate resilient drylands development[END_REF], and thus between the current state of knowledge and the nature of interventions which continue to restrict pastoral mobility, privatise access to natural resources and fragment rangelands. Modes of action ignore significant advances in understanding, which show how these interventions compromise the abilities of pastoralists to maintain a complex relationship with the environment and to exploit climatic variability as a factor of production [START_REF] Galvin | Fragmentation in Semi-Arid and Arid Landscapes: Consequences for Human and Natural Systems[END_REF][START_REF] Catley | Pastoralism and Development in Africa: Dynamic change at the margins[END_REF].

The Middle Valley of the Senegal River offers an example of these dynamics. Fifty years of public action have seen the pastoralists excluded from the Valley, which was steered towards irrigated agriculture. Having been thus "stabilised" in the hinterland, they have lost access to the differentiated habitats that they used during the seasonal transhumance, and have come to rely on only the pastures of the dry zone, which vary greatly from place to place and from year to year. The Valley is currently the focus of growing investment in the agrobusiness sector, with new hydro-agricultural developments even in the hinterland, on rangelands and forested areas that constitute important pastoral resources (Koopman, 2012a;[START_REF] Re | Comment on accapare la terre, saga Senhuile-Senethanol continue[END_REF][START_REF] Soullier | Les effets des agrobusiness sur les petits producteurs dans la vallée du fleuve Sénégal : résultats de trois études de cas[END_REF].

After having questioned the pertinence of these objectives of standardising and stabilising pastoral systems in light of the changes in pastoral practices in the Middle Valley, we will look beyond the current modernist rhetoric to examine why intensification and its underpinning are so persistent in shaping pastoral development and public action in this region of Senegal.

The article draws on data produced during doctoral research into dairy production in Senegal [START_REF] Magnani | Le Lait local au Sénégal : Intensifier pour développer ? Dynamiques socio-techniques et Anthropologie des pratiques[END_REF] 1 with a particular focus on the social business project of an industrial dairy which has collected pastoral milk from around the city of Richard Toll since 2006. The dairy proposes a model integrating the local sugar industry and pastoralists to stabilise pastoral production and even promote social harmony between the two groups, in a context of historical tension over land grabbing by industries. Feed inputs (sugarcane residues and industrial cattle feeds) are available on credit to sedentarise dairy cows throughout the year.

We are thus interested in studying the introduction of the dairy's social business into this context, the deployment of its collection and development programmes and the reaction it has provoked among pastoralists. Finally, the industry's contradictory views of pastoral systems and the role of intensification are discussed, in relation with the dynamics of the expansion of agrobusiness in the Senegal River Valley.

1 Fieldwork was carried out for a total of twelve months between 2011 and 2013, combining the study of local written sources with open interviews (139) and participant observation. In the Middle Valley, we studied the interactions between the dairy business and pastoralists, in light of the historical context of development interventions. On one hand, we focused on the interests, logic and visions of the industrial dairy producers and their allies. Interviews were held with dairy staff members (the CEO, directors of collection, collectors, technicians), and stakeholder representatives (danone.communities, Crédit Agricole, NGO Gret, CSS). On the other hand, we monitored five extended families of Fulani pastoralists in the jeeri of Richard Toll and their attitudes to milk collection and technical packages. Families varied in terms of: level of participation in collection; access to dairy markets; livestock systems; family composition and organisation. Extended stays were repeated over three years participating in routine activities and engaging in discussions with family members (the head of family, his brothers and other relatives, his wife/wives, their children and their wives). Every year, we met some of these pastoralists on their transhumance routes. In addition, ad hoc surveys were conducted with five other families to discuss and test specific findings.

The politics of livestock production in African drylands and the pastoral world

Intensification: a driver of livestock production policies in African drylands Intensification, i.e. the improvement of techno-economic productivity, is a dominant technical model in agronomic and zootechnical sciences which has provided the conceptual frame of reference in the development of agriculture and livestock farming in the majority of industrialised countries. It follows a linear logic with "intensive" inputs (fertilisers, phytosanitary products, cattle feed, water, etc.) used to liberate plant and animal systems from environmental constraints and so maximise production (Griffon et al. 2015: 43). As applied to livestock farming, this model, further drawing on negative portrayals of pastoralism, has been the principal force shaping interventions in pastoral development in African drylands [START_REF] Bernus | En guise de conclusion : las pasteurs nomades africains, du mythe éternel aux réalités présentes[END_REF][START_REF] Pouillon | Sur la «stagnation» technique chez les pasteurs nomades: Les Peuls du Nord-Sénégal entre l'économie politique et l'histoire contemporaine[END_REF][START_REF] Hodgson | Images & Interventions: The Problems of Pastoralist Development[END_REF][START_REF] Ancey | Le pastoralisme au Sénégal, entre politique « moderne » et gestion des risques par les pasteurs[END_REF].

While colonial activity in the livestock sector in the Sahel was dominated by the battle against epizootics, with independence, public intervention increasingly took the form of pastoral hydraulics systems [START_REF] Boutrais | Le zébu et le vétérinaire : un siècle d'histoire de l'élevage en Afrique de l'Ouest et du Centre[END_REF].

Pastoral hydraulics programmes, which received funding from the 1950s onwards, aimed to ensure that pastures, hitherto used on a seasonal basis when temporary water sources (pools and sumps) appeared, could be exploited all year round. This reflected public authorities' stated aims of increasing herd sizes, sedentarising pastoralists and modernising livestock farming [START_REF] Baroin | L'hydraulique pastorale, un bienfait pour les éleveurs du Sahel ?[END_REF]. Numerous "modern" structures, cement wells and mechanised boreholes, were built to complement, or replace, artisanal wells and sumps in pastoral areas. While pastoral hydraulics systems had a number of positive effects, they nonetheless had a major disadvantage in destructuring local ways of regulating access to rangelands, which in the Sahel are based on priority usage rights granted on the grounds of cultural or territorial belonging, on socio-political relations, and on participation in the construction and upkeep of water points. Pastoral hydraulics promoted "public" access to water and pastures (Thébaud et Batterbury, 2001: 76). The public infrastructure and the high flow rate of mechanised boreholes saw cattle become more concentrated, mobility practices change and seasonally-used pastures being permanently occupied [START_REF] Thébaud | Politiques d'hydraulique pastorale et gestion de l'espace au Sahel. In Sociétés pastorales et Développement[END_REF]. This failure to consider the social and political dimensions of water management in pastoral areas provoked forms of resistance and conflict [START_REF] Bernus | Hydraulique pastorale et gestion des parcours[END_REF].

At the same time, a misunderstanding of pastoral mobility led decision-makers to promote land use that was illadapted to the climate and characteristics of pastoral societies. Ranching and other forms of rational management of pastures, implemented between the 1960s and the 1990s, aimed to integrate livestock farming commercially and limit the supposed degradation of rangelands. Based on incompatible concepts brought in from other contexts, these forms of managing pastures through enclosure had a number of negative effects: land became fragmented [START_REF] Galvin | Fragmentation in Semi-Arid and Arid Landscapes: Consequences for Human and Natural Systems[END_REF]); pressure on "free" pastures increased [START_REF] Tache | Rangeland enclosures in Southern Oromia, Ethiopia: an innovative response or the erosion of common property resources? In Pastoralism and Development in Africa: Dynamic change the margins[END_REF]; pastures were suboptimally exploited; biodiversity was lost; exclusion and conflict increased [START_REF] Oxby | Ranches collectifs en Afrique[END_REF][START_REF] Thébaud | Recognising the effectiveness of Traditional Pastoral Practices: Lessons from a controlled grazing experiment in Northern Senegal[END_REF][START_REF] Catley | Pastoralism and Development in Africa: Dynamic change at the margins[END_REF].

Organised in the wake of severe droughts, the 1977 United Nations International Conference on Desertification examined the phenomenon of drying in the Sahel, attributing responsibility to local systems of landholding and pastoral activity [START_REF] Bernus | Les causes de la désertification : les thèses en présence[END_REF][START_REF] Fratkin | Pastoralism: Governance and Development Issues[END_REF]. This hypothesis legitimised policies to reduce mobility that drew on thinking lacking any scientific foundation [START_REF] Swift | Desertification. Narratives, Winners and Losers[END_REF][START_REF] Behnke | The end of Desertification? Disputing Environmental Change in the Drylands[END_REF][START_REF] Davis | The Arid Lands: History, Power, Knowledge[END_REF]. Indeed the continuity in the way development services thought about problems and their solutions in Sahel environments explains the persistence of ill-suited conceptions of land management. Thus, from the 1980s and 1990s, models of integrated natural resource management called for local plans in order to promote decentralised resource management [START_REF] De Haan | An overview of the World Bank's involvement in pastoral development[END_REF]. However, the plans were implemented using a bureaucratic vision of participation and a simplistic and apolitical conception of the "community". Their implementation at the level of the village was ill-suited to pastoral systems and practices [START_REF] Marty | La gestion de terroirs et les éleveurs : un outil d'exclusion ou de négociation[END_REF] because they underestimated the central role played by mobility in the Sahel and the low level of pastoralist representation in rural councils [START_REF] Khazanov | Nomads and the outside world[END_REF][START_REF] Batterbury | Local environmental management, land degradation and the "gestion des terroirs" approach in West Africa: Policies and Pitfalls[END_REF].

