P Bustamante

C F Morales

B Mikkelsen

M Dam

F Caurant

Trace element bioaccumulation in grey seals Halichoerus grypus from the Faroe Islands

Keywords: Heavy metals, Distribution, Detoxification, Marine mammals, Pinnipeds, Sub-arctic

68 grey seals (Halichoerus grypus) were sampled in the Faroe Islands archipelago during the summer period in 1993 to 1995. Concentrations of Cd, Cu, Hg, Se and Zn were measured in liver, kidney and muscle. All elements except Zn exhibited lowest concentrations in muscle. Liver displayed the highest concentrations of Cu, Hg, Se and Zn while kidney exhibited the highest Cd concentrations. However, trace element concentrations within tissues were influenced by sex and age. Thus, females showed clearly higher Cd concentrations than males. Age was the most important factor influencing the concentration of Cd, Hg and Se in liver, and of Cd and Hg in kidney. A strong positive correlation between Cd, Hg and Zn in kidney suggests the occurrence of a detoxification process involving metallothionein proteins. Similarly, strong positive correlation between Hg and Se and molecular Hg:Se ratio close to 1 in liver suggest the occurrence of the demethylation process leading to the formation of mercuric selenide granules. High Hg concentrations might be related to fish consumption by grey seals. However, such a piscivorous diet cannot be

INTRODUCTION

Situated in the Northeast Atlantic Ocean, the Faroe Islands are a relatively long distance from major sources of anthropogenic pollution. Nevertheless, marine top predators from this area, such as long finned pilot whales Globicephala melas or white-sided dolphins Lagenorhyncus acutus, exhibited very high cadmium (Cd) and mercury (Hg) concentrations in their tissues [START_REF] Julshamn | Trace element intake in the Faroe Islands. I. Element levels in edible parts of pilot whales (Globicephala meleanus)[END_REF][START_REF] Caurant | Ecological and biological factors controlling the concentrations of trace elements (As, Cd, Cu, Hg, Se, Zn) in delphinids Globicephala melas from the North Atlantic Ocean[END_REF][START_REF] Dam | Analyses of mercury and organochlorines in individual marine mammals from the Faroe Islands[END_REF], [START_REF] Gallien | Cadmium-containing granules in kidney tissue of the Atlantic white-sided dolphin (Lagenorhyncus acutus) off the Faroe Islands[END_REF]). These concentrations were much higher than those reported for individuals from temperate areas which are subject to significant pollution from human activities [START_REF] Mackey | Trace element concentrations in cetacean liver tissues archived in the National Marine Mammal Tissue Bank[END_REF][START_REF] Law | Metals and organochlorines in pelagic cetaceans stranded on the coasts of England and Wales[END_REF]. In fact, toxic metals in top marine predators from the Faroe Islands often reach the threshold level at which metabolic disorders appear in humans [START_REF] Nogawa | Cadmium[END_REF]. However, such effects are difficult to detect in wild animals such as marine mammals. Recently, [START_REF] Gallien | Cadmium-containing granules in kidney tissue of the Atlantic white-sided dolphin (Lagenorhyncus acutus) off the Faroe Islands[END_REF] investigated cellular alterations in relation to Cd concentrations in the kidney of white-sided dolphins from the Faroe Islands. This study reported the occurrence of calcium phosphate granules in this organ which could result from an effective detoxification process of Cd but could also lead to some alteration of the functioning of the kidney. Cd could also be detoxified by proteins regulating essential elements (e.g. copper, Cu, or zinc, Zn) such as ferritin or metallothionein [START_REF] Das | Metallothioneins in marine mammals[END_REF]. Considering Hg, other processes are involved in its co-precipitation with selenium (Se) to produce non-toxic mineral granules of tiemannite [START_REF] Martoja | Identification of tiemannite as a probable product of demethylation of mercury by selenium in cetaceans[END_REF][START_REF] Nigro | Intracellular storage of mercury and selenium in different marine vertebrates[END_REF].

Top marine predators are mainly exposed to trace elements through the food [START_REF] Aguilar | Biological factors affecting variability of persistent pollutant levels in cetaceans. In: Reijnders PJH[END_REF]. Thus, the consequence of a specialised diet for a marine mammal is an exposure either to very low or very large amounts of poorly or highly concentrated toxic element in the prey.

For example, very high Cd concentrations in the kidney of pilot whales from the Faroe Islands have been related to their teutophageous diet [START_REF] Caurant | Cadmium contamination in pilot whales Globicephala melas: source and potential hazard to the species[END_REF], Bustamante et al. 1998a). However, the lactating pilot whales displayed higher Hg concentrations which have been explained by an increase of the fish proportion in their diet during the nursing period because fish are more energetic than cephalopods [START_REF] Caurant | Ecological and biological factors controlling the concentrations of trace elements (As, Cd, Cu, Hg, Se, Zn) in delphinids Globicephala melas from the North Atlantic Ocean[END_REF]. Following these conclusions, piscivorous marine mammals such as seals would be expected to have high Hg and low Cd concentrations in their tissues.

In this study, the concentration and distribution of five trace elements, Cd, Cu, Hg, Se and Zn, have been determined in a reported piscivorous marine mammal species [START_REF] Mikkelsen | Summer diet of grey seals (Halichoerus grypus) in Faroese waters[END_REF] from the Faroe Islands, the grey seal Halichoerus grypus. Therefore, the primary objectives of this work were to investigate the influence of biological (sex, maturity stage and age), ecological (diet) and geographical factors on the bioaccumulation of these trace elements. Particular attention was granted to interactions between toxic Cd and Hg with essential Cu, Se and Zn. Furthermore, trace element concentrations were compared to other seal species and to grey seals from other areas. Cd and Hg concentrations were also considered from an ecological point of view.

MATERIALS AND METHODS

Sampling

During the summer of 1993 to 1995, 68 grey seals were caught at the Faroe Islands (Fig. 1), in an co-operation between the Museum of Natural History of the Faroe Islands and the Norwegian Institute of Fisheries and Aquaculture, with the aim to study the diet of this poorly investigated population [START_REF] Mikkelsen | Summer diet of grey seals (Halichoerus grypus) in Faroese waters[END_REF]. These sampled animals have given the unique opportunity to collect organs and tissues for metallic and organic contaminant investigations [START_REF] Dam | Analyses of mercury and organochlorines in individual marine mammals from the Faroe Islands[END_REF]. Samples for trace element analysis, i.e. liver, kidney and muscle, have been stored at -20°C in individual plastic bags until use. Furthermore, teeth were used for age determination. Biological parameters of the seals (length, weight, blubber thickness, and age) for each sex and maturity stage are given in Table 1.

Analytical procedure

All the material used for the treatment of the samples was cleaned, then decontaminated during 24 hours in a solution composed by 35 ml of HNO 3 65% and 50 ml of HCl 36% for 1 L Milli-Ro quality water.

Fresh samples were freeze dried and then grounded to powder. The mean of the ratio between wet weight and dry weight was about 3.4 for liver and muscle, and 4.1 for kidney. Two aliquots of approx. 200 mg of each homogenised dry sample were digested with 3.5 ml of 65% HNO 3 at 60°C for 3 d. The digested contents were then diluted to 10 ml in Milli-Q quality water. Cd, Cu, Se and Zn were assayed using flame and graphite furnace atomic absorption spectrophotometer Varian 250 Plus with deuterium background correction.

For Hg measurements, aliquots ranging from 0.5 to 10 mg of dried material were analysed directly for total Hg in an Advanced Mercury Analyser spectrophotometer, Altec AMA 254.

Hg determination involved evaporation of Hg by progressive heating until 800°C under oxygen atmosphere for 3 min and subsequent amalgamation on a Au-net. Afterwards, the net was heated to liberate the collected mercury and was subsequently measured by UV atomic absorption spectrophotometry.

The analytical accuracy was assessed using dogfish liver DOLT-2 (NRCC) and dogfish muscle DORM-2 (NRCC) as reference materials. Analyses were also validated through international intercalibration exercises (e.g. [START_REF] Coquery | The analytical performance study for the Medpol region : determination of trace elements and methylmercury in estuarine sediment sample IAEA-405[END_REF]). The standards were treated and analysed under the same conditions as the seal samples. Results were in good agreement with the certified values and recoveries of the metals ranged from 93 to 105%. Detection limits (µg.g -1 dry wt) were 0.004 for Cd, 0.5 for Cu, 3 for Zn, 0.8 for Se, and 0.005 for total Hg. All trace element concentrations in seal tissues are reported in µg.g -1 wet wt (wwt).

