Frédérick

Lemarchand Frédérick
email: frederick.lemarchand@unicaen.fr

Particle Given Name

Starting from a fieldwork carried out in the Republic of Tatarstan (Russia) on industrial pollution and the necessity to support gardeners in changing their practices, the present research opens a socioanthropological perspective on the (sub)urban garden. The datcha is first and foremost a Soviet institution that has now spread to all Russian cities to become a social, cultural, and intergenerational phenomenon.

U N C O R R E C T E D P R O O F TRADITIONAL FARMING GARDEN

Anatolie, a 50-year-old worker, grows tomatoes, cucumbers, zucchinis, beans, cabbages, potatoes, etc., in the so-called Runo garden in Kadisheva (150 plots). In this garden, which he bought in 1980, you can find the whole range of vegetables available in this region of Tatarstan. In front of the house, a few flowers grow for decorative purpose, next to medicinal plants (mint, lemon balm) which the Russians use extensively. He even used to raise pigs and rabbits for a long time, thus making his garden a mini-farming business.

The products from his garden and the breeding of his animals provide for all the food basics he and his family need all year long. He grows seeds in the city and plants them in June. The vegetables are then canned to last over the winter period. Anatolie goes to the garden every evening from the beginning of May and until the harvest; he also spends his weekends there.

The datcha, and above all the garden, has an essential economic function in his budget balance. He comes to the datcha "to work, not to rest" except in winter, when he can enjoy the bagna (a traditional sauna-like Russian bath).

As a child, he used to observe his parents, who also have a garden, but he prefers saying he learnt the farming techniques on his own. Anatolie only has very little contact with his neighbors; they sometimes exchange knowledge and know-how tips to avoid pests or to grow this or that plant, but there is nothing constant or regular in these conversations which he sees as little compliance talks and basic good manners. The collective garden is an institution that dates back to the first years of the Soviet Union and that enabled urban people to purchase a plot of land-with an average size of 600 m 2 -in order to start an agricultural activity for domestic purposes. At the very start, each garden depended directly on the institution to which it belonged:

This was sometimes a factory, a specialized university, an administration, a hospital, a school, etc. The concept first appeared under Staline and allowed urban citizens to receive minimum wages by their own means of production based on the model of the pieces of land that were distributed to the kolkhoz workers. The collective garden got its real kick start in the two last decades of the Soviet Union (Ortar 2005). It played a major role in the economic survival that came along with the huge transition crisis of 1990 and 1991; however, its vocation cannot merely be confined to the economic sphere, as we are going to see further on. Nowadays, more than twenty-five years after the collapse of the USSR, it remains an important part of the Russians' lives as it provides around ten million urban dwellers, that grew up in the urban-industrial age, with the only possibility of finding a path to stability and of getting back in touch with nature. "Gigantic and soulless cities, endless lines outside the shops, individual freedoms trampled upon, poorly insulated homes and small flats in which entire families cope with promiscuity the best they can, authorized food which we know is contaminated since it comes from Chernobyl… What is the meaning of life in such a world? Against overwhelming odds, the building of small houses and overnight shelters makes its inhabitants forget, for a weekend at least, about their worries," this is how Ronan Hervouet chronicles the genealogy of an original institution which prefigures what we will now call "urban farming," whose early form is the collective garden. To be precise, this "suburban" (1) farming is reported to affect 65-80% of Russian people nowadays. Although geographically situated in the outskirts of big cities, sometimes up to ten kilometres away, the collective garden is a little bit like a "green town" right beside the metropole: There are main "avenues" from which smaller driveways merge, that contain many plots-sometimes many thousands-on which the famous datcha can be found inevitably, as a new version of the former garden shelter, which the landlords initially built themselves with the help of family members and friends, and which has now become a family home, or at least a secondary home in which families get together at weekends, between May and September. It is not uncommon for mothers to settle there for the holidays. People from every social background are working there side-by-side, there are all kinds of crops, such as vegetables, fruit, flowers, plants, people literally live there, sometimes part of the year, particularly women and children, families and generations gather to participate in a series of activities that are prohibited in the city.

AQ4 AQ5 4 L. Frédérick U N C O R R E C T E D P R O O F A WARMLY CONVIVIAL DATCHA (collective garden of Soutchi, 700 plots)
Galina, a 56-year-old retired woman, used to work as a corporate official in a

Kazan-based firm. The company in which she worked provided her family with this land in 1990. When they first arrived, they had to build it all up and arrange everything on this sand field that had been created after the building of a bridge. Twenty-five lorries full of land materials were needed to make the ground livable. After that, her husband started building the house and she started setting up the garden. "Men take care of physical work, such as pickaxing for instance. The distribution of domestic work is not systematic, but gardening is rather something for women. Gardening is thought of as a female task." The garden is first and foremost a living place where she can rest and spend time with her family (children, grandchildren) and her friends.

Since they have arrived at the time of the great crisis caused by the break-up of the former Soviet Union, there has been an obvious increase in capital gains from the datchas (upstream from the city, on the banks of the Volga, where there is a micro-climate), which have become more and more valuable financially.

As soon as they arrived, they started planted fruit trees and the bushes; the rest of the vegetable crops have been gradually developed (potatoes, cucumbers, tomatoes, etc.).

Galina's garden is much more diverse and richer now that she is retired and that her children are grown up and on their own. She keeps remaining seeds from one year to the next and buys some more from a catalog (she grows more than ten tomato varieties). Before planting, she has a look at the lunar calendar (in specialized magazines and publications). The quantity she produces is enough to avoid buying basic products (tomatoes, cucumbers) in the warm season, and she can even preserve food for the winter months.

Galina lives on the plot for the whole "season," from June to October; her husband (who still works) joins her in the evening. Their grandchildren spend most of the school holidays there.

Her garden does not really have an economic function, and the experience of gardening has a rather hedonistic and aesthetic dimension and serves the "love of beautiful things." Therefore, the garden is of course a place to rest, but also a place to experiment new things. The experience gathered year after year allows her to test new ways to grow crops in association (this plant grows faster next to that plant, etc.), to test biological control (this plant moves away the parasites that affect that type of fruit) and even agroecology (ashes or soap-based mixtures as substitutes to artificial fertilizer). Galina learnt gardening with her parents who had an individual house with garden. She has not had the opportunity to pass on her knowledge and AQ6 5 Russian Collective Gardens: A Story of Institution … 5

U N C O R R E C T E D P R O O F
skills to her children yet, because of their lack of interest in the matter. However, her grandchildren sometimes help her in small tasks. She maintains good relations with her neighbors who share their experience with her, exchange seeds, etc.

However, they are not friends but "garden neighbors."

A Family-Institution Above All

Most of the gardens we have visited date back to the 80s, sometimes even to the 70s, which means that two and sometimes three generations get together there. The first generation, that had been given the plot in the Soviet period, is slowly dying; however, the challenges concerning the future and the development of those gardens still remain an issue for all three generations. So there is obviously more than one single kind of relation to collective gardens, and there is obviously no "model garden," but rather a typology of agricultural practices, of expectations, of social relations, that are deeply rooted in the historical development of collective gardens.

The first "pioneer" generation (ours date back to the eighties, which is quite late on the history scale of the collective garden) has been given gardens "for free" in the framework of collectivism, whereas the following generation had to, and still have to, invest heavily to acquire a plot. In terms of size, the collective gardens differ from one another (ranging from a few dozens to several thousands of plots), just like their quality also differs: the garden of Soutchi, in which we carried out our investigation, near the built-up area of Kazan (1.2 million inhabitants), and at the same time upstream from the city, on the Volga riverside, on a sand island on which there is direct and private access to the river; this has become a "must" for the inhabitants. However, those recreational and aesthetical qualities will not make the happiness of those who wish to make a food production profitable; these people will have to look for a richer land with less frequent flooding, and nevertheless less expensive. Roughly speaking, the historical movement that we wish to describe here ranges from productive gardens to leisure gardens, and all hybrid and intermediate forms. However, other characteristics may arise, as we will see. Therefore, it is quite tricky to fully understand the collective garden institution without considering its historicity, without interviewing different generations of Russians, pioneers, heirs, or buyers of these precious plots; actually, this is prerequisite to draft an exploratory typology of the gardeners in line with their values and expectations (Fig. 5.3).

So these are the generations we will consider throughout this study, even if these categories cannot be held as representative of the all individuals who are supposed to belong to these generations.

-The 60-80-year-old generation: the "pioneers," characterized by their deep rural and farming roots; strongly attached to the food productive use of the gardens -The 40-60-year-old generation: the "heirs," urban generation whose "farming culture" was acquired in the garden This means that all age-groups play a role that it at least as important as the part played by social classes, both being historically speaking involved in a process of understanding the attitudes and practices of the gardeners. The perspective of the intergenerational transmission of gardening is a crucial factor: Inheritance, whenever accepted, is seen by most people as a moral duty to carry on the work begun by the parents who cleared the land, fortified and cropped it, planted trees, built a house (the datcha), etc. The weight of this burden to perpetuate ancient family traditions may seem paradoxical when seen through the perspective of current aspirations of the heirs to transform the garden and sometimes even getting rid of it.

Hélène took over the datcha and the garden based on the moral duty to respect the legacy of her parents, in order to live "in accordance with traditions" even though Author Proof

U N C O R R E C T E D P R O O F
this has never been her own personal choice. "This garden is like a suitcase without a handle: a heavy load that you cannot leave or even just lay down for a while."

