Dinesh Atchuthan

Angel Santamaria-Navarro

Nicolas Mansard

Olivier Stasse

Joan Solà

Odome- Try

Odometry Based on Auto-Calibrating Inertial Measurement Unit Attached to the Feet

Odometry Based on Auto-Calibrating Inertial Measurement Unit

Attached to the Feet Dinesh Atchuthan1 , Angel Santamaria-Navarro2 , Nicolas Mansard 1 , Olivier Stasse 1 , Joan Solà 1,2 Abstract-Location of pedestrian in indoor environment remains an open problem. A cheap and reliable sensor in this context is the inertial measurement units (IMU), carried by the pedestrian while he/she is walking. However, due to the bias of both the accelerometer and the gyroscope, integrating directly the inertial measurements leads to tremendous drift, as the state of the system (position, orientation, velocity, bias) is not fully observable. In this paper, we consider the specific case where an IMU is attached to one of the pedestrian's feet. We exploit specific prior knowledges (i.e. the fact that the foot lands at zero velocity on a horizontal plane) in order to make the full state of the IMU observable. The inertial measurements and these prior knowledges are gathered in a graphical model (a factor graph), and are exploited to build a maximum-likelihood estimator. The technical difficulty is to handle the size of the graph such that it is tractable in a limited time window, that we do by relying on the pre-integration technique. In that existing framework, our contributions are to reformulate the pre-integration method using quaternions while giving a simpler algebraic formulation, and to apply this method for estimating the human foot-pose during walking. We validate these concepts on several longrange trajectories capture with human subject and compare the results with ground-truth measurements (coming from a motion capture system) and previous results of the state of the art.

I. INTRODUCTION

Context: Indoor person localization is an open challenge in various situations: location-based life improving services, firefighters localization and navigation, patients tracking motion monitoring, medical observation, accident monitoring, mobility and independence of partially-sighted or blind persons, etc. As GPS are not available indoor, and because relying on a network of fixed sensors (cameras, RFID) also raised many open questions, an appealing way to localize a body in space is to use odometry information measured by embedded inertial measurement units (IMUs). In this context, while performing the integration it is mandatory to take into account the IMU biases. As the biases vary with time and physical conditions, it must be estimated on-line while processing the measurements. Furthermore, it is desirable that additional information coming from other sensors can be integrated in the same estimation process. Similarly to the strategies adopted in simultaneous localization and mapping (SLAM), sparse measurements or additional information (e.g. coming from intermittent absolute localization, or from a sparse sensor network) would benefit to the localization process when available. With these requirements coming from the context in mind, we propose to define an estimator based on graphical models, able to accurately and efficiently integrate inertial measurements while estimating the IMU biases. Thanks to the graphical model, the estimator will then be able to fuse additional measurements coming from other sensors or additional prior information provided by the application. The setup considered in this work is a pedestrian walking on structured terrain (flat floor or stairs) with an IMU attached to one of his or her feet.

Methodology: Graphical methods have been extensively used to implement such fusion strategies [START_REF] Thrun | The graph slam algorithm with applications to large-scale mapping of urban structures[END_REF], [START_REF] Kaess | isam: Incremental smoothing and mapping[END_REF]. They are well-suited to gather information from sensors and draw conclusions. The underlying principle is to consider that despite all the information gathered from the sensors, we still have uncertainties about the true state of the world due to imperfections of the sensors. Several states of the world can thus be considered as probable. Relying on probabilistic formulations is a way to find out the most probable one. Furthermore, graphical representation are able to accurately model complex estimation problems [START_REF] Koller | Probabilistic graphical models: principles and techniques[END_REF] in a versatile way.

Graphical models have been used for large modeling estimation problems by means of sparse networks of constraints and particularly in robotics where SLAM and visual odometry problems have reached a high degree of maturity in great part thanks to these tools. The graphical representation also allows for the design of powerful nonlinear estimation solvers, which can be built taking into account the needs for accuracy, robustness and computational performances.

In order to keep the problem tractable and maintain realtime performance, a key point is to prevent the graph from being too large given a time window. IMUs are challenging in this regard, as their high frequency measurement rate create large sets of data. Pre-integration of IMU measurements helps to reduce the size of the underlying graph by squeezing 100 to 1000 measures into a single pre-integrated Bayesian node [START_REF] Lupton | Efficient integration of inertial observations into visual slam without initialization[END_REF]. Direct pre-integration leads to a dependency of the resulting node on the initial integration conditions, implying to integrate again (and again) when an optimizer process the graph. It was later suggested to make this pre-integrated data independent from the initial state from which it was computed [START_REF] Forster | Imu preintegration on manifold for efficient visual-inertial maximum-a-posteriori estimation[END_REF]. Consequently, the IMU measurements can simply be disregarded even when the initial "pre-integration" conditions change while the numerical solver optimized the maximum-likelihood trajectory.

Contributions: In this paper, we follow a similar methodology. We define a graphical model where pre-integrated data are added at key-frame instants (about 2Hz), summarizing IMU measurements captured at about 1kHz. The state that we want to estimate considers the position, orientation and linear velocity (dimension 9) of the IMU attached to the foot, along with the time-varying accelerometer and gyroscope biases (dimension 6). We also implement the prior knowledge that the foot lands horizontally, by adding Bayesian nodes when the foot lands and takes off. This prior knowledge make the considered state observable. We then use a numerical solver to maximize the likelihood of the measurements and prior knowledge along the past trajectory in a sliding window.

The first contribution of this paper is to reformulate the pre-integration method introduced in [START_REF] Forster | Imu preintegration on manifold for efficient visual-inertial maximum-a-posteriori estimation[END_REF] using quaternion representation and to give a detailed and simpler algebraic derivation. The second contribution is to apply this method for estimating the human foot-pose during walking. To this end, we build a graphical model formulation of the problem by gathering information. Once the formulation is completed, a non-linear least squares optimizer is used to solve the problem and find the most probable solution in the leastsquare sense [START_REF] Agarwal | Ceres solver[END_REF].

II. GRAPH-BASED INERTIAL-KINEMATIC ODOMETRY

A. Quaternion rotations

We define the quaternion-by-vector product so that

q v q ⊗ v ⊗ q * , (1)
where q * denotes the dual quaternion of q. The symbol ⊗ stands for the product of quaternions and corresponds to the quaternion-by-vector which performs a 3D rotation of an input vector v. Notice that if R is the rotation matrix equivalent to the quaternion q, then q v = R v. This straightforward equivalence enables us to define all the forthcoming IMU pre-integration algebra in a way that allows a direct transcription between the S 3 and SO(3) spaces of representation.

