Abdelkrim Bahloul

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

Yacine Chitour

Dynamic Parameters Identification of an Industrial Robot: a constrained nonlinear WLS approach

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, with an end-effector composed of a spherical handle, fixed on a force sensor. This robot is intended to experiments in the field of Physical Human-Robot Interactions (PHRIs), 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. A validation step permits to check the efficiency of this approach for the Denso robot.

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. This is for example the case in [Jlassi et al., 2014] where the authors have addressed the co-manipulation problem which consists in achieving a master-slave relationship between an industrial robot and a human operator (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. Moreover, it is hard, say impossible, to get an accurate Computer-Aided-Design (CAD) model in order to obtain a good approximation of some inertial parameters.

Then, the only way to get a good dynamical model is the use of identification techniques applied to experimental data, that can be found in [START_REF] Walter | Identification of Parametric Models from Experimetal Data[END_REF]. 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 dynamical model is of utmost importance because it determines the number of parameters to be estimated. This issue has lead the researchers to distinguish between the notions of link inertial parameters and base parameters, as 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 andGans, 2015, Gautier andKhalil, 1991]. Most of people suggested a data acquisition in closed-loop, using a jointposition control with a simple proportional controller designed to ensure a desired trajectory tracking. Even if the closedloop 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 designed as periodic functions, corresponding to a sum of sinusoids with appropriate features, while guaranteeing an acceptable Signal-to-Noise-Ratio (SNR) during the acquisition. This allows the inputs to meet the expected excitation properties for 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) approach can easily be performed [Swevers et al., 2007, Jin andGans, 2015]. Most of works have rather used the Weighted Least Squares (WLS) technique to prevent the effects of inaccurate data. To this end, the data are averaged over one period and weighted by the covariance matrix of the torque measurements, computed by taking into account all the recorded periods. 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, and explains the constrained nonlinear WLS approach. Then, Section 3 proposes the application to the Denso VP-6242G robot. Finally, some conclusions are proposed in Section 4.

Basics on robot identification

Consider the general case of a rigid robot having n revolute joints, with 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 in [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 the 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 kinematic joint variables of the robot, called the measurement matrix [START_REF] An | Estimation of inertial parameters of rigid body links of manipulators[END_REF]. By using the same notations as in [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. The first ten parameters of θ i are called the inertial parameters for the link i, as indicated in [START_REF] Yoshida | Verification of the positive definiteness of the inertial matrix of manipulators using base inertial parameters[END_REF]. Then, θ is built by concatenating the θ i (i = 1, ..., n).

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 parameters' vector is called the base parameter vector, denoted by θ B , and contains n θ B components. Relation (2) can thus 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 keeping the robot integrity, it is better to excite 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 gain, is performed to follow a given trajectory in joint space that meets a number of desired requirements. In identification, the choice of the excitation signal is important, because it should "excites all the parameters" to identify. 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 [Gautier and Khalil, 1988], [Gautier and Khalil, 1991], [Lennart, 1971]. Moreover, the desired trajectory should be designed so that it is periodic during a long time range in order to ease the statistical analysis of the results [START_REF] Swevers | Dynamic model identification for industrial robots[END_REF], each period being built to be a PES and the number of periods should be greater than n. Finally, the amplitudes of the PES should be within an allowable range of motion, in order to comply with the robot safety limits, and it should maximize the Signal-to-Noise-Ratio (SNR) for each measured output signal needed for the robot identification.

One can easily design such PES with the requested properties and uses them for the robot identification as desired trajectories for the joint positions. If the proportional gains of the position feedback control are high enough, then the tracking errors between the measured and the desired joint positions become small enough to ensure that the measured positions will have properties close to the ones of the desired trajectories.

Signal processing

In general, the measured (joint torques and positions) and computed (joint velocities and accelerations) data are noisy.

These data can not be directly used in identification because of the closed-loop feedback control that might create correlations between the noises and the signals of the closed-loop system. This can introduce some unknown biases in the values of the identified parameters [START_REF] Brunot | A pragmatic and systematic statistical analysis for identification of industrial robots[END_REF]. To avoid this undesirable effect, the data are filtered before being used by the estimation algorithms. This is done off-line thanks to a low-pass filter with a unit gain at low frequencies and a frequency cut-off set a decade after the highest existing frequency in the desired trajectories. In practice, a forward plus backward filtering of the noisy data is performed in order to get a zero-phase filtering of these data. 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. Given a periodic signal in discrete time, denoted by x(k), with P full periods and K samples per period. The average period of x(k), denoted by x(k), is obtained through the relation

x(k) = 1 P p=P ∑ p=1 x(k + K(p -1)). (5)
Finally, it may sometimes be useful to undersample the data if the sampling frequency is too high compared to the frequency bandwidth of interest.

Let q and τ be the joint positions and torques after applying the whole signal processing described before; q and q are the resulting joint velocities and accelerations, suitably computed by numerical differentiation. The data are assumed to check the following relation at sample time k, derived from ( 4)

τ(k) = D B q (k) , q (k) , q (k) θ B + ρ (k) , ( 6
)
where ρ is an (n × 1) vector of error terms, gathering the noises and the unmodelled dynamics. It is assumed to have a zero-mean, and uncorrelated samples. The sets of N samples retained 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, ( 6) leads to

Y = W θ B + R, (8)
which is an overdeterminated set of linear equations in the unknown parameters in θ B .

The conditioning number associated with the regressor matrix W allows to measure the sensitivity of the solution θ B to the noises affecting the measurements of τ, q and eventually q and q. Therefore, the post-processed data should reduce the conditioning number, to ensure the convergence of the identification process towards an unbiased vector of parameters [Gautier andKhalil, 1991, Janot et al., 2014].

Estimation of the base parameter vector

For a full rank regressor matrix W , and a zero-mean additive independent Gaussian noise for R, an estimation θB of θ B can be obtained by solving the following WLS minimization problem [START_REF] Swevers | Dynamic model identification for industrial robots[END_REF]:

θB = arg min θ B W T Σ -1/2 (Y -W θ B ) 2 (9)
whose optimal solution is given by

θB = CW T Σ -1/2 Y, (10)
where Σ denotes the covariance matrix of the actuator torque data and C := W T Σ -1/2 W -1 is the covariance matrix of the estimated parameters' vector. The matrix Σ is a block diagonal matrix composed of N matrices of dimension (n × n) and denoted Σ k , corresponding to the covariance matrix of the actuator torques computed at the sample time k. Its expression is given by:

Σ k = 1 (P -1) P ∑ p=1 T p (k) -τ (k) T p (k) -τ (k) T , (11)
where T p (k) stands for the p th period at the sample time k of the torque measurements τ, on which has been applied only the filtering and the decimation steps. The computation of θB using the relation ( 10) is very tractable, but this solution does not ensure that the corresponding inertial matrix is positive definite. In the sequel, we consider this additional constraint to the problem in (9), which becomes:

θB = arg min θ B W T Σ -1 (Y -W θ B ) 2
such that M(q, θB ) > 0 ∀q. The problem (12) consists in minimizing the squared norm of the weighted error between the measured and computed joint torques, under the constraint that the corresponding inertia matrix is always positive definite, i.e. 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 constraints on physical parameters of the links composing the manipulator, lead to an inertia matrix which is positive definite. The link constraints in [START_REF] Yoshida | Verification of the positive definiteness of the inertial matrix of manipulators using base inertial parameters[END_REF] are:

m i > 0, i = 1, ..., n i I g i > 0, ( 13
)
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 , (14)
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.

