Jean-Claude Croizé

Academic Views on the Economics of Construction: French Variations (1920-1970)

INTRODUCTION

The first half of the 20 th century in France saw few doctorate theses written concerning the issue of housing, and even fewer placing emphasis on the role played by the compared economics of construction projects. While the rental crisis and financing problems were subject to in-depth developments, any approach examining the respective costs of different types of housing generally remained ignored. A detailed study of sources reveals that only two theses defended in Paris have made the economics of projects a fundamental aspect of their argument. The first dates back to 1921 and was written by Henri Sellier (1883Sellier ( -1943)), who had graduated from a major business school, was an experienced socialist politician and an administrator in the Office Public d'Habitations à Bon Marché du Département de la Seine (Seine department affordable housing service) created in 1916 to manage the construction of social housing in the Paris suburbs. The second was in 1945 by Claude Olchanski, an engineer having graduated from the Ecole Centrale in 1935 and who fairly rapidly extended his education by a doctoral curriculum. The common points of these two theses are that they were focused in the problems of social housing, written in the critical moments following two world wars and published -a fairly rare occurrence. Those points aside, they were completely dissimilar, whether in terms of the education and personality of the authors, the style and contents of the presented economic argument or, finally, the resulting conclusions as to the type of project that should be pursued. Concerning the scientific canons of applied economics, the approach taken by C. Olchanski, essentially based on affirmations of principle without any real concrete observations, is clearly far less convincing than that taken by H. Sellier. However, we shall show that the former literally annihilated the position held by his predecessor and that its characterising methods continued to be accepted by university juries over the following 20 years. The argument conforms to an a priori conception of town planning and the architecture of housing. Its function is more illustrative than demonstrative and this raises the question of economics as a scientific discipline applied to town planning and construction.

THE THESIS BY HENRI SELLIER (1921)

H. Sellier's thesis is developed over nearly a thousand pages, without counting the 250 pages of appended documents. Rather than being exclusively concerned by the Paris region, the text proposes a global reading ABSTRACT: Depending on whether they date from the 1920s or the 1940s and later, doctoral theses using the compared economics of construction projects as a central argument are characterised by a considerable difference in tone and content. During the 1920s, single family homes were recommended whereas during the 1940s and later, it was housing blocks that were advocated. Although not at all based on concrete observations, the interpretation that prevailed as from the 1940s has nevertheless continued to reign and contributed to justifying the policy then chosen by the public authorities in terms of new buildings. However, this interpretation has also contributed to maintaining a gap between the consensus of the elites and the popular perception of the problem. of the "housing crisis" in France as well as an approach to housing and town planning policies in 18 countries, essentially European but also including the United States, Canada and Australia. Apart from its analytical side, the thesis also aims to support a concrete project concerning the urbanisation of the city's suburbs and the role to be held by the then fledging social housing sector in France. From this point of view, one of the decisive aspects corresponds to the economic equation of the works being promoted. The policy position is dryly laid out in just a few pages hidden away in the heart of the text and then illustrated at great length towards the end of the thesis by the presentation of 15 projects concerning new social housing complexes. H. Sellier begins by dealing with the issue of the cost of land. Citing Greater London and Greater New-York as examples, he simply discards the vision of the dense pedestrian city and the inevitable overcrowding that this would generate. He bases himself on the reorganisation of transport systems to justify the spatial spread of large cities: "Today […] the reorganisation of transport systems makes it possible to imagine the creation of worker agglomerations in suburban regions as yet not reached by industrial appreciation" (Sellier 1921, p. 251). In these areas undergoing urbanisation, sites are negotiated at between "four and 20 Francs a metre". H. Sellier specifically mentions an average price of 10 Francs in the town where he is mayor: Suresnes, adjoining Paris on the west bank of the river Seine and facing the Bois de Boulogne. These price conditions authorise very well spaced urban layouts in which single family homes play a fundamental role, even in the context of social housing. Moving on to the economics of construction, H. Sellier contrasts housing blocks that need to be built from heavy masonry, such as the programmes that were then being planned for construction on Paris' old fortifications, with single family homes that could by then be built using lighter reinforced concrete or breeze block structures able to guarantee satisfactory sustainability and comfort. In these conditions, he stated that for a three-room house corresponding to the canonical social housing volume, it was possible to obtain a single family home at a cost of 28 000 Francs as opposed to 40 000 Francs for a unit in a social housing block. This obviously left a considerable margin to absorb the added cost of single family homes resulting from the installation of networks: roads and services, sewers, water and gas pipework. Although he believed that these costs should, much like public highways, be assumed by local authorities, H. Sellier finally decided to incorporate them at an added cost estimated at "4 000 to 5 000 Francs" per house. Finally, by integrating the cost of the land on the basis of 300 square metres at 10 Francs a metre for an individual plot, he arrived at an all-in price for a single family home of around 35,000 Francs as against over 40 000 Francs for an equivalent apartment in a housing block. The spatial organisation proposed for these housing estates was largely inspired by the experience of the English garden cities and the German Gartenstädte. H. Sellier makes particular reference to the "remarkable book by R. Unwin, Town Planning in Practice" (Sellier 1921, p. 258), from which he quotes extensively (particularly, pp. 273-284) and includes ten drawings. This partial translation represents an original and is quite different from the language adopted for the same passages in the French version of the book which was only published in 1923.

The very insistent reference to R. Unwin's text specifically aims to justify certain composition principles. For reasons concerning the economics of the project and urban aesthetics, the spatial organisation is based on groups of adjoining houses. There was then the question of architectural style. While the construction methods, local facilities and comfort of the housing were intended to be "modern", the author nevertheless based himself, for these projects initially developed by the "housing service architects", on a historicising approach referring back to the past: "the (housing) models should be inspired by the classical styles of the old buildings to be found in the Ile-de-France region [as] the local styles, because of secular traditions, were determined by climateric conditions" (Sellier 1921, p. 285).

The analyses made by H. Sellier and his chosen options find there concrete expression in the evocation of 15 garden city projects being designed or which were already beginning to be built on land owned by the Seine department or its housing service (Sellier 1921,pp. 596-880). One of the operations which had already started was a project located in the Lilas commune, "just 1 200 metres" from the walls of . Given their proximity to the Paris gateways, the land areas remaining available for construction were not very big. The acquired surface was just a little larger than six hectares and the resulting project was one of the smallest programmed by the housing service: just 212 houses, while on other sites up to a thousand houses were to be built. The programme includes:

-119 houses with three main rooms plus "kitchen and W.C.", with surface areas varying from 47 to 59 m 2 depending on the layout, -67 houses with four main rooms plus "kitchen and W.C.", with a surface area of around 60 m 2 , -23 houses with five main rooms plus "kitchen and W.C.", whose surface areas are not specified.

In 1920, the largest of the work contracts was signed, and this made it possible to check the assertions of the author concerning the economics of the project. For the construction as such and the development of private plots ranging in size from 150 to 250 m 2 , 17 contractors were invited to tender and this resulted in prices for the three room houses varying from 22 000 to 27 000 Francs depending on the types. For the entire programme, the construction contract and the development of the plots represented 6 025 000 Francs, being around 28 400 Francs per house. The expenses linked to the construction of roadways, infrastructure networks and fencing came to 3 300 Francs per house. Finally, the land was bought at 19 Francs a square metre, resulting in a cost of 5 700 Francs per house. This gave a total of 37 400 Francs, excluding fees and contingencies. As can be seen, the level of the land cost explains why the 35 000 Francs threshold was exceeded, with the cost structure essentially complying with the fundamental equation presented above. It is also probable that this operation, which was underway at the time the thesis was being written, represented one of the bases for the formulation of a general approach to prices.

THE THESIS BY CLAUDE OLCHANSKI (1945)

In the thesis he wrote between 1942 and 1945, C. Olchanski took a completely different approach and arrived at opposite conclusions concerning the issue of the cost of construction. Following a particularly well documented study on social housing in France, which underlined its limits, and an in-depth analysis of the methods to be adopted in terms of housing assistance, the author arrived at the issue of the most desirable form of housing in a final chapter entitled "Construction techniques" (Olchanski 1946, p. 188-198). While accepting that the single family home might be preferred by certain workers, "especially those working in the mines", he then gave a detailed critique of the idea of the garden city, resulting in a succinct appreciation that was no less than a denunciation: "From an economic point of view, garden cities are particularly expensive given the extensions of roadways, pipework, the large number of foundations, structural walls and roofs" (Olchanski 1946, p. 190). The exorbitant cost of single family homes led him to turn his attention to the charms of housing blocks: However, one can take advantage of the considerably reduced cost of housing blocks to improve comfort. Central heating and refuse chutes can be envisaged, making life easier for households while reducing expenses and handling. […] The cost of creating roadways for garden cities could be partially reduced and the saving specifically used for facilities such as lifts, garages and better materials (Olchanski 1946, pp. 190-191).