B. Graph-based iterative optimization

In graph-based optimization, the problem is represented as a graph, where the nodes refer to the variables, and the edges, called factors, represent the geometrical constraints that link between variables produced by the measurements. The state x is modeled as a multi-variate Gaussian distribution, and in our case it includes foot poses and velocities (p, q, v) and IMU biases (a b , ω b ) at selected keyframes along the trajectory (see Fig. 1). For each factor, we can define an error or a residual r as the discrepancy between a measurement z and its expectation given the involved state variables,

r(x) = h(x) + v -z, v ∼ N (0, Ω -1 ) (2)
being h(x) the sensor measurement model and Ω the information matrix of the measurement Gaussian noise v. Importantly, the functions h(x) and r(x) are very sparse, since only a small handful of blocks of x are involved in each factor, which results in a loosely connected graph. In case of variables defined on manifolds, such as quaternions or rotation matrices, we must rewrite (2) as r(x) = (h(x) ⊕ v) z.

The ⊕ and symbols correspond to the addition and Detailed factor graph for the initial keyframe and two steps. Circles: state blocks for position (p), orientation quaternion (q), velocity (v), accelerometer bias (a b ), gyrometer bias (ω b ). Orange: initial pose factor. Red: kinematic factor (deduced from additional sensors). Purple: zero-velocity factor. Green: IMU's delta pre-integration factor. Blue: bias drift factor. Cyan: bias absolute factor. subtraction operators on the manifold (see e.g. Eq. ( 25) in Section III, or Eq. [START_REF] Chirikjian | Stochastic Models, Information Theory, and Lie Groups, ser. Applied and Numerical Harmonic Analysis[END_REF](29)(30)(31) in Appendix I).

The maximum a posteriori estimation is obtained by iteratively minimizing the Mahalanobis squared norm of all linearized errors

∆x * = arg min ∆x k r k (x) + J k ∆x 2 Ω -1 k (3)
being x the state estimate at the current iteration, and J k the Jacobian of the k-th residual r k (x) (with

J k = ∂(h k (x) z k )
/∂∆x in the case of variables lying on a manifold) and Ω k is the information matrix of the k-th measurement. Current methods use the Cholesky [START_REF] Kummerle | g 2 o: A general framework for graph optimization[END_REF], [START_REF] Ila | SLAM++-A highly efficient and temporally scalable incremental SLAM framework[END_REF] or the QR [START_REF] Dellaert | Square root SAM: Simultaneous localization and mapping via square root information smoothing[END_REF], [START_REF] Kaess | iSAM2: Incremental smoothing and mapping using the bayes tree[END_REF] matrix factorizations to solve for ∆x * , which is then used to update the current state estimate. The process is iterated until convergence. Incremental methods [START_REF] Ila | SLAM++-A highly efficient and temporally scalable incremental SLAM framework[END_REF], [START_REF] Kaess | iSAM2: Incremental smoothing and mapping using the bayes tree[END_REF] update the problem directly on the factorized matrices, obtaining important speed-ups.

C. Keyframe variables

During a biped walk, we take profit of certain situations where precise and reliable assumptions can be made. For example, the foot velocity is null during its support phase. At these selected instants, we create the keyframes that will produce a chain of states. These states are linked by the measurements, forming our factor graph (Fig. 1). Each keyframe f i contains the following state blocks: the foot's position, velocity and orientation data, plus the IMU's accelerometer and gyrometer biases,

f i = p i v i q i a b,i ω b,i . (4)

D. Description of factors

The types of factor considered in our graph are illustrated in Fig. 1. Each factor k requires its own information matrix Ω k , and its residual function r k (x). These residual functions are detailed hereafter.

1) Absolute factors: These include initial position and orientation (orange in the figure), zero velocity (purple), and bias magnitude (cyan). Each residual depends on a single state block, which is compared against a reference z k ,

r k (φ i ) = φ i -z k (5)
where φ i is one among {p i , v i , a b,i , ω b,i }. For the quaternion we implement the residual using the operator on the sphere of dimension 3 manifold, denoted S 3 (see (30) in Appendix I for further details),

r k (q i ) = q i z k = Log(z * k ⊗ q i ) (6)
2) Bias drift factors (blue): These are relative factors that allow the bias estimates to drift with time at a controlled rate. Each bias drift residual depends on two state blocks, namely

r(a b,i , a b,j ) = a b,j -a b,i r(ω b,i , ω b,j ) = ω b,j -ω b,i (7)
3) Complementary factors (red): These relate position and orientation between two consecutive steps as it can be provided by other sensors than IMU or methods using human walking specificities,

r(p i , q i , p j , q j ) = q * i (p j -p i ) -y k Log(z * k ⊗ q * i ⊗ q j ) (8)
where y k and z k are respectively the relative position and quaternion measurements. 4) IMU pre-integrated factors (green): These factors are by far the most complex ones and are described in details in the next section.

III. IMU PRE-INTEGRATION IN S 3 AND SO(3) A. Overview

Due to the different rates of IMU data and keyframe creations, hundreds of IMU measurements need to be integrated to generate a motion factor linking two consecutive keyframes. In addition to that, the integration of the motion equations in an absolute reference frame strongly depends on the initial conditions of orientation, velocity and IMU bias. Therefore, the changes in the estimates of these magnitudes (inherent to the iterative nature of the optimization) affect the whole motion integral. Delta pre-integration theory was developed to avoid the need of re-integrating all IMU data at each iteration [START_REF] Lupton | Efficient integration of inertial observations into visual slam without initialization[END_REF], [START_REF] Forster | Imu preintegration on manifold for efficient visual-inertial maximum-a-posteriori estimation[END_REF]. On the one hand, this theory defines new motion magnitudes called deltas, which are independent of the initial conditions for orientation and velocity, and thus depend only on the IMU data and bias. On the other hand, the effect of the changes in the bias estimates is linearized so that the deltas can be corrected a posteriori, i.e., when computing the residual, using pre-computed Jacobians.

In this section, we revise the IMU pre-integration theory, providing three contributions: 1) a segmentation of the computation pipeline (from measurements, to body magnitudes, to the current delta, and to the integrated delta); 2) a physical interpretation of the delta magnitudes; and 3) a simpler yet rigorous algebraic approach, valid for both the S 3 (quaternion) and SO(3) (rotation matrix) manifolds, which takes profit of the pipeline segmentation and the chain rule to compute the otherwise cumbersome Jacobians [START_REF] Forster | Imu preintegration on manifold for efficient visual-inertial maximum-a-posteriori estimation[END_REF]. Important complements are provided in Appendix I for the sake of background and completeness.