Let us denote the link inertial parameters mentioned in subsection 2.1 by θ I i . The base parameters vector θ B is a function of θ I i , Fs i and Fv i (i = 1, . . . , n), whose expression can be derived analytically. Hence,

θ B = f {θ I i , Fs i , Fv i } i=1,...,n . (15)
Let us define the link physical parameters θ P i as the vector whose components are the elements of i I g i , r i and m i . Some components of θ I i are also included in θ P i , like m i . However, other components of θ I i depend linearly (like mr i ) or nonlinearly (like i I i ) in the components of θ P i . By denoting h the general relation derived from ( 14), between the vectors θ I i and θ P i , it follows:

θ I i = h(θ P i ), i = 1, . . . , n. (16)
Using the relations ( 15) and ( 16), the base parameters vector θ B can be rewritten as a nonlinear function, denoted by g, of

ϑ i T := θ P i T Fs i Fv i : θ B = g({ϑ i } i=1,...,n ). (17)
According to [START_REF] Yoshida | Verification of the positive definiteness of the inertial matrix of manipulators using base inertial parameters[END_REF], to have a positive definite inertia matrix, it is sufficient that all m i and i I g i contained in the equation ( 17) satisfy the condition (13). However, the set of admissible m i and i I g i is not unique. In [START_REF] Yoshida | Verification of the positive definiteness of the inertial matrix of manipulators using base inertial parameters[END_REF], it is called virtual parameters. The problem ( 12) is transformed into a Constrained WLS (CWLS) optimization new problem in the unknown parameter vector

ϑ T = ϑ 1 T • • • ϑ n T : 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. (18)
The constraint on the estimated inertia tensor matrix is equivalent for this last to have all its eigenvalues positive. The estimated values of Fs i and Fv i can only be positive, which justifies the addition of constraints on these parameters in (18). To finish the procedure, the estimated vector θ is substituted into (17) to obtain the corresponding estimation of the base parameter vector θB , needed to build the estimated inertia matrix.

Validation

To check the validity of the estimated parameters by the proposed procedure, these parameters are used to reconstruct the joint torques which are compared with the measured ones. For this purpose, the post-processed kinematic joint variables are used as inputs for the inverse dynamic model in (2) with the estimated parameters. This validation step is necessary to have an information about the confidence interval of the estimated parameters, and at the same time, about the model validity.

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 Fig. 1. A force sensor is fixed between a spherical handle, devoted to PHRI experiments, and the end-effector. The dynamic model is computed by 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.

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
Table 1 shows the MDH parameters of the Denso VP-6242G robot, extracted from Fig. 2. By using the SYMORO+ software package [Khalil andCreusot, 1997, Khalil et al., 2014] with these parameters, the dynamical model of the robot for the identification is obtained. The base parameters vector θ B is of dimension (48 × 1), and the regressor matrix D B is of dimension (6 × 48).

Table 1: Kinematic parameters of the Denso robot.

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, randomic 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 has been taken greater than the number of base parameters to identify in order to ensure the PES's feature [Walter andPronzato, 1997, Lennart, 1971]. In addition, the higher frequency was constrained by the limit frequency, defined by:

f i = A q,i 2πA q,i ,
where A q,i and A q,i are the maximum allowed amplitudes for the joint position and velocity of the joint 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 given in the Denso Robot datasheet, that gives a relation between positioning time and motion angle, for a given load carried by the end-effector. To enhance the estimation reliability, the periodic excitation signals have been built with 12 periods, with 380 sec per period, and a sampling time of 10 -3 sec. The duration of one period depends on the fundamental frequency and on the limit frequency.

Each initial joint position is set to the center of its corresponding joint motion range. In addition, the movement starts and stops with zero joint velocities and accelerations. For this, a phase of immobility of 4 sec is appended at the beginning and at the end of the periodic signals. During these phases, the robot remains at the initial position. A connection phase of 5 sec is also appended to connect the initial joint positions of the robot with the excitation signals. The total excitation time is 4578 sec. Table 2 presents the joint motion range [q i,m , q i,M ], the amplitudes A q,i and A q,i , the limit frequency f i , and the proportional gain K p i of the joint-position controller for each axis J i .

Table 2: Parameters used to generate the inputs.

Axis [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 the 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 zero-phase filtering through a low-pass Butterworth filter of order 1 with a cut-off frequency set to 10 Hz. Joint velocities and accelerations are computed by a suitable numerical differentiation of the filtered joint positions. To reduce the noises due to numerical differentiation, the resulting velocity and acceleration signals are also filtered in the same way. In a third step, the data corresponding to the phases of immobility and connection are withdrawn in order to keep only the periodic parts of the data. The data are then averaged over the 12 periods. In a last step, since the sample frequency (10 3 Hz) is higher than the filter cutoff frequency (10 Hz), the data are undersampled with a factor of 10, which reduce the size of the useful data, but also the sample frequency of these data to 10 2 Hz. This frequency remains comfortably higher than the highest frequency contained in the filtered data (Tab. 2). Hence, the data should not be affected a lot by this decimation factor. A zoom between the instants 1200 and 1400 sec of the signals of measured joint position and torque, and calculated velocity and acceleration of the joint 1, before (blue) and after (red) filtering are shown by the figure 3. We can observe that the noisy measurements are correctly filtered. We conclude that the choice of the filter parameters (cut-off frequency and order) is adequate. The important error in the joint acceleration signal is interpreted by a significant noise associated with this signal, as it results from a double differentiation of the joint position.

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

Parameters estimation

Once the regressor matrix W , the covariance matrix of the torque data Σ and the torque vector Y has been constructed, the condition number of W was checked as well as its full rank feature. In the case of the VP-6242G Denso robot, ϑ is of dimension (66 × 1). The estimation of the parameter vector ϑ was performed by solving the CWLS optimization problem in (18). For this, we used the Matlab function fmincon that allows to find a minimum solution of the constrained nonlinear multivariable problem.

The table 4 shows two sets of numerical values of the base parameter vector θ B estimated by solving the WLS problem in ( 10) and the CWLS one in ( 17) & ( 18). The third column of the table presents the standard deviation σ of the estimated parameter vector, defined as the squared root of the diagonal elements of the matrix C.

The standard deviation σ of each parameter in Tab. 4 is small enough compared to the corresponding estimated value. It means that we can be confident in the parameter estimation.

The table 5 shows, for each link i, the virtual mass m i and the minimum eigenvalue of the virtual inertia tensor matrix i I g i .

This table shows that the condition ( 13) is satisfied, ensuring a positive definite inertia matrix derived from the estimated parameters.

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 set of measurement than the one exploited for the identification is used. These new data were obtained by using a new input signal but with the same features as the one used for the identification (PES + periodic. . . ). The feedback control is used with the same proportional gains. The obtained signals are different compared to those obtained during the identification. The post-processed joint torques are compared with those resulting from the application of the corresponding joint variables (q, q and q) on the dynamical model of the robot, using the identified parameters. In Fig. 4, the measured torques after filtering are compared with those calculated using the identified parameters.

The figures in Fig. 4 illustrate a good quality of reconstruction of the torques. 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. To this end, we used a nonlinear weighted least squares formulation of the identification problem under nonlinear constraints in the dynamic parameters. The identified parameters and the dynamic model of the robot were 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 [Jlassi et al., 2014]. [ 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). Direct calculation of minimum set of inertial parameters of serial robots. IEEE Trans. on Robotics and Automation, pages 368-373.

[Gautier and Khalil, 1991] Gautier, M. and Khalil, W. (1991). Exciting trajectories for the identification of base inertial parameters of robots. In Proc. of the IEEE Conf. on Dec. and Ctrl. (CDC), pages 494-499.

[Janot et al.

Figure

  Figure 1: VP-6242G Denso robot.