Basing himself on these expectations, it was only natural that C. Olchanski would declare that he was "fundamentally in favour of the construction of tall buildings", an option whose dimensional characteristics were detailed a little further: "Six or seven storey rental buildings […] need to make way to taller 15 to 20 storey high rise buildings" (Olchanski 1946, p. 191). This would obviously result in having to absorb a number of constraints, such as the rationalisation of vertical ducts which, in itself would call for the organisation of housing unit layouts around a sanitary core incorporating the kitchen, bathroom and W.C. It would also call for the correction of certain inconveniences noted following the construction of the first tall buildings in France. These included disruptions affecting heat distribution in the buildings, and called for the abandoning of district heating networks given their "very high cost" resulting in unprofitable management, as witnessed in Villeurbanne (in the suburbs of Lyon) and Paris itself (Olchanski 1946, p. 195-196). The general lines resulting from this approach and the mentioned subjects of concern generally heralded the development of building systems in France during the 1950s and 1960s. This impression is further reinforced by the decision taken to opt for in-situ concrete as the main method used to construct the loadbearing structures of buildings. The comments made by C. Olchanski concerning collective heating systems are clearly based on an understanding of operational audits. But can the same be said concerning the rest, being his fundamental economic views? An initial observation able to throw a shadow of doubt lies in the fact that housing buildings, whether social or private, subsequently rarely reached a height of "15 to 20 storeys". In 1974, throughout France, there were only 174 housing blocks exceeded a height of 50 metres, of which 55 were located in Paris itself [START_REF] Tilmont | [END_REF]Croizé 1978, p. 269), and hardly any others have been built since then. This is easy to see in French town and, in particular, in large social housing complexes. A characteristic example is provided by the housing complex in Sarcelles (north of Paris), built between 1955 and 1975, where the clients privileged four to five storey constructions that corresponded to the limit above which post-war regulations imposed the incorporation of a lift. This result, clearly visible throughout France, immediately leads one to believe that the ad-vantage that an abstract vision promised to draw from the stacking of floor levels was not as considerable as expected. Even if one admits that the benefit of high buildings really existed, the general result leads one to cast a critical eye on the peremptory affirmations made by C. Olchanski. In the absence of any reference whatsoever to observations made on site, the point of view proposed by C. Olchanski is fundamentally only based on arithmetic "evidences" that are supposed to govern development and construction economics, but which are all questionable. It is obvious that the quantities of foundations, when expressed in terms of square metre of floor level are lower for housing blocks than for single family homes, but can these foundations be compared? Another, even more questionable obvious point concerns the "structural walls". Apart from the fact that, once again, the nature of the object changes over the height of the building, it is the arithmetic logic that is at fault in this situation. Certainly, a housing block supported by transversal cross-walls, alternating three and six metre spans and corresponding to an average of four metres, determines a ratio of "structural walls" equal to 0.25 linear metres per square metre of gross plan area, while a square-shaped family home covering a surface area of 100 m² and whose loadbearing peripheral structure is completed by secondary bearings on partitions would have a ratio of 0.40. But, in the case of a single family home, the ratio of "structural walls" includes the construction of elevations that, even if these are not loadbearing, are no less expensive to build in housing blocks given that the same materials are generally used. To compare what is comparable, it is therefore necessary to add an elevations ratio to the transversal "structural walls" ratio which, in the case of social housing blocks, is generally between 0.20 and 0.25. If this is done, then the performance of the housing block is less favourable than that of the single family home and this divergence is increased if one takes into consideration the attic rooms made possible by traditional roofs. When everything is taken into consideration for the construction as such, the only point among the affirmations made by C. Olchanski that is able to resist criticism is the one concerning the roofs and, more specifically, flat roofs, which can hardly be called a determining factor. The argument is even less convincing when one notes that the approach exclusively concerns the production of floor slabs and completely ignores habitable floor space and the considerable amount of common space, known in the past as "serving spaces", whose indispensable presence has the effect of reducing the proportion of truly habitable floor space in a standard housing block level to around 75%. For the rest, the only illustration given by the author to support his vision of the economics of construction corresponds to a statistic concerning the cost per habitable room provided by employers in the iron and steel industry and based on the experience of workers' estates. The difference in favour of housing blocks is not particularly expressive: "10 000 to 30 000 Francs at 1938 prices" per room in a single family home as against "14 000 to 24 000 Francs at 1938 prices" in a housing block. It should be added that in these employers' estates, single family homes could be vast villas occupied by senior executives, while accommodation in housing blocks was reserved for poorer workers. Within this context where the configuration of buildings and the characteristics of the habitable rooms (both in terms of size and finishes) faithfully copied the social hierarchy, the only meaningful element concerns the minimum costs respectfully recorded concerning single family homes and housing blocks. The concerned statistic thus provides proof to the opposite as there is a 30% divergence in favour of the single family home as presented by H. Sellier. Were these ideas considered by C. Olchanski? He does not make reference to them, although it is possible to note a clear reining-in of his point of view in the last few lines of his thesis. Circumventing the issue of construction as such, he concludes by professing that "the value of high rise housing blocks lies above all in the reduced level of costs required for the construction of roadways, sewers and water, gas and electricity supplies" (Olchanski 1946, p. 198).

AN UNSUBSTANTIATED ARGUMENT THAT NEVERTHELESS CONTINUES TO HOLD SWAY

This leads us from the apparent arithmetic of building to that of infrastructures and development which represent the strongest and most durable point of the argument stating that the small family house is an expensive product. A collection of services that do not seem in any way to worry H. Sellier is now presented as a determining factor despite the fact that its substance has hardly changed. The evidence is presented without nuance and nothing that might question the basis of the affirmation is provided. The fact that the cost of laying out a single family home is counterbalanced by the considerable advantage of the cost of the building is naturally lost from sight. No mention is made of the fact that the layout expenditure represents a very secondary element whose importance in the total cost is hardly any greater than the loss of efficiency linked to common spaces in housing blocks. No mention is made of the fact that the public works system had undergone increases in productivity at least equivalent to that to be found in the housing sector, a factor that, above all, profits urbanisation methods requiring the most roadways and networks. Finally, much like the approach taken to the construction cost as such, the allegation of an exorbitant cost is not based on any real observations. As from the 1940s, learned opinion rested on its laurels and satisfied itself for many years by simply reiterating the same types of assertions as those made by C. Olchanski, assertions that still continue to make themselves heard. But when it comes down to the reality of the situation and as far as we know, there is only one analysis concerning the cost of roadways and networks that draws a comparison between housing estates and housing block complexes, and its conclusions are completely different. This study was carried out some time later around 1970 under the direction of P. Merlin, Ponts et Chaussées engineer general and professor at the Ecole Nationale des Ponts et Chaussées. The operational data used for this study resulted in a representation of the variation of development costs per housing unit in the form of "U" curves, with the low point corresponding to a density of 25 houses per hectare for single family homes and a density of 60 housing units per hectare for housing blocks. While it is clear that the optimum level for housing blocks (7 500 Francs at 1967 prices per housing unit) is more favourable than that for houses (9 000 Francs at 1967 prices per house), the divergence is not so great, and the cost of housing block units exceeds that of the single family home optimum as soon as a density of 80 housing units per hectare is attained. In other words, a documented approach to costs immediately questions the evidence of an arithmetic simply based on ideas. Although easier to demonstrate -there has been no moment throughout the 20 th century when, at comparable finishes and volumes, the construction of a single family home has proven more expensive than that of a unit in a housing block -the thesis concerning the construction as such also continued to durably profit from academic unction. This can be seen in the doctoral work carried out by J.E. Havel, crowned at the Paris Faculty of Arts in 1956, which immediately saw the publishing of a compendium called Habitat et Logement as a paperback by Presses Universitaires de France for use by students as a reference for issues concerning housing. In this work, reprinted four times up to 1985 without its contents undergoing any significant revisions, the author predicts a progressive cessation of the production of single family homes. He gives two reasons for this taking place (although completely belied by what subsequently took place in France): a "town planning reason" corresponding to the conditions governing the development of metropolises, and an "economic reason" based on the nature of construction. This second aspect, being the only one of concern to us here, is reduced to its simplest expression: "On condition that the buildings are not too tall, it is cheaper per housing unit to locate several housing units rather than a single home under one roof" (Havel 1974, p. 19). It is clear that this manner of treating the economics of a building reveals a remarkable prudence given that the author restricts himself to the only good reason available to him, or proof of an extraordinary irresponsibility. In any case, it is clear that the insufficiently based thesis written in the 1940s was transformed into a generally accepted popularised ideology and this leads to questions being asked as to the nature of the processes that have successfully transformed a falsehood into a scientific assumption. In contrast with the thesis written by H. Sellier, one of the salient features of the works that received approval from university juries as from the 1940s was the lack of a real basis on which to make concrete observations. This same characteristic is also to be found in the thesis defended by J.C. Kourganoff in 1963, Une solution au problème du logement: l'industrialisation du bâtiment (A housing solution or problem: the industrialisation of construction). Having given a detailed presentation of the various concrete-based prefabrication methods, the author professes that in terms of structural works "all the advantages [of large panel precasting] permit a cost reduction of around 10% to 25% when compared with the traditional sector" (Kourganoff 1963, p. 132). But he then goes on to admit that he had not been able to obtain any "accounting documents" able to prove this point because "each company [considers] that these are secret documents" (Kourganoff 1963, p. 139). In other words and once again, this is an unverified affirmation and it is surprising that a jury where two of the three members were very well-known professors of economics at the University of Paris -J. Marchal and A. Piettre -was able to crown a doctoral work where the central argument of the thesis lacked any real basis. The probable reason was that the approach taken, simply based on the handling of ideas, was familiar and thus acceptable to professors of political economics highly interested in conceptual constructions. However, this approach is nevertheless inappropriate within the context of a problem of applied economics, where the observation and measurement of realities should represent fundamental conditions underlying the validity of the analysis. In the presence of a consensus on theoretical ideas that ought to conclude by practical verification, and without this consensus being based on concrete observations, it cannot be assumed that its source could be found in the sphere of economic thinking itself. C. Olchanski provides a key to interpret this prejudice imported from other sources. In the passage where he discusses the glorious future of "15 to 20 storey" buildings (Olchanski 1946, p. 191), he refers twice to the writings of Le Corbusier, particularly citing La Maison des Hommes, published in Paris in 1942. It was therefore under the influence of an understanding of modernity propagated by "modern movement" architects and town planners that the economic approach came to neglect the facts and simply based itself on a profession of faith. It should be added that this new religion also reflected the professional interests of those involved in architectural and urban design, first among these being engineers and architects. C. Olchanski seeks to assert the new role given to engineers by large construction operations (pp. 194-196). This same type of insistence is apparent in the increasing importance of intellectual investment in the preliminary studies and organisation that can be seen in the works by J.E. Havel (pp. 21 and 118) and J.C. Kourganoff (p. 171). While assistance from conceptual intellectuals can justly seem indispensable in heavy construction, the same cannot be said for small houses, a field where they could even experience certain failures. This is exemplified by the stinging letdown suffered by Le Corbusier and his developer H. Frugès between 1924 and 1926 with the abandoning of their working class houses designed for the Pessac site in the outskirts of Bordeaux. The loop on which the economic analysis of the "moderns" is based closes in on itself as soon as one realises that, in its general form, the idea according to which building production activity is linked to the number of floor levels derives specifically and exclusively from the experience of heavy construction. On large building sites, the productivity of the structural works is mediocre on ground level and below, where the most nonrepetitive operations take place, and gradually improves with the standard upper floor levels up to an optimum level and then deteriorates again for the taller buildings. In this mechanical progress, the salient point is that there is a break in work processes every time the production teams have to return once again to dig around at the bottom of the excavations and that, consequently, productivity can never be good for single family houses. However, this appreciation, inspired by the rhythms of heavy construction, is contradicted by observations made in the field. The relative simplicity of a house allows production agents to easily memorise the structure and consequently capitalise a horizontal productivity that literally steps over the excavations and foundations. Single family home builders state that, like those workers erecting standard floor levels, a production team having built the same model two or three times is perfectly able to control difficulties, anticipate supply requirements, etc., simply working from the memory of previous identical houses, to an extent that any changes need to be clearly and insistently explained to avoid the risk of seeing an exact copy of the initial model. The effects to be expected from this horizontal productivity are at least comparable to those obtained from vertical blocks, and it should be noted that the benefits are obtained without having to use an unwieldy organisation and inspection system. The relative symmetry that exists between the productivity respectively provided by horizontal and vertical repetitiveness was lost from sight in analyses made during the 1940s and subsequently. As soon as this is seen in perspective, at least conceptually, the economic reasoning accompanying the aesthetic/urban popularised ideology of the "moderns" becomes no more than pure tautology. Fundamentally, housing blocks provide productive advantages because this type of construction corresponds to the only option under consideration. Providentially, this option also coincides with the professional interests of the highly vocal architectural corporations. The consensus of players then gave the unfounded assertion all its backing and dispensed with any checking procedures, even in scientific environments.