B. State integration in the absolute reference frame

We define the world-referenced states of the IMU by x = (p, v, q) where p stands for the position, v for the velocity and q for the orientation encoded as a quaternion. The time evolution of x is governed by the kinematic equation,

ṗ = v v = g + q a q = 1 2 q ⊗ ω (9)
where g denotes the gravity vector and we identify b = (a, ω) as the body magnitudes, that is, the magnitudes of acceleration and angular velocity measured by the IMU and expressed in its reference frame. These body magnitudes are obtained at discrete times t j from biased and noisy IMU measurements, i.e.,

a j a m,j -a b,j -a n ω j ω m,j -ω b,j -ω n , (10)
with • m the measurements, • b the biases, and • n the noises. Assuming constant body magnitudes within the IMU sampling period δt t kt j , we have the discrete-time relation:

p k = p j + v j δt + 1 2 gδt 2 + 1 2 q j a j δt 2 v k = v j + gδt + q j a j δt q k = q j ⊗ Exp(ω j δt/2) (11)

C. Delta definitions

Consider a non-rotating reference frame that is free-falling at the acceleration of gravity g, and name it G t . An ideal (unbiased and noiseless) IMU glued to this frame would measure null linear accelerations and angular velocities. Any non-null measurements would be due to a relative motion of the IMU with respect to G t .

At a given keyframe instant t i , we initialize G i at x i = (p i , v i , q i ). At a later keyframe instant t j (j > i), G j has fallen according to g, and the state of our moving body is now at x j = (p j , v j , q j ). The motion variation, denoted ∆ ij , is defined as the state variation in position, velocity and orientation of our body between G i and G j , that is,

∆p ij = q * i p j -p i -v i ∆t ij - 1 2 g∆t 2 ij ∆v ij = q * i (v j -v i -g∆t ij ) ∆q ij = q * i ⊗ q j ( 12
)
where ∆t ij t jt i is the time duration between the two keyframes. Notice that this definition of ∆ ij is the same as provided in [START_REF] Lupton | Efficient integration of inertial observations into visual slam without initialization[END_REF], [START_REF] Forster | Imu preintegration on manifold for efficient visual-inertial maximum-a-posteriori estimation[END_REF], and we have given it here a clear physical meaning. It is worth to notice that the deltas form a group under the composition law ∆ ik ∆ ij ⊕ ∆ jk , defined by: [START_REF] Santamaria-Navarro | Highfrequency mav state estimation using low-cost inertial and optical flow measurement units[END_REF] with identity ∆ 0 = [(0, 0, 0), (0, 0, 0), (1, 0, 0, 0)], and inverse ∆ ji ∆ -1 ij shuch that ∆ -1 ⊕ ∆ = ∆ ⊕ ∆ -1 = ∆ 0 (the inverse expression is not given for space reasons). At any time j we can recover the state estimate x j from the state estimate x i and the motion delta ∆ ij :

∆p ik = ∆p ij + ∆v ij ∆t jk + ∆q ij ∆p jk ∆v ik = ∆v ij + ∆q ij ∆v jk ∆q ik = ∆q ij ⊗ ∆q jk
p j = p i + v i ∆t ij + 1 2 g∆t 2 ij + q i ∆p ij v j = v i + g∆t ij + q i ∆v ij q j = q i ⊗ ∆q ij (14)

D. Incremental delta pre-integration

Substituting the integration Eq. ( 11) in the delta definitions [START_REF] Invensense | Imu mpu6050[END_REF], we obtain the incremental delta pre-integration,

∆p ik = ∆p ij + ∆v ij δt + 1 2 ∆q ij a j δt 2 ∆v ik = ∆v ij + ∆q ij a j δt ∆q ik = ∆q ij ⊗ Exp(ω j δt) (15)
with ∆ ii = ∆ 0 . Interestingly, ( 15) is analogous to the motion of a body in an inertial frame under constant acceleration and rotation rate. Notice that by letting the reference frame fall with gravity, we get rid of the dependence on gravity in the integration equations, and only the body magnitudes drive the integral. Indeed, we can define a proper delta δ jk from the current body magnitudes b j = (a j , ω j ) b m,i -b b,j -b n,j at time t j ,

δp jk = 1 2 a j δt 2 δv jk = a j δt δq jk = Exp(ω j δt) (16)
and write the integration (15) as the composition

∆ ik = ∆ ij ⊕ δ jk (17)
described in [START_REF] Santamaria-Navarro | Highfrequency mav state estimation using low-cost inertial and optical flow measurement units[END_REF]. Typically, we take the biases at the keyframe time t i , that is, b b,j = b b,i . In the following, we will identify ∆ with the pre-integrated delta, and δ with the current delta.

E. Jacobians

We note all Jacobians with J y x ∂y/∂x and refer the reader to Appendix I for details on the development of all non-trivial Jacobian blocks in this section.

1) Jacobians of the body magnitudes: from Eq. ( 10) we have:

J b bm = I 6 J b b b = -I 6 J b bn = -I 6 . (18)
2) Jacobians of the current delta: We have from [START_REF] Ojeda | Personal dead-reckoning system for gpsdenied environments[END_REF],

J δ jk bj =   1 2 Iδt 2 0 Iδt 0 0 J r (ω j δt)δt   ∈ R 9×6 (19)
where we develop the lower-right block as in Appendix I-E.1.

3) Jacobians of the delta composition: We differentiate the delta composition [START_REF] Kwanmuang | Filtering and tracking for a pedestrian deadreckoning system[END_REF] described in [START_REF] Santamaria-Navarro | Highfrequency mav state estimation using low-cost inertial and optical flow measurement units[END_REF],

J ∆ ik ∆ij =   I Iδt -∆R ij δp jk × 0 I -∆R ij [δv jk ] × 0 0 δR jk   ∈ R 9×9 (20a) J ∆ ik δ jk =   ∆R ij 0 0 0 ∆R ij 0 0 0 I   ∈ R 9×9 (20b)
where ∆R ij and δR jk are the rotation matrix deltas corresponding to the respective quaternion deltas ∆q ij and δq jk .

We develop all the non-trivial blocks as in Appendix I-E.2 and Appendix I-E.3.

F. Incremental delta covariance integration

Let Q ∆ be the covariance of the pre-integrated delta, and Q n the one of the measurement noise. For convenience, we first compute the covariance of the current delta,

Q δ = J δ bn Q n J δ bn , (21)
where J δ bn = J δ b • J b bn is the noise Jacobian, obtained with [START_REF] Groves | Inertial navigation versus pedestrian dead reckoning: Optimizing the integration[END_REF][START_REF] Skog | Fusing the information from two navigation systems using an upper bound on their maximum spatial separation[END_REF] and the chain rule. The delta covariance is then integrated with

Q ∆ ik = J ∆ ik ∆ij Q ∆ij J ∆ ik ∆ij + J ∆ ik δ jk Q δ J ∆ ik δ jk , (22)
using Jacobians [START_REF] Sukkarieh | A high integrity imu/gps navigation loop for autonomous land vehicle applications[END_REF], and starting at Q ∆ii = 0 9×9 .