The Economic Role: Distinguishing Discourse and Facts

In the early 1990s, as Russia was deep in economic crisis, the gardens have played a significant and essential role in daily nutrition; however, it is surprising to note that, when asked, most gardeners today tend to deny the economic basis of their work. It has often been said that if we had to take calculations of inputs (buying or hiring of the land, buying of agrochemical products, of fertilizers, eventual buying of plants and seeds, etc.) on the one hand and of outputs on the other hand, the balance would be negative; except for monoculture exploitations, maybe (potatoes for instance).

But these are extremely infrequent and usually grown whenever a family finds itself in the situation of inheriting two plots: One of the plots can be used in essentially productive "business" activities; in other words, it is dedicated to selling agricultural products on local markets. It is important to add that the agricultural products delivered by the kolkhoz are cheap and generally of good taste quality (when the extensive cultivation is carried out on good soil conditions).

The gardeners readily admit that the garden products provide varied and healthy food, thus denying the true health hazards arising from pollution of the river in the present case, but at the same time, they all agree to say that it would be more profitable for them to buy vegetables on markets or from the kolkhoz, particularly in the season when the prices are low. But these are only words intended to show the non-utilitarian nature of the gardens and no one really tried to make such a calculation, since it would only be of limited relevance here. We shall note here the existence of the rhetoric of economic disinterest, which means that the real purposes of the gardens are to be found somewhere else: keeping in touch with nature (banned notion in the Soviet industrialist speech), convivialism, recreational and educational activity, etc.

From the economic point of view (in the sense of exchanges), we could state that the gardens are places "for free" following the logic of giving. Here, the use of the adjective "free" refers to the work of nature that human beings have been selling

and buying since Neolithic times: All we have to do is plant or seed to harvest the fruit. We then save the seeds, and the cycle goes on. This has indeed become a key issue of careful thoughts given to "nature-provided services," also known as environmental amenities.

This principle of free availability is directly linked to the very logic of living "masters" of the house. Following a period of empirical observation, we were led to think that the garden is rather a place for women, as it is part of the imaginary continuity of the house. This does not mean that men are inactive, since he has a responsibility-with the support of neighbors and family members-to build and maintain the datcha and its "outbuildings" (toilets, sauna, greenhouses) and to perform the hardest household chores (plowing, ensure manure supply). In some gardens, at the very beginning, it was necessary to import the whole of the arable land; this was a typically masculine task (Fig. 5.4).

"The datcha is not a place to develop friendships," says Hélène, "In the garden, you get to know people but you do not make friends." The idea that the sociability networks among gardeners are different or even distinct from the urban friendship Author Proof

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networks is not uncommon. Alfia also emphasizes this distinction between the friendly relations she developed in the city and those she developed in the datcha since, she says, "at the datcha, you socialize with your direct neighbors, you do not choose them; in the city, friendship is more selective but the relationships are richer." This is how people regain the ancestral automatic solidarity, particularly in mutual assistance practices, without really considering their neighbors as heart friends. Nevertheless, Alphonso keeps on insisting, like many others, on the existence of convivial moments (the people from his garden often share grilled meals), with a traditional meal to celebrate the end of the season in October. According to him, the relationships are "easier at the datcha than at the Institute, you can talk to people without bothering about social status." Hence, the garden is at the same time a social marker (having a "great" garden is ego-boosting), but also, paradoxically, an eraser of social status, particularly in huge gardens where all social strata from the ex USSR work side-by-side (ranging from the skilled-or not-worker to the director). It goes without saying that the "new Russians" who belong to the financial oligarchy take over other places. However, there is a great deal of socializing practices; all along our stay, our hosts have made real efforts to invite a number of friends to join in and thus find the opportunity to show us the inimitable samovar, topped with its usual boot, old fashion-like, and of course, the traditional Russian barbecue. The meal ritual refers to other various ritualistic procedures from the early customs, just like in western practices: the use of fire, alcoholic beverages, the investment of the outside world, etc.

THE DATCHA-(ecological) COUNTRY HOUSE

Raphael and Alfia, 42 and 45 years old, respectively, builder in the building industry and biologist, live in Kazan and own a 600 m 2 plot on which they grow potatoes, tomatoes, onions, cucumbers, beans, mainly in summer.

Raphael built his datcha step-by-step, starting in the nineties, when they bought the garden. In the case of this family, the products grown in the garden have absolutely no economic value. Alfia is the only one taking care of the garden, since Raphael is busy building the house. Raphael works in the private sector and has no time to work in the garden and enjoy it. They could easily "cover the yard with asphalt and place decorative plants," she says. But the interesting thing about the garden is to "watch the crops grow," says Alfia, insisting on the recreational side of the garden for children: One of the main goals of the garden is to "bring the children back to nature" by making it a mini-environmental education center. Alfia has never learnt gardening and her knowledge in biology and her job only help indirectly. She says that she can "feel" what plants need just by looking at them, even though she learnt a few basics from her parents. The datcha may in time become a real holiday house; this is how they bought the plot. For them, the garden is above all a means to forget about their routine work in the city, which, they think, Baudrillard (1967) on the dialectic that seem to underlie our world of domestic objects: "A whole category of objects seems to evade the rules of a system that we have just analysed (functional): these are baroque, folkloristic, exotic, antique objects. They seem to contradict the requirements of a functional numeracy in response to wishes of another kind: testimony, memory, nostalgia, escape. There is always a temptation really to mean that they represent the survival of a traditional and symbolic order. Although these objects are different, they are all part of modernity, and this is where their double meaning emerges." Wouldn't it be the same logics for collective gardens? It was instituted at the beginning of the twentieth century, essentially for economic reasons, and over time, it has become an institution of remembrance of a relation to nature that got lost in the development of the urban-industrial project; however, it is dedicated to social remembrance.

Though it was genuinely a support for memory, at least, this is what the aesthetic and theory of the gardens teaches us [START_REF] Yates | The art of memory[END_REF], the garden would now find its place in the Art of Remembrance. Since it provides landscape captures, that is to His 400 m 2 garden is located in Kadicheva, on the edge of the city, near the factories, in the south part of Kazan. In 1980, Idar visited a friend in this garden and he saw a "for sale" sign on the datcha. It was love at first sight.

Since then, he has grown tomatoes, onions, garlic, various flowers… he has a good standard of living and does not need to earn money from the garden.

However, it cannot be denied that his production of vegetables is a direct advantage for his own economy; his wife always cans the excess production to keep food for the winter season. In fact, for Ildar more than for others, his garden has become the continuity of his workshop, or even "a workshop per se" as he says, a kind of vegetal workshop in which the movement of the work of art and the movement of nature both commune: "When I am surrounded by plants, I can rest, ideas cross my mind and I draw them on the canvas, it opens my eyes and nature is right here, I can hear the birds singing;

this is the truth about my life."

The transmission of the "art of gardening" shall be done through the work of art more than through social relationships themselves. Hence, some canvas include remnants from the old wheat fields that used to surround the garden, and some others contain representations of garden flowers. According to his own sayings, he learnt gardening through the farming culture that his father left behind him. He had settled in Kazan in the thirties, in an individual house with garden, in which he reproduces the organization of rural life (gardens, trees, farmyard, animals, etc.).

The aesthetic vocation of the garden seems to be a particularly vital concern and does take here a really specific dimension in which the garden stands as a symbol for much more than a "beautiful place," but for the place itself in which beautiful things can be created. Ildar hangs out with neighbors and close friends, with whom he has more "intellectual" than practical relations. In that sense, the word datcha is returning to its original meaning that is a second country home in which the ruling class invited people from good society.

Collective Garden, Landscape, and Transmission

We now have to consider the anthropological challenges of the contemporary garden properly speaking, by means of an empirical analysis whose limits we are well aware of. Finally, it is only inhabited a few months in a year and remains, most of the time a familial or personal "rustic utopia" of a production obtained from a small "nature monument" which structures expectations. In the garden of Sotchi, Hélène thought that "gardens need to be kept alive because they represent nature, they shall not disappear, men need nature." At this point of our analysis, we think it is helpful to highlight the theoretical contributions of landscape aesthetics and of the art of gardening with the aim to underline the epochal dimension-hypothetically, of course-that structures the connection between gardeners and their terroir/territory (Fig. 5.5).

Let us quickly recall what A. Berque stated: "Societies organize their environment according to their own interpretation of it and, conversely, they interpret it according to the way they organized it." Therefore, the aesthetic connection we are interested in right now finds its roots at the limits between cultural and biological history, at the place in which the gardener finds himself literally "engaged" with his environment. This affordance (the French borrowed the word from the English language), according to Berque, is at the same time of ecologic and cultural nature and enables an attachment to the landscape, a possibility to inhabit this world (from habere: to hold, to take, in Latin). There are only few institutional representations of the garden-in contrast, painting of nature landscapes-except for the individual domestic iconography containing family portraits, since the garden stands out as a separate landscape category per se (just like literature and painting). By opposition to the administered and streamlined universe of the Soviet city-the standardization of which still remains stunning to western people-the garden rises out of the earth to create intimate spaces and build relationships between the self and others through

Conclusion

The recent evolution of the datcha through an approach based more and more on aesthetics and less and less on production could be seen as an attempt to move beyond modernity (which is here the genuine economic function of the collective garden) has started. Of course, this is not a matter of reverting to the original empathy of the subject (the farmer) toward the object (nature) but of going beyond this distinction. Following the model western suburban gardens, each plot tends to become a kind of small eco-museum, an eco-emblematic temple of our time, a small nature monument that does not tell the "great victorious national Tales" anymore but rather small particular stories of universal value. Augustin Berque tells us that the post-modern paradox has enabled a re-sanctification of nature "in proportion to the profane knowledge brought by science." This dynamics can be understood from the metamorphosis and transmissions of the gardens generation after generation, and from the restoration that enables their survival, even if their function has changed. If reality seems to be complex, it is because all the above-mentioned dimensions can coexist within a single garden, just like the datchas are home to all generations.