Administrations in the second half of the twentieth century primarily sought to promote exclusive land use and the growth of sedentary forms of livestock farming. Pastoralists faced with land fragmentation were less able to rely on their mobility to find unstable resources and were deprived of irreplaceable resources. Propositions to increase the use of feed inputs and replace local races of cattle often lacked any analysis of their economic and ecological sustainability [START_REF] Boone | Comparing Landscape and Infrastructural Heterogeneity within and between Ecosystems[END_REF].

Since the start of this century, a better understanding of the realities of pastoral systems has led to changes.

Pastoral hydraulics systems have, in certain contexts, been introduced with the help of close analyses of local land use and sociopolitical dynamics, as well as inclusive concertation processes [START_REF] Krätli | Evaluation et capitalisation de 20 ans d'interventions du groupe AFD portant sur le secteur de l'hydraulique pastorale au Tchad[END_REF]. Furthermore, over the last fifteen years the majority of West African Sahel countries have drawn up legal texts concerning pastoralism showing significant advances (recognition of pastoral mobility and transhumance corridors, etc.).

However, the effects of these measures were minimised by a number of major problems: pastoral use of the land which remains secondary to infrastructure investments; a poor understanding of interactions between pastoralism and agriculture; the very limited application of legal texts [START_REF] Hesse | Will pastoral legislation disempower pastoralists in the Sahel?[END_REF].

Despite the formal recognition of the value of pastoral practices, intensification remains, especially in recent qualified forms such as sustainable intensification, both the standard technoscientific paradigm in pastoral development in Africa and an underlying factor in the continuity of land and agricultural policies that disadvantage pastoralism.

New ways to look at pastoralism and the management of uncertainty: putting variability at the heart of production

While the goals of stabilising and standardising pastoral production have persisted [START_REF] Krätli | Valuing variability: New Perspectives on climate resilient drylands development[END_REF], a series of multidisciplinary scientific works over the last twenty-five years have renewed the understanding of the complex interactions between pastoral systems and semi-arid habitats. For Krätli (2017: 142), this change stems from a reexamination of the notion of ecosystem equilibrium in ecology in the 1970s, and the influence of this thinking in the ecology of arid climates and the understanding of pastoral systems in the 1980s. A number of studies have shown that such habitats, characterised by rainfall patterns with systematic spatial, inter-and intra-annual variability, cannot be considered as being stable and in equilibrium [START_REF] Ellis | Stability of African pastoral ecosystems: Alternate paradigms and implications for development[END_REF][START_REF] Behnke | Rethinking range ecology: implications for rangeland management in Africa[END_REF]Scoones, 1994). In these environments, the rains constitute the principal factor determining the presence and evolution of plant species which are subject to random and changing dynamics. These studies have contested the scientific validity of notions underpinning the models of rational pasture management in these environments, such as carrying capacity [START_REF] Sayre | The genesis, History, and Limits of Carrying Capacity[END_REF][START_REF] Sayre | The Politics of Scale: A History of Rangeland Science[END_REF], and overgrazing, thought to lead to desertification. The studies have thus laid the foundation for a better understanding of pastoral systems, recognising mobility as an essential practice that encourages the dispersal of cattle and limits pressure from herds during the annual growing season on which pastures rely [START_REF] Turner | The New Pastoral Development Paradigm: Engaging the Realities of Property Institutions and Livestock Mobility in Dryland Africa[END_REF]. The degradation of rangelands is thus attributed to attendant circumstances such as severe constraints on the mobility and growth of herds brought on by the extensive use of cattle feeds (Homewood, 2008: 69).

Scientific and political approaches to risk-aversion and vulnerability reduction have interpreted mobility and other strategic pastoral practices (such as diversification) as a means to minimise the dangers posed by the climate (Ancey et al. 2009: 5). At the same time, close studies of the practices of certain groups of Wodaabe pastoralists in Niger [START_REF] Schareika | Know to move, move to know ecological knowledge and herd movement strategies among the Wodaabe of southern Niger[END_REF][START_REF] Krätli | Cows who choose domestication. Generation and management of domestic animal diversity[END_REF] have shown how climatic variability can be an opportunity to be exploited rather than a risk to be minimised. Variable rainfall and a diversity of soil types, topographies and vegetation allow mobile pastoralists to exploit a range of different pastures at the optimum stage of their growth and over a longer period than in stable and homogenous climatic conditions [START_REF] Krätli | Living off uncertainty: The intelligent Animal Production of Dryland Pastoralists[END_REF]. This capacity to exploit the short-term effects of climatic variability on the nutritional value of plants, at both a small and a large scale, is the key to ensuring high-quality animal nutrition to improve the performance of herds of local races selected for such demanding conditions on the basis of their ability to withstand periods of undernutrition without danger (Krätli, 2015: 19-20). Whether variability represents a risk or an opportunity depends on the characteristics of the livestock systems and their capacity to manage uncertainty from one day to the next [START_REF] Roe | High reliability pastoralism[END_REF][START_REF] Krätli | Valuing variability: New Perspectives on climate resilient drylands development[END_REF]. This calls into question the universality of the notion of intensification evaluated against the criteria of efficiency (per animal, unit of surface area or worker), founded on the idea of overcoming the environment through inputs, capital and investment in infrastructure. For [START_REF] Krätli | Time to outbreed animal science? A cattle-breeding system exploiting structural unpredictability: the Wodaabe herders in Niger[END_REF], other "intensive" factors (knowledge, qualified labour, relationships) underpin pastoral production and constitute forms of social, cultural and political organisation in pastoral societies. The strong identification and cohesion between the social group and its animal component, as seen in the selection of races, plays an essential role in the construction of an active relationship with the environment [START_REF] Krätli | Cows who choose domestication. Generation and management of domestic animal diversity[END_REF]. Relationships and sociopolitical knowledge underpin not only pastoralists' mobility but also flexible and negotiated access to services and resource creation in the land they use [START_REF] Schareika | Know to move, move to know ecological knowledge and herd movement strategies among the Wodaabe of southern Niger[END_REF]Bonnet et al. 2013;[START_REF] Casciarri | [END_REF].

In habitats in which risk-taking is structural and can be advantageously exploited, pastoralists accentuate the flexibility and diversity of their production systems to exploit a wide range of potential situations (Krätli, 2015: 41). This entails maximising the options available, for example by maintaining multiple transhumance routes, dividing the herd and the family at strategic moments, or building complementary relations with agriculturalists [START_REF] Bonnet | Une famille et son système d'exploitation pastoral sans frontières, entre Niger, Tchad et Nigeria[END_REF]. Emery [START_REF] Roe | Making the most of mess. Reliability and policy in today's management challenges[END_REF] emphasises the management of the structural variability of the environment through a range of options for possible action, together with flexibility and know-how in real-time implementation, as the key factors in the efficient management of uncertainty in domains of public action subject to high levels of risk (airport traffic, energy flow management, etc.). Drawing on Roe's approach, Krätli (2017a) underlines an inherent paradox in pastoral development in the drylands: in considering variability in the environment and in systems of production as a problem to be minimised, pastoral development interventions in fact reduce the internal flexibility of pastoral systems that allows pastoralists to manage and exploit climate variability. Instead of inducing stability, this process exacerbates the turbulence engendered by climate variability and results in more vulnerable pastoral systems.

This paradox is particularly characteristic of the relationship between development and pastoralism in the Middle

Valley of the Senegal River.

Pastoralism, development and agrobusiness in the Middle Valley of the Senegal River

Development interventions and dynamics of change in pastoral systems

The Valley of the Senegal River has long been settled, giving rise to complex and powerful political structures at a regional level. As a result it is home to a variety of different populations including Toucouleurs, Fulani, Moors, the Bambara and Wolofs (Boutillier et al., 1962: 15-21). Land use management in the Valley was historically structured by two adjacent and heterogenous agro-ecological zones: the waalo, the riverbed and floodplain, and the jeeri, the dewatered dune area which runs parallel to the Valley. Until recently these two areas, each defined in opposition to the other, were used for agriculture and livestock farming in a complementary manner (Schmitz, 1986). The waalo was organised into strips running perpendicular to the river, allowing for different uses of the land throughout the season: fishing during flood periods, followed by flood-recession agriculture and then livestock farming to consume residues left after the harvests of the dry season (Boutillier et Schmitz, 1987: 540).

Pastoralists practised seasonal transhumance migrations between the waalo and the jeeri. The jeeri was exploited from the beginning of the rainy season until the ponds dried out during the cold dry season. During the hot dry season, the pastoralists moved to the Valley to feed their herds with agricultural residues, manure the fields and exchange their produce with agriculturalists. This system was practised in a number of different ways, allowing pastoralists to provide high-quality and diversified nutrition to their herds throughout the year [START_REF] Touré | Peul du Ferlo[END_REF]. From the 1950s onwards, a vast programme of pastoral hydraulics was implemented in the jeeri, and more generally in the whole pastoral region of the Ferlo, with a view to facilitating the permanent exploitation of pastures and sedentarising the pastoralists. The construction of boreholes led to a major decline in transhumance migrations to the waalo, engendered the relative stabilisation of pastoralists in rainy season camps and meant the rules governing the use of pastures around ponds in the jeeri were abandoned [START_REF] Barral | Le Ferlo des forages[END_REF].