Statistical analysis

Comparison of metal concentrations between species were tested by one-way ANOVA (after log transformation of data when necessary) followed by the Tukey multiple comparison test in the MINITAB 13.1 Software. Hypothesis of normal distribution was tested using the Anderson-Darling test and equality of variance by the Bartlett test. The significance level for statistical analyses was always set at α = 0.05.

RESULTS

Levels of trace elements and organotropism

Cd, Cu, Hg, Se and Zn concentrations in liver, kidney and muscle for each sex and maturity stage are presented in Table 2. Cd and Hg concentrations varied greatly among tissues.

Kidney exhibited the highest Cd concentrations (15.8 ± 24.6 µg.g -1 wwt) followed by liver (5.06 ± 8.63 µg.g -1 wwt) while muscle showed Cd concentrations several order of magnitude lower (0.05 ± 0.14 µg.g -1 wwt) (Table 2). As expected for a toxic element, the coefficients of variation for Cd were particularly elevated in all the tissues, i.e. 155% for kidney, 170% for liver and 280% for muscle. Among the three tissues analysed, liver exhibited the highest Hg concentrations (59.7 ± 70.4 µg.g -1 wwt) followed by kidney (2.93 ± 2.47 µg.g -1 wwt) and muscle (0.74 ± 0.65 µg.g -1 wwt) (Table 2). The coefficients of variation for Hg were relatively elevated, particularly for liver (118%) but also for kidney and muscle (84 and 88%, respectively). Liver also exhibited the highest Se concentrations (23.0 ± 26.2 µg.g -1 wwt) followed by kidney (5.47 ± 1.43 µg.g -1 wwt) and muscle (0.27 ± 0.10 µg.g -1 wwt). For Se, the coefficients of variation were lower than 40% in kidney and muscle but higher than 100% in liver.

Liver exhibited the highest Cu concentrations (38.7 ± 18.1 µg.g -1 wwt) while concentrations were relatively low in kidney and muscle (3.1 ± 0.5 µg.g -1 wwt and 1.5 ± 0.3 µg.g -1 wwt, respectively). As expected for an essential element, coefficients of variation were low for Cu, i.e. 15%, 25% and 47% in kidney, muscle and liver, respectively. Liver also showed the highest Zn concentrations (57 ± 10 µg.g -1 wwt) followed by muscle (41 ± 9 µg.g -1 wwt) and kidney (27 ± 7 µg.g -1 wwt). For Zn, the coefficients of variation were lower than 30% in the three tissues analysed.

Influence of gender

In the grey seals from the Faroe Islands, Cd was the only element exhibiting a significant difference between sexes. Thus, Cd concentrations in kidney were significantly higher (p < 0.001) in adult females than in adult males (i.e. 40.8 ± 28.8 and 10.5 ± 4.69 µg.g -1 wwt, respectively) resulting from Cd accumulation rates 5 times higher in females (Fig. 2). In liver, males exhibited significantly lower Cd concentrations (p < 0.001) with 1.76 ± 0.27 µg Cd.g -1 wwt while females exhibited mean concentrations of 13.2 ± 11.0 µg.g -1 wwt, resulting from Cd accumulation rates 10 times higher (Fig. 2).

No other significant differences between sexes were found for the other metals in grey seals tissues.

Influence of maturity stage and age

Cd concentrations in the three tissues of mature individuals are higher than those of immature animals (F = 47.40 p < 0.001), (Table 2). Moreover, Cd was significantly correlated with age in kidney and liver (Fig. 2). In the former organ, the correlation is linear for both male and female (r = 0.947 p < 0.001 and r = 0.818 p < 0.001, respectively). However, the correlation between hepatic Cd and age fitted a logarithmic adjustment for males (r = 0.747 p < 0.001) but a linear one for females (r = 0.672 p < 0.001) (Fig. 2).

Higher Hg concentrations in the three tissues of mature individuals are encountered compared to immature (F = 23.91 p < 0.001). Hepatic and renal Hg concentrations increased linearly with age (r = 0.882 p < 0.001 and r = 0.733 p < 0.001, respectively) (Fig. 3).

Hepatic Se concentrations differed significantly (F = 82.48 p < 0.001) between immature (5.69 ± 6.51 µg.g -1 wwt) and mature individuals of both sexes (49.2 ± 22.9 µg.g -1 wwt). Se concentrations were correlated with age only in liver (r = 0.857 p < 0.001). Furthermore, hepatic Cu concentrations were significantly lower (F = 6.86 p < 0.002) in immature (32.3 ± 15.9 µg.g -1 wwt) than in mature seals (48.6 ± 16.9 µg.g -1 wwt) and renal Cu concentrations in both sexes were significantly higher (F = 6.02 p < 0.004) in immature seals (3.2 ± 0.4 µg.g -1 wwt) than in the mature ones (2.9 ± 0.5 µg.g -1 wwt). However, Cu concentrations in the tissues of grey seals were not correlated with age.

In both sexes, mature seals showed significantly higher Zn concentrations in kidney (F = 55.36 p < 0.001) than did the immature individuals (34.2 ± 6.6 µg.g -1 wwt and 22.8 ± 2.5 µg.g -1 wwt, respectively). Therefore, renal Zn increased linearly with age (r = 0.796 p < 0.001). However, Zn concentrations in liver and muscle have not been found to be correlated with age.

Metallic correlation

Table 3 shows the correlation between trace elements within the three tissues. In kidney, Zn was correlated with Cd (r = 0.907 p < 0.001) and Hg (r = 0.698 p < 0.001) (Fig. 4). Renal Hg concentrations were also strongly correlated to Se (r = 0.688 p < 0.001) and to Cd (r = 0.773 p < 0.001) (Fig. 4).

In liver, Cd concentrations were correlated to Se, Hg and Zn (p < 0.001, Table 3). Hg and Se concentrations exhibited a linear relationship for both sexes (r = 0.989 p < 0.001) (Fig. 5).

Thus, the calculated molar ratio between Hg and Se was also found to be correlated with age (r = 0.642 p < 0.001) and tended to a Hg:Se ratio close to 1 (Fig. 5).

In muscle, only a negative correlation was found between Cu and Hg (Table 3).

DISCUSSION

In contrast to traditionally hunted pinniped species, i.e. harp and hooded seals, which have been extensively studied for trace elements and organic compounds bioaccumulation (see the review of [START_REF] Muir | Arctic marine ecosystem contamination[END_REF], grey seal has only been investigated in few cases and often with few individuals (Morris et al. 1989[START_REF] Frank | Metal concentrations in seals from Swedish Waters[END_REF][START_REF] Law | Trace metals in the livers of marine mammals from the Welsh coast and the Irish Sea[END_REF][START_REF] Bustamante | Etude des processus de bioaccumulation et de détoxication d'éléments traces (métaux lourds et terres rares) chez les mollusques céphalopodes et bivalves pectinidés. Implication de leur biodisponibilité pour le transfert vers les prédateurs[END_REF][START_REF] Teigen | Heavy metal content in liver and kidneys of grey seals (Halichoerus grypus) in various life stages correlated with metallothionein levels: some metal-biding characteristics of this protein[END_REF][START_REF] Dam | Analyses of mercury and organochlorines in individual marine mammals from the Faroe Islands[END_REF][START_REF] Nyman | Current levels of DDT, PCB and trace elements in the Baltic ringed seals (Phoca hispida baltica) and grey seals (Halichoerus grypus)[END_REF], probably because most of the grey seal populations are either protected in their living areas or not traditionally hunted. Generally, only stranded animals, by-caught during fisheries or killed in small numbers with special authorisations are used for ecotoxicological analyses. Thus, the sampling realised in the Faroe Islands to study the grey seal diet in this archipelago provided a great opportunity to investigate the bioaccumulation of trace elements in a supposed healthy marine mammal population.