Figure 2 :

 2 Figure 2: Robot frames for MDH convention.

Figure 3 :

 3 Figure 3: Data for axis 1 before (blue) and after (red) filtering (left), and the corresponding signal errors (right).

Figure 4 :

 4 Figure 4: The filtered measured and computed torques.

  , 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-IntegratedManufacturing, 31:21-29. [Jlassi et al., 2014] Jlassi, S., Tliba, S., and Chitour, Y. (2014). An event-controlled online trajectory generator based on the human-robot interaction force processing. Industrial Robot: An International Journal,

Table 3 :

 3 Features of the motors of the Denso VP-6242G robot

		135, +135]	135	±168.7882 0.1989 1.2838
	J 2	[-45, +90]	67.5	±126.4223 0.2981 1.6683
	J 3	[-90, -40]	25	±168.3147 1.0715 4.4711
	J 4	[-155, +155]	155	±202.1053 0.2075 1.3116
	J 5	[-90, +90]	90	±205.1282 0.3627 1.7577
	J 6	[-160, +160]	160	±203.6364 0.2025 1.6678

Table 4 :

 4 Numerical values of θ B and standard deviation of parameters σ . Fv 6 15.74 15.51 7.91e -3

	θ B CWLS WLS	σ	θ B CWLS WLS	σ
	zzr 1	7.10	9.05 3.64e -2 yz 4 -0.06 -0.07 2.83e -3
	Fs 1 49.75 49.38 7.68e -3 zzr 4	0.06 -0.86 5.71e -3
	Fv 1 150.81 151.39 2.78e -2 mx 4	0.30	0.24 7.84e -4
	xxr 2 -5.96 0.20 4.46e -2 myr 4 0.20	0.20 6.08e -4
	xy 2 -1.01 -1.22 2.15e -2 Fs 4 24.63 24.62 4.75e -3
	xzr 2 -1.17	-1	1.35e -2 Fv 4 21.55 21.17 1.13e -2
	yz 2 -0.97 -0.81 2.19e -2 xxr 5 0.22	0.29 4.87e -3
	zzr 2 17.29 17.71 2.56e -2 xy 5	0.01	0.013 2.42e -3
	mxr 2 18.67 18.77 2.54e -3 xz 5 -0.02 -0.01 1.73e -3
	my 2	0.28	0.31 1.22e -3 yz 5	0.01	0.01 2.06e -3
	Fs 2 63.64 64.61 1.12e -2 zzr 5	0.56	0.59 1.96e -3
	Fv 2 185.75 180.34 4.80e -2 mx 5	0.13	0.13 4.58e -4
	xxr 3 9.04 -0.32 2.89e -2 myr 5 2.12	2.11 4.79e -4
	xyr 3 0.41	2.27 1.91e -2 Fs 5 20.45 20.40 3.79e -3
	xz 3	0.05	0.10 5.68e -3 Fv 5 29.29 29.12 9.64e -3
	yz 3	0.04	0.04 5.97e -3 xxr 6 -0.07 -0.08 2.34e -3
	zzr 3	4.37	4.20 4.14e -3 xy 6	0.03	0.03 1.24e -3
	mxr 3 -5.16 -4.98 1.24e -3 xz 6	0.02	0.02 1.27e -3
	myr 3 8.77	8.79 1.30e -3 yz 6	0.00	0.00 1.36e -3
	Fs 3 54.78 54.87 8.10e -3 zz 6	0.00	0.05 2.29e -3
	Fv 3 87.92 86.78 2.95e -2 mx 6	0.10	0.10 4.04e -4
	xxr 4 -0.21 0.13 7.32e -3 my 6 -0.05 -0.05 3.51e -4
	xy 4	0.19	0.19 3.34e -3 Fs 6 19.08 19.11 3.91e -3
	xz 4	0.23	0.21 2.81e -3

Table 5 :

 5 Checking of the constraints in (13).

	Link	1	2	3	4	5	6
	λ min	i I g i	0.01 0.01 0.01	0.01 0.01 0.01
	m i	6.22 2.07 17.99 20.95 1.93 38.45

Université Paris-Sud XI UFR des Sciences d'Orsay

Laboratoire des Signaux & SystèmesPôle Automatique & Systèmes


Dr Paco Bustamante

C Garrigue

L Breau

F Caurant

W Dabin

J Greaves

R Dodemont

Trace elements in two odontocete species (Kogia breviceps and Globicephala macrorhynchus) stranded in New Caledonia (South Pacific)

Keywords: Heavy metals, Cadmium, Mercury, Nickel, Marine Mammals, Pacific Ocean

liver, muscle and blubber tissues of two short-finned pilot whales (Globicephala macrorhynchus) and two pygmy sperm whales (Kogia breviceps) stranded on the coast of New Caledonia have been analysed for 12 trace elements (Al, Cd, Co, Cr, Cu, Fe, organic and total Hg, Mn, Ni, Se, V, and Zn). Liver was shown to be the most important accumulating organ for Cd, Cu, Fe, Hg, Se, and Zn in both species, G. macrorhynchus having the highest Cd, Hg, Se and Zn levels. In this species, concentrations of total Hg are particularly elevated, reaching up to 1452 µg.g -1 dwt. Only a very low percentage of the total Hg was organic. In both species, the levels of Hg are directly related to Se in liver. Thus, a molar ratio of Hg:Se close to 1.0 was found for all specimens, except for the youngest K. breviceps. Our results suggest that G. macrorhynchus have a physiology promoting the accumulation of high levels of naturally occurring toxic elements. Furthermore, concentrations of Ni, Cr and Co are close to or below the detection limit in the liver and muscles of all specimens. This suggests that mining activity in New Caledonia, which typically elevates the levels of these contaminants in the marine environment, does not seem not to be a significant source of contamination for these pelagic marine mammals.

INTRODUCTION

Heavy metals generally occur at very low concentrations in oceans [START_REF] Bryan | Pollution due to heavy metals and their compounds[END_REF].

Nevertheless, most of marine organisms concentrate trace elements at higher concentrations than those occurring in their environment. This process, currently described as bioaccumulation, concerns toxic elements such as Cd or Hg, as well as essential ones such as Cu, Fe, Se, or Zn. Slight variations of heavy metal concentrations in the environment of marine organisms could lead to a significant increase of their metal burdens. Enrichment of sea water in heavy metals may occur naturally by local environmental processes, such as volcanism or upwellings. In addition to this natural origin, human activities can lead to increases of trace element concentrations in coastal waters, subsequently leading to an increase of metal burdens in biota.

In New Caledonia, mining activities plus strong natural erosion due to tropical rainfall have resulted in enrichment of several metals in coastal waters (mainly Co, Cr, Fe and Ni), and consequently in the coral reef food webs [START_REF] Monniot | Cellular sites of iron and nickel accumulation in ascidians related to the naturally and anthropic enriched New Caledonian environment[END_REF]). These authors reported high metal burdens in several species of filter-feeding ascidians from shallow waters. However, the impact of metal contamination does not appear to be limited to coastal waters and, in fact, high levels of Co, Cr and Ni have also been reported in the tissues of a cephalopod living in deeper waters, the nautilus, Nautilus macromphalus [START_REF] Bustamante | Bioaccumulation of 12 trace elements in the tissues of the nautilus Nautilus macromphalus from New-Caledonia[END_REF].

