Nathalie Coquillé

Soizic Morin
email: soizic.morin@irstea.fr

Fitness of teratological morphotypes and heritability of deformities in the diatom Gomphonema gracile

Keywords: Gomphonema gracile, morphology-based assessment, teratology, transmissibility of morphological characters, phenotypic variability, fitness Highlights 

Diatom teratologies have intrigued scientists since the XIXth century, with respect to their causes and origins. These deformities, mainly observed in long-term cultures or under high levels of pollution, were poorly considered, until they were recently found to be potential indicators of toxic impairment of freshwaters. However, very little is known about their ecology.

In this study, the growth and fitness of morphologically distinct descendants of the same cell line of Gomphonema gracile (teratological vs. non teratological forms) were compared over a typical growth cycle. Contrary to expectations, teratological populations grew slightly faster, at a rate of 0.47 ± 0.03 divisions.day -1 , versus 0.41 ± 0.04 for the normal morphotype. They had similar physiological performances as non-teratological forms. They did not differ in their movement velocities, but the trajectory of teratological forms was more linear, likely as a consequence of their elongated outline. Under the same culture conditions, no competitive exclusion of one phenotype over the other was demonstrated on the time scale of an exponential growth cycle (9 days). Moreover, the deformities were faithfully reproduced over time, and no evidence of decreased viability in teratological forms was provided.

These new insights call into question the common hypothesis that deformed diatoms are altered individuals produced by unfavorable conditions and thus highlight ecosystem dysfunction. They call for further investigations of their ecology.

Introduction

Diatoms are unicellular brown microalgae with an important ecological role in the functioning of freshwaters [START_REF] Morin | Benthic diatom monitoring and assessment of freshwater environments: Standard methods and future challenges[END_REF]. Diatom species identification is based on the morphological features of their siliceous cell wall, the frustule: valve shape and symmetry, cell dimensions, length:width ratio, specific ornamentations (presence and number of raphes, orientation and density of striae, etc.). Practically, diatom identification assumes that the features of the frustule are constant for a given species. A range of length and width variability exists, as the result of the natural morphological variation in diatoms occurring over their life cycle, consequence of their peculiar reproduction cycle [START_REF] Mann | Size and sex[END_REF].

Besides morphological variations associated with development, polymorphism can also result from environmental stress (phenotypic variation) or natural genetic variability [START_REF] Håkansson | A study of variation in valve morphology of the diatom Cyclotella meneghiniana in monoclonal cultures: effect of auxospore formation and different salinity conditions[END_REF]. Notably, [START_REF] Rose | What constitutes Gomphonema parvulum? Long-term culture studies show that some varieties of G. parvulum belong with other Gomphonema species[END_REF] documented morphological changes over the life cycle in clones of Gomphonema parvulum, complicating the definition of clear species boundaries. Continued culturing resulted in cell size reduction and changes in morphology, potentially leading to the identification of 3 different species. Polymorphism can be an adaptive response of diatom species to a shift in environmental conditions and can result from changing selective pressures [START_REF] Kociolek | Variation and polymorphism in diatoms: the triple helix of development, genetics and environment. A review of the literature[END_REF]. Trobajo (2007) also detected changes in the morphology of Nitzschia frustulum stemming from environmental variations; diatoms were significantly more elongate under increasing salinities and nitrogen concentrations. Frustule deformities or teratologies (abnormal outline or ornamentations) are beyond normal phenotypic variations. They can be induced during valve formation, either by inimical conditions or under long-term artificial culture conditions (see review in Falasco et al., 2009a). Numerous observations of deformed diatoms in laboratory cultures were attributed to cell crowding [START_REF] Barber | Observations on some deformities found in British diatoms[END_REF] or culture senescence (Falasco et al., 2009a). Recently, [START_REF] Windler | Influence of bacteria on cell size development and morphology of cultivated diatoms[END_REF] reported the major influence of bacteria associated with diatoms in the long-term maintenance of laboratory cultures. They found that cultivation under axenic conditions reduced population growth and promoted morphological changes (cell size reduction, frustule aberrations) in pennate diatoms, compared to xenic cultures.

The teratological character is, thus, commonly accepted to result from unhealthy conditions, as discussed in [START_REF] Lavoie | Diatom teratologies as biomarkers of contamination: are all deformities ecologically meaningful?[END_REF], either in laboratory cultures (lack of essential accompanying bacteria, [START_REF] Windler | Influence of bacteria on cell size development and morphology of cultivated diatoms[END_REF] or in the field (induction by toxic contamination, Falasco et al., 2009a). For this reason, lower fitness is expected in teratological diatoms, and some types of deformities are even suspected to be lethal [START_REF] Arini | Cadmium decontamination and reversal potential of teratological forms of the diatom Planothidium frequentissimum (Bacillariophyceae) after experimental contamination[END_REF]. The assumption that abnormal diatoms may be outcompeted by normal phenotypes under optimal conditions, and ultimately eliminated from the populations, is based on the following empirical observations. First, their rare occurrences: teratologies are infrequent and generally recorded at relative abundances not exceeding 1% (Morin et al., 2012a), in particular under field conditions. Second, they generally appear under altered environments, and were shown to progressively disappear with a return to normal conditions. For instance, [START_REF] Arini | Cadmium decontamination and reversal potential of teratological forms of the diatom Planothidium frequentissimum (Bacillariophyceae) after experimental contamination[END_REF] observed that the abundances of cadmium-induced teratologies in Planothidium frequentissimum decreased with decontamination. Consistently, the recovery of normal morphology after sexual reproduction in deformed diatoms from long-term cultures suggests Code de champ modifié that teratologies do not result from genetic drift [START_REF] Granetti | Alcune forme teratologiche comparse in colture di Navicula minima Grun. e Navicula seminulum Grun[END_REF]. Still, the fact that teratological forms are rarely dominant in samples has until now limited the possibility to experimentally validate the hypothesis of competitive exclusion of deformed phenotypes over time.

Given this background, an experiment was carried out to assess the heritability of the teratological character and the viability of abnormal cells. To this end, cell lines descending from laboratory-cultured Gomphonema gracile which had diverged into two morphological variants were used: a normal phenotype and a markedly deformed one. The objectives of this study were: 1) to compare the fitness of both phenotypes under the same culture conditions, and 2) to assess the heritability of the teratological character in diatoms, taking into account the potential influence of closely-associated bacteria. To reach these objectives, both cultures were assessed over 9 days for population dynamics (viability, growth kinetics), cell morphology (cell dimensions, altered frustule), physiology (photosynthesis) and behavior (mobility features). The first hypothesis was that the deformities would be reproduced with cell duplications, while normal phenotypes would be restored with sexual reproduction. The second hypothesis was that the teratological character, even if heritable, would alter the global metabolism of the species, which would be observable through reduced performances in the endpoints studied.

Materials & Methods

Biological material.

A pennate diatom was isolated from a field sample (Rebec, upstream section of the Leyre river, Southwest France) in December 2013 and established in culture [START_REF] Coquillé | Use of diatom motility features as endpoints of metolachlor toxicity[END_REF]. During the first month that they were cultured (March 2014), cells exhibited typical features of Gomphonema gracile Ehrenberg [START_REF] Reichardt | Gomphonema gracile Ehrenberg sensu stricto et sensu auct. (Bacillariophyceae): A taxonomic revision[END_REF]. Approximately one year later, the parental line of G. gracile (further named GGRA) gave rise to two morphologically distinct (but homogenous within one culture) descendant cell lines continuing to reproduce vegetatively. The first phenotype, called GNF (Gomphonema normal form), was smaller than the parent culture, less lanceolate and had more rounded apices. The second one, called GTF (Gomphonema teratological form), was 2-fold larger than GNF, and all cells exhibited a typical deformity in valve outline ("boomerang shaped", Type 1 deformity in Falasco et al., 2009b).

Before the experiment, GNF and GTF populations were almost pure. They were maintained in separate cultures in sterile Dauta medium [START_REF] Dauta | Conditions de développement du phytoplancton. Etude comparative du comportement de huit espèces en culture. I. Détermination des paramètres de croissance en fonction de la lumière et de la température[END_REF] at 17°C in a thermostatic chamber 610 XAP (LMS LTD ® , UK) at 67 ± 0 µmol.m -2 .s -1 with a dark:light cycle of 8:16 h. Non-axenic cultures were grown in 100-mL round borosilicate sterile glass flasks previously heated to 450°C for 6 h and autoclaved 20 min at 121°C.

Experimental design.

The experiment, carried out in March 2015, was run during nine days under the conditions affording Gomphonema's growth without nutrient depletion over time, as used in [START_REF] Coquillé | Use of diatom motility features as endpoints of metolachlor toxicity[END_REF]. GNF and GTF cultures were inoculated at 30,000 cells.mL -1 in sterile Dauta medium (40 mL final volume). As it was likely that a small percentage of the other phenotype would be found in those cultures, the experimental cultures were labelled Ctrl (control) and Trtg (teratological), respectively, in order to avoid confusion between phenotypes and treatments. Triplicate cultures were used for each treatment (Ctrl and Trtg) and incubated simultaneously in a thermostatic chamber 610 XAP (LMS LTD ® , UK), under the same environmental conditions as the mother cultures.

On days 1, 2, 3, 6, 7, 8 and 9, population dynamics (viability, growth kinetics), cell morphology (cell dimensions, deformities), physiology (photosynthesis) and behavior (mobility features) were analyzed. On each sampling day, parameters derived from chlorophyll-a fluorescence were first measured, directly on the cultures. Then, the flasks were gently shaken to homogenize the suspensions before sampling 1 mL of culture under the flame. The sample was then aliquoted as follows: 125 µL for the quantitative analysis of live and dead diatoms, 100 µL for mobility measurements, and 200 µL to prepare permanent diatom slides. On the last day of the experiment (day 9), 3 mL of homogenized suspension was used to perform Rapid Light Curves and the remaining volume of culture was softly filtered on previously ashed Whatman GF/C ® filters that were immediately frozen at -20°C before molecular analyses of the associated bacteria.