As in other pinniped species (e.g. [START_REF] Wagemann | Trace metals and methylmercury : associations and transfert in harp seal (Phoca groenlandica) mothers and pups[END_REF][START_REF] Dietz | Lead, cadmium, mercury and selenium in Greenland marine mammals[END_REF][START_REF] De Moreno | Heavy metals in Antarctic organisms[END_REF][START_REF] Julshamn | Trace element levels in harp seal (Pagophilus groenlandicus) and hooded seal (Cystophora cristata) from the Greenland Sea. A multivariate approach[END_REF][START_REF] Fant | Mercury, cadmium, lead and selenium in ringed seals (Phoca hispida) from the Baltic Sea and from Svalbard[END_REF], each trace element analysed was mainly concentrated in a specific tissue. Thus, the highest concentrations of Cu, Hg, Se and Zn were found in the liver whereas kidney contained the highest Cd concentrations (Table 2).

However, within a given population, several factors like sex, reproductive status, age and diet greatly influence the concentration of trace elements within tissues.

In marine mammals, trace elements are mainly incorporated in the body via food, thus diet can be considered as the main factor that determines the load of a species [START_REF] Aguilar | Biological factors affecting variability of persistent pollutant levels in cetaceans. In: Reijnders PJH[END_REF]. Therefore, intake via food is supposed to represent the bulk of trace element intake.

Diet has been investigated on the same individuals of this study, and showed that grey seals from the Faroe Islands feed exclusively on fish during the summer period; males and females displaying a similar diet according to their stomach contents [START_REF] Mikkelsen | Summer diet of grey seals (Halichoerus grypus) in Faroese waters[END_REF].

However, very elevated Cd concentrations in their tissues is not in accordance with a piscivorous diet. Indeed, very low Cd exposure would result from fish consumption as most fish species generally display relatively low Cd concentrations when considering the whole animal (Bustamante et al. 2003). In the light of the present results, it seems likely that the diet of grey seals in Faroese waters changes during the year, and thus include a significant proportion of cephalopods, strongly increasing their exposure to Cd (Bustamante et al. 1998a). In fact, the diet of grey seals from the northern temperate waters appears to be very dependent of the season [START_REF] Hammond | The diet of grey seals in the Inner and Outer Hebrides[END_REF][START_REF] Pierce | Diet selection by seals[END_REF][START_REF] Vallee | Introduction to metallothionein[END_REF]. Reported results were closely similar to those of [START_REF] Mikkelsen | Summer diet of grey seals (Halichoerus grypus) in Faroese waters[END_REF] for the summer period, but in autumn, winter and spring, grey seals increased the proportion of cephalopod in their diet. Such a shift in diet might occur for the Faroe grey seals, and would explain the high Cd concentrations found in kidney and liver.

Even if investigations on the grey seals diet in the Faroe Islands showed that there is no sexrelated difference in their diet [START_REF] Mikkelsen | Summer diet of grey seals (Halichoerus grypus) in Faroese waters[END_REF], Cd concentrations determined in liver and kidney revealed a significant gender-related difference. Thus, females exhibited significantly higher renal and hepatic concentrations than males (Table 2, Fig. 1). [START_REF] Nyman | Current levels of DDT, PCB and trace elements in the Baltic ringed seals (Phoca hispida baltica) and grey seals (Halichoerus grypus)[END_REF] also reported higher Cd concentrations in the liver and kidney of female grey seals from Baltic Sea and from Sable Island. Similar gender difference observed in the Antarctic fur seal (Arctocephallus gazella) and the Baïkal seal (Phoca sibirica) was partly explained by different feeding habits between males and females (de [START_REF] De Moreno | Heavy metals in Antarctic organisms[END_REF][START_REF] Watanabe | Agedependent accumulation of heavy metals in Baikal seal (Phoca sibirica) from the Lake Baikal[END_REF]. Such a difference in metal concentrations is sometimes attributed to the sexual dimorphism [START_REF] Caurant | Ecological and biological factors controlling the concentrations of trace elements (As, Cd, Cu, Hg, Se, Zn) in delphinids Globicephala melas from the North Atlantic Ocean[END_REF][START_REF] Watanabe | Agedependent accumulation of heavy metals in Baikal seal (Phoca sibirica) from the Lake Baikal[END_REF]). This could be the case here since males weigh up to 290 kg while females do not exceed 191 kg. Moreover, female seals seem to have higher feeding rates than males, essentially because of the energetic cost of reproduction , viz. gestation and lactation, while males reduce drastically their feeding during the mating and moulting seasons. For example, an adult ringed seal weighing about 70 kg might ingest 1200 to 1300 kg of food per year, whereas an adult female weighing about 60 kg needs 1600 kg per year [START_REF] Ryg | Estimates of energy expenditure and energy consumption of ringed seal (Phoca hispida) throughout the year[END_REF]. Considering that males and females feed on the same species, and that grey seals might have a similar feeding dimorphism as the ringed seals, the uptake of Cd would be greater for females because of the greater quantities of ingested food vs body weight. These results also suggest that Cd transfer to foetus through the placenta or to calves via milk is very limited. It cannot be excluded that this variation could be associated with a difference in metabolic pathways linked to hormone cycle, obviously different in both sexes [START_REF] Caurant | Ecological and biological factors controlling the concentrations of trace elements (As, Cd, Cu, Hg, Se, Zn) in delphinids Globicephala melas from the North Atlantic Ocean[END_REF]. Increase of trace element concentrations with age was observed for Cd in kidney and liver but gender differences in the accumulation rates are noteworthy (Fig. 2). In liver, increasing of Cd concentrations with age was different between sexes, the accumulation fitted a logarithmic adjustment only for males. Such a logarithmic shape for Cd accumulation has been previously shown in the liver of the long-finned pilot whale from the Faroe Islands [START_REF] Caurant | Ecological and biological factors controlling the concentrations of trace elements (As, Cd, Cu, Hg, Se, Zn) in delphinids Globicephala melas from the North Atlantic Ocean[END_REF] This may suggest an equilibrium between assimilation and excretion of Cd in liver as shown for humans after 50 years old [START_REF] Friberg | Cadmium in the environment[END_REF]. In grey seals, this equilibrium would appear from 12 years old in males while in females, Cd was linearly accumulated with age. However, the present sampling lacks very old females as their maximum age was 27 years old while they can live more than 35 years.

When comparing trace element concentrations between seal species, Zn and Cu concentrations appear to be in the same order of magnitude than those reported for other pinniped species (Table 4), probably because these essential elements are submitted to homeostatic regulation in marine mammal tissues [START_REF] Law | Metals in marine mammals[END_REF]. However, Cd, Hg and Se exhibited among the highest values reported for pinnipeds in the literature. Thus, hepatic Se in the grey seal from the Faroe Islands varied from 1.17 to 99.9 µg.g -1 wwt and were comparable to the high hepatic Se concentrations ranging from 1.30 to 65.3 µg.g -1 wwt in the ringed seal from Western Canadian Arctic [START_REF] Wagemann | Overview and regional and temporal differences of heavy metals in Arctic whales and ringed seals in the Canadian Arctic[END_REF]. High Se concentrations in liver were also reported for grey seals from the Baltic sea (2.7-79.2 µg.g -1 wwt) and from Sable Island (9.3-83 µg.g -1 wwt) [START_REF] Nyman | Current levels of DDT, PCB and trace elements in the Baltic ringed seals (Phoca hispida baltica) and grey seals (Halichoerus grypus)[END_REF]. Concentrations of Hg and Cd are globally well documented in seals (Table 4). Generally, seals from polar areas exhibited high levels of hepatic Hg and renal Cd. Surprisingly for a species largely distributed in the temperate waters, grey seals also generally displayed very high Hg concentrations in liver. Present results for grey seals from the Faroe Islands follow this trend as their Hg concentrations vary from 1.13 to 238 µg.g -1 wwt in liver. Concerning Cd, grey seals from the Faroe Islands appeared to be atypical compared to those from Baltic Sea or Sable Island (Table 4). Indeed, they displayed Cd concentrations in kidney comparable to those of seals from the Arctic and clearly higher Cd concentrations than grey seals from Baltic Sea or Sable Island.