CONCLUSION

The understanding of the economics of construction represents a fundamental point in the option taken in favour of a particular mode of urbanisation. In the period from 1920 to 1970, doctoral theses crowned by the University of Paris were read and understood in two successive ways. The first dates to the beginning of the 1920s and favours the city of houses project. The second, which reigned from the 1940s to the 1960s, backed a development project that took the form of housing blocks. Unlike the first, the second presented itself as a simple affirmation of principle and, in the terms used to express this affirmation, it would have been very difficult to give it documented concrete substance by field observations concerning prices. This did not prevent the affirmation from contributing to the production of real effects. These corresponded to the period of just a few years during which, in around 1960, apartments in housing blocks represented up to three-quarters of new dwellings built in France. This second understanding, which had the consensus of the elites, rather than finding its source in an independent economic contribution to construction expertise, was to be found in an a priori conception of modernity that inspired postulates concerning economic views as well as aspects of aesthetics and construction techniques. Inasmuch as, from an economic point of view, these were constantly belied by facts, an ever-wider gap grew between the construction culture sought by the elites and the popular perception which was convinced that, by keeping a close control over prices, the single family house continued to be an affordable product, at least in the very large number of urbanisation sectors where the cost of land did not represent an insurmountable obstacle. The more general lesson that can be drawn from this episode is undoubtedly the idea that we would expose ourselves to similar types of risks if, for whatsoever reason, we once again cultivated a vision of project economics subject to a doctrine and which did not take the observation of the real situation into consideration.

Figure 1 :

 1 Figure 1: Garden city projects for the Paris region: feasibility study by architects André Arfvidson, Joseph Bassompierre and Paul de Rutté;(Sellier 1921, p. 256)


Francesca Musiani

Walls Built Up, Walls Written Down: Of Symbolic Value, Material Effectiveness and Media Representation of Barriers in Padua, Italy

HAL is

Introduction

Tell me thy mind; for I have Pisa left And am to Padua come, as he that leaves A shallow plash to plunge him in the deep And with satiety seeks to quench his thirst.

--William Shakespeare, The Taming of The Shrew (1590) Padua is a city of 210,000 inhabitants, in the North-eastern Veneto region of Italy. As William Shakespeare knew well, it hosts one of the most ancient universities in the world; it is also surrounded by a prosper industrial area, and constitutes a notable touristic and religious attraction, due to the important remains of the medieval city and to the Cathedral of St Anthony, a landmark relished by pilgrims worldwide. Despite its qualities, though, in the last few years Padua has not been depicted primarily as a place where to relieve one's academic or artistic thirst: to give it a place in the media spotlight, instead, have been its "walls". Barriers: from the one in Via Anelli, the most famous one so far in the international press, to other, smaller and more recent barriers that, by themselves and as part of a larger discourse on integration and security, have also received a great deal of attention in local newspapers and newscasts.

Expanding and updating a line of analysis I have started in 2007, 1 this essay means to contribute to the investigation of the "Padua Walls" phenomenon. By trying to move a step further from current debates on negative and positive features of the proliferation of "walls" in Europe and the world, I argue that such barriers -and the politics behind them -should be read as symptoms more than as solutions (regardless of their actual effectiveness as such). I propose an interpretive key for the "Padua Walls" phenomenon that treats them as signals of a lingering malaise (of which Padua is a case study but by no means the only example) that stems from the current devolution of concepts such as solidarity, belonging, community. 2 By doing so, I address both the concreteness and materiality of such barriers and of their construction, and the representation that media have produced, in parallel, of them as processes and concepts. Particular attention is paid, in the blend of case studies and discussions that constitutes this article, to the juxtaposition of symbolic value and practical efficacy of the "Padua Walls", and its implications in the formation of societal rites and policy-making choices.

Yet More Walls? The "Valeri" School as a Case Study Alle loro domande abbiamo il dovere di rispondere, tanto più perché sono confusi. Non hanno capito cosa è accaduto. La diversità sarà il tema del giorno, psicologica e sociale. 3 --Ignazia Nespolo, director of the "Diego Valeri" elementary school, shortly after the installation of the net between the school and the C.T.P. (2008) The last "wall" built-up in Padua is to be found, or should be, at the end of Via Monte Santo, number 24. It has been erected during the Easter holidays of 2008, with the aim of separating the elementary school "Diego Valeri" from the "Centro Territoriale Permanente" (i.e., Permanent Territorial Centre). 4 In this centre, men and women gather every day to learn Italian language and societal practices, while acquiring a certificate that will attest of their professional qualifications in a variety of handicraft jobs. They range in age from early teens to late fifties; they come from Mediterranean Africa, former Soviet republics, the Far East of Asia; they hope to use their diploma as plumbers, cooks, nurses. What has been labelled, like some of its infamous predecessors, as a "wall" in its own right, is now bound to become the redeeming fracture between two realms that have interacted, in apparent peace and with little or no complications, for the fourteen years of their co-existence. But if one actually goes to Via Monte Santo -in fact, a blind alley -the "wall" is not to be seen, nor could it be, as there is no construction made of brick and mortar that the word could remind of: it is actually a barrier, a wide-mesh net of metallic wire, two metres in height and ten in length, precarious and bound to collapse at any time. Children students of the "Valeri" school usually enter the main gate, as they have done for years, at half past eight. Adult students of the C.T.P. enter the gate of the Centre, just a few meters away, half an hour later. The closeness of their entrance gates has always enabled them to smile at each other, wave at each other. Even after March 2008, they keep on smiling and waving. Children run in the backyard during the pauses between classes with untamed happiness, despite the cold spring. Fear -the most problematic one, the one that refuses rationality and does so for no particular reason, except an all-encompassing but vague sense of anguish -apparently lies within adults only. 5 The reason? A few days earlier, a young man from Bangladesh, student at the C.T.P., has wanted to take a picture of the yard where a few kids were playing -he said -in order to be able to show to his far-away family where he was, in the company of whom, studying what, in his new host country. This act, certainly an ingenuous move, but not a vicious one, did probably constitute a violation of the boy's privacy, as many are ready to admit; an undesirable act for a parent, and maybe it was; but it went so far as being described as the move of a potential paedophile, and that, for sure, it was not. 6 A "media moment" ensued, a complaint was filed, protests rose. For a few days, common sense and reason disappeared, as other episodes showed: a man whose habit was to distribute small toys to kids outside the school, for advertisement purposes, was suspected to distribute "envelopes" with unspecified, harmful content; two journalists monitoring events in front of the gate were deemed too suspicious-looking and dismissed by the Carabinieri, the Italian military police. The teachers of the C.T.P., by disposition of the educational institution itself, were instructed to accompany the adult students of the establishment directly into classes, as a precautionary measure. This blind fear, with no discernible direction or cause, further aggravated by the excessive liberties taken by media in their representations of facts, led the director of the "Valeri" to build that barrier, almost out of "therapeutic necessity". That entanglement of wires, if touched and seen even briefly, appears as supremely useless with respect to its alleged purpose of separation -the infamous picture could still be taken at present -and even more, of protection from physical invasions of the "Valeri" school's space, invasions that would be easy to achieve for whoever willing to do so, regardless of the mobile. 7 The barrier's only purpose is the attempt to bring a temporary peace of mind to a few tormented parents; a great example of placebo effect, it is certainly no "wall". But this introductory story serves as an example of how the ethnicization of a family and community's anxieties8 reprises a recently consolidated convention in media discourses, the one that tells the story of an intolerant, racist, almost segregationist town.

