WINE BRANDS OR BRANDED WINES? THE SPECIFICITY OF THE FRENCH MARKET IN TERMS OF THE BRAND

Keywords: Brand Equity, wine brands, branded wines, involvement, subjective knowledge Paper type: Research Paper

Purpose -The purpose of this article is to show that the branded wine concept refers to a very heterogeneous category as regards wine made in France, but this sort of wine can appeal to certain types of consumers. Design/methodology/approach -An initial qualitative study was carried out to explore consumer representation as regards branded wine. A second, quantitative, study enabled us, through a cluster analysis, to identify brand-sensitive consumer segments in the wine field. Findings -There is a divergence in consumer representation between novices and experts. The former consider A.O.C.s (Appellation d'Origine Contrôlée, a French official label of protected geographical indication) and regions as brands whilst the latter have a narrower vision of what a branded wine means. The "discoverers", the youngest consumers (18-29 years old), who are interested in wine and have little knowledge of it are most liable to be influenced by wine brands. The novices and routine consumers are also brand sensitive but to a lesser degree. The experts, on the other hand, are not influenced by brands.

Research limitations/implications -The influence of the brand derives from the declarative. A more indirect measure which mixes the brand with other wine attributes would be preferable. The use of a sample of convenience means results can only be generalized with caution. Practical implications -There indeed exists a place for branded wines on the French market but an association is needed with other attributes such as the origin and/or the grape variety. Originality/value -Little research has been devoted to the French consumer's acceptance of branded wines.

Introduction

In France, regular consumption of wine is declining and is being replaced by more occasional consumption which is more closely focused on immediate pleasure and quality at a reasonable price. In the face of such an obvious statement of fact, certain producers have adapted their production in accordance with the wishes of these new, non-traditional consumers. Individual or collective marketing strategies have been put into place and have been translated into: new brands; new packaging (cans, bags in box and 25cl); new labels which break with traditional codes and new ways of selling (sales by Internet for example).

Among the various initiatives being taken one appears to stand out: the development of a brand strategy. The major wines and spirits groups embarked on this strategy a long time ago since it has enabled them to simplify what they offer to the consumer and provide the latter with a product whose quality stays constant. The Baron Philippe de Rothschild group were the first in France when they launched the Mouton Cadet brand, a mythical brand from the 1930s, which capitalized on the renown of Château Mouton Rothschild. Wine merchants rapidly followed this strategy by developing their own brands and using their commercial power to ensure their success (for example JP Chenet, Grand Chaix de France group; Baron de Lestac, Castel group). Today, several trade syndicates also develop their brands (Le flacon , Cotes de Bourg ; e-motifs, Bordeaux supérieur), as do retailers (Pierre Chanau, Auchan) and a few small producers (l'R de rien by François de Ligneris). The brand notion, therefore, does not reflect a single coherent entity in the wine field as much as it refers to different production methods (blending in certain cases, production from a single estate in others) and therefore variable quality levels. As a result, the brand notion is not clear in consumers' minds: Eight French consumers out of ten cannot give a correct name of a wine brand, 60 % of them give the name of a terroir or a château when they are asked to name a brand [START_REF]Le vin, l'achat, la confiance et la marque : le cas du consommateur français[END_REF]. Despite this poor knowledge, certain wine brands achieve record sales every year (36 million bottles in 2005 for Vieux Pape, 90 million bottles for JP Chenet in 2004) which is a proof of the substantial potential which characterizes this type of strategy.

The prime objective of this article is to clarify the brand notion when it is applied to wine in the French context. The article also aims to understand the scope of its influence on consumers' behaviour and identify possible groups of consumers for whom the brand plays an important role.

A review of the literature will highlight the necessary adaptation of the brand concept as regards wines' product category as well as the role that the brand can potentially play in the wine-purchasing process. A qualitative study will help to clarify the brand concept. It will be followed by a quantitative one whose aim is to identify brand-sensitive consumers in the field of wine. After these developments, we will discuss the interest the players have in embarking on strategies aimed at developing branded wines.

Theoretical background

The brand is defined as "a name, term, sign, symbol, or design, or a combination of these, intended to identify the goods or services of one seller or group of sellers and to differentiate them from those of competitors" (American Marketing Association). According to numerous scholars, the pure and simple transposition of this generic definition is problematic as regards wine [START_REF] Boulet | Les comportements de consommation de vin en France[END_REF]D'Hauteville, 2004;Sirieix, 2001). We therefore put forward a specific notion of the wine brand: "a wine brand is a cluster of attributes which defines the identity of the wine in the eyes of the buyer" [START_REF] Lockshin | La marque et le vin[END_REF]. This 'brand constellation' notion, despite its interest, does not constitute a wine brand definition in itself for it allows us neither to clearly define the outline nor to classify the different branded wines found on the market. Moreover, many empirical studies carried out in Australia, the United States and Europe show that the brand, as an attribute, has varied degrees of importance (Table I). For the Australian consumer, the brand is only mentioned in fourth position, even though "marketed" wines are widespread in Australia [START_REF] Aurifeille | Investigating situational effects in wine consumption: a means-end approach[END_REF][START_REF] Quester | Product involvement in consumer wine purchases: its demographic determinants and influence on choice attributes[END_REF][START_REF] Rasmussen | Wine choice behaviour: the effect of regional branding[END_REF]. In the United States, the brand is found in third position although the grape variety is the most important attribute [START_REF] Zaichkowsky | Measuring the involvement construct[END_REF]. For the Irish, the brand is placed in second position, just after the country of origin. [START_REF] Koewn | Purchasing behaviour in the Northern Ireland wine market[END_REF]. The manner in which the French consumer chooses between different wine attributes is still unknown. [START_REF] Rasmussen | Wine choice behaviour: the effect of regional branding[END_REF] Australia [START_REF] Aurifeille | Investigating situational effects in wine consumption: a means-end approach[END_REF] The But, if the power of the brand attribute is established in literature, only "strong" brands could have such an effect on consumer behaviour. The brand strength is conceptualized by the brand equity construct. Brand equity is determined by brand awareness, perceived quality, consumers' loyalty and brand associations or brand image [START_REF] Aaker | Building strong brands[END_REF]. For the French market, what we usually consider as a brand for the other products categories is not necessarily associated with a strong brand when it concerns wine, although there are some exceptions like Mouton Cadet, Baron de Lestac... Some of them suffer from a lack of awareness and/or their perceived quality is not very high. They are often associated to downmarket wines like La Villageoise, a wine sold in plastic bottles.

Table I -Wine attributes importance in different countries

Australia

Conceptual model and research propositions

From the consumer's point of view, the brand acts as a heuristic of choice, as a risk limiter according to Roselius (1971) and Jakoby and Kaplan (1972) and as a sign of quality which gives consumers an indication of the quality of the product prior to consumption and/or helps consumers to remember a level of quality associated with a product they have already consumed. A sign of quality is: "an information summary (an overall knowledge or a concentration of learning) that is reinforced by product display, or a family of products, from a signal allowing consumers to identify and recognize the product: a logo, a symbol, a name, etc." [START_REF] Mazé | Quality signals and governance structures within European agro-food chains: a new institutional Economics approach[END_REF]. By replacing other information, the brand simplifies the selection process. In the food industry, the requirement for quality means that the brand notion -seen as a sign of quality -is a first-rate strategic asset [START_REF] Belik | Food Retailing, Quality Signals and the Customer Defence[END_REF]. However, the brand notion applied to wine remains ambiguous for certain consumers. They do not possess a clear perception of what a branded wine is. Specifically, consumers tend to infer the same status to generic types -grape and region -as they do to specific brands [START_REF] Gluckman | A consumer approach to branded wines[END_REF]. Certain regions or certain terroirs in France (Bordeaux, Alsace, Provence, Languedoc, Burgundy, etc.) take the role of the brand both for the foreign consumer (Mora, 2008, p. 21) and for the domestic one [START_REF] Boulet | Les comportements de consommation de vin en France[END_REF][START_REF] Gluckman | A consumer approach to branded wines[END_REF][START_REF] Holter | Listening to the brand[END_REF]. Nevertheless, it is at best a generic brand whose identity is not necessarily very clear since it is the result of a very high number of producers (more than 10, 000 for Bordeaux alone). On the other hand, for the New World, the approach is different: the consumer buys a grape variety (Cabernet Sauvignon), a brand (Casillero del Diablo) or the name of a company (Mondavi). In the last instance, the brand masks an extremely wide variety of origins: for example, Mondavi buys wine in Italy and Chile and sells it under a single brand name. In Australia, only involved consumers are considering region of origin as an important choice factor in the wine-buying decision making process [START_REF] Mc Cutcheron | Region of origin and its importance among choice factors in the wine-buying decision making of consumers[END_REF].

The legal point of view strengthens the complexity of French regulations on viti-vinicultural brands. For example, to be registered as a brand, the sign in question must be distinctive -it must not be the necessary, generic or usual designation of the product -and non-deceptivenot mislead the public on the nature, quality or geographical origin of the product -(articles 711-1 and following of the Code of Intellectual Property). Once these legal provisions have been respected, the company has a wide choice as regards the creation of a brand name. A place-name (name of a château, a hamlet) can be registered as a brand on condition that it indeed corresponds to the vineyard in question (Château Haut-Brion, Petrus) Finally, from the producer point of view, the notion of brand wine is confusing. Thousands of labels and operators are present on wine market and most of them are emerging from relatively small and family businesses. All of these brands cannot be considered as real "wine brands" because these small producers cannot offer themselves the powerful tools of advertising and promotion indispensable to build mass market awareness and brand equity.