The meaning of the garden thus finds itself at a crossroads between the wish of the elderly to perpetuate solidarity in the family, with the garden's production being strictly divided up between family members (particularly toward progeny) but also dispatched among neighbors and friends in order to structure a sociability network.

However, the new aspiration of the post-Soviet generation that is now old enough to procreate introduces an intergenerational break (abandonment of the agricultural activity or even of the garden) which (dialectically) calls for greater family

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Fig

  Fig. 5.1 A gardening woman posing in her garden

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  The 20-40-year-old generation can be of two types: on the one hand, the "new Russians," who tend to develop the occidental-model-based pavilion datcha, this means that it has no vegetable garden; on the other hand, the "young ones" as bearers of new aspirations, and quite reluctant to garden cropping, encouraging new recreational and aesthetic purposes of these gardens.

Fig

  Fig. 5.3 Datchas and gardens along the Volga

  beings reproduction and results in another socio-anthropological principle: It is possible to give out the harvest of nature (through our own work), without losing it, just like we can duplicate computer files or share knowledge. This is how the release for free circulation of crops including seeds, beans, plants (especially in AQ11 8 L. Frédérick Layout: T1_Standard Book ID: 429280_1_En Book ISBN: 978-3-319-72732-5 Chapter No.: 5 Date: 28-12-2017 Time: 3:12 pm Page: 8/19 U N C O R R E C T E D P R O O F spring), but also of empirical knowledge and know-how, occurs between neighbors, family members, or friends. These exchanges/gifts were theorized by Marcel Mauss and gained widespread acceptance (Caillé 1989); they involve a concept of reciprocity-which also fosters biodiversity!-through barter trade practices and all kind of non-monetary transactions such as neighborly goodwill. We had the opportunity to experience this logic of gift every time we visited the gardens; we left back home with arms full of flowers, fruit and vegetables each time and were also often kindly invited to use the bagna. THE ANTI-CRISIS GARDEN In 1980, Tamara and Victor, 48 and 52 years old, were "pioneers" in their garden in Soutchi, which today counts 400 plots, each of 400 m 2 . They wanted a garden to bring up their children in the middle of nature, while the falling living standards resulting from the perestroika did not allow any vacation or even leisure time in the State's various recreational centers. He uses to work 20 days in a row in the garden and then takes ten days' rest. She spends all her free time there, that is to say from May to September, taking paid vacation here and unpaid time off there. The production of tomatoes, cucumbers, salads, berries, condiments provides partial food self-sufficiency. The economic function of the garden emerged gradually along with the drastic fall in living standards and the declining purchasing power of the working class that started ten years ago. A great part of the production is consumed locally (to the most possible extent), at least during the summer season. Fresh fruits and vegetables are said to taste better; the remainder products are preserved for the winter season. Tamara belongs to the urban generation and has learnt gardening "spontaneously," reading books and magazines, talking her colleagues' advice, and experiencing things. The children and grandchildren have been socialized through garden work; the grandparents take care of their grandson there all summer long. The aesthetic function of the garden is present but secondary. Paradoxically enough, it was much more present at the beginning, when the economic function of the garden was not yet the first concern. The datcha was built up by the husband, with the help of his friends. It was the first step, the garden followed. Proximity network, automatic solidarity among neighbors. Exchange of products and seeds. Mutual assistance, particularly for hard work and household repairs.Work, social linksThe issue of work is central in the garden. Work here refers to an activity that involves high-intensity exercise dedicated to change the world-change the land in the present case-to get a product out of it. Gardening a 400-600 m 2 plot is an activity that consumes time and attention, sometimes tedious, that could be a 5 Russian Collective Gardens: A Story of Institution … job for a single person, from spring to autumn. This is what happens in "permaculture" micro-farms that have developed in Europe for the last few years. It should be noted that some people, like retirees, unemployed or part-time workers, take this time. Some others, like employees or freelancers, spend all their free time there, including holidays and weekends. The value of labor occupies a prominent place. The act of gardening is particularly described as a teaching medium for young children: The harvested fruit and the freedom to enjoy consuming it is the product of the work dedicated to nature as a reward for our labor. Older people often use the following proverb to express this connection "You cannot have bread without stalks of wheat!" Just like in the rest of the society, in Russia, the act of gardening is a reality that happens to have a division by sex: Women (sometimes men) take care of the crops. It is fairly rare to see both being simultaneously

Fig

  Fig. 5.4 Leisure, family, nature

  is tedious. Social relationships there are limited and "urban," except for a few close friends that they know from the garden. The datcha is modeled on the French country house, where they meet friends that are "external" to the garden. Their three young children even have little summer friends here, that they meet each year.5.4 The Garden as a Work of Art Dedicatedto Remembrance and as a Vector for the Transmission of the Farming Culture During this investigation, we found evidence that could possibly validate the assumption that the garden could be a place of memory and transmission of the farming culture in the Soviet and post-Soviet society. Indeed, many gardeners from the pioneer category admitted that they spent their childhood in the country, in small villages, in connection with the land, the land of the kolkhoz, in connection with animals and with the last Russian farmers, before the Soviet system declared the peasant society as a completely insolvent social class. When asked "where did you learn gardening?", older people frequently answer: "in the village where I grew up," whereas others tell us about their family life in city houses with gardens (there are still a few of those houses in some parts of Kazan, as in many old Russian cities. What we call "memory of the farming culture," is much more than just a series of skills and know-how: It is a collection of concepts and representations of the world, based on particular values and around a collective memory; it is common to all farming cultures that developed on several continents from the year 1000 to the twentieth century. The reproduction of family and social structures, the predominance of particular socializing models (family, friends, neighbors), over secondary socializing models (institutions, trade, State), the development of non-monetary trade (exchange, mutual assistance, gift logic), the direct transmission of skills and know-how, the worries to preserve the environment, the connection to the land, the preservation of collective memory, the development of self-production and home consumption, and finally, the will to maintain personal freedom places are the main characteristics of the memory of farming culture, the ones that industrial and technical modernity simply swept aside, supposedly in the name of Reason[START_REF] Bitoun | Du collectif au communautaire. À propos des réseaux familiaux dans la Russie post-soviétique[END_REF]. The sacrifice of the whole farming population on the altar of productivism and modernity has, indeed, played a particularly violent part in the Soviet experiment that preached for their anthropological change into a working class; to that aim, they were locked into factory farms named kolkhoz, to fit in with the ruling ideology. The repression of peasant movements and the planned destruction of rural societies even turned into a real genocide, in the initial times of the Russian revolution(De Crisnoy 1978).

  This is how one may understand the keen interest of Russians in the gardens, since they serve as a support for the inscriptions of remembrance that has never been fully erased from the farming culture, even though the social, economic, and political class structure of the "peasant society" finally disappeared, as it did in Western Europe(Mendras 1995). Beyond the materiality of things, our investigation led us to discover the extremely rich and complex side of the existing memorial relations, through the testimonies of the three or four generations, the oldest of which still holds the living memory of the Soviet system experiment, and even of the twentieth-century totalitarianism, from the garden institution and the memory of peasant societies. The farming culture, in terms of ethos (a set of values) and praxis (set of historically oriented practices), can be found at different levels of the practices and representations of the gardeners, especially of the "pioneers," who were the first to colonize the land, sometimes with a heavy hand. Its main characteristics are (open-ended list): -The development of non-monetary trade -The act of giving excess production to neighbors and friends -Mutual assistance for tedious tasks and the building of the house -The limitation in the development of the garden's productive capacities -Ecological awareness (more or less implicit) -The establishment of a relationship between working the land and freedom -Direct transmission of experience -Inputs self-production and family consumption of the products. The purposes of the French family or professional use of the garden, whose institutional codes are historically varied, are quite the same. From this point of view, the garden is a symbol of the essential downside to urban and industrial modernity whereby the practices, skills, and social logics that the institutions of modernity have erased in the name of Reason (and economic profitability) can be updated. It is somewhat reminiscent of the reflections undertaken by Jean

  landscape can be understood in its aesthetic and nature-sensitive meaning (Berque), the garden could possibly be seen as a medium between an unovertaken past seeking for modernization-the pre-modern anthropological inheritance-and a present that cannot respond to anthropologically fundamental needs such as rooting, giving "for free," and living a "good life." Our interview with the painter Ildar Zaripov (exhibition at the Tretiakov Museum of Moscow) has brought much like to this subject.THE GARDEN OF AN ARTISTIldar Zaripov, a 54-year-old Tatar painter, is a well-known figure of Kazan.

  conception of the garden goes deep into the "Russian mind" in its relation to nature. The garden is "intrinsically pure" and helps balance physical and psychological health; this is an image that can also refer to Japanese gardens: "Garden work can also be a way to rest; physical activity brings inspiration and creativity. When I work in the garden, I think."