Chlorophyll-a fluorescence-related endpoints.

Parameters derived from chlorophyll-a fluorescence were measured on the intact biofilms, by means of a PHYTO-PAM (Heinz Walz, GmbH, Germany) equipped with an emitter-detector unit (PHYTO-EDF). Benthic settlement potentially leads to the formation of cell aggregates; therefore ten randomly selected measurements of the effective quantum yield (photosynthetic efficiency) and chlorophyll-a content estimated by chlorophyll-a fluorescence were performed. To do this, a home-made system was used for reproducible direct measurements on the bottom of the flasks. The median of 10 values per sample was then used for statistical analyses.

On day 9, 3 mL of suspension were used to perform Rapid Light Curves (RLC, [START_REF] White | Rapid light curves: A new fluorescence method to assess the state of the photosynthetic apparatus[END_REF] generated with the PHYTO-PAM in ED mode. Briefly, samples adapted to low light irradiance (50 μmol.m -2 .s -1 ) for 20 minutes were sequentially exposed to increasing actinic irradiances (9 light levels ranging from 64 to 1,964 μmol.m -2 .s -1 ) for 10 seconds, separated by a saturating flash. The relative electron transport rate of photosystem II in response to the light pulse was then plotted against irradiance. The following parameters were extracted from the curves fitted on the model of [START_REF] Eilers | A model for the relationship between light intensity and the rate of photosynthesis in phytoplankton[END_REF]: photosynthetic efficiency at low light intensity (initial slope of the curve), maximal electron transport rate and onset of light saturation.

Determination of population growth kinetics.

Diatom counts were carried-out on fresh material in a Nageotte counting chamber, using light microscopy at 400x magnification (Olympus BX51, Olympus Optical Co. GmbH, Germany). Diatom cell density and mortality were estimated for each replicate sample as described in [START_REF] Morin | Effects of a bactericide on the structure and survival of benthic diatom communities[END_REF]. Solitary cells and those forming associations in the counts were distinguished. Density data were recorded as cells.mL -1 and the logarithmic increase in population was plotted as a function of time unit, to calculate growth rates (GR, expressed in divisions.day -1 during exponential growth) following the formula provided in [START_REF] Morin | A comparison of specific growth rates of periphytic diatoms of varying cell size under laboratory and field conditions[END_REF], and the carrying capacity (i.e. maximum size reached during the stationary phase) of the cultures.

Mobility features.

The percentage of motile cells, as well as their velocity and trajectory, were determined using CASA (computer-assisted sperm analysis) plug-in [START_REF] Wilson-Leedy | Development of a novel CASA system based on open source software for characterization of zebrafish sperm motility parameters[END_REF] of ImageJ software under the specific measurement conditions adapted to G. gracile by [START_REF] Coquillé | Use of diatom motility features as endpoints of metolachlor toxicity[END_REF]. A 20-µL drop of sample was deposited onto a microscope slide and video acquisition (Archimed TM , Microvision Instruments) was performed after 2-3 min. Velocity average path (VAP), velocity curvilinear (VCL), velocity straight line (VSL) and linearity (LIN = VSL/VAP, describing the curvature of the trajectory) [START_REF] Rurangwa | The measurement of sperm motility and factors affecting sperm quality in cultured fish[END_REF] were then calculated from 260 frames corresponding to 10 seconds of film in total.

Diatom cell morphology.

Organic matter in the samples was removed by adding hydrogen peroxide to the diatom suspensions and kept overnight at room temperature. They were then rinsed with distilled water and centrifuged, before preparing permanent slides according to EN 14407:2014, by mounting the clean samples in Naphrax (provided by Brunel Microscopes Ltd, UK). Then, they were observed at 1,000x magnification (Leica DMRB, Germany), for the determination of the percentage of normal (symmetrical) and deformed (asymmetrical) Gomphonema individuals, based on >100 individuals per replicate sample. Additionally, at least 10 measurements of cell linear dimensions (length, width, thickness) and of striae density were performed in each replicate sample. Average cell biovolume was then calculated using the mathematical equation of [START_REF] Hillebrand | Biovolume calculation for pelagic and benthic microalgae[END_REF] for weakly heteropolar forms (elliptic cylinder).

A return to the origin material (i.e. samples from [START_REF] Coquillé | Use of diatom motility features as endpoints of metolachlor toxicity[END_REF] was made in order to measure, in the same way, the morphological characters of GGRA cells, thus providing elements for comparison and understanding of the morphological range of variation of this culture after 1 year.

Bacterial fingerprinting.

Each replicate filter collected on day 9 was used to analyze the bacterial communities closely associated with the diatoms, i.e. embedded in their extracellular polysaccharides (EPS). Nucleic acids were extracted with the FastDNA SPIN kit for soils (MP Biomedicals, France) and the 16S-23S intergenic spacer region from the bacterial rRNA operon was amplified as described in [START_REF] Pesce | Combined effects of drought and the fungicide tebuconazole on aquatic leaf litter decomposition[END_REF], using the universal primers S-D-Bact-1522b-S-20 and L-D-Bact-132-a-A-18. Automated ribosomal intergenic spacer analyses (ARISA) were performed on an Agilent 2100 Bioanalyzer (Agilent Technologies, France) and the resulting profiles were exported from the Agilent 2100 Expert software.

Data analysis.

All statistical analyses were performed with R 3.2.2 [START_REF] Ihaka | R: A language for data analysis and graphics[END_REF].

After having checked for normality and homogeneity of variances, linear models for fixed effects (lm) were implemented (nlme package). For each endpoint, the effect of culture (Ctrl vs. Trtg), date, and their interaction, were tested sequentially by the model. The results are illustrated as figures in the manuscript. Detailed values and statistics output can be found in Appendix 1.

A t-test was used to compare the parameters extracted from the curves fitted for growth kinetics and RLC between cultures. Additionally, for growth, the kinetics of the two phenotypes in each culture were compared.

For all analyses, a p-value below 0.05 was considered statistically significant.

The endpoints raising significant culture and/or date effects were plotted in a Principal Component Analysis (PCA), followed by Hierarchical Clustering to identify the main groups of data, using the FactoMineR package [START_REF] Lê | FactoMineR: An R Package for Multivariate Analysis[END_REF].

Results

Diatom morphology: cell dimensions and teratology

During the first months of culture (2014), cells from the original material (GGRA) were identified as small specimens of Gomphonema gracile. Valves were quite isopolar in outline and were 28.91 ± 0.12 µm long and 5.94 ± 0.04 µm wide (Figure 1). Striking differences were observed between the parental line (GGRA) and the cultures used in this study (Figure 1). Indeed, GNF individuals were slightly more heteropolar with more rounded apices and valves were smaller (21.92 ± 0.09 µm long and 5.92 ± 0.03 µm wide). Moreover, GTF cells were more lanceolate (33.88 ± 0.10 µm long and 6.17 ± 0.03 µm wide) but showed a deformed valve outline (boomerang shape, Figure 2). In all cases, the invagination of the frustule was located opposite to the stigma present in the central area. No difference in the density of striae was found, with average values of 17.00 ± 0.09 striae in 10 µm (n=200).

As a consequence of these differences in linear dimensions, the cell biovolumes calculated over the duration of the experiment (7 days for GGRA and 9 days for GTF and GNF) showed significant differences (p<0.001) between GGRA (457 ± 14 µm 3 , n=150), GNF (334 ± 11 µm 3 , n=210) and GTF (543 ± 16 µm 3 , n=210). Cell biovolume of both descendant cell lines tended to slightly decrease with time, and significantly smaller cell sizes were found on days 6 and 9 (p<0.05) (Figure 3A). Very few deformed individuals were observed in the Ctrl cultures (0.34 ± 0.12%, n=2617) (Figure 4). Cells were in the size range of GNF individuals, but the deformity was similar in location as in GTF (Figure 4). In Trtg cultures, only 7.7 ± 0.7% of the cells (n=2693) were not deformed, and were morphologically very close to GNF individuals (21.07 ± 0.38 µm long, 6.00 ± 0.07 µm wide; n=65).

Growth kinetics

Significant differences in cell densities were observed as a function of time in both cultures, featuring typical growth kinetics with the stationary phase reached from day 6 (Figure 3B). The percentage of dead diatoms decreased continuously on the first dates, simultaneously to the exponential cell increase. Then, mortality increased when the stationary phase was reached (culture x date interaction, p<0.05, Figure 3C).

Despite the absence of any statistical difference in overall growth rates between Ctrl (GR=0.46 ± 0.01 divisions.day -1 ) and Trtg cultures (GR=0.49 ± 0.04 divisions.day -1 ) in the exponential growth phase (p=0.63), t-tests revealed statistical differences in the specific growth rates of GNF and GTF phenotypes in Ctrl and Trtg cultures (Figure 5, p<0.001 in both cases). Indeed, GNF populations grew faster in the Ctrl units (0.46 ± 0.01 divisions.day -1 ) than in the Trtg ones (0.37 ±0.08 divisions.day -1 ), where they reached their stationary phase one day later (day 8 instead of day 7). GTF had the same growth characteristics as GNF in the Ctrl (GR= 0.45 ± 0.06 divisions.day -1 , stationary phase starting on day 7). Conversely, in the Trtg units, they showed higher division rates (0.49 ± 0.04 divisions.day -1 vs. 0.37 ±0.08 divisions.day -1 for GNF) and consequently attained their maximal cell density earlier (on day 6, Figure 3B). Therefore, significant interaction between culture and date was highlighted for cell densities, as a result of the delay in reaching maximal cell numbers in GNF (on day 7, Figure 3B).

The carrying capacity (maximum population size) in cell density was about one third lower for Trtg cultures (397,800 ± 31,700 cell.mL -1 , average values for days 7 to 9) compared to Ctrl cultures (616,200 ± 44,400 cell.mL -1 , average values for days 7 to 9) (Figure 3B). However, the total biovolume occupied (i.e. cell densities x individual biovolume) did not differ between experimental units from day 7, with an average of 197 ± 12.10 6 µm 3 .mL -1 (Figure 3D).

