Jean-Philippe Mauxion

Christian Chevalier

Nathalie Gonzalez
email: nathalie.gonzalez@inrae.fr

Complex cellular and molecular events determining fruit size

Keywords: organ growth, fruit development, molecular regulation, crop engineering

The understanding of plant organ size determination represents an important challenge especially because of the significant role of plants as food and renewable energy sources and the increasing need for plant-derived products. Most of the knowledge on the regulation of organ growth and the molecular network controlling cell division and cell expansion, the main drivers of growth, is derived from arabidopsis. The increasing use of crops, such as tomato, for research, is now bringing essential information on the mechanisms underlying size control in agronomical important organs. This review describes our current knowledge, still very scarce, of the cellular and molecular mechanisms governing tomato fruit size and proposes future research to better understand the regulation of growth in this important crop.

Tomato fruit, an excellent model to study growth and development Fruit size regulation

In flowering plants, fruits are crucial organs since they protect the seeds during their development and allow their dispersal after maturation. Fruits also form an essential part of human diet and largely contribute to human health by providing a large variety of compounds including fibres, vitamins or phenolic compounds. Among the fruits produced worldwide, tomato is one of the most consumed. Tomato (Solanum lycopersicum) fruit is a low caloric source with high nutritional qualities since it contains lycopene, ascorbic acid, flavonoids and potassium. In addition to its specific biochemical properties and nutrient importance, with a short life cycle, high seed production, tomato has become a broadly used model for research on fleshy fruit physiology and development, a niche that cannot be filled by the model plant arabidopsis (Arabidopsis thaliana) producing a dry fruit, the silique. Indeed, while the silique grows after fertilization with little tissue differentiation, until it reaches its final length and then enters a senescence program, the growth of the tomato fleshy fruit is accompanied by important tissue differentiation, followed by the entry in a complex biochemical program, the ripening, which makes the fruit attractive and ready to disperse seeds [START_REF] Gómez | Molecular programme of senescence in dry and fleshy fruits[END_REF]. The tremendous genetic diversity present in both wild and cultivated tomatoes, for a large number of which genome sequences are available, provides an extensive reservoir of resources available for genetic studies and trait discovery [START_REF] Rothan | Trait discovery and editing in tomato[END_REF]. Especially, the domestication of tomato, which triggered the modifications of a wide range of morphological and physiological characters compared to its ancestral parents, resulted in a huge diversity in fruit weight and shape [START_REF] Bergougnoux | The history of tomato: From domestication to biopharming[END_REF], thus providing key experimental systems to study growth determination. The diversity in fruit weight is very well exemplified when comparing the wild Solanum pimpinellifolium producing fruits weighing around 1 g with the domesticated Solanum lycopersicum var. lycopersicum bearing fruits of more than 1 kg. Despite this huge diversity in fruit size obtained through domestication, the underlying cellular changes and genetic networks are still poorly known. Most of the knowledge on the molecular networks regulating growth is derived from studying the arabidopsis leaf, a model that was very valuable to define the actors in this process [START_REF] Vercruysse | Comparative transcriptomics enables the identification of functional orthologous genes involved in early leaf growth[END_REF]. However, since the wiring of the networks might vary between different species, the translatability can sometimes be difficult. With the rapid advances in deep sequencing, in quantitative genetics and gene editing technologies, it is now possible to directly identify the components and connections of regulatory networks and potentially modify them in crops for breeding. These technologies are easily applicable to tomato, making of this plant an excellent model to dissect the genetic networks determining fruit growth. In this review, we present the current knowledge of the cellular and molecular mechanisms that govern tomato fruit size, and discuss future outlook on research to understand organ size determination.

Tomato fruit growth: the pericarp, site of a complex set of cellular events determining final fruit size After a period of vegetative growth, the transformation of the shoot apical meristem (SAM) into an Inflorescence Meristem (IM) marks the onset of the reproductive phase. In several plants, including tomato, the vegetative growth continues concomitantly to the reproductive phase through the activation, at the basis of the last initiated leaf, of a lateral meristem, also named sympodial meristem, thus defining the sympodial growth character [5]. As for the vegetative axis, the inflorescence shows a sympodial development in most of the cultivated tomatoes. The IM differentiates into a Floral Meristem (FM) to give rise to one flower and a new IM arises from the FM. This type of development gives the zigzag pattern to the tomato inflorescence as illustrated in Figure 1A. Once the FM differentiates, the development of the flower primordium will determine the organisation of the flower composed of four types of organs: the sepals, the petals, the stamens and the carpel. Wild tomato flowers are generally composed of 5 sepals, 5 petals, 5 stamens fused in cone and the pistil resulting from 2 fused carpels, is formed by the ovary, the style and the stigma [START_REF] Brukhin | Flower development schedule in tomato Lycopersicon esculentum cv. sweet cherry[END_REF], while cultivated tomatoes can contain up to 10 fused carpels such as in the Giant Heirloom tomato variety [START_REF] Lippman | Lycopersicon pimpinellifolium and L. esculentum var. Giant Heirloom[END_REF]. The tomato fruit differentiates after fertilisation from a pre-existing structure after fertilisation, the ovary, and is composed by the pericarp, the locular tissue surrounding the seeds, the placenta, the columella and the septum corresponding to the fused edge of the carpels (Figure 1B). The pericarp, corresponding to the fleshy part of the fruit differentiates from the ovary wall. During and after flower development, two cellular events, cell division and cell expansion, occurring in different cell types, at different developmental times and different rates will determine the final fruit size. Figure 2 illustrates in details the different steps of tomato fruit development, with a particular insight for the pericarp.

Tomato flower development can be divided into 20 stages and carpel formation initiates at stage 4 [START_REF] Brukhin | Flower development schedule in tomato Lycopersicon esculentum cv. sweet cherry[END_REF]. Between stage 11 and maturity, the ovary displays intensive growth: the volume of the ovary wall increases by 2-fold and its thickness by 25% [START_REF] Renaudin | Cell layer-specific patterns of cell division and cell expansion during fruit set and fruit growth in tomato pericarp[END_REF]. This growth is mostly supported by anticlinal cell divisions, increasing the number of cells in a given cell layer. Only one cell layer originating from a periclinal cell division is added to the ovary wall after stage 11 to reach around 9 cell layers at maturity. At stage 18, the ovary reaches its mature stage and growth is then arrested. Flower development ends at the anthesis stage which corresponds to the pollination and the fertilization of the ovary, leading to fruit set and triggering the onset of fruit development. At anthesis, the cells composing the ovary wall of the mature ovary, i.e. the future pericarp, have a homogeneous size with a square shape [START_REF] Renaudin | Cell layer-specific patterns of cell division and cell expansion during fruit set and fruit growth in tomato pericarp[END_REF][START_REF] Musseau | Identification of Two New Mechanisms That Regulate Fruit Growth by Cell Expansion in Tomato[END_REF]. The pericarp is made up of different tissues, the exocarp, the mesocarp and the endocarp, corresponding to distinct cell layers which behave differently at the cellular level (Figure 1C) [START_REF] Pabón-Mora | Comparative anatomical and developmental analysis of dry and fleshy fruits of Solanaceae[END_REF]. At anthesis, the exocarp corresponds to the three outer layers (E1, E2, E3), the endocarp to the two inner layers (I2, I1) and between the two, the four central layers form the mesocarp (M) [START_REF] Renaudin | Cell layer-specific patterns of cell division and cell expansion during fruit set and fruit growth in tomato pericarp[END_REF]. Interestingly, the histological analysis of 20 tomato lines showing a wide diversity in final fruit weight, has shown that the pericarp characteristics at anthesis are mostly conserved regarding thickness, cell area and number of cell layers [START_REF] Cheniclet | Cell Expansion and Endoreduplication Show a Large Genetic Variability in Pericarp and Contribute Strongly to Tomato Fruit Growth[END_REF], showing that the size of the pericarp and consequently that of the fruit, is mainly determined after anthesis.

The successful fruit set is characterized by the growth resumption inside the ovary due to cell division activity [START_REF] Renaudin | Cell layer-specific patterns of cell division and cell expansion during fruit set and fruit growth in tomato pericarp[END_REF]12]. After fruit set, tomato fruit growth is classically described as the succession of two phases, a phase of cell division followed by a phase of cell expansion.

However, this view is very simplistic, since detailed quantification of cell division and cell expansion within the pericarp has shown that these two processes co-exist and overlap very early during fruit growth (Figure 2) [START_REF] Renaudin | Cell layer-specific patterns of cell division and cell expansion during fruit set and fruit growth in tomato pericarp[END_REF][START_REF] Pabón-Mora | Comparative anatomical and developmental analysis of dry and fleshy fruits of Solanaceae[END_REF][START_REF] Xiao | Integration of tomato reproductive developmental landmarks and expression profiles, and the effect of SUN on fruit shape[END_REF]. In addition, cell layer-specific patterns of cell division and cell expansion have been described, highlighting the complex coordination of these two processes during fruit growth. For example, the different parts of the pericarp behave differently with the highest mitotic index found in the exocarp. Moreover, within the exocarp, the three cell layers do not show similar division plane orientations. The outermost layer, E1, increases the number of cells through anticlinal divisions thus driving the increase in fruit perimeter and thus volume. The cells from the two other exocarp layers (E2 and E3), generate the new mesocarp cells layers (M') through periclinal divisions. To a lesser extent, the endocarp layer I2 takes part in the formation of few new mesocarp layers [START_REF] Renaudin | Cell layer-specific patterns of cell division and cell expansion during fruit set and fruit growth in tomato pericarp[END_REF]. Only few divisions, periclinal or oblique, occur in the mesocarp. Depending on the genotype, cell division in the pericarp extends until 5 to 25 Days Post Anthesis (DPA), respectively in the wild tomato Solanum pimpinellifolium and in a large cultivated tomato variety Levovil [START_REF] Xiao | Integration of tomato reproductive developmental landmarks and expression profiles, and the effect of SUN on fruit shape[END_REF]14]. In the small cherry tomato wva106 variety, this period of 9 days after pollination results in an increase of cell number by 30-fold in E1 and 19-fold in E2 [START_REF] Renaudin | Cell layer-specific patterns of cell division and cell expansion during fruit set and fruit growth in tomato pericarp[END_REF]. Depending on the genotype, the number of cell layers in the pericarp ranges from 9 to 26 cell layers [START_REF] Pabón-Mora | Comparative anatomical and developmental analysis of dry and fleshy fruits of Solanaceae[END_REF][START_REF] Cheniclet | Cell Expansion and Endoreduplication Show a Large Genetic Variability in Pericarp and Contribute Strongly to Tomato Fruit Growth[END_REF][START_REF] Xiao | Integration of tomato reproductive developmental landmarks and expression profiles, and the effect of SUN on fruit shape[END_REF].