In summary, grey seals from the Faroe Islands exhibited among the highest renal Cd and hepatic Hg concentrations compared to other pinnipeds, particularly those from lower latitudes (Table 4). Very high Hg concentrations in grey seals from the Irish Sea were related to feeding habits in a very contaminated area, the Liverpool Bay, where their preys are enriched in Hg [START_REF] Law | Trace metals in the livers of marine mammals from the Welsh coast and the Irish Sea[END_REF]). In the Faroe Islands, such an enrichment due to industrial contamination does not exist. Consequently, the high Hg concentrations in the tissues of the grey seals might be considered as the consequence of background levels. In contrast, global Cd enrichment in the Arctic remained unclear. In fact, local enrichment have been noted when comparing marine mammal populations throughout the Arctic but it does not explain this phenomenon on a global scale [START_REF] Wagemann | Overview and regional and temporal differences of heavy metals in Arctic whales and ringed seals in the Canadian Arctic[END_REF]. Several authors have proposed that a phenomenon of Cd abnormality occurs in polar and subpolar areas, leading to very high Cd concentrations in many invertebrates and vertebrates species [START_REF] Petri | Trace metal in the crustaceans in the Antarctic Ocean[END_REF][START_REF] Bargagli | Elevated cadmium accumulation in marine organisms from Terra Nova Bay (Antarctica)[END_REF], Bustamante et al. 1998b[START_REF] Zauke | Heavy metals in fish from the Barents Sea (summer 1994)[END_REF]. Several results suggest that such an abnormality has also to be considered in the Faroe Islands. Indeed, similarly to polar regions, soluble trace element concentrations in seawater appear to be very low around this area [START_REF] Mart | Trace metal levels in the eastern Arctic Ocean[END_REF], but high Cd concentrations, reaching up 9.06 ± 3.38 µg.g -1 wwt and 6.55 ± 1.97 µg.g -1 wwt have been found in different cephalopod species (i.e. Loligo forbesi, Todarodes sagittatus and Eledone cirrhosa) and in the queen scallops Aequipecten opercularis caught around the archipelago, respectively [START_REF] Bustamante | Etude des processus de bioaccumulation et de détoxication d'éléments traces (métaux lourds et terres rares) chez les mollusques céphalopodes et bivalves pectinidés. Implication de leur biodisponibilité pour le transfert vers les prédateurs[END_REF], Bustamante et al. 1998a). Similarly, in coastal waters, the dog-whelks Nucella lapillus and limpets Patella sp. displayed Cd concentrations of 28 µg.g -1 wwt and 10 µg.g -1 wwt, respectively [START_REF] Dam | Integrated ecological monitoring in the coastal zone; Environmental Pollutants. The Food and Environmental Agency of the Faroe Islands[END_REF].

Furthermore, other marine mammal species from the Faroe Islands, i.e. the long-finned pilot whales Globicephala melas and the white-sided dolphins Lagenorhynchus acutus, also exhibited very high concentrations of Cd and Hg in their tissues [START_REF] Julshamn | Trace element intake in the Faroe Islands. I. Element levels in edible parts of pilot whales (Globicephala meleanus)[END_REF][START_REF] Caurant | Ecological and biological factors controlling the concentrations of trace elements (As, Cd, Cu, Hg, Se, Zn) in delphinids Globicephala melas from the North Atlantic Ocean[END_REF][START_REF] Gallien | Cadmium-containing granules in kidney tissue of the Atlantic white-sided dolphin (Lagenorhyncus acutus) off the Faroe Islands[END_REF]Olsen et al., in press). Marine mammals are currently considered as useful bioindicators of trace element contamination in the environment because of their high trophic level and their wide distribution. Differences in trace element concentrations between individuals from different areas may be due to different exposures through food rather than metabolic differences. In consequence, continued release of toxic metals such as Cd or Hg in the environment would be of particular concern in these areas.

Toxicological aspects for individuals

Within a single individual, the behaviour of trace elements depends on the different regulation and/or detoxification processes, leading to their storage in the tissues or to their excretion.

Extremely high levels of toxic Hg and Cd in mature grey seals may trigger cellular and physiological damages of the organs of storage. Thus, renal dysfunction is expected to appear when Cd concentrations exceed 50 µg.g -1 wwt in humans [START_REF] Elinder | Cd exposure and health risks : recent findings[END_REF]. Mature grey seals exhibited Cd concentrations in kidney close to that limit (36.3 ± 28.8 µg.g -1 wwt) with the oldest females exceeding it by far (see Fig 1). Furthermore, most of the mature grey seals from this study exhibited Hg concentrations exceeding the threshold levels of 60 µg.g -1 for liver damage in mammals (AMAP 1998). Nevertheless, according to their body mass and their blubber thickness (Table 1), seals were found to be in good health. This strongly suggest that grey seals from the Faroe Islands would have developed very efficient detoxification process that allow them to cope with such high Cd and Hg concentrations in their tissues.

Liver and kidney of grey seals have been reported to contained high levels of metallothionein which could trap toxic metals such as Cd [START_REF] Olafson | Isolation of heavy metal binding proteins from marine vertebrates[END_REF][START_REF] Teigen | Heavy metal content in liver and kidneys of grey seals (Halichoerus grypus) in various life stages correlated with metallothionein levels: some metal-biding characteristics of this protein[END_REF].

The primary role of metallothionein is to bind essential metals like Cu and Zn and to serve as an intracellular protein involved in metal homeostasis [START_REF] Vallee | Introduction to metallothionein[END_REF]. However, Cd shows a great affinity for metallothionein, leading to a competition with Zn for binding sites and to a reduction of the toxic effects of Cd [START_REF] Tsalev | Atomic absorption spectrometry in occupational and environmental health practice[END_REF]. Thus, displaced Zn would induce the metallothionein synthesis, increasing the number of binding sites within the renal cells. If this hypothesis is true, Cd and Zn would be accumulated jointly. Significant correlation between Zn and Cd (Fig. 4) in the kidney of grey seals from the Faroe Islands strongly suggest the occurrence of an effective detoxification process of Cd involving metallothionein in this organ.

In grey seal liver, Hg concentrations were strongly positively correlated with Se during the life span (Fig. 5). It has been reported that selenium apparently exerts a protective influence against Hg toxicity and seems to govern its hepatic accumulation by the formation of mercuric selenide (HgSe) granules [START_REF] Pelletier | Mercury-selenium interactions in aquatic organisms: a review[END_REF][START_REF] Cuvin-Aralar | Mercury and selenium interactions: a review[END_REF][START_REF] Nigro | Intracellular storage of mercury and selenium in different marine vertebrates[END_REF]. HgSe granules (tiemannite) have been identified in the liver of seabirds, marine mammals and humans [START_REF] Martoja | Identification of tiemannite as a probable product of demethylation of mercury by selenium in cetaceans[END_REF][START_REF] Pelletier | Mercury-selenium interactions in aquatic organisms: a review[END_REF][START_REF] Hansen | Distribution of dietary mercury in a dog. Quantification and localisation of total mercury in central and nervous system[END_REF][START_REF] Nigro | Intracellular storage of mercury and selenium in different marine vertebrates[END_REF]. Moreover, many studies also reported that Hg and Se are correlated in a 1:1 molar ratio as in HgSe (e.g. [START_REF] Koeman | Mercuryselenium correlation in marine mammals[END_REF][START_REF] Nielsen | Distributional pattern of zinc, cadmium, mercury, and selenium in livers of hooded seals (Cystophora cristata)[END_REF][START_REF] Wagemann | Methylmercury and total mercury in tissues of arctic marine mammals[END_REF]. Grey seals from the Faroe Islands exhibited a Hg:Se molar ratio in liver tending towards 1 (Fig. 5). This strongly suggests the presence of tiemannite granules as a result of coprecipitation of Hg with Se. A molar ratio between hepatic Hg and Se close to 1 in grey seals were found to occur for mature males and females. They displayed the same kinetics of accumulation with age which supposes a similar detoxification process of Hg in liver for both sexes. This also suggests that pregnancy and lactation are not efficient processes of elimination for females. Moreover, the annual moult, probably participating to the elimination of some Hg, is not sufficient to counteract the high assimilation of Hg.

CONCLUSION

Grey seals from the Faroe Islands showed very high Cd and Hg concentrations in their tissues. These Cd concentrations are particularly elevated compared to those in other grey seal populations. The Cd and Hg concentrations in the oldest individuals are clearly higher than the threshold levels for toxic effect which induces a threat to their health status. However, very efficient detoxification processes, involving metallothionein protein and co-precipitation of Hg with Se, probably account for the good condition of the analysed seals. Furthermore, the present results highlight that Faroe Islands also show a Cd "abnormality" as previously reported in polar oceans. Finally, the very high tissular Cd contents lead us to suspect important changes in the diet of the seals during the year. Hence, seals may also feed on cephalopods, and that might account for the high Cd concentrations found in the oldest individuals.