Via Anelli: a Legacy and a Burden

Non è un muro, ma una recinzione, che si frappone fra due luoghi.9

--Marco Carrai, town councillor for security in Padua, shortly after the construction of the Via Anelli Wall (2006) (T)he development of more effective conflict regulation (can be achieved by) building fences low enough for good neighbourliness to develop.

--Nina Fallentin Caspersen, Good Fences Make Good Neighbours?, (2002) The Padua Wall, and more recently the Padua of Walls, have become recognizable labels in European press and public debates on immigration and integration. The most (in)famous "wall", the one in Via Anelli, is the first chronologically to have occupied the media spotlight. For two years between 2006 and 2007, it has been reported on in the national and international press, with mixed levels of accurateness and completeness, more than the famous touristic and religious landmarks of the city. The world-renowned Cappella degli Scrovegni and the cathedral of St. Anthony, to name just two of them, have been overshadowed by documentaries, special TV reports and paper articles,10 all describing a dark barrier of iron gone rusty, ninety-six metres long and three high: the "wall" between Via Anelli and Via De Besi. The barrier contours a former ghetto of six buildings, three hundred apartments of roughly thirty square metres each, where families and groups (up to ten people per apartment) squatted beyond the limits of capacity: immigrants that rented just a bed, a one-time usage of the shower or the kitchen. And sneaking into this desperate reality of hundreds of people, for the despair of the neighbourhood and its inhabitants, were not only the loud music, the garbage and the excessive beer drinking, but the brawls and mostly, the drug dealing. As it has been extensively analysed by now, this is why the "wall" was born, to make it harder for dealers to disappear in occasion of the sudden arrivals of the police.11

What now? The "wall" still presides over a no man's land, but of a different kind, one that is bound to change for the best relatively soon, and maybe already is. The six buildings (originally built to act as dormitories for a few hundred students of the nearby University of Padua) voided by the end of 2007. More than 400 families of regular immigrants that were the unwilling co-protagonists of the out-of-control situation have either been relocated in other parts of the city thanks to the local administration's mediation, or have been able to do so on their own. The urban requalification of the area has been one of the main points of Mayor Flavio Zanonato's recent campaign for re-election, and if the promises made will be kept (Zanonato has succeeded in being re-elected in June 2009),12 half of the area (about 12,000 square metres) will be redeveloped as a new residential neighbourhood, and the other half as offices buildings. This might well mean better days for all stakeholders, as the president of the lobbying committee for the Stanga quarter says: "things are going way, way better". 13 The inhabitants of the neighbourhood should, after some very difficult years, find some more peace than they were able to experience for years, along with a higher commercial estimation of their estate properties. More specifically, the immigrant families that were the former inhabitants of the six buildings are living in more decent places, and far from the forced cohabitation with criminals, find tranquillity and stop being associated with the criminals themselves. However, many argue that the price paid by the municipality, in terms of message given to the local citizenry and eventually to the world, has been too high by choosing the construction of the barrier as the most suitable solution. Besides the more or less menacing physical appearance it might assume, a wall remains a wall, a symbol stronger than most one could think of, "explosive from a communication perspective". 14 One can wonder what does this mean, at the present stage, in terms of the burden left to the city of Padua.

Padua, the City of Walls?

Finalmente da qualche giorno sono ritornata a dormire in pace!15 --Gisella "la Gisa" Scanferla, inhabitant of Via Manara, Padua (2008) To name only the foremost of these burdens, every barrier built in Padua after the Via Anelli one -whatever the purpose and the aspect -now becomes a wall in media and communication discourses. This is certainly a convention and an effective label for journalists to attract attention, but also a reminder of ghosts past, that force the municipality to come to terms with the unpleasant reality: it is not enough to force drug dealers out of an area for them to just disappear into thin air -expulsed from Via Anelli, all the effort that pushers have needed has been to move the centre of their dealing of a few hundred metres, in the parking of the Centro Giotto mall close by. And how is this dealt with? New barriers, two gates made of metallic grid, specifically designed against over-jumping, called "Orsogrill". For a cost of 20,000 Euros, they separate two streets from the parking of the mall: Via Galliano, for seven metres, and Via Venezia for six. 16 What strikes at a first sight is the total uselessness of these barriers. In Via Galliano, just at the sides of the gate, there is a smaller wall, this time made of bricks, less than a metre high. It is the easiest thing to jump over this as a first step to climb the higher barrier, and this is what most of the dealers do every time they need, seemingly with little fear of being caught or disturbed in their activities. Another "wall" was built in Via Cairoli, a small street close to the train station and the avenue connecting it to downtown, Corso del Popolo. The barrier in question is in this case a simple horizontal bar, like the one you would find at the entrance of a garage, that enables the way into the street only to pedestrians, with the alleged aim -not dissimilar from the Via Galliano one -to make things a little less easy for the (mostly Italian) clients of the (mostly Moroccan and Nigerian) pushers that are the sad legacy of the Via Anelli evacuation.17

The most recent addition to the "Padua Walls" reported by the press is the one in Via Manara. Once again, no brick-and-mortar wall, but rather a flowerbed with no flowers, a few metres in length, that forbids any access by car to the two "buildings of the shame" in the street, entirely occupied by prostitutes, who show up here and there in the street to lead clients into the houses. 18 A situation that, day after day and night after night, became unsustainable for the inhabitants of the immediate neighbourhoods -and among them, a dynamic housewife that has become a popular figure at Stanga, Gisella "la Gisa" Scanferla, the drive behind the gathering of signatures that led to the intervention in the street. "Between the prostitution and drugs under my windows, I was unable to sleep, so I just started screaming," she said. Still, despite the fact that the barrier has temporarily helped to increase the quality of her sleep, she firmly believes that the wall of Via Anelli has merely shifted problems, not solved them, and the one erected in her street is not going to be more effective. "They blew on confetti, these barriers are palliatives. All we will achieve is the walling of our town, and it will be us that live in prison."19

Imagining Safety: Walls as a Symbolic Exorcism of Fear

What about uncertainty, insecurity, loneliness and the future being a site of fear instead of hope? (…) What about seeing in the neighbourhood only a jungle to be warily and fearfully watched, in the stranger only a beast to hide from? (…) Life has not got to be like this.

--Zygmunt Bauman, Alone Again: Ethics After Certainty (1992) These barriers in Padua, of high symbolic value but very little material usefulness, thus join the first Via Anelli wall, which is now left to overlook an empty space soon to be inhabited by those who will be able to afford it at a substantial price. Are these 130 metres of barriers, all put together, enough to label Padua as the "city of the Walls"? This stereotype appears to blend the politics of fear together with another kind of politics, which an Italian commentator described as the "politics of false imagination". 20 Fear always calls for simple, straightforward and iron-fisted answers -especially the lingering fear that combines social uncertainty with urban degradation, lack of basic principles of civil life with petty, street-wise crime; the kind of fear that transforms the reality of the threats to personal safety into perception of pervasive insecurity. There is nothing more definite in appearance than a protective barrier to separate oneself from problems, of whatever kind they may be: as Morello and Camarda point out: "(t)he solidity of an extreme measure will stay, as well as having indicated a solution in front of a failure, that is what terrifies most people."21 A "wall" provides people with a chance to feel safe, or at least to imagine safety -in a way, to deceive themselves: for some time, it allows not to look at reality. Therefore, here is the construction of "walls" in Padua: wherever they are needed, whenever they are needed. If they are the way to exorcise a collective psychic syndrome, appease a wave of emotions, it matters very little that they are "just" symbolic, or even, phoney.