Concomitantly to the intensive cell division period, the mesocarp cells (M) expand slightly before anthesis and then show a high rate of expansion directly after anthesis until 20 DPA, resulting in an increase of the initial volume by 1550-fold in the wva106 variety [START_REF] Renaudin | Cell layer-specific patterns of cell division and cell expansion during fruit set and fruit growth in tomato pericarp[END_REF]. After the division phase, cells of the other layers enter progressively in expansion leading for example to an increase in volume of 12-fold for cells in the E1 and 400-fold in the I1. Contrary to the original mesocarp cells, the cells from the new mesocarp layer (M') start to expand directly after their formation and continue until 36 DPA to reach an increase of 1350-fold in volume in the wva106 variety. As for the cell division, the orientation of cell expansion is important for pericarp growth. Indeed, a detailed phenotypic characterization of fruit cellular parameters in 12 mutants presenting different fruit weight and tissue morphology has revealed that anisotropic cell expansion, expansion along the abaxial-adaxial axis, is an important parameter for pericarp thickness control [START_REF] Musseau | Identification of Two New Mechanisms That Regulate Fruit Growth by Cell Expansion in Tomato[END_REF].

The intense cell expansion period during fruit growth is characterized by the occurrence of the endoreduplication process [START_REF] Joubès | Molecular and Biochemical Characterization of the Involvement of Cyclin-Dependent Kinase A during the Early Development of Tomato Fruit[END_REF]. Endoreduplication is the result of a modified cell cycle, named endocycle, during which DNA synthesis occurs independently from mitosis [START_REF] Joubès | Endoreduplication in higher plants[END_REF][START_REF] Edgar | Endocycles: a recurrent evolutionary innovation for post-mitotic cell growth[END_REF].

Endoreduplication which leads to an increase in ploidy level, takes place already before anthesis since few nuclei of an 8C DNA content have been observed [START_REF] Renaudin | Cell layer-specific patterns of cell division and cell expansion during fruit set and fruit growth in tomato pericarp[END_REF]. During fruit development, the iteration of endocycles leads to increased DNA content from 4C until 512C in some tomato cultivars [START_REF] Cheniclet | Cell Expansion and Endoreduplication Show a Large Genetic Variability in Pericarp and Contribute Strongly to Tomato Fruit Growth[END_REF]. In the pericarp, ploidy levels and cell areas are positively correlated [START_REF] Bourdon | In planta quantification of endoreduplication using fluorescent in situ hybridization (FISH): In situ endoreduplication assessment of plant nuclei[END_REF]. [START_REF] Bourdon | Evidence for karyoplasmic homeostasis during endoreduplication and a ploidy-dependent increase in gene transcription during tomato fruit growth[END_REF] showed that endoreduplication acts as a morphogenetic factor involved in cell size control according to the 'karyoplasmic ratio theory': it contributes to maintain homeostasis of cytoplasmic components in a highly structured cellular system, where multiple physiological functions are integrated to support cell growth during fruit development [START_REF] Bourdon | Evidence for karyoplasmic homeostasis during endoreduplication and a ploidy-dependent increase in gene transcription during tomato fruit growth[END_REF]. The contribution of endoreduplication in the determination of cell size is supported by a dynamic model of tomato fruit development that includes cell division [START_REF] Baldazzi | Organ-wide and ploidy-dependent regulation both contribute to cell-size determination: evidence from a computational model of tomato fruit[END_REF].

After this intense growth period, the number of cells is multiplied by 15, the cell volume by 170 and the pericarp volume by 2600-fold in the wva106 variety [START_REF] Renaudin | Cell layer-specific patterns of cell division and cell expansion during fruit set and fruit growth in tomato pericarp[END_REF]. The pericarp is thus made of a heterogeneous population of cells with small cells on the outside and larger cells in the middle of the tissue [START_REF] Bourdon | In planta quantification of endoreduplication using fluorescent in situ hybridization (FISH): In situ endoreduplication assessment of plant nuclei[END_REF]. This variation in final cell size might result from the different contribution of each cell layer to the fruit growth. Indeed, external layers could support the increase in volume through periclinal divisions and the inner layers might contribute to the increase in volume of the fruit mostly through expansion [START_REF] Renaudin | Cell layer-specific patterns of cell division and cell expansion during fruit set and fruit growth in tomato pericarp[END_REF]. The occurrence in a coordinated manner of these two events triggers the transformation of a 1-2 mm ovary into a 2-10 cm fruit in diameter.

Despite the existence of a large diversity in tomato fruit phenotypes, fruit pericarp growth can be described as the succession of overlapping and interconnected cellular events with different onsets, with different rates and duration in function of the cell layers: anticlinal, periclinal and oblique cell divisions, and isotropic and anisotropic cell expansion (Figure 2). As a consequence, the final fruit size can only be achieved through a strict spatial and temporal control and coordination of these events. The analysis of mutants, transgenic lines or tomato genotypes with altered fruit size and shape led to the identification of genes involved in some of these processes. In the following section, we describe genes that are involved in each process, and present how altering the different phases of fruit development starting from ovary development until the onset of ripening, can affect the final size of the fruit (Figure 3). We also point the still missing information that would allow building a genetic network for fruit growth determination.

Final fruit size: a highly regulated process from the ovary development to fruit ripening

Increasing carpel/locule number by altering meristem size

Since the fruit is derived from the pre-existing ovary after fertilization, one can expect that an alteration in ovary size might affect final fruit size. A first mean to produce larger fruits by modifying the size of the ovary is well exemplified in the tomato beefsteak variety. In this variety, the number of locules, the cavities derived from fused carpels harboring the seeds, reaches up to 10, thus leading to a fruit that weighs approximating 1 kg, while wild small tomatoes or small-fruited cultivars only contain two locules [START_REF] Rodríguez | Distribution of SUN, OVATE, LC , and FAS in the Tomato Germplasm and the Relationship to Fruit Shape Diversity[END_REF]. This increase in locule number, corresponding to carpel number, is determined as early as floral meristem development and organisation start [START_REF] Mayer | Role of WUSCHEL in Regulating Stem Cell Fate in the Arabidopsis Shoot Meristem[END_REF][START_REF] Xu | A cascade of arabinosyltransferases controls shoot meristem size in tomato[END_REF]. Two natural mutations, lc (locule number) and fas (fasciated), mainly control the number of locules in tomato. Lc and fas are affected in the arabidopsis orthologous genes WUSCHEL (WUS) and CLAVATA3 (CLV3) respectively, which are involved in meristem organisation (Figure 3A). In arabidopsis, WUS encodes a transcription factor involved in the maintenance of stem cell identity within the shoot apical meristem [START_REF] Laux | The WUSCHEL gene is required for shoot and floral meristem integrity in Arabidopsis[END_REF]. An overexpression of AtWUS produces flowers with supernumerary organs lacking the most central organs [START_REF] Xu | Activation of the WUS gene induces ectopic initiation of floral meristems on mature stem surface in Arabidopsis thaliana[END_REF]. In tomato, 2 single-nucleotide polymorphisms (SNP) in the downstream region of the putative orthologous gene, SlWUS, are responsible for the increase in locule number in the lc mutant [START_REF] Muños | Increase in Tomato Locule Number Is Controlled by Two Single-Nucleotide Polymorphisms Located Near WUSCHEL[END_REF]. The occurrence of these SNPs are hypothesized to suppress the binding of the transcriptional repressor AGAMOUS that negatively regulates WUS such as in arabidopsis [START_REF] Liu | AGAMOUS Terminates Floral Stem Cell Maintenance in Arabidopsis by Directly Repressing WUSCHEL through Recruitment of Polycomb Group Proteins[END_REF]. As a result, the expression of SlWUS is increased in floral buds of lc which in turn may allow the maintenance of a larger stem cell population resulting in increased locule numbers [START_REF] Chu | Tomato locule number and fruit size controlled by natural alleles of lc and fas[END_REF][START_REF] Van Der Knaap | What lies beyond the eye: the molecular mechanisms regulating tomato fruit weight and shape[END_REF]. As a second important locus for locule number determination in tomato, the fas locus harbours a modification in the promoter of CLAVATA3, SlCLV3 [START_REF] Xu | A cascade of arabinosyltransferases controls shoot meristem size in tomato[END_REF]. In arabidopsis, CLV3 encodes a secreted glycopeptide involved in the restriction of meristem size through the activation of the receptor kinase CLV1 [30]. The loss-of-function mutant clv3 produces enlarged SAM and FM with supernumerary flowers [START_REF] Clark | CLAVATA3 is a specific regulator of shoot and floral meristem development affecting the same processes as CLAVATA[END_REF]. In arabidopsis the production of double mutants demonstrated that a WUS/CLV3 negative feedback loop determines the organisation and the number of flower organs [START_REF] Schoof | The Stem Cell Population of Arabidopsis Shoot Meristems Is Maintained by a Regulatory Loop between the CLAVATA and WUSCHEL Genes[END_REF]. Interestingly, SlCLV3 shows similar pattern of expression as SlWUS [START_REF] Chu | Tomato locule number and fruit size controlled by natural alleles of lc and fas[END_REF], and lc and fas loci have synergistic effects on locule number and thus fruit size when combined. The presence of the fas locus alone increases inflorescence branching in addition to locule number [START_REF] Xu | A cascade of arabinosyltransferases controls shoot meristem size in tomato[END_REF]. The downregulation of SlCLV3 through RNAi approach shows similar phenotypes, but also has deleterious effects such as the development of ovaries within the initial ovary [START_REF] Chu | Tomato locule number and fruit size controlled by natural alleles of lc and fas[END_REF]. In addition, SlCLV3 is down-regulated in a fas background showing that the fas mutation is a partial loss-of-function of SlCLV3 [START_REF] Chu | Tomato locule number and fruit size controlled by natural alleles of lc and fas[END_REF]. Interestingly, [START_REF] Chu | Tomato locule number and fruit size controlled by natural alleles of lc and fas[END_REF] showed a positive trend between locule number and FM size resulting from the effects of lc and fas. Two additional mutants, fasciated and branched (fab) and fasciated inflorescence (fin), also display enlarged meristems, fasciated flowers with more floral organs and produce larger fruits as a consequence of additional carpels [START_REF] Xu | A cascade of arabinosyltransferases controls shoot meristem size in tomato[END_REF]. The genes underlying these phenotypes in the fab and fin mutants correspond to CLV1 and an arabinosyltransferase, respectively (Figure 3A). In fab, a missense mutation was found in CLV1 and in fin, missense and deletion mutations leading to an absence of transcripts were found in a predicted HYDROXYPROLINE O-ARABINOSYLTRANSFERASE (HPAT). In arabidopsis, CLV1 encodes a receptor kinase which binds to CLV3 as to restrict WUS expression [START_REF] Fletcher | Signaling of Cell Fate Decisions by CLAVATA3 in Arabidopsis Shoot Meristems[END_REF]. The rescue of arabinosyltransferase mutants by an arabinosylated CLV3 showed that CLV3 must be fully arabinosylated to perform its function [START_REF] Xu | A cascade of arabinosyltransferases controls shoot meristem size in tomato[END_REF]. In arabidopsis, the significance of arabinose modifications is less clear since null mutants for HPAT genes do not have a clv phenotype [START_REF] Macalister | Hydroxyproline O-arabinosyltransferase mutants oppositely alter tip growth in Arabidopsis thaliana and Physcomitrella patens[END_REF]. The fab and fin mutations have additive effect and thus act in the determination of meristem size through the WUS/CLV pathway. The loss of function of the EXCESSIVE NUMBER OF FLORAL ORGANS (SlENO) gene results in an increase of the FM size leading to the production of larger multilocular fruits, a phenotype that is much more pronounced in a lc mutation background [START_REF] Fletcher | Signaling of Cell Fate Decisions by CLAVATA3 in Arabidopsis Shoot Meristems[END_REF]. SlENO encodes a transcription factor belonging to the superfamily APETALA2/ETHYLENE RESPONSIVE FACTOR (AP2/ERF), which is supposed to regulate directly SlWUS (Figure 3A) [START_REF] Fletcher | Signaling of Cell Fate Decisions by CLAVATA3 in Arabidopsis Shoot Meristems[END_REF]. During domestication, a 85pb deletion in the SlENO promoter was selected leading to a reduction of its expression, and thus bigger fruits [START_REF] Fletcher | Signaling of Cell Fate Decisions by CLAVATA3 in Arabidopsis Shoot Meristems[END_REF]. Among the actors putatively involved in locule number determination are the following genes: INHIBITOR OF MERISTEM ACTIVITY (SlIMA) and KNUCKLES (SlKNU) encoding respectively, a MIni zinc-Finger (MIF) and a transcription factor belonging to the C2H2 zinc-finger protein family (Figure 3A) [35,[START_REF] Sicard | Meristem activity during flower and ovule development in tomato is controlled by the mini zinc finger gene INHIBITOR OF MERISTEM ACTIVITY[END_REF]. The loss-of-function of SlIMA and SlKNU enlarges fruit size through an increase in carpel number, while the overexpression leads to the opposite effect, i.e. a decrease in fruit size. Together with TOPLESS, these two proteins form a transcriptional complex that recruits Histone deacetylase 19, as to regulate negatively the expression of SlWUS, and thus impair stem cell activity within the floral meristem [35].