More precisely, a survey of the managerial practices reveals that the French commercial environment is characterized by three major types of brand strategy.

The first, the "merchant brand", corresponds to wines sold by merchants [START_REF] Bomsel | Vin, produit et information[END_REF], quoted by Gherbi, 2004) such as Malesan, Baron de Lestac, Celliers des dauphins, J. P. Chenet etc. These are generally blended wines. It is a wine which is made, bottled and packaged by a merchant who puts his/her own name and brand on the label. It is characterized by the fact that it guarantees a result to the consumer -the quality is constant -and by the fact that the product has been made to suit the market. For the second -the "producer brand" -the production process is the central element: it guarantees a striving for quality, a means of production dedicated to obtaining a "good wine" and the origin [START_REF] Bomsel | Vin, produit et information[END_REF]. This category includes, for example, château wines. Any wine estate with the means to grow vines and make wine can take the name of a château and sell its wine under this name as long as it is an A.O.C.. The third type includes wine sold under a store's brand. These brands have an important place in France since they accounted for more than 32% of sales in large and medium-sized retail outlets in 2007, which represents 6 points growth compared to 1998 (Viniflhor, 2008a). In fact, this category covers clearly distinct strategies [START_REF] Gherbi | Marques et foires de vin[END_REF]. The case of a retailer's brand name being displayed on the label remains relatively rare since consumers are not always prepared to show a wine carrying a retailer's logo at their table (for example, wines from Leader Price, a hard discounter). Reserved brands are wines bottled exclusively for a retailer (Pierre Chanau, Auchan's own brand). The brand is only available in the outlets of a single retailer but the same wine can be distributed by a competitor under a different name. "Reference" brands serve as a discreet reminder of the retailer's name (La sélection Auchan) through the use of a fixed neck-band label.

In conclusion, branded wines, on the French market, refer to a very heterogeneous category of wines, especially as regards production methods. The existence of different conceptions of brand, the strong reputation of some AOC and the various brand strategies followed by wine producers and wine merchants are quite confusing for consumers while we can suppose that it will not be the case for experts, in particular for people working in the wine sector. That's why we formulate a first research proposition P 1 : P 1 . In the field of wine, the representation of brand will differ between experts and consumers.

The moderating role of involvement

The wine-buying process is influenced by several personal variables among which we find involvement. "involvement is a state of interest, motivation or arousal" [START_REF] Rotschild | Perspectives on involvement: current problems and future directions[END_REF].

Involvement towards the product is defined as a perceived personal interest for the product from a given consumer [START_REF] Celsi | The role of involvement in attention and comprehension processes[END_REF]. It influences the consumer's behaviour [START_REF] Flynn | A Short, Reliable Measure of Subjective Knowledge[END_REF][START_REF] Laurent | Measuring consumer involvement profiles[END_REF]. As regards the buying of wine, the role of involvement has been empirically validated on several occasions [START_REF] Aurifeille | Global vs International involvement-based segmentation: a cross national study[END_REF][START_REF] Barber | Purchase attribute of wine consumers with low involvement[END_REF][START_REF] Lockshin | Consumer Purchasing Behaviour for Wine: what we know and where we are going[END_REF][START_REF] Lockshin | Using product, brand and purchasing involvement for retail segmentation[END_REF]Quester andSmart, 1996, 1998). Higher involved consumers use more information and are interested in learning more, while low involved consumers tend to simplify their choices and use risk reduction strategies [START_REF] Lockshin | Consumer Purchasing Behaviour for Wine: what we know and where we are going[END_REF]. For example, highly involved consumers place less emphasis on the price than consumers who have low involvement (Zaichkowsky, 1998) and low involved consumers tend to give importance to back label information [START_REF] Barber | Purchase attribute of wine consumers with low involvement[END_REF]. The involvement shown in the wine can also have an impact on the use or not of the "brand" attribute in a purchase [START_REF] Aurifeille | Global vs International involvement-based segmentation: a cross national study[END_REF]. Consumers with low involvement simplify their choice by utilizing price, label, design, grape variety and brand. By contrast, consumers with high involvement are more inclined to use complex information cues [START_REF] Barber | Purchase attribute of wine consumers with low involvement[END_REF]. Brand acts as a risk limiter and we can expect that this attribute is more relevant for consumers who have low involvement in wine, which leads us to hypothesis H 2 .

H 2 -The involvement shown in the wine moderates the impact of the brand in the choice of the wine. The higher the involvement in the wine, the lower the brand influence on consumer.

The moderating role of knowledge

Expertise is a multi-dimensional construct resulting from familiarity with the product category -the behavioural component of expertise since it is the result of experience with the product [START_REF] Alba | Dimensions of Consumer Expertise[END_REF] -and knowledge of the product. It is defined as "the possession of a large body of knowledge and procedural skill" [START_REF] Chi | Expertise in problem solving[END_REF]. Knowledge remains the most important determinant in wine consumption [START_REF] Hussain | Determinants of wine consumption of US consumers, an econometric analysis[END_REF]. It is generally thought that knowledge includes a subjective dimension -what the consumer believes he/she knows -and an objective dimension -what he/she really knows - [START_REF] Alba | Dimensions of Consumer Expertise[END_REF][START_REF] Brucks | The effect of product class Knowledge on information search behavior[END_REF][START_REF] Park | Consumer Knowledge Assessment[END_REF]. Subjective knowledge influences the choice of variables used to infer the wine's quality level [START_REF] Aurier | Consommation du vin en France : une analyse à partir des contextes de consommation[END_REF]Dodd et alii 2005;[START_REF] Edward | The expert wine taster[END_REF][START_REF] Lockshin | The effect of price and oak flavour on perceived wine quality[END_REF][START_REF] Perrouty | Impact des interaction entre marques et régions d'origine sur la valeur perçue d'un vin : proposition de prise en compte de l'expertise perçue du consommateur[END_REF][START_REF] Solomon | Psychology of novice and expert wine talk[END_REF]. Among these studies, only two include a French sample. [START_REF] Aurier | Consommation du vin en France : une analyse à partir des contextes de consommation[END_REF] explored the impact of expertise on the capacity to memorize attributes and the importance given to attributes. According to a European study, carried out with German, Austrian, British and French consumers, [START_REF] Perrouty | Impact des interaction entre marques et régions d'origine sur la valeur perçue d'un vin : proposition de prise en compte de l'expertise perçue du consommateur[END_REF], the importance given to the brand varies according to the consumers' degree of expertise. For the novices, it is in fifth position whilst for the experts it is at the bottom of the classification. On the other hand, the "brand*region" interaction is the first attribute that the experts take into account. This study only presents agglomerated results. Therefore, we cannot deduce the importance that the French consumer gives to the brand but we can suppose that the brand influence depends on the subjective knowledge of wine according to previous studies [START_REF] Perrouty | Impact des interaction entre marques et régions d'origine sur la valeur perçue d'un vin : proposition de prise en compte de l'expertise perçue du consommateur[END_REF]. Because of the low number of empirical studies devoted to the impact of the brand and of subjective knowledge on wine-buying in a French context, it is relevant to formulate hypothesis H 3 .

H 3 -Wine subjective knowledge moderates the impact of the brand in the choice of the wine. The higher the wine knowledge, the lower the brand influence on consumer.

Methodology

Two studies were carried out. The first one is an exploratory qualitative study while the second one is more explanatory and quantitative.

Study 1

The first study aims at found evidence for the first research proposition P 1 (in the field of wine, the representation of brand will differ between experts and consumers). In order to identify what the experts and the consumers consider as a brand in the field of wine, a qualitative study was carried out on two samples. On one hand, a sample of experts was constituted thanks to students doing a Master in Wine marketing (see Table II for the composition of expert sample) They are considered as experts because they have a good level of knowledge in wine marketing, wine business, wine law and wine production process. On the second hand a sample of "average consumer" was collected. This population is supposed to be much more heterogeneous as regards its level of expertise. Two open questions were asked to the respondents.

Question 1: "How would you define a branded wine?" The answers highlight the consumers' and experts' representations of branded wines. Question 2: "Can you name the branded wines that you know? Reply according to what you consider to be a branded wine" The answers give an indication of the objective level of knowledge towards the wine, for experts and consumers.

The corpus was then subjected to a manual thematic analysis.

Study 2

The purpose of this second study (quantitative study) is to found evidence for hypothesis H 2 (the moderating role of the consumer's implication on the importance granted to the brand during the choice of the wine) and H 3 (the moderating role of the consumer's expertise on the importance granted to the brand).

A questionnaire was given out to the sample of consumers described above (n = 190). The consumption frequency was measured by a nominal scale with four categories: non consumer; very occasional consumer (less than once to twice a week); occasional (once to twice a week) and regular (every day or almost). In terms of knowledge, a subjective measure was used in accordance with the conclusions of [START_REF] Flynn | A Short, Reliable Measure of Subjective Knowledge[END_REF]. Respondents expressed their knowledge through 4 items reflecting a general feeling of knowledge, expertise in comparison to others and familiarity with wine [START_REF] Korchia | The Effects of Brand Associations on Three Constructs[END_REF]. Involvement in wine was measured by a four-item scale inspired by the brand interest scale developed by [START_REF] Korchia | The Effects of Brand Associations on Three Constructs[END_REF], Table III. This scale initially developed for the brand is suitable since it is applied to wine. A single item of the 8 had to be discarded. The « involvement » and « knowledge » dimensions provide satisfactory internal reliability. The influence of the brand when buying wine was measured by an item ("The presence of a brand on the label could positively influence my choice") for which the respondents had to indicate their degree of agreement on a 1 (totally disagree) to 4 (totally agree) scale.