Physiology

No significant difference was observed in chlorophyll-a derived parameters between Ctrl and Trtg (p=0.42). Chlorophyll-a fluorescence followed a bell-shaped curve and peaked on day 6 (Figure 3E). Photosynthetic activity (Figure 3F) increased on the first days of exponential growth, and then slightly decreased over time (from day 6).

The RLC did not highlight any differences between treatments in the use of light by the cultures (Appendix 2). Indeed, similar values were obtained for Ctrl and Trtg photosynthetic efficiency at low light intensity (0.23 ± 0.00 in average, p=0.09), as well as the maximum electron transport rate (95.1 ± 7.6 μmol electrons.m -2 .s -1 , p=0.83), reached from the saturating irradiance of 415.9 ± 30.1 μmol.m -2 .s -1 (p=0.90).

Behavior

In both cultures, cells grew benthically, and were mostly solitary. Up to 40 ± 2% cells (Ctrl, day 2) had the potential to form aggregates, principally forming star-shaped associations (Figure 3G). The abundance of cell clumps was always higher in Ctrl cultures (p<0.001) and decreased over time whatever the culture from day 2 (p<0.01). For this reason, on the first days, the percentage of mobile diatoms was so low that mobility parameters could not be determined appropriately. When the cultures reached their stationary phase, the percentage of cells forming aggregates drastically decreased and the percentage of mobile cells increased significantly (Figure 3H), simultaneously to a decrease of benthic forms (as assessed through the chlorophyll-a settled on the bottom of the flasks, Figure 3E). Striking differences in motility were observed between cultures (p<0.001): in the Ctrl, the percentage of mobile cells gradually increased from <5% (day 6) to 18.9 ± 3.4% (day 9). Oppositely, 36.8 ± 2.7% cells were mobile in the Trtg cultures from day 6 to 8, then decreased to 21.5 ± 3.4% on the last day of the experiment. On the last days, the percentage of associated cells was low (5.6 ± 2.6% in Ctrl and 1.3 ± 0.5% in Trtg cultures), and the cells grew mostly in suspended, loose agglomerates, potentially indicating biofilm senescence. No significant difference was found between cultures with respect to movement velocity; however, the trajectory was more linear in Trtg (p<0.05) (Appendix 1).

Global patterns in sample variation

The two first dimensions of the PCA explained the same amount of data variability, reaching 68.43% of combined variance (Figure 6A). The optimal clustering reached after applying the PCA discriminated four groups (Figure 6B).

The first component of the PCA expressed a temporal gradient. It discriminated between samples collected on the first days of sampling (exponential growth phase), located on the left half-panel, and cultures corresponding to the stationary phase (last sampling days), located on the right half-panel. Positive values along this dimension were correlated with increasing carrying capacity (total cell biovolume, cell density) as well as other endpoints related to termination of growth: higher mortality, increasing percentages of mobile cells associated with decreasing cell aggregation.

The second PCA component separated treatments, with Ctrl clustered on the lower halfpanel and Trtg on the upper half-panel. Sample discrimination was mostly related to the morphological descriptors (cell dimensions, biovolume, percentage of teratologies), and with more linear trajectories in Trtg on the last days of sampling.

ARISA profiles

Amplification of the 16S rDNA genes on the filters did not give rise to banding patterns in one replicate sample of Ctrl (likely due to an experimental error), which was consequently discarded. Fingerprinting of bacterial communities (Appendix 3) highlighted that Ctrl and Trtg cultures shared 3 major peaks (above a threshold of 100 relative fluorescence units in height from the baseline), and that no major differences were found between Ctrl and Trtg. However, a minor peak (below 50 fluorescence units) was detected around 623bp, but only in the Trtg samples.

Discussion

Implications of deformities for fitness and survival

Teratologies did not impact performance in GTF populations

Results of this study are in complete disagreement with common assumptions that deformed individuals are impaired. Indeed, the deformed culture of Gomphonema gracile (GTF) did not exhibit a longer lag phase compared to the controls and growth rates of the GTF populations were similar or higher than those of GNF (Figure 5). Growth rates of the GTF population were higher than that of GNF in Trtg cultures, and similar in Ctrl cultures, possibly resulting in higher competitive abilities of GTF individuals, compared to GNF ones, under specific conditions. This is in contradiction with the observations made by [START_REF] Windler | Influence of bacteria on cell size development and morphology of cultivated diatoms[END_REF], where teratological cultures had grown more slowly than normal cultures. However, it is worth noting that, in their study, teratologies were suspected to result from axenicity, which was not the case here.

The carrying capacity (maximum cell density in the stationary phase) was certainly lower in Trtg than in Ctrl (~400,000 cells.mL -1 vs. ~600,000 cells.mL -1 ). However, these differences were likely caused by space availability more than growth abilities: total biovolume occupied in the stationary phase was similar in Ctrl and Trtg cultures. In the same way, [START_REF] Windler | Influence of bacteria on cell size development and morphology of cultivated diatoms[END_REF] observed that their normal and teratological cultures of Achnanthidium minutissimum reached similar chlorophyll concentrations in the stationary phase. Thus, competition for space (and subsequent access to resources such as nutrients and/or light) was probably the main driving factor in kinetics for both cultures in this experiment.

Besides growth kinetics, the physiological and behavioral endpoints assessed did not show lower performances of GTF populations, contrarily to what was expected. Photosynthetic efficiency was similar in Trtg compared to Ctrl cultures and fell into the range of other measurements carried-out on G. gracile [START_REF] Coquillé | Use of diatom motility features as endpoints of metolachlor toxicity[END_REF]; Table 1). In this experiment, the mobility features (percentage of mobile cells and velocities) of GNF and GTF individuals were below the values reported by [START_REF] Coquillé | Use of diatom motility features as endpoints of metolachlor toxicity[END_REF]. Nevertheless, differences were found between Ctrl and Trtg: more mobile individuals were found within GTF populations and they moved more linearly than GNF cells (Figure 6). This may be a consequence of their more elongated valve outline. No differences were found, however, in movement velocity, in agreement with Bertrand's work on the motility of several diatom species (1990,1999). Based on analyses of five distinct populations, he also demonstrated that velocity was independent of cell size within a species [START_REF] Bertrand | La vitesse de déplacement des diatomées[END_REF].

To sum up, the morphological changes that occurred in Gomphonema gracile did not impair its performance, based on the endpoints assessed, when cultured alone. The fact that GNF and GTF displayed similar responses in cultures where they were dominant does not prejudge their behavior when found together. Superseding of GTF by GNF would be expected based on [START_REF] Arini | Cadmium decontamination and reversal potential of teratological forms of the diatom Planothidium frequentissimum (Bacillariophyceae) after experimental contamination[END_REF]'s work, arguing for a relative decrease in the percentage of deformed diatoms under optimal growth conditions.

Coexistence of GNF and GTF morphotypes

The teratological forms had higher growth rates and higher cell dimensions, thus higher cell surface in contact with their environment for nutrient uptake. Moreover, the cells tended to form large floating bulks of solitary individuals, whereas they formed benthic mats in [START_REF] Coquillé | Use of diatom motility features as endpoints of metolachlor toxicity[END_REF]. This may stem from ageing with long-term culturing, as well as from the morphological changes over time in G. gracile. These associations were more striking in the GTF cultures; deformed diatoms may thus be less adhesive than the normal forms. This slightly distinct lifestyle can be an adaptation of this phenotype, larger than GNF and more silicified, to modify its sinking rates and/or maximize its access to resources (nutrients, light). Such adaptive mechanisms have been observed in small lacustrine Stephanodiscus species [START_REF] Kociolek | Variation and polymorphism in diatoms: the triple helix of development, genetics and environment. A review of the literature[END_REF]. Therefore, these adaptations may confer a competitive advantage to GTF individuals over the normal morphotype under certain circumstances. The low percentage of non-teratological forms in GTF, stable over time, tends to confirm this hypothesis.

The percentage of deformed individuals in Ctrl fell into the range of the abundances occurring "naturally" in the field, i.e. below 0.35% (Morin et al., 2012a). The GTF phenotype did not significantly increase over time in Ctrl cultures, indicating that GNF was not outcompeted (in agreement with the GR values of GNF and GTF in Ctrl units, Figure 3). However, the differential growth of GNF and GTF in Trtg units suggests that a massive outbreak of teratological individuals, owing to an extreme event and/or repeated toxic exposure, could lead to competitive exclusion of their normal congeners. Neury-Ormanni et al. ( 2017) performed a competition experiment with a balanced GNF:GTF inoculum under the same physicochemical conditions as in the present study. In their experiment, no significant differences in growth were found, compared to the individual kinetics of GNF and GTF, and both phenotypes co-occurred at a 1:1 ratio until the stationary phase was reached. Therefore, dedicated competition experiments using several GNF:GTF ratios would constitute a potential way to confirm this theory and determine a threshold above which teratological diatoms would irreversibly dominate over normal ones. However, there is evidence from translocation experiments [START_REF] Tolcach | The effect of translocation of microbenthic communities in a polluted lowland stream[END_REF] and laboratory investigations (Morin et al., 2012b) that diatom immigration may contribute to re-colonization when toxic contamination is removed, and mask a small population of deformed individuals kept alive. Indeed, in the field, continuous immigration of normal morphotypes and competition with several other species likely impedes the sustainable presence of teratological diatoms under uncontaminated conditions.

Transmission of the teratological character over time

Consistency in the teratological feature

In this study, the culture of deformed Gomphonema gracile (GTF) was maintained with classical growth kinetics at abundances exceeding 90%, suggesting that the deformity was non-lethal. In long-term cultures, frustule aberrations were demonstrated to increase as valves decrease in length in several diatom species (e.g. [START_REF] Hostetter | Polymorphism in the diatom Pinnularia brebissonii in culture and a field collection[END_REF][START_REF] Torgan | Morphological irregularity and small cell size in Thalassiosira duostra maintained in culture[END_REF]. In this study, on the contrary, GTF cells were larger than the other population, although at the same development stage as the non-teratological populations (GNF). All deformed diatoms from Trtg and Ctrl exhibited a typical deformed valve outline with symmetry loss (Figure 1 and Figure 2), although the few deformed diatoms in Ctrl were smaller than the GTF populations (Figure 2).