Current literature on heavy metal concentrations in New Caledonian marine lower trophic level organisms is scarce (e.g. [START_REF] Monniot | Cellular sites of iron and nickel accumulation in ascidians related to the naturally and anthropic enriched New Caledonian environment[END_REF][START_REF] Bustamante | Bioaccumulation of 12 trace elements in the tissues of the nautilus Nautilus macromphalus from New-Caledonia[END_REF], and no data for marine mammals have been published to date. In this work, baseline information is presented for the concentrations of 12 trace elements in the tissues and organs of two odontocetes species, i.e., pygmy sperm whale, Kogia breviceps (de Blainville, 1838), and short-finned pilot whale, Globicephala macrorhynchus (Gray, 1846) for which very few information on trace elements are available. These marine mammals give the opportunity to investigate the impact of mining activities on high trophic level organisms stranded in New Caledonia. It also provides information on the bioaccumulation and detoxification processes of Cd and Hg in marine mammals from a tropical zone, toxic elements which are currently reported to raise the question of physiological damages in the tissues of top marine predators.

MATERIALS AND METHODS

Sampling and sample preparation

In spring 1997, two short-finned pilot whales (Globicephala macrorhynchus) and two pygmy sperm whales (Kogia breviceps) stranded on the coasts of New Caledonia. These animals were autopsied shortly after death. Stomach contents were collected and stored in 90% ethanol for later diet analyses. Teeth were extracted for ageing and skin samples were collected for genetic analysis. Tissues and organs (liver, blubber and muscle) were sampled for heavy metal and radionuclides analyses [START_REF] Garrigue | Impact of the human activities in short-finned pilot whales (Globicephala macrorhynchus) and pygmy sperm whale (Kogia breviceps) of the South West Pacific ocean by mesuring Cs-137, K-40 and Pb-210[END_REF]. Separated tissue samples were placed in decontaminated glass vessels and stored at -20°C. They were then freezedried, finely ground and stored in plastic vials.

The two stranded G. macrorhynchus were probably part of a bigger pod observed in the vicinity of the stranding location on the day of stranding. This species is commonly encounter outside of the lagoon by long liners in both nearshore and pelagic environments but there is no evidence that they are resident in the area. In fact, seasonal inshore to offshore movements are related to the distribution of squid they feed on (Olson and Reily 2001).

Little is know on the status of K. breviceps in New Caledonia as they are very discrete animals, rarely observed alive. Most of the information on this species come from stranded animals which have been documented earlier in New Caledonia [START_REF] Robineau | Sur deux spécimens du genre Kogia (Cetacea, Physeteridae) en Nouvelle-Calédonie[END_REF][START_REF] Sylvestre | On a specimen of pygmy sperm whale Kogia breviceps (Blainville, 1838) from New Caledonia[END_REF].

Age determination

Teeth were used for age determination, following the recommendations of Neilsen (1972) and [START_REF] Perrin | Age determination of toothed whales and sirenians[END_REF]. Teeth taken up from the lower jaw were cleaned, fixed and stored in 70% glycerined alcohol. Before sectioning and staining, teeth were decalcificated with DC3 (Labonor©). Sections were then examined to count the growth layer groups (GLGs) assuming 1 GLG equals 1 years, as described by [START_REF] Perrin | Age determination of toothed whales and sirenians[END_REF]. Three series of several independent readings were done for each tooth section according to [START_REF] Hohn | Bias in dolphin age structure due to age estimation technique[END_REF]. All readings were recorded to the nearest whole year and age was expressed as mean ± SD for each individual.

Stomach contents analysis

Stomach contents were washed and the contained elements were sorted by type. Fish species were determined from the otoliths by J. Rivaton from the laboratory of marine biology of IRD (Nouméa, New Caledonia). Cephalopod species were determined from the beaks by Dr R.

Young from the University of Hawaii.

Metal analysis

Metal analyses were performed by inductively coupled plasma atomic emission spectrophotometry (ICP-AES) for Al, Co, Cr, Cu, Fe, Mn, Ni, V and Zn, by atomic absorption spectrophotometry (AAS) for Cd, Cu, Se and Zn, and with an Advanced Mercury Analyser (AMA) for total and organic Hg after extraction.

For ICP-AES measurements, 2 aliquots of approx. 500 mg of each homogenised dry sample were digested in Teflon containers with 4 ml of 65% HNO 3 and 1 ml of 30% H 2 O 2 using a microwave digester (ANTON-PAAR, Perkin Elmer). The digested contents were made up to 25 ml with Milli-Q quality water. Elements were analysed by ICP-AES with an OPTIMA 3200 DV, Perkin-Elmer. Multicomponent Spectral Fitting Models were used to correct for spectral interference between elements.

For AAS measurements, 2 aliquots of approx. 300 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 AMA measurements, aliquots ranging from 10 to 50 mg of dried material were analysed directly for total Hg in a Advanced Mercury Analyser spectrophotometer (Altec AMA 254).

Hg determination involved evaporation of Hg by progressive heating until 800°C was reached and then held under oxygen atmosphere for 3 min, and subsequent amalgamation on a Au-net.

Afterwards, the net was heated to liberate the collected mercury, subsequently measured by UV atomic absorption spectrophotometry. The same procedure was performed for the analysis of organic Hg after extraction adapted from [START_REF] Uthe | Rapid semimicro method for the determination of methyl mercury in fish tissue[END_REF]. Organic Hg was extracted from 2 aliquots of approx. 500 mg of each homogenised dry sample using 2 ml of acidic sodium bromide (30% NaBr in 4N H 2 SO 4 ), 4 ml of cupric sulfate (2.5% CuSO 4 in milli-Q quality water) and 10 ml of toluene under agitation for 10 min in glass flasks. The organic phase was then separated and used for the analysis in the AMA.

Quality control was assured using dogfish liver DOLT-2 (NRCC) and dogfish muscle DORM-2 (NRCC) as reference materials for AAS and AMA, and dogfish muscle DORM-1 (NRCC) for ICP-AES. These standards were treated and analysed under the same conditions as the samples. The results were in good agreement with the certified values (Table 1).

Detection limits (µg.g -1 ) were 0.004 for Cd, 0.5 for Cu, 3 for Zn, 0.8 for Se, 0.005 for total Hg and 0.2 for organic Hg for AAS and AMA analyses. For ICP-AES analyses, detection limits were 0.006 for Al, 0.040 for Co, 0.013 for Cr, 0.005 for Cu, 0.051 for Fe, 0.002 for Mn, 0.010 for Ni, 0.009 for V and 0.008 for Zn (µg.g -1 ). Metal concentrations in tissues are reported in µg.g -1 dry wt.

RESULTS

Main features, age and diet

The main features of the 4 specimens sampled, one male and one female G. macrorhynchus and one male and one female K. breviceps, are reported in Table 2, with the prey species identified from their corresponding stomach contents and their ages. Considering their ages, the two G. macrorhynchus may have been sexually matured as sexual maturity occurred at 9 years for females and between 13 and 16 for males [START_REF] Olson | Pilot whales[END_REF]. Considering K. breviceps,, the size of sexual maturity have been documented to be 2.7m to 3.0m for males and 2.6 to 2.8m for females of (Leatherwood et al., 1983). Furthermore, K. breviceps appears to reach sexual maturity between 3 and 5 years old (Plön, in prep.). In the light of this data the two K. breviceps presented in this paper may have been sexually matured.

All the animals with the exception of the male K. breviceps were already stranded when samples were collected. This last one was first alive, but it has been euthanasied after the failure of its refloat. The autopsies didn't provide any evident reasons for the death of the animals. Parasites were only found in great quantity in the male K. breviceps, with a stomach full of Anisakis simplex (Nematodes). This specimen could have suffered of a parasitose, stranded individuals from this species being frequently heavily infected by intestinal nematodes (McAlpine, 2002).

On the other hand, the female G. macrorhynchus was probably pregnant before the stranding as part of a foetus was found in its vicinity. This female may have been fasting as its stomach was empty (Table 2).