Caption to figures

Figure 1 .

 1 Figure 1. Map of the Faroe Islands. Number and position of grey seals sampled in the summer period in 1993-95 are indicated.

Figure 2 .Figure 3 .Figure 4 .

 234 Figure2. Halichoerus grypus. Renal and hepatic Cd concentrations (µg.g -1 wwet) in relation to age in male (q) and female(v)

  Figure 1

Table 1 .

 1 Halichoerus grypus. Characteristics (sex, length, weight, dorsal blubber thickness and age) of the individuals sampled in the FaroeIslands between 1993 and 1995

	Sex	N	Length	Weight	Blubber thickness	Age
	Sexual maturity		(cm)	(kg)	(mm)	(years)
	Male
	Mature	4	212.0 ± 11.9	229.3 ± 68.4	35.0 ± 10.0	17.0 ± 5.2
	Immature	18	136.5 ± 15.7	56.8 ± 20.8	22.1 ± 4.7	1.9 ± 1.3
	Whole	22	150.3 ± 33.3	89.6 ± 76.6	24.9 ± 7.7	4.6 ± 6.4
	Female
	Mature	23	176.4 ± 8.5	152.0 ± 20.8	39.7 ± 8.5	14.3 ± 4.5
	Immature	23	133.7 ± 10.5	49.4 ± 11.4	22.6 ± 4.0	2.3 ± 1.1
	Whole	46	154.6 ± 23.6	99.6 ± 54.4	31.1 ± 11.1	8.3 ± 6.9
	Whole individuals	68	153.2 ± 27.0	96.4 ± 61.9	29.1 ± 10.5	7.1 ± 6.9

Table 3 .

 3 Halichoerus grypus. Correlation between trace elements within the different tissues. Not underlined : p<0.05 ; underlined : p<0.001.

Acknowledgements. We are grateful to KA Fagerheim, Institute of Marine Research, Bergen, for age determination of the seals and to I. Gallien and T. Guyot, University of La Rochelle, for their technical assistance. This work was supported financially by the Regional Council of Poitou-Charentes and Rhodia.


Abdelkrim Bahloul

Sami Tliba
email: sami.tliba@u-psud.fr

Yacine Chitour

Dynamic Parameters Identification of an Industrial Robot With and Without Payload

Keywords: Industrial Robot, Closed-Loop Identification, Constrained Optimization

This paper brings an identified model for a 6 degrees of freedom (dof) industrial robot, the Denso VP-6242G robot, first without payload, then with a payload. This last is composed of a force sensor fixed between a spherical handle and the robot end-effector. This equipped end-effector is intended to experiments in the field of Physical Human-Robot Interactions (PHRI), for co-manipulation purposes. The control algorithms that are necessary to achieve a good PHRI, require a good knowledge of the robot dynamical model, especially the inertia matrix which should be positive definite whatever the configuration of the robot. However, most of industrial robots are supplied without any datasheet containing the inertial parameters nor Computer-Aided-Design (CAD) model. Hence, we propose to apply an identification procedure to experimental data, based on the Inverse Dynamic model Identification Method (IDIM). To ensure the positive definiteness of the inertia matrix, the used optimization step addresses the problem of nonlinear Weighted Least Squares (WLS), derived from the mathematical formulation of the identification problem, under a set of nonlinear constraints in the parameters.

Introduction

In control engineering field, most of the advanced nonlinear control techniques require the knowledge of the system's dynamical model. It is the case for many control problems concerning industrial robot manipulators, for which good trajectory tracking has to be carried out. Many works about Physical Human-Robot Interactions (PHRI) rely on the principle of trajectory tracking, as in [START_REF] Jlassi | An event-controlled online trajectory generator based on the human-robot interaction force processing[END_REF]. In these papers, the authors worked on the co-manipulation problem, which consists in achieving a master-slave relationship between an industrial robot and a human operator (HO), while making the PHRI safe and transparent for the HO. A dynamical model contains kinematic and dynamic parameters. The kinematic parameters are known as the parameters of the Modified Denavit-Hartenberg convention (MDH) [START_REF] Khosla | Parameter identification of robot dynamics[END_REF].

It is not difficult to extract these latter based on the robot datasheet provided by the manufacturers. However, dynamic parameters, which are inertial and friction parameters, are rarely available in such datasheet. Also, it is difficult, say impossible, to get a Computer-Aided-Design (CAD) model in order to obtain a good approximation of some inertial parameters. Then, the use of identification techniques applied to experimental data [START_REF] Walter | Identification of Parametric Models from Experimetal Data[END_REF] become the only way to get a good dynamical model. This topic has received a great attention by the robotics community during the last thirty years. Several important issues have been addressed by researchers. A non exhaustive list of issues can be found in [START_REF] Swevers | Dynamic model identification for industrial robots[END_REF]. Among them, the obtaining of a parametrized dynamical model is of utmost importance because it determines the number of parameters to be estimated. This issue has raised a great number of works that has lead the researchers to distinguish between the notions of base parameters and link inertial parameters. These keywords were introduced in [Gautier and Khalil, 1990, Gautier, 1990]. Basically, the base parameters are a kind of parameters' regrouping within the motion equations, that allows to formulate these motion equations as a linear relation in these parameters. This turns out to be useful when deriving an algorithm of parameters' estimation. Another issue concerns the experimental design, including the robot excitation [Jin and Gans, 2015]. Most of people suggested a data acquisition in closed-loop, using a joint-position control with a simple proportional controller designed to ensure a desired trajectory tracking. Even if the closed-loop feature creates some correlations between the noise affecting the measurements and the other signals within the closed-loop structure, this approach turns out to be quite efficient in the parameters' estimation if the measured signals are well post-processed with a suitable filtering [Janot et al., 2014, Brunot et al., 2017]. The desired trajectories are almost always taken as a sum of sinusoids with appropriate magnitudes, phases and frequencies, in order to maximize the Signal-to-Noise-Ratio (SNR) during the acquisition and to provide a persistent excitation, which ensures the parameters' identifiability. Finally, the estimated parameters' computation method is closely related to the kind of model used for identification. The Inverse Dynamic model Identification Method (IDIM) is the most popular one since it provides an equivalent formulation of the torques that is linear in the base parameters. Hence, the Least Squares (LS) algorithm can easily be performed [START_REF] Swevers | Dynamic model identification for industrial robots[END_REF], Jin and Gans, 2015, Vuong and Jr., 2009]. Most of works have rather used the Weighted Least Squares (WLS) technique to prevent the effects of inaccurate data. Nevertheless, there is no guarantee that the estimated parameters lead to a positive definite inertial matrix [START_REF] Yoshida | Verification of the positive definiteness of the inertial matrix of manipulators using base inertial parameters[END_REF].

In this paper, we propose to combine a nonlinear WLS estimation technique under a set of nonlinear constraints in the dynamic parameters, that ensures the inertia matrix to be positive definite. The paper is organized as follows: Section 2 introduces the basics on robot identification. It explains the used method based on a constrained nonlinear WLS. Then, Section 3 proposes the application of this method to the Denso VP-6242G robot, in order to identify a model of the robot with and without a payload. Finally, Section 4 concludes this paper.

Basics on robot identification

Consider the general case of a rigid robot composed of n revolute joints, n serial links and a fixed base. The kinematic parameters are assumed to be well known. The dynamic parameters stands for the inertial parameters of the links as defined by [START_REF] Yoshida | Verification of the positive definiteness of the inertial matrix of manipulators using base inertial parameters[END_REF], and the usual Coulomb & viscous friction coefficients as indicated in [START_REF] Swevers | Dynamic model identification for industrial robots[END_REF].