Valve asymmetry is the most frequent type of deformity in Gomphonema species (Falasco et al., 2009b). Similarly incised valves have been described as abnormal G. parvulum [START_REF] Victoria | Assessing the disturbance caused by an industrial discharge using field transfer of epipelic biofilm[END_REF] and G. gracile [START_REF] Morin | Metal-induced shifts in the morphology of diatoms from the Riou Mort and Riou Viou streams (South West France)[END_REF] in natural communities under toxic contamination, where they were associated with normal specimens. Indeed, the consistency of this feature reproduced over time in the Trtg units suggested either that a new species emerged (with another strain of associated bacteria as suggested by ARISA profiles; Appendix 3), or that boomerang-shaped outline deformation preferentially occurs in Gomphonema.

Heritability of the teratology throughout the experiment

Heritability of teratologies was empirically demonstrated through the reproduction of deformed Gomphonema gracile in the Trtg cultures over the 9-day experiment. Indeed, the percentage of GTF cells was stable through time, although cultures grew in cell numbers. This may have resulted from i) mechanical transmission through generations by vegetative division [START_REF] Round | The Diatoms. Biology & morphology of the genera[END_REF][START_REF] Dassow | Relationships between growth rate, cell size, and induction of spermatogenesis in the centric diatom Thalassiosira weissflogii (Bacillariophyta)[END_REF] of the deformed clones and/or ii) higher growth rates in GTF cultures, potentially masking the recovery of normal forms (with lower growth rates, as inferred by GNF growth kinetics in Trtg cultures; also see section 4.1.1). Restoration of maximal size in GTF on day 7 (Table 1), coinciding with stabilization of cell numbers (plateau phase) and the decrease of benthic cells suggested that they underwent sexual reproduction at the timescale of the 9-day experiment. Even though a slight decrease in the percentages of deformities was observed in GTF after sexual reproduction (89.4 ± 4.0% on day 8, Figure 4), it seems that the genetic and/or epigenetic cause of teratologies is most likely.

Reversibility of teratologies is generally assumed; for instance [START_REF] Granetti | Alcune forme teratologiche comparse in colture di Navicula minima Grun. e Navicula seminulum Grun[END_REF] observed in long-term cultures that deformed Navicula species restored their normal morphology after sexual reproduction, leading him to discard the genetic cause of teratologies. However, [START_REF] Mclaughlin | Teratological forms[END_REF] stated that, if the variation of morphology is well defined, consistent and reproducible, teratologies should be considered as varieties of the species. In line with this, Jüttner et al. ( 2013) described a Gomphonema with a deflection in the head and foot poles as a new species, based on its frequent occurrence and large geographical distribution, thus assuming genetic distinctness. As generally observed in long-term cultures, continuous culturing resulted in a decrease in cell size over time for both phenotypes. Size differences between GNF and GTF populations were perpetuated and maintained for 6 extra months [START_REF] Ezzedine | Le FlowCAM : protocoles appliqués à la différentiation morphologique et au calcul de biovolumes de Gomphonema gracile, 34ème Colloque de l[END_REF]: in August 2015, GNF cells averaged 17.35 ± 0.15 µm (n=160) in length. In the same way, continuous decrease also occurred in GTF populations that were 29.59 ± 0.14 µm (n=320) long. The deformities were not reversed after the predictable rounds of sexual reproduction over this extra 6-month period. The continuity of the teratological feature, repeated throughout the GTF population in varying sizes of individuals, also argues in favor of a new variety [START_REF] Mclaughlin | Teratological forms[END_REF]. Further investigations would thus be required (i) to characterize both GNF and GTF genomes in depth in order to identify the potential mutations, to discard or not the genetic causes of diatom teratologies and (ii) to characterize the two epigenomes via the study of DNA methylation and epigenetic causes of diatom teratologies.

Long term persistence of the teratological feature suggests genetic and/or epigenetic control

In this study, both Ctrl and Trtg cultures were issued from a unique parental line which had diverged morphologically. Initially (i.e. when GTF appeared), deformation of this cell line may have been induced by mechanical causes such as crowding in the cultures or by changes in the accompanying bacteria (rather than axenicity, as bacteria were found in both cultures at the end of the experiment). The ARISA profiles differed slightly between cultures by the presence of one small peak in Trtg, suggesting that another strain of bacteria was present in these cultures. Hypotheses regarding a previous exposure to chemical insults or inappropriate culture conditions can be discarded. Indeed, the diatom was isolated from a pristine site in Rebec tributary, and then cultivated using a culture medium under laboratory conditions that were previously shown to be adapted to G. gracile's growth [START_REF] Coquillé | Use of diatom motility features as endpoints of metolachlor toxicity[END_REF]. Besides, both GNF and GTF morphotypes were cultivated under identical conditions that proved to be appropriate given their growth kinetics, thus endorsing the deformity as teratological.

Although the body of work dealing with diatom teratologies is vast (Falasco et al., 2009a), [START_REF] Lavoie | Diatom teratologies as biomarkers of contamination: are all deformities ecologically meaningful?[END_REF], the processes involved in the formation of abnormal cells are still unclear and it has never been proved whether they resulted or not from epigenetic mechanisms or genetic alteration. Better knowledge at the molecular level and more specifically at the epigenetic level is necessary because of the conservation of the epigenetic machinery in diatoms, its potentially role in phenotypic modification [START_REF] Tirichine | Recent progress in diatom genomics and epigenomics[END_REF] and, contrary to genetic factors, ease in evaluating some parameters such as DNA methylation. Indeed, the identification of genetic alteration is hardly assessable directly since few genomes have been sequenced and annotated, making it difficult to target the genetic loci responsible for frustule morphology and to identify potential alterations.

Conclusions

The phenotypic plasticity in diatoms makes heritability difficult to assess, but thanks to unexpected changes in cultures from the same parental line, cultures of morphological variants of Gomphonema gracile (normal and abnormal phenotypes) made it possible to comparatively study them. The results of this study showed that teratologies were reproduced over time in both Ctrl and Trtg cultures, to variable extent depending on the experimental units considered. Moreover, teratology did not significantly affect physiology nor behavior, disputing the previous assumptions that abnormal diatoms are not competitive and are only found as a transient state, useful to point out extremely adverse environmental conditions. Thus, the similarity in the performance of GTF individuals, compared to normal forms (GNF), has implications for the improvement of knowledge about the ecology of teratological diatoms, and for the environmental interpretations made in hydrosystems where they are found. Indeed, this study provides evidence that abnormal diatoms, likely to appear by chance, are viable individuals and may hold out against normal forms under "favorable" conditions. Consequently, much care must be paid to them in biomonitoring studies, before stating that the presence of teratologies reflects the degradation of water quality.

Apart from the ability to transmit teratological characters as seen in the microscopical observations of diatom morphology and discussed in this paper, the growth and physiology data strongly advocate for a genetic and/or epigenetic origin in GTF. In future, special attention should be given to diatom teratologies from the genetic and epigenetic standpoint to understand if they result from alterations in genome and/or epigenetic modifications, to their ecological preferences.

6.

analyses. Emilie Saulnier-Talbot edited this manuscript and provided helpful suggestions. This study was carried out with financial support from the French National Research Agency (ANR) in the framework of the Investments for the Future Programme, within the Cluster of Excellence COTE (ANR-10-LABX-45). (2015). All values are mean ± standard error over the experiment, except * corresponding to the stationary phase and † that were only measurable on days 6 to 9; n=number of individuals measured/counted, N= number of samples.

Figure captions:

£ : GGRA values are from [START_REF] Coquillé | Use of diatom motility features as endpoints of metolachlor toxicity[END_REF]control cultures). Effects of Culture, Date and Interaction between culture and date result from modelling; n.s.: not significant.

Figure 1 .

 1 Figure1. Diatom cell dimensions (length and width, in µm) in the Ctrl (white diamonds, n=210) and Trtg (black diamonds, n=210) cultures, compared to the parental culture (GGRA, grey diamonds, n=150). Significant differences in length were found between Ctrl and Trtg (p<0.001).

Figure 2 .

 2 Figure 2. External (left) and internal (right) views of teratological valves from GTF cultures (SEM microphotographs).

Figure 3 .

 3 Figure 3. Temporal evolution in Ctrl (white diamonds) and Trtg (black diamonds) cultures of A-Individual cell biovolumes (µm 3 ), B-Diatom cell densities (cells.mL -1 ), C-Mortality (%), D-Total cell biovolume (µm 3 per mL), E-Photosynthetic efficiency (relative units r.u.), F-Chlorophyll-a measured on the bottom of the flasks (µg.cm -2 ), G-Percentage of cells forming associations (%) and H-Percentage of mobile cells (%, n.d. = not determined because the number of mobile individuals was too low). Linear mixed-effects models highlight a significant culture effect (*) for individual biovolumes (A, p<0.001), significant date effects ( †) for individual biovolumes (A, p<0.05), photosynthetic efficiency (E, p<0.05) and chlorophyll-a content (F, p<0.001), while interactive effects between culture and date ( ‡) are found for growth kinetics (cell densities B, p<0.001; total cell biovolume C, p<0.001 and mortality D, p<0.05) and the percentage of cells in associations or motile (G and H, p<0.01).

Figure 4 .

 4 Figure 4. Teratological forms. Left panel: Percentage of deformed individuals (%) in Ctrl (white diamonds, n=2617) and Trtg (black diamonds, n=2693) cultures. * denotes a significant culture effect (p<0.001) identified by the linear mixed-effects model. Right panel: Light microscopy photomicrographs of the teratological Gomphonema found in Ctrl (down) and in Trtg cultures (top). Scale bar: 10 µm.