In tomato, the control of meristem size by the WUS-CLV pathway is thus essential for fruit size determination through the regulation of locule number (Figure 3A). Interestingly, this trait has been selected during domestication to produce large fruit-bearing plants by modulating the WUS-CLV signalling module mainly through mutations in cis-regulatory elements [START_REF] Yuste-Lisbona | ENO regulates tomato fruit size through the floral meristem development network[END_REF][START_REF] Wang | Dissecting cis-regulatory control of quantitative trait variation in a plant stem cell circuit[END_REF].

Further research is now needed to identify the complete set of transcriptional regulators responsible for the modulation of this genetic network.

Promoting cell division in the ovary and the fruit

Cell division control during ovary development

During flower development, cell division is the main driver for growth inside the ovary. The spatial modification of the rate or duration of cell division in the ovary will thus influence its final size and consequently final fruit size. Three QTLs, namely fs8.1, sun and ovate, controlling fruit elongation within the cultivated tomato germplasm, are involved in the regulation of cell number along different growth axes of the ovary with fs8.1 being the only one to ultimately increase fruit weight (Figure 3B) [START_REF] Rodríguez | Distribution of SUN, OVATE, LC , and FAS in the Tomato Germplasm and the Relationship to Fruit Shape Diversity[END_REF]39]. The fs8.1 locus is present in processing tomatoes, referred to as square tomatoes [START_REF] Ku | fs8.1, a major QTL, sets the pattern of tomato carpel shape well before anthesis[END_REF]. In plants harbouring the fs8.1 locus, the fruit shape index, corresponding to the ratio between the longitudinal and equatorial diameter, is different from plants harbouring the WT allele and leads to more elongated and heavier fruits [39]. This effect of fs8.1 originates from the elongation of the ovary through the increase in cell number in the proximal-distal direction without any change in the medio-lateral direction (Figure 3B). In the abaxial-adaxial direction, an increased number of cell layers was also found in the fruit possibly leading to thicker pericarp. While cell size was not altered in the ovary, cells were smaller in the mature fruit pericarp of the fs8.1 fruits. So far, the identity of the gene underlying the fs8.1 locus remains unknown [39].

Two other major QTLs control fruit elongation: these are sun and ovate that do not lead to an increased fruit weight, on the contrary to fs8.1, [START_REF] Wu | SUN Regulates Vegetative and Reproductive Organ Shape by Changing Cell Division Patterns[END_REF][START_REF] Wu | The control of tomato fruit elongation orchestrated by sun, ovate and fs8.1 in a wild relative of tomato[END_REF]. Ovate confers to fruits a pear shape by increasing cell number in the proximo-distal direction and decreasing cell number in the mediolateral direction in the ovary, thus leading to increased proximal end of the fruit (Figure 3B) [START_REF] Van Der Knaap | Extremely elongated tomato fruit controlled by four quantitative trait loci with epistatic interactions[END_REF]. In sun, elongated fruits are formed which contain more cells along the proximo-distal direction within the pericarp and the columella, while less cells are produced in the mediolateral direction in the columella and the septum (Figure 3 B) [START_REF] Wu | SUN Regulates Vegetative and Reproductive Organ Shape by Changing Cell Division Patterns[END_REF]. As for ovate and fs8.1, the changes in sun occur during ovary development, but fruit elongation is mainly promoted shortly after anthesis. The genes underlying ovate and sun have been identified and correspond respectively to a member of the OVATE family protein (OFP) proposed to regulate cytoskleton organisation [START_REF] Liu | A new class of regulatory genes underlying the cause of pear-shaped tomato fruit[END_REF][START_REF] Hackbusch | A central role of Arabidopsis thaliana ovate family proteins in networking and subcellular localization of 3-aa loop extension homeodomain proteins[END_REF] and to a member of the IQ67-domain (IQD) protein family that is involved in Ca 2+ signal transduction and cellular trafficking [START_REF] Abel | Genome-wide comparative analysis of the IQD gene families in Arabidopsis thaliana and Oryza sativa[END_REF][START_REF] Xiao | A Retrotransposon-Mediated Gene Duplication Underlies Morphological Variation of Tomato Fruit[END_REF]. In ovate, the mutation results in a premature stop codon [START_REF] Liu | A new class of regulatory genes underlying the cause of pear-shaped tomato fruit[END_REF][START_REF] Hackbusch | A central role of Arabidopsis thaliana ovate family proteins in networking and subcellular localization of 3-aa loop extension homeodomain proteins[END_REF] while in sun the phenotype is caused by an interchromosomal duplication leading to increased expression of SlSUN [START_REF] Jiang | Genome organization of the tomato sun locus and characterization of the unusual retrotransposon Rider[END_REF]. However, the mode of action of these two genes in the control of cell division remains totally elusive and further research should provide insight into the relation between cellular trafficking and cell proliferation.

In conclusion, sun, ovate and fs8.1 control different mechanisms regulating ovary and fruit elongation acting on different spatial and temporal features of cell division (Figure3B). The synergistic interaction between these 3 loci suggest that these three genes are involved in distinct pathways which may converge at a common node for the regulation of proximo-distal organ patterning (Figure 3B) [START_REF] Wu | The control of tomato fruit elongation orchestrated by sun, ovate and fs8.1 in a wild relative of tomato[END_REF][START_REF] Wang | A Comparison of sun, ovate, fs8.1 and Auxin Application on Tomato Fruit Shape and Gene Expression[END_REF]. These pathways may involve hormone regulation [START_REF] Wu | The control of tomato fruit elongation orchestrated by sun, ovate and fs8.1 in a wild relative of tomato[END_REF][START_REF] Wang | A Comparison of sun, ovate, fs8.1 and Auxin Application on Tomato Fruit Shape and Gene Expression[END_REF], but this still remains to be deciphered. Recently, it was shown that an auxin application during ovary development leads to elongated pear-shaped fruits resulting from cellular changes similar to the effects of ovate [START_REF] Wang | A Comparison of sun, ovate, fs8.1 and Auxin Application on Tomato Fruit Shape and Gene Expression[END_REF]. However how these three genes involved in fruit shape determination exert their roles in the control of cell division patterning still requires more investigations to be understood.

Cell division control during both the ovary and the fruit development

The process of domestication in tomato has resulted in the selection of plants presenting a large diversity in fruit shape, but also in larger fruit size. About thirty QTLs related to fruit size/weight have been identified in tomato [START_REF] Grandillo | Identifying the loci responsible for natural variation in fruit size and shape in tomato[END_REF]. The fw2.2 locus (for fruit weight QTL of chromosome 2, number 2) is responsible for up to 30% of the fruit weight variation [START_REF] Alpert | High-resolution mapping and isolation of a yeast artificial chromosome contig containing fw2.2: A major fruit weight quantitative trait locus in tomato[END_REF]. The gene underlying fw2.2 locus, SlFW2.2, encodes a protein containing a PLAC8 (Placentaspecific gene 8 protein) motif predicted to be important for the membrane localisation of the protein and belongs to the multigene CELL NUMBER REGULATOR (CNR) family [START_REF] Guo | Cell Number Regulator1 Affects Plant and Organ Size in Maize: Implications for Crop Yield Enhancement and Heterosis[END_REF]. Two different alleles, a "large fruit allele", present in modern tomatoes, and a "small fruit allele" inherited from wild tomato ancestors, differ mainly from polymorphisms in the upstream regulatory region of the gene and lead to spatial and temporal differences of expression [START_REF] Frary | fw2.2: A Quantitative Trait Locus Key to the Evolution of Tomato Fruit Size[END_REF].

The "large fruit" allele is expressed earlier during fruit development, while the "small fruit" allele is expressed later and maintained longer [START_REF] Cong | Natural alleles at a tomato fruit size quantitative trait locus differ by heterochronic regulatory mutations[END_REF]. In plants harbouring the "large fruit" allele, the ovary is larger, mainly due to an increase in the number of cells without any change in cell size showing that SlFW2.2 is involved in regulation of cell number (Figure 3B) [START_REF] Frary | fw2.2: A Quantitative Trait Locus Key to the Evolution of Tomato Fruit Size[END_REF]. In addition, at early stage of fruit development, the mitotic index is increased without any change in cell size recorded in the placenta and the pericarp and is negatively correlated with the expression of SlFW2.2 [START_REF] Cong | Natural alleles at a tomato fruit size quantitative trait locus differ by heterochronic regulatory mutations[END_REF][START_REF] Cong | FW2. 2 and cell cycle control in developing tomato fruit: a possible example of gene co-option in the evolution of a novel organ[END_REF]. The increase in cell division not followed by a modification of the thickness of the pericarp might indicate that SlFW2.2 act as a negative regulator of anticlinal cell divisions (Figure 3C). In several plants species, orthologues of SlFW2.2 are also involved in the regulation of the reproductive organ size such as in maize (Zea mays), where the overexpression of ZmCNR1 leads to the formation of small organs [START_REF] Guo | Cell Number Regulator1 Affects Plant and Organ Size in Maize: Implications for Crop Yield Enhancement and Heterosis[END_REF]. Despite many studies on FW2.2, the mechanism of action by which such a membrane protein can negatively regulate cell number and thus fruit size, as well as the exact changes occurring at the cellular level (cell division rate, cell division duration...) are not yet understood.