From the 1970s onwards these changes were amplified in the Lower and Middle Valley by new hydro-agricultural programmes which were developed with a view to diversifying both subsistence and industrial agriculture following the construction of a network of dams. In this context, the Compagnie Sucrière Sénégalaise (CSS), the largest agro-industry in the country, was created in Richard Toll in 1970. This redevelopment of the Valley as an exclusively agricultural area was one of the factors 2 behind the end of transhumance migrations to the waalo, entailing the loss of seasonal access to heterogeneous resources that complemented the pastures of the jeeri.

Extended families were often forced to divide their time between agricultural and pastoral activities [START_REF] Santoir | Décadence et résistance du pastoralisme. Les Peuls de la vallée du fleuve Sénégal[END_REF], a difficult exercise with mixed results (Santoir, 1983: 151-160).

2 Along with the droughts of the 1970-80s and the Mauritania-Senegal Border War of 1989.

In their accounts, elderly members of the families interviewed recall drastic changes. Pastoralists consider themselves more mobile today than in the past. Previously, mobility was mostly limited to the rainy season. With the first rains families moved to the jeeri, where the older members would stay to sow millet while younger members headed south in search of the erratic first rains before returning once the rainy season set in. Currently, mobility begins in the dry season as pastures around nearby camps and boreholes are progressively exhausted.

Pastoralists thus follow changing routes during a period when nutritional options are limited. Exclusion from the Valley has left pastoralists more exposed to the high variability of the regional climate. In an attempt to compensate for low-quality resources and frequent scarcities, pastoralists use expensive industrial cattle feeds, entailing difficult decisions about distribution within the herd. The women interviewed explain that being settled in the jeeri accentuates the seasonal character of dairy production and leads to the loss of valuable economic exchanges with agriculturalists (milk, cattle / cereal, money). Interventions in pastoral development have promoted a transition from systems practising agriculture and pastoralism, which had functional links in the Valley (resources and exchanges), towards specialised pastoral systems operating in a homogenous but variable ecological habitat which depend solely on the sale of cattle for the purchase of cereals, water and cattle feeds (Magnani, 2016: 298-325).

La Laiterie du Berger, a pastoral social (agro)business

Inspired by a Mauritanian dairy which has collected pastoral milk since 1989, the Laiterie du Berger (LdB) was founded by a young Senegalese veterinarian in 2006, at a time of growing denunciations of mass powdered milk imports in a country home to a large number of livestock farmers. The Valley and the city of Richard Toll were chosen because of the large herds in the hinterland, their good connections with the rest of the country by road and the presence of agro-industries, most notably the Compagnie Sucrière Sénégalaise (CSS). LdB has a transformation capacity of over 10,000 litres/day and sources its milk from around 600 pastoralists operating within a 35 km ring around the dairy. The collection area includes both the waalo and the jeeri, though the jeeri supplies the vast majority of the milk3 .

Between 2006 and 2008 LdB transformed only local milk to create a diversified range of high-quality products.

However, too little milk was collected to meet the dairy's needs (around 1000 litres/day in 2007) and it underwent major financial difficulties. In 2008 danone.communities, the social business 4 foundation of the multinational group, became a shareholder, joining the founding Bathily family and the I&P investment fund 5 , and revolutionised the dairy's activities. Other investors followed in the shape of Grameen Crédit Agricole Foundation and the ethical investment fund Phitrust in 2010 and Danone S.A. in 2012. LdB thus entered the mass market for curdled milk, a move in line with the stated objective of danone.communities to improve human nutrition. Danone provided key skills in areas including production, marketing and distribution, and a new range (Dolima) was created to promote the products. Powdered milk was introduced to facilitate industrial production by rendering it less reliant on collected milk, which is in surplus during the rainy season but of limited supply and expensive in the dry season. In 2010 collection was restructured to reduce costs and support growth in the volume of marketed products (820 tonnes compared to 430 tonnes in 2007). The primary challenge was to ensure overall growth while reducing seasonal variability. A credit system for cattle feeds and measures to support production were implemented from 2011. These efforts bore fruit with the excellent returns of the 2011 campaign (915 tonnes of milk), though they were largely a result of the exceptional rainfall during the 2010 rainy season which allowed the pastoralists to limit their mobility. Enthusiasm quickly faded with the difficulties of the following year.

The very dry 2011 rainy season meant that the pastoralists left the collection area early (from January 2012). In an attempt to encourage pastoralists to keep some of their dairy cows on site and so maintain collections, LdB proposed sugarcane residue, supplied by CSS, on a credit basis. Many pastoralists accepted because mobility was difficult and risky: water from the boreholes was expensive for transhumant pastoralists and pastures were rare along transhumance routes to the south. This strategy was successful in maintaining collection levels (637 tons by the end of the year) but pastoralists fell into heavy debt as they were forced to take out a considerable amount of credit in order to ensure the survival of the dairy cows and calves. Despite a high-quality 2012 rainy season the situation in 2013 was still uncertain. The effects of the 2011 drought continued to be felt because of the highly seasonal nature of bovine reproduction, meaning pastoralists left on transhumance to avoid their milk being seized as debt recovery. Collection totalled 700 tonnes for the year, while a record volume of 2,200 tonnes of marketable products was produced6 . This major discrepancy served to underline the difficulties that the LdB faced in increasing and stabilising pastoral milk collection throughout the year7 .

Standardising systems or making them more diverse and flexible? A conceptual discrepancy

This failure is not only technical, but above all conceptual, stemming from a poor understanding of pastoral systems and the logic behind them as well as of their attitudes to the LdB milk collections. As a general rule, participating in milk collection is profitable for pastoralists during the rainy season and for a part of the cold dry season, when milk production does not require feed inputs and dairy cows are at peak lactation. As milk prices at the weekly markets in the jeeri are very low during this season, the new commercial opportunities offered by LdB are very important in allowing pastoralists to get maximum value for their produce. However, during the dry season, selling to LdB is profitable only when natural pastures are available. As pastures become exhausted, which can happen earlier or later depending on the quality of the preceding rainy season, income from milk sales no longer covers the cost of inputs needed to feed the cattle (CSS sugarcane residues, industrial cattle feeds). The pastoralists who agree to keep their dairy cows at the main camp for collection by LdB therefore sell their milk at a loss, at least during a part of the dry season8 . To understand why some nevertheless choose to do so, it is necessary to look at factors beyond the desire to augment dairy production and income: 1) Continuous participation in milk collection during the dry season allows pastoralists to secure milk sales during the rainy season when there is surplus milk and the dairy prioritises its most loyal suppliers. This is particularly appealing to pastoralists with large herds because income from the milk produced by all dairy cows can cover debts and generate considerable profits.

2) Selling milk during the dry season is a means of obtaining feed inputs on credit, which is a major advantage especially during droughts. Given the current conditions of the inputs market, credit is essential for families with small herds and no other revenue sources. This can become a trap because debt can absorb all dairy income across several years, greatly disadvantaging women, who traditionally received it.

3) Pastoralists use collection services to consolidate a classical pastoral strategy. They split the family and the herd during the dry season, settling the most fragile members of both the families and herds (the elderly, children, dairy cows and calves) in the camp for the dry season. They are thus spared the difficulties of the transhumance while the rest of the family and the majority of the herd are more mobile. The dairy cows that remain ensure a milk supply for the elderly and children who cannot survive on rice alone.

Despite working together, industrial dairy producers and pastoralists have very different rationales and objectives.

The dairies aim to encourage relatively specialised producers and stabilise pastoral milk production, without considering the economic viability of such a programme. This does not really reduce variability in production but its management and associated costs are externalised by the industrial producers and passed onto pastoralists. On the other hand, pastoralists look to get maximum use out of natural pastures, maintain the multifunctional quality of their systems and use the milk as much to feed their family and their calves as sell it. The pastoralists adapt the dairy's practices in order to make their systems more flexible and increase their options, and so better manage their operations in a difficult context.

The implicit dimensions of Intensification and Social Business: the interests of agrobusiness and the appropriation of pastoral resources

Having illustrated the parallel trajectory of development interventions and pastoralist practices in the Middle

Valley, and more specifically the discrepancy between the objectives of industrial dairy producers and pastoralists in the LdB collection area, it is instructive to come back to the paradox underlined by Krätli. Fifty years of policy designed to encourage the stabilisation and artificialisation of pastoral systems have produced some effects the opposite to those intended. Far from becoming sedentary as planned, pastoralists have become more mobile, at the worst time of the year, without precise routes to follow, and despite unfavourable conditions for pastoral mobility. Similarly, instead of being sheltered from the dangers of climatic variability, the pastoralists are more exposed to its risks. Indeed industrial feeds are an easy solution to keep cattle alive in hard times and their systematic use enables a partial decoupling of livestock population from pasture dynamics. However, feeds are expensive, excluding some pastoralists, accentuating inequalities and necessitating difficult decisions about distribution. Finally, they provide only very partial compensation for the loss of access to the resources of the Valley, which are diverse and so complement the pastures of the jeeri. LdB's intended artificialisation of pastoral systems thus collides with economic and ecological constraints.