5

  Russian Collective Gardens: A Story of Institution … 15 U N C O R R E C T E D P R O O Frather spend that money on children's games and on all comfort and amenities for the datcha. Moreover, her occupation only leaves very little time for leisure activities. Guselle also admits her lack of interest in gardening; at the most, she is thinking of planting raspberries and blackcurrant berries for the children. The household does not need a garden to have best quality products since Guselle's mother owns a large plot (600 m 2 ) and provides her family with fruit and vegetable during the nice season and canned products for the winter season. Although she rules out working in the garden, Guselle enjoys fishing on the Volga with her husband; they own a small motorboat which they use for this purpose. Guselle and her husband keep up with the neighbors; her neighbor brings her fruit and vegetables whenever she has too much of it, even though they do not belong to the same social class. The discussions are friendly: meal sharing, mutual invitations to birthday parties, games (chess), etc.

  transformation of the datchas finally appears to be a powerful anthropological factor that reveals the changes of Russian society (and, on a broader level, of post-Soviet societies like Ukraine and Belarus), caught between, on the one hand, the continuation of the modern industrial dream involving a tear-off from the land and, on the other hand, the dream of going back to nature, thus maintaining a solid bond with tradition, family, and the land. New forms of sociability and of land use forms might arise from this preservation of species, knowledge, know-how and memories that may all serve as a basis for transition societies.

  To put it in a nutshell: It has a very poor economic value, except in cases of acute crisis. It is definitely a place to socialize, but it is more appropriate to develop "mechanical" relationships with neighbors than real elective friendships. It remains a place for meditation that is deeply rooted within the central community, that is, family, in which people can work/meditate on their own from time to time.

Author Proof

the cropping of the land. The point here is that modernity, and most particularly the Soviet scientism that dedicated a boundless passion to the artificial, had distanced itself from nature and founded its anthropology outwardly from it. From the Renaissance onward, landscapes start being set apart from nature, [START_REF] Datcha Blues ; Belin | Paysages, représentations des paysages du siècle de Lumières à nos jours. La Manufacture[END_REF]; this new vision was introduced by the non-peasant strata, since farmers, the country children, are unable to step back and understand these changes (this is the reason why farmers were unable to aestheticize nature). Hence, city dwellers were the first to discover-here to be understood as "invent"-rural landscape by combining three kinds of factors: natural, technic, and symbolic. Gardens, parks, become the natural backdrop for "beautiful landscapes', garden fence were to nature what frames were to paintings: institutionalizing contemplation. Beauty is set aside, suspended; that is the one we were able to admire, within our gardeners' (women for the most part) intimate spaces. But let us not forget that, until the Revolution and probably still afterward, Russian society (except for an aristocratic elite that was closely linked to the Enlightenment) was a deeply rooted rural and farming society. For most people, this change in the aesthetic approach of nature emerged with a move toward industrialization in the twentieth century, in conjunction with the institution of collective gardens. This sanctification of nature is consubstantial with the end of family farming, but this will receive no further debate. The hurtling of Soviet modernity [START_REF] Moore | Social origins of dictatorship and democracy: lord and peasant in the making of the modern world Ortar N (2005) Les multiples usages de la datcha des jardins collectifs[END_REF]) involved a three dimensional, identical, and standardized urban space, which resulted in the neutralization of real sites. A famous Soviet comedy sheds light on this reality through the story of

THE POST-SOVIET URBAN DATCHA

Guselle is 29 years old and works as a shopkeeper in Kazan; she took over a piece of land from his brother-in-law in 1998. It must be seen as an opportunity rather than as an active decision. This land was chosen for its location, near the city and on the banks of the Volga. It contains a datcha without a garden and thus without any vegetable crops and is surrounded by lawn arranged for children games. Her house, as well as that of her brother-in-law, has been built up on the site, following the European model: They have a prefabricated house; his husband assembled the panels and bounded it all with bricks; the second house has been built by professionals. However, her husband built the bagna, a traditional Russian "sauna." Here, the datcha is exclusively devoted to rest: "We don't think that we need a garden, we come here once a week to rest." Guselle explains this choice by telling us that a garden entails considerable expenses and that she and her husband would

AQ3

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AQ4

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AQ5

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AQ6

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AQ7

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AQ8

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AQ9

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AQ10

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AQ11

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AQ12

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AQ13

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AQ14

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AQ15

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AQ16

Please check the clarity of the sentence 'Gardens, parks…institutionalizing contemplation'.

Author Proof

Please check and confirm the edit made in the sentence 'This sanctification of nature…no further debate'.

AQ18

The citations 'Moore (1969), Bitoun and Dupont (2006)' has been changed

to [START_REF] Moore | Social origins of dictatorship and democracy: lord and peasant in the making of the modern world Ortar N (2005) Les multiples usages de la datcha des jardins collectifs[END_REF], [START_REF] Bitoun | Du collectif au communautaire. À propos des réseaux familiaux dans la Russie post-soviétique[END_REF]' to match the author name/date in the reference list. Please check here and in subsequent occurrences, and correct if necessary.

AQ19

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AQ20

Please check the clarity of the sentence 'New forms of sociability…for transition societies'.

AQ21

References [START_REF] Alexiévitch | La Supplication. Lattès[END_REF]), Mendras (1967)' are given in the list but not cited in the text. Please cite in text or delete from the list.

AQ22

Please provide complete details for references [START_REF] Moore | Social origins of dictatorship and democracy: lord and peasant in the making of the modern world Ortar N (2005) Les multiples usages de la datcha des jardins collectifs[END_REF]


Zeliang Zhang
email: zeliangzzl@163.com

Zebo Zhou

Jin Wu

Shuang Du

Hassen Fourati
email: hassen.fourati@gipsa-lab.grenoble-inp.fr

Fast Linear Attitude Estimation and Angular Rate Generation

Keywords: Attitude estimation, Kalman filter, Wahba's problem, angular rate estimation

This paper focuses on the design of an approach to estimate attitude Euler angles and virtual gyroscope output based on a linear Kalman filter and attitude information compensation. First, the rotation transformation is built between the body frame and the reference frame by means of an accelerometermagnetometer triad. The attitude quaternion is invoked for parameterization of orientation which leads to the Kalman filter fusing also the angular rate measurements. Furthermore, to compute the virtual-gyro output in the case of gyroscope failures and obtain bias-free angular rate estimates, virtual gyro Kalman filter is that forms a novel angular rate estimation approach. Some experiment scenarios are given to illustrate the validity and efficiency of the proposed attitude and angular rate estimation approaches.

I. INTRODUCTION

As attitude estimation is crucial for the dead reckoning navigation, great endeavors have been devoted to improving the attitude estimation accuracy and reliability. There are mainly two categories of attitude estimation approaches. One generates attitude estimates along with other navigation quantities, e.g. position, velocity and timing information [START_REF] Tasdemir | Efficient computation of the position, velocity and time estimation algorithm on a GNSS processor using interpolation[END_REF], [START_REF] Zhou | Integrated navigation system for a low-cost quadrotor aerial vehicle in the presence of rotors influences[END_REF], [START_REF] Britting | Inertial navigation system analysis[END_REF]. The other is solving attitude solution by observation vector pairs matching, typically magnetometers, accelerometers and rate-gyroscopes (MARG) sensors [START_REF] Hemerly | Attitude and heading reference system with acceleration compensation[END_REF], [START_REF] Wang | Design and implementation of an AHRS based on MEMS sensors and complementary filtering[END_REF], [START_REF] Batista | Low-cost Attitude and Heading Reference System: Filter design and experimental evaluation[END_REF]. In aerospace engineering and related geodetic applications, the latter is much more preferred avoiding the strong state parameters coupling existing in the former one [START_REF] Zhou | Optimal Recursive and Sub-Optimal Linear Solutions to Attitude Determination from Vector Observations for GNSS/Accelerometer/Magnetometer Orientation Measurement[END_REF]. For an attitude measuring system with MARG sensors, the sensor outputs usually contain the system noises due to internal and external factors [START_REF] Hemerly | Attitude and heading reference system with acceleration compensation[END_REF], [START_REF] Wang | Design and implementation of an AHRS based on MEMS sensors and complementary filtering[END_REF], [START_REF] Suh | Orientation estimation using a quaternion-based indirect kalman filter with adaptive estimation of external acceleration[END_REF], [START_REF] Thienel | A coupled nonlinear spacecraft attitude controller/observer with an unknown constant gyro bias[END_REF]. Therefore, an efficient fusion method is essential for integrating those complementary sensors. A common approach to multi-sensor data fusion is complementary filters [START_REF] Wang | Design and implementation of an AHRS based on MEMS sensors and complementary filtering[END_REF], [START_REF] Wu | Fast Complementary Filter for Attitude Estimation Using Low-Cost MARG Sensors[END_REF], [START_REF] Wang | A nonlinear complementary filter approach for MAV 3D-attitude estimation with low-cost MARG/ADS[END_REF]. The frequency domain based filter structure allows for a straightforward implementation without requiring high performance signal processing units [START_REF] Merhav | Aerospace Sensor Systems and Applications[END_REF]. Alternatively, Kalman filtering methods (KF) are intensively used for attitude estimation [START_REF] Welch | An Introduction to the Kalman Filter[END_REF]. It involves a set of mathematical equations that produce an optimal recursive solution in the sense of minimum mean square estimation [START_REF] Zhou | Equality constrained robust measurement fusion for adaptive Kalman filter based heterogeneous multi-sensor navigation[END_REF]. For nonlinear dynamic systems, the extended Kalman filter (EKF) and unscented Kalman filter (UKF) were developed for achieving the suboptimal solution of nonlinear system models [START_REF] Kandepu | Applying the unscented Kalman filter for nonlinear state estimation[END_REF], [START_REF] Marins | An extended Kalman filter for quaternion-based orientation estimation using MARG sensors[END_REF]. For those non-Gaussian noise contained systems, critical issues of KF theory are addressed and discussed in [START_REF] Zhou | Critical issues on Kalman filter with colored and correlated system[END_REF].