G. Delta correction with new bias

Let ∆ and b b be respectively the pre-integrated delta and the bias values used during pre-integration. Since the bias estimates change at each iteration of the optimizer, we need to update the delta according to the new bias values b b . We do so with the linearized update,

∆ = ∆ + J ∆ b b (b b -b b ) , (23)
where J ∆ b b is the pre-integrated bias Jacobian, computed incrementally using also the chain rule,

J ∆ ik b b = J ∆ ik ∆ij J ∆ij b b -J ∆ ik δ jk J δ jk b b . (24)
with J

δ jk b b = J δ jk b J b b b . This Jacobian starts at J ∆ii b b = 0 9×9 .

H. Residuals

The computation of the residuals for the IMU delta factors (see Fig. 1, green) requires: the state estimates x i and x j ; the current bias estimates b b,i ; the pre-integrated delta ∆ ij ; the bias used during pre-integration b b,i ; and the pre-integrated bias Jacobian J ∆ij b b . The process is best understood if split into smaller steps: we first compute a corrected delta ∆ ij using ( 23); then we compute a predicted delta ∆ ij using [START_REF] Invensense | Imu mpu6050[END_REF]; and finally we compute the residual with

r(x i , x j , b b,i ) =    ∆p ij -∆p ij ∆v ij -∆v ij Log( ∆q * ij ⊗ ∆q ij )    ∈ R 9 . (25)
Its information matrix is given by Ω = Q -1 ∆ik .

IV. EXPERIMENTS

We use the dataset made available thanks to Angermann et. al. [START_REF] Angermann | A high precision reference data set for pedestrian navigation using footmounted inertial sensors[END_REF] to validate our method and compare the results to provided outputs from the state-of-the-art Kalman filter. Our method is applied on several scenarios from these dataset and we present typical results obtained with two representative cases. The first sets of data correspond to a human walking back and forth while the second example is related to a walking pattern describing a eight-shape. Both IMU and motion capture data are provided at 100 Hz.

Then, we will investigate the use of additional sensors to demonstrate the feasibility of fusion strategies using a low cost IMU running at 1 kHz (Invensense's MPU6050 [START_REF] Invensense | Imu mpu6050[END_REF]).

A. Method

Keyframes are created at the beginning and ending of each support phase of the selected foot according to ZUPT detection provided by the dataset. Factors active in the graph (see Fig. 1) are: initial position and yaw; zero velocity, bias drift, and IMU pre-integration. We only use the bias magnitude and zero velocity constraint factors in the initial keyframe. All the graph is optimized after each keyframe creation so that these estimates can be used for future estimations with new keyframes. Zero velocity constraints are applied as a fixed prior for the optimizer, meaning that corresponding variables will not be estimated but considered as parameters. As a consequence, we need to be confident that timestamps detected as zero velocity instants really match static phases of the IMU. Otherwise we would be imposing a constraint inducing a wrong estimate of the trajectory.

In order to show how interesting fusion strategies can be, we simulate the use of an odometry sensor providing the displacement of the foot between two frames at a frequency that is lower than IMU. This specific case is a common use of IMUs in fusion strategies to reduce the drift error due to IMU's biases [START_REF] Santamaria-Navarro | Highfrequency mav state estimation using low-cost inertial and optical flow measurement units[END_REF]. With a better estimation of its biases, the IMU can then be used to detect events related the human wearing the device. Such strategy can be implemented with RFID sensors or more basically with visual odometry. In our case, we use motion capture information to reconstruct odometry between consecutive keyframes, allowing us to create keyframes during the flying phases of the foot. As in the usual ZUPT-aided inertial navigation, zero-velocity constraints are imposed only on keyframes created during contact phases. Kinematic odometry is also added between all consecutive keyframes (see Fig. 1).

B. Results

1) State estimation using ZUPT only:

As motion capture data are not used during the experiments, the system is not provided with enough information to be able to precisely estimate the vertical orientation of the IMU due to its nonobservability from the IMU measurements directly. As a consequence, the estimation of the state of the foot is not able to converge to its real value. In other words, the foot trajectory can be recovered up to a rotation around the gravity axis. In the following, we manually translate the first estimated states to the initial reference one and rotate the estimated trajectories in order to compare our results against the ground-truth measurements. Our system is able to estimate the state of the system to a precision close to the state-of-the-art 9-state Kalman filter [START_REF] Foxlin | Pedestrian tracking with shoe-mounted inertial sensors[END_REF] as shown in Fig. 3.

Besides, the experiment shows satisfying results in terms of computational times. Indeed, 3.1 seconds are enough to integrate all the data corresponding to a 50 seconds experiment, that is more than 5000 IMU data, to build and to optimize the graph each time a keyframe is created with our framework, with a total of 80 keyframes. It would be hard, if not currently impossible, to get such results using the IMU without a proper pre-integration method. The optimization part is currently handled by Google Ceres optimizer [START_REF] Agarwal | Ceres solver[END_REF] using the sparse structure of the problem. All in all, it takes 98µs in average to read and integrate a single IMU measurement including the computation of jacobians.

2) State estimation using ZUPT and sensor fusion: The strength of the optimal estimation can also be found in the fusion strategies. Fig. 2 shows the reconstructed foot trajectories for the two cases: without and with the flying keyframe information. Adding kinematic information between keyframes enhances the observability of the system and allows to a better estimation. A major advantage of IMU's pre-integration theory is the ability to use past preintegrations corrected with current estimates of keyframes and biases as simply as it takes to integrate a single IMU data. This removes the need of linearization of intermediate IMU data between previous and current estimates of the state on which the integration must be performed. We also notice that the use of a flying keyframe makes the bias estimation more stable.

V. RELATED WORK

Person localization using a foot-mounted IMU was first introduced in [START_REF] Hutchings | System and method for measuring movement of objects[END_REF]. Pedestrian Dead Reckoning (PDR) methods (aka Personal Navigation Devices), make use of one or more IMU installed on the body of the subject. The main idea of PDR techniques is to integrate inertial measurements with Zero Velocity Update (ZUPT) constraints to reduce errors [START_REF] Ojeda | Personal dead-reckoning system for gpsdenied environments[END_REF]. This work is extensively used in IMU-based human localization works and various fields [START_REF] Kwanmuang | Filtering and tracking for a pedestrian deadreckoning system[END_REF] analyzes the gait of a walking person with PDR method to estimate the direction of the shoe, thus the walking direction, and measure stride length. Shoe-mounted IMU is still considered as a possible way to accurately localize persons in an indoor environment Fig. 2. Top: trajectory estimation during human walking with an IMU attached to a foot. Continuous, dashed and dashed-dot lines are respectively: ground truth, estimation with zero velocity constraints only, estimation using zero velocity constraint and 1 odometry measurement during foot's flying phase. Odometry was here built from motion capture data. Bottom: Evolution of corresponding estimated IMU biases due to lower drift errors when compared to body-mounted solutions [START_REF] Groves | Inertial navigation versus pedestrian dead reckoning: Optimizing the integration[END_REF] . Various strategies can be considered to improve the localization results of foot-mounted IMU navigation. Prior information can be exploited when merging the measurements of several IMUs, for example relative to the maximum step length the pedestrian could do when using two foot-mounted IMUs [START_REF] Skog | Fusing the information from two navigation systems using an upper bound on their maximum spatial separation[END_REF].