Table III -Wine interest and knowledge measurement scale

A cluster analysis including the variables of interest, knowledge, consumption frequency and age was carried out in order to identify the consumer segments where the brand has the greatest influence. We took a three-stage clustering approach, according to [START_REF] Cannon | Buyer-Seller Relationships in Business Markets[END_REF], [START_REF] Homburg | Configurations of Marketing and Sales: A Taxonomy[END_REF] procedures. The three core issues in clustering are 1) determining the number of clusters, 2) assigning observations to clusters, and 3) assessing the stability of cluster assignments.

Results of Study 1: the specificity of the wine brand concept

The thematic analysis of the first question (How would you define a branded wine?). enables us to clarify the brand notion in the minds of experts and consumers.

For the experts (sample 1), five associations emerge. They represent the core meanings of what wine represents in the minds of consumers. A branded wine is:

(1) A wine with constant quality (43 % of respondents)

The experts associate a branded wine with a "wine which has a constant quality over time" or with "regular quality".

(2) A wine characterized by a strong marketing approach (28 %)

The marketing approach can concern the packaging, the communication, the distribution and the merchandising: "easy to pick out on the shelves […] same marketing tools as spirits";

"it is a wine which is easy to pick out in the shop because it has strong identifying characteristics"; "a wine which is well distributed, present in shops and in the media, with well thought-out and sophisticated packaging and a simple and suggestive name".

(3) A standard wine (24 %) A branded wine, according to the experts, refers to the "standardization of the product"; to "a standard quality wine", "democratic", and "not very complex". It "goes against the terroir".

(4) A wine made by a merchant (24 %) A branded wine is closely associated with a merchant's wine resulting from blending.

(5) A mass-produced wine (9.5 %) To a lesser extent, the experts associate branded wines with high-volume production.

In the minds of the other group (n = 190), a branded wine is defined by four types of attribute:

(1) A wine whose origin is known: terroir and appellation (26 % of respondents), château, estate (23 %)

The brand serves to identify the origin of the product, either through the producer (estate, château) or a region of production, a terroir. .

(2) A wine whose reputation is well established (22 %)

The respondents associate the branded wine with "a wine which is known and recognized" and with "reputation".

(3) A wine with high perceived quality (17 %) According to the respondents, a branded wine is a quality wine. Quality is expressed both in gustatory terms ("a wine with a nice taste") and also in more objective terms in as much as the wine is certified by recognized specialists ("A recognized wine : experts and the general public" "A wine with a medal") or through labels ("A branded wine is one which follows quality criteria such as the A.O.C.").

(4) A wine with a powerful and prestigious image (5.3 %) Branded wines, as seen by consumers, also benefit from a distinctive and prestigious image: "wine which has character and stands out from others"; "wine which is almost unique in terms of taste and history"; "prestige"; "a wine which you cannot be indifferent to, which gently stimulates your taste buds".

In conclusion, two elements are apparent. On one hand, branded wines represent different things in the minds of consumers than in those of experts. For the group described as experts, the wine brand conjures up associations with "marketed wines". It is a narrow vision when compared with that of the sample of consumers. For the latter, the perceived quality is relatively high, whilst for the experts it is seen as simply standard or constant. According to the consumers, the brand enables us to identify the origin of the wines -terroir or producerwhilst for the experts it is essentially a question of blended or merchants' wines whose producer cannot be identified. Finally, for consumers, branded wines are known and recognized. They have a high awarenes value. The constant quality, their standard character and the association with a merchant's wine are referred to by consumers but in a far lower proportion than by experts. These answers probably come from expert consumers who refer to "marketed wines".

The analysis made on the second question (name some wine brands) enables us to go further in terms of how a consumer describes a wine brand. Table IV shows the results of the reclassifications carried out on the answers to this open question (reorganisation of the answers into 6 categories indicated in the table below). The analysis of the content clearly shows that the notion of the brand in the minds of the consumers does not correspond to what we commonly agree to call a brand and what experts consider as a brand. The A.O.C.s make up 64.6 % of the answers given as supposed names of brands. They are followed by names of châteaux. Brands in the strict sense represent less than 10 percent of the answers given by consumers while they represent 88 percent for experts.

What can appear at first sight as confusion in the minds of consumers enables us to highlight three elements. Firstly, the brand in the wine field is a cluster of attributes. It takes on a more complex character than in other areas of consumption. Secondly, what the consumer names as a wine brand (region, appellation, château) possesses all the characteristics of a brand in the "marketing" sense of the term. Therefore it is appropriate to talk of a "region equity" [START_REF] Orth | Place-Based Marketing Strategies: A Cross-national Perspective for Wine[END_REF] and of a "château equity" which become key elements upon which the players in this sector must base their sales efforts. These attributes function as a brand and act upon consumers' buying decisions. Equally, if confusion is great for the large majority of respondents, it remains absent for the group defined as experts.

Based on the results of the qualitative survey, it is possible to clarify the brand notion in the wine context. We could represent the different brands of wine in two ways: a) the assumed quality associated with the brand (high vs. low) and b) the level of expertise in wine (experts vs. average consumers). Thanks to this distinction, three levels of wine brands appear (figure 1) which represent different degrees of brand concepts applied to the word of wine: wine brands, branded wines and lastly stricto sensu branded wines (or « marketed » wines). These three levels of wine brands are associated with very different product attributes, as shown in figure1.

The first level corresponds to the consumer perceptions (wine brands). This is the most heterogeneous representation which gathers all the elements considered as brands by the consumer. Within this level of representation, we can therefore include, for example, the origin, the grape variety and the « château » term.

The second one is the branded wines representation which is close to the legal notion of the viti-cultural brand. This category includes brands created by merchants, vins de pays with a brand name and retailers' own label brands, for example. These names have to possess a high level of consumer awareness and a good image in order to play the full role of the brand in the eyes of the consumer.

The third degree is the experts' representation of branded wines. It is made up of « marketed » wines or stricto sensu branded wines. These can be defined as blended wines made in cellars by merchants or by other producers (for example, wine cooperatives), sold under powerful brand names, targeting constant and standard quality and produced on a large scale. In our empirical study, the experts' notion corresponds more closely to the definition of the stricto sensu branded wine.

Figure 1.

Representations of brands in the French wine context

Result of Study 2: the role of the brand in the wine buying process

To perform the cluster analysis, people who declare not buying and not consuming wine were discarded from the sample. Only 177 responses were used. To begin with, a graphic analysis (hierarchical classification) is carried out to determine the number of clusters. Thanks to this analyse, four groups are identified. The measure used is the square of the Euclidian distance with Ward's aggregation method. The dendrogram displays the existence of four distinct groups. Finally, clustering 20 randomly selected sub samples from the data, each containing two-thirds of the sample, we found strong support for a four-cluster solution.

In the second stage, a dynamic cluster analysis (Diday, 1973;Diday, 1993) was carried out in order to specify the profile of the groups and in order to assign observations to clusters (Table IV). Dynamic cluster analysis is equivalent to K-means method used by [START_REF] Homburg | Configurations of Marketing and Sales: A Taxonomy[END_REF] according to Jourdan and Jolibert (2006, p. 371). Finally, to asses the stability of cluster assignment, we randomly split the sample in halves and perform a discriminant analysis. This analysis involves deriving the linear combination(s) of the independent variables that will discriminate best between the a priori defined groups, that is to say, novice consumers, routine consumers, discoverers and expert consumers. In discriminant analysis, independent variables are multiplied by their corresponding weight and these products are added together. The result is a discriminant score for each individual. The average of these discriminant scores within a particular group is referred as centroid. The first sub sample was used to identify the discriminant function(s) and determine the centroids. Then, each object in the second half were assigned to the nearest cluster centroid obtained from the first half. As a result, we obtained four cluster assignments for each object. The cross-validation indicates that 96.6 percent observations were correctly assigned. More over, 94 percent of non-selected observations were correctly assigned. Thus the stability of the cluster assignment is demonstrated.

Tableau IV -Cluster analysis

Class

The first class is made up of very occasional consumers (they drink wine less than 1 or 2 times per week), whose knowledge and involvement in wine is the lowest. These are novice consumers. They are between 30 and 45 years old.

The second group comprises young, occasional consumers (they drink wine 1 or to times per week), aged between 18 and 29. Their knowledge of wine is average but their involvement in it is high. These are discoverers who would like to become expert consumers (they wish to know more about wine).

The third class gathers together occasional consumers who are more than 45 years old. Their knowledge of wine is relatively high and their involvement in it is average compared to discoverers and experts. These are routine consumers.

Finally, the last group is dominated by expert, regular consumers of wine (they drink wine every day or almost) and are more than 45 years old. It is in this group that knowledge of wine and involvement in it are the greatest.

A one-way ANOVA was then conducted to compare the influence of brand between the four clusters. Even thought the brand influence is stronger for less knowledgeable consumers (m=2.73 for novices; m=2.78 for discoverers) compare to more knowledgeable one (m= 2.67 for routine consumers; m=2.67 for experts), the differences are not statistically significant (F 3; 163 = 0,229, p > 0.05). More over, the brand influence is stronger for discoverers while their involvement in wine is higher compared to the novice or to the routine consumers.