Gyroscope measures the angular rate of a moving object in terms of inertial principles. There is an ordinary differential equation connecting attitude quaternion and angular rate:

dq ω,k dt = 1 2 [Ω×] q ω,k-1 = 1 2     0 -ω x -ω y -ω z ω x 0 ω z -ω y ω y -ω z 0 ω x ω z ω y -ω x 0     q ω,t-1 (1)
where q ω,k is the quaternion state at the time epoch k and ω denotes an angular rate component. Combination of accelerometers and magnetometers is popular in compensating for gyroscope drift [START_REF] Suh | Orientation estimation using a quaternion-based indirect kalman filter with adaptive estimation of external acceleration[END_REF]. Alternatively, fusing accelerometers and magnetometers with gyroscope readings can greatly exempt the noise influences from attitude solution [START_REF] Wang | Design and implementation of an AHRS based on MEMS sensors and complementary filtering[END_REF]. For the aspect of computation efficiency, many representative methods have been developed, like Gradient Descent Algorithm (GDA) [START_REF] Wang | A nonlinear complementary filter approach for MAV 3D-attitude estimation with low-cost MARG/ADS[END_REF], Gauss Newton Algorithm (GNA) [START_REF] Tian | An adaptive-gain complementary filter for real-time human motion tracking with MARG sensors in free-living environments[END_REF], [START_REF] Liu | An improved quaternion GaussC Newton algorithm for attitude determination using magnetometer and accelerometer[END_REF], Levenberg-Marquadt Algorithm (LMA) [START_REF] Fourati | A nonlinear ?ltering approach for the attitude and dynamic body acceleration estimation based on inertial and magnetic sensors: Bio-logging application[END_REF], [START_REF] Fourati | Complementary observer for body segments motion capturing by inertial and magnetic sensors[END_REF], etc. addressed as the classical Wahbas problem [START_REF] Wahba | A Least Squares Estimate of Satellite Attitude[END_REF]. In addition, compensation strategies are also introduced in the fusion process in the presence of magnetic distortion [START_REF] Roetenberg | Compensation of magnetic disturbances improves inertial and magnetic sensing of human body segment orientation[END_REF] and external accelerometer [START_REF] Hemerly | Attitude and heading reference system with acceleration compensation[END_REF].

Beside attitude determination, angular rate also plays an important role ensuring the flight safety of aero-vehicles, particularly the stabilization system and flight control systems [START_REF] Zhao | Design of an Angular-Rate Compensation Based Strap-down Antenna Stabilization System[END_REF]. However, gyroscope may do not work properly under some circumstances, where the output data will be totally erroneous or unavailable. This leads to the divergence for a traditional complementary filter. The observer cannot work properly either. To continuous produce angular rates, virtual gyro is feasible by using accelerometers and magnetometers [START_REF]Building a virtual gyro[END_REF]. However, conventional methods making use of (2) to approximately compute the derivative quantity will inevitably cause large error,

q = d q dt ≈ qk -qk-1 δt (2)
Fig. 1: Attitude calculation and angular rate estimation This is due to the quaternion estimate derived from accelerometers and magnetometers contains noises which greatly degrade angular rate estimation accuracy. The paper aims to design an efficient KF structure to accommodate MARG sensors for reliable and accurate attitude as well as angular rate estimation in the scenario of gyroscope failure. Subsequently, the solved attitude quaternion is utilized as the observation model which will be further implemented in KF with the angular rate state model established by gyroscope readings. Conversely, when the gyroscope failure occurs, the attitude information derived from accelerometers and magnetometers will be applied to recover the angular rate information through a dedicated KF. The rest of paper is organized as follows: Section II depicts the principle of attitude determination with MARG sensors. Angular rate estimation strategy is proposed in the case of gyroscope failure in Section III. Section IV presents the experiments and analysis. Finally, conclusions Section V.

II. ATTITUDE ESTIMATION WITH MARG SENSORS

In this section, the structure of attitude is constructed based on KF with the Wahba's solution through the combination of tri-axial accelerometers and magnetometers and angular rate from Fig. 1.

Estimating relations between body frame (denoted as bframe, right-front-up) and reference frame (denoted as r-frame, east-north-up, i.e. ENU) using accelerometers and magnetometers yields attitude information, which is self-contained in transition matrix. Two sets of vector observation pairs related to the transformation between b and r frames are established as follows:

a b = C b r a r a b = C b r a r (3)
where

a b = (a x , a y , a z ) T , m b = (m x , m y , m z ) T , a r = (0, 0, -g) T , m r = (0, m N , m U )
T denote the normalized observation vectors of accelerometers and magnetometers in b and r frames, respectively. C b r is the direction cosine matrix (DCM) (simplified as C). The superscript T denotes the transpose operation.

To find the optimal attitude matrix from multiple vector observations, great deals of efforts are made and most of them can be traced back to the Wahba's problem [START_REF] Wahba | A Least Squares Estimate of Satellite Attitude[END_REF], which aims to minimize the loss function defined by

L(C) = 1 2 n i=1 a i b i -Cr i 2 (4)
where C denotes the optimal DCM and || • || stands for the Euclidean norm. b i and r i denote the normalized observation vectors in body frame b and reference frame r, respectively. a i is the weight of the i-th vector observation pair satisfying

n i=1 a i = 1 (5)
To solve Wahba's problem and improve the computation efficiency, various of methods have been developed such as Davenport's q-method [23], Markley's fast optimal attitude matrix (FOAM) method [START_REF] Markley | Attitude determination from vector observations: A fast optimal matrix algorithm[END_REF], Shuster and Oh's quaternion estimator (QUEST) algorithm [START_REF] Shuster | Three-axis attitude determination from vector observations[END_REF] etc. In this contribution, we introduce the fast linear attitude estimation method (FLAE) to estimate the attitude by using accelerometer/magnetometer vector pairs [START_REF] Wu | Fast Linear Quaternion Attitude Estimator Using Vector Observations[END_REF]. It is faster than existing representative algorithms. The conventional Wahba's problem is then converted to the following equations with respect to quaternions as

√ a 1 D b 1 = √ a 1 CD r 1 √ a 2 D b 2 = √ a 2 CD r 2 (6)
in which D i = (D ix , D iy , D iz )(i = 1, 2) are the observation vectors. Obviously, (3) is equivalent to [START_REF] Batista | Low-cost Attitude and Heading Reference System: Filter design and experimental evaluation[END_REF]. Converting Wahba's problem to an eigenvalue problem as [START_REF] Wu | Fast Linear Quaternion Attitude Estimator Using Vector Observations[END_REF] Wq = (1 + ε)q

where q = (q0, q1, q2, q3) T denotes attitude quaternion vector and ε denotes the error factor. W is a matrix related to observer vectors and its relevant definition and derivations can be found in [START_REF] Wu | Fast Linear Quaternion Attitude Estimator Using Vector Observations[END_REF], [START_REF] Caruso | Applications of magnetic sensors for low cost compass systems[END_REF]. Apparently, as 1 + ε is an eigenvalue of W , the problem is shifted to finding the eigenvalue that is closest to 1. To calculate the eigenvalue of the matrix W, the characteristic polynomial of W is defined as

f (λ) ∆ = det(W -λI 4×4 ). (8)
det(•) represents the determinant. Thus it can be further derived to

f (λ) = λ 4 + τ 1 λ 2 + τ 2 λ + τ 3 (9)
and its symbolic solution is calculated by

λ 1 = 1 2 √ 6   T 2 --T 2 2 -12τ 1 - 12 √ 6τ 2 T 2   λ 2 = 1 2 √ 6   T 2 + -T 2 2 -12τ 1 - 12 √ 6τ 2 T 2   λ 3 = - 1 2 √ 6   T 2 + -T 2 2 -12τ 1 + 12 √ 6τ 2 T 2   λ 4 = - 1 2 √ 6   T 2 --T 2 2 -12τ 1 + 12 √ 6τ 2 T 2   ( 10
)
where the parameter τ 1 , τ 2 , τ 3 and T 2 are all detailed in [START_REF] Wu | Fast Linear Quaternion Attitude Estimator Using Vector Observations[END_REF].

λ is chosen nearest to 1. In this way, the solving process of is significantly shortened.