A parametric equation of motion in these parameters can be formulated, in continuous time, as:

M(q, θ ) q + N(q, q, θ ) = τ, (1)
where q, q and q denote the (n × 1) vectors of joint positions, velocities and accelerations respectively, called kinematic joint variables. τ is the (n × 1) vector of joint torques; M(q, θ ) denotes the (n × n) inertia matrix which is symmetric and positive definite; N(q, q, θ ) is the (n × 1) vector that gathers the Coriolis, centrifugal, gravity and friction torques. Both terms depend on the dynamic parameters' vector denoted θ , of dimension (n θ × 1), in a linear manner. It is assumed that all the components of q and τ are measured with noisy sensors.

Choice of the parameters for the IDIM approach

The IDIM consists in rewriting the left side of (1) as a linear relation in θ as follows:

τ = D(q, q, q)θ . ( 2
)
where D is a (n × n θ ) matrix that only depends on the joint variables of the robot, called the measurements matrix [START_REF] An | Estimation of inertial parameters of rigid body links of manipulators[END_REF]. By using the same notations as [START_REF] Khalil | Symoro+: A system for the symbolic modelling of robots[END_REF] for the link i, we can define the following dynamic parameters:

xx i , xy i , xz i , yy i , yz i , zz i are the components of the inertia tensor matrix i I i around the origin O i of the link frame R i ; -mx i , my i , mz i are the first moments;

m i is the mass of the link; -Fs i , Fv i are the Coulomb and viscous friction coefficients of a friction model linear in these parameters.

The above parameters are gathered in the following vector:

θ i T = xx i xy i xz i yy i yz i zz i mx i my i mz i m i Fs i Fv i .
(

) 3
where T denotes the transpose operator, and θ is built by concatenating the θ i (i = 1, ..., n). The first ten parameters of θ i are called the inertial parameters for the link i, as indicated by [START_REF] Yoshida | Verification of the positive definiteness of the inertial matrix of manipulators using base inertial parameters[END_REF].

In [Gautier and Khalil, 1990, Gautier, 1990], the authors have proposed to determine which are the parameters that have no influence on the dynamics of the robot. They derived some rules for the regrouping of the inertial parameters and the corresponding relationships. The regrouped inertial parameters are called minimum inertial parameters. The new parameter vector is called the base parameter vector θ B of n θ B components. Relation (2) can be rewritten as

τ = D B (q, q, q)θ B , (4)
where D B is a (n × n θ B ) matrix, with n θ B < n θ .

Closed-loop data acquisition and excitation signals

For the sake of preserving the robot integrity, it is matter to drive the robot while mastering its configuration at each sampling time, in order to avoid self collisions or collisions of the robot with its environment. Hence, a joint position feedback control with a simple proportional controller, with suitable adjusted gains, is performed to follow a given trajectory in joint space that meets some desired requirements. In identification, the choice of the excitation signal is important, because it should allow that "all the parameters to estimate are excited". A signal with this feature is called a Persistent Excitation Signal (PES). A PES used to identify n θ B parameters must contains at least n θ B sinusoids of different frequencies [START_REF] Walter | Identification of Parametric Models from Experimetal Data[END_REF], [Gautier and Khalil, 1988], [Lennart, 1971]. In addition, the desired trajectory should be designed so that it is periodic during a long time range with a number of period grater than n in order to allow the statistical analysis of the results [START_REF] Swevers | Dynamic model identification for industrial robots[END_REF]. Moreover, the values taken by the designed position trajectories should comply with the robot allowable limit range of motion, and at the same time maximize the Signal-to-Noise-Ratio (SNR)

of the interesting measured signals. Such generated signals are typically used in identification as desired trajectories for the joint positions. If the proportional gains are high enough, then the tracking errors between the measured joint positions and the desired ones are small enough to consider them having similar properties than the desired periodic trajectories, each trajectory being built to be a PES.

Signal processing

Because of the noises that affect the sensors, the measured data (joint torques and positions) can not be directly used in identification because of the closed-loop feedback control that might creates correlations between the noises and the signals of the closed-loop system. This can strongly influence the values of parameters to identify [Brunot et al., 2017].

To attenuate the undesirable effects of noise on the estimated parameters, it is matter to filter these data before their use in the estimation procedure. This is done off-line thanks to a low-pass filter with a unit gain at low frequencies and a frequency cut-off roughly set a decade after the highest existing frequency in the desired trajectories. To avoid the drawbacks that are inherent to causal linear filtering, a forward plus backward filtering of the noisy data is performed to get a zero-phase filtering of all the measurements. Furthermore, since the applied excitation signals contain many periods, an average period of each signal is computed over all the available periods in order to reduce the computational burden of the estimation algorithm and to provide statistical information about the estimation confidence. Given a periodic signal in discrete time, denoted s(t), with P full periods K samples per period. The average period of s(t), denoted by s(t) is computed as follow:

s(t) = 1 P p=P ∑ p=1 s(t + K(p -1)). (5)
Finally, to reduce the computational burden, it may be useful to undersample the data if the sampling frequency is very higher than the frequency bandwidth.

Let τ and q be the resulting joint torques and positions after applying all the signal processing steps described before; q and q are the resulting joint velocities and accelerations, computed by a suitable numerical differentiation of q and a Université Paris-Sud XI UFR des Sciences d'Orsay

4/13

Laboratoire des Signaux & Systèmes Pôle Automatique & Systèmes zero-phase filtering to reduce the numerical noises. Assume the data contains N samples per period for each of these variables. These data are assumed to check the following relation at sample time t, derived from ( 4)

τ(t) = D B q(t), q(t), q(t) θ B + ρ(t) (6)
where ρ is an (n × 1) vector of error terms, gathering the noises and the unmodelled phenomena. It is assumed to have a zero-mean, and uncorrelated samples. The sets of N samples kept after the whole signal processing described above are used to define:

Y :=     τ(1) . . . τ(N)     , W :=     D B q
(1), q(1), q(1) . . .

D B q(N), q(N), q(N)     , R:=     ρ(1) . . . ρ(N)     , (7)
where Y , R are (n N × 1) vectors, and W is (n N × n θ B ) matrix. Then, by using these new variables, (6) becomes

Y = W θ B + R, (8)
which is an overdeterminated set of linear equations in the unknown parameters in θ B . It is worth at noting that the conditioning number of the regressor matrix W allows to measure the sensitivity of the solution θ B to the residual noises affecting the data in τ, q, q and q. Therefore, the signal processing step should reduce as much as possible this indicator while ensuring the convergence of the identification procedure toward a vector of parameters that is unbiased and plausible [Janot et al., 2014].

Estimation of the base parameter vector

By assuming that W is of full rank and that the components of R are independent and form a zero-mean Gaussian sequence, an estimation θB of θ B can be obtained by solving the following constrained WLS optimization problem:

θB = arg min θ B W T Σ -1/2 (Y -W θ B ) 2 such that M( q, θB ) > 0. ( 9
)
where Σ denotes the covariance matrix of the actuator torque data, which is a block diagonal matrix composed of N matrices of dimension (n × n) and denoted Σ t . This last corresponds to the covariance matrix of the actuator torques at the sample time t and is given by:

Σ t = 1 (P -1) P ∑ p=1 (T p (t) -τ (t)) (T p (t) -τ (t)) T , (10)
where T p (t) denotes the p th period at the sample time t of the torque measurements τ, on which has been applied only the filtering and the decimation steps of the signal processing procedure, say without the average computing one.