We decided to split the sample in three parts as regards to wine subjective knowledge: low (n=46; subjective knowledge < 2), average (n=62; subjective knowledge between 2 and 2.75) and high knowledge (n=66; subjective knowledge > 2.75). The average level of subjective knowledge was 2.39 and the standard deviation 0.73. A new one-way ANOVA was carried out in order to compare the brand influence between the three groups. The brand influence is stronger for the low knowledgeable group (m=2.98) and weaker for the high knowledgeable group (m=2.2). The difference between the "low knowledge" group and the "high knowledge" group as well as the difference between the "average knowledge" group (m=2.93) and the "high knowledge" group are significant (p<0.05). Thus, hypothesis H 2 (the involvement shown in the wine moderates the impact of the brand in the choice of the wine: the higher the involvement in the wine, the lower the brand influence on consumer) is partially supported. Finally, the same procedure was used to compare brand influence between low, average and high involvement groups but none of the differences were significant. Thus H 3 (Wine subjective knowledge moderates the impact of the brand in the choice of the wine. The higher the wine knowledge, the lower the brand influence on consumer) is not supported.

General discussion and conclusion

What emerges from the first study is that experts and consumers have different representations of brand in the field of wine. Experts consider that only standard massproduced "marketed wines" made by wine merchants are branded wines while, in consumers' mind, wine brands are associated to high quality, prestige, reputation and awareness. More over, the brand concept is not clearly perceived by the consumer: there is confusion between the brand and the A.O.C. Several factors account for this confusion. Firstly, certain A.O.C. wines are price-positioned very closely to marketed wines (between 1.5 and 2.5 euros). However, the A.O.C. alone does not suffice to sell a wine. Spared until 2004, this segment has been affected by the crisis since then. With its 450 appellations, what it offers is often considered complex whilst the vins de pays, with greater room for manoeuvre, have introduced marketing strategies designed to simplify what they sell. For example, Boire et Manger is a range of wine with colourful packaging which suggest which dishes go with the wines (fish, lamb or poultry). Secondly, certain practices foster confusion between brand and château. Many châteaux sell branded wines. A novice consumer could easily confuse a Mouton Cadet with a Château Mouton Rothschild. Certain brands make multiple references to our imagination of life in the château through the name (Baron de Lestac, anagram of Castel), in the packaging (château de Cadillac on the label of the Les hauts de Lestac wine) or in commercial communication (joint advertising of the Cellier des Dauphins brand and of Château de Rochegude, Relais et Château de la Drome) and maintain this confusion.

The second study shows that the brand is probably an appropriate response to certain consumer segments although our results are not statistically significant. This can be first explained by the measure of brand influence we used in the quantitative study. This was an influence expressed by the respondents and not the direct measurement of behaviour. A second explanation of this result concerns what each group of consumer (novice or expert) considers as a wine brand. More over, it is according to what she/he considers as a brand that each respondent has answered this question. The qualitative study has shown that the consumer has a very broad perception of the brand notion. Experts and novice consumers are probably not influenced by the same branding strategy. The study 1 shows that consumers are sensitive to awareness, reputation and prestige. For the novice consumers, perhaps AOC, regions, "châteaux" are more able to reach these characteristics than wine merchants' brands, except some well known brands like "Mouton Cadet". If producers and wine merchants want to convince consumers to buy branded wines, they have to capitalize on existing brands or to create new strong brands. More over, the cluster analyse reveals the existence of an interesting class of wine consumers "the discoverers". They are young "emerging wine learners" coming from the novices group. They declare to be positively influenced by brands. It's important to differentiate novice consumers from discoverers because they tend to be sensitive to more complex attributes, traditionally used by the experts, like origin, vintage and production [START_REF] Barber | Purchase attribute of wine consumers with low involvement[END_REF].

For several years, brands have been presented as a miracle solution to enable the French wine industry to escape from the crisis. Has this happened? We must bear in mind that the fall in wine consumption in France is a structural phenomenon (70 litres per inhabitant per year in 2005 compared to 160 in 1965). Brands alone cannot reverse this trend. However, our results can help producers in defining brand strategies. Here is a five-point answer.

1. French wine making is closer to a craft than an industrial process while high production volumes are necessary to hope to recoup the investments needed to develop a brand. Often, small producers have to be brought together before a genuine marketing approach can be embarked upon.

2. The development of powerful brands should not be to the detriment of the consumer's expectations in terms of quality and price. In 2008, the average price paid in France was 2.99 euros per litre [START_REF] Viniflhor | Les achats de vins tranquilles par les ménages français pour leur consommation à domicile -Campagne 2007-2008[END_REF]. The qualitative study shows that even if consumers have difficulties naming branded wines, they have a very clear view of the qualities that they should possess. It must be "a wine whose quality is known and recognized" (Study 1). Quality and awareness are two determinants of brand equity [START_REF] Aaker | Building strong brands[END_REF]. In this respect, wine is the same as other product categories: the brand should reassure the consumer. It is unlikely that consumers will be satisfied with a wine with merely an image.

3. Producers and merchants must focus on range brands which reduce marketing investments, facilitate a change in attitude towards new products and strengthen consumer awareness of the brand equity. This is, for example, the strategy followed by the Grands Chaix de France with the JP Chenet brand. The same brand name is used to sell different wines all around the world. In a longitudinal study, [START_REF] Wilcox | Facets of brand equity and brand survival -a longitudinal examination[END_REF] found a positive relationship between brand equity (brand recognition and perceived quality) and probability of brand survival. A stretched brand is more able to match consumer awareness and, thus, to survive.

4. Co-branding strategies must be given top priority in order to reassure the consumer. Several types of wine-specific alliances can be envisaged. The brand/name of merchant alliance is desirable if the merchant group has a good reputation. The Cordier firm, for example, puts its name on most of its wines: Collection privée, Agathe, Prestige and Terres d'Héritage. The brand/origin alliance is particularly interesting given that these two attributes are closely linked in the mind of the consumer. The origin/brand interaction is certainly an asset to be exploited for both the vins de pays and the A.O.C. The origin provides an extra guarantee. In this alliance, the place/region equity and the brand equity interact to strengthen the product image. For example, Bordeaux can play such a role. The brand/grape variety/origin alliance can also serve as a guarantee. Although grape variety is traditionally considered as a secondary attribute in France, it must not be neglected given the healthy state of the varietal vins de pays segment (+ 18.3 % in value and + 17.8 % in volume in 2007), (VINIFLHOR, 2008a). In this category, red wines (Merlot and Cabernet Sauvignon grape varieties) make up the greatest market share (61 %) with an increase of 24 % in 2007. But rosé varietal vins de pays (with a 21% market share) are also enjoying growing success: + 27.5 % in volume for Cinsault and + 19.8 % for Grenache. This is another way to strengthen brand equity.

5. Finally, the brand can provide an appropriate response to certain consumer segments, especially to discoverers. New brand names convey a semantic change and show a willingness to stand out from the field of the château: E-motifs, Le flacon, Virginie de France, « Maestral, L'infernal and Tandem by DP. It is not sure that breaking existing codes is desirable for traditional consumers and for neo consumers (author, 2009). This remark is also applicable to the foreign consumer. When she/he buys a French wine, she/he is probably looking for one which is typical of this category rather than a wine which appears closer to a New World one because of its packaging. The branded wines which have the best sales in France are those which « copy » château wines in terms of design and packaging.

In conclusion, this research has certain limits which constitute paths to improvement. Firstly, the influence of the brand has been considered as an isolated attribute and from the brand name point of view. In reality, the brand is an attribute among others and we need to add other attributes, by using, for example, a conjoint analysis or an information display board to better understand the importance of the brand in the choice of a wine compared to other cues like intrinsic cues, aesthetic cues and packaging and information on back label, for example. Such a method would allow to by-pass the declarative measure of brand influence used in this research.

Secondly, the changes in the French market are not restricted to purely quantitative aspects. The occasions when wine is drunk are also changing [START_REF] Aurier | Consommation du vin en France : une analyse à partir des contextes de consommation[END_REF]. The image of wine as a drink accompanying daily meals is in sharp decline -when it is associated with a meal, it is essentially for a festive or a weekend one -and new occasions when wine is drunk are developing (apéritif and a moment of relaxation with friends). The influence of the brand can vary according the occasion.

Finally, it would be appropriate to explore the attraction of French branded wines for international consumers. When they buy a French wine, are they attracted by a branded wine or by one which respects the traditional codes ?