Defining N and transforming N to N via elementary row operations, we obtain

N = W -λI 4×4 → N =     1 0 0 χ 0 1 0 ρ 0 0 1 υ 0 0 0 ζ     (11)
Thereby, the fundamental solution system is given by:

q =     q 0 q 1 q 2 q 3     =     χ ρ υ -1     (12)
with its norm of

q = χ 2 + ρ 2 + υ 2 + 1. (13)
With the attitude quaternion solution calculated from [START_REF] Merhav | Aerospace Sensor Systems and Applications[END_REF], the linear observation model at epoch k can be established as:

l k = H k x k + ε k (14)
where l k is the observation vector obtained from the (14);

x k denotes the quaternion state to be estimated; the design matrix H k connecting the state vector to the observation vector becomes unit identity matrix I with dimensions of 4×4; ε k is Gaussian distributed with the variance of Q ε k . A tri-axial gyroscope senses the 3D angular rate of a certain object with outputs in its body frame as ω = (ω x , ω y , ω z ) T . For a rigid body, its rotation can be alternatively represented by quaternion due to its numerical computation stability. The quaternion and the angular rate are associated with [START_REF] Tasdemir | Efficient computation of the position, velocity and time estimation algorithm on a GNSS processor using interpolation[END_REF]. Discretized equation can be modelled as

q ω,k = 1 2 δt[Ω×]q ω,k-1 + q ω,k-1 (15)
where δt denotes the sampling interval of gyroscope. Thus (15) can be treated as a dynamic model of the KF,

x k = Φ k,k-1 x k-1 + w k (16)
where Φ k,k-1 denotes the transition matrix transferring the previous one state information into that of the current one.

According to [START_REF] Marins | An extended Kalman filter for quaternion-based orientation estimation using MARG sensors[END_REF], the transition matrix is then expressed by:

Φ k,k-1 = 1 2 δt[Φ×] + I 4×4 (17)
w k denotes the zero-mean process noise with variance of Q w k . Then the predicted state and its covariance matrix are respectively computed by:

xk = Φ k,k-1 xk-1 (18)
Q xk = Φ k,k-1 Q xk-1 (Φ k,k-1 ) T + Q w k ( 19
)
The time update set of KF equations are:

xk = xk + K k (l k -H k xk ) (20)
Q xk = (l k -H k xk )Q xk ( 21
)
K k = Q xk H T k (H k Q xk H T k ) -1 + Q ε k ( 22
)
where xk = qk and Q xk = Q qk are KF estimate and its covariance, respectively. K k is the so-called gain matrix.

As time epoch increasing, the quaternion is estimated by implementing ( 18)-( 22).

III. ANGULAR RATE ESTIMATION WITH VIRTUAL GYROSCOPE A. Virtual gyroscope based Kalman Filter

When the gyroscope works improperly, angular rate information may be incorrect. Attitude quaternion can still be acquired with the solution to (3), as if accelerometer and magnetometer runs consistently and normally. To smooth the calculated quaternion, a virtual gyroscope based KF is established. Supposing that consecutive first-order derivative of quaternion keeps invariant, the state equation can be modelled as:

qk q k = I 4×4 0 4×4 δtI 4×4 I 4×4 qk-1 q k-1 + wk (23)
where the state matrix is chosen with xk = ( qT k q T k ) T . In order to distinguish it from the previous KF state in Section II, we denote the x with the superscript ∼ as the state vector consisting of quaternion and its derivative. Thereby, the corresponding transition matrix is

Φk,k-1 = I 4×4 0 4×4 δtI 4×4 I 4×4 (24)
and wk denotes the zero-mean process noise with covariance matrix of Q wk . The quaternion vector obtained from the ( 12) is still used as observation vector, thus linear observation model at epoch k is established as:

l k = Hk xk + εk (25)
where the design matrix Hk becomes such as:

Hk = (0 4×4 I 4×4 ) (26)
and εk denotes the zero-mean observation noise with variance of Q εk . The new Kalman filter's implementation process is similar to ( 18)- [START_REF]Building a virtual gyro[END_REF].

B. Angular rate estimation

With quaternion and its first derivative obtained from new KF, the angular rate can be estimated according to the arithmetic of quaternion as follows:

Ωk = 2 qk ⊗ q * k-1 (27)
where ⊗ represents the quaternion product, and the superscript * stands for the conjugate of quaternion. It can also be solved by means of Euler Angles according to the relation between quaternion and Euler Angles as follows:

φ = arctan 2(q 2 q3 + q0 q1 ) q2 0 -q2 1 -q2 2 + q2 3 (28)
θ = arcsin(2(q 0 q2 -q1 q3 )) (29)
ψ = arttan 2(q 1 q2 + q0 q3 ) q2 0 + q2 1 -q2 2 -q2 3 (30)
φ, θ and ψ denote roll, pitch and yaw estimated angles, respectively. Then the angular rate is acquired by differential operation of Euler angles referring to its definition that:

ωx,k = d φ dt ≈ φk -φk-1 δt (31) ωy,k = d θ dt ≈ θk -θk-1 δt (32) ωz,k = d ψ dt ≈ ψk -ψk-1 δt (33)

IV. EXPERIMENTS AND RESULTS

An experimental platform is designed to conduct various experiments. Uranus2 produced by Beijing Beyond Core Electronic Technology Co., Ltd. provides the output of tri-axial gyroscope, accelerometer and magnetometer. TTL to USB module is applied so that the sensor data from Uranus2 can be saved into computer. MATLAB r2016 is used for data processing and analysis. We put the MARG element at rest for a while, then we rotate it, trying to keep around the center of the mass. The samples are collected by using the above equipment and the raw data is drawn in Fig. 2.

Figure 3 shows the solution to attitude quaternion obtained with acceleration and magnetometer, which is very noisy. Time consumption of QUEST and FLAE is presented in Table I. Obviously, Quaternion gets more smooth and has better precision after MARG-KF, when gyroscope measurements are fused. The corresponding Euler angles are presented in Fig. 4. Three methods are employed to estimate angular rate in the case of absent gyroscope readings for comparison purpose:

1) Non-filtered quaternion (NFQ) with ( 2) and ( 27); 2) Non-filtered Euler angles (NFEA) with ( 28)-(33); 3) Our Proposed virtual gyroscope KF (VGKF).

Figure 5 shows the derivative of quaternion in (2) and the result of NFQ is shown in Fig. 6. The estimated quaternion derivatives are too noisy thus cover the true signals. Therefore, it is not suitable for calculating angular rate.

Seen from Fig. 7, NFEA is also unreliable to convert the quaternions directly to Euler angles without filtering. The results and reasons are very similar to NFQ. The reason why angular rate cannot be directly calculated is that the two consecutive quaternions and their first derivations are very sensitive to the quaternion errors which will further be significantly augmented thus analytically propagate into the estimated results. The proposed VGKF is designed to solve such problem. Figure 8 shows the quaternion solution of the proposed VGKF. Though it is not as good as the original gyroscope readouts, its uncertainty has been extensively minimized. Likewise, as shown in Fig. 9, the accuracy of its derivative has been significantly improved as well. It should also be noted that VGKF is effective and reaches a good consistency with the actual angular rate from gyroscope readings as shown in Fig. 10. The state model of attitude is constructed based on Kalman Filter theory. Two different structures of Kalman filtering are designed to obtain accurate attitude estimates as well as the angular rates that significantly determines the robustness of the system in case of failures and faults in rate-gyroscope i.e. the solution to the angular rate estimation is also put forward for the absence of gyroscope data. Experimental results show that the proposed solution is effective. In the future, fault detection, isolation and error compensation will be comprehensively investigated and applied to make MARG sensor's fusion results more accurate and reliable.

ACKNOWLEDGMENT

Fig. 2 :

 2 Fig. 2: Raw data from Uranus2.

Fig. 3 :Fig. 4 :

 34 Fig. 3: Quaternion of Wahba's solution calculated with accelerometer and magnatometer (blue line) and MARG-KF (red line)

Fig. 5 :

 5 Fig. 5: The derivative of quaternion in (2).

Fig. 6 :Fig. 7 :Fig. 8 :

 678 Fig. 6: Angular rates of NFQ (red line) and references (blue line)

Fig. 9 :Fig. 10 :

 910 Fig. 9: The derivative of quaternion in (20) (blue line) and that in VGKF (red line)

  This work is supported by the National Natural Science Funds of China (No. 41604025 and 41704029), the State Key Laboratory of Geodesy and Earth's Dynamics (Institute of

TABLE I :

 I Time consumption of QUEST and FLAE

	Time Consumpution (×10 -4 s)
		QUEST	FLAE
	1	0.67	0.54
	2	0.79	0.49
	3	0.92	0.47
	4	0.88	0.54
	5	0.72	0.46
	6	0.73	0.55
	7	0.60	0.34
	8	0.74	0.42
	9	0.80	0.39
	10	0.63	0.21
	11	0.79	0.44
	12	1.43	0.77


Nabil Hameurlain
email: nabil.hameurlain@univ-pau.fr

An Optimistic Approach for the Specification of more Flexible Roles Behavioural Compatibility Relations in MAS

Keywords: Rôles, interaction, compatibilité optimiste, substitutabilité Roles, interaction, components, optimistic compatibility, substitutability

Dans cet article, nous nous focalisons sur une nouvelle approche de définition d'une compatibilité plus flexible des rôles dans les SMA. Nous proposons une architecture formelle pour la spécification des rôles et leur composition, prenant en compte la préservation de propriétés comme la complétion et la terminaison propre des rôles. Nous mettons en évidence le lien existant entre la compatibilité et la substitutabilité des rôles, et plus particulièrement, nous montrons que les relations de compatibilité ainsi définies sont préservées par la substitutabilité.

Introduction

Roles are basic buildings blocks for defining the organization of multi-agent systems (MAS), together with the behaviour of agents and the requirements on their interactions. Usually, it is valuable to reuse roles previously defined for similar applications, especially when the structure of interaction is complex. To this end, roles must be specified in an appropriate way, since the composition of independently developed roles can lead to the emergence of unexpected interaction among the agents.