The newly-re-elected mayor of the city, Flavio Zanonato (at present, one of the few leftwing mayors in north-eastern Italy), has showed and shows in his recent public statements on security matters in Padua a blend of common sense, artificial calmness and straight-to-the-point attitude that only partially conceals his irritation. Can the net at the "Valeri" school be possibly defined as a wall, if not tongue-in-cheek? -he asks rhetorically. Is a garage door a wall? Can a flowerbed be one? 22 The anxieties of the Paduans reflect those most people in the Veneto region: figure out how they can best defend the well-being and comfortable living standards they have earned with hard work, after a history that goes from the glorious past of the "Serenissima" Republic of Venice to phases of absolute poverty. In this scenario, a keen irritation by the mayor of Padua can be perceived when comparisons are made between him and many of his homologues in other Venetian cities, that have often preferred the elementary and reassuring recipe of "order and cleanliness" in their work as administrators -having already too many troubles, to put it in sociologist Ilvo Diamanti's words, in promoting urban aesthetics to be able to address the deeper issues of urban ethics. 23 Rather than as a placebo, the first citizen of Padua describes the "ghost walls" of Padua more in terms of a drug administered early in the disease to present more extensive, or more complicated, damage. One can very well think that the "Valeri" net only has a placebo effect, but this is not the essential issue at stake, he says. It is a matter of priorities: the municipality built the barrier due to the perception of its necessity by the families of the children students, and a more important objective is that educational institutions can still be effective ones for "us and them. I don't want the us and them to exist." 24 Fourteen percent of the student population of Padua is of immigrant descent, and rising; for the administration, it is crucial that this percentage keeps on rising. If the "ridiculous" net had not been put in place, the following year many of those students would not have enrolled at the same school due to family pressures -a much more despicable defeat than a few metres of net, the mayor says. Even if possibly legitimate for a mayor in critical circumstances like the ones at stake, this reasoning, which responds to a very precise political choice and strategy, only rises new and controversial questions. If one gives a barrier to some of his citizens because this is the answer they "need", doesn't it set a critical precedent? What is the point where answers needed by some but arguably undesirable for others, and/or potentially dangerous, will be denied rather than provided? Who is going to make the choice of not providing them? These questions would better be explored, and the reason is well summarized by this blogger on the issue: "if he really doesn't want the us and we to exist (…) if he doesn't want (the barrier) to exist, he better not build a phoney, placebo, symbolic wall. Because if it is symbolic for him, for the families that requested it it's very much real, and when it won't work, they will ask for a better one."25 Securitisation: Our "Hard-Won Idiocy"

If there is a lucky relevance in the concept of liquid fear, it is the physical image of what, not having a solid content, slides over, trickles through chinks and floods any surface that comes across.

If applied to a specific case, the concept materialises in its solid ambivalence.

--Michela Morello & Rosj Camarda, Il muro di Padova: un muro di solida paura (2008) Despite the highly critical reviews of its immigration politics of recent years, catalysed by the explosive public image of the "wall and walls," it could be argued that Padua is coping reasonably well with the immigration wave that is pervading the Veneto region. Entrepreneurs depend on immigrants as workforce just as immigrants depend on them as employers; a solidarity net is present and influential vis-à-vis local political organisations; in this context, the use of the "pervasive immigration is pervasive criminality" paradigm is not only a mistake, but a "hard-won idiocy" to paraphrase Italian actor and singer Giorgio Gaber, that can be paid heavily in the future. Beyond the representations elaborated by political and media entities, as the easiest way to obtain a vast and convenient audience, it is obviously hard to believe that the problems of today and tomorrow can be shrunk into the simplification of the relationship between immigration, criminality and insecurity: ethnicizing the social crisis is not the way to solve it. This goes beyond the realm of Padua and that of Veneto, despite the great success that the message of securitisation,26 more police, more coercion, more expulsions, has had in the recent European elections, in Italy and a number of EU countries. 27 At least one thing is certain: that as a relevant issue, security is an all-encompassing question -one that creates a generalized consensus, not in terms of how to cope with it at national and regional levels, but in terms of the public interest it fosters for everybody, as individuals and members of different and overlapping communities.

At the same time, precisely because of its pervasiveness, it is very difficult for researchers to try and split the concept of security into its main components, that might be easier to act upon separately. A recent, comprehensive research at the national level in Italy has outlined how the citizens' demand for security does in fact include other, and more diverse, preoccupations. 28 Forty to sixty percent of the interviewees cite as a source of perceived lack of security the degradation of territory, food, climate; a third of them is concerned about possible economic troubles; two-thirds are convinced that economic and social conditions will only worsen to the detriment of their children's future. Criminality and threats to personal, domestic and familiar security only represent one, and not the most problematic, facet of security, the study concludes. Other fears linger, and imply a discussion and rethinking of traditional notions and claims such as prevention, assistance, "future".29

Conclusions. Symptoms, Not Solutions: Walls and the Devolution of Solidarity and Community

L'appartenenza non è un insieme casuale di persone non è il consenso a un'apparente aggregazione l'appartenenza è avere gli altri dentro di sé. (…) Sarei certo di cambiare la mia vita se potessi cominciare a dire noi. 30 Giorgio Gaber, Canzone dell'appartenenza ("Un'idiozia conquistata a fatica", 1997)

Most of the last four years of my life have been spent outside of Padua. It is and remains my town, though, and I maintain a keen interest in dynamics such as the Padua Walls not only as an Italian and Paduan citizen, but as a sociologist and observer of the birth and development of a European public space in its local manifestations. I hope that the balance between sense of belonging and physical distance, that currently represents for me the link to my hometown, can allow me to witness at the right "distance" what is happening there, beyond an imprecise sense of nostalgia and the usual stereotypes applied abroad to Italians in general, and in Italy to Venetians in particular. It is in such a state of mind that I think about the Padua Walls, and I realize that -beyond discourses on their undeniably strong symbolic value and the challenge they pose in terms of how to communicate particular mindsets, priorities, integration and immigration policies -they are just one, the most media-savvy, part of the picture. The debate on these phoney walls, that become rock-solid barriers mostly because of the ways in which citizenry and media construct and represent them, hardly conceals in my eyes what are the bigger, more pervasive problems of Italian society and politics, well represented by my town's reality. This reality is, to me, one of a land that has a long history of emigration, and has still not learned how to be one of immigration for such an important flow of people; a town unstitched from its own urban environment, a demos that has not yet understood the new configurations it is adopting, that came too fast for their own good. As it is the case for many Venetian and Italian areas, Padua suffers from a disease that one of its local glories, movie director Carlo Mazzacurati, has recently described as "welfare devoid of cultural nourishment."

The "walls" are the point of the iceberg -the most visible symptom of this disease and at the same time, its temporary cure, enacted only when local outbursts of the disease became unsustainable. But as it often happens in Italian politics, elites think short-term. Rather than the "walls," and what they might or might not contribute to solve, what should constitute material for reflection at a much deeper level are the new places and paths of aggregation, personal habits, collective rites of the city -all pragmatic signs of the powerlessness to renovate values and social links, an impotence that economic wellbeing has weakened, not improved. Material of reflection should be the fact that a regular benchmark in University students' lives is the massive absorption of "spritz", the typically Paduan alcoholic beverage that hundreds of adolescents drink, to the point of exhaustion, every Wednesday night. What are the implications of the fact that for Paduan youth, the highlight of the week is a rite that leaves them almost unconscious because of the drinking, and the urban environment dirty and soiled by dozens of plastic cups, vomit, and urine? Food for thought should be the observation that drug dealing does not only happen in a mall parking alongside a very visible barrier, but in the small streets of the old town, in the shadows of historical buildings. Shouldn't the awareness that this more discrete drug commerce aims at reaching the same "market" of educated youth weakened by the spritz, and often succeeds in doing so, have any implications for local policy choices? Further reflections could, and should, build upon the painfully high number of deadly car accidents involving youth; the death of meaningful parts of local cultures such as movie theatres or home-made fabric shops, to the profit of multiplexes and malls; the "university-as-a-parking" concept versus the incredibly high number of people for whom the dream of a lifetime is to be a participant in "L'Isola dei Famosi". 31 Zygmunt Bauman says: "There is a point somewhere down the slope, now perhaps passed, at which people find it hard to conceive of any benefit they could derive from joining forces. (…) As some of the old, once solid, entities underwriting and endorsing individual identities lie in ruins, while others are fast losing their holding power, there is a demand for new ones". 32 Ultimately, what is really conveyed by the story of the Padua Walls is the quiet acceptance of a lingering unhappiness about the current "devolution" of concepts such as solidarity, belonging, community. An unhappiness that, beyond the walls, should worry responsible citizens and policy-makers at a much deeper level: because the quietness of the acceptance can at any time turn into rebellion, and the lingering unhappiness can abruptly detonate. The static, almost entrancing, presence of a wall -even if misleading with respect to its intended purpose -can be a very true signal of this danger; one we should rapidly decipher and act upon, for our own good, that of our cities, and that of our communities.

Francesca Musiani, The Padua Wall : Immigration, Conflict, and Integration, Peace & Conflict Monitor,

October 2007. 2 "Devolution" is used here in its meaning, antonym to evolution, of "decline, deterioration", rather than in its political signification of power transfer from national to regional levels.

"We have an obligation to answer their questions (N.d.A. of the children students), even more so because they are confused. They didn't understand what happened. Diversity, psychological and social, will be the theme of the day." (my translation)

Felice Paduano, All'elementare Valeri è calata la barriera, Il Mattino di Padova, 23 March 2008.

Elvira Scigliano, Valeri : genitori soddisfatti, Il Mattino di Padova, 20 March 2008.

Adina Agugiaro, I protettivi muri di Padova, Il Mattino di Padova, 19 March 2008.

Costanza Costanzo, Sono un'insegnante : questa è una sconfitta, Il Mattino di Padova, 16 March 2008.

As defined by Giuseppe D'Avanzo, in Tra i muri fantasma di Padova : false barrière contro la paura, La Repubblica, 31 March 2008.

« It is no wall, but a fence, that interposes between two places. » (my translation)

See e.g. Christian Fraser, Ring of Steel Divides Padua, BBC News, 28 September 2006 ; Don Murray, The Wall of Padua, CBC News, 29 January 2008 ; Hans Karssenberg, Walls of Incompetence, Inspiring Cities, 29 August 2006.

SeeMusiani (2007) for a more detailed explanation of the facts and analysis of the Via Anelli specific case.

Staff Writer, Cosi Flavio si è ripreso Padova, Il Mattino di Padova, 22 June 2009.