Given that the technoscientific model of intensification has engendered disruption and upheaval while failing to live up to most of its promises, why has it been so persistent? Despite its destructuring effects on the ecological basis of pastoral production, the model is presented by industrial dairy producers as the only way to ensure the survival of pastoralism in the face of shrinking pastoral land. Indeed a new process of agricultural colonisation, originating in the Valley, is underway. With possibilities in the Valley now exhausted, a number of agrobusiness projects have channeled water from the River so that land in the jeeri rangelands can be cultivated. The Senhuile-Senethanol project has appropriated 20,000 ha of the Ndiael nature reserve around Lake Guiers. Part of the forest, which is an important resource to pastoralists, has been destroyed, while the infrastructure has encircled villages and fragmented the surrounding area, provoking a strong reaction from inhabitants and civil society in Senegal (Koopman, 2012a;[START_REF] Word | Sacrifier notre Futur: Comment le projet Senhuile-Senethanol menace l'environnement et détruit les communautés locales[END_REF][START_REF] Re | Comment on accapare la terre, saga Senhuile-Senethanol continue[END_REF]. Another scheme around Lake Guiers, the Projet de Développement Inclusif et Durable de l'Agrobusiness (PDIDAS), funded by the World Bank, plans to develop 10,000 ha for private investment in agriculture. However, the implementation of the project has proven difficult because of disagreements over the allocation of land. Finally, as part of its development plan, CSS has acquired approximately 5,000 additional hectares (meaning a total of 15,000 ha) of rangelands in the jeeri. While CSS provides a considerable quantity of agricultural residues through the dairy, storage and delivery costs must be met by the pastoralists. Free herbaceous resources are thus removed, to be replaced by agricultural residues which have to be bought. LdB's decisions seem contradictory when one considers that removing rangeland and replacing it with the sale of feeds will likely limit milk production in the jeeri and accentuate its seasonality. Through their strategic partnership with the sugar industry, a major actor in the local politics of land and water use, the industrial dairy producers indirectly support the land grabbing underway. The technoscientific model of intensification thus continues to play a major political role, falling short of and indeed contradicting the discourse reflecting the characteristics of the area. Firstly it is the keystone of the opportunistic alliance between LdB and CSS, serving as an instrument to define shared representations and common interests, following the definition of "development model" given by [START_REF] Mosse | Is Good Policy Unimplementable? Reflections on the ethnography of Aid Policy and Practice[END_REF][START_REF] Mosse | Cultivating development. An Ethnography of Aid Policy and Practice[END_REF] 9 . Secondly, it helps to legitimise the interests of agrobusiness and depoliticise the appropriation of natural resources, representing an example of "governing by rendering technical" (Ferguson, 1990;[START_REF] Li | The Will to Improve. Governmentality, Development, and the Practice of Politics[END_REF].

Questioning the role of livestock intensification leads us to examine how successfully social business meets its stated aim of finding a balance between societal and commercial objectives. The LdB social business is presented as a novel economic model that brings together a range of diverse actors: foundations and investment funds, a multinational dairy, NGOs, backers, international cooperation agencies and research institutions. The model pools expertise from strategic domains and ensures favourable access to public development funds and private funding.

Danone's central role in guiding and supporting LdB is in line with its strategy to expand in Africa, where it has acquired a number of major dairies since the end of the 2000s [START_REF] Bouchet | Africa: a new potential of growth for Danone through multiple acquisitions[END_REF] 10 . LdB allows Danone to promote a positive image of the company, a central concern in today's world, but also to help run, with limited investment, a company which is now the second biggest player in the Senegalese market. Moreover, Danone has acquired valuable experience in a number of domains, such as building and running formal and informal commercial channels, experimenting with models of local production, understanding the West-African market, and creating a successful brand.

More generally, the social business model, like the corporate social responsibility model, allows actors in agrobusiness to not only forge partnerships with each other, but also develop broad coalitions of actors likely to support the legitimisation of their political stances and to create favourable power relations within international development decision-making circles [START_REF] Binet | Le rôle des entreprises et des fondations privées dans la gouvernance mondiale agricole et alimentaire[END_REF]. This mirrors the general evolution of aid, in which private actors play an ever more central role [START_REF] Gabas | Nouveaux regards sur la coopération pour le développement et ses transformations[END_REF]).

Yet, when measured against the societal objectives that Fulani pastoralists consider important, the LdB project appears much less novel than its economic model. The dairy has indeed created a formal milk market that provides pastoralists an important opportunity to commercialise milk, while pastoralists can adapt LdB's incentive programmes to give themselves more room for manoeuvre in running their livestock systems in difficult circumstances. However, the LdB social business ignores the historical factors behind fundamental changes in pastoral practices and resource management, as well as the power relations and political choices that underpin them. By working in an opportunistic and strategic partnership with CSS, LdB shows itself to be incapable of working to reform the models of land use and resource management that disadvantage pastoralists. At the same time the spread of this new model of agricultural colonisation in the hinterland of the Valley risks compromising the durability of pastoral systems and creating conflict. The Senegalese state accords absolute priority to investments in agrobusiness in the Valley, to the point of developing strategies to try to circumvent existing land law, which was judged insufficient to "safeguard" private investors (Bourgoin et al., 2016: 15) 11 . This policy is pursued despite the few available studies of the consequences of growing agrobusiness investment in the Valley showing mixed results in terms of integrating farming systems and creating salaried employment, and an indisputably negative impact on pastoral activities [START_REF] Soullier | Les effets des agrobusiness sur les petits producteurs dans la vallée du fleuve Sénégal : résultats de trois études de cas[END_REF].

This case study provides a good illustration of the dynamics of land fragmentation and the private use of resources which are spreading rapidly in the Sahel, particularly in humid zones. The privatisation of strategic areas once shared between multiple uses in different seasons based on negotiations between different social and professional groups, has a major impact on pastoralism. It is also an example of the contradictions that characterise the actions of development aid agencies: against a backdrop of multiple crises and revolts across large parts of the Sahel, they proclaim a renewed interest in pastoralism and reinvest in pastoral development after decades of neglect, all while continuing to favour the implementation of policies which destructure and disadvantage pastoral systems.

Conclusion

We have thus shown how, in the context under study, development interventions shaped by the technoscientific model of intensification have failed in their attempt to standardise and stabilise pastoral systems in the Valley.

Production has become more variable and pastoral mobility more unpredictable and varied from year to year.

In this context LdB's actions have had contradictory effects. On the one hand, the intervention of industries which aim to stabilise and artificialise livestock farming is adapted by pastoralists who, making use of the diversity and flexibility of their systems, give themselves a greater range of strategies to better manage an array of complex constraints over which they have little control. On the other hand, the technicist approach of industrial dairy producers and their partners serves to justify, depoliticise and reproduce decisions which serve the interests of agrobusiness, such as replacing pastoral resources with feed inputs that must be bought. These dynamics exacerbate the constraints acting on the pastoralists.

It is therefore necessary to underline the political dimensions and power relations hidden in the technicisation of pastoral development interventions and include them in an open and informed public debate: the lack of land rights adapted to the specific needs of pastoralism leads to land grabbing, exclusion from strategic resources in humid zones, and precarious access to public services in pastoral areas. Equally, it is clearly imperative to deconstruct the rhetoric about reconciling the demands of profit seeking with social development, and to examine how it helps to legitimise the growing role of private business in shaping and implementing public development initiatives. In this case study, social business appears more like a means to exploit the vacuum left by public authorities incapable of devising inclusive territorial development policies in drylands.

The new wave of agricultural colonisation in the Senegal River Valley hinterland testifies to the revival and expansion of a longstanding tendency for spatial specialisation in agriculture and livestock farming in the drylands of West (Koopman, 2012b) and East Africa [START_REF] Fratkin | Ethiopia's Pastoralist Policies: Development, Displacement and Resettlement[END_REF][START_REF] Galaty | Unused land and unfulfilled promises: justifications for displacing communities in east Africa[END_REF]Schlee, 2014). It is thus urgent to fundamentally rethink land use patterns in humid zones and irrigated areas to ensure different users have access to resources and to promote functional interaction between agricultural and pastoral activities.

The case study at the centre of the article perfectly illustrates these contradictions. The destruction of part of the Ndiael reserve has had serious consequences in reducing the diversity of agro-ecosystems, with negative effects for both socioeconomic activities (small-scale farming, pastoralism, foraging) and the environment. Given the fragmentation and partitioning of humid and dry zones in the region, further developments in dry zones are likely to accentuate these dynamics and their negative effects.

Changing the paradigm will rather require preserving or encouraging new complementarities between agricultural and pastoral activities in diversified ecological zones, in an approach founded on understanding that promotes interaction and cogeneration between the different communities of the living environment. Resources would thus not be taken for granted and seen as a stock to be exploited in a more or less considerate manner, but rather understood as the product of interactions between local societies and their environment, mediated through herds of ruminants in pastoral settings [START_REF] Hubert | A paradigm shift in livestock management: From Resource sufficiency to Functional Integrity[END_REF]Krätli, 2017b). Simply transferring agricultural residues from irrigated land reserved for crop production to pastoral areas is not a renewable practice. It entirely ignores ecological processes, while also raising the problem of the cost of collecting, stocking and distributing the residues in question.