Cell division control during fruit development

Starting with the same pool of cells inside the ovary, a modification of the cell division rate or duration after anthesis can also affect the final size of the fruit. Among the QTLs related to fruit weight/size, fw3.2 is the second major locus controlling tomato fruit mass [START_REF] Chakrabarti | A cytochrome P450 regulates a domestication trait in cultivated tomato[END_REF]. The study of nearly isogenic lines that differ for the allele at fw3.2, has revealed that the increase in fruit size appears during fruit development. At mature stage, cytological analysis showed an increase in the number of cell layers within the pericarp, leading to larger fruit whereas cell size remains unchanged (Figure 3C) [START_REF] Chakrabarti | A cytochrome P450 regulates a domestication trait in cultivated tomato[END_REF]. The increase in cell layer number and the delayed fruit ripening suggest an extension of the cell division period. The gene underlying fw3.2 was identified as being an orthologue of AtKLUH/CYP78A5 shown to control organ size in arabidopsis and encoding a CYTOCHROME P450 [START_REF] Chakrabarti | A cytochrome P450 regulates a domestication trait in cultivated tomato[END_REF][START_REF] Anastasiou | Control of Plant Organ Size by KLUH/CYP78A5-Dependent Intercellular Signaling[END_REF]. In plants carrying the large fruit allele of fw3.2, a mutation in the upstream region was proposed to lead to an increase in SlKLUH gene expression. However, recently, the pan-genome establishment after long read sequencing of 100 diverse tomato lines, revealed that the increased expression of SlKLUH is caused by a tandem duplication of the gene at the fw3.2 locus [START_REF] Alonge | Major Impacts of Widespread Structural Variation on Gene Expression and Crop Improvement in Tomato[END_REF]. This gene dosage effect at fw3.2 was confirmed by the use of CRISPR-Cas9 genome editing targeting one to several copies of SlKLUH [START_REF] Alonge | Major Impacts of Widespread Structural Variation on Gene Expression and Crop Improvement in Tomato[END_REF]. Several orthologues of SlKLUH may also regulate fruit mass since in chile pepper a fw3.2 QTL associated with KLUH has been found as in tomato [START_REF] Chakrabarti | A cytochrome P450 regulates a domestication trait in cultivated tomato[END_REF]. In maize leaves, the orthologue of SlKLUH, ZmPLA1, triggers an extended phase of cell division allowing a higher biomass production and an improved seed yield when overexpressed [START_REF] Sun | Altered expression of maize PLASTOCHRON1 enhances biomass and seed yield by extending cell division duration[END_REF]. Although KLUH seems to control cell division in different plant species, its mechanism of action, postulated to act through the production of a still unknown mobile signal, remains to be elucidated [START_REF] Anastasiou | Control of Plant Organ Size by KLUH/CYP78A5-Dependent Intercellular Signaling[END_REF].

Effect of altering the cell cycle machinery

The correct control of cell number during flower or fruit development is thus a key component for final fruit size control. One way to study the impact of cell division on fruit growth is to target directly genes regulating the cell cycle. The progression throughout the successive phases of the mitotic cycle is controlled by heterodimeric protein complexes made of a catalytic subunit referred to as CYCLIN-DEPENDENT KINASE (CDK), and a regulatory subunit CYCLIN (CYC). The CDK-CYC complex is highly regulated at post-transcriptional level by proteolysis, phosphorylation or binding of regulatory proteins [START_REF] De | The ins and outs of the plant cell cycle[END_REF]. However, strongly altering the expression of cell cycle regulators can promote cell division rate, duration or pattern but also alter cell expansion, often not leading to an increase in fruit size, thus showing the interconnection existing between these two processes [START_REF] Czerednik | Regulation of tomato fruit pericarp development by an interplay between CDKB and CDKA1 cell cycle genes[END_REF][START_REF] Mathieu-Rivet | Functional analysis of the anaphase promoting complex activator CCS52A highlights the crucial role of endo-reduplication for fruit growth in tomato: Endo-reduplication and fruit growth in tomato[END_REF]. For example, gain and loss-of function of SlCCS52A (CELL CYCLE SWITCH 52A), encoding a protein part of the complex ANAPHASE PROMOTING COMPLEX/CYCLOSOME CCS52A (APC/C CCS52A ) targeting CYCLINs for destruction through proteolysis, lead to similar fruit phenotype namely a reduction of size but differing at cellular level. Indeed, downregulation of SlCCS52A impaired cell expansion without affecting cell division showing the involvement only after the cell proliferation phase. The kinetics study of the gain-of-function lines fruit growth revealed an extent of cell expansion in late stages of fruit development and a reduction of anticlinal division supposed to promote the increase in volume of the fruit [START_REF] Mathieu-Rivet | Functional analysis of the anaphase promoting complex activator CCS52A highlights the crucial role of endo-reduplication for fruit growth in tomato: Endo-reduplication and fruit growth in tomato[END_REF]. This extend of cell expansion was accompanied by an increased ploidy level supporting the proposed role of endoreduplication in promoting growth.

Unfortunately, of all genes described above that are involved in the control of cell division, no direct connection to the regulation of the cell cycle machinery has been described. Obtaining this information would help finding potential common targeted components of this machinery and thus further building the gene regulatory network determining tomato fruit size. In addition, too few mutants affecting the endocycle have been studied and for mutants affected in cell expansion, as described below, often, no information is available on cell ploidy. To demonstrate the role of endoreduplication in cell expansion control, the analysis of both parameters in mutants should be done systematically.

Altering cell expansion

Cell expansion starts right after fruit set in the mesocarp cells, extends till ripening [START_REF] Renaudin | Cell layer-specific patterns of cell division and cell expansion during fruit set and fruit growth in tomato pericarp[END_REF][START_REF] Pabón-Mora | Comparative anatomical and developmental analysis of dry and fleshy fruits of Solanaceae[END_REF][START_REF] Cheniclet | Cell Expansion and Endoreduplication Show a Large Genetic Variability in Pericarp and Contribute Strongly to Tomato Fruit Growth[END_REF][START_REF] Xiao | Integration of tomato reproductive developmental landmarks and expression profiles, and the effect of SUN on fruit shape[END_REF] and is responsible for a rapid and major increase in fruit size. Among the QTLs controlling fruit mass, fw11.3 explained as much as 8% of fruit weight variation [START_REF] Grandillo | Identifying the loci responsible for natural variation in fruit size and shape in tomato[END_REF]. The CELL SIZE REGULATOR (CSR) gene underlies the fw11.3 locus [START_REF] Mu | Fruit weight is controlled by Cell Size Regulator encoding a novel protein that is expressed in maturing tomato fruits[END_REF]. SlCSR encodes a protein of unknown function with a low level of expression in the fruit, only after the cell division phase. Cytological analysis of near isogenic lines showed an increase in pericarp thickness resulting from an increase in mesocarp cell size without any change in the number of cell layers [START_REF] Mu | Fruit weight is controlled by Cell Size Regulator encoding a novel protein that is expressed in maturing tomato fruits[END_REF]. The expression of the mutated allele in the wild type background highlighted that the allele increasing fruit weight encodes a truncated protein acting as a dominant allele acting as a gain of function. The orthologous gene for SlCSR in arabidopsis belongs to the FANTASTIC FOUR proteins (FAF) involved in the regulation of SAM size through a negative regulation of AtWUS [64]. SlCSR and AtFAFs are likely to share the same biochemical function within the cell but in different tissues [START_REF] Mu | Fruit weight is controlled by Cell Size Regulator encoding a novel protein that is expressed in maturing tomato fruits[END_REF]. This function needs to be investigated in addition to the speculated involvement of SlCSR, based on co-expression data, in the antagonistic action of auxin and cytokinin on cell enlargement [START_REF] Mu | Fruit weight is controlled by Cell Size Regulator encoding a novel protein that is expressed in maturing tomato fruits[END_REF].

In tomato, the up-regulation of several transcription factors belonging to the GROWTH REGULATING FACTOR (GRF) family led to pleiotropic effects including shorter cotyledons, large flowers and higher plants [START_REF] Cao | Regulations on growth and development in tomato cotyledon, flower and fruit via destruction of miR396 with short tandem target mimic[END_REF]. In these plants expressing higher levels of SlGRF1 to -5, fruit size and weight are increased resulting from an increased size of the epidermal cells [START_REF] Cao | Regulations on growth and development in tomato cotyledon, flower and fruit via destruction of miR396 with short tandem target mimic[END_REF].

The SlGRF genes are thought to regulate growth by different means since opposite phenotypes on cell size are observed in the cotyledons and fruits of the SlGRF1 to -5 mutants. These differences are also observed in arabidopsis leaves with AtGRF1 and -2 controlling cell size whereas AtGRF5 regulates cell proliferation [66,[START_REF] Kim | The AtGRF family of putative transcription factors is involved in leaf and cotyledon growth in Arabidopsis[END_REF]. Further studies would be needed to specify the function of each individual SlGRF in the control of these cellular processes and to identify the targets of these transcription factors.

The overexpression lines for the putative transcription factor, FRUIT SANT/MYB-LIKE1 (SlFSM1) harbour smaller fruits [START_REF] Machemer | Interplay of MYB factors in differential cell expansion, and consequences for tomato fruit development: FSM1, FSB1 and MYBI interactions control cell size[END_REF] characterized by a thinner pericarp resulting from a decreased cell expansion. In these plants, cell expansion in leaves and hypocotyl is also impaired showing that SlFSM1 acts as a suppressor of cell expansion in various organs. The closest orthologues of SlFSM1, the Antirrhinum RADIALIS (AmRAD) and arabidopsis RADlike 2 (AtRL2) are involved in the asymmetries and radially symmetric flowers, respectively [START_REF] Baxter | Diversification and co-option of RAD-like genes in the evolution of floral asymmetry[END_REF][START_REF] Corley | Floral asymmetry involves an interplay between TCP and MYB transcription factors in Antirrhinum[END_REF]. Looking for the protein partners of SlFSM1 allowed the identification of FRUIT SANT/MYB BINDING PROTEIN 1 (SlFSB1) and SlMYB1 was found to interact with SlFSB1 [START_REF] Machemer | Interplay of MYB factors in differential cell expansion, and consequences for tomato fruit development: FSM1, FSB1 and MYBI interactions control cell size[END_REF]. Based on this interaction study using the tomato proteins and the AtRAD model network in arabidopsis, a binding competition of SlFSB1 by SlFSM1 and SlMYB1 was proposed as the mechanism involved in the regulation of differential cell expansion during fruit development [START_REF] Machemer | Interplay of MYB factors in differential cell expansion, and consequences for tomato fruit development: FSM1, FSB1 and MYBI interactions control cell size[END_REF][START_REF] Corley | Floral asymmetry involves an interplay between TCP and MYB transcription factors in Antirrhinum[END_REF]. It will be necessary to verify this model by altering the expression of these different players in single and higher order mutants and study the effect on fruit growth.