Metal analysis

Heavy metal and organic mercury concentrations in the liver, muscle and blubber of G. macrorhynchus and K. breviceps are presented in Table 3. Co, Cr and Ni concentrations in all tissues and organs fall below the detection limit or close to it (i.e. in liver). Among these tissues, liver is the most important accumulating organ for Cd, Cu, Fe, Hg, Se, and Zn and to a lesser extent for Mn and V. However, the two G. macrorhynchus exhibit higher hepatic levels for Cd, Cu, Hg, Se and Zn than K. breviceps while both species have similar hepatic levels of Mn and V. Fe is the only metal having higher concentrations in the liver of K.

breviceps than in the one of G. macrorhynchus.

In muscle, Mn in G. macrorhynchus and V in both mammals are below the detection limits.

The remaining trace elements were within the same order of concentration in the muscle of both species (Table 3). The only exception was Hg, where concentrations were 5 times higher in G. macrorhynchus muscle compared to K. breviceps.

Blubber has generally low trace element concentrations. However, Cr exhibits the highest concentrations among the three tissues (Table 3). Despite its strong affinity to lipids, organic Hg concentrations in blubber were an order of magnitude lower than in liver and muscle.

Figure 1 shows the hepatic concentrations of inorganic Hg and Se of marine mammals in relation to age together with the inorganic Hg:Se molar ratio for each individual. In both species, hepatic inorganic Hg is directly related to hepatic Se. Consequently, a molar ratio close to 1.0 is found in all specimens, except for the youngest K. breviceps (6 years old) for which this ratio was 0.13 (Figure 1). Nevertheless, both species exhibit very different ratio organic:total Hg in their tissues (Figure 2) with K. breviceps showing a higher percentage of organic Hg than G. macrorhynchus in liver (aver. 13% vs 0.5 %) and in muscle (aver. 75 % vs 14 %).

DISCUSSION

Trace element levels

Heavy metal concentrations in the tissues of marine mammals are globally well documented but they concern mainly species having strong interactions with man, i.e. hunted for meat consumption, by-caught during fishing or living in coastal areas. Furthermore, very few studies have investigated trace elements such as Co, Cr, Ni or V although they are potentially toxic, probably because these trace elements are not bioaccumulated in large amounts in mammalian tissues [START_REF] Thompson | Heavy metals in marine vertebrates[END_REF]. Nevertheless, such elements can be used as tracers of contamination when an enrichment due to anthropogenic activities occurs. In Alaska, [START_REF] Mackey | Bioaccumulation of vanadium and other trace metals in livers of Alaskan cetaceans and pinnipeds[END_REF] have shown an increase of V in the tissues of pinnipeds and cetaceans. The bioaccumulation of V in biota and its transfer to the top marine predators has been related to the contamination of sea water by oil residues in this area. Similarly, the consequence of intense mining activities in New Caledonia must be monitored by the measurement of the concentrations of Ni and its associated elements, mainly Co and Cr, in the food webs around the island. Analysis in the tissues of the short-finned pilot whales Globicephala macrorhynchus and the pygmy sperm whales Kogia breviceps have not revealed any increase of concentrations for these three metals compared to other marine mammals species from various areas (Table 4). With the exception of Cr in the blubber of the male G. macrorhynchus (2.51 µg.g -1 dwt), concentrations remained close to or below the detection limits. Considering that these pelagic animals could have preyed on species living around the island as suggested by the examination of their full stomach, our results suggest that these metals are not easily transferred in the food web of these pelagic odontocetes. To assess the impact of mining activities on marine mammals, further studies should be conducted on more coastal species known to be resident of the impacted area, such as the bottlenose dolphin (Tursiops truncatus) or the dugong (Dugong dugon) that spend all their life in the waters of the New Caledonian lagoon.

Most of the studies on the bioaccumulation of trace elements in marine mammals have focused on toxic Cd and Hg, which are well bioaccumulated in mammalian tissues [START_REF] Thompson | Heavy metals in marine vertebrates[END_REF]). Nevertheless, numerous rare species have been poorly investigated and there is a lack of data for G. macrorhynchus and K. breviceps. Table 5 shows the paucity of information reported for these two species. The present study provides new information on metal concentrations in these marine mammals. The four odontocetes stranded in New Caledonia exhibited very high levels of Cd and Hg in liver, reaching 464 and 1452 µg.g -1 dwt, respectively. However, G. macrorhynchus displayed much higher concentrations of Cd and Hg than K. breviceps (Table 3).

Both species occupy a high and similar trophic levels (4.3 and 4.4 for G. macrorhynchus and K. breviceps, respectively), assessed by stable isotope analysis [START_REF] Pauly | Diet composition and trophic levels of marine mammals[END_REF]. They mainly prey upon squid although this may be implemented by a large proportion of fish for G. macrorhynchus (around 40%) and a lower one for K. breviceps (around 20%) in certain areas [START_REF] Pauly | Diet composition and trophic levels of marine mammals[END_REF]. The concentrations of Hg in the liver of G. macrorhynchus sampled in New Caledonia suggest that fish constitute an important prey items for this species as fish are considered to be the main Hg source for marine top predators [START_REF] Law | Trace metals in the livers of marine mammals from the Welsh coast and the Irish Sea[END_REF]. This was confirmed by the analysis of stomach contents showing several fish species in the diet of G. macrorhynchus (Table 2). However, no fish remains were found in the stomach contents of K. breviceps but its diet included several crustaceans species which are known to have very low Hg contents [START_REF] Cossa | Le mercure milieu marin. Biogéochimie et écotoxicologie[END_REF].

Similar exposures to Cd would occur for both species considering the high dietary intakes due to cephalopod consumption [START_REF] Bustamante | Cephalopods as a vector for the transfer of cadmium to top marine predators in the north-east Atlantic Ocean[END_REF]) that represent 60% and 75% of the diet of G. macrorhynchus and K. breviceps, respectively [START_REF] Pauly | Diet composition and trophic levels of marine mammals[END_REF]. Nevertheless, G. macrorhynchus had hepatic Cd concentrations of one order of magnitude higher than K. breviceps (Table 3). It appears from the scarce data available in the literature that K. breviceps generally have lower Cd concentrations than G. macrorhynchus (Table 5). This suggests that diet does not explain alone the high concentrations of Cd in the tissues of G. macrorhynchus and that a particular physiology promoting the accumulation of naturally occurring Cd could be envisage for this species.

Detoxification processes

Extremely high levels of toxic Hg and Cd may trigger cellular and physiological damages of the target organs, especially kidney [START_REF] Gallien | Cadmium-containing granules in kidney tissue of the Atlantic white-sided dolphin (Lagenorhyncus acutus) off the Faroe Islands[END_REF]. Despite the lack of the main storage organ for Cd analyses (i.e. kidney), Cd concentrations encountered here in liver suggest even higher concentrations in kidney as it is always the case in marine mammals [START_REF] Aguilar | Biological factors affecting variability of persistent pollutant levels in cetaceans[END_REF]. Renal dysfunction has been linked to Cd concentrations in liver exceeding 20 µg.g -1 wwt (approx. 100 µg.g -1 dwt) [START_REF] Honda | Studies on bioaccumulation of heavy metals in marine mammals[END_REF][START_REF] Fujise | Tissue distribution of heavy metals in Dall's porpoise in the northwestern Pacific[END_REF]. G. macrorhynchus had Cd concentrations in liver far higher than that limit (i.e. 225 and 464 µg.g -1 dwt), while the livers of K. breviceps were clearly below that limit (Table 3). Thus, Cd detoxification processes should be particularly efficient in the liver and kidney of G. macrorhynchus to support such high concentrations and needs to be investigated further.