Rethinking current models of development requires major shifts in conceptualisation. Rather than being seen as existing independently of human activities, "natural" resources must be considered as social constructions shaped by the practices, norms, values and references underpinning production systems (Figuié et Hubert, 2012: 307).

This requires shifting the focus from a static and linear analysis to a dynamic that encompasses processes, relationships and contexts. Knowledge, production practices and forms of social organisation must be seen as key elements of these processes (Krätli, 2015: 82). There lie, in our opinion, the central challenges facing the future of pastoralism not only in the Senegal River Valley but, more generally, in the African drylands.

The presence of a more lucrative local market (500 FCA franc/litre compared to 225 CFA franc/litre paid by LdB at this time) discourages waalo livestock farmers from supplying LdB.

An economic model based on reinvesting profits rather than generating dividends which aims to reconcile the company's profitability and its social dimension[START_REF] Yunus | Building Social Business Models: Lessons from the Grameen Experience[END_REF]).

Investisseurs et Partenaires is an investment fund which finances small and medium-sized enterprises in Africa.

LdB thus became Senegal's second largest dairy business.

These dynamics continued beyond the period of study. In 2018 LdB agreed to a rise in the price of milk to 300 CFA franc/litre. This increased purchase price is likely to have repercussions on collection that it would be interesting to follow.

In 2010-2011, an exceptional year, pastoralists were able to sell at a profit all year around; in 2011-2012, a severe drought year, they sold at a loss for the whole dry season (seven months); in 2013, a "normal" year, they sold at a loss only at the end of the dry season (three months).

In the work cited, Mosse shows that rather than shaping practices on the ground, "development models" (e.g. "participation", "community development", etc.) function as systems to ensure shared and coherent representations and maintain political support for a range of actors with different interests.

Notably Fan Milk in Ghana, Brookside in Kenya and the Centrale laitière in Morocco, with a total value of more than one billion euros.

In order to facilitate the allocation of 20,000 ha to Senhuile-Senethanol, the state removed the protected status of the peripheral zone of the Ndiael reserve, land over which it had direct control. To "safeguard" expected private investments in the PDIDAS project, the state has tried without success to introduce a system of land registration that would circumvent local authorities and so contravene existing law.


Guillaume Vailland

Valérie Gouranton

Marie Babel

Cubic Bézier Local Path Planner for Non-holonomic Feasible and Comfortable Path Generation

Keywords: Non-holonomic Motion Planning, Motion and Path Planning, Human Factors and Human-in-the-Loop

In the case of non-holonomic robot navigation, path planning algorithms such as Rapidly-exploring Random Tree (RRT) rarely provide feasible and smooth paths without the need of additional processing. Furthermore, in a transport context like power wheelchair navigation, passenger comfort should be a priority and influence path planning strategy. In this paper, we propose a local path planner which guarantees bounded curvature value and continuous Cubic Bézier piecewise curves connection. To simulate and test this Cubic Bézier local path planner, we developed a new RRT version (CBB-RRT*) which generates on-the fly comfortable path adapted to non-holonomic constraints.

I. INTRODUCTION

Path planning is an important field of robotics, control theory and artificial intelligence [START_REF] Lavalle | Planning algorithms[END_REF]. It refers to the process of finding a way from a start state to a goal state under constraints. In particular, path planning is crucial for autonomous and semi-autonomous robot navigation in unknown environments. It allows the robot to find safe control states or a safe path to reach a given goal state. Among the multiple path planning algorithms that exist, the Rapidlyexploring Random Tree (RRT) [START_REF] Lavalle | Rapidly-Exploring Random Trees: A New Tool for Path Planning[END_REF] algorithm stands out for its efficiency in quickly exploring unknown spaces and for its low structure complexity, which allows it to be easily optimized or upgraded. Indeed, over the years, many versions of RRT have been proposed [START_REF] Lavalle | Rapidly-Exploring Random Trees: Progress and Prospects[END_REF]- [START_REF] Otte | RRTX: Asymptotically optimal single-query sampling-based motion planning with quick replanning[END_REF] among which an asymptotically optimal version RRT* [START_REF] Karaman | Incremental Sampling-based algorithms for optimal motion planning[END_REF] that has largely contributed to its widespread use. RRT and RRT* both generate a collision-free path composed of piecewise linear paths between states.

However, a trajectory composed of linear piecewise paths is not suitable for non-holonomic robots, in particular for differential robots such as power wheelchairs. Indeed, their kinematic and dynamic constraints prevent them from to follow path with too much curvature. In addition, within a differential robot transport scenario, user comfort is closely linked to angular accelerations and jerk energy [START_REF] Labakhua | Smooth trajectory planning for fully automated passengers vehicles[END_REF]. As such, comfort also depends on the smoothness of the trajectory i.e. the trajectory curvature [START_REF] Solea | Trajectory planning with velocity planner for fully-automated passenger vehicles[END_REF], [START_REF] Bevilacqua | Path planning maximising human comfort for assistive robots[END_REF]. Even when walking, people tend to limit curvature maximum value and variations [START_REF] Arechavaleta | An optimality principle governing human walking[END_REF]. In order for a path generated by a path planner to be both feasible by a differential drive robot and comfortable for a transported user, it must be smoothed by limiting curvature variation and curvature maximum value. To this end, 3 different approaches exist.

The first one consists in handling curvature constraints at the control level while following a reference path. In [START_REF] Cecco | PCsliding for vehicles path planning and control : Design and Evaluation of Robustness to Parameters Change and Measurement Uncertainty[END_REF], a smoothly path following method respecting kinematic constraints and based on Clothoid is presented. Authors in [START_REF] Park | A smooth control law for graceful motion of differential wheeled mobile robots in 2D environment[END_REF] propose a Lyapunov-based feedback control law along with a path following strategy consisting in reaching reference path states one after the other. Their control law regenerates a feasible local path between each state and provides comfortable motion based on curvature velocity adaptation. However, relying on control to ensure path smoothness can lead to a suboptimal path, including unnecessary turns as the reference path is not smooth.

The second common approach applies a smoothing algorithm on the reference path after its planning and before the control step. Post-smoothing algorithms take a reference path composed of different states or control points and tweak piecewise edges to generate a path respecting smoothing constraints. Multiple smoothing methods exist based on different interpolation mechanics and typical curves like Dubin's, Clothoid or Bézier curves. In [START_REF] Choi | Continuous Curvature Path Generation Based on Bézier Curves for Autonomous Vehicles[END_REF], low degree Bézier curves are used in corners and sharp turns to obtain a continuous curvature path i.e. G2-continuous. The works [START_REF] Yang | An Analytical Continuous-Curvature Path-Smoothing Algorithm[END_REF] and [START_REF] Yang | Continuous curvature pathsmoothing algorithm using cubic Bézier spiral curves for non-holonomic robots[END_REF] present a method based on Bézier transition curves, also known as Bézier spirals, to smooth a series of states into a G2-continuous path. In [START_REF] Zhou | Bézier curve based smooth path planning for mobile robot[END_REF], authors also use Bézier curves to smooth sharp turns and connect piecewise linear paths with each other. The algorithm in [START_REF] Bevilacqua | Path planning maximising human comfort for assistive robots[END_REF] generates a comfortable path by joining the states while minimizing curvature variation, integral and curve length. It uses the G1 Hermite Interpolation Problem with Clothoid and then tweaks angles to achieve G2-continuity. Authors in [START_REF] Simba | Real-time smooth trajectory generation for nonholonomic mobile robots using Bézier curves[END_REF] generate a C2-continuous and locally controllable path from a set of points by inserting Quintic Bézier curves between segments. In [START_REF] Heiden | Gradient-Informed Path Smoothing for Wheeled Mobile Robots[END_REF], authors propose an innovative method called Gradient Informed Path Smoothing (GRIPS). Unlike other algorithms, GRIPS deforms the path shape by locally optimizing the state locations. As such, this algorithm is able to correct locally sub-optimal states. However, post-smoothing algorithms require extra execution time and sometimes additional expensive collision checks [START_REF] Bevilacqua | Path planning maximising human comfort for assistive robots[END_REF] while the path planner already spent time to ensure collisionfree states. In addition, a post-smoothing generated path might be globally sub-optimal as states disrespecting curvature constraints are selected in the first place. Starting from GRIPS, if locally correcting state locations to integrate more constraints is a viable solution, one could ask why not directly integrate these constraints when generating states and path. This is the main idea behind the third approach to enhance path smoothness i.e. incorporating curvature constraints inside the path planner algorithm to generate feasible and comfortable path on-the-fly. Many solutions adapted to different path planners exist [START_REF] Mcleod | Real-time adaptive non-holonomic motion planning in unforeseen dynamic environments[END_REF], [START_REF] Silva | Clothoid-based global path planning for autonomous vehicles in urban scenarios[END_REF]. Focusing on RRT, multiple solutions emerged over the years using the same tools i.e. interpolation curves and post-smoothing methods, but in a realtime approach.