Although the concept of role has been exploited in several approaches [START_REF] Dastani | Role Assignment in Open Agent Societies[END_REF][START_REF] Cabri | BRAIN: a Framework for Flexible Role-based Interactions in Multi-agent Systems[END_REF][START_REF] Zambonelli | Developing Multiagent Systems : The Gaia Methodology[END_REF] in the development of agent-based applications, no consensus has been reached about what is a role and how it should be specified and implemented. In our previous work [START_REF] Hameurlain | Specification of Role-based Interactions Components in MAS[END_REF], we have shown that the facilities brought by the Component Based Development (CBD) approach [START_REF] Szyperski | Component Software-Beyond Object-Oriented Programming[END_REF] fit well the issues raised by the use of roles in MAS. In this context, we have proposed RICO (Role-based Interactions COmponents) model for specifying complex interactions, and study the compatibility semantics of roles. The RICO model is based on the Component-nets formalism which combines Petri nets and the componentbased approach.

In this paper, we focus on a new approach to the definition of role-components compatibility, and provide a formal framework for modelling roles and their composition. The contributions of this paper are: [START_REF] Alfaro | Interface Automata[END_REF] to provide a new approach to the definition of more flexible rolecomponents compatibility and substitutability relations, [START_REF] Dastani | Role Assignment in Open Agent Societies[END_REF] to show the existing link between compatibility and substitutability relations, namely the preservation of the compatibility by substitutability.

Roles modelling 2.1 The Component-nets formalism

Backgrounds on Labelled Petri nets. A marked Petri net N = (P, T, W, M N ) consists of a finite set P of places, a finite set T of transitions where P ∩ T = ∅, a weighting function W : P × T ∪ T × P → N, and M : P ⎯→ N N is an initial marking. A transition t ∈ T is enabled under a marking M, noted M (t >, if W(p, t) ≤ M(p), for each place p. In this case t may occur, and its occurrence yields the follower marking M', where M'(p) = M(p) -W(p, t) + W(t, p), noted M(t> M'. The enabling and the occurrence of a sequence of transitions σ ∈ T * are defined inductively. The preset of a node x ∈ P ∪ T is defined as • x = {y ∈ P ∪ T, W(y, x) ≠ 0}, and the postset of x ∈ P ∪ T is defined as x • = {y ∈ P ∪ T, W(x, y) ≠ 0}. We denote as LN = (P, T, W, M N , l) the (marked, labelled) Petri net in which the events represent actions, which can be observable. It consists of a marked Petri net N = (P, T, W, M N ) with a labelling function l: T ⎯→ A ∪ {λ}. Let ε be the empty sequence of transitions, l is extended to an homomorphism l * : T * ⎯→ A * ∪ {λ} in the following way: l(ε) = λ where ε is the empty string of T * , and l * (σ.t) = l * (σ) if l(t) ∈ {λ}, l * (σ.t) = l * (σ).l(t) if l(t) ∉ {λ}. In the following, we denote l * by l, LN by (N, l), and if LN = (P, T, W, M N , l) is a Petri net and l' is another labelling function of N, (N, l') denotes the Petri net (P, T, W, M N , l'), that is N provided with the labelling l'. A sequence of actions w ∈ A * ∪ {λ} is enabled under the marking M and its occurrence yields a marking M', noted M(w>> M', iff either M = M' and w = λ or there exists some sequence σ ∈ T * such that l(σ) = w and M(σ> M'. The first condition accounts for the fact that λ is the label image of the empty sequence of transitions. For a marking M, Reach (N, M) = {M'; ∃ σ ∈ T * ; M(σ> M'} is the set of reachable markings of the net N from the marking M.

Components nets (C-nets).

A Component-net involves two special places: the first one is the input place for instance creation of the component, and the second one is the output place for instance completion of the component. A C-net (as a server) makes some services available to the nets and is capable of rendering these services. Each offered service is associated to one or several transitions, which may be requested by Cnets, and the service is available when one of these transitions, called accepttransitions, is enabled. On the other hand it can request (as a client) services from other C-net transitions, called requesttransitions, and needs these requests to be fulfilled. These requirements allow focusing either upon the server side of a C-net or its client side.

Notation. We denote by [I] and [O],

which are considered as bags, the markings of the Input and the Output place of CN, and by Reach (CN, [I]), the set of reachable markings of the component-net CN obtained from its initial marking M N within one token in its Input place I. Besides, when we deal with the graphical representation of the C-nets, we use ! and ? keywords for the usual sending (required) and receiving (provided) services together with the labeling function l instead of the two labeling functions l Prov and l Req .

Definition 2.2 (soundness)

Let CN = (P ∪ {I, O}, T, W, M N , l) be a Component- net (C-net).
CN is said to be sound iff the following conditions are satisfied:

1. Completion option: ∀ M ∈ Reach(CN, [I]), [O] ∈ Reach(CN, M).

Reliability option

: ∀ M ∈ Reach(CN, [I]), M ≥ [O] implies M = [O].
The Completion option states that, if starting from the initial state, i.e. activation of the C-net , it is always possible to reach the marking with one token in the output place O. Reliability option states that the moment a token is put in the output place O corresponds to the termination of a C-net without leaving dangling references.

Composition of C-nets. The parallel composition

of C-nets, noted ⊕ : C-net × C-net → C-net,
is made by communication places allowing interaction through observable services in asynchronous way. Given a client C-net and a server C-net, it consists in connecting, through the communication places, the request and the accept transitions having the same service names: for each service name, we add one communication-place for receiving the requests/replies of this service. Then, all the accept-transitions labelled with the same service name are provided with the same communication-place, and the client C-net is connected with the server C-net through these communication places by an arc from each request-transition towards the suitable communicationplace and an arc from the suitable communication-place towards each accept-transition.

Specification of roles

In our RICO model [START_REF] Hameurlain | Specification of Role-based Interactions Components in MAS[END_REF], a role component is considered as a component providing a set of interface elements (either attributes or operations, which are provided or required features necessary to accomplish the role's tasks), a behaviour (interface elements semantics), and properties (proved to be satisfied by the behaviour).

In this paper, we only consider behavioural interface of roles that is their behaviour specified by the C-nets together with the set of (provided and required) services. • Serv is an interface, a set of public elements, through which RC interacts with other role components. Serv = (Req, Prov), where Req is a set of required services, and Prov is the set of provided services by RC. Since the life-cycle of roles is specified by C-nets, we say that a component role satisfies the completion (resp. terminates successfully) if and only if its behaviour that is its underlying C-net satisfies the completion option (resp. terminates successfully). The composition of two role-components is also a rolecomponent, and this composition is associative.

Definition 2.4 (Roles composition)

A Role RC = (Behav, Serv) can be composed from a set of (primitive) Roles, RC i = (Behav i , Serv i ), i = 1, …, n, noted RC = RC 1 ⊗… ⊗RC n , as follows:

• Behav = Behav 1 ⊕ …⊕ Behav n .
• Serv = (Req, Prov), Req = ∪ Req i , and Prov = ∪Prov i , i=1, …, n.

Compatibility of roles

In component-based software engineering, classical approaches for components compatibility deal with components composition together with their property preservation [START_REF] Alfaro | Interface Automata[END_REF]. In our previous work, we have used this approach for role-based interaction components and study some compatibility relations [START_REF] Hameurlain | Formalizing Compatibility and Substitutability of Role-based Interactions Components in MAS[END_REF]. In this paper, the basic idea behind the optimistic approach for rolecomponents compatibility is to consider explicitly the context of use of roles (environment) in the definition of roles compatibility relations. First, let define the notion of role's environment. We let ENV(RC), the set of the environments of the role component RC.

The role component RC 1 is considered an environment of RC 2 iff both their sets of interfaces completely match.

Given a role-component and its environment, it is possible to reason about the completion and the proper termination of their composition. Based on that, we define two notions of usability:

Definition 3.2 (usability)

1. RC is weakly usable iff ∃ Env ∈ ENV(RC), Env ⊗ RC satisfies the completion option. We say that Env weakly utilizes RC.

2. RC is strongly usable iff ∃ Env ∈ ENV(RC), Env ⊗ RC terminates successfully. We say that Env strongly utilizes RC. RC' is not weakly usable. 1 The names of transitions are drawn into the box.

Example 1: Let's take the example of the ticket service and the customer. Figure 1 shows RC 1 representing the behaviour of the customer, and RC 2 the behaviour of the Ticket-service. The Ticket service initiates the communication by sending (two) Tickets and waits of their payment (VISA and/or eCash). By receiving the Tickets, the customer determines the kind of payment of these two tickets. It is easy to prove that roles RC 1 and RC 3. RC' is not weakly usable since there is no environment which can weakly utilize it. Indeed, roles RC 3 and RC 4 are the two possible roleenvironments of RC' (according to the behaviour of RC' described by the language {Ticket!.Visa?, Ticket!.eCash?}), nevertheless, for instance the occurrence of the sequence {Ticket!.Ticket?.eCash!} in RC 3 ⊗ RC' (as well as in RC 4 ⊗ RC') yields a deadlock-marking that is a marking where no transition is enabled. This is because of an error in role-component RC': an internal decision is made (either Visa? or eCash?), when sending the Ticket, and not communicated properly to the environment [START_REF] Alfaro | Interface Automata[END_REF].

We are finally ready to give adequate definitions for roles behavioural optimistic compatibility relations, which are based on the weak and the strong usability.