D'Avanzo (2008). (my translation).

Michela Morello & Rosj Camarda, Il muro di Padova: un muro di solida paura, Sociologia Urbana e Rurale 86, 2008.

"Finally, in the last few days I was able to sleep peacefully!" (my translation).

Gabriele Righetto, Elaborare un'urbanistica dell'accoglienza, Il Mattino di Padova, 22 August 2008.

Felice Paduano, C'è chi scommette su Via Cairoli, Il Mattino di Padova, 16 March 2008.

Staff Writer, Via Manara, barriera contro lo spaccio, Il Mattino di Padova, 21 October 2007.

D'Avanzo (2008). (my translation).

Barbara Spinelli, Bendati verso il precipizio, La Stampa, 30 March 2008.

Morello & Camarda (2008).

Eric Jozsef, Immigrés aux pieds du mur, Libération, 7 April 2008.

Ilvo Diamanti, L'infinita periferia dell'Italia, La Repubblica, 2 December 2007.

D'Avanzo (2008).

Sociologia/Demopazzia, blog, 31 March 2008 (available at http://demopazzia.splinder.com/tag/sociologia?from=20) (my translation).

See Ulla Holm, The Implication of the Concept of the French State-Nation and 'Patrie' for French Discourses on (Algerian) Immigration, Copenhagen Peace Research Institute Working Paper, 2002 : securitisation is the process by which a matter of public concern shifts to being framed as a matter of emergency, requiring extreme measures as the only possible way to cope with the exigencies of the situation.

Elisa Molino, I temi principali delle elezioni europee in Italia, Euros du Village, 27 May 2009

Ilvo Diamanti (eds.), La sicurezza in Italia. Significati, immagine e realtà. Seconda indagine sulla rappresentazione sociale e mediatica della sicurezza, Research report by Demos & Pi and the Pavia Observatory, for Unipolis Foundation, November 2008, p. 2.

Ibid., p. 6.

To belong / does not mean a random set of people / it is not the consensus to a seeming aggregation / to belong / is to have others inside oneself. / (…) I would be certain I can change my life / if only I could start to say "we". (my translation).

Popular reality show inspired by the American « Survivor ».


Lara Briñon Arranz
email: lara.brinon-arranz@inrialpes.fr

Alexandre Seuret
email: alexandre.seuret@gipsa-lab.inpg.fr

Carlos Canudas De Wit
email: carlos.canudas-de-wit@gipsa-lab.inpg.fr

Lara Briñón Arranz

Carlos Canudas

Contraction Control of a Fleet Circular Formation of AUVs under Finite Communication Range

This work proposes a novel control algorithm dedicated to multi-agent systems with nonlinear dynamics. The aim of this paper is for the agents to form a circular formation whose center is fixed and whose radius is given by a time-varying reference. The problem of uniform distribution of all the agents along the circle is also addressed under the assumption of limited communication range. This communication constraint is tackled by using a cooperative control scheme which includes the Laplacian matrix of the communication graph (distancedependent). The multi-agent system is simulated with Matlab. Videos showing the simulations are accessible though Web 1 .

I. INTRODUCTION

Control of multi-agent systems has received a lot of attention in recent years [START_REF] Olfati-Saber | Consensus and cooperation in networked multi-agent systems[END_REF], [START_REF] Leonard | Collective motion, sensor networks and ocean sampling[END_REF]. Particulary, the problem of collective or cooperative control of an autonomous systems group is an important developing field motivated by a number of application in many areas including cooperative control of underwater and unmanned air vehicles (AUVs and UAVs) [START_REF] Fiorelli | Adaptive sampling using feedback control of an autonomous underwater glider fleet[END_REF], [START_REF] Raffard | Distributed optimization for cooperative agents: Application to formation flight[END_REF], consensus [START_REF] Olfati-Saber | Consensus and cooperation in networked multi-agent systems[END_REF], [START_REF] Olfati-Saber | Consensus problems in networks of agents whit switching topology and time-delays[END_REF], formation control [START_REF] Paley | Stabilization of symmetric formations to motion around convex loops[END_REF], [START_REF] Sepulchre | Stabilization of planar collective motion: All-to-all communication[END_REF], flocking [START_REF] Olfati-Saber | Flocking for multi-agent dynamic systems: Algorithms and theory[END_REF], distributed sensor networks [START_REF] Leonard | Collective motion, sensor networks and ocean sampling[END_REF], [START_REF] Ögren | Cooperative control of mobile sensor networks: Adaptive gradient climbing in a distributed environment[END_REF] and rendezvous [START_REF] Dimarogonas | On the rendezvous problem for multiple nonholonomic agents[END_REF]. Formation control and motion coordination have been extensively studied. The reader can refer to [START_REF] Leonard | Collective motion, sensor networks and ocean sampling[END_REF], [START_REF] Sepulchre | Stabilization of planar collective motion with limited communication[END_REF], [START_REF] Martínez | Motion coordination with distributed information[END_REF], [START_REF] Ögren | A control lyapunov function approach to multiagent coordination[END_REF], [START_REF] Sepulchre | Stabilization of planar collective motion: All-to-all communication[END_REF], [START_REF] Sepulchre | Graph laplacian and lyapunov design of collective planar motions[END_REF] among many others. These studies concern circular and parallel formations [START_REF] Leonard | Collective motion, sensor networks and ocean sampling[END_REF], [START_REF] Sepulchre | Stabilization of planar collective motion: All-to-all communication[END_REF], [START_REF] Sepulchre | Stabilization of planar collective motion with limited communication[END_REF], [START_REF] Sepulchre | Graph laplacian and lyapunov design of collective planar motions[END_REF], but also motions of formation induced by flocking [START_REF] Olfati-Saber | Flocking for multi-agent dynamic systems: Algorithms and theory[END_REF], [START_REF] Reynolds | Flocks, herds, and schools: A distributed behavioral model[END_REF]. This paper focusses on the problem of design control strategies for a class of non linear multi-agent systems to achieve circular formation. Interesting results have been already proposed in [START_REF] Leonard | Collective motion, sensor networks and ocean sampling[END_REF] and [START_REF] Sepulchre | Stabilization of planar collective motion with limited communication[END_REF] to deal with a time-invariant problem, when the circular formation has a fixed center and a constant radius. A relevant problem is now to relax these constraints and to consider time-varying formations. This problem belongs to the fundamental transformations of circular formations [START_REF] Leonard | Virtual leaders, artifitial potentials and coordinated control of goups[END_REF]. These transformations are pertinents to some applications where the agents should perform collaborative tasks requiring the formation to displace towards an a priori unknown direction and adjust to some particular form. For instance, in source seeking applications, the formation should displace in the source gradient direction and contract its size to adapt to the level curves of the source plume. 1 Simulations are accessibles in the CONNECT project web at http://www.lag.ensieg.inpg.fr/connect/ In the context of the source seeking for underwater vehicles, it is relevant to constrain the agents in an appropriate shape, for instance circular, to avoid unnecessary energy waist. Moreover, ensuring that the agents are uniformly distributed along the circle might be more adequate to produce efficient search motions.

Another difficulty in the underwater fleet formation problem is due to the information transmission in a marine media. Communication between agents is confronted with several difficulties such as signal distorsion and interference, doppler effect, etc. Communication in shallow water amplifies these limitations. In this work, we assume that the communication between each agent is "good enough" within a particular range specific to the application. Therefore, the previously described contraction formation control will be studied under such a limited-range communication assumption, where the communication graph depends on the agent's relative position [START_REF] Olfati-Saber | Consensus and cooperation in networked multi-agent systems[END_REF], [START_REF] Olfati-Saber | Consensus problems in networks of agents whit switching topology and time-delays[END_REF], [START_REF] Ren | Consensus seeking in multi-agents systems under dynamically changing interaction topologies[END_REF].

Note that a first contribution concerning the translation of a circle is proposed in [START_REF] Briñón | Translation control of a fleet circular formation of auvs under finite communication range[END_REF]. However the case of contraction (or, equivalently, expansion) of a circular formation is still an open problem. In the present work, a control law is developed so that the formation is able to track a time-varying radius reference. An additional component of the control law is also added to achieved the uniform distribution of the agents along the time-varying circle. Moreover, this collaborative control law stands for the case of range-dependent graph, and provides some simulations showing the asymptotic convergence.

The paper is organized as follows. The following section recalls an existing results of the field of circular formation control and shows their limitations. Section III exposes the main contribution of the article which deals with the contraction and the expansion of the formation. Section IV proposes an extension to achieve the uniform distribution for the communication constraint described above. Simulations of multi-agent systems tracking a circular formation with a time-varying radius are given in Section V.

Notation. A complex number z is written in boldface and is expressed as z = x + iy where i 2 = -1 and where x = Re{z} and y = Im{z} correspond to the real and the imaginary part of z. The notations |z| = z, z 1/2 and ∠z stand for the magnitude and the argument of the complex number z. Denote z 1 , z 2 the product Re{z T 1 z 2 }, where z T 1 represents the conjugate transpose of z 1 . Note that the real part (respectively the imaginary part) of a complex number z can be written as z, 1 (and respectively z, i ). Thus, for any complex functions z 1 and z 2 , the equality

z 1 , i z 2 , 1 -z 1 , 1 z 2 , i = z 1 , iz 2 holds.
This paragraph presents some basic tools of graph theory. When an agent k communicates with an agent j both agents are called neighbors. The set of neighbors of agent k is denoted by N k . The communication topology for the groups of agents can be represented by means of a graph G(V, E) where V = {1, 2, ..., N } is the set of vertices (agents) and E = {(k, j) : j ∈ N k } the set of edges (communication links) such that (k, j) ∈ E if agent k communicates with agent j.