The solution proposed in [START_REF] Yang | An efficient Spline-based RRT path planner for nonholonomic robots in cluttered environments[END_REF] executes a local check of path feasibility before state connection and generates a valid path based on Bézier piecewise curves with null curvature at each states, thus ensuring G2-continuity. Authors also present different sampling, collision-checking and pruning techniques to enhance performances of the RRT, then defining the Spline RRT (SRRT). However SRRT fails to generate piecewise path on-the-fly as each new state connection requires the complete re-parameterization of the path from the start to the new state instead of simply appending a new independent piecewise Bézier curve path as presented in [START_REF] Neto | Feasible RRTbased path planning using seventh order Bézier curves[END_REF]. Indeed, their solution uses independent Bézier curve as piecewise path after approximating the cost to go to a new state using Dubin's curves. However, while the use of seventh-order Bézier curves ensures curvature continuity with null curvature at each state, it also leads to heavy polynomial calculations. Furthermore, the Bézier curves and their curvature values are not involved in the evaluation of the distance cost to a new state: this can still lead to inconsistent state choices in terms of comfort. In [START_REF] Park | Feedback motion planning via non-holonomic RRT* for mobile robots[END_REF], authors proposed a new local path planner based on a Lyapunov control law to generate piecewise curves and to evaluate distance between states. The method takes into account comfort constraints and eliminates inaccessible ones. [START_REF] Sobue | RRT-Based Path Planning Considering Initial and Final Pose under Curvature Constraints for Nonholonomic Wheeled Robot[END_REF] also proposed a different local path planner based on Clothoid G1 fitting to extend constraints and to ensure the elimination of inaccessible states. However, discontinuities between piecewise Clothoid path remain, due to Clothoid representation complexity and to G1 fitting algorithm. Authors in [START_REF] Chi | Risk-DTRRT-Based Optimal Motion Planning Algorithm for Mobile Robots[END_REF] and [START_REF]Autonomous Robotic Exploration by Incremental Road Map Construction[END_REF] include the Line-of-Sight algorithm (LOS) in their path planning process to check if two states can be connected under non-holonomic constraints in addition to the usual collision check.

All those methods proved themselves efficient and functional. Yet, they are still suffering from drawbacks, either because of the use of complex piecewise curves or high degree splines or because they do not fulfill all comfort and nonholonomic kinematic constraints. As such, in this paper, we propose a new local path planner based on low degree Cubic Bézier curves. Combined with path planning algorithms such as RRT*, it generates comfortable and non-holonomic robot compliant paths on-the-fly. We first present the local path planner in section II. Section III presents a new RRT* version, called CBB-RRT*, based on our local path planner. CBB-RRT* performances are exposed and compared to existing RRT* ones. Finally, we discuss our local path planner and implementations limitations and usability in section IV.

II. CUBIC B ÉZIER BASED LOCAL PATH PLANNER

A. Problem Statement

Considering a two-dimensional space X with obstacles whose position and geometry are known and 2 states S init , S goal . X f ree refers to X space free of obstacle. Path planners like RRT address the problem of finding a valid path from S init to S goal if it exists. A path is considered valid if it meets all path planner constraints. The most usual global constraint is for the path to be collision-free i.e. belonging to X f ree . However, in order for the path to be feasible by a non-holonomic robot and comfortable for a transported user, more constraints need to be satisfied. A path is comfortable for a user if its maximum curvature value and curvature variations are minimized as a pedestrian would naturally do [START_REF] Arechavaleta | An optimality principle governing human walking[END_REF]. Indeed, curvature is inversely proportional to angular acceleration and is linked to jerk energy, which are known to be discomfort factors [START_REF] Solea | Trajectory planning with velocity planner for fully-automated passenger vehicles[END_REF]. A path is feasible by a non-holonomic robot if it fulfills its kinematic and dynamic constraints. Those constraints are also represented by the maximum curvature of the path as the maximum curvature is inversely proportional to the minimum curvature radius that the robot is able to achieve. Finally, to enhance path stability, the path should be G2-continuous, meaning that its curvature should be continuous.

If the path is defined as a parametric curve g(t) where t stands for the curve parameter in R, then the curvature κ(t) can be calculated as

κ(t) = | ġ(t) × g(t)| | ġ(t)| 3 . (1)
As shown in [START_REF] Lavalle | Planning algorithms[END_REF], the path parameterization should be at least second order differentiable. In order to obtain a valid path, its absolute maximum curvature value must be less than the maximum value achievable by the robot and tolerated by the user. To summarize, the generated path must fulfill 3 main constraints :

     |κ(t)| ≤ min(κ robot , κ user ), g(t) is G2-continuous, g(t) ∈ X f ree , (2)
with κ robot the maximum curvature achievable by the robot and κ user the maximum curvature tolerated by the user. Note that the curve should also globally limit curvature variations, thus limiting sharp turns. While the third constraint is generally fulfilled by the path planner, we present in the following section a new local path planner to produce piecewise paths that meet curvature constraints and result in a global G2-continuous path once merged together.

B. Proposed Local Path Planner

To generate a path, several path planners, like RRT, connect piecewise curves between states. In most of them, those piecewise curves are linear and do not comply with any constraints other than not crossing an obstacle. We here propose a new local path planner based on Cubic Bézier curves to validate new states and to connect them to the tree. Bézier curves are parametric curves whose shape can be modified by tweaking a set of control points. The main advantage of Bézier curves lies in their simple parametrization based on Bernstein polynomial B i (t). Cubic Bézier curves are defined by a set of four control points P 0 , P 1 , P 2 , P 3 and a third order Bernstein basis polynomial such as P (t) the Cubic Bézier curve parametrization is defined by

P (t) = w 0 * B 0 (t) * P 0 + w 1 * B 1 (t) * P 1 + w 2 * B 2 (t) * P 2 + w 3 * B 3 (t) * P 3 , (3)
B 0 (t) = (1 -t) 3 , B 1 (t) = 3 * t * (1 -t) 2 , B 2 (t) = 3 * t 2 * (1 -t), B 3 (t) = t 3 ,
with w i weighting basis coefficients. In this paper w i = 1 for each i in order to simplify calculations. Using equations ( 3) and ( 1) we can compute the Cubic Bézier curve's curvature for any value of t. In particular, as shown in [START_REF] Sederberg | Computer aided geometric design[END_REF], its curvature at t = 0 is given by

κ(t 0 ) = w 0 w 2 w 2 1 n -1 n h |P 0 -P 1 | 2 = 2 3 h |P 0 -P 1 | 2 , (4)
with n being the Bézier curve order and h the perpendicular distance from P 2 to the line P 0 P 1 as shown in Fig. 1. Using those expressions, we can ensure that each piecewise curve composing the final path meets the maximum curvature constraint stated in [START_REF] Lavalle | Rapidly-Exploring Random Trees: A New Tool for Path Planning[END_REF]. Indeed, we can evaluate any piecewise curve curvature and invalidate the curve if its value exceed maximum curvature value κ max . As the final path is a composition of those piecewise Bézier curves, its final curvature will not exceed the maximum predefined value.

The last constraint to fulfill is the curvature continuity of the final path i.e. the curvature continuity between piecewise curves. Considering a new state S new and a possible state S candidate with which S new can be connected without crossing any obstacle (Fig. 2). S candidate is already accessible through a piecewise Cubic Bézier curve P (t p ), t p0 ≤ t p ≤ t p3 with t p the curve P parameter in R and t pi the parameter value so that P (t pi ) = P i . S new could be connected to S candidate using one piecewise Cubic Bézier curve Q(t q ), t q0 ≤ t q ≤ t q3 with t q the curve Q parameter in R and t qi the parameter value so that Q(t qi ) = Q i . Fig. 2: New default state connection case with P (t p ) a C-Shaped Bézier Curve in blue, S candidate an accessible state and S new the new state to connect.

We need to ensure that at a link state S link between the two piecewise Bézier curves, both P (t p ) curvature κ p (t p ) and Q(t q ) curvature κ q (t q ) are equal (Fig. 3). In other terms that κ p (t link ) = κ q (t q0 ) with P (t link ) = Q(t q0 ) = S link . In most of related works, piecewise curves are connected at each state such as S link is then equal to S candidate . Fig. 3: Default case solution and its curvature profile. Vertical axis gives curvature κ(t) and horizontal axis gives parameter t. In this solution, t link = 0.4 i.e. P (0.4) = S link .

The particularity of our work is that S candidate and S new positions are not start and end point of the Bézier piecewise curve. Indeed, they are rather used as third and fourth control point Q 2 and Q 3 respectively. As a result, the final heading of the robot stays tangent to line S candidate S new as a classical RRT path with linear piecewise curves would suggest. But more importantly, the first control point Q 0 , equal to the link state S link also belongs to the curve P (t p ) at a given t link with t p0 ≤ t link ≤ t p3 . This configuration allows turns to be anticipated and reduces path curvature as a human would do.

Thus, at a given t link , we know the position of three of the four Q(t q ) control points (Q 0 , Q 2 and Q 3 ). However, Q(t q ) and P (t p ) still need to be G2-continuous meaning that position, derivative and curvature values of Q(t q0 ) and P (t link ) must be equal. To do so, we can tweak the last unknown control point Q 1 .