Figure 5 .

 5 Figure 5. Population dynamics of GNF and GTF phenotypes during the experiment, in the Ctrl (A) and Trtg (B) cultures. Experimental results are shown by: open symbols, GNF; solid symbols, GTF. The dashed and solid lines indicate the best-fitting growth curves for normal (GNF) and teratological (GTF) forms, respectively; growth rates (GR, in divisions.day -1 ) and duration of exponential phase considered are specified for each data series. Note the logarithmic scale on the Y-Axis.

Figure 6 .

 6 Figure 6. Principal component analysis (PCA) based on the endpoints significantly affected by treatment (culture) and/or date. A-Variables factor map. B-Projection of the individuals, labelled according to a posteriori clustering outputs. Grey arrows show temporal changes for both cultures.

  Fig. 1

  Fig. 3

Fig. 6 23

 6 Fig. 6

Acknowledgements

Authors thank Gwilherm Jan (Irstea Bordeaux) for his precious technical help, Evane Thorel (Irstea Bordeaux) for performing the RLCs, Michel Coste (Irstea Bordeaux) and PLACAMAT (UMS3626) for providing the SEM microphotographs, as well as Christophe Rosy and Bernadette Volat (Irstea Lyon) who performed DNA extraction and bacterial diversity


Yang Zhang

Vigen Arakelian
email: vigen.arakelyan@insa-rennes.fr

Baptiste Veron

Damien Chablat

Baptiste Véron

Key Features of the Coupled Hand-operated Balanced Manipulator (HOBM) and Lightweight Robot (LWR)

Keywords: Handling of heavy payloads, hand-operated balanced manipulator, gravity balancing, lightweight robot, dynamic behavior

HAL is

Introduction

Workers in industries such as manufacturing and assembly, frequently manipulate heavy objects. However, manual processing is often repetitive and becomes tedious, it reduces efficiency and leads to back pains, injuries and musculoskeletal disorders. It is obvious that traditional robot installations can offer several benefits compared to manual operation: improved repeatability, increased precision and speed. However, industrial robots still have many weaknesses compared to humans. For example, currently industrial robots have a limited ability to perceive their surroundings, which requires costly safety arrangements in order to avoid serious injury. These safety arrangements are particularly important and costly when working with installations of large and powerful industrial robots. It is obvious that serial robots have a poor payload-to-weight ratio. For a six-degrees-of-freedom general-type serial robot, it is less than 0.15 [0]. For example, a robotic arm handling an object of must have a weight of at least . The purchase, installation and operation of such a robot is quite expensive. In addition, the heaviness of the robot and of the payload complicates the dynamics of the system, making it difficult to move accurately and quickly. This becomes especially noticeable during assembly processes, when heavy parts must be installed on a surface with guiding pins. In such a case, the robotic arm has to move smoothly and any sudden movement may damage the mechanical surface of the part. Such a task is not easy to achieve. Thus, autonomous manipulation does not always provide expected reliability and flexibility.

Advantages of the coupled HOBM and LWR

In our view, balancerrobot systems such as power assist robotic systems may be perfectly used for heavy object manipulation. The combination of motion programming of a lightweight robot and simplicity of a hand-operated balanced manipulator (HOBM) may make the system far better than the application of an individual robot arm.

Let's now consider HOBM applications. The HOBM is a handling system with a simple mechanical actuator in which the manipulated object in any position of the workspace is balanced. Such a state of constant balance allows displacements of heavy objects to be achieved manually. The advantages of these manipulators relatively to industrial robots are the simplicity of their construction and their low cost. They have a great weight-carrying capacity and a very large workspace. The implantation of HOBM in existing production line is very simple without the need of important additional surfaces, special auxiliary devices or essential reorganization of the production lay-out. Different approaches and solutions devoted to the design and balancing of HOBM have been developed and documented [START_REF] Olsen | Balanced assembly[END_REF]- [START_REF] Arakelian | Gravity compensation in robotics[END_REF].

These manipulators have found a broad application in several fields of industry where it is necessary to carry out mechanization of heavy manual work. The production of HOBM can be found in several countries, for example, «Dalmec» (Italy), «Balaman» (Japan), «Conco-Balancer» (USA, Fig. 1), «Auto-Balancer» (Germany), «Triom» (Czech Republic), «Yaplex» (UK, Fig. 2), «CEM» (France), etc. The use of such manipulators includes a mode of operation when mechanical devices and humans cooperate to hold and move objects.

Let's now consider a HOBM and a LWR cooperation for handling of heavy parts. In other words, let us consider a new coupled system in which an operator is replaced by a LWR (Fig. 3).

It should be noted that such an approach has drawn attention of researchers and engineers since a long time. The new method of coordinative control of a robot arm and HOBM [START_REF] Kikuchi | Heavy parts assembly by coordinated control of robot and balancing manipulator[END_REF] has been developed in order to automate batch production processes, including heavy parts assembly. Fig. 4 shows the coupled system called the «Hitachi Progress Robot» having a payload capacity of . The characteristics of the robot arm and the HOBM used in this coupled system have been following: a five degrees of freedom robot arm with payload capacity: 100N, maximum velocity:

, repeatability: and a four degrees of freedom HOBM with payload capacity:

and maximum velocity:

. The performance of the Hitachi Progress Robot was a payload capacity of , maximum vertical velocity:

, maximum horizontal velocity: , vertical repeatability:

and horizontal repeatability: . However, nowadays, taking into account the great capabilities of manual lightweight robots, which allow human intervention to control and guide the payload, such a cooperation becomes much more efficient since it does not exclude the possibility of having a human in the workspace of a robot. Thus, it can reduce costs for space and safety measures as shared space is possible.

Optimal design of the cooperative workspace

When designing coupled systems, it is necessary to keep in mind that they consist of two units with different characteristics. However, some of their parameters can be modified during the cooperation of these units. One of the first is to consider structural compliance, i.e. any movement of the payload carried out by means of a LWR must be accompanied by a HOBM. If there is a discrepancy between the movements of these two units, the coupled system will be blocked.

The design of units can also be modified. The vertical axis of the HOBM is usually able to rotate over 360 degrees to provide the largest workspace (Fig. 5). However, in the coupled system with joint workspace, the HOBM uses only a small portion of its reachable space due to the workspace of the LWR, which are usually limited in its volume. Thus, the design of the HOBM can be modified to be adapted to the new conditions. The vertical axis of the HOBM can be brought closer to the LWR, and the static balance can be saved with a counterweight on the opposite side of the coupled system workspace (Fig. 6). Such an arrangement is more optimal in terms of the cooperative workspace. Practical implementation of such modifications may look as shown in Fig. 7.

It should also be noted that the cooperative workspace of the coupled system must be collision and singularity free. Let's illustrate with an example. In Fig. 8 is presented a coupled system in which the HOBM is in the singular configuration. In the case of the conventional usage of the HOBM, this configuration does not present any inconvenience, since the operator will not move the payload in the radial direction. He will remove the load from the singular position of the manipulator and then perform the necessary movements. However, in a coupled system, it is indispensable to take this into account when planning a trajectory of the LWR, since such a movement cannot be performed. Thus, it is necessary to avoid not only the singular configurations of the LWR but also of the HOBM.

Behavior of the coupled system in dynamic mode

Behavior of the coupled system in a static mode when the velocities of links the HOBM are limited does not present any special problems. In this mode, the inertial forces are significantly less than the gravitational. The payload is completely balanced by the HOBM and the LWR assumes low loads. However, in case of increasing of accelerations, the inertia forces also increase and, respectively, the efficiency of gravitational balancing decreases. Therefore, the HOBM with massive links creates additional loads on the LWR. Let's consider the loads of a HOBM on the lightweight manipulator. In the coupled system, the payload is moved by the LWR. Thus, knowing the vector of joint angles of the LWR, the vector of Cartesian velocities can be determined from:

where, is the Jacobian matrix of the LWR. The displacements and velocities of the payload are the input parameters for the HOBM. Hence, where, is the Jacobian matrix of the HOBM and is the vector of joint angles of the HOBM.

Thus, knowing the vector of joint angles, the inertial forces and moments of the HOBM can be determined and the loads due to these forces and moments in the joints will also be established. Now, the force-torque vector acting on the payload due to the HOBM can be expressed by the relationship: This force-torque vector will create supplementary torques in the joints of the lightweight manipulator. The dynamic equations describing the input torques of the lightweight manipulator with the HOBM action can be expressed as:

where, Let's consider an illustrative example through a coupled system including the HOBM having the structure similar to the manipulator given in Fig. 8, i.e. with two rotating links (1), ( 2) and a rigid telescopic axis (3) for vertical displacements of the payload and a six-degrees-of-freedom general-type LWR. The mass-inertia characteristics of units are given in tables 1 and 3, where for the i-th link the mass is denoted as , the length denoted as , the location of the center mass from the previous joint denoted as , the axial moment of inertia relative to the center of mass of the link denoted as , the transverse moment of inertia relative to the center of mass of the link denoted as , and . The Denavit-Hartenberg parameters of the LWR are given in table 2. For numerical simulations the following input motion has been applied: 0.07 0.092 [0, 0, 0.0126] 5.72×10 -5 5.95×10 -5 6.57×10 -5 The input torques of the LWR are given in Fig. 9: (a) without HOBM (b) taking into account inertial forces of the HOBM. One can see from Fig. 9, the inertia forces of the HOBM significantly increase the loads on the actuators of the LWR. This example clearly shows that the influence of the inertia of the HOBM can be significant during high-speed movements of the LWR. Thus, it is necessary to take into account when calculating loads on the actuators, not only the inertia of the payload but also the inertia of the HOBM.