  , what is your level of knowledge of wines in general? (1 = non-existent ; 4 = excellent) average consumer, would you say that your knowledge of wine is((1 = non-existent ; 4 = excellent)

  Finally, the brand can be unconventional(Mouton Cadet). The name of the brand cannot refer to an A.O.C.. As such, the brands Domaine de la Romanée Conti, Fort Médoc or Vieux Cahors were removed since they included a name of an A.O.C. in their denomination. A few exceptions to this principle exist: Bouquet de Provence (the brand name existed before the Cotes de Provence 'appellation') and Château Grillet, which is both the name of a château and an A.O.C., for example. French law therefore makes a very clear distinction between a brand and an A.O.C.. This legal wide conception as regards the creation of wine brands could entail a bigger confusion in consumers' mind.

	brand (Château Lynch-Bages).
	. Only A.O.C.
	wines can use the terms "clos (walled vineyard), château, domaine, tour (tower), mont, côte
	(hillside)". However, local wines can mention the geographical origin since they are produced
	in a one and the same "pays" (a département or a terroir : Vin du Pays d'Oc, for example) and
	furthermore they can add qualitative terms such as « mas » (traditional farmhouse) or
	"domaine", considered as more characteristic of the country than the term "château". On the
	other hand, this is not possible for table wines. The name of the owner can be established as a

Table II -

 II Study

		1 -Sample composition
		Sample 1 : experts sample	Sample 2 : average consumer sample
	Size	21	190
	Age	from 21 to 27	from 18 to 89
		mean = 23	mean = 42
	Origin	Aquitaine : 33%	Aquitaine : 52%
		Other region producing wine	Other	region	producing	wine
		(Burgundy, Alsace, Languedoc): 66%	(Burgundy, Alsace, Languedoc) : 14%
		Other French region : 0%	Other French region : 33%

Table IV -

 IV Classification of branded wines named

	branded wines)
	merchant wines	37	3.8	9.5	2.4
	Grape varieties	27	2.8	0	2
	Foreign wines	20	2	2.5	0.6
	Total	967	100	100	100
		Total answers	Sample 1	Sample 2
		Sample 1 + 2	Expert	Consumers
				students	n = 190
				N = 21
		Absolute	Relative	Relative	Relative
	Catégories	frequency	frequency	frequency	frequency
	Origin : AOC, terroirs, regions	530	54.8	0	64.6
	Names of châteaux	179	18.6	0	20.6
	Commercial brands (stricto sensu	174	18	88	9.8

château grape variety AOC vins de pays blended wines / merchant wine wine cooperatives High perceived quality Low perceived quality Retailers' own label brands

	Average	1.38	2.36	2.44	3.09	134,91	< 0.001
	knowledge of
	wine
	Average	1.85	3.32	2.45	3.70	87,45	< 0.001
	involvement in		Expert perception
	wine Age Percentage of STRICTO SENSU 30-45 BRANDED WINE 16,5	18-29 30	More than 45 30	More than 45 23,5	63,47 -	< 0.001 -
	respondents		constant quality
	strong			BRANDED WINE
	marketing approach	Foreign wine
	mass-produced wine
						Prestigious
						image
						Known
						origin
					Reputation
					WINE BRANDS
			Consumer perception
						F Test
		Novice consumers	Discoverers	consumers Routine	consumers Expert	F	Stat. sign.
	Consumption	Less than 1 to	1 to 2 times	1 to 2 times	Every day or	36,47	< 0.001
	habits	2 times per	per week	per week	almost
		week


Valentin Riviere

Augustin Manecy

Stéphane Viollet

Agile robotic fliers: a morphing based approach

come

Objective

Flying through cluttered environments requires an outstanding level of agility, which often involves the ability to trigger aggressive maneuvers to quickly avoid obstacles or pass through gaps at high speed. In the living world, agility is not restricted to ying insects or even small birds such as hummingbirds. Larger birds such as goshawks [START_REF] Packham | Goshawk Flies Through Tiny Spaces in Slo-Mo!, The Animal's Guide to Britain, Episode 3 -BBC Two -YouTube[END_REF] and budgerigars [START_REF] Schiner | Minding the gap: in-ight body awareness in birds[END_REF] are able to negotiate cluttered environments at high speed despite their relatively large wingspan. How do they manage to perform tasks of this kind? By morphing their shape dynamically and reducing their wingspan swiftly by tucking up their wings. Morphing abilities give a ying robot agility by momentarily reducing its wingspan while keeping a suciently high payload. Morphing does not require any aggressive maneuvers but fast embedded mechanisms for folding up the robot's structure, as described in [START_REF] Luca | Bioinspired morphing wings for extended ight envelope and roll control of small drones[END_REF] for a winged drone.

In the eld of robotics, Unmanned Aerial Vehicles (UAVs) are being used increasingly in cluttered and indoor environments for various purposes such as search and rescue expeditions [START_REF] Tomic | Toward a fully autonomous UAV: Research platform for indoor and outdoor urban search and rescue[END_REF], mapping [START_REF] Nex | UAV for 3D mapping applications: A review[END_REF] and exploration [START_REF] Shim | Autonomous Exploration In Unknown Urban Environments For Unmanned Aerial Vehicles[END_REF]. The latest ying robots therefore have to be able to avoid collisions and handle narrow gaps successfully. Quadrotors, with their hovering and Vertical Take-O and Landing (VTOL) abilities, are certainly among the best candidates for meeting these requirements.

Here we focused on designing a narrow gap-crossing strategy which was implemented on a quadrotor. One previous strategy, which has been widely studied consisted in performing aggressive maneuvers to make the quadrotor change its attitude swiftly in order to pass through a vertical or tilted window [START_REF] Mellinger | Trajectory generation and control for precise aggressive maneuvers with quadrotors[END_REF]. Recent studies [START_REF] Falanga | Aggressive quadrotor ight through narrow gaps with onboard sensing and computing using active vision[END_REF][START_REF] Loianno | Estimation, Control, and Planning for Aggressive Flight With a Small Quadrotor With a Single Camera and IMU[END_REF] have succeeded in developing autonomous robotic gap crossing skills based on on-board sensing and computing processes. However, this aggressive attitude control approach has several limitations: the robots have to reach high velocities and angular accelerations which require low inertia of the robot's body as well as high sensor refresh rates, especially in the case of visual sensors so as to prevent blur motion and maintain accurate position estimation with respect to the gap to be crossed.

To address this issue, a new approach was adopted based on morphological changes. Previous authors have presented various types of quadrotors in which the size of the structure can be adapted either passively or dynamically for dierent purposes. Non-actuated structures were used by [START_REF] Mintchev | Insect-Inspired Mechanical Resilience for Multicopters[END_REF] to ensure resilience to collision and by [START_REF] Mintchev | Foldable and Self -Deployable Pocket Sized Quadrotor[END_REF] to obtain a self-deployable system facilitating the robot's transport. Actuated structures were used by [START_REF] Desbiez | X-Morf : a crashseparable quadrotor that morfs its X-geometry in ight[END_REF] to reduce the wingspan of a hovering robot or to reduce the robot's volume with a scissor-like foldable structure in [START_REF] Zhao | The Deformable Quad-rotor : Design, Kinematics and Dynamics Characterization, and Flight Performance Validation[END_REF]. Simulated robotic platforms with morphing abilities have been endowed by [START_REF] Barbaraci | Modeling and control of a quadrotor with variable geometry arms[END_REF] with full attitude control and by [START_REF] Hintz | Design and dynamic modeling of a rotary wing aircraft with morphing capabilities[END_REF] with an interesting tilting rotor mechanism.

Here we present a novel morphing approach whereby a ying quadrotor is endowed with an actuated elastic morphing structure which enables it to cross any gaps encountered at high speed.

As shown in the supplementary video, the folded robot is able to pass through apertures that are narrower than the unfolded robot. Section 2 describes in detail the design and the dynamic model on which the morphing robot's structure was based. The control laws and strategy used to stabilize the robot during the folding and unfolding steps are described in section 2.4. The experimental results presented in the last section 3 show the performances of which the Quad-Morphing robot is capable.

Material and Methods

2.1

Hardware and Software Overview

As shown in gure 1, we designed and constructed an aerial robotic platform (Quad-Morphing robot) to test the ability of an aerial robot to pass through a gap smaller than its wingspan without any need of aggressive maneuvers. The hardware architecture of the Quad-Morphing robot was based on a previous custom-made platform developed at our lab [START_REF] Manecy | X4-MaG: A Low-Cost Open-Source Micro-Quadrotor and its Linux-Based Controller[END_REF], which consisted of (see gure 2):

• a Gumstix R Overo R 's linux-based Computer-On-Module (COM) for high-level control (attitude/position/folding control) and communication with the ground station via WiFi.

• a NanoWii board carrying a 6-axes Inertial Measurement Unit (IMU MPU6050), which can be used to control manually the quadrotor.

• A very fast and accurate servomotor (MKS DS92A+) actuating the folding system.

• a Rotor Controller board (RCB): a custom-built board giving a low-level control of the rotational speed propellers and providing connections between all the components.

The servomotor implemented on the robot was as fast and light as possible. The folding system was designed so that the two arms could rotate concomitantly to fold or unfold the structure, using a single actuator. Further details about the folding system are given in the following section.