Firstly, in order for Q(t q0 ) and P (t link ) positions to be equal, S link must belong to both P (t p ) and Q(t q ) curves. This constraint is fulfilled as far as we take a point on P (t p ) curve as first Q(t q ) curve control point Q 0 . Secondly, we can ensure that the derivative of Q(t q0 ) is equal to P (t link ) if the Q 1 control point relies on the P (t link ) tangent. Finally, using equation ( 4), we can express the G2-continuity constraint as a system to solve for the Q 1 position according to

     Q 0 = P (t link ) = Q(t q0 ), t p0 ≤ t link ≤ t p3 , Q 1 ∈ Ṗ (t link ), k 0 = 2 3 h0 |Q0-Q1| 2 , (5)
with Ṗ (t link ) being the P tangent at t link , k 0 the curvature value of P (t p ) at t link and h 0 the perpendicular distance from Q 2 to the line Q 0 Q 1 . Regardless of the curvature sign, we find 2 solutions to the system (5) :

x q1 = ± 2 3 | h0 k0 | 1 1+m 2 link + x q0 , y q1 = m link * (x q1 -x q0 ) + y q0 , (6)
with x qi and y qi the coordinates of the Q i control point and m link the slope of Ṗ (t link ). Once the correct solution sign is selected depending on the P (t p ) current direction, the final control point Q 1 position is known and the curve Q(t q ) can be drawn as in Fig. 3. Now, the maximum curvature of Q(t q ) can be evaluated and the new state and piecewise curve can be validated or rejected depending on the curvature constraint. Note that the computation of Q(t q ) does not require any change in the P (t p ) curve. This ancestor independence provides more flexibility to the path planner algorithm and better performance as the path does not need to be fully reparametrized with each new state. It is yet to set the convenient t link which determines S link and Q 0 positions and greatly influences the Q(t q ) curvature profile and maximum. Fig. 4 shows different possible configurations and the resulting P (t p ) and Q(t q ) curves. Furthermore, depending on the P (t q ) curve shape, a certain range of t link values will produce a curvature discontinuity (see Fig. 5). Indeed, when P is S-shaped, for a certain range of t link near Fig. 5: S-Shape P Curve with t link = 0.4 producing an invalid solution.

the inflection point, neither of the two solutions in equation ( 6) is both in the right direction and of correct sign. This is due to the configuration of the control points and can easily be expressed as conditions. If P is S-shaped, t link will provide a valid solution if the configuration meets the conditions sign(x q0 ) = sign(k 0 ) if y p3 ≥ y q0 + m link (x p3 -x q0 ), sign(x q0 ) = sign(k 0 ) if y p3 < y q0 + m link (x p3 -x q0 ), (7) with x qi , y qi , x pi , y pi the P (t p ) and Q(t q ) control points coordinates and x q0 the x derivative of P (t link ) whose sign gives P x direction.

Another impossible configuration happens when curvature k 0 is null. In that case we can set Q 1 equal to Q 2 and the resulting path will remain G2-continuous as long as previously stated conditions are fulfilled (equation ( 7)). Note that the validity of t link only depends on P (t p ) curve's shape and control points. Thus, a consistent t link value for future cubic Bézier curve connection can be computed regardless new state position. Note that our method is applicable in any dimension as it relies on n-dimensional properties. The use of a two-dimensional space in this paper is only to facilitate understanding.

This proposed local path planner allows to generate a Cubic Bézier piecewise curve between 2 states and to evaluate its curvature. Then, this curvature value can be used as a piecewise curve validation criterion to fulfill constraints (equation ( 2)), as well as a local piecewise path cost value in the overall algorithm process.

III. CUBIC B ÉZIER BASED RRT* (CBB-RRT*)

RRT is a path planner that allows fast exploration of an unknown environment [START_REF] Lavalle | Rapidly-Exploring Random Trees: A New Tool for Path Planning[END_REF]. RRT generates a collision-free path by combining piecewise linear paths between random states. Over the years, many enhanced versions have been proposed. One of the most used is the RRT* version that generates an asymptotically optimal tree by introducing a rewiring step to the RRT tree extension method [START_REF] Karaman | Incremental Sampling-based algorithms for optimal motion planning[END_REF]. In RRT*, a random state is found but not directly linked to the nearest in-tree state. State proximity is determined using euclidian distance i.e. a state is considered to be near to another if its euclidian distance is under a certain value η. First, the nearest in-tree state is use to create a new state in the direction of the random state at η maximum distance. Then, the new state is connected to the near in-tree state that provides the cheapest local piecewise path cost becoming the new in-tree state. This two step approach allows the use of different evaluation cost methods to find the nearest state, the near states and the final parent state of the steered state. Finally, once the new state is in tree, the rewiring step occurs i.e. the steered state becomes the parent of its near in-tree states if the cost to reach them is lower than the actual.

A. CBB-RRT* algorithm and rewiring strategy

We implemented a Cubic Bézier based RRT* version (CBB-RRT*) using the proposed Cubic Based local path planner (algorithm 1) to test it in a real case scenario. RRT* was chosen because it is the simplest asymptotically optimal RRT version and largely used in various domains. However, the presented path planner could be implemented in the exact same way in various RRT versions as a replacement of the linear local path planner [START_REF] Chi | Risk-DTRRT-Based Optimal Motion Planning Algorithm for Mobile Robots[END_REF], [START_REF] Wang | Collisionfree path planning method for robots based on an improved rapidlyexploring random tree algorithm[END_REF]- [START_REF] Arslan | Use of relaxation methods in samplingbased algorithms for optimal motion planning[END_REF]. As in RRT* [START_REF] Karaman | Incremental Sampling-based algorithms for optimal motion planning[END_REF], InitT ree() method initialises the tree T with a root state and RandomState() method uniformly generates a random state s random . Extend() method extends T by one new state s new as described earlier and the N ear() method finds all the s new near in-tree states S near based on euclidian distance like RRT*. In its overall process, CBB-RRT* only differs from RRT* algorithm by its rewiring strategy in order to be compliant with the proposed local path planner. Indeed, the Cubic Bézier based local path planner generates piecewise paths dependent from their parent curve shape and parametrization. Thus, rewiring a state, meaning changing its piecewise curve, will recursively invalidate descendant piecewise path. In other word, if a piecewise path changes, continuity with next piecewise paths is broken which invalidates all path. Therefore, using our proposed local path planner requires another rewiring strategy than the RRT* one. The CBB-RRT* rewiring strategy is an extension of the RRT* rewiring strategy that occurs inside Extend() method. For all near in-tree state, we verify if it has been rewired with HasBeenRewired() method. If it has been rewired, the U pdateDecendant() method is applied. All s near children are gathered in S children using the GetChildren(). For all children, if a new piecewise path from s near that meets all constraints can be found using the M eetConstraints() method, then the piecewise curve is updated using U pdateP iecewieCurve() method and a recursive call happens to try to rewire all descendants. Otherwise, all child descendants are gathered in S descendant using GetDescendants() method, and removed from the tree using the RemoveV ertices() method and saved in a state stack S. To avoid losing too many states, all states in S will be reprocessed by CBB-RRT* as a random state. Indeed, if S is not empty (Alg. 1 Line 3), the last state from S will be used as the new random state (Alg. 1 Line 7)

B. Simulation results

To show the impact of our local path planner once implemented in a RRT version, we compared CBB-RRT* to RRT* by running both algorithms in similar known 2D environments For both algorithms the random states came in the same order from the same uniformly sampled set. In all simulations, the maximum distance and near criterion has been arbitrary set to η = 4 and the number of iterations to N = 2000. In CBB-RRT*, the link parameter value has been set to t link = 0.5 for every C-Shaped Cubic Bézier piecewise curve and set to a multiple value of curve inflection t when S-Shaped. In a dynamic path planning scenario, maximum curvature value κ max can be set according to robot linear velocity to ensure respecting robot kinematic constraints and comfort standard like the ones stated in [START_REF] Solea | Trajectory planning with velocity planner for fully-automated passenger vehicles[END_REF]. For those static simulation, the maximum curvature was arbitrary set to κ max = 1.0.

As we can see in Fig. 6, trees generated by CBB-RRT* and their overall exploration area are smaller. This is due to a more constrained state validation but also to the different rewiring strategy. Furthermore, overall CBB-RRT* tree structure and descendants appeared different even though composing states are similar. Indeed, using our local path planner as a cost evaluation function, CBB-RRT* prioritizes reachable states with smaller curvature turns and generates a curvature bounded continuous path as shown in Fig. 7. As no curvature constraints is considered in RRT* and as its generated path is unfeasible by a non-holonomic robot without further process, no curvature profile for RRT* is available.