The problem (9) consists in minimizing the squared norm of the weighted error between the measured and computed joint torques, under the constraint that the reconstructed inertia matrix M( q, θB ) is always positive definite, say with positive eigenvalues, whatever the robot configuration. A sufficient condition for the inertial matrix to be positive definite for each configuration of the manipulator is given in [START_REF] Yoshida | Verification of the positive definiteness of the inertial matrix of manipulators using base inertial parameters[END_REF]. The authors have proved that the following constraints on the link physical parameters for each link composing the manipulator, lead to a definite positive inertia matrix:

m i > 0 and i I g i > 0, i = 1, . . . , n (11)
where m i and i I g i are the mass and the inertia tensor matrix around the center of mass g i of the link i.The relation between i I i and i I g i is given by [START_REF] Yoshida | Verification of the positive definiteness of the inertial matrix of manipulators using base inertial parameters[END_REF]]:

i I i = i I g i + m i r T i r i E 3 -r i r T i , (12)
where r i = x i y i z i T is the vector from O i to g i , and E 3 is the (3 × 3) identity matrix.The link inertial parameters of subsection 2.1 are denoted by θ I i . The base parameters' vector θ B is a nonlinear function of θ I i , Fs i and Fv i denoted by

θ B = f {θ I i , Fs i , Fv i } i=1,...,n , (13)
whose expression can be derived analytically as reported in [Khalil andCreusot, 1997, Khalil et al., 2014]. Let define the link physical parameters θ P i as the elements of i I g i , r i and m i . Some elements of θ I i are also in θ P i (like m i ). However, other elements have a linear (like mr i ) or nonlinear (like i I i ) relation with elements of θ P i . By denoting h the general relation derived from (12), between θ I i and θ P i , it comes:

θ I i = h (θ P i ) , i = 1, . . . , n. (14)
Using the relations ( 13) and ( 14), the base parameters' vector θ B can be rewritten as a nonlinear function, denoted by g,

of ϑ i = θ T P i Fs i Fv i T : θ B = g {ϑ i } i=1,...,n . (15)
According to [START_REF] Yoshida | Verification of the positive definiteness of the inertial matrix of manipulators using base inertial parameters[END_REF], a sufficient condition to have a positive definite inertia matrix is that all m i and i I g i contained in (15) must satisfy the conditions in (11). However, the solutions in m i and i I g i are not unique. In [START_REF] Yoshida | Verification of the positive definiteness of the inertial matrix of manipulators using base inertial parameters[END_REF], they form a set of virtual parameters. The problem in (9) becomes a new Constrained WLS (CWLS) optimization problem, in which the solution is sought by solving:

θ = arg min ϑ W T Σ -1 (Y -W g(ϑ )) 2
such that m i > 0, i I g i > 0,

Fs i > 0, Fv i > 0, i = 1, . . . , n (16)
Note that i I g i > 0 is equivalent for its eigenvalues to be strictly positive. Moreover, the estimated values of Fs i and Fv i can only be positive, that is why these constraints have been added in (16). Finally, the estimated base parameters' vector θB is obtained by substituting the estimated vector θ in (15). Note that, because of its nonlinear feature w.r.t. the physical parameters, the optimization problem in ( 16) may contain several local minima. It should then be tackled by global optimization solvers. The global minimum seeking may be a tedious task.

Payload parameters identification

The joint torques in Y can be seen as the sum of the ones resulting from the robot bodies Y r , and those of the robot payload Y p [START_REF] Swevers | Dynamic model identification for industrial robots[END_REF] (plus R the vector of unknown noises and unmodelled dynamics):

Y = Y r +Y p + R (17) = Y r +W p θ p + R, (18)
where W p is a (n × n θ p ) regressor matrix; θ p is a vector of parameters composed of the payload inertial parameters and the variation of joints friction parameters (∆Fs i and ∆Fv i ) for all the joints. Indeed, the friction parameters may change when a payload is added to the robot [START_REF] Swevers | Dynamic model identification for industrial robots[END_REF]. As the frame of the payload is fixed w.r.t. the last link, W p is composed by the columns of W which correspond to all the joint friction parameters, and to the base inertial parameters of the last link. Note that W is the derived regressor matrix of the robot with its payload. To identify the payload parameters, the acquisition of two data series is necessary. The first corresponds to the robot without the payload, while the second is acquired for the robot with its payload. The estimation of θ p can be obtained by solving the following problem: θp = arg min

θ p W T p Σ -1 (Y -Y r -W p θ p ) 2
such that m p > 0, n I g p > 0,

∆Fs i > 0, ∆Fv i > 0, i = 1, . . . , n (19)
where Y r contains the torques data from the first data series, whereas Y and W p contains the second data series.

Validation

To check the validity of the estimated parameters by the proposed procedure, these parameters are used to reconstruct the joint torques and compared to the measured ones. For this purpose, the joint positions, velocities and accelerations are used as inputs for the inverse dynamic model in (2) with the identified parameters. This validation step is necessary to have information about the confidence intervals of the identified parameters, and at the same time about the validity of the dynamical model of the robot.

3 Case study : Denso VP-6242G robot

Dynamic identification model of the robot

The Denso VP-6242G robot is a manipulator with six revolute joints, depicted in Figure 1. As shown in Fig. 1, the robot end-effector can be equipped with a force sensor and a spherical handle for PHRI experiments. The dynamical model is computed using the parameters of the Modified Denavit-Hartenberg convention (MDH) [START_REF] Khalil | A new geometric notation for open and closedloop robots[END_REF].

Figure 2 shows the frames attached to each joint of the robot according to this convention. Table 1 shows the MDH parameters of the Denso VP-6242G robot, extracted from Fig. 2. By using the SYMORO+ software package Table 1: Kinematic parameters of the Denso robot Khalil andCreusot, 1997, Khalil et al., 2014] with these parameters, the dynamic model of the robot for identification is calculated. It results in a base parameters' vector θ B of dimension (48 × 1), and a regressor matrix D B of dimension (6 × 48). The base parameters' vector of the payload θ p is a (19 × 1) vector.

i α i d i r i θ i i α i d i r i θ i 1 0 0 l 1z q 1 4 - π 2 -l 3x l 3z + l 4 q 4 2 π 2 0 0 q 2 + π 2 5 π 2 0 0 q 5 3 0 l 2 0 q 3 - π 2 6 - π 2 0 l 5 q 6 [

Excitation signals

The used excitation signals, for each axis, have been designed as a sum of 55 basic sinusoids of same amplitudes, random phases and different frequencies. Each resulting sum was scaled to comply with its corresponding range of joint motion (see Table 2), set to keep the robot safe. The frequencies have been chosen to be integer multiples of a fundamental frequency. The number of sinusoids is greater than the number of base parameters to identify in order to obtain a PES [Lennart, 1971]. Also, all frequencies are lower than the limit frequency, defined as follow:

y 0 z 0 x 1 y 1 z 1 , x 2 y 2 z 2 x 3 y 3 z 3 x 4 , x 5 y 4 z 4 , y 5 z 5 x 6 y 6 z 6 (R 0 ) (R 1 ), (R 2 ) (R 3 ) (R 4 ), (R 5 ) (R 6 ) C 0 C 1 C 1 C 2 C 2 C 3 C 3 C 4 C 4 C 5 C 5 C 6
f i = A q,i 2πA q,i , (20)
where A q,i and A q,i are the maximum allowed amplitude of the joint position and velocity for the joint actuator i. The A q,i are determined to avoid the collisions between the robot and its environment, and the self collisions between some parts of the robot. The A q,i are derived from the actuator positioning time characteristic, that gives a relation between positioning time and motion angle, according to the weight of the load carried by the manipulator. These excitation signals are used as desired inputs for the robot in closed-loop, through a joint position feedback control with proportional gains. To have a more accurate estimation, the excitation signals are created with 12 periods, with 380 sec per period. This number of periods is greater than n = 6, which allows to compute the square root inverse of the covariance matrix. The sampling time is 10 -3 sec. The duration of one period depends on the fundamental frequency and on the limit frequency. To ensure that the robot does not exceed the range of joint motion, the initial joint positions are set in the middle of this range. In addition, the movement starts and stops with zero joint velocities and accelerations. For this, a phase of immobility of 4 sec is added at the beginning and at the end of the movement. During this phase, the robot remains at its initial position. A connection phase of 5 sec is also inserted to connect the initial joint position of the robot with the excitation signals. The total excitation time is of 4578 sec. Table 2 presents the range of the joint motion [q i,m , q i,M ], the amplitudes A q,i , A q,i , the limit frequencies f i and the proportional gain K p i of the joint-position controller for each axis J i .

[q i,m , q i,M ] [ • ] A q,i [ • ] A q,i [ • /s] f i [Hz] K p i J 1 [-

Data processing

First, the measurements of the joint currents and positions are recorded. To obtain joint torques, the joint currents are multiplied by their corresponding torque constants K c i and motor gear ratios G r i , presented in table 3. Then, the data are filtered by using a low-pass Butterworth filter, with a cut-off frequency of 10 Hz, and of order 1. Joint velocities and accelerations are computed by a suitable numerical differentiation of the filtered joint positions. To reduce possible noises due to numerical differentiation, the velocities and accelerations signals are also filtered by the same filter. In a third step, the data corresponding to the phases of immobility and connection are deleted. The average periodic data are computed over the 12 periods as in (5). In the last step, since the sample frequency (10 3 Hz) is too high compared to the filter cutoff frequency (10 Hz), the size of the data are reduced by an undersampling of factor 10, that makes the signals with a sample frequency equal to 10 2 Hz. This frequency remains sufficiently high compared to the highest frequency contained in the data (Table 2). Hence, the data should not be affected too much by this decimation.