Mechanical Design and Model

As shown in gure 3, the Quad-Morphing robot was based on a classical quadrotor platform, the mechanical structure of which was greatly adapted to make the robot able to reduce its wingspan dynamically. To simplify the mechanical design, a straightforward approach was used, which consisted in using two pivot links to allow the two arms supporting the robot's propellers to

Size parameters

The Quad-Morphing robot was designed with a 400g payload. The body length l b and arm length l a (see gure 3) were sized with respect to the propeller's radius r p real . During the design phase, we also examined the use of a slightly larger propeller radius (r p = 70mm) than the actual length (r p real = 64mm) to prevent the propellers from touching each other. The robot had the following main dimensions, as shown in gure 3:

r p real = 64mm r p = 70mm l a = 2.r p = 140mm l b = 4.r p = 280mm (1)

Dynamic model

To rotate from the inertial frame I to the robot's frame R (see gure 1), we used ZYX Euler angles, which corresponds to the rotation matrix R dened as follows:

ψ: Yaw around the Z-axis θ: Pitch around the Y'-axis φ: Roll around the X-axis

In the rst step, we modeled the Quad-Morphing robot using Newton's equations of motion for dynamic rigid bodies [START_REF] Hamel | Dynamic modelling and conguration stabilization for an X4-yer[END_REF], including the thrust and torques applied to the robot, the gyroscopic

ξ = v m v = -mg -→ z I + Γ (1,:) .ω 2-→ z R -K v v Sum of forces in I = -mg -→ z I + R.   0 0 Γ (1,:) .ω 2  
Normal force produce by propellers

-K v v Ṙ = RΩ × I robot (γ) Ω = M G Sum of the moments at G in R = -Ω × I robot (γ)Ω Gyroscopic term + Γ (2→4,:) (γ)ω 2
Torques produce by propellers

Where ξ = v and v are respectively the robot's speed and its acceleration expressed in the inertial frame I, Ω × is the skew symmetric matrix of the body's rates, m is the mass, I robot is the inertia matrix, R is the rotation matrix, Γ is the control matrix (see equation 5), where Γ (1,:) corresponds to the rst line of the matrix Γ, and ω is the column vector of the propellers' rotational speed. The changes in the inertia İrobot were neglected since they were taken to be temporary disturbances occurring only during folding maneuvers, i.e., during a very short period (about 200ms, see section 2.3). The inertial accelerations of the arms canceled each other out because they moved in opposite directions during the folding and unfolding processes (see gure 3).

Torques and thrust generated by the quadrotor depend on the square of the propellers' rotational speed, according to the propeller's physics [START_REF] Mises | Theory of ight[END_REF], as follows:

F pi = c T .ω 2 τ pi = c D .ω 2 (3)
where F pi and τ pi are the thrust force and drag moment produced by the i-propeller, respectively. c T and c D are the thrust and drag coecients, respectively.

Torques on the roll and pitch axes also depend on the folding angle γ (see gure 3). The control matrix Γ transforms each propeller's speed into a thrust force T Σ and moments τ roll,pitch,yaw as follows:

    T Σ τ roll τ pitch τ yaw     =             4 i=1 F pi 4 i=1 y i .F pi - 4 i=1 x i .F pi 4 i=1 τ pi             = Γ(γ).     ω 2 1 ω 2 2 ω 2 3 ω 2 4     ω 2 (4)
Where T Σ and τ roll,pitch,yaw are the total thrust and torques applied to the three axes in the robot's frame, respectively. x i and y i are the distances on the x-axis and y-axis of the i-propeller. The coecients of the matrix Γ depend on geometrical parameters which are given by:

Γ(γ) =     c T c T c T c T -c T . l b 2 .cos(γ) c T . l b 2 .cos(γ) c T . l b 2 .cos(γ) -c T . l b 2 .cos(γ) -c T .( L 2 + l b 2 .sin(γ)) -c T .( L 2 -l b 2 .sin(γ)) c T .( L 2 + l b 2 .sin(γ)) c T .( L 2 -l b 2 .sin(γ)) c D -c D c D -c D     (5)
The coecients of the matrix Γ are updated in real time to take into account the changes occurring in the folding angle γ due to the rotation of the servomotor (see gure 3). As expected in view of the design of the folding structure, the moment around the roll axis becomes uncontrollable when the folding angle is equal to 90 • (see second line of matrix Γ in ( 5)).

Inertia

The robot's inertia R I robot (G) during the folding process, calculated on the basis of the center of mass G with respect to the robot's frame R, depends on the folding angle γ and can be decomposed into the following three matrices: the body's inertia R I body (G) and the two arms' inertia R I arm1 (A) and R I arm2 (A ), calculated on the basis of the arms' centers of mass A and A , respectively.

R I robot (G) = R I body (G) + R I arm1 (A) + R I arm2 (A ) (6)
Computer-Aided-Design software provided the inertia matrix terms in the inertial frame for the body and arms as follows:

R I body (G) =   I bx 0 0 0 I by 0 0 0 I bz   ; A I arm1 (A) = A I arm2 (A ) =   I ax 0 0 0 I ay 0 0 0 I az   ( 7
)
The formula is calculated for just one arm by obtaining the arm's inertia on the robot's center of mass G in the robot's frame R, using Steiner's theorem and the parallel axis theorem:

R I arm1 (A) = R A→R . A I arm1 (A).R t A→R with R A→R =   cos(γ) sin(γ) 0 -sin(γ) cos(γ) 0 0 0 1   (8) R I arm1 (G) = R I arm1 (A) + m arm1 . R D( -→ GA) with R D( -→ GA) =   z 2 A 0 -x A .z A 0 x 2 A + z 2 A 0 -x A .z A 0 x 2 A   ; -→ GA =   x A 0 z A   (9)
Substituting ( 9) into ( 6) , we obtain: As we can see, the inertial matrix R I robot (G) stays diagonal during the folding process, which would not be the case if the arms were rotating in the same direction. We therefore chose the mechanical conguration described in gure 3 with the two arms rotating in opposite directions.

R I robot (G) = diag   I bodyx +
It can also be seen from equation [START_REF] Mintchev | Insect-Inspired Mechanical Resilience for Multicopters[END_REF] that the inertia depends on the folding angle γ on the roll and pitch axes. The controller's gain is therefore automatically adjusted, depending on the state of the robot's structure (folded or unfolded).

From equation [START_REF] Mintchev | Insect-Inspired Mechanical Resilience for Multicopters[END_REF], the changes in the inertia occurring on each rotational axis due to the folding were calculated:

∆I robotx = -43% ∆I roboty = +11% ∆I robotz = 0% (11)
As expected from the folding mechanism, the inertia on the roll axis decreases dramatically by 43%, whereas the inertia on the pitch axis increases by only 11%. The inertia on the yaw axis remains unchanged. The increase in the pitch inertia by about 11% of its initial value when the robot is unfolded led us to increase the PID controller gain on the pitch axis by this amount accordingly. The decrease in the roll inertia by about 43% reects the existence of greater instability in the folded position, but the robot's stability was maintained passively by placing the center of mass below the center of thrust in our design.

Modeling the folding system

As shown in gure 4, the servomotor regulates the robot's wingspan l ws by adjusting the folding angle γ, as well as by changing the robot's length L in line with the following equations (see gure 3 for denitions of the parameters):

L(γ) = l b + 2.r p real + l a .sin(γ) l ws (γ) = 2.r p real + l a .cos(γ) (12)
A new metric called the folding ratio, dened as the ratio between the folded and unfolded wingspan, was written as follows:

η = l ws (γ = 90 • ) l ws (γ = 0 • ) = 2.r p real 2.r p real + l a (13)
As shown by equation ( 13), the gain in terms of the wingspan is directly related to geometric parameters, namely the propeller radius and the length of the arms. In our prototype, the fully folded structure (i.e., γ = 90 • ) can adopt a wingspan l ws equal to 128mm, which corresponds to a folding ratio of η = 48%, whereas the wingspan of the unfolded structure (i.e., γ = 0 • ) is equal to 268mm (see gure 4). In other words, the folded robot is more than 2 times smaller than the unfolded one, which means that the robot can theoretically pass through a gap 2 times smaller than its usual wingspan. The same applies to the robot's length L: the folding ratio is also given in the case of the length in gure 4. Once the wings have folded up, the increase in the robot body's length is 34%. small bumps appear only during unfolding due to the use of elastic wires in the mechanism (see gure 3). However, the small amplitude of these fast bumps (lasting less than 50ms) make them negligible.

The robot can achieve complete folding, i.e., when the wingspan reaches 95% of its nal value, within only ∆t f old = 230ms (mean = 230ms, std = 6ms, 8 experiments) and complete unfolding within only ∆t unf old = 310ms (mean = 310ms, std = 5ms, 8 experiments). Gap Crossing Scenario

Here we present a scenario which consists in passing through a gap at high speed. The transversal crossing speed adopted on the X-axis was 2.5m.s -1 , which corresponds to a good trade-o between a short folding time ∆t f old and the limited ight space available for our experiments. In all these experiments, the width of the gap was smaller than the unfolded robot's wingspan, which caused the robot to adopt the folded conguration, as shown in the frames extracted from a video-recorded gap crossing test (see gure 6).

This scenario can involve three dierent modes, the activation of which depends on the position of the robot with respect to the gap (see gure 7):

• Full control mode: The attitude and position controllers are fully activated and run in real time onboard the robot. Thanks to the trajectory planner described in gure 9, we can generate a feasible trajectory in terms of the acceleration and the speed in order to make the robot reach the speed V Ax as fast as 2.5m.s -1 in the steady state when crossing the point A (see gure 7).

• Degraded control mode: immediately after the folding of the two arms, the integrator output signal (see equation ( 15)) delivered by the roll attitude controller is held constant.

The position of point A prior to the gap is determined by applying the following equation:

∆X f old = V Ax .∆t f old , where V Ax and ∆t f old are the robot's speed at point A and the folding time, respectively.

• Recovery control mode: once the gap has been passed, a recovery mode procedure is initiated in order to re-stabilize the robot at point B, which is dened by a position with respect to the position of the gap:

∆X unf old = L(γ=90 • ) 2 .
We also implemented a supervisor which makes it possible to switch sequentially between the three modes described above so as to adjust the gains and activate the various controllers as required, depending on the robot's position along the trajectory imposed by the planner.