II. PROBLEM FORMULATION AND PRELIMINARIES

A. Model of agents

Consider a set of N agents (vehicles) whose dynamics are given by the standard agent model commonly used in the literature to model AUVs restricted kinematics [START_REF] Leonard | Collective motion, sensor networks and ocean sampling[END_REF], [START_REF] Paley | Stabilization of symmetric formations to motion around convex loops[END_REF], [START_REF] Sepulchre | Stabilization of planar collective motion: All-to-all communication[END_REF], [START_REF] Sepulchre | Stabilization of planar collective motion with limited communication[END_REF], [START_REF] Sepulchre | Graph laplacian and lyapunov design of collective planar motions[END_REF], [START_REF] Lin | Necessary and sufficient graphical conditions for formation control of unicycles[END_REF] and [START_REF] Sepulchre | Group coordination and cooperative control of steered particles in the plane[END_REF]:

ṙk =v k e iθ k (1a) θk =u k ( 1b
)
where k = 1, . . . , N , r k and θ k represent the position vector and the heading angle, as illustrated in Figure 1. The variables v k , u k are the control inputs. This model corresponds to a kinematic unicycle fitting with model properties subject to a simple nonholonomic constraint.

The problem considered here is to design a control law such that the group of AUVs forms a circle whose center is fixed and whose radius traks a time-varying reference R d (t) as described in Figure 1. R d (t) is considered here as an external reference.

B. Preliminaries

Some previous works on the field of coordinated control and specifically on planar collective motions, use the kinematic model in which each vehicle moves in the plane subject to planar steering control, which is our model (1) with constant velocity v k = v 0 = 1, ∀k. In [START_REF] Leonard | Collective motion, sensor networks and ocean sampling[END_REF], the authors suggest a control law to converge to a circular formation center at a particular and constant c. It corresponds to the center of mass and is obtained by solving a consensus algorithm. The control law uses the relative position vector from the center to vehicle k defined as

rk = r k -c = 1 N N j=1 (r k -r j ).
For such a formation, the authors propose the following theorem:

Theorem 1 (Leonard et al. [START_REF] Leonard | Collective motion, sensor networks and ocean sampling[END_REF]) Consider the vehicle model [START_REF] Olfati-Saber | Consensus and cooperation in networked multi-agent systems[END_REF] with v k = v 0 = 1, ∀k. Then the control law:

u k = ω 0 (1 + κ rk , ṙk ) (2)
where κ > 0 and |ω 0 | = 0, ensures that all the agents converge to a circular formation centered at c and of radius

R 0 = v 0 /|ω 0 |.

C. Fundamental limitations

These previous results are only applicable to the case of a fixed formation center c, and a constant radius R 0 . In this situation, it is sufficient to design a control law such that the velocity of all the agents is constant (for instance v k = 1, ∀k). However, when it comes to the case of a time-varying radius R d (t), a limitation appears naturally. The variation of the radius can not be greater than the velocity of the agents otherwise the tracking can not be achieved. Hence a new strategy which tackles the objectives needs to be developed. The velocity v k becomes a new and necessary control input to overcome this mechanical constraint. Then, in the sequel, the variables (v k , u k ) and (r k , θ k ), respectively, are the inputs and the state of the agent k. In the latter, the notations r and θ denote the vectors containing the position and headings of all the agents.

III. CONTRACTION CONTROL DESIGN

Consider the problem of tracking a circular formation defined by a constant and known center c and a timevarying radius. Assume that the radius reference R d is always positive and its first and second time-derivative are known and bounded. Moreover, the following assumption is required:

Assumption 1. Let t s > 0 be a sufficiently large time to be defined latter. Assume the radius R d satisfies the conditions:

∀t < t s , R d (t) = R 0 , Ṙd (t) = Rd (t) = 0
Remark 1 This assumption corresponds to a kind of initialisation of the multi-agent systems. The idea is to permit the agents to reach a circular formation with a constant radius and then to start tracking the time-varying radius reference, as shown in Figure 3. This assumption is not restrictive since this initialization protocol would be used in practice.

The main contribution of the present article is the introduction of new variable rk such that:

rk = rk R d (3)
scaling the relative velocity. This new system of coordinates rk are designed so that it does not depend on the radius reference. The circular motion is normalized also with unit radius then | ṙk | = |ω 0 |. Consider now that the dynamics are driven by:

ṙk = |ω 0 |e iψ k (4)
where ψk is the only control input to stabilize the new system to the circular motion. Therefore this problem is equivalent to the one treated in Theorem 1.

A new control law is proposed in the following theorem:

Theorem 2 Consider three positive scalars > 0 and

0 < R 1 < R 2 . Let |ω 0 | = 0 and κ > 0 be two control parameters. Let R d : R → [R 1 , R 2 ]
be a twice differentiable function, with bounded first and second time-derivatives, which satisfies Assumption 1 and the condition:

∀t, Ṙd (t) < R d (t)|ω 0 | (1 + ) (5)
Then the control law:

v k = R d |ω 0 |e iψ k + Ṙd R d rk (6a)
u k = 1 - Ṙd R d ṙk , rk v 2 k ψk + rk , i ṙk v 2 k (R d Rd -2 Ṙ2 k ) R 2 k (6b) ψk =ω 0 (1 + κ rk , ṙk ) (6c)
with the initial conditions ψ k (0) as:

ψ k (0) = θ k (0) (7)
makes all the agents defined by (1) converge to a circular motion of center c, and of radius the time-varying reference R d . The direction of rotation is determined by the sign of ω 0 .

Proof: The convergence to the formation is analyzed with the Lyapunov function:

S(r, ψ) = 1 2 N k=1 | ṙk -iω 0 rk | 2
Evaluating the derivative of S(r, ψ) along the solutions of the resulting closed-loop system (4) with (6c) leads to:

Ṡ(r, ψ) = N k=1 ṙk -iω 0 rk , i ṙk ψk -iω 0 ṙk = ω 0 rk , |ω 0 |e iψ k (ω 0 -ψk ) = -κ N k=1 ω 0 rk , |ω 0 |e iψ k 2 ≤ 0
Therefore S(r, ψ) is an suitable Lyapunov function for this system. Note that when S(r, ψ) = 0 the dynamics of agents satisfy ṙk = iω 0 rk which is the kinematic relation for the rotation of the rigid body. Thus, the agents asymptotically reach the circular formation centered at c and of time-varying radius R d with fixed angular velocity |ω 0 | = 0.

The next step of the proof concerns the design of the control inputs of the original system. Considering (1a), it is easy to see that v k and θ k are given by:

v k = |ṙ k | and tan θ k = ṙk , i ṙk , 1
Using (3), the control input v k is thus straightforwardly given by (6a). A more particular attention is addressed to the input u k . An expression of θk is obtained by computing the derivative of tan(θ k ) as follows:

θk (1 + tan 2 θ k ) = d dt ṙk , i ṙk , 1 or equivalently θk = ṙk , 1 2 ṙk , 1 2 + ṙk , i 2 • rk , i ṙk , 1 -ṙk , i rk , 1 ṙk , 1 2
Using the properties of the operator •, • , described in the notation, the relation is obtained: A control law for the agents to follow a time-varying radius of a circular formation is designed. Note that this control law has singular points when v k = |ṙ k | is zero. This singular point occurs if there exists a time t c such that:

θk = rk , iṙ k ṙk , ṙk = rk , i ṙk
∠r k (t c ) = -ψ k (t c ), | Ṙd (t c )| R d (t c ) |r k (t c )| = R d (t c )|ω 0 | (8)
To avoid the singular situation when v k = 0, the initialization protocol described in Assumption 1 is required. Thanks to Theorem 2, the multi-agents system converges asymptotically to the circular formation centered at c and of radius R 0 . This means that there exists a time t s such that:

∀t > t s , |r k (t) -1| = rk (t) R d (t) -1 <
This inequality can be rewritten as

| Ṙd (tc)| R d (t c ) |r k (t c )| < | Ṙd (t c )|(1 + ). By vertu of (5), this implies ∀t > t s , | Ṙd (t)| R d (t) |r k (t)| < R d (t)|ω 0 |
which is in contradiction with [START_REF] Olfati-Saber | Flocking for multi-agent dynamic systems: Algorithms and theory[END_REF]. Thus the singular point v k = 0 is avoided.

Remark 2 Consider the vehicle model ( 1) with a constant radius of the circle formation R d = R 0 . Then, the the angles ψ k and θ k are equal, and the control law (6) is the same control as in Theorem 1 with a different κ:

v k = R 0 |ω 0 | and u k = ψk = ω 0 (1 + κ R 2 0 rk , ṙk )
Remark 3 In our approach, the angular velocity of the agents ω 0 is considered constant, therefore the linear velocity of the agents v k must be time-varying. However, an other control law can be developed for a constant linear velocity of the agents modifying the angular velocity.

IV. COOPERATIVE CONTROL DESIGN UNDER COMMUNICATION CONSTRAINS

In the previous section, a control law ensures that the agents reach a circular formation with the time-varying radius R d . This section is dedicated to the problem of homogenizing the distribution of the agents along the circle. The case of all-to-all communication and fixed communication graph have already been studied in [START_REF] Sepulchre | Stabilization of planar collective motion with limited communication[END_REF]. Applying this method to the present contraction control law is straightforward, as shown in the similar translation control law developed in [START_REF] Briñón | Translation control of a fleet circular formation of auvs under finite communication range[END_REF]. Moreover in practice, considering fixed communication graphs is not realistic since two linked agents could be very far away from one another.