Marine mammals are exposed to methyl Hg through fish consumption, but only a small fraction of the total Hg in liver and muscle of G. macrorhynchus was found to be organic Hg, i.e. <1% and <15% of the total Hg, respectively (Fig. 2). This is far below the percentage of organic Hg to total Hg that is usually found in these tissues of adult marine mammals, which generally ranges from 3 to 20% for liver and from 70 to 95 % for muscle [START_REF] Caurant | Mercury in pilot whales: possible limits to the detoxification process[END_REF][START_REF] Wagemann | Methylmercury and total mercury in tissues of arctic marine mammals[END_REF]. [START_REF] Gaskin | Mercury, DDT, dieldrin, and PCB in two species of Odontoceti (Cetacea) from St Lucia, Lesser Antilles[END_REF] also reported values ranging from 2 to 17 % for organic Hg in the liver of G. macrorhynchus from the Lesser Antilles, but muscle had only 42 to 60% of total Hg in the organic form. Therefore, organic Hg concentrations in liver and muscle of G. macrorhynchus from New Caledonia are relatively similar to those from Lesser Antilles [START_REF] Gaskin | Mercury, DDT, dieldrin, and PCB in two species of Odontoceti (Cetacea) from St Lucia, Lesser Antilles[END_REF]. Apparently, the low fraction of hepatic organic Hg appear to be due to very high total Hg concentrations. However, such a low organic fraction in muscle of G. macrorhynchus from New Caledonia remains questionable. It has been suggested that residual mercury could be mobilised and concentrated from muscle and blubber in other tissues prior to death in G. macrorhynchus from the Cumberland Islands [START_REF] Stoneburner | Heavy metals in tissues of stranded short-finned pilot whales[END_REF]. This author explained that a stress period, viz. fast, could lead to such remobilization. The very low percentages of organic Hg in blubber support this speculation.

It is noteworthy that K. breviceps preferentially feeding on cephalopods and shrimp (Table 2), had concentrations of organic Hg in their tissues similar to that of G. macrorhynchus.

Cephalopods and shrimp displayed lower methyl Hg contents than fish, i.e. from 29 to 55% vs 53 to 94%, respectively [START_REF] Cappon | Chemical form and distribution of mercury and selenium in edible seafood[END_REF]. Compared to G. macrorhynchus, higher percentages of organic Hg in the tissues of K. breviceps related to lower total Hg contents in liver could be explained by a lower rate of hepatic demethylation. Low percentages of methyl Hg in liver have been reported for many marine mammals species (e.g. [START_REF] Itano | Mercury and selenium levels in striped dolphins caught off the Pacific coast of Japan[END_REF][START_REF] Wagemann | Methylmercury and total mercury in tissues of arctic marine mammals[END_REF]. This supports the idea of continuous demethylation of methyl Hg occurring in liver throughout the animal's life span, subsequently leading to 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 delmethylation 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 localization 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 [START_REF] Koeman | Mercury selenium 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] Law | Metals and organochlorines in tissues of a Blainville's beaked whale (Mesoplodon densirostris) and a killer whale (Orcinus orca) stranded in the United Kingdom[END_REF][START_REF] Wagemann | Methylmercury and total mercury in tissues of arctic marine mammals[END_REF]. G. macrorhynchus and K. breviceps from New Caledonia had a Hg:Se molar ratio close to 1 and a low percentage of organic Hg in liver (Fig. 1 &2). This suggests the presence of tiemannite granules as a result of demethylation of organic Hg in liver. However, the youngest K. breviceps, a 6 years old male (Table 2), had a low hepatic Hg:Se ratio due to low total Hg concentrations. This specimen also exhibited an elevated percentage of hepatic organic Hg (Fig. 2). [START_REF] Palmisano | Speciation of mercury in dolphin liver : a two-stage mechanism for the demethylation accumulation process and role of selenium[END_REF] have shown that demethylation of Hg by Se is efficient reaching a threshold Hg concentration of 100 µg.g -1 wwt (approx. 500 µg.g -1 dwt) in the liver of the dolphin Stenella coeruleoalba. Although this threshold should be different from one species to another, it clearly appears that the young K. breviceps had Hg concentrations far below such a threshold.

CONCLUSION

The present study provides new information on trace elements concentrations in the tissues of two rare marine mammals species from a tropical area. Very low Ni, Co and Cr concentrations in the tissues of G. macrorhynchus and K. breviceps suggest that industrial extracting activities in New Caledonia does not represent a significant source of contaminants for these two particular species. On the other hand, very high Cd and Hg concentrations in the liver of these marine mammals were related to cephalopod and fish consumption. Interspecific differences in the bioaccumulation, i.e. highest Cd and Hg concentrations in G. macrorhynchus, remain questionable and should be related to the physiology of this species. Muscle 3.60 ± 0.33 0.57 ± 0.04 < dl < dl 0.9 ± 0.0 820 ± 12 5.16 ± 0.13 3.75 ± 0.11 0.12 ± 0.02 < dl 3 ± 0 < dl 67.1 ± 0.9 dl : detection limit. wet : dry wt ratio are 4.5, 4.0 and 1.6 for liver, muscle and blubber, respectively.

Figure 1 .

 1 Figure 1. Concentrations of inorganic Hg (x) and Se (q) together with Se:Hg molar ratio (v) in G. macrorhynchus and K. breviceps from New Caledonia.

Figure 2 .

 2 Figure 2. Percentage of organic Hg in the muscle (striped), liver (white) and blubber (grey) of G. macrorhynchus and K. breviceps from New Caledonia.

Table 2 .

 2 Characteristics of the odontocetes and preys identified in their stomach contents. Age is the mean ± SD of 3 counting of growth layer groups.

	Species	Sex	Length (m)	Age	Prey identified in the stomach content
					Fishes :
					Bathyclupea malayana (Bathuclupeidae)
					Antigoniia sp. (Caproidae)
					Synagrops sp. (Acropomatidae)
					Diaphus sp. (Myctophidae)
					Cubiceps sp. (Nomeidae)
	Globicephala macrorhynchus	♂	5.4	14 ± 1	Chlorophthalmus sp.(Clotophthalmidae) Cephalopods : Stenoteuthis sp. (Ommastrephidae)
					3 unidentified species (Ommastrephidae)
					Moroteuthis sp. (Onychoteuthidae)
					Lycoteuthis sp. (Lycoteuthidae)
					Histioteuthis sp. (Histioteuthidae)
					5 unidentified species (Histioteuthidae)
		♀	3.5	12 ± 2 Empty stomach
					Shrimps :
					Pasiphea sp. (Pasiphaeidae)
					Gnathophausia ingens (Mysidacea)
		♂	3.1	6 ± 1	Meningodora sp. (Oplophoridae) Cephalopods :
					Histioteuthis sp. (Histioteuthidae)
					Enoploteuthis sp. (Enoploteuthidae)
					2 unidentified species
	Kogia breviceps				Shrimps :
					Pasiphea sp. (Pasiphaeidae)
					Gnathophausia ingens (Mysidacea)
					Meningodora sp. (Oplophoridae)
		♀	3.0	19 ± 3	Cephalopods :
					Taonius sp. (Cranchidae)
					Histioteuthidae
					Enoploteuthidae
					Octopoteuthidae

Table 3 .