In some cases, the alteration in pericarp thickness can be uncoupled from fruit size. For instance the loss-of-function of the GUANYLATE-BINDING PROTEIN1 (SlGBP1), induces a decrease in pericarp thickness through a decrease in cell size; however, the final fruit size remains unchanged [START_REF] Musseau | The Tomato Guanylate-Binding Protein SlGBP1 Enables Fruit Tissue Differentiation by Maintaining Endopolyploid Cells in a Non-proliferative State[END_REF]. In these plants, the difference in pericarp thickness only appears after 20 DPA, and is accompanied by an early stop of cell expansion and the re-entry in division state of the cells indicating that SlGBP1 is involved in the maintenance of the differentiation program in pericarp cells through a yet unknown mechanism.

Hormone and fruit growth regulation

Auxin and cell division

The modification of genes involved in hormonal regulation can impact on fruit size since important changes in hormone contents occur during fruit growth [START_REF] Mariotti | Fruit-set and Early Fruit Growth in Tomato are Associated with Increases in Indoleacetic Acid, Cytokinin, and Bioactive Gibberellin Contents[END_REF]. In pre-anthesis ovary in arabidopsis, the AUXIN/INDOLE-3-ACETIC ACID (Aux/IAA) factors repress the auxin signal by sequestering the AUXIN RESPONSE FACTOR (ARF), transcription factors which regulate the expression of auxin response genes. Hence the ovary remains in a phase of dormancy, in which cell division activities are inhibited [START_REF] Weijers | Developmental specificity of auxin response by pairs of ARF and Aux/IAA transcriptional regulators[END_REF]. Fertilization triggers an increase in auxin content leading to the destruction of the Aux/IAA and the release of the ARFs which then become available to transcribe their target genes and consequently trigger the resumption of the cell division process [START_REF] Pandolfini | Molecular dissection of the role of auxin in fruit initiation[END_REF]. In tomato, treatment of unpollinated ovary by auxin can mimic the fecundation and leads to the development of pathenocarpic fruit [START_REF] Gustafson | Inducement of Fruit Development by Growth-Promoting Chemicals[END_REF]. The increase in auxin concentration inside the ovary following pollination is an important trigger for the growth of the ovary [START_REF] Mariotti | Fruit-set and Early Fruit Growth in Tomato are Associated with Increases in Indoleacetic Acid, Cytokinin, and Bioactive Gibberellin Contents[END_REF]. In tomato, the ARF family consists in 22 proteins [START_REF] Zouine | Characterization of the Tomato ARF Gene Family Uncovers a Multi-Levels Post-Transcriptional Regulation Including Alternative Splicing[END_REF]. SlARF9 expression is triggered by pollination and reaches the highest expression at 6 DPA, a pattern similar to auxin accumulation in the fruit [START_REF] Mariotti | Fruit-set and Early Fruit Growth in Tomato are Associated with Increases in Indoleacetic Acid, Cytokinin, and Bioactive Gibberellin Contents[END_REF]. The loss-and gain-of-function of SlARF9 result in larger and smaller fruits respectively [77]. Both at early and mature fruit stages, the SlARF9 RNAi lines show a decrease in cell sizes and more cell layers in the pericarp. In contrast, fruits from the pTPRP-SlARF9 line present an early increase in cell size and a decrease in cell layer number at later stages. Thus, SlARF9 seems to act as a negative regulator to fine-tune cell division during fruit growth [77]. Surprisingly the decrease in SlARF5 expression, using an amiRNA, leads to similar small fruit phenotype as the SlARF9 overexpression [START_REF] Liu | Tomato AUXIN RESPONSE FACTOR 5 regulates fruit set and development via the mediation of auxin and gibberellin signaling[END_REF]. No obvious difference on fruit morphology was observed in early dividing fruit of amiSLARF5 lines but at later stages, the pericarp contained less cell layers, due to a shorter period of cell division, and larger cells compared to wild type plants. SlARF5 could thus be a positive regulator of cell division [START_REF] Liu | Tomato AUXIN RESPONSE FACTOR 5 regulates fruit set and development via the mediation of auxin and gibberellin signaling[END_REF].

Auxin can also modulate the regulation of auxin responsive genes through the action of repressor proteins such as SlIAA17 [START_REF] Su | The Auxin Sl-IAA17 Transcriptional Repressor Controls Fruit Size Via the Regulation of Endoreduplication-Related Cell Expansion[END_REF]. SlIAA17 is highly expressed in the fruit at 10 DPA when cell expansion starts and its expression declines gradually up to the breaker stage. This peak of expression corresponds to one of the bimodal peak of auxin occurring at 10 and 30 DPA [12]. The study of SlIAA17 by RNAi approach has shown that the decrease in expression of this gene leads to the production of larger fruits through an increase of the pericarp cellular size without modification in the number of cell layers [START_REF] Su | The Auxin Sl-IAA17 Transcriptional Repressor Controls Fruit Size Via the Regulation of Endoreduplication-Related Cell Expansion[END_REF]. SlIAA17 interacts with several ARF proteins including SlARF5 [START_REF] Su | The Aux/IAA, Sl-IAA17 regulates quality parameters over tomato fruit development[END_REF]. Interestingly, the decrease of SlIAA17 and SlARF5 expression leading to opposite phenotype could corroborate with a repressor function of SlIAA17 on SlARF5. The role of auxin in regulating fruit growth seems complex and depending on the developmental stage of the fruit, different responsive proteins are involved. Additional research is thus needed to understand the role of these auxin responsive genes and their possible connections during the course of fruit development.

Gibberellins and cell expansion

Many studies have demonstrated the important role of GA for fruit growth regulation using mutants or exogenous treatments [81,[START_REF] Groot | The role of endogenous gibberellin in seed and fruit development of tomato: Studies with a gibberellin-deficient mutant[END_REF]. As for auxin, a treatment of unpollinated ovaries with gibberellins (GA) leads to the formation of parthenocarpic fruit [START_REF] Wittwer | Some Effects of Gibberellin on Flowering and Fruit Setting. 123[END_REF]. Auxin and GA pathways are interconnected as GA treatment induces an increase in auxin content and, in turn, auxin induces GA biosynthesis [START_REF] De | The role of auxin and gibberellin in tomato fruit set[END_REF]. Nevertheless, GA seems to be mainly involved in cell expansion process in the fruit. PACLOBUTRAZOL RESISTANCES 2 (PRE2), belonging to the bHlH transcription factor family, is induced by GA and mediates plant response to GA [START_REF] Zhu | Overexpression of SlPRE2, an atypical bHLH transcription factor, affects plant morphology and fruit pigment accumulation in tomato[END_REF]. SlPRE2 overexpression lines exhibit a slight increase in fruit diameter whereas loss-of-function lines show a decrease in fruit size [START_REF] Zhu | The bHLH transcription factor SlPRE2 regulates tomato fruit development and modulates plant response to gibberellin[END_REF]. In RNAi lines for SlPRE2, the mesocarp cell size is reduced leading to a thinner pericarp. SlPRE2 seems to show similar function as AtPRE1 since both proteins are involved in cell elongation through GA modulating response [START_REF] Zhu | The bHLH transcription factor SlPRE2 regulates tomato fruit development and modulates plant response to gibberellin[END_REF][START_REF] Hao | Interactions between HLH and bHLH Factors Modulate Light-Regulated Plant Development[END_REF][START_REF] Lee | Overexpression of PRE1 and its Homologous Genes Activates Gibberellin-dependent Responses in Arabidopsis thaliana[END_REF]. The downregulation of another transcription factor involved in GA pathway, SlGRAS2, leads to a reduction of pericarp cell size and thus smaller fruit [START_REF] Li | Silencing GRAS2 reduces fruit weight in tomato: GRAS2 is involved in fruit development[END_REF]. SlGRAS2 is expressed from ovary wall at anthesis to 10 DPA fruit. In the RNAi lines targeting SlGRAS2, the ovary wall is thinner but no change in the final number of cell layers in the pericarp was observed showing the involvement in SlGRAS2 in cell expansion regulation. In these lines, both GA biosynthesis and signal transduction pathways are inhibited.

The increased expression of the transcription factor CYCLIN DOF FACTOR 4 (SlCDF4) under the control of PHOSPHOENOLPYRUVATE CARBOXYLASE promoter (pPPC2) used for a fruit specific expression with highest expression during the cell expansion phase [START_REF] Fernandez | Flexible Tools for Gene Expression and Silencing in Tomato[END_REF], leads to the production of larger fruits through an increase in both cell layers and cell sizes [START_REF] Renau-Morata | The targeted overexpression of SlCDF4 in the fruit enhances tomato size and yield involving gibberellin signalling[END_REF]. In these plants, the hormone content is modified with higher GA and lower auxins levels. SlCDF4 may play a dual role on auxin and gibberellin synthesis thus regulating both cell division and expansion. The increase in fruit size and in GA content had already been observed with the overexpression of another member of the family, SlCDF3 [START_REF] Renau-Morata | Ectopic Expression of CDF3 Genes in Tomato Enhances Biomass Production and Yield under Salinity Stress Conditions[END_REF] although its effect at cellular level was not described. As for auxin, GA plays an important role all along fruit development for cell enlargement control, but many of the genes involved in GA signal transduction still need to be discovered. In addition, even if a crosstalk between auxin and gibberellins seems to exist, its regulation to maintain the balance between cell division and cell expansion is not properly understood.

Concluding remarks and future outlook

Tomato fruit is a complex 3-dimensional structure that relies on cell division and cell expansion to develop fully. These two processes occur in different cell types at different developmental stages and at different rates creating a high complexity of interconnected events, requiring a highly fine coordination. This complexity and fine coordination were already described for the planar arabidopsis leaf, often used as model to study growth mainly in 2-D, along two axes 'base-to-tip' and the 'middle-to-margin' [93] while in the silique, cell expansion is the main driver of growth after fertilisation [94]. In tomato, the large diversity in fruit shape results from growth patterns occurring along three axes -"proximo-distal", "medio-lateral" and "abaxialadaxial"-making of this organ an excellent model, although challenging, to study growth in 3-D. In tomato, final fruit size can be altered through changes in cell division, in its direction, duration or rate, but these changes can occur as early as in the ovary or in the developing fruit itself, in different zones of the fruits, and according to cells dividing in an anticlinal, periclinal, or oblique manner. Similarly, an alteration in cell expansion either anisotropic or isotropic can influence the final fruit size. Due to this large diversity of events that can influence final fruit size, yet not all described in detail, the changes that can affect positively fruit size are difficult to apprehend fully, since they can occur alone or in combination. Capturing the effects of the alteration of one or several events at a 3-D level will definitely provide essential information to better apprehend the high complexity of cellular events needed to form a fully grown and functional fruit but will require computational models to integrate multiple cellular parameters.