In the case of underwater communication, the quality of the link is strongly affected by the distance between two agents [START_REF] Stojanovic | Recent advances in high rate underwater acoustic communications[END_REF]. It might be more interesting to consider distancedependent communication graph. This means that each agent can only receive information from its close neighbors. Hence, a communication area is introduced. Assume this area for any agent is defined by ρ which is the critical communication distance given by the characteristics of the communication devices and of the environment of the AUVs. It is assumed to be the same for all AUVs. The condition to get a communication between k and j is expressed as:

k ∈ N j and j ∈ N k ⇐⇒ |r k -r j | 2 ≤ (2ρ) 2
Based on the graph theory, a time-varying Laplacian matrix L(t) is defined as:

L k,j =    d k , if k = j -1, if |r k -r j | ≤ 2ρ 0 otherwise (9)
where d k is the degree of vertex k, defined as the number of its neighboring vertices. In such a situation, the following theorem holds.

Theorem 3 Consider two positive scalars

0 < R 1 < R 2 and a twice differentiable function R d : R → [R 1 , R 2 ],
with bounded first and second time-derivatives. This function satisfies Assumption 1. Let the control parameters be such that |ω 0 | = 0, κ > 0, and assuming the condition ( 5) is satisfied. Let G(t) be the communication graph, L(t) be the corresponding Laplacian matrix and the critical communication distance ρ satisfies:

ρ ψ (k-1)k ψ k(k+1) ψ (k+1)(k+2) d (k-1)k > 2ρ d k(k+1) = 2ρ
ρ > R 2 sin π N ( 10
)
Then the control law [START_REF] Paley | Stabilization of symmetric formations to motion around convex loops[END_REF] with

ψk = ω 0 (1 + κ rk , ṙk ) -∂U ∂ψ k U (ψ) = -K N [N/2] m=1 1 2m 2 e imψ , Le imψ (11)
and initial conditions ψ k (0) as:

ψ k (0) = θ k (0)
ensures that all agents reach the circular formation centered at c of radius R d (t). Moreover the uniform distribution of the agents along the circle is achieved.

Proof: The stability is analyzed by the composed Lyapunov function V (r, ψ) = κS(r, ψ) + U (ψ) whose derivative satisfies V (r, ψ) ≤ 0. Thanks to Theorem 2, the control law (6) makes all the agents reach the circle centered at c and radius R d . Then, consider the potential function [START_REF] Sepulchre | Stabilization of planar collective motion with limited communication[END_REF]:

U (ψ) = - K N [N/2] m=1 1 2m 2 N k=1 U k m (ψ)
where U k m (ψ) can be expresed as:

U k m (ψ) = d k - N j=1,j =k L k,j (t) cos mψ kj
where ψ kj = ψ k -ψ j denotes the relative angle between agents k and j. Note that

N k=1 U k m =< e imψ , L(t)e imψ >.
The objective of the collaborative control is to minimize the function U (ψ), or equivalently to maximize the functions U k m (ψ) to achieve the uniform distribution. Without loss of generality, consider agent k. U k m (ψ) represents the potential functions associated to agent k. The maximum of these functions is obtained when the relative angles between agent k and its neighbors is π/m. This means that the angle between agent k and its neighbors will tend to π/m. This works for all m and this finally leads to an increase of the angles between connected agents until the communication between them is lost. As shown in Figure 2, the geometry of the problem ensures that the connection between agent k and a neighbor j is lost when:

sin ψ kj 2 = ρ R d (t)
On the other side, U k m (ψ) is discontinuous because of the definition of the Laplacian matrix L. Note that the communication with any agent, for instance j, leads to a contribution in the potential function of the following type:

1 -cosψ kj ≥ 0 Thus, if a communication is lost, a positive contribution is removed. Therefore, the potential functions decrease discontinuously. Finally the agents are deployed along the circle. The condition [START_REF] Dimarogonas | On the rendezvous problem for multiple nonholonomic agents[END_REF] ensures that this expansion guarantees that the agents are connected at least in d 0 -circular graph.

Applying Theorem 7 from [START_REF] Sepulchre | Stabilization of planar collective motion with limited communication[END_REF], the fact that G is a circular graph implies that the splay pattern, (N, N )-pattern, corresponding to the uniform distribution is locally asymptotically stable. No other local critical point is achieved because other critical points of the potential function require that a link between agents is broken and consequently an increase of the potential function. Therefore all the agents are uniformly distributed along the circle. Thanks to change of coordinates (3), the dynamic closed-loop equation corresponding to our approach (time-varying radius) is time-invariant, hence LaSalle principle can be applied.

Remark 4

The set of curve-phase arrangements that are balanced modulo 2π/N (uniform distribution) is asymptotically stable for K > 0. Moreover if K < 0 the control law of Theorem 3 forces convergence to the synchronized circular formation [START_REF] Sepulchre | Stabilization of planar collective motion with limited communication[END_REF]. Remark 5 As in Remark 1, if the reference radius is chosen constant, R d (t) = R 0 , then the control law [START_REF] Dimarogonas | On the rendezvous problem for multiple nonholonomic agents[END_REF] still holds.

Remark 6

The same framework can also be applied to the case of circular formation control to track a time-varying center [START_REF] Briñón | Translation control of a fleet circular formation of auvs under finite communication range[END_REF].

V. SIMULATION RESULTS

This section presents the simulations of the multi-agents system composed of AUVs whose dynamics are defined in [START_REF] Olfati-Saber | Consensus and cooperation in networked multi-agent systems[END_REF]. In all simulations the controller parameters are κ = 1 and ω 0 = 1. The control parameter to achieve the uniform distribution is K = 0.1.

Figure 3 shows the evolution in time of the relative position magnitudes |r k | of five agents controlled by ( 6) from Theorem 2. The five agents follow the time-varying radius reference R d (t). This function satisfies Assumption 1 and condition [START_REF] Olfati-Saber | Consensus problems in networks of agents whit switching topology and time-delays[END_REF].

Figure 4 shows the trajectory of only one agent governed by the control law defined in Theorem 2 during the contraction motion defined by the time-varying radius reference R d (t) from Figure 3. The tracking of the circle contraction is achieved for any random initial conditions (position and heading of the agent).

Figure 5 shows the evolution of five agents and its distribution along a fixed circle whose radius is constant R 0 = 5m. Each figure shows a snapshot from the same simulation. The five agents are governed by the control law defined in Theorem 3. The critical communication distance ρ = 3.5 satisfies the condition [START_REF] Dimarogonas | On the rendezvous problem for multiple nonholonomic agents[END_REF]. Thanks to the timevarying communication graph is complete, from a certain instant, the agents achieve the uniform distribution all over the circle at t = 30s.

VI. CONCLUSIONS

We presented a contraction control law that stabilizes a circular formation centered at fixed center and tracking a time-varying radius of the circle. This radius is a given reference which is known for all the agents. Moreover, this paper proposes a cooperative control algorithm to achieve the uniform distribution of the agents along the circular formation. This algorithm integrates with the contraction control a potential function which reaches its minimum in the desired uniform configuration. This potential function is designed taking into account the communication constraints between agents. The result of this combination is a cooperative control of a planar particle model with limited communication to track a time-varying reference. The obvious following step is combined the translation [START_REF] Briñón | Translation control of a fleet circular formation of auvs under finite communication range[END_REF] and contraction laws in order to control the main transformations of the circle.

At this time, it is assumed that all agents have perfect knowledge of the position of the fixed center c and of the radius reference R d and its first and second derivatives. One can consider this assumption as a very restrictive one. However, this constitues a first step of our research and further developments would consider a cooperative algorithm which will avoid this assumption.

Fig. 1 .

 1 Fig. 1. Illustration of the problem formulation.

v 2 k

 2 To express this equation in terms of the previous control variable ψk (change of coordinates), note that: ṙk = ṙk = R d ṙk + Ṙd rk rk = rk = iR d ṙk ψk + 2 Ṙd ṙk + Rd rk Therefore the control law (6b) is obtained.

Fig. 2 .

 2 Fig. 2. Formation of communication chains during the contraction motion.

Fig. 3 .

 3 Fig. 3. Simulation of five agents with the controller designed in Theorem 2. The time-varying radius reference (dashed black line) represents the circle contraction from R 1 = 7m to R 3 = 1m crossing R 2 = 4m. The color lines represent the distance to center of each agent.

Fig. 4 .

 4 Fig. 4. Simulation of an agent with the control law (6) from Theorem 2. The control law parameters are ω 0 = 1 and κ = 1. The trajectory of the agent (the dashed red line) shows the time-varying radius reference (figure 3) followed. The figure shows three snapshots. The blue agent represents the initial condition R d (0) = 7m. The reds ones represent an intermediate state R d (65s) = 4m and the final state R d (85s) = 1m.

Fig. 5 . 3 . 5 .

 535 Fig. 5. Simulation of five agents with the controller designed in Theorem 3 and range-dependent communication. The critical communication radius is ρ = 3.5. Each figure shows the communication graph represented by the blue lines.

VII. ACKNOWLEDGEMENTS

This research is supported by FeedNetBack project and CONNECT project. FeedNetBack is a recently accepted EU STREP project FP7-ICT-2007-2 and the CONNECT project is funded by ANR (Agence Nationale de la Recherche), PSIROB06-174215