Fusion strategies with information coming from different sensors can also be used to improve localization results as it is already done in robotics: GPS information [START_REF] Sukkarieh | A high integrity imu/gps navigation loop for autonomous land vehicle applications[END_REF], [START_REF] Hide | Investigating the integration of a foot-mounted imu and gnss antenna[END_REF], [START_REF] Gao | Data fusion with two nonlinear constraints on kalman filtering[END_REF], received signal strength indicator (RSSI) from wireless communication [START_REF] Malyavej | Indoor robot localization by rssi/imu sensor fusion[END_REF] using wireless local area networks or radio-frequency identification (RFID) tags placed at known locations [START_REF] Ruiz | Accurate pedestrian indoor navigation by tightly coupling foot-mounted imu and rfid measurements[END_REF] along with other drift reduction methods such as zero velocity updates, zero angular-rate updates (ZARU) and the use of magnetometers. Using these strategies might be a successful solution to overcome the drift observed in methods using IMU and to obtain positioning errors of approximately 1.5 m [START_REF] Ruiz | Accurate pedestrian indoor navigation by tightly coupling foot-mounted imu and rfid measurements[END_REF]. In [START_REF] Chdid | Inertialvision sensor fusion for pedestrian localization[END_REF], a foot-mounted IMU is fused with a waist-mounted visual odometry system to update the state of the system composed of its position, velocity and acceleration. This last system was used recently [START_REF] Pierce | Incorporation of a foot-mounted imu for multi-sensor pedestrian navigation[END_REF] to design a fusion strategy requiring measurements only once per human step instead of every time step. Fig. 3. Top: trajectory estimation during human 8-shaped walking phases with an IMU attached to a foot. Stars in blue and red colors are respectively the reference estimated states provided in the dataset and the estimation with our approach. The continuous green line is the ground truth as given by the motion capture system. Middle: Evolution of estimated IMU biases and orientation of the device. Biases are estimated only for keyframes and considered as constant between them. Bottom: Evolution of euclidean distance errors between estimates and the ground truth for this 8-shaped walking trajectory.

More information can be structured into a map following a SLAM approach [START_REF] Angermann | Footslam: Pedestrian simultaneous localization and mapping without exteroceptive sensorshitchhiking on human perception and cognition[END_REF], leading to a bounded error growth to 1 meter. This FootSLAM uses dynamic Bayesian network and loop-closure strategies. The idea exploited here is to use the normal human behavior consisting on relying on visual information to guide the motion and avoid obstacles.

Previously cited example tend to show how important it is for pedestrian inertial navigation system to be able to deal with the localization drifts due to the integration of IMU's data. From this analysis, we see that two important aspects have been investigated to solve pedestrian localization: i) exploiting some specificities of human behavior with the inertial measurements as prior knowledge and ii) fusing IMU with additional complementary sensors. In this paper, we have shown that using a graphical model is a sane and efficient way to encode prior knowledge about the human behavior (horizontal foot during zero-velocity phases). While we are not exploiting any absolute measurement, the drift resulting of the odometry integration is contained to some reasonable margin (i.e. comparable to the accuracy obtained when a rough map is used). An additional feature of our approach is that it is easy to extend the graphical model, either with additional prior knowledge, or with measurements coming from additional sensors. For example, fusing absolute but noisy measurements like GPS, RFID or RSSI would be straight forward.

VI. CONCLUSION

We have presented a method to measure foot movement during an IMU attached to the foot and exploit available knowledge extracted from the gait phases, such as zero velocity and IMU bias dynamics. Measurements and prior knowledge have been described in a graphical model where the full IMU state (position, orientation, velocity, bias) is observable. We then used nonlinear optimization techniques based on factor graphs, which has proved to be a flexible and powerful fusion framework. For this, we have revised the IMU pre-integration theory, and proposed an implementation in the quaternions manifold, with simpler derivations than previous works, and with physical interpretations, which we believe go in the direction of improving the clarity of the method. Results showed that this estimation method is able to properly estimate the bias, then leading to an accurate odometry where the drift remains reasonable, even after minutes of integration. The method easily extends to additional prior knowledge or additional sensors. We also plan to use it to accurately track the odometry of a biped robot, while fusing the inertial measurements of the robot feet with the encoders measurements of its kinematic chain. Further work are needed to make the system less critical to wrong ZUPT detections. To achieve this goal we can change the ZUPT implementation strategy from a fixed parameter to an estimated one starting with a zero prior and low variance.

APPENDIX I DEFINITION OF THE DERIVATIVES IN S 3 AND SO(3)

A. Exp and Log maps in S 3 and SO(3)

We use vectorized versions of the exponential and logarithmic maps in the rotation groups S 3 (quaternion) and SO(3) (rotation matrix), and denote them with capitalized names Exp() and Log() (see Fig. 4, left). They operate directly on the vector space R 3 , and use either quaternions for S 3 ,

q = Exp(θ) cos(θ/2) u sin(θ/2) (26a) θu = Log(q) 2 qv arctan( qv , qw) qv , (26b)
where q (qw, qv), or rotation matrices for SO(3),

R = Exp(θ) I + sin θ [u] × + (1 -cos θ) [u] 2 × (27a) θu = Log(R) θ(R -R ) ∨ 2 sin θ , (27b)
with θ = cos -1 trace(R)-1

2

, and where • ∨ , known as the vee operator, is the inverse of the skew operator [•] × . Their exact form (q or R) is always clear by the context. Since the quaternion

✓ q p q = p ✓ ✓ = q p S3 R 3 ✓ q S3 R 3 q = Exp(✓)
Fig. 4. The S 3 manifold is a unit sphere in R 4 , here represented by a unit circle (blue), where all unit quaternions live. The tangent space to the manifold is the hyperplane R 3 , here represented by a line (red). The Exp() and Log() operators map elements of R 3 to/from elements of S 3 . The ⊕ and operators relate elements of the manifold with elements in the tangent space. (Likewise, these figures illustrate the SO(3) manifold.) implementation is one of our contributions, in the following we will refer to the rotation groups S 3 and SO(3) with the unique name S 3 , although everything applies equally to SO(3).