So far only a few models have been developed to integrate some, but not all, cellular parameters possibly influencing final fruit size in tomato [START_REF] Baldazzi | Organ-wide and ploidy-dependent regulation both contribute to cell-size determination: evidence from a computational model of tomato fruit[END_REF][START_REF] Baldazzi | Towards multiscale plant models: integrating cellular networks[END_REF][START_REF] Fanwoua | A dynamic model of tomato fruit growth integrating cell division, cell growth and endoreduplication[END_REF].

Through the study of mutants and the identification of genes underlying important QTLs, a number of fruit growth regulators influencing cell division or cell expansion have been identified. In many cases, these potential homologues of these genes/QTLs were also described in other plants species. For example, homologues of FW2.2 have been found in papaya (Carica papaya), peach (Prunus persica), grape vine (Vitis vinifera) [START_REF] Beauchet | search of the still unknown function of FW2. 2/CELL NUMBER REGULATOR[END_REF] in which they are associated with fruit weight QTLs, and also in physalis (Physalis floridana) or rice (Oryza sativa) in which they regulate leaves, floral organs, berries, and seeds size, and plant height and seed size, respectively [START_REF] Beauchet | search of the still unknown function of FW2. 2/CELL NUMBER REGULATOR[END_REF]. A homologue of SlSUN may also underlie fruit shape variation in cucumber [START_REF] Pan | Round fruit shape in WI7239 cucumber is controlled by two interacting quantitative trait loci with one putatively encoding a tomato SUN homolog[END_REF] and an orthologue of SlKLUH may regulate fruit weight in chile pepper [START_REF] Chakrabarti | A cytochrome P450 regulates a domestication trait in cultivated tomato[END_REF]. In several of these plants, functional studies are not always easy to carry to understand the mode of action of these genes and for the search of new growth regulators. The availability of genome sequences for multiple wild and cultivated tomato plants, the possibility to edit the genome of tomato and easily transform it make that information obtained from tomato on the mechanisms underlying size control could be used to search for genes controlling organ size in other crops and/ or for engineering favourable alleles. However, although several genes/QTLs involved in organ size determination have been identified, in numerous cases, their nature, exact effect on the cellular processes are often not described and the mode of action of these regulators remains poorly understood. It is regretful that of the almost 30 FW QTLs identified so far only for 3, the gene behind the QTL is known, even if the function of the related protein is often not understood. This lack of knowledge on the genetic regulation of several processes determining fruit growth does not allow to build a solid regulatory network that could be manipulated in order to modify fruit growth. The important nodes and their associated partners need to be discovered. The construction of this network can be achieved through the identification of proteins partners of the growth regulating proteins, their targets or regulatory elements. With additional information on the exact effect and mechanism of action for each regulator, rational combinations between mutants of genes enhancing for example cell division and cell expansion could be a good solution for modifying fruit size and thus probably fruit quality. These combinations could be achieved by crossing mutants or through the use of CRISPR-Cas9 genome editing technologies that allow the production of deletions, but also creating targeted insertions, exchanging amino acids and modulating gene expression for one or several targeted genes [START_REF] Čermák | A multipurpose toolkit to enable advanced genome engineering in plants[END_REF]100].

Tomato domestication led to the selection of favourable traits essentially aiming at improving yield through the increase of fruit size or fruit number. Polymorphism/mutations in several of the genes described in this review, such as FAS, OVATE, SUN or FW2.2 contributed to this improvement. However, often, this selection was at the expense of other desirable traits such as nutritional features or stress tolerance. For example, modern commercial tomato varieties, which often produce numerous and/or large fruits, contain lower amounts of important flavour metabolites (sugars, acids, amino acids, volatiles…) than old varieties [101], suggesting a tradeoff between quality and size/yield. This trade-off originates from a loss of genetic diversity in domesticated cultivars, which, probably randomly/indirectly, triggered the loss of favourable alleles or the co-selection of unfavourable alleles in the absence of positive selection [101-103].

The analysis of the genome, transcriptome and metabolome in more than 400 tomato accessions has shown that changes in metabolite content through domestication might have been caused by a linkage of genes nearby the selected alleles of genes associated with larger fruits [104]. In the actual context of climate change, a loss of crop yield due to the increasing occurrence of environmental stresses together with the actual consideration of consumers preferences toward fruits of better quality create a need to combine yield-related traits and tolerance-to-stress and/or quality-related traits. To achieve rapidly these combinations, molecular engineering using CRISPR-cas9 technology could be exploited for producing superior tomato varieties with multiple favourable traits by specifically targeting genes involved in fruit growth, fruit flavour and response to stress. Wild relatives or old varieties show a better adaptation to environmental constraints or can produce larger amounts of fruit quality related metabolites [101,103,105], de novo domestication could help combining these traits. In a wild tomato, [START_REF] Zsögön | De novo domestication of wild tomato using genome editing[END_REF] have targeted six important loci, including OVATE, FW2.2 and CLV3, for key domestication traits through molecular engineering using CRISPR-cas9 technology to create loss of function alleles, and have succeeded in improving most of the targeted traits in these plants [106].

However, as mentioned previously, this targeted molecular breeding will only be possible through a better knowledge of the genetic basis of the traits of interest including fruit size control.

In conclusion, the combination of in-depth understanding of gene regulatory networks, of their effects at cellular level when mutated with the use of genome editing represent a promising engineering strategy for future crop improvement and tomato represents an excellent model both for obtaining this knowledge and for direct application (see also outstanding questions).

Figure 1 .

 1 Figure 1. Inflorescence architecture, fruit tissues and pericarp cell layers. A: Inflorescence of wva106 variety showing the zigzag inflorescence pattern. B: Tomato fruit at mature stage and equatorial cross section. C: cellular drawings of a pericarp section at mature stage. The names of cell layers are according to Renaudin et al. (2017) [8].

Figure 2 .

 2 Figure 2. Different developmental stages of tomato fruit development (cultivar wva106) at fruit, pericarp and cellular level. From inside to outside the circle, the different phases of development (cell division phases, cell expansion phase and ripening) are shown as pictures of ovaries and fruits (stage 11 to 40 DPA), fruit equatorial cross sections and cellular drawings of pericarp sections (s: stage, A: anthesis and number for DPA). Dividing cells are represented in blue and expanding cells in orange. The scale has been conserved along the development,

Figure 3 .

 3 Figure 3. Molecular mechanisms determining tomato fruit growth. A. Genes influencing fruit locule number through the regulation of meristem size. B. Genes influencing fruit size and shape though the regulation of cell division patterns in the ovary. From the left to the right are represented a longitudinal section of a tomato flower, a longitudinal (top) and a transversal (bottom) section of an ovary with the different division patterns (proximo-distal, adaxialabaxial and medio-lateral, the genes influencing these cell division patterns, the models explaining the changes in cell division pattern in mutants of these genes and the consequences on fruit shape and size of these mutations. C. Genes influencing fruit growth through the regulation of cell division and /or expansion in the pericarp and consequences on pericarp thickness. Abbreviations: ARF (AUXIN REPONSE FACTOR), CDF (CYCLIN DOF FACTOR), CLV (CLAVATA), CSR (CELL SIZE REGULATOR), ENO (EXECESSIVE NUMBER OF FLORAL ORGANS), FSM (SANT/MYB-like), FW (FRUIT WEIGHT), GBP (GUANYLATE-BINDING PROTEIN), GRAS (GIBBERELLIC ACID INSENSITIVE, REPRESSOR OF GAI, and SCARECROW), GRF (GROWTH REGULATING FACTOR), HPAT (HYDROXYPROLINE O-ARABINOSYLTRANSFERASE), IAA (INDOLE-3-ACETIC ACID), IMA (INHIBITOR OF MERISTEM ACTIVITY), KNU (KNUCKLES), PRE (PACLOBUTRAZOL RESISTANCES) and WUS (WUSCHEL). Ab: abaxial; Ad: Adaxial; M: medio; L: lateral; P: proximal; D: distal.

Acknowledgements

The authors express their deepest thanks to Jean-Pierre Renaudin and Catherine Cheniclet who provided several images used to build figures 1 and 2. The authors would like to apologize to colleagues whose work has not been included in this review.


Sebastien Garnier
email: sebastien.garnier@ls2n.fr

Kevin Subrin
email: kevin.subrin@ls2n.fr

A metrological device for robot identification

Keywords:

Nowadays, industrial robots are increasingly used for heavy manufacturing tasks such as milling, drilling, deburring or sanding. Twenty years ago, researchers began to identify scientific bottlenecks and have made contributions on robot performance in terms of repeatability and accuracy. We are currently observing many methods and tools to apply to improve robot performances through their geometric, kinematic and dynamic modelling. There are often laboratory tools, not compatible with the needs of companies i.e. economically compatible, easy to install, easy to use with a good integration to industrial lines. In this context, we propose a new device to identify robot performances based on the famous ballbar used for the calibration of machinetools. This paper thus deals with the design methodology, its design and environment of use as well as its performance in robot identification.

Introduction

Nowadays, industrial robots are increasingly used for tasks that require accuracy. With the development of technology, robot manufacturers are offering both proprioceptive systems for path control such as force sensor or double encoding actuators. There are also exteroceptive systems such as high-speed cameras that, after calibration, allow precise robot positioning. However, in manufacturing environments where tasks are subject to stress with large fluctuations in force (e.g. machining), the implementation of geometric, kinematic or even dynamic models is a must to improve robot accuracy [START_REF] Klimchik | Efficiency evaluation of robots in machining applications using industrial performance measure[END_REF]. These models involve a set of parameters that need to be identified : lengths between the robot joints, apparent stiffness, moving masses, inertia, friction or backlashes. Designing a new metrological tool to improve robot performances through parameters identification must reply to the industry need. Nowadays, literature performs identification with an expensive tool such as laser tracker ( [START_REF] Dumas | Joint stiffness identification of six-revolute industrial serial robots[END_REF], [START_REF] Ambiehl | New method for decoupling the articular stiffness identification[END_REF],[4],[5], [START_REF] Kamali | Optimal experiment design for elasto-geometrical calibration of industrial robots[END_REF], [START_REF] Guérin | Optimal measurement pose selection for joint stiffness identification of an industrial robot mounted on a rail[END_REF]) but to identify heavy robots with large workspace, this approach is questionable : comparing robot accuracy (around 1mm), robot repeatability (around 0.1mm), is a metrological tool accuracy of 0.005mm pertinent ? Moreover, its implementation is often cumbersome and costly: robot immobilization for a few days, definition of postures where the targets are visible by the laser tracker, definition of postures in accordance with the literature, definition of working reference points, geometric identification and finally elastostatic (with and without mass) [START_REF] Dumas | Joint stiffness identification of six-revolute industrial serial robots[END_REF]. Constructing a real loop of measurement offers advantages being closer to the system to measure but its integration is a key to facilitate its use. The novelty of this article concerns the design of a patented metrological measuring system based on the principle of a machine tool ballbar. The article is structured as follows. Section 2 reviews the measuring systems and methods to apply a wrench. Section 3 focuses on a technical approach to define the specifications and presents the system. Section 4 focuses on the analysis, the identification and the performances of the system. The conclusion and the perspectives are finally discussed.