A zoom between the instants 1200 and 1300 sec of the signals of measured joint position and torque, and calculated velocity and acceleration of the joint 1, before and after filtering are shown by the figure 3 (corresponds to the robot with the payload). We can observe that the noisy measurements are suitably filtered. We conclude that the choice of the filter parameters (cut-off frequency and order) is good. The important error in the joint acceleration signal is interpreted by a significant noise associated with this signal, resulting from a double differentiation of the noisy joint position measurement.

We consider that these post-processed data are ready to be used in the sequel of the identification procedure.

Parameters estimation

The regressor matrices and the torque vectors were built for the two cases: with and without the payload. We have checked that these matrices are of full rank. In the case of the VP-6242G Denso robot, ϑ is of dimension (66 × 1) and ϑ p is (22 × 1). The estimation of the parameter vectors ϑ and ϑ p consists in solving the CWLS optimization problem in (16).

For this, we used a global optimization solver of Matlab, based on its function fmincon that allows to find a minimum solution of the CWLS problem. Table 4 shows two sets of numerical values of the base parameter vector θB estimated with and without the payload robot.

Table 5 shows numerical values of the payload base parameters, containing the variation of the joint friction coefficients.

Torque reconstruction

Torque reconstruction is a step for checking the validity of the estimated parameters, and at the same time the corresponding dynamical model. For this, a different measurement series than the one exploited for the identification, but with the same features, is used. We have used two ways to reconstruct the torques of the robot with the payload. The first is by using the parameters estimated in the case of the robot with this last. The second is by using the parameters calculated without the payload, for which we add the friction variations and payload parameters, to the friction and the 6 th link parameters, respectively. The figures in Fig. 4 show, for the six joints: the measured torques after filtering (blue); the computed torques with θ B found with the payload robot (green); the computed torques using θ B found without the payload robot to which is added θ p (red). The figures in Fig. 4 illustrate a good quality of reconstruction of the torques. It is clear that the reconstruction with the parameters calculated with the payload is better than the one resulting from the added parameters, because of the number of errors sources. The dynamical model of the robot and the identified parameters can be considered acceptable and used to apply control techniques.

Conclusion

In this paper, we were interested in identifying the dynamic parameters of the industrial manipulator robot Denso VP-6242G, with and without its handle. To this end, we have used a nonlinear weighted least squares formulation of the identification problem under nonlinear constraints in the dynamic parameters. The identified parameters and the dynamical model of the robot have been validated by the torque prediction approach. The identification method appeared to be efficient in giving parameters that lead to a positive definite inertia matrix. Future works will concern the use of the identified model of the Denso robot to achieve a PHRI for a co-manipulation purpose, as proposed in [START_REF] Jlassi | An event-controlled online trajectory generator based on the human-robot interaction force processing[END_REF]. [ Brunot et al., 2017] Brunot, M., Janot, A., Carillo, F., andGarnier, H. (2017). A pragmatic and systematic statistical analysis for identification of industrial robots. In Proc. of the IEEE Int. Conf. on Advanced Intelligent Mechatronics (AIM), pages 559-564, Munich, Germany.

[ Gautier, 1990] Gautier, M. (1990). Numerical calculation of the base inertial parameters of robots. In Proc. of the IEEE Int. Conf. on Robotics and Automation (ICRA), pages 1020-1025.

[Gautier and Khalil, 1988] Gautier, M. and Khalil, W. (1988). On the identification of the inertial parameters of robots.

In Proc. of the IEEE Conf. on Dec. and Ctrl. (CDC), pages 2264-2269.

[Gautier and Khalil, 1990] Gautier, M. and Khalil, W. (1990)

Figure 1 :

 1 Figure 1: VP-6242G Denso robot.

Figure 2 :

 2 Figure 2: Robot frames for MDH convention.

Figure 3 :

 3 Figure 3: Data signals for axis 1 with and without processing: measured joint position and torque (top), and computed joint velocity and acceleration (bottom).

Figure 4 :

 4 Figure 4: Comparison of the measured torques after filtering and the computed torques calculated in two ways.

Laboratoire des Signaux & Systèmes Pôle Automatique & Systèmes 5/13 Université Paris-Sud XI UFR des Sciences d'Orsay

Laboratoire des Signaux & Systèmes Pôle Automatique & Systèmes 7/13 Université Paris-Sud XI UFR des Sciences d'Orsay

Table 2 :

 2 Features for the excitation signals' design Axis

Table 3 :

 3 Motor specifications for the studied robot

	Axis	J 1	J 2	J 3	J 4	J 5	J 6
	K c i	0.38 0.38 0.22 0.21 0.21 0.21
	G r i	120	160	120	100	100	100

Table 4 :

 4 Numerical values of θ B with and without the payload.

	θ B	Without	With	θ B Without With	θ B Without With
	zzr 1	5.16	7.10	zzr 3 3.07	4.37	xz 5	0.01 -0.02
	Fs 1 47.44 49.74 mxr 3 -4.15 -5.16 yz 5	0.03	0.01
	Fv 1 122.89 150.81 myr 3 5.76	8.77 zzr 5 0.28	0.56
	xxr 2 -3.28 -5.96 Fs 3 52.23 54.78 mx 5 0.08	0.13
	xy 2 -1.60 -1.01 Fv 3 83.55 87.92 myr 5 0.40	2.12
	xzr 2 -1.30 -1.17 xxr 4 -0.16 -0.21 Fs 5 19.30 20.45
	yz 2 -0.85 -0.97 xy 4	0.14	0.19 Fv 5 24.77 29.29
	zzr 2 15.32 17.29	xz 4	0.25	0.23 xxr 6 -0.02 -0.07
	mxr 2 16.02 18.67	yz 4 -0.03 -0.06 xy 6 -0.02 0.03
	my 2	0.14	0.28	zzr 4 0.06	0.06	xz 6 -0.02 0.02
	Fs 2 60.72 63.64 mx 4 0.29	0.30	yz 6	0.00	0.00
	Fv 2 168.22 185.75 myr 4 0.21	0.20	zz 6	0.05	0.00
	xxr 3 7.43	9.04	Fs 4 24.04 24.63 mx 6 -0.02 0.10
	xyr 3 0.15	0.41	Fv 4 19.21 21.55 my 6 -0.01 -0.05
	xz 3	0.07	0.05	xxr 5 0.05	0.22	Fs 6 18.72 19.08
	yz 3	0.01	0.04	xy 5	0.00	0.01 Fv 6 11.85 15.74

Table 5 :

 5 Numerical values of θ p .

	θ p	Value	θ p	Value	θ p	Value	θ p	Value
	∆Fs 1	3.11	∆Fv 3 14.37 xxr p	2.65	mx p	0.43
	∆Fv 1 33.35 ∆Fs 4	1	xy p -0.20	my p	0.05
	∆Fs 2	4.48	∆Fv 4	3.61	xz p	0.43	∆Fs 6	0.45
	∆Fv 2 22.26 ∆Fs 5	1.68	yz p	0.05	∆Fv 6	4.62
	∆Fs 3	2.17	∆Fv 5	4.61	zz p	0.15

  . Direct calculation of minimum set of inertial parameters of serial robots. IEEE Trans. on Robotics and Automation, pages 368-373. [Janot et al., 2014] Janot, A., Vandanjon, P.-O., and Gautier, M. (2014). A generic instrumental variable approach for industrial robot identification. IEEE Trans. on Ctrl. Syst. Tech., 22(1):132-145.

[Jin and Gans, 2015

] Jin,

J. and Gans, N. (2015)

. Parameter identification for industrial robots with a fast and robust trajectory design approach. Robotics and Computer-Integrated Manufacturing, 31:21-29. Université Paris-Sud XI UFR des Sciences d'Orsay 12/13 Laboratoire des Signaux & Systèmes Pôle Automatique & Systèmes

Laboratoire des Signaux & SystèmesPôle Automatique & Systèmes

This work was partially supported by the ICODE institute, research project of the Idex Paris-Saclay.