B. The additive and subtractive operators in S 3 and SO(3)

The 'plus' operator, ⊕ : S 3 × R 3 → S 3 , composes a reference element R ∈ S 3 with a (often small) rotation specified by a vector of θ ∈ R 3 that is tangent to the S 3 manifold at R, yielding an element S ∈ S 3 (see Fig. 4, right). The 'minus' operator, : S 3 × S 3 → R 3 is the inverse of the above. These operators are defined for both q and R, q = p ⊕ θ p ⊗ Exp(θ)

S = R ⊕ θ R Exp(θ) (28)
θ = q p Log(p * ⊗ q) (30)

θ = S R Log(R S) . (31)

C. The four possible derivative definitions

For functions f : R m → R n , the derivative is defined classically using the standard operators {+, -},

∂k(R) ∂θ lim δθ→0 k(R ⊕ δθ) -k(R) δθ ∈ R n×3 . ( 35
)
It might be worth noticing that all these Jacobians are independent of the representation chosen (S 3 or SO(3)).

D. Right Jacobian of S 3 and SO(3)

We define the right Jacobian as,

Jr(θ) ∂ Exp(θ) ∂θ ∈ R 3× 3 , (36)

Fig. 1 .

 1 Fig. 1.Detailed factor graph for the initial keyframe and two steps. Circles: state blocks for position (p), orientation quaternion (q), velocity (v), accelerometer bias (a b ), gyrometer bias (ω b ). Orange: initial pose factor. Red: kinematic factor (deduced from additional sensors). Purple: zero-velocity factor. Green: IMU's delta pre-integration factor. Blue: bias drift factor. Cyan: bias absolute factor.

  Euclidean distance error of estimates compared to ground truthkalman estimate Graph estimate (keyframes)

∂f (x) ∂x lim δx→0 f

 δx→0 (x + δx) -f (x) δx ∈ R n×m ;(32)for functions g : S 3 → S 3 , we use the operators {⊕, },∂g(R) ∂θ lim δθ→0 g(R ⊕ δθ) g(R) δθ ∈ R 3×3 ;(33)for functions h : R m → S 3 , we use {+, },∂h(x) ∂x lim δx→0 h(x + δx) h(x) δx ∈ R 3×m ;(34)and for functions k : S 3 → R n , we use {⊕, -},

R 3 → S 3 :S 3 ×R 3 → R 3 :R

 33333 and implement it using (34). It admits the closed form[28, pag. 40],Jr(θ) = I -1 -cos θ θ 2 [θ] × + θ -sin θ θ 3 [θ] 2 × . (37) The function f (ω) = Exp(ωδt)produces elements of S 3 from vectors ω ∈ R 3 . Its Jacobian with respect to ω follows from (34), but is better obtained from (36) and the chain rule, The rotationf (R, v) = q v = R v produces vectors of R 3 from elements R ∈ S 3 and vectors v ∈ R 3 .The first Jacobian is defined by (35) and developed as Exp(δθ)v -Rv δθ = lim δθ→0 R•(I + [δθ] × )v -Rv δθ = lim δθ→0 R [δθ] × v δθ = lim δθ→0 -R [v] × δθ δθ = -R [v] ×where we used the properties Exp(δθ) ≈ I + [δθ] × and [a] × b = -[b] × a.The second Jacobian is defined by (32) and yields,∂q v ∂v = ∂Rv ∂v lim ∂v→0 R•(v + ∂v) -Rv ∂v = R .3) Function S 3 ×S 3 → S 3 : The function f (Q, R) = q⊗r = Q R produces rotation composition. Its Jacobians are computed from (33), using the property Exp(Rθ) = R Exp(θ)R ,

CNRS -LAAS, Toulouse, France, {first.last}@laas.fr

IRI, UPC, Barcelona, {asantamaria,jsola}@iri.upc.edu

ACKNOWLEDGMENT

This work has been supported by EUROC FP7-2013-NMP-ICT-FOF, Loco3d ANR-16-CE33-0003, the Spanish Ministry of Economy and Competitiveness under Project EB-SLAM (DPI2017-89564-P), and by the Spanish State Research Agency through the Mara de Maeztu Seal of Excellence to IRI MDM-2016-0656.


D Planson

B Asllani
email: bbesar.asllani@insa-lyon.fr

H Hamad

M.-L Locatelli
email: dmarie-laure.locatelli@laplace.univ-tlse.fr

R Arvinte

C Raynaud

P Bevilacqua
email: gpascal.bevilacqua@insa-lyon.fr

L.-V Phung

Near Breakdown Voltage Optical Beam Induced Current (OBIC) on 4H-SiC Bipolar Diode

Keywords: 4H-SiC, Bipolar diode, high voltage device, OBIC, TCAD simulation, Electroluminescence

This paper presents OBIC measurements performed at near breakdown voltage on two devices with different JTE doses. Overcurrent has been measured either at the JTE periphery or at the P + border. Such overcurrent is present due to the electric field enhancement near the breakdown voltage. This hypothesis is proved by the electroluminescence. TCAD simulation of two different JTE doses yielded similar results to the OBIC measurements.

Introduction

Silicon Carbide (SiC) is an attractive semiconductor material for high power and high temperature applications. In order to reach the expected breakdown voltage, an effective junction termination is required to spread the peripheral electrical field lines. Among different techniques used for periphery protection, a Junction Termination Extension (JTE) is often chosen. The key parameters are the accurate dose of the electrically activated implanted dopants and the control of the semiconductor surface charge passivation. In order to check the implanted dose, we can use SIMS (Secondary Ion Mass Spectrometry), which is a destructive way to measure the concentration profile of the implanted species. Nevertheless, it does not allow to determine the electrically active dopants, neither is it possible to measure the effective charge density related to the passivation layer used. Optical Beam Induced Current (OBIC) technique is a powerful means to analyze the electric field distribution at the edge of the device periphery without damaging it. In this paper, the OBIC technique is applied to high voltage bipolar diodes to analyze the experimental behavior of the periphery protection with respect to the applied reverse voltage.

Experimental Setup

In this experimental setup, a 349 nm UV pulsed laser is used to generate electron-hole pairs (EHPs). An optical bench consisting of two semi-reflecting mirrors and a focusing lens is controlled with LabView to move the position (i.e. on x, y and z) of the focal point. At the focal point the spot diameter is about ~30 µm and the beam power density is up to 100 GW/cm 2 . This energy is high enough to generate electron-hole pairs (EHPs), so that an OBIC current could be measured. The OBIC principle has already been described in [1]. The high voltage test devices are placed in a vacuum chamber. The laser beam passes through the vacuum chamber window to reach the device under test. The surface of the diode is scanned with a step of 10 µm at several voltages. The measurements were realized on two different square-shaped bipolar diodes protected with a single JTE, namely device 1 and device 2. Both devices have been realized on a thick 4H-SiC n-type epilayer, doped at ~1´10 15 cm -3 . The main difference is the Al doping level of the JTE and the epilayer thickness, as described in Table 1.