Definition 3.3 (compatibility)

Let RC 1 and RC 2 be two weakly (resp. strongly) usable roles. RC 1 and RC 2 are Weakly (resp. Strongly) Optimistic Compatible, noted RC 1 ≈ WOC RC 2 (resp. RC 1 ≈ SOC RC 2 ), iff RC 1 ⊗ RC 2 is weakly (resp. strongly) usable.

Example 2:

As an example, it is easy to prove that roles RC 1 and RC 2 , shown in figure 1, are weakly optimistic compatible that is RC 1 ≈ WC RC 2 holds since RC 1 ⊗ RC 2 is weakly usable. Indeed, RC 1 ⊗ RC 2 satisfies the completion option. Besides, the two roles RC 3 and RC 5 shown in figure 2 are strongly optimistic compatible that is RC 3 ≈ SOC RC 5 holds since RC 3 ⊗ RC 5 is strongly usable. Indeed, RC 3 ⊗ RC 5 terminates successfully.

Substitutability of roles

We show the existing link between compatibility and substitutability concepts, and namely their combination, which seems necessary, when we deal with incremental design of usable components-role. Our main interest is to define behavioural subtyping relations (reflexive and transitive) capturing the principle of substitutability [START_REF] Liskov | A Behavioral Notion of Subtyping[END_REF]. We define two subtyping relations based upon the preservation of the (weakly and strongly) utilizing of the former role by any role of its environment.

Definition 4.1 (behavioural subtyping)

Let RC i = (Behav i , Serv i ), Serv i = (Req i , Prov i ), i=1

Conclusion and related work

The aim of this paper is to present a new and optimistic approach to the definition of role-components behavioural compatibility and substitutability relations. The paper provides a framework for modelling usable rolecomponents together with their composition. This framework is discussed in terms of roles compatibility and substitutability relations. We furthermore investigated the link between compatibility and substitutability relations by showing that substitutability is compositional and the compatibility is preserved by the substitutability.

Related work.

The optimistic approach to the definition of components compatibility has been originally introduced in [START_REF] Alfaro | Interface Automata[END_REF] for interface automata. Unlike traditional uses of automata, the authors proposed an optimistic approach to automata composition. Two interface automata are (optimistic) compatible, if there exists a legal environment for these two automata, i.e. an environment such that no deadlock state is reachable in the automata obtained by the composition of the two interface automata and that environment. This work is close to ours, since our weak optimistic compatibility relation for role-components is related to the optimistic compatibility relation defined for automata composition. Our approach can be seen as an extension of this work, since it deals in addition with strong optimistic compatibility, which is related to the proper termination property. In [START_REF] Martens | Analyzing Web Service Based Business[END_REF], the concept of usability is used for analyzing web service based business processes. The authors defined the notion of usability of workflow modules, and studied the soundness of a given web service, considering the actual environment it will by used in. Based on this formalism together with the notion of usability, the authors present compatibility and equivalence definitions of web services. This approach is close to ours, since the compatibility of two workflow modules is related to our strong optimistic compatibility of rolecomponents. Our approach can be seen as an extension of this work, since we define in addition the notion of weak optimistic compatibility and study the existing link between compatibility and substitutability.

Definition 2 . 1 ( 2 .

 212 C-net) Let CN = (P ∪ {I, O}, T, W, M N , l Prov , l Req ) be a labelled Petri net. CN is a Component-net (C-net) if and only if: l. The labelling of transitions consists of two labelling functions l Prov and l Req , such that: l Prov : T ⎯→ Prov ∪ {λ}, where Prov ⊆ A is the set of provided services, and l Req : T ⎯→ Req ∪ {λ}, where Req ⊆ A is the set of required services. Instance creation: the set of places contains a specific Input place I, such that • I = ∅, 3. Instance completion: the set of places contains a specific Output place O, such that O • = ∅.

Definition 2 . 3 (

 23 Role Component) A Role Component for a role ℜ, noted RC, is a 2-tuple RC = (Behav, Serv), where, • Behav is a C-net describing the lifecycle of the role ℜ.

Definition 3 . 1 (

 31 Environment) Let RC 1 = (Behav 1 , Serv 1 ) and RC 2 = (Behav 2 , Serv 2 ), be two roles such that Serv i = (Req i , Prov i ), i=1, 2.CP 2 is called an environment-role (or environment) of CR 1 , and vice versa, iff Req 1 = Prov 2 , Req 2 = Prov 1 .

Fig 1 .Fig 2 .

 12 Fig 1. RC 1 weakly utilizes RC 2 , where l(a)= Ticket, l(b) = Visa, l(c) = eCash. 1

  Compatibility relations form a hierarchy: ≈ SOC ⇒ ≈ WOC

  2 are weakly usable, since RC 1 weakly utilizes RC 2 and vice versa.

	The role RC 1 is not strongly usable, since
	the unique (weakly usable) environment
	of RC 1 is the role RC 2 , and RC 1 ⊗ RC 2
	satisfies the completion option but does
	not terminate successfully. In figure 2, the
	ticket service RC 5 initiates de
	communication by sending one Ticket
	and waits of the payment (either Visa
	or eCash). The role components RC 3
	and RC 4 are two examples of the
	customer's behaviour. By receiving the
	Ticket, they solve an internal conflict
	and determine the kind of payment. The
	roles RC 3 and RC 5 (resp. RC 4 and RC 5 )
	are strongly usable, since for instance
	RC 3 strongly utilizes RC 5 (resp. RC 4
	strongly utilizes RC 5 ) and vice versa. Last
	but not least, let us take the ticket service
	RC' shown in figure

  ,2, be two roles, such that: Prov 1 ⊆ Prov 2 and Req 1 ⊆ Req 2 2 . 1. RC 2 is less equal to RC 1 w.r.t Weak Substitutability, denoted RC 2 ≤ WS RC 1 , iff ∀ Env ∈ ENV(RC 1 ), Env weakly utilizes RC 1 ⇒ Env weakly utilizes RC 2 . 2. RC 2 is less equal to RC 1 w.r.t Weak Substitutability, denoted RC 2 ≤ SS RC 1 , iff ∀ Env ∈ ENV(RC 1 ), Env strongly utilizes RC 1 ⇒ Env strongly utilizes RC 2 . As an example, consider the roles RC 4 and RC 1 . RC 1 ≤ WS RC 4 holds since the unique environment that weakly utilizes RC 4 is the role RC 5 , and RC 5 ⊗ RC 1 satisfies the completion option. These two roles RC 1 and RC 4 are not related by the strong subtyping relation that is RC 1 ≤ SS RC 4 does not hold, since RC 5 ⊗ RC 1 does not terminate successfully. Last but not least, consider the roles RC 4 and RC 3 ; RC 3 ≤ SS RC 4 holds since the role RC 5 (which is the unique environment) that strongly utilizes RC 4 also strongly utilizes RC 3 . Indeed RC 5 ⊗ RC 3 terminates successfully. Prov 2 ⊆ Req ∩ Prov 1 . This condition is due to the fact that if the environment utilizes services provided by CR 2 that are not provided by CR 1 , then it would be possible that new incompatibilities arise in the processing of these provided services. Serv 1 ), RC 2 = (Behav 2 , Serv 2 ) be two roles where Serv i = (Req i , Prov i ), i = 1, 2. Let Env = (Behav, Serv) such that Req ∩ Prov 2 ⊆ Req ∩ Prov 1 . 1. Env ≈ WOC RC 1 and RC 2 ≤ WS RC 1 ⇒ Env ≈ WOC RC 2 and Env ⊗ RC 2 ≤ WS Env ⊗ RC 1 . 2. Env ≈ SOC RC 1 and RC 2 ≤ SS RC 1 ⇒ Env ≈ SOC RC 2 and Env ⊗ RC 2 ≤ SS Env ⊗ RC 1 .

	utilizes the former role is also able to
	weakly (resp. strongly) utilize the new
	role.
	Weak (resp. Strong) Substitutability guarantees the transparency of changes of roles to their environment. In both weak and strong subtyping relations, the (super-) role component RC 1 can be substituted by a (sub-) role component RC 2 and the environment of the former role RC 1 will not be able to notice the difference since: (a) the sub-role has a larger set of required and provided services (Req 1 ⊆ Req 2 and Prov 1 ⊆ Prov 2 ) than the super-role, and (b) any environment that weakly (resp. strongly) compatibility preservation) Let RC 1 = services that is: Req ∩ Theorem 4.1 (compositionality and Example 3: Property 4.1 (Hierarchy of subtyping) The relations ≤ H , H ∈ {WS, SS}, are preorder (reflexive and transitive) and form a hierarchy: ≤ SS ⇒ ≤ WS . The following core theorem of this paper states two fundamental properties of roles compatibility and substitutability relations. First, substitutability relations are compositional: in order to check if Env ⊗ RC 2 ≤ H Env ⊗ RC 1 , H ∈{WS, SS}, it suffices to check RC 2 ≤ H RC 1 , since the latter check involves smaller roles and it is more efficient. Second, substitutability and compatibility relations are related as follows: we can always substitute a role CR 1 with a sub-role CR 2 , provided that RC 1 and RC 2 are connected to the environment Env = (Behav, Serv) by the same provided (Behav 1 ,

The sub-role component has a larger set of (required and provided) services (Req 1 ⊆ Req 2 and Prov 1 ⊆ Prov 2 ) than the super-role component.