IV. DISCUSSION

A. Usability and Limitations

While relying on RRT* features like fast exploration and asymptotical optimallity, CBB-RRT* generates a smooth and comfortable path that meets all previously stated constraints (equation ( 2)). Indeed, the use of our local path planner guarantees path curvature continuity and limitation on which comfort and feasibility depend. Because path curvature is bounded by a specified value, it is achievable by any nonholonomic robots. In addition, the path provided by CBB-RRT* is parametrized. Path can be discretized and position, heading and curvature are known at any time. This is a huge advantage at control step as the robot can adapt its velocity to respect comfort constraints. Furthermore, our local path planner could be used within any other path planning, path smoothing and control algorithms such as more advanced RRT versions like NC-RRT [START_REF] Wang | Collisionfree path planning method for robots based on an improved rapidlyexploring random tree algorithm[END_REF], Risk-DTRRT [START_REF] Chi | Risk-DTRRT-Based Optimal Motion Planning Algorithm for Mobile Robots[END_REF], DT-RRT* [START_REF] Chen | A Fast and Efficient Double-Tree RRT*-Like Sampling-Based Planner Applying on Mobile Robotic Systems[END_REF], BIT* [START_REF] Gammell | Batch Informed Trees (BIT*): Sampling-based optimal planning via the heuristically guided search of implicit random geometric graphs[END_REF] or RRT# [START_REF] Arslan | Use of relaxation methods in samplingbased algorithms for optimal motion planning[END_REF]. Beyond control and path planning domains, our local path planner could be useful in data interpolation or design fields [START_REF] Hu | An extension algorithm for B-splines by curve unclamping[END_REF] as a solution to G2-continuous piecewise connection with only third degree polynomial curves [START_REF] Wolberg | Monotonic cubic spline interpolation[END_REF].

However, using our local path planner, CBB-RRT* breaks piecewise curve symmetry and requires a specific rewiring strategy to work. This is due to the ancestor dependency of Cubic Bézier piecewise curves. As such, it takes more iterations than RRT* for the same amount of exploration and its rewiring complexity is higher. Also, generating piecewise Cubic Bézier curves instead of linear paths is more expensive in terms of control points calculations, collision checks and data transfers. Nonetheless, many optimizations can be developed to enhance CBB-RRT* overall performance.

B. Optimizations

Note that for comparative purposes, each CBB-RRT* algorithm step has been modified as little as possible whereas it could be optimized for the specific use of our local path planner. For example, a more precise proximity evaluation function would allow to refine the nearest state selection and connect random states more often. To this end, the proximity function could take into account heading difference between states, or piecewise curve length approximation like in [START_REF] Neto | Feasible RRTbased path planning using seventh order Bézier curves[END_REF] with Dubin's curve, or piecewise curvature value using our local path planner. Even though the rewiring strategy has been extended and differs from the original,it can be optimized by a profound redesign based on more recent strategies [START_REF] Otte | RRTX: Asymptotically optimal single-query sampling-based motion planning with quick replanning[END_REF], [START_REF] Moon | Kinodynamic planner dual-tree RRT (DT-RRT) for two-wheeled mobile robots using the rapidly exploring random tree[END_REF]. Finally, the sampling strategy that generates random states can also be improved by using or combining various solutions, such as goal oriented sampling [START_REF] Kang | Sampling-based motion planning of manipulator with goal-oriented sampling[END_REF], [START_REF] Akgun | Sampling Heuristics for Optimal Motion Planning in High Dimensions[END_REF], incremental direct [START_REF] Choudhury | Regionally accelerated batch informed trees (RABIT*): A framework to integrate local information into optimal path planning[END_REF], [START_REF] Gammell | Batch Informed Trees (BIT*): Sampling-based optimal planning via the heuristically guided search of implicit random geometric graphs[END_REF], ellipsoidal direct sampling [START_REF] Gammell | Informed RRT*: Optimal sampling-based path planning focused via direct sampling of an admissible ellipsoidal heuristic[END_REF] and weighted sampling [START_REF] Janson | Fast marching trees: A fast marching sampling-based method for optimal motion planning in many dimensions[END_REF].

Regarding our local path planner, some choices would deserve further attention and investigation. For example, tweaking the weight of the Cubic Bézier basis coefficients w i could change the curve shape and provide smoother local piecewise curve while still meeting constraints as they are involved in the initial curvature (equation ( 4)). Also, the use of polynomial based Cubic Bézier curve was motivated by calculation simplicity but using other Cubic Bézier based curves could be considered such as T-Bézier curves [START_REF] Li | Planar T-Bézier curve with approximate minimum curvature variation[END_REF] or H-Bézier curves [START_REF] Zhao | Shape control of cubic H-Bézier curve by moving control point[END_REF]. Indeed, those non-polynomial Bézier based curves provide more flexibility and tweaking parameters than polynomial based ones. Finally, evaluation of piecewise curve maximum curvature and the finding of the ideal t link value could be optimized using lookup tables or more advanced strategies.

V. CONCLUSION This paper presents a new Cubic Bézier based local path planner that generates G2-continuous Cubic Bézier piecewise curves. This local path planner could find interests in many different fields. In a non-holonomic transport robot path planning context like power wheelchair navigation, trajectory curvature is directly linked to feasibility and comfort. As such, we presented the CBB-RRT* algorithm, a classical RRT* version using the proposed local path planner. While some CBB-RRT* computational steps have to be further investigated to improve its performance, it generates smooth, comfortable paths, feasible by non-holonomic robots without any additional steps.

VI. AKNOWLEDGEMENT This work is carried out as part of the INTERREG VA FMA ADAPT project "Assistive Devices for empowering disAbled People through robotic Technologies" http://adaptproject.com/index.php. The Interreg FCE Programme is a European Territorial Cooperation program that aims to fund high quality cooperation projects in the Channel border region between France and England. The Program is funded by the European Regional Development Fund (ERDF)

Fig. 1 :

 1 Fig. 1: Initial curvature. The Cubic Bezier curve is in blue and its three first control points are noted as P 0 , P 1 and P 2

7 Fig. 4 :

 74 Fig. 4: Both S and C Cubic Bézier shapes P Curve cases and arbitrary set t link value. Curve curvature direction, sign and value are represented by green normals.It is yet to set the convenient t link which determines S link and Q 0 positions and greatly influences the Q(t q ) curvature profile and maximum. Fig.4shows different possible configurations and the resulting P (t p ) and Q(t q ) curves. Furthermore, depending on the P (t q ) curve shape, a certain range of t link values will produce a curvature discontinuity (see Fig.5). Indeed, when P is S-shaped, for a certain range of t link near

Algorithm 1 : 4 s 5 i 7 s 8 s 9 S

 145789 CBB-RRT* body 1 T ← InitT ree(s init ); S ← ∅; 2 while i < N do 3 if S.Empty() then random ← RandomState(); ← i + 1; 6 else random ← S.PopBack(); new ← Extend(T , s random ); near ← Near(T ,s new ); 10 for s near ∈ S near do 11 if HasBeenRewired(s near ) then 12 UpdateDescendants(T , s near );

Algorithm 2 : 3 if 4 T 6 else 7 S

 23467 UpdateDescendants Method1 S children ← GetChildren(T , s near ); 2 for s child ∈ S children do MeetConstraints(s near , s child ) then .UpdatePiecewiseCurve(s near , s child ); 5 UpdateDescendants(T , s child ); descendant ← GetDescendants(T , s child );

8 T 9 S

 89 .RemoveVertices(S descendants ∪ s child ); ← S descendants ∪ s child

  (a) RRT* in a simple environment. (b) CBB-RRT* in a simple environment.(c) RRT* in a complex environment.(d) CBB-RRT* in a complex environment.

Fig. 6 :

 6 Fig. 6: RRT* and CBB-RRT* with η = 4.0, N = 2000, κ max = 1.0. Red triangle represents the start state and its direction and red circle represents the goal. Blue lines represent complex environment solution paths.

Fig. 7 :

 7 Fig. 7: Fig 4.(d) solution path curvature profile. Vertical axis gives curvature κ(t) and horizontal axis gives parameter t.smoothing and control algorithms such as more advanced RRT versions like NC-RRT[START_REF] Wang | Collisionfree path planning method for robots based on an improved rapidlyexploring random tree algorithm[END_REF], Risk-DTRRT[START_REF] Chi | Risk-DTRRT-Based Optimal Motion Planning Algorithm for Mobile Robots[END_REF], DT-RRT*[START_REF] Chen | A Fast and Efficient Double-Tree RRT*-Like Sampling-Based Planner Applying on Mobile Robotic Systems[END_REF], BIT*[START_REF] Gammell | Batch Informed Trees (BIT*): Sampling-based optimal planning via the heuristically guided search of implicit random geometric graphs[END_REF] or RRT#[START_REF] Arslan | Use of relaxation methods in samplingbased algorithms for optimal motion planning[END_REF]. Beyond control and path planning domains, our local path planner could be useful in data interpolation or design fields[START_REF] Hu | An extension algorithm for B-splines by curve unclamping[END_REF] as a solution to G2-continuous piecewise connection with only third degree polynomial curves[START_REF] Wolberg | Monotonic cubic spline interpolation[END_REF].However, using our local path planner, CBB-RRT* breaks piecewise curve symmetry and requires a specific rewiring strategy to work. This is due to the ancestor dependency of Cubic Bézier piecewise curves. As such, it takes more iterations than RRT* for the same amount of exploration and its rewiring complexity is higher. Also, generating piecewise Cubic Bézier curves instead of linear paths is more expensive in terms of control points calculations, collision checks and data transfers. Nonetheless, many optimizations can be developed to enhance