Control and State Estimation

All the control laws, the estimator and the trajectory planner described in gure 8, are implemented on the Gumstix R computer on module via the RTMaG toolbox [START_REF] Manecy | An open-source SIMULINK toolbox for Linux-based real-time robotic applications[END_REF] developed at our laboratory and with QUARC R running in the MATLAB R environment in the ground station with WiFi communications. Position estimation and yaw measurements are provided by o-board sensors: a Vicon R system of localization was used to determine the robot's position in real time and to emulate a magnetometer, which is not implemented on our platform. The motion capture system (the VICON system) can locate with a great accuracy [START_REF] Manecy | X4-MaG: A Low-Cost Open-Source Micro-Quadrotor and its Linux-Based Controller[END_REF] the Quad-Morphing robot in our ight arena, which is equipped with 17 cameras, with great accuracy.

Quadrotor robots are not fully actuated systems: four inputs corresponding to the four propeller's speeds control six outputs, which are the six degrees of freedom of the robot's rigid body (attitude and position in 3D). To control systems of this kind, we used two cascaded controllers (as described in gure 8): one position controller providing the thrust and two accelerations in the horizontal plane, and one attitude controller which receives horizontal accelerations and yaw angles as inputs and delivers outputs consisting of the three torques (roll, pitch and yaw). The motor controller then determines the propellers' speeds by means of the control matrix Γ, the inputs of which are the thrust and the three torques.

Position and yaw estimation

The 3-D position and the heading are the only measurements acquired by the motion capture system at a sampling frequency of 500Hz. The data are then ltered by a Kalman lter to reduce the noise and sent via WiFi at a frequency of 200Hz to the Gumstix R computer embedded on board.

Attitude estimation

A complementary lter [START_REF] Mahony | Nonlinear Complementary Filters on the Special Orthogonal Group[END_REF] was added for estimating the robot's attitude and de-biasing the rate gyros. Unfortunately the IMU does not include any magnetometers for estimating the heading, which was specied in real time by the ground station via WiFi. With the gyro and accelerometer measurements Ω and -→ g imu , respectively, we obtain:

       q = 1 2 q ⊗ p( Ω -b -α) ḃ = k b .α α = k a • - → g ×( q - → g imu) - → g 2 + k v s.ṽ (14)
Where ⊗ is the Hamilton product, p(v) is dened by p(v) = 0 v t , • is the Hadamard product, and is the quaternion-vector product (dened by q v = q 0 v t q -1 ). The quaternion error is dened by q = s ṽ t = q-1 vicon ⊗ q, s and ṽ are the scalar part and the vectorial part of the error respectively, k a = k a1 k a2 0 and k v = 0 0 k v3 are weighting matrices which enable us to use the accelerometer alone to determine the roll and pitch values and the external Vicon R to determine the yaw value.

Attitude and Position Controllers

The quaternion attitude controller implemented on-board based on [START_REF] Brescianini | Nonlinear Quadrocopter Attitude Control[END_REF] [START_REF] Christopher | Quaternion-Based Hybrid Control for Robust Global Attitude Tracking[END_REF], ensures overall asymptotic stability. The following control law was adopted:

Ω des = sign(s eq ).K Ω .ṽ eq τ des = I. k τ .(Ω des -Ω) + k int t 0 e q .dt (15) Where qeq and e q are the quaternion and the vector error, respectively, dened by: e q = seq .ṽ eq qeq = seq ṽeq t = q-1 ⊗ q des (16)

The attitude required is given directly by XY-Axis accelerations and thrust adjustments imposed by the position controller:

   φ des = sin -1 m T des (a 1,des sin ψ -a 2,des cos ψ) θ des = sin -1 m T des (a 1,des cos ψ + a 2,des sin ψ) (17)
The position controller implemented was a proportional-integral-derivative (PID) controller dened as follows:

a F eedBack = k p (ξ des -ξ) + k i t 0 (ξ des -ξ)dt + k d dξ des dt -v (18)
By adding a feed-forward term, the required thrust T des and acceleration a 1:2,des were directly obtained on the X and Y axes as follows:

   T des = m cos φ cos θ a 3,F eedBack + g + d 2 ξ 3,des dt 2 a 1:2,des = a 1:2,F eedBack + d 2 ξ 1:2,des dt 2 (19)
Numerical values of the controller coecients are given by:

k Ω k Γ k int
k p k d k i X 0 3 0 Y 8 6 2 Z 11 3 1
There is no direct adaptation term in the PID controller. The control adaptation is made by updating the coecients of the control matrix Γ as described in 2.2.

Trajectory planning

As described in gure 9, a pre-lter was added to generate speeds and accelerations which are compatible with the robot's dynamics. This trajectory planner consists of three cascaded integrators ensuring smooth accelerations, which are injected into the feed-forward position controller. Physical constraints (speed and acceleration limits) were also added to each integrator by specifying saturation values giving feasible trajectories. This trajectory generator features a good trade-o between computational ressources and physical constraints requirements (more complex trajectory generator could have been used as [START_REF] Mellinger | Trajectory Generation and Control for Quadrotors[END_REF] or [START_REF] Tee | Control of nonlinear systems with full state constraint using a barrier lyapunov function[END_REF]). T s is the sampling time, which is equal to 10ms, K = 1 and τ = 500ms.

Recovery Control

To achieve complete stabilization of the robot once the gap has been crossed, we implemented a recovery control procedure consisting of a control state machine inspired by [START_REF] Faessler | Automatic re-initialization and failure recovery for aggressive ight with a monocular vision-based quadrotor[END_REF].

The state mechanism involves four sequentially event-triggered steps depending on the conditions dened as follows:

1.

Step 1: attitude stabilization: only the attitude controller is turned on with (0, 0, 0) as the required attitude on the three rotational axes (roll, pitch and yaw) and the thrust are kept constant at T = m.g to compensate for gravity.

Step 2 is carried out once the following condition 1 has been reached: CONDITION 1:

       |θ| < 20 • |φ| < 20 • | θ| < 10rad.s -1 | φ| < 10rad.s -1 (20) 2.
Step 2: vertical speed control: the feedback control of the robot's vertical speed is turned on with the required speed equal to zero. When the speed conditions dened below in [START_REF] Brescianini | Nonlinear Quadrocopter Attitude Control[END_REF] are satised, the required vertical position z des becomes equal to the estimated vertical position ẑ just before switching to step 3.

CONDITION 2: | ż| < 0.3m.s -1

⇒ z des = ẑ 3.

Step 3: Longitudinal and lateral speed control: activation of the horizontal speed control with the required speed equal to zero and the vertical position control with a new required vertical position. When condition 3 relating to the X and Y axes ( 22) is satised, the position controller locks the actual estimated positions x, ŷ before switching to step 4.

CONDITION 3:

|v x | < 0.5m.s -1 |v y | < 0.5m.s -1 (22)

⇒

x des = x y des = ŷ 4.

Step 4: full control: activation of the attitude and position control system with new required positions ξ des = (x des , y des , z des ) t .

Metrics and calibration

Metrics

As the Quad-Morphing robot is the rst prototype showing both morphing and gap crossing abilities, some new metrics were adopted in order to show the robot's performances, especially their repeatability. The main metric adopted for this purpose was the projected wingspan on the gap plane on the Y-axis, called w proj (see gure 10), which was dened as follows:

w proj (γ, ψ) = l ws (γ) cos ψ (23)
When the robot is folded, with (

L = L(γ = 90 • ) = l b + l a + 2.r p real l ws = l ws (γ = 90 • ) = 2.r p real 12):
Which leads us to avoid colliding with the gap, with the width of which is denoted w gap :

w proj (ψ) = 2.r p real cos ψ < w gap (25)
Likewise on the Z-axis in relation with the robot's height h and the elevation angle , which corresponds to the angle between x R , the robot's axes and x G , the gap's axes on the (Ox G z G ) plane, with the height of the gap dened by h gap :

h proj ( ) = h cos < h gap (26)
with:

= -tan -1 tan θ cos ψ (27)
As shown in gure 10, we introduced the two points denoted w lef t and w right which correspond to the left and right edges of the cross section between the gap and the robot's span on the Y-axis (h up and h down for the top and bottom edges, respectively, on the Z-axis):

w lef t = ∆Y + wproj 2 -∆X. tan ψ w right = ∆Y - wproj 2 -∆X. tan ψ h up = ∆Z + hproj 2 -∆X. tan h down = ∆Z - hproj 2 -∆X. tan (28)
(28) shows the importance of having an ecient and accurate ψ-angle control, but this can also be said in the case of the Y-axis and Z-axis control in order to minimize ∆Y and ∆Z, i.e., the distance between the robot's center of mass and the geometrical center of the gap on the Y-axis and the Z-axis in the gap's frame G, as can be seen in gure 10. We also considered the case where the robot is outside the gap: this situation requires new denitions of the various points of interest, as follows (see gure 10):

if ψ ≥ 0 w lef t = ∆Y + L(γ) 2 sin ψ + lws(γ) 2 cos ψ w right = ∆Y + L(γ)
2 sin ψ -wproj (γ,ψ) 2 otherwise w lef t = ∆Y + L(γ) 2 sin ψ + wproj (γ,ψ) 2

w right = ∆Y + L(γ) 2 sin ψ -lws(γ) 2 cos ψ if ≥ 0 h up = ∆Z + L(γ) 2 sin + h 2 cos h down = ∆Z + L(γ) 2 sin ψ - hproj (γ, ) 2
otherwise h up = ∆Z + L(γ) 2 sin + hproj (γ, ) 2
h down = ∆Z + L(γ) 2 sin ψ -h 2 cos (29)

Calibration

To improve the robot's performances, several experiments were conducted with the same gapcrossing speed V A X = 2.5m.s -1 in order to compensate for constant perturbations on the Y-axis and the Z-axis during folding by biasing (∆Y bias and ∆Z bias ) the robot's position with respect to the center of the gap. The biases were determined by nding the middle of the most extreme trajectories during our experiments when the robot's center of mass was on the same plane as the gap:

for ∆X = 0: ∆Y bias = max(w lef t )+min(w right ) 2

∆Z bias = max(wup)+min(w down ) 2

Therefore to compensate for these biases, the required positions in the gap frame G during the approach now become:

Y des = -∆Y bias Z des = -∆Z bias (31)

Experimental Setup

The Vicon R motion system was used instead of an embedded magnetometer and to determine the robot's position in real time. Our RT-MaG custom toolbox [START_REF] Manecy | An open-source SIMULINK toolbox for Linux-based real-time robotic applications[END_REF] was used to run the Simulink model on our embedded Linux computer module and to monitor the data in real time with Quanser R Real-Time Control (QUARC R ) running on the ground station. A video of the experimental setup is provided in the attached les.