2 1 11 2 1 1 (0 t ) 2 ( ) ( ) ( t ) 2 1 ( ) ( t ) 2 i i f f f f f t t t t t t t t                                    with 1 40 i     , 1 40 f   , 0.2s   , 2 f ts  ,     1 1 f i f t        , /     , θ 2 =-45°, θ 3 =90°, θ 4 =-225°, θ 5 =90°
Behavior of the coupled system in a dynamic mode is completely different for a HOBM with a cable lift assuming vertical movements of the payload (Fig. 8). In this case, the dynamic loads on the LWR occur in the form of oscillations of the HOBM at the end of the operating cycle when the LWR stops. These oscillations essentially depend on the friction in the joints of the HOBM. Such a dependence is shown in Figure 10. One of the ways of reduction of these unwanted oscillations is the increasing the friction on the joints of the HOBM.

Unfortunately, increasing the friction in the joints of the HOBM creates a drag force that the robot has to overcome for any movement. Then, two efforts are in competition: 1) the inertial effort due to the oscillations of the HOBM, and 2) the drag effort created by the friction. Reducing 1) means increasing 2). Thus, an optimal friction has to be found such that the drag effort is minimized and the oscillation reduction remains efficient. Such an optimization highly depends on the application for the coupled system. Indeed, the efforts will mainly depend on the friction, of course, but they will also depend on the accelerations and trajectories imposed by the lightweight robot and the payload.

One possible method to perform this optimization is to run a design of experiment (DOE). In our case, the measure studied is the maximal effort applied on the robot. The parameters of the DOE are 1) the friction in the joints of the HOBM, 2) the mass of the payload, 3) the acceleration. A response surface design is chosen (centralcomposite) in order to build a meta-model of our system. This meta-model is a quadratic model that gives us the influence of each parameter on the measured effort.

Then, this model can be used to tune the parameters. For instance, Fig. 11 shows how to tune the parameters to obtain a maximal effort on the robot not exceeding 120 N.

Conclusions

Manual handling of loads involves the use of the human body to lift and carry loads. Most manufacturing systems require some manual handling tasks. When performed incorrectly or excessively, these tasks may expose workers to fatigue and injury. A variety of techniques and tools exist for automatic handling of heavy loads. Lightweight robots and hand-operated balanced manipulators cooperation is an effective way. In this case, for handling of heavy payloads by a HOBM an operator is replaced by a LWR. Taking into account the great capabilities of manual lightweight robots, which allow human intervention to control and guide the payload, such a cooperation is efficient since it does not exclude the possibility of having a human in the workspace of a robot. The present study deals with the key features of the coupled HOBM and LWR. There are shown the design particularities of the cooperative workspace, the need to consider singular configurations of the HOBM, the method for determination of inertia effects of the HOBM on the LWR. It is revealed that in a dynamic mode the HOBM with massive links creates additional loads on the LWR, which can be significant. The given numerical simulations show the important increasing of the input torques due to the inertia forces of the HOBM. Behavior of the HOBM with cable lift and the LWR is also examined. It is disclosed that there are significant oscillations of the rotating links of the HOBM with cable lift after stopping the LWR. It is proposed to eliminate these unwanted oscillations by controlling friction in the joints of the HOBM.

Fig. 1 .Fig. 2 .

 12 Fig. 1. Conco-Balancer (USA).Fig. 2. Sapalem Manipulator (UK).

Fig. 3 .

 3 Fig. 3. LWR and HOBM cooperation for handling of heavy parts.

Fig. 4 .

 4 Fig. 4. Hitachi Progress Robot (Japon).

Fig. 5 . 6 .

 56 Fig. 5. Workspace of the HOBM. Fig. 6. Modified HOBM for cooperation with LWR.

Fig. 7 .

 7 Fig. 7. Frame of the usual HOBM (a) and its modified version (b) for balancerlightweight robot cooperation.

Fig. 8 .

 8 Fig. 8. Coupled system in which the HOBM is in the singular configuration.

Fig. 9 .

 9 Fig. 9. Input torques of the LWR: (a) without HOBM (b) taking into account inertial forces of the HOBM.

Fig. 10 .

 10 Fig. 10. Oscillations of the rotating links of the HOBM with cable lift after stopping the LWR.

Fig. 11 .

 11 Fig.11. Acceleration limit for F = 120 N.

Table 2 .

 2 and θ 6 =0°. Denavit-Hartenberg parameters of the LWR

	Table 1. Mass-inertia characteristics of
		the HOBM
	Link			Joint	(rad)	(m)	(m)	(rad)
		(kg) (m) (m) (kgm²)	1		0	0.1273	π/2
	1	30.97 1.4 0.57 9.28	2		-0.612	0	0
	2	23.56 1.5 0.74 5.21	3		-0.572	0	0
	3	2.13 0.6	0.3 0.06	4		0	0.163941	π/2
				5		0	0.1157	-π/2
				6		0	0.0922	0

Table 3 .

 3 Mass-inertia characteristics of the LWR

	Link	(kg)


Keywords: Haptic control, force control, transparency, co-manipulation, humanrobot interaction, feedback, operational space, joint space, reduced model, parallel robot

Haptic control of the parallel robot Orthoglide P. LEMOINE a , P. P ROBET a , M. GAUTIER a , D. CHABLAT a , Y. AOUSTIN a a. Laboratoire des Sciences du Numérique de Nantes, UMR CNRS 6004 + email [START_REF] Guegan | Dynamic modeling of the Orthoglide[END_REF] 1 rue de la Noë, BP 92101 F-44321 Nantes Cedex 3, France Ecole Centrale de Nantes, Université de Nantes, philippe.lemoine@ec-nantes.fr, Pierre-philippe.Robet@univ-nantes.fr, Maxime.Gautier@univ-nantes.fr, damien.chablat@cnrs.fr, and Yannick.Aoustin@univ-nantes.fr

Résumé :

Cet article traite de la conception d'une commande de rétroaction haptique du robot parallèle Orthoglide pour effectuer des tâches de co-manipulation. Nous rappelons les différents modèles géométrique, cinématique et dynamique de Orthoglide. A partir de la mesure de la force d'interaction entre l'opérateur humain et l'effecteur final du robot, une trajectoire de référence de la plate-forme est calculée dans l'espace Cartésien. Cette trajectoire de référence est projetée dans l'espace articulaire pour obtenir la trajectoire de référence des variables actives de l'articulation linéaire. Un modèle dynamique simplifié est proposé et justifié pour concevoir une loi de commande de couple calculée des articulations linéaires actionnées dans l'espace articulaire. L'étude théorique et les résultats expérimentaux sur Orthoglide montrent comment les robots industriels rigides classiques avec une bande passante en boucle fermée à vitesse et position élevées peuvent être adaptés à des tâches de co-manipulation très efficaces. Cet article offre des perspectives intéressantes pour de nombreuses applications fondées sur l'interaction robot/humain dans un environnement industriel.

Abstract :

This paper adresses the design of a haptic feedback control of the parallel robot Orthoglide to perform co-manipulation tasks. We recall the different geometric, kinematic and dynamic models of Orthoglide.

From the measurement of the interaction force between the human operator and the end effector of the robot a reference trajectory of the platform is computed in the Cartesian space. This reference trajectory is projected in the joint space to obtain the reference trajectory of the active linear joint variables. A simplified dynamic model is proposed and justified to design a computed torque control law of the active linear joints in the joint space. Theoretical study and experimental results on the Orthoglide show how classical rigid industrial robots with high velocity and position closed loop bandwidth can be adapted for very efficient co-manipulation tasks. This paper offers interesting perspectives to numerous applications based on the interaction robot/human in an industrial environment.

Mots clefs : Commande haptique, commande en effort, transparence, comanipulation, interaction homme-robot, asservissement,espace opérationnel, espace articulaire, modèle réduit, robot parallèle.

Nomenclature

-m : Meter.

-Kg : Kilogram.

-s : Second.

-N : Newton.

-Hz : Hertz.

-rad : Radian.

-dB : Decibel.

-0 R p : Reference frame.

m p (Kg) : Mass of the platform of Orthoglide.

g = 9.81 m.s -2 : Constant gravity.

-0 g = 0 0 g ⊤ : Vector of acceleration of gravity, referred to reference frame 0 R p .

-

q a (3 × 1) = ρ 1 ρ 2 ρ 3 ⊤ :
Vector of the actuated linear joint variables, associated to the linear actuators of Orthoglide.

q na (6 × 1) is the vector of the joint variables not actuated of Orthoglide.

-qa (3 × 1) = ρ1 ρ2 ρ3 ⊤ : Time derivative of q a . -qna (6 × 1) : Time derivative of q na . -qa (3 × 1) = ρ1 ρ2 ρ3 ⊤ : Time derivative of qa .
qna (6 × 1) : Time derivative of qna .

q(9 × 1) = q a q na ⊤ : Vector of the generalized coordinates of Orthoglide.

q(9 × 1) = qa qna ⊤ : Time derivative of q.

q(9 × 1) = qa qna ⊤ : Time derivative of q.

-0 P p (3×

Introduction

A lot of avances in robotic technologies have led to the emergence of new applications that involve physical interactions between human and robots. For these new applications, it is necessary to control the position and interaction forces between the robot effector and the human. Humans react to unforeseen changes in daily life and perform skillful manipulation tasks. Today's rigid industrial robots have good repeatability, which is in the order of a hundredth of a millimeter at the end effector, and high dynamics of the drive chain. Its bandwidth can then reach several tens of hertz [START_REF] Khalil | Modeling, identification and control of robots[END_REF]. These characteristics make it possible to obtain fast and precise movements of the robots. It is then possible to extend the applications of these robots to co-manipulation and teleoperation thanks to the haptic feedback. Several contributions to strengthen the interaction between the robot and the human can be thus identified. For example Lie et al [START_REF] Li | Human-guided robotic co-manipulation : Two illustrative scenarios[END_REF] formulated a human-guided co-manipulation problem to take advantages of both human knowledge and the robot's capacities in a stable manner. The force amplification case in co-manipulation with an industrial robot is addressed by Lamy et al [START_REF] Lamy | Overcoming human force amplification limitations in co-manipulation tasks with industrial robot[END_REF] with presented theoretical and experimental results. Peternel et al [START_REF] Peternel | Online human muscle force estimation for fatigue management in human-robot co-manipulation[END_REF] propose to manage muscle fatigue in human-robot co-manipulation. A machine learning technique is used to enable online predictions of muscle forces in different arm configurations and endpoint interaction forces. Then a fatigue management system can operate online. Despite the remarkable existing applications that we can observe, there are few industrial application interactions between human and robots. There are still open problems. How to design an efficient haptic feedback with an industrial multi-body robot ?