 3 Age and metal concentrations (µg.g -1 dwt) in the tissues of odontocetes from the New Caledonia.

	Tissue	Age	Al	Cd	Co	Cr	Cu	Fe	Total-Hg Organic-Hg	Mn	Ni	Se	V	Zn
	Globicephala macrorhynchus ♂	14 ± 1
	Liver		1.38 ± 0.45 225.3 ± 0.4	< dl	< dl	37.4 ± 0.3	1472 ± 7	1411 ± 24	11.7 ± 0.4	7.1 ± 0.2	< dl	627 ± 43	0.06	135.7 ± 0.6
	Muscle		2.62 ± 0.69 0.79 ± 0.03	< dl	< dl	0.8 ± 0.1	347 ± 29	32.8 ± 2.0 4.41 ± 0.09	< dl	< dl	9 ± 1	< dl	61.1 ± 2.4
	Blubber		1.53 ± 0.14 0.95 ± 0.03	< dl	2.51 ± 0.01	0.4 ± 0.1	187 ± 8	11.0 ± 0.8 0.47 ± 0.05 0.17 ± 0.01	< dl	4 ± 1	< dl	21.3 ± 0.3
	G. macrorhynchus ♀	12 ± 2
	Liver		1.07 ± 0.11 464.4 ± 5.4	0.04	< dl	51.0 ± 1.3	1535 ± 17	1452 ± 79 1.70 ± 0.01	6.8 ± 0.2	< dl	758 ± 39	0.10	113.3 ± 2.1
	Muscle		0.88 ± 0.26 1.48 ± 0.03	< dl	< dl	1.5 ± 0.1	622 ± 78	27.3 ± 1.1 3.29 ± 0.06	< dl	< dl	6 ± 1	< dl	49.8 ± 1.4
	Blubber		1.15 ±0.00 0.84 ± 0.01	< dl	0.32 ± 0.08	0.2 ± 0.1	18 ± 2	3.20 ± 0.22 0.21 ± 0.02	< dl	< dl	3 ± 0	< dl	17.3 ± 1.3
	Kogia breviceps ♂	6 ± 1
	Liver		2.11 ± 0.29 28.8 ± 0.8	< dl	< dl	8.1 ± 0.1	2503 ± 11 7.86 ± 0.14 1.25 ± 0.12	5.2 ± 0.2	< dl	21 ± 1	0.10	52.3 ± 1.6
	Muscle		6.58 ± 0.17 0.41 ± 0.01	< dl	0.03	1.7 ± 0.2	977 ± 18	6.07 ± 0.17 4.65 ± 0.01 0.26 ± 0.01	< dl	6 ± 1	< dl	42.9 ± 0.7
	K. breviceps ♀	19 ± 3
	Liver		17.0 ± 0.5	47.5 ± 1.3	0.05	< dl	17.5 ± 0.9	3120 ± 84	77.3 ± 0.7 7.03 ± 0.06	5.0 ± 0.1	< dl	25 ± 1	0.68	54.3 ± 0.8

Table 4 .

 4 Heavy metal concentrations (µg.g -1 wwet) in the liver of odontocete species from various areas.

	Species	Locality	N	Cd	Co	Cr	Cu	Fe	Total-Hg	Organic-Hg	Mn	Ni	Se	Zn

Acknowledgements. We are particularly grateful to Richard Young from the University of Hawaii for cephalopod determination and to Jacques Rivaton from the IRD of Nouméa for fish determination. We also thanks the four anonymous reviewers for their helpful comments on this work.


Trust on the Internet: How the French ccTLD .FR Went From a Remarkable to a Speculative System

Clement Genty, Henri Samier, Simon Richir Arts et Métiers ParisTech, LAMPA, Angers, France email: clement.genty@ensam.eu Abstract-The Domain Name System (DNS), was invented in 1983 because it was too hard for the human brain to memorize IP addresses. The DNS works as a phone directory, setting a link between letters, the domain name, and an IP address. Layered and structured since its creation, the domain name made it possible to identify the linked resource and to have confidence in its content. However, this classification system was quickly replaced a big bang of naming possibilities, where the first comer is the first and sole served. This survey aims to study the repercussing of the naming rules of the French ccTLD, the .FR. As an introduction and in section I, we will see how an area of trust has been created through the ".FR". Then, through the section III and IV, how the easing of registration and use rules initiated confusion over the identification and trust by the domain name. Finally, we propose three ways to create the identification-trust link.

Domain Name System -Internet Trust -ccTLD -Internet Economics -Web Privacy -Semantic Web

I. INTRODUCTION

In 1984, J. Postel and J. Reynolds wrote the RFC920 [START_REF] Postel | Domain Requirements[END_REF], establishing the first domain names extensions. At the time, the idea was to read this sequence of alphanumeric characters from right to left, the extensions hierarchizing the domain names. COM, ORG, NET, EDU, MIL and ARPA became the first [START_REF] Postel | [END_REF]. They will remain for posterity as generic constituents, called Generic Top Level Domain (gTLD). Annie Renard and Jean-Yves Babonneau managed the .FR since September 2, 1986. Not being guided by any mimicry, the two researchers chose a hierarchical organization made of sub-domains and "le droit au nom", the entitlement to a domain name. Thus, the major part of professions, associations and governmental organizations will have their own private sub-domain name space. This structuring led them to contact the National Lawyer Union, representing the lawyer, the order of Geomatics Engineering Union, INPI, the French WIPO, etc.

These rules of registration were listed in a naming charter where the "droit au nom" prevailed. Each entity had to respect the structure of the .FR ccTLD. Some users, however, preferred the use of a .COM domain name, less expensive and offering less restrictive registration conditions than the .FR, and unexposed to such administrative procedures.

Faced with these criticisms, the INRIA decided to take actions: in 1997, its value fell by 23% and in 1998 by 22%. This situation made the registration of .FR domain names cheaper than .COM.

To register a .FR domain name, the applicants had to be legal entities, to file a request by fax, which was individually checked before the registration. This administrative burden made the .FR domain name space less used, compared to European ones, less structured. The German ccTLD, .DE, allowed any registration since its delegation by Jon Postel, in November, 1986. Any applicants could have a domain name at the second level domain, i.e., directly in .DE.

Despite the administrative load that it generated, the French system of the .FR avoided the problem of cybersquatting, which was in the interest of domain names owners [START_REF] Afnic | Contrefaçon de marques et usurpation de noms de domaine, où en est la jurisprudence ?[END_REF]. Indeed, the feeling of the trust in the .FR naming space was established. Similarly, numerous surveys highlighted the benefits of the French ccTLD.

Pressures, whether administrative or mercantile made the AFNIC, the newly formed association managing the .FR, to abandon the old registration rules: deletion of the "droit au nom" in 2004, opening to private individuals in 2006, deletion of most of the sub-domains in 2007 and allowance of one and two-characters domain names registration in 2014 [START_REF] Afnic | All about AFNIC Press kit[END_REF].

The number of .FR domain names registrations became a Key Point Indicator for the AFNIC, as evidenced on its chief executive's resume [START_REF] Weill | [END_REF].

The liberalization of the French ccTLD, .FR, had an important influence on the strategy of deposits. Once a flagship and application of French research, the .FR is managed by a semi-state associated structure that cannot act against the loss of confidence in domain names. If everybody can register anything, the legitimacy has given way to speculation.

The merchandising of computing resources, such as IP addresses [START_REF] Barbet | Epuisement et marchandisation d'une ressource commune dans l'Internet: le cas des adresses IP[END_REF] and now domain names, involves risks for the functioning of Internet [START_REF] Barbet | Les conséquences de la marchandisation croissante des ressources essentielles au fonctionnement du réseau Internet[END_REF].

Today, 3 million domain names are registered in .FR: 60% by organizations, 40% by individuals. While the deposits are supposed to be only opened to European citizens, Australia and China represent respectively the eleventh and fourteenth place of the countries of registration [START_REF] Afnic | Open data AFNIC[END_REF].