Table 1. Specifications of the two devices under test The metallized anode contact is square-shaped, with a side length of 720 µm, and a corner curvature radius of 200 µm. A cross section of the device is shown in Fig. 1.

The surface of the diode is scanned by the laser beam focused by several lenses to a spot size of ~30 µm. A schematic description and a picture of the experimental bench are shown in Fig. 2. The measurement is performed in a vacuum chamber able to sustain high voltages up to 10 kV.

Results and Analysis

Tests have been carried out at voltages between 800 V to 2850 V as shown in Fig. 3 for device 1 and for device 2. For the voltages near breakdown the electric field becomes high. Consequently, the

Pump

Electrical feedthrough

Chuck transparent window

OBIC experimental bench

Valve

Vacuum chamber

EHPs, which are generated by the UV beam in the space charge region are accelerated by this high electric field, thereby acquiring enough kinetic energy to generate new EHPs, through impact ionization. This is the pre-avalanche regime, which leads to an increase of the OBIC signal [1]. Fig. 3. OBIC current measured at different increasing voltages on device #1 (left) and device #2 (right).

For device #1 having the high JTE dose, an increase in the OBIC signal could be observed at the edge of the JTE near the breakdown voltage. This phenomenon is correlated with the observed electroluminescence due to the radiative recombination of EHPs generated by avalanche multiplication [2][3], as shown in Fig. 4 left. For device #2 having a low JTE dose, near the breakdown voltage an increase in the OBIC signal could be observed at the edge of the P + region. In this case also the phenomenon can be correlated with the observed electroluminescence as shown in Fig. 4 right.

TCAD simulations have been performed on both structures using Sentaurus Synopsys [START_REF]Sentaurus Device User Guide Version F[END_REF]. The description of the device structure takes into account the real doping levels and dimensions. We Simulation results confirm that a JTE with a high dose (device #1) the OBIC signal is more intense at the JTE border, due to higher electric field at this exact point. In the case of the lower JTE dose (device #2) the highest OBIC current intensity is obtained at the P + border, since the JTE fails to protect and the highest electric field is located at the anode border.

Summary

This paper presents OBIC measurements performed on JTE-protected bipolar diodes at near breakdown voltages. Two bipolar diodes with different JTE doses (i.e. high and low) have been analyzed. A strong discrepancy appears from one device to another, which is correlated with electroluminescence and simulation results.

Fig. 1 .

 1 Fig. 1. Cross section of the protected bipolar PiN diode.

Fig. 2 .

 2 Fig. 2. Schematic of OBIC experimental bench (left), and picture of the setup (right)

Fig. 4 .

 4 Fig. 4. Electroluminescence observed on device #1 (left) and device #2 (right) near breakdown voltage.

  Fig. 5. Simulation results of OBIC current for both structures (device #1 from 800 V up to 2350 V and device #2 from 1000 up to 2850 V) and the corresponding electric field distribution at near breakdown voltage for both cases.

Acknowledgments

The authors would like to thank the FilSiC research program for financial support and also gratefully acknowledge Dr. Gregory GROSSET and Lionel DUPUY for the realization of test structures.


Anne Condamines

The Emotional Dimension in Terminological Variation: The Example of Transitivization of the Locative Complement in Fishing

Keywords: emotional dimension, Internet as corpus, terminology variation, transitivization

You can have no idea of the depths of emotion felt by fishing clubs and anglers generally

) Salmon Fishing in the Yemen. London: Phoenix, p. 116.

Introduction

Generally speaking, studies of terms do not take the role of emotion into consideration. When building terminological databases to improve the clarity of communication, emotion is considered as a parasitic factor. As a result, even when variation is accounted for, it only concerns temporal, geographical, or diastratic parameters. Because most studies aim at working with consensual knowledge, the texts used in textual terminology mainly belong to genres devoid of any expression of emotion (handbooks, encyclopedias, didactic documents, etc.).

However, contrary to what is generally acknowledged, some situations in specialized fields may generate emotions, either because some extra-linguistic elements generate stress, or, on the contrary, enthusiasm, or because the field essentially requires emotional involvement, such as sports or hobbies. This contribution tackles the fact that when emotion is involved, it can impact the way terms work in discourse.

The presentation draws upon the description of cases of transitivization of the locative complement in the field of fishing. Indeed, it is possible to find utterances in French such as j'ai déjà pêché cette rivière (ʻI've already fished this river') instead of j'ai déjà pêché dans cette rivière (ʻI've already fished in this river'). The initial hypothesis is that this kind of violation of the code is possible in situations in which anglers are emotionally involved in their activity.

In order to test this hypothesis, I used the Internet as a corpus and searched for all the occurrences of [pêcher (prep) (det) rivière]. I took into account the nature of the websites in which the different occurrences appear. After an overview of the issue (part 2), the results for French are presented (part 3). The phenomenon of transitivization is then analyzed in other languages (English, Spanish and Italian) and with other French verbs (part 4). Finally, general issues are addressed regarding the role of emotion in specialized situations and the link between terminology and embodied cognition (part 5). Theoretical and practical questions are raised such as the meaning of the verbs used (is it the same with or without a preposition before the locative complement?), the need to take such phenomena into account in terminological models, and the difficulty of detecting and characterizing them.

Overview of the issue

This part discusses the problem of the absence of the emotional dimension in terminology studies. This absence is mainly due to the purpose of traditional studies, i.e. to build terminologies in scientific or technical fields in order to improve communication within these fields (2.1). When building these terminologies, very few studies have included texts with an emotional dimension. In fact, only a few have examined specialized discourse belonging to sports or hobbies but very rarely from a terminological perspective (2.2).

The limits of textual terminology

Over the last few decades, Wüster's approach to terminology has been questioned. His General Theory of Terminology (GTT) [START_REF] Wüster | The Machine TOOL. An Interlingual Dictionary of Basic Concepts[END_REF]) has been considered as too prescriptive and too remote from real usages. With the development of natural language processing (NLP), it soon became clear that, in many cases, the prescriptive approach underlying the GTT corresponded neither to the form nor to the meaning of real text usages. This led to the development of new approaches such as socioterminology [START_REF] Guespin | Socioterminology Facing Problems in Standardization[END_REF]), the Communicative Theory of Terminology [START_REF] Cabré | Terminology Theory, Methods and Applications[END_REF] or Sociocognitive Terminology [START_REF] Temmerman | Towards New Ways of Terminology Description. The Sociocognitive Approach[END_REF].

All of these new approaches recommend taking real discourses into account in order to observe and describe terms in their natural linguistic setting. Furthermore, they can all be characterized as belonging to textual terminology, which claims that terms can only be analyzed in their real uses [START_REF] Pearson | Terms in Context[END_REF].