The purpose of this paper is to prove that it is possible to achieve a haptic feedback with a parallel robot called Orthoglide [START_REF] Chablat | Architecture optimization of a 3-dof translational parallel for machining applications, the orthoglide[END_REF]. This robot has three prismatic joints that allow high Cartesian accelerations of the effector as well as uniform precision in the work area. To perform a haptic feedback the measure of the motor currents is an attractive idea to avoid the use of a force sensor. However the drive chains of the industrial robots generally include mechanical reducers, mechanical coupling systems between several drive chains, or motion conversion mechanisms. All these mechanical systems introduce friction that can absorb up to 80% of the mechanical power [START_REF] Gorinevsky | Force control of robotics systems[END_REF]. These frictions depend on the temperature, the humidity of the environment, the mechanical constraints applied to the robot. Finally, these drive chains are often not very transparent. This means that an external force applied to the effector must be high to obtain a movement of the robot. These technological characteristics mean that a fine control of the robot's force on its environment or a co-manipulation control are not possible by simply measuring the motor currents.

The addition of a force sensor is necessary to take into account the interaction robot/environment or man/robot. Thus the effector of Orthoglide (a platform) is equipped with a force sensor. Two feedback controls are defined for Orthoglide. The first one, which controls the joint variables, is performed with a linearizing control law, the well-known "computed torque" method. The new input consists of the addition of a desired acceleration and a correction in position, velocity in order to asymptotically cancel the position error, whose behavior is governed by a linear differential equation. Disturbances such as an unknown stiffness of the environment are mainly rejected by the feedback control of the joint variables.

Unexpected collisions of the robot with the environment must also be managed by this feedback control of the joint variables. It must therefore be able to trigger an emergency stop. The second feedback control is dedicated to haptic feedback. It includes the effector, the sensor and the environment or user with whom it interacts. The bandwidth of this haptic feedback control is lower than that of the feedback velocity and position control of the joint rigid variables. The bandwidths of the joint control as well as the internal current loop of the drives are such that their actions can be considered equivalent to that of gain compared to the haptic feedback. For the haptic feedback control the input is the desired force, the output is the force measured by the force sensor. The difference between these two forces is calculated and a dissipative force is added. The net force is converted into a Cartesian acceleration by applying the equivalence, force / (mass acceleration) with a variable gain. This Cartesian acceleration is integrated to define a velocity and position references in the operating space. These Cartesian reference trajectories are projected into the joint space to obtain the acceleration, velocity and position references of the feedback control of the joint variables. Different applications can be considered for the haptic feedback as follows [START_REF] Devie | Impedance control using a cascaded loop force control[END_REF] :

-For a man/robot collaboration task, the transparency of the robot is required. The operator must not feel the inertial forces of the robot to be able to guide the effector freely.

-For a force control task, the difference between the desired force and the measured force is converted into a velocity reference in the operating space. The velocity/force conversion gain is a stiffness parameter whose choice is such that it ensures the stability of the hybrid feedback control. If the difference between the desired force and the measured force is converted into an acceleration reference, a dissipative virtual force must be added to the force applied by the environment or operator. This dissipative force ensures that the robot stops when the environment or the operator no longer exerts any action on the force sensor. This last method method is applied in our case. The perspective of this work is to perform a teleoperation task between Orthoglide and another parallel robot with three prismatic joints and a cardan link composed of the revolute joints.

The rest of the paper is outlined as follows. Section 2 is devoted to the presentation of Orthoglide, its geometric, kinematic, and dynamic models. The statement of the problem is developed in section 3 to explain our strategy. Our experimental results are presented in section 4. Section 5 offers our conclusion and perspectives.

The parallel robot Orthoglide

General presentation of Orthoglide

The parallel robot Orthoglide has three parallel P RP aR identical legs, see Figure 1 a). The P , R, and P a stand for Prismatic, Revolute and Parallelogram joint, respectively. Each leg has one active prismatic joint and six passive revolute joints, see [START_REF] Chablat | Architecture optimization of a 3-dof translational parallel for machining applications, the orthoglide[END_REF] and [START_REF] Molina | Application of predictive control techniques within parallel robot[END_REF]. The interesting features of the Orthoglide are a regular Cartesian workspace shape, which is shown Figure 1c and uniform performances in all directions, and good compactness. Robot Orthoglide was designed for high-speed machining. The machine reaches a tool velocity of 1.2 m/s and an acceleration of 20 m/s 2 at the isotropic configuration. The bandwidth of the actuator chain, taking into account its electromagnetic constant, is 243 Hz. To avoid any mechanical vibration we limit it to 15 Hz. However, this value is still important in relation to the dynamics of the human gesture during a co-manipulation task. For human gesticulatory, it is difficult for the hand to oscillate at greater than 4.5 Hz, see [START_REF] Xiong | Hand motion gesture frequency properties and multimodal discourse analysis[END_REF]. Furthermore now with this limitation Orthoglide satisfies the ISO standard 10218 and in particular the following constraint : the effector velocity should not exceed 0.25 m/s, see [START_REF] Devie | Commande hybride force-position d'un robot avec ou sans capteur d'effort externe[END_REF]. The motors transform a revolute motion in a translation motion through a ball screw. Each actuator is equipped of an encoder sensor that the resolution at the shaft output of the ball screw is equal to 2.5 10 -6 m per encoder point. The results of the identification of joint drive gains and dynamic parameters of Orthoglide can be found in [START_REF] Briot | Global identificiation of joint drive gains and dynamic parameters of parallel robots[END_REF]. a)

B 1 i 1 P x z y j 1 A 1 C 1 A 2 B 2 C 2 A 3 C 3 B 3 b) x z y L Workspace Q 2 Q 1 c)
F 1: a) Orthoglide's photography, b) Geometric design of Orthoglide, c) Workspace limits of Orthoglide.

Geometric modeling

Let us introduce the following constraint equations linking the actuator positions q a with the Cartesian positions 0 P p of the platform :

(x p -ρ 1 ) 2 + y 2 p + z 2 p = L 2 x 2 p + (y p -ρ 2 ) 2 + z 2 p = L 2 x 2 p + y 2 p + (z p -ρ 3 ) 2 = L 2 (1)
with L is the link lengths such that L = C i B i ; the linear joint variables are equal to ρ i = A i B i (i = 1, 2, 3), see Figure 1 b). The inverse geometric model (IGM ) defines the actuator positions q a = ρ 1 ρ 2 ρ 3 ⊤ as function of the Cartesian positions 0 P p . With reference to Figure 1 b) IGM is as follows :

ρ 1 = x p + 1 -y 2 p -z 2 p ρ 2 = y p + 1 -x 2 p -z 2 p ρ 3 = z p + 1 -x 2 p -y 2 p (2)

Inverse kinematic model of Orthoglide

The following kinematic models (IKM ) are introduced in [START_REF] Guegan | Dynamic modeling of the Orthoglide[END_REF].

1. The inverse kinematic model defining the velocity vector qa = ρ1 ρ2 ρ3

⊤ can be written as :

qa = 0 J -1 p 0 V p (3)
Here 0 J -1 p is the inverse Jacobian matrix of Orthoglide. Its expression is as follows :

0 J -1 p =      1 - xp ρ 1 -xp - xp ρ 1 -xp - yp ρ 2 -yp 1 - yp ρ 2 -yp - zp ρ 3 -zp - zp ρ 3 -zp 1      (4)
This matrix is always regular in the working space. Jp qa

3. The second order inverse kinematic model of Orthoglide can be deduced from the time derivative of (3) as follows : qa = 0 J-1

p 0 V p + 0 J -1 p 0 Vp (6)

Dynamic model of Orthoglide

The Cartesian platform acceleration 0 Vp can be calculated with the direct dynamic model (DDM ) as follows, [START_REF] Guegan | Dynamic modeling of the Orthoglide[END_REF], [START_REF] Guegan | Identification of the dynamic parameters of the orthoglide[END_REF], and [START_REF] Molina | Application of predictive control techniques within parallel robot[END_REF] :

0 Vp = A(q) -1 robot [ 0 J -⊤ p Γ -h(q, q) robot ] (7)
Here

-A(q) -1 robot = 3 i=1
[A(q) -1 ix ] + I 3 m p is the inertia matrix (3 × 3) of Orthoglide with ist movable platform. -A(q) robot is the inertia matrix (3 × 3) of Orthoglide with its movable platform. A(q) robot is a positive definite matrix and therefore always invertible. -h(q, q) robot is the vector of Coriolis, gravitation and centrifuge effects (3 × 3) of Orthoglide with its movable platform.

-Γ = [Γ 1 Γ 2 Γ 3 ] ⊤ is the force vector of the actuators at the output of the ball screws of the actuators. Taken into account that there is no rotation of the platform its dynamic equation can be written as follows :

0 F p = 0 Vp m p -0 gm p , (8)
where 0 F p is the vector, which represents the net external force applied on the platform. Substituting ( 5) into ( 7) yields :

0 J ⊤ p A(q) robot ( 0 J p qa + 0 Jp qa ) + 0 J ⊤ p h(q, q) robot = Γ (9)
Equation ( 9) represents the inverse dynamique model in the joint space.