Crossing the gap

In the eight experiments presented here, we can see the robot's extreme positions during the nal approach and the crossing of the gap (20 × 20cm 2 ). All the positions are given in the gap frame G, where the origin is taken to be the center of the gap.

As shown in gure 11, the robot was able to perform 8 consecutive gap crossing trials without colliding or touching the sides of the gap. Figure 11 shows edges w lef t and w right (as dened in gure 10) in the case of each experiment versus the robot's position on the X G -axis and h up , h down gives the positions of the edges of the robot on the (Ox G z G ) plane. The area between the two blue dashed vertical lines indicates possible positions where the robot is liable to collide with the gap (the gap's width and height are presented in horizontal solid red lines in the gures) and the X-axis corresponds to the robot's center of mass on the X G -axis. In the gure 11, we can see the occurrence of a loss of altitude due to the lower available thrust in the folded position. Once the robot's arms have been folded, the two rotors placed just above the robot's body lead to an overlapping eect which is responsible for the loss of propeller lift. The resulting loss of altitude is Figure 13 gives data on the angular rates recorded when the robot's position was 2m ahead of the gap and when the robot started folding its wings. As expected in terms of the angular rates, this gure shows that low values (never exceeding 100 • /s) occurred on all the axes before crossing the gap plane.

Comparative results

In order to make quantitative comparisons, we recorded nine unfolded robot ights without the gap at the same speed (V X = 2.5m.s -1 ) and recorded the results presented in gure 14 and gure 15.

This gures give an idea of the robot's performances on lateral axis Y in comparison with the folded robot scenario: it can be seen here that the robot can pass safely through a gap which has a minimum width of (w gap ) min = 332mm. This result can be compared with the minimum gap width (w gap ) min = 180mm with the folded robot. Minimum passable gaps are plotted in black in gure 15.

The maximum projected wingspan (w proj ) max observed during all these experiments was also compared with the robot's wingspan while crossing the gap ( wproj lws ) max . The projected wingspan value ( 105% of the actual wingspan value) in the morphing robot can be explained by the yaw perturbations which occurred during the folding process. We therefore sought to determine the minimum passable gap width in the case of each conguration (with/without morphing abilities). To quantify the advantages of this novel conguration, we took the ratio between the gap size which could be crossed by the robot with and without morphing abilities:

η meas = (w gap ) min,with morph (w gap ) min,without morph = 54% (32)
This value can be compared with η = 48%, which is the theoretical gain in the passable gap width in the case of the morphing robot (as detailed in 2.3).

Conclusion

In this paper, a new aerial robotic platform endowed with morphing capabilities is presented. The control laws developed for our Quad-Morphing robot were based on a large body of literature on the non-linear control of quadrotors, including aspects such as attitude estimation and trajectory planning. As observed in studies on birds, our robot can suddenly reduce its wingspan by 50% within a very short time (about 250ms) in order to pass through a gap such as a small square aperture that can be equal to 54% of the robot's unfolded wingspan. We have also presented a gap crossing scenario with a crossing speed as fast as 2.5m.s -1 , which is similar to the forward speed of birds in ight [START_REF] Vo | Anticipatory Manoeuvres in Bird Flight[END_REF]. As bird's wings tuck back against their body, the particularity of our morphing robot is its ability proposed by [START_REF] Falanga | Aggressive quadrotor ight through narrow gaps with onboard sensing and computing using active vision[END_REF].

By adopting new metrics for characterizing the performances of the morphing robot, we have shown that adjusting the yaw angle (< 7 • here) directly aects the robot's gap crossing performances (by dramatically increasing the projected wingspan). Better performances could no doubt be achieved by improving the thrust-to-weight ratio (1.5 in the case of our platform) and the rotor's drag coecient, or by introducing tilting rotors giving yaw-control with thrust. This novel morphing structure does not have to make aggressive maneuvers to make the aerial robot cross a gap at high speed. Morphing improves the trade-o between payload and fast dynamics. The same morphing principle could be applied to a bigger and heavier quadrotor, assuming that the rotor folding mechanism shows suciently fast dynamics. Without having to reduce the payload, it should be possible to equip a future morphing quadrotor with a relatively bulky xed camera so that autonomous gap crossing can be based entirely on an embedded visual system. Unlike strategies requiring aggressive maneuvers, the angular rates of the Quad-Morphing robot's body consistently reached low values here (always less than 100 • /s) during the approach phase towards the gap, which can be easily compensated for when implementing an accurate visionbased positioning system. When a robot is ying towards a gap, taking the decision to fold up its structure or not on the basis of visual cues alone will be the next challenge to be met by the Quad-Morphing robot.

Figure 1 :

 1 Figure 1: (Left) Photo of the Quad-Morphing platform. (Right) Computer-Aided-Design view of the Quad-Morphing platform ying towards a gap while rotating (folding) the arms supporting its four propellers to reduce its wingspan smoothly and quickly so as to avoid colliding with the gap.

Figure 2 :

 2 Figure 2: Hardware description: all the signals are transmitted via the custom-made RCB board giving a feedback control of the propeller speeds and voltage levels.

Figure 3 :

 3 Figure 3: Linkage scheme for the Quad-Morphing robotic platform equipped with an elastic folding mechanism. A servomotor drives the pulley to make the two arms carrying the propellers rotate quickly, resulting in the folding (or unfolding) of the robot's structure. The angle γ, called the folding angle, can range between 0 • (unfolded) and 90 • (folded).

Figure 4 :

 4 Figure 4: Wingspan and various length considerations about wingspan changes depending on the folding angle γ. The folding ratio (see equation (13)) was dened in order to characterize the robot morphing ability in terms of wingspan reduction.

Figure 5

 5 Figure 5 shows experimental curves (8 distinct experiments are presented here) depicting the time course of the folding angle γ and folding ratio η during a folding and unfolding procedure. Data acquisition was made with a Vicon R Sytem motion capture. It can be noted in gure 5 that

Figure 5 :

 5 Figure 5: Folding angle (in blue) and folding ratio (in red) versus time

Figure 6 :

 6 Figure 6: Bottom view: sequence of the Quad-Morphing platform passing through a gap.

Figure 7 :Figure 8 :

 78 Figure 7: Side view of the gap crossing scenario including the three modes which were activated sequentially, depending on the robot's position along its trajectory: 1) Full Control before reaching point A, 2) Degraded Control from point A to B, 3) Recovery Control after point B

Figure 9 :

 9 Figure 9: The trajectory planner generates accelerations, speeds and positions compatible with feasible trajectory. The integrators are presented here in their discrete forward-Euler form, where

Figure 10 :

 10 Figure 10: Top view during gap crossing with w lef t and w right and metric w proj

  not totally compensated for by the controller, which is subjected to thrust limitations in order to prevent the motors from being saturated and to keep full control of the robot's pitch and yaw, and thus to keep a robust control on the (Ox G y G ) plane as shown in gure 11. The thrust is limited by the propellers' intrinsic power, which did not suce to maintain a constant ight altitude when substantial yaw perturbation occurred.

Figure 11 :

 11 Figure 11: Projected wingspan and height versus relative robot position to the gap

Figure 12 :

 12 Figure 12: Euler angles during gap crossing and recovery procedure. Time origin corresponds to the beginning of the folding process.

Figure 13 :

 13 Figure 13: Normalized angular rate distribution before folding in the case of 8 trajectories.

Figure 14 :

 14 Figure 14: Results obtained with and without morphing abilities

Figure 15 :

 15 Figure 15: Projected wingspan with unfolded robot versus the robot's position relative to the gap. Two virtual gaps are shown with both congurations: unfolded and folded

  I bodyz + I az + 2.m arm .x 2

	
		(10)
	A

2.(I ax . cos 2 (γ) + I ay . sin 2 (γ)) + 2.m arm .z 2 A I bodyy + 2.(I ax . sin 2 (γ) + I ay . cos 2 (γ)) + 2.m arm .(x 2 A + z 2 A )

Acknowledgement

Authors would like to thank J. Diperi and M. Boyron for their technical support, and J. Blanc for improving the English manuscript. This work was supported by CNRS, Aix-Marseille University, Provence-Alpes-Cote d'Azur region and the French National Research Agency (ANR) with the Equipex/Robotex project.