The number of registrations in .FR naming space is similar to the Italian's ccTLD. These figures, although apparently high, are considerably lower than those of Germany (.DE), 16 millions [START_REF] Denic | DENIC eG: Wir sind .de[END_REF], and the Netherlands (.NL), 5.7 millions [START_REF] Sidn | SIDN : Jouw wereld. Ons Domein[END_REF]. This situation has an important consequence on the identification-trust link, as showen in Figure 2. Originally, the French extension .FR had two goals:

• Identification: people are able to know the associated content by reading the domain name;

• Trust: registration rules exist before each deposit. People can trust the authority of the registrant;

III. IMPACT ON IDENTIFICATION

The absence of a naming charter defined for French administrative entities, apart from the .GOUV.FR subdomain, prevents the identification function of the domain name. Under the former AFNIC charter, French embassies were supposed to be named under the form AMBA-YYY.FR, YYY being the name of the city or the country. Nowadays, embassies use the address AMBAFRANCE-XX.ORG, where XX is the ISO3166 country code. In this case of French embassies, it is simply not possible to identify with certainty a website on the basis of its domain name. This situation exists since the liberalization of the French ccTLD .FR for commercial intent.

France overseas, represented by ISO3166 codes, is also impacted by the lack of numerical coherence.

IV. IMPACT ON TRUST

An Internet address can both inspire implicit confidence and be a lure that can disturb consumer information. Let us take the recent case of addresses on the subject of abortion. The voluntary termination of pregnancy, commonly written and called IVG in France, has been authorized in the country since 1975. Many Internet websites, using the government's communication codes, act as official information websites. This situation is an issue given that 80% of young women aged 15-30 find the obtained information on the Internet credible. 57% get information on health issues via the Internet [START_REF] Hcefh | Rapport n°2013-0912-HCE-008 relatif à l'accès à l'IVG_Volet 1-Information sur l'avortement sur Internet[END_REF]. It is thus essential to give them a technical tool to identify reliable information on the Internet, as search engines do not include the veracity of the words in the search results. As we can see in Figure 3, subdomains work.

Conditions of the questionnaire: answer by form. 137 students with an average age of 18 years: 90 women, 47 men. 129 had their baccalaureate in 2016, 8 in 2015. 10 passed their C2I, a French IT and Internet certificate., 127 did not. One can thus define that it is a predominantly female population, being 18 years old and not being trained to the bases of the good understanding of the Internet. Task: Rank these websites according to the confidence level: 0-1-2-3 (0 for the website you trust the less, 3 the more). Respondents are not allowed to click on the links, only identification by the domain name is possible. It can thus be noted that trust via the sub-domain ".GOUV.FR" is a reality. So-called "reserved" space, registration of domain names with this extension is only possible for the French Government. It is thus possible to develop and encourage the creation of spaces of trust.

Domain name

Confronted with AFNIC's encouraging press releases on the ".FR's confidence", it can be noted that this extension has a classification similar to the extension .ORG considered "open", although enjoying an apparent image of confidence. .NET, considered as an alternative to .COM, occupies the last place.

V. PROPOSALS

Creation of a French trust area

Faced with the difficulties generated by the liberalization of the .FR zone, which has become a commercial area, we now suggest using the .FX extension as a closed zone. The .FX extension, unused until now by France, originally represents metropolitan France. It is thus possible to use it as a hierarchical space with a right to the name for any holder of any right. Thus, through a logical hierarchy, it will be easy to define the legitimacy of depositors. Therefore, by creating and assigning namespaces for any user, France would become the first country to provide a domain name to its nationals:

• Free of a domain name and associated email address for any French entity or individual;

• Creation of a space of confidence, .FX, in addition to a commercial space, .FR;

• Strengthening of certain digital sovereignty in the face of confidentiality gaps (Yahoo, PRISM program, etc.);

As the .FX extension is part of the ISO 3166 code, France does not have to pay fees to the ICANN as it would be if the country intended to generate a new gTLD. This new space could be funded by delegating another unused extension, .CP (originally meant to stand for the Clipperton atoll) to an interested organization or company, just as Norway allowed the Netherlands to manage the extension .BV (corresponding to the Bouvet island, BV meaning besloten vennootschap, Ltd, in Dutch).

Formerly, the length of hierarchical domain names appeared as redhibitory, at a time when users often had to manually type domain names into their browsers. However, in 2017, the access to the major part of the information on the Internet is carried out through a search engine, the domain name being mainly used to identify the source. This will make it easier to index and archive.

As a conclusion, a major advertising campaign carried out by the APIE, could require depositors to use .FX instead of .FR. The rules of identification via the .FX space would be explained through the B2I and C2I, French IT and Internet Certificates [START_REF]'éducation nationale, de l'enseignement supérieur et de la recherche[END_REF].

Fighting speculation in the area.

In order to strengthen the .FR zone, it is suggested to propose the registration of domain names in .FR for a decennial period, similar to trademarks functionment, instead of annual fees. The financial curb would reduce the number of speculative registrations, motivated by an attractive rate. The fact of having to spend ten times as much, admittedly for ten times more temporal coverage, will generate a financial mechanism of restraint. The commitment contracted for every ten years, may be paid in annual installments.

A second step will be the regularization of domain name registrants, including the phasing out of domain names registered by non-European registrants. Alternatives, proposed by the registrars, exist, called local presences. The follow-up of the exit of Great Britain from the European Union will have to be carried out.

Delegation of overseas extensions

With a view to territorial homogeneity, it is advisable to encourage the French Government to have the extensions of Guadeloupe, Martinique and French Guyana delegated by AFNIC. Similarly, Saint-Barthelemy and Saint-Martin will have to be represented by a TLD subject to the possibility of registrations.

VI. CONCLUSION

These three proposals will serve to reinforce the French zones in the digital namespace. The proposed French system will be able to operate in the same way as the USA's system, which uses closed extensions (.GOV, .MIL, .EDU) and public (.COM, .BIZ, .US). It is essential today, in the face of the development of foreign solutions, to ensure digital sovereignty for France and its fellow citizens, through coherent and representative charters of qualifications and titles.

Figure 1 .

 1 Figure 1. Architectures of domain names MAIL.EXAMPLE.COM, WWW.EXAMPLE.NET and NICE.FRTwo years later, Jon Postel created the first geographical Top Level Domain, grouped by countries and territories. This will be the ccTLD, Country-Code Top Level Domain. Using the ISO3166 postal standard [3], he picked the two-character country codes to create 243 extensions. This amount evolved after that, following the geopolitic situation. The fall of the Soviet Union and Yugoslavia has partially affected this list. Figure1gives an example of tree structure of the DNS.

Figure 2 .

 2 Figure 2. Identification-Trust link[START_REF] Genty | Noms de domaine et marques d'entreprise : de la disruption des politiques de nommage à celle des usages[END_REF]

•

  Saint Pierre et Miquelon, Réunion, TAAF, Wallis-Futuna and Mayotte inherit of an open naming charter similar to that of the .FR; • Guadeloupe, Martinique and French Guyana have ccTLDs which are not managed by AFNIC despite the Postal and Telecommunications code provisions [13]; • Saint-Barthelemy (.BL) and Saint-Martin (.MF) have non-delegated extension, despite the stated will of Saint-Barthelemy [14]; • Clipperton (.CP) has a non-delegated ccTLD; NB: French Polynesia (.PF) and New Caledonia (.NC) are managed by other public bodies in agreement with the competent territorial authorities [15].

•

  Of the 209 domain names beginning with "AMBAFRANCE", only 149 are official; • Of the 150 official websites of the Embassies, only 138 comply with the AMBAFRANCE-XX.ORG charter; The registration under .ORG being open to all, the preventive filing of domain names is thus necessary, as France has done for North Korea, where it does not have an embassy. AMBAFRANCE-KP.ORG was registered on December, 19. 2000 by the Ministry of Foreign Affairs.