3 Problem statement

In the Cartesian space

The objective is to generate a trajectory of the platform Orthoglide in reaction to a force applied by the human operator, in order to perform the most accurate co-manipulation task possible. The robot must therefore not resist the movement that results from interaction with human. This interaction must therefore be transparent to the operator. A force sensor, ATI Delta SI-165-15 from Schunk company, is attached to the platform of Orthoglide. This force sensor allows us to measure the three components along x-axis, y-axis, and z-axis of the force, which is applied by the operator. These three force components are measured with a sampling frequency f s = 1 ∆ , which is equal to 6 kHz. The measured data are filtered by using a Butterworth filter with a cut-off frequency equal to 25 Hz. To define the desired Cartesian acceleration of the platform let us introduce two virtual terms.

First for safety it is important that the platform stops when no effort is applied to it by the operator. It is also important that when interacting between the robot and the operator, the latter, when applying a force to the platform, feels an inertial effect of the robot in order to better modulate the acceleration of the platform. This makes it easier for the operator to achieve the desired platform positioning at any time during the co-manipulation task. Therefore we introduce the following virtual force along each axis such as :

F l virtual =      µ sign( lp ) if lp = 0 µ sign(F l ) if |F l | µ and lp = 0 F l if |F l | < µ and lp = 0 (10)
with l ∈ x, y, z and µ = 0.8 N, and where F l is the force measured by the force sensor along the l-axis.

Secondly let us also introduce a virtual mass m virtual as parameter to deduce an acceleration from an effort. By using these previous parameters we calculate the desired Cartesian acceleration of the platform as follows :

ẍp = F x -F x virtual m virtual , ÿp = F y -F y virtual m virtual , zp = F z -F z virtual m virtual . (11)
The Cartesian acceleration is considered constant during the sampling period ∆. So the Cartesian motion is uniformly along each direction x, y, and z during the sampling period ∆. Therefore the desired Cartesian velocity and position vectors are expressed as follows where at each sampling time t k = k∆, k = 0, • • • , n the new the components of the Cartesian velocity vector 0 V p and of the Cartesian position vector 0 P p will be as follows :

ẋp (t k ) = ẍp (t k )∆ + ẋp (t k-1 ) ẏp (t k ) = ÿp (t k )∆ + ẏp (t k-1 ) żp (t k ) = zp (t k )∆ + żp (t k-1 ) (12)
and

x p (t k ) = ẍp (t k ) ∆ 2 2 + ẋp (t k-1 )∆ + x p (t k-1 ) y p (t k ) = ÿp (t k ) ∆ 2 2 + ẏp (t k-1 )∆ + y p (t k-1 ) z p (t k ) = zp (t k ) ∆ 2 2 + żp (t k-1 )∆ + z p (t k-1 ) (13)
with 0 V p (t -1 ) = 0, 0 P p (t -1 ) = 0, and the following initial conditions 0 V p (t 0 ) = V 0 and 0 P p (t 0 ) = P 0 . The variables ẍp , ÿp , and zp are those calculated with (11).

In the joint space

From the constraint equations (1), by using the IGM (2) and the Cartesian coordinates [START_REF] Guegan | Identification of the dynamic parameters of the orthoglide[END_REF] we can define the desired reference trajectory vector q d a for the three active linear joint variables. Similarly from the velocity of the Cartesian coordinates [START_REF] Guegan | Dynamic modeling of the Orthoglide[END_REF], by using the IKM (3) and the inverse Jacobian matrix (4) we can define the desired joint velocity vector qd a . Finally from the acceleration of the Cartesian coordinates [START_REF] Briot | Global identificiation of joint drive gains and dynamic parameters of parallel robots[END_REF], by using the second order IKM (6) we can define the desired joint acceleration qd a .

Control law the joint space

We have to design a control law in the joint space. Our strategy is to define a PID control law by using a simplified model of the dynamic behavior of Orthoglide. To simplify the dynamic model we make two assumptions. First the most part of the inertia seen by each rotary motor is due to the inertia moment of te drive chain. From this physical observation about the mechanical design of Orthoglide we consider for the simplified model an inertia matrix, which is a constant diagonal matrix. Secondly the two combined characteristics a high sampling frequency and great accuracy of each encoder sensor allow to obtain the joint active variables q a and qa without any filter. It is then possible to design a feedback with high gain values. These high gain values allow to compensate the Coriolis, centrifugal, gravity, and friction effects, which are represented by the vector h(q, q). Therefore the simplified model is a decoupled two integrator model as follows :

   d 11 0 0 0 d 22 0 0 0 d 33    qa = Γ, (14)
where the desired behavior of the robot is such that qa = w(t) with :

w(t) = qd a + K p (q d a -q a ) + K i t 0 (q d a -q a )dτ + K d ( qd a -qa ). (15)
Here the gain matrices K p , K i , and K d are (3 × 3) diagonal matrices. The numerical values of the diagonal elements of the matrix 0 J ⊤ p A(q) 0 J p are very close, due to the identical design of the three legs of Orthoglide. Therefore d ii , i = 1, 2, and 3 are set equal to the maximum modulus d max of the diagonal elements of 0 J ⊤ p A(q) 0 J p . Therefore we can design for each active joint the same PID controller with the following scalar coefficients k p , k i , and k d . From qa = w(t) the introduction of the Laplace operator s yields for each joint :

(Q(s) -Q d (s))(s 3 + k d s 2 + k p s + k i ) = 0 (16)
Equation ( 16) can be written as follows :

(Q(s) -Q d (s))[(s + ω n )(s 2 + 2ζω n s + ω 2 n )] = 0, (17)
with k d = (2ζ + 1)ω n , k p = (2ζ + 1)ω 2 n , and k i = ω 3 n . By tuning ζ = 1 the controller gains are such that a transfer function is obtained with a real pole of multiplicity three, which is located in the complex left half plane. This means that (17) becomes :

(Q(s) -Q d (s))(s + ω n ) 3 = 0. ( 18
)
To obtain a feedback control in the joint space with a cut-off frequency (-3 dB) equals to 15 Hz, we take ω n = 188 rad/s to compute the gains k p , k i , and k d . This pulsation ω n is twice the pulsation corresponding to 15 Hz (94 rad/s).

To summarize following the method of the computed torque the force vector Γ is computed through [START_REF] Devie | A cascade loop structure in force and position to control a bilateral teleoperation robotic system[END_REF] substituting qa with w(t).

Experimental results

A co-manipulation task over a period of 30 seconds is presented here. The operator moves the platform freely in the workspace, then at time t = 16.5 s puts an additional 4.11 kg mass on the platform to test the robustness of the haptic control. Figure 2 presents the evolutions as function of time of the three actuator forces during the co-manipulation. The effect of the additional mass is observable through the vertical dashed line defining t = 16.5 s. The jump of Γ 3 acting following the vertical z-axis is almost equal to 40 N, that is coherent with the value 4.11 kg. There is also an effect on the force Γ 1 and Γ 2 acting along the x-axis and y-axis respectively. The measured forces by the force sensor are shown Figure 3.

To avoid chattering effects on the measures around the value 0 N of the force sensor a thresholding of 0.5 N is taken into account. These profiles show that during the co-manipulation the experimenter has not to apply more efforts to move freely the platform, despite the addition of a 4.11 kg mass. A similar observation can be made from the coordinates of the Cartesian position of the platform, 4.11 kg mass does not affect the platform position, Figure 4. Let us remark that during the motion of the platform the magnitude of the tracking errors of the active linear joint variable does not exceed 10 -5 m. The strategy of focusing on the use of the reduced model ( 14) and the second-order system stabilization with PID feedback (15) rather than explicitly compensating for gravity is effective and has the advantage of being robust. Indeed, explicitly compensating for the effect of an additional mass requires knowing it a priori. These results prove that entire actuation chain, force and position sensors, acquisition cards and a well-defined control of active variables provide haptic control to perform a co-manipulation task that is comfortable for the human and accurate. To illustrate the quality of the co-manipulation task a video was made during this experiment and it is in free access through this link : //uncloud.univ-nantes.fr/index.php/s/BjrYmceM3FnDzXc

Conclusion

In this paper we prove that it is possible to design a haptic feedback for a complex robot with closed structures, the parallel robot Orthoglide. Rigorous physics arguments make it possible to define a reduced linear model in order to take into account the dynamics of the robot Orthoglide in the control laws of the joint variables. Experimental results prove that thanks to high gain values of a feedback control based on a reduced model the reference trajectories of the active joints are perfectly tracked. Moreover, experimental tests show that the addition of a significant mass on the effector does not disturb the robot's behavior during a co-manipulation task. Similarly, an unexpected elastic or rigid contact of the effector with an obstacle does not cause unstable behavior of the robot. These experimental results prove that robust co-manipulation tasks can be performed with industrial robots without the need for costly specific adaptations. First our perspective is to extend our work to a six-axis serial robot. The displacement of the effector will be the result of a composition of rotational and translational movements. Secondly we want to investigate the teleoperation tasks, see [START_REF] Devie | A cascade loop structure in force and position to control a bilateral teleoperation robotic system[END_REF]. Indeed Orthoglide has a little brother, the parallel robot Orthoglide five-axis, which is an evolution of the present Orthoglide, with two additional degrees of freedom on its effector, see [START_REF] Jha | Influence of the trajectory planning on the accuracy of the orthoglide 5-axis[END_REF].

:

  1) = x p y p z p ⊤ : Vector of the Cartesian position of the platform of Orthoglide with respect to 0 R p . -0 V p (3×1) = ẋp ẏp żp ⊤ : Vector of the Cartesian velocity of the platform of Orthoglide with respect to 0 R p . Vector of the Cartesian acceleration of the platform of Orthoglide with respect to 0 R p .

2 .

 2 The second order direct kinematic model of Orthoglide gives the Cartesian platform acceleration 0 Vp as function of the joint acceleration vector qa = ρ1 ρ2 ρ3 ⊤ of the active joint variables and the velocity vector qa as follows : 0 Vp = 0 J p qa + 0

F 2 :

 2 Profiles as function of time of the actuator forces during the experiment of co-manipulation of Orthoglide.

F 3 :F 4 :

 34 Profiles as function of time of the measured forces applied on the platform of Orthoglide. Profiles as function of time of the Cartesian position 0 P p of the platform of Orthoglide.