Systems and methods review to identify robots behavior

Current approaches

The evolution of robotic systems is the result of improvements involving the fields of mechanics, electronics and control. Indeed, over the last thirty years, robots have evolved through new mechanical architectures (serial, parallel, hybrid robot), with increasingly advanced drive technologies (Harmonic drive [START_REF] Christopher | Modeling and control of the mitsubishi pa-10 robot arm harmonic drive system[END_REF], double-encoding actuators [START_REF] Klimchik | Robotic manipulators with double encoders: accuracy improvement based on advanced stiffness modeling and intelligent control[END_REF], gravity compensator [START_REF] Klimchik | Stiffness modeling of robotic manipulator with gravity compensator[END_REF]) allowing compactness and improving accuracy while limiting backlashes [START_REF] Michael Ruderman | Modeling and identification of elastic robot joints with hysteresis and backlash[END_REF]. However, these evolutions are accompanied by improvements in terms of control to identify friction and ensure a stable behavior of the robot [START_REF] Ps Shiakolas | On the accuracy, repeatability, and degree of influence of kinematics parameters for industrial robots[END_REF]. The measurement of robot performance is based on the following protocols namely : ISO 9283:1998 about Industrial Robots -Performance Criteria and Related Test Methods [START_REF] Iso | Manipulating industrial robots performance and criteria[END_REF]. It addresses the one-directional pose accuracy and repeatability measuring the difference between the position reached and the position controlled in terms of average deviation and maximum dispersion (Fig. 1). The measuring equipment is not specified in this norm and literature provides many equipments to characterize the robot performance. Laser tracker is generally used as it provides an accuracy (depending on the distance to be measured) of several in a workspace of several 3 or to compare the performance of new equipment. Understanding the deflection of the robot under stress requires the implementation of a stress such as an associated mass [START_REF] Dumas | Joint stiffness identification of six-revolute industrial serial robots[END_REF], a pneumatic system [START_REF] Archenti | A new method for circular testing of machine tools under loaded condition[END_REF] or an electrical system with cables [START_REF] Kamali | Optimal experiment design for elasto-geometrical calibration of industrial robots[END_REF] allowing the transmission of the forces associated with a measuring device to be synchronized. The Tab. 1 lists the works carried out in this field underlying the equipment used, the protocol, the device and the information extracted from the measurements. The Fig. 2 highlights the implementation.

Figure 2: Dedicated system to evaluate the elastostatic parameters. In 1, method with a weigth [START_REF] Dumas | Joint stiffness identification of industrial serial robots[END_REF]; in 2, method with a ballbar [START_REF] Nubiola | Absolute robot calibration with a single telescoping ballbar[END_REF]; in 3, Loaded Double Ball Bar [START_REF] Archenti | A new method for circular testing of machine tools under loaded condition[END_REF]; in 4, method with a cable driven parallel robot [START_REF] Kamali | Optimal experiment design for elasto-geometrical calibration of industrial robots[END_REF] References Review of work in terms of measurement and identication methodology

Criticism of the different approaches

These methods have a loading system and a measuring system that are often dissociated : the data must be synchronized. The deflection measurement is estimated from a theoretical model. There is a sensitivity on the identification of the position of the load and its direction. Some methods exist to identify the center of the wrist such as trilateration [START_REF] Ambiehl | New method for decoupling the articular stiffness identification[END_REF]. Moreover, in the case of a weight, the first axis is not under load and two test campaigns must be carried out. The approach requires several hours to have sufficient data to estimate the robot parameters. In this context, a new patented system has been designed based on the ballbar system.

Technical Approach and concept

Principle of a bestseller: ballbar measurement

The ballbar is a measuring device mainly used in the world of machine-tools. Measurements are made by moving a prismatic joint at low speed in order to ignore the dynamic aspects and have a very accurate estimation of the spindle position. This very simple device allows an elementary implementation to evaluate a very large number of defects on the various axes of the machine tool. The implementation of such a system on a robot could be complex. First of all, the measuring range is small compared to the working space of the robot which can be about 2m. On a cartesian machine, the ballbar allows the identification of two axes simultaneously on a plane. However, for a robot, setting up a test in a plane is not suitable because all the axes will be solicited. However, the idea of loading 2 robot axes at the same time seems relevant in order to evaluate the health of specific actuators for example. Moreover, the identification of the system is essential and requires to have enough data to estimate the parameters allowing to properly estimate the robot behavior.

Requirement specification

In order to design a metrological device for robot identification, we considered the following specifications :

• Identification of heavy robot with large workspace (>1m50) and high payload (>150kgs)

• Synchronized number of axes for robot defect observation : 2 axis at least (saddle trajectory)

• Quality of the reference frame : fixed on the ground • Dimension of the task to be observed : 6 dimensions

• Quality of the loading force : in the two directions (push and pull) Concerning the performances of the robot, the specifications are :

• Accuracy of the system : below 0.2mm

• Repeatability of the system : below 0.1mm

• Variation of robot positioning/deflection: over several tens of millimeters under 2500N

• Measurement quality of the force : a few newtons

Discussion about the design

The simplest solution is to connect the robot to a line between the robot end effector and the floor. From then on, the SPS (Spherical Joint (3DoFs) -Prismatic Joint (1 DoFs) and Spherical Joint (3DoFs)) solution appears, but it needs to be simplified as it is redundant of order 1. The Spherical joint can correspond to the series of 3 Revolute joints (R) whose axes of rotation converge at a point. In our application, we have decomposed our Spherical joint (S) into an Universal joint (U) and a Revolute joint (R) whose axes remain coincident with the center of the Universal joint (U). We are looking to perform measurements on large and heavy industrial robots. We limit the radius of the sphere to about 1m. The angles should cover a half-sphere. The accuracy of the sensors therefore depends on the position of the measurement on the device. Indeed, the measurement of an angle at the base of the mechanism used to calculate the position of the end effector will be higher than that used to define the orientation of the end effector at the end of the arm. One can quickly estimate the order of magnitude needed for the sensors based on their position and the angle at the base of the device. In this way, we define 4 cases, see Tab. 2 and Fig. 3. The first case takes into account a low accuracy on each Revolute joint ( ) of the Universal joint (U). The second case takes into account a high accuracy for each Revolute joints. The third one considers a high accuracy at the base of the equipment. Finally, the last one simplifies the architecture to avoid redundant architecture considering an Universal Joint at the basis instead of a spherical one. The parameters of the model used for this study are the final dimensioning. At last, we define the accuracy as the ratio of cost based on the encoders in the Tab. 3. To reach an optimal configuration in terms of accuracy regarding cost, a study is performed where it is assumed that the accuracy reached by the system follows a normal centered distribution with a standard deviation equal to the accuracy divided by 2. Monte Carlo type study is played with 10 6 runs. The probability distribution model chosen is of "gamma" type (Eq.1 and 2).

( | , ) = 1 Γ( ) -1 - (1)
where

Γ( ) = ∫ ∞ 0 --1 (2)
Fig. 4 presents the accuracy which can be expected. On the abscissa axis, we find the error in and in ordinate, the frequency normalizing the set to 1. For each model, in continuous line, we find the raw data and in dotted line the model estimates the values of the Tab. 4. The second case is the more accurate but the more expensive as well. The forth case is chosen as it divides the price of sensors by 2 and it highlights an inaccuracy up to 23% regarding the best one. Accuracy regarding cost for encoders and glass ceramic ruler

Accessibility analysis

The universal joint orientation has an impact on the preferred test area to be carried out. To validate our design, we calculate the value of the manipulability index discretizing the workspace on the surface of a sphere with a diameter of 2m. The values obtained are then classified into 3 groups (red, violet and green) where the green colour represents the best values [START_REF] Peter I Corke | A robotics toolbox for matlab[END_REF]. Fig. 5.A and Fig. 5.B present the results with a first link that can be horizontal or vertical respectively.

In the case of the first mechanism (Horizontal), a preferential measuring area is located at the center of the device while the second is located at the periphery of the mechanism. Therefore, regarding the ballbar's requirements, the configuration with a first link to be horizontal is chosen (obvious choice). Results highlighting accuracy and cost. Model IV is chosen

Concept

The final mechanism is a UPUR mechanism (Universal joint (2 revolute joints) -Prismatic joint -Universal (2 revolute joints) -Revolute joint). The mechanical structure of the device is shown in Fig. 6. This equipment includes a base link, a universal passive joint described by two elementary revolute joints, a linear actuator (SMC double acting pneumatic cylinder MGP series), a Universal passive joint described by two elementary Revolute joints, a Revolute passive joint providing rotation to end effector. The system is installed with the following seven sensors: two absolute encoders for the first Universal joint (Heidenhain RCN 2310), a positioning sensor for prismatic joint (Heidenhain LIC 4003), a force sensor for measuring the force (HBM U9C), two absolute encoders for the second Universal joint (Heidenhain ROC 437F). A human-machine interface (HMI) (Fig. 7) has been developed allowing the display and acquisition of measured quantities (angles, distance, force) through Labview. The interface helps deducing the positions and orientations of the upper plate center connected to the robot. The HMI allows the acquisition of static points at the request of the operator or from a trigger programmed on the robot. The information about the recorded points is displayed in a point table and can be exported in ASCII format. For each position, synchronized force and position data are recorded. The software also allows to launch continuous acquisitions with a sampling rate of one millisecond. In the case of continuous acquisition, to optimize performance, the display of the 3D device and the table of recorded points is disabled. During continuous acquisition, the data is stored in a buffer memory. At the end of the recording, the export function is automatically started. The operator must select a path to save the ASCII file with the same information as before.

Analysis, identification and performances of the system

A general approach to identifying a robot, whether geometric, elastostatic, kinematic or dynamic, is to compare the acquisition of data by an external sensor of known accuracy and then use these data to identify parameters using a model fitting algorithm. The device used for data acquisition is a laser tracker. This involves installing a laser tracker and measuring the position of the end-effector using reflectors namely here T-MAC. This method is frequently used in industry. The visibility of the reflectors by the laser tracker is very important to obtain substantial readings. This imposes constraints on the robot end-effector path, as the reflector installed at the end-effector must be fully visible to the laser tracker in order to obtain satisfactory readings. As our system is a mechanical system, its design, geometry and mechanical properties are inacurate with respect to the theoretical model (CAD), which is considered geometrically perfect. It is therefore necessary to identify the parameters of the system to evaluate its overall accuracy.

In order to identify the equipment, a Denavit-Hartenberg Modeling (DHM) [START_REF] Khalil | Modeling, identification and control of robots[END_REF] is performed. The transition from frame -1 to frame is expressed as a function of the following four parameters.

• : angle between -1 and , corresponding to a rotation between -1

• : distance between -1 and along -1

• : angle between -1 and , corresponding to a rotation between

• : distance between -1

and along

The transformation matrix defining the frame in the frame -1 is given by : Theoretical DHM parameters for the system

-1 = ⎡ ⎢ ⎢ ⎢ ⎣ ( ) -( ) 0 ( ) ( ) ( ) ( ) -( ) - ( ) ( ) ( ) ( ) ( ) ( ) ( ) 0 0 0 1 ⎤ ⎥ ⎥ ⎥ ⎦ j Oset 1 0 0 0 170 0 2 /2 0 1 0 /2 3 /2 0 2 0 /2 4 /2 0 0 3 +668.5 -/2 5 /2 0 4 0 /2 6 0 0 5 0 /2 7 /2 0 6 -182 -/2
The system is now set up (Fig. 8). The geometrical target values coming from CAD model are entered in the Tab. 5.

Performance analysis of the system

In order to obtain the measurement accuracy of the prototype (trueness and repeatability), a load qualification test is carried out during which the TCP coordinates of the robot are measured. The results obtained by the system are then compared with those measured by a metrological tool known for its accuracy and repeatability, a LEICA laser tracker. For this purpose, a robot cell equipped with a KUKA KR270 robot is used. The qualification protocol is broken down as follows:

• Realization of an empty trajectory, with stops on 30 measuring points,

• Recording of the TCP coordinates on 30 points by the device and the laser tracker,

• Achieving the same trajectory under load,

• Recording of the TCP coordinates on 30 points by the device and the laser tracker,

• Comparison of the relative movements of the TCP over 30 points

• Analysis of the measurement accuracy of the device.

• Several levels of solicitation will be performed pushing and pulling mode with 1000N and 2500N

We observe mainly T-Mac Base frame to study the performance of the system regarding repeatability and accuracy (Fig. 9). The qualification path consists of 30 measuring points (Fig. 10). The robot executes this trajectory at a constant linear speed of 0.1m/s, with a 5-seconds stop at each point to allow stable coordinate acquisition.

Repeatability measurement

Measurement repeatability is evaluated while trajectories are played 5 times consecutively. Measurement repeatability is calculated at each position using the standard formula. This repeatability is due to both the robot positioning repeatability and the measurement repeatability. Articular repeatability of the system is studied with and without load. To begin, a modeling is performed taking into account the real positioning of the various joint regarding each others. After evaluation of the DHM parameters see Tab. 6, we obtain all the defect of our device due to manufacturing and assembling. We therefore compare the repeatability measured with the device regarding that measured with the laser tracker. Tab. 7, Tab. 8 and Tab. 9 present our results and highlights that our system repeatability is under 0.03mm 3D Trueness trial on an industrial robot KR270 with a laser tracker with optimization of DHM parameters

Accuracy under loadings

Our objective is to validate the performance of our system to give the position of T-MAC reference frame in comparison with the laser tracker. Two configurations are tested : while pushing and while pulling with 1000N and 2500N. Without correction model, it can be observed some differences highlighting the additional work that will be needed to identify industrial robot under stress meaning while pushing or pulling it with this device (Fig. 11). While the behavior of the prismatic joint seems to be well understood, we performed a finite element analysis of the Universal joint to see its behavior under load. The software 3D Experience is used with the following boundary conditions: the use of an aluminum alloy and a force of 2500N oriented towards the center of the Universal joint, the fact of ensuring that the mesh size has a small influence on the results given by the software, the consideration of different conditions for the modeling of the assembly (global contact, use of connectors). As a result, a deformation of the base is observed (deformation between Frame 1 and Frame 2 of Fig. 8) which must be taken into account in the model and which is not previously identified. Preliminary results are presented (Fig. 13) and show a correlation between the offset between the tracker and the device measurements and the positioning of the lower Universal joint. Our future work will be focused on the implementation of the FEA analysis inside the software to be able to study the behavior of an industrial robot under stress without being disturbed by the device behavior.

Conclusion and perspectives

This paper highlights the performance of a new patented system to apply a wrench and to measure the key elements to improve robot performance in terms of accuracy under load. This system is a newer technology that is efficient, easier to use and must provide all the requisite of calibration in one system. The dynamic loader allows the positions of a robot in the workspace to be measured very quickly for different loading cases. Indeed, the measurement of the 30 positions for the 5 loading cases and with repeatability (i.e. 390 measurement points) took less than one hour. For comparison, with the tracker method previously used for elastostatic identification of robots, one day was needed to measure 30 positions for 30 robot joint configurations with only two loading cases. This device is really interesting for industrial applications based on the installation time. Moreover, we can evaluate easily the robot health evaluating the deviation of its accuracy/unaccuracy during defined period. Moreover, this allows us to make decoupled identifications (2 axes by 2 axes) whereas the literature generally proposes a global identification of all the parameters. We have highlighted in past work [START_REF] Ambiehl | New method for decoupling the articular stiffness identification[END_REF], the importance for example of identifying the first 3 axes stiffnesses of the robot from that of the wrist because there is a factor of 10 on the values to identify. Perspectives will be dedidated to the identification under load of this device. Increasing its accuracy by solving problems in geometry and mechanical responses, hence becomes a research topic for our research activities.

Figure 1 :

 1 Figure 1: Accuracy (a) and repeatability (b) according ISO 9283:1998

Figure 3 :

 3 Figure 3: Studied architecture : RRRPRRR(Case I to III) -RRPRRR (Case IV) -R means Rotoïd and P Prismatic

Figure 4 :

 4 Figure 4: Architecture regarding Accuracy

Figure 6 :

 6 Figure 6: UPUR to sollicitate industrial robot

Figure 7 :

 7 Figure 7: Human Machine Interface to synchronize data in terms of force and position colorblack

Figure 8 :

 8 Figure 8: Positioning of the various frames regarding[START_REF] Khalil | Modeling, identification and control of robots[END_REF]

Figure 9 :

 9 Figure 9: Trajectory in a plane of Radius 400mm

Figure 10 :

 10 Figure 10: 30 positions on a radius 400mm

Figure 11 :

 11 Figure 11: Robot deection measurement with push and pull movement with 1000N and 2500N

Figure 12 :

 12 Figure 12: Finite Element Analysis of the system basis at Position 3 -Von Mises stresses (A) -Displacement vector (B)

Figure 13 :

 13 Figure 13: Correlation between the deformation of the device base seen by the laser tracker/device and the Finite Element Analysis of the base

Table 1

 1

		Measurement	Identication Methodology
	Dumas et al. 2011 [2]	Weight and Tracker	Complete pose method (3 positions and 3 orientations) with 2 steps
			to determine the 5 last articular stiness and the rst one. See
			Fig.2.1
	Guerin et al. 2014 [7]	Weight and Tracker	Partial Pose Method (3 positions) to identify a 6 Degrees of Free-
			dom industrial robot located on a track
	Nubiola et al. 2014 [15]	Ballbar	One xture is attached to the robot base and the other to the
			robot end-eector, and each having three magnetic cups. 72 poses
			of the tool xture, with respect to the base xture, it is possible to
			measure six distances with the ballbar between the magnetic cups
			on the tool xture and the magnetic cups on the base xture, and
			thus calculate the pose with high accuracy. See Fig. 2.2
	Nubiola et al. 2014 [16]	Optical CMM (Coor-	A laser tracker and an optical CMM are compared to evaluate a full
		dinate Measuring Ma-	kinematic calibration and compliance parameters relative to joint
		chines) compared to	stiness.
		Laser tracker
	Theissen et al. 2014 [4]	Double Loading Ball-	The measuring methodology utilizes the Double Loading Ball Bar to
		bar [14] + Tracker	customize wrench vectors and a laser tracker to measure the system
			response. In particular, the Double Loading Ball Bar creates the
			closed-force-loop to create a ow of forces similar to the intended
			application of the robot. See Fig. 2.3
	Wu et al. 2015 [5]	Weight and Tracker	it mainly focuses on the methodology i.e. Partial pose method (3
			positions)
	Ambiehl et al. 2017 [3]	Weight et tracker	Elasto-static identication : comparison between 3 approaches :
			complete Pose method (3 positions and 3 orientations), Partial
			pose method (3 positions) and Decoupled partial pose where the 3
			rst joint are identied in an independant way than the 3 last one
	Filion et al. 2018 [17]	Portable photogram-	A portable photogrammetry system (the MaxSHOT 3D) compared
		metry system is com-	with a laser tracker (the FARO laser tracker) to improve robot
		pared to Laser tracker	position accuracy
	Kamali et al. 2019 [6]	Cable Driven Parallel
		Robot and tracker

Setup includes a parallel cable-driven mechanism for applying loads and a laser tracker for measuring the tool center point. See Fig.

2

.4

Table 2 4

 2 congurations to be studied in terms of accuracy;

	Sensor	Accuracy	Ratio of cost
	Encoder Low accuracy	20	1
	Encoder High Accuracy	5	4
	Glass ceramic ruler Zerodur	3 m	2

Table 3

 3

Table 4

 4

	Model	Mean( m)	Variance	a	b	Cost
	I	61.05	1331	2.61	23.37	8
	II	15.3	83.2	2.62	5.83	26
	III	20.01	137.6	2.69	7.42	15
	IV	18.89	126.5	2.64	7.15	13

Table 5

 5

Table 7

 7 Articular trueness trial on an industrial robot KR270 with a laser tracker without loading and below 0.09mm with 1kN loading. The robot's positioning repeatability measured with the device is therefore very close to that measured by the laser tracker. The first two points of the series loaded at 1kN have a fairly high repeatability, visible to both the tracker and the device. This study allows us to validate the capability of measurement of the device regarding traditional measurements via Laser Tracker.

	1	-0.0007	0.00016	-0.0011	168.18	0
	2	1.570	-0.00014	1	-0.720	1.57045
	3	1.570	0.0001	2	-0.00012	1.576
	4	1.570	-3.39E-5	0	3 + 667.039	-1.57
	5	1.595	-0.0001	4	0.00023	1.566
	6	-0.000	0.0003	5	-0.0002	1.56706
	7	1.567	0.00068	6	-185.05	0
	Table 6
	Evaluation of DHM parameters
			Average Repeatabilty	Maximum Repeatabilty
			0		1KN	0	1KN
		1 0.0011	0.0025	0.0028	0.0068
		2 0.0010	0.0022	0.0037	0.015
		3	0.015	0.045	0.033	0.12
		4 0.0028	0.0056	0.014	0.053
		5 0.0020	0.0062	0.0037	0.016

Table 9

 9