One of the most important problems tackled by textual terminology is to build terminologies from texts, either monolingual or multilingual. These terminologies are based on knowledge representation in the form of a network in which both the nodes and the links are labelled with linguistic elements. Building this kind of representation from texts has generated a large number of studies, methods and tools for spotting terms and conceptual relations within texts (see for example Bourigault et al. 2001;[START_REF] Buitelaar | Ontology Learning from Text: Methods, Evaluation and Applications[END_REF][START_REF] Auger | Pattern-based Approaches to Semantic Relation Extraction: A State-of-the-art[END_REF][START_REF] Sierra | Definitional Verbal Patterns for Semantic Relation Extraction[END_REF]. Even when the main objective is not to build such a network, it generally constitutes the first step of the study. In textual terminology, the texts included in the corpus are not everyday texts but rather texts considered as representative of the consensual knowledge in a scientific or technical field, and are therefore drawn from textual genres such as handbooks, general overviews, courses and so on. In order to build terminological networks, these kinds of texts are said to be rich in knowledge patterns [START_REF] Bowker | Working with Specialized Language. A practical guide to using corpora[END_REF]. This is not surprising because they all have a didactic purpose, in which defining terms is an important function. Another important characteristic of these texts is that they contain very few first-person pronouns or evaluative adjectives. Since the texts are considered to contain shared knowledge, the responsibility for the content does not lie with an individual writer but rather with a writer representing a "speech community" [START_REF] Hymes | Models of the Interaction of Language and Social Setting[END_REF].

It is clear that the aim of defining terms has led researchers to focus only on certain textual genres that are devoid of emotion. This observation raises two kinds of questions. On the one hand, is it possible to combine terminology and emotional expression and on the other, if we accept that emotion can occur in specialized fields, to what extent may it lead to variation in how terms are described? In the rest of the chapter I show that these two questions are far from being marginal.

Variation and emotion in specialized discourses

Very few researchers have studied how terms work in specialized texts belonging to other fields than science or technology such as hobbies or sports, specifically in situations where speaker involvement in the discourse is high. Even when terminological variation is taken into account, the types of variation considered do not concern the emotional dimension but rather elements of time, degree of expertise or regional differences [START_REF] Condamines | Variations in Terminology. Application to the Management of Risks Related to Language Use in the Workplace[END_REF][START_REF] Freixa | Causes of Denominative Variation in Terminology. A Typology Proposal[END_REF]Ibekwe et al. 2007). While studies on the discourse of sport exist (for example, Lavric et al. 2008), they do not analyze the terms in order to build a dictionary or to facilitate translation but rather to illustrate a cultural specificity.

The only studies focusing on variation linked to speech communities of professionals sharing the same motivations concern jargons. This denomination is always negatively connoted, however: "Jargons have been relegated to a lower level of language and have not received the scholarly attention they deserve" (Depecker 1994:736). They are very often considered as a way of isolating a community from the rest of the world: "The reason that all these words [argot, jargon, lingo, and slang] have disparaging connotations is that outsiders dislike being outsiders" (Bernstein 1995:237).

Nevertheless, I contend that in specialized domains belonging to sports or hobbies, what appears as a jargon (in the sense of terms or usages far from those used in "neutral situations") must be described and registered in a dictionary and, sometimes, may be explained directly by the subjective involvement of the speaker.

I shall illustrate this phenomenon with data from the domain of fishing. The starting point of the study was my surprise at hearing an angler say in French: "j'ai déjà pêché cette rivière" ('I have already fished this river'). For a non-angler like myself, this sentence seems to be incorrect because the only object which can be fished is a fish (or a crustacean). As a linguist, my first hypothesis was that anglers allow themselves to infringe the rule concerning the nature of the object only in situations with a strong personal involvement. My second hypothesis was that this transitivization plays a particular role for anglers. 2Another specificity of this sentence is that the term concerned is a verb. The study of verbs in terminology is recent. It is generally considered that terms are nouns or noun groups in 70% of cases. Very few studies have been conducted on verbs. Nevertheless, recently, verbs have been considered interesting for spotting terms and even as terms [START_REF] Condamines | Un exemple d'utilisation de connaissances de sémantique lexicale: acquisition semi-automatique d'un vocabulaire de spécialité[END_REF][START_REF] Condamines | Searching for and Identifying Conceptual Relationships via a Corpus-based Approach to a Terminological Knowledge Base (CTKB): Method and Results[END_REF][START_REF] L'homme | What can Verbs and Adjectives Tell us about Terms?[END_REF][START_REF] L'homme | Le verbe terminologique: un portrait de travaux récents[END_REF].

In order to explore the role of emotion in transitivization in the fishing domain, I decided to carry out a study on the only available corpus likely to contain enough occurrences of various communicative situations: the Internet.

The study on French

The study on French is presented in detail in [START_REF] Condamines | Quand la passion autorise la transitivisation d'un circonstanciel de lieu[END_REF], and the main results are summarized here. In 3.1, I present the results with the verbal form, pêcher. I then consider the derived adjective, pêchable. Finally, I show how other characteristics (syntactic or semantic) generally associated with transitivity are relevant for describing the examples in which pêcher and rivière are related without a preposition.

The verb pêcher

Using Google, I focused on the simultaneous occurrence of the two forms pêcher and rivière(s). These two forms have the advantage of being non-ambiguous if they are contiguous; all the occurrences concern the infinitive form of the verb pêcher and the noun denominating the real object ʻriver'.3 I focused only on the infinitive form of the verb because pêche would have been too ambiguous. In French, it corresponds to several persons of the present tense of the verb, to the nominalization and even to a fruit (a peach). In order to control the structures I wanted to study, I placed a bracket before and after the structures. Finally, I only searched for structures containing either a definite (la/les) or an indefinite determiner (une/des). The four search items were as follows: (1) pêcher dans DET rivière(s); (2) pêcher en rivière(s); (3) pêcher sur (DET) rivière(s); (4) pêcher DET rivière.

Examples:

(1) Nous mettons à votre disposition un bateau pour pêcher dans la rivière en bas du jardin.

'At the bottom of the garden there is a boat available for fishing in the river.'

(2) J'affectionne surtout de pêcher en rivière. ʻI'm particularly fond of river fishing.'

(3) Je vais aller pêcher sur la rivière Yamaska à Granby samedi s'il ne pleut pas. ʻI'm going to fish on the river Yamaska in Granby on Saturday if it isn't raining.'

(4) Il nous proposa de pêcher la rivière Matane. ʻHe suggested we fish the river Matane.'

Note that some occurrences of the structures appear several times in exactly the same sentence. In this case, I counted only one occurrence. A total of 1474 occurrences were found. Table 1 summarizes the results obtained for the four French structures in all the websites. From these initial results, two remarks can be made: the supposedly transgressive form (without a preposition) is far from rare, it accounts for 17.7% of all the occurrences; the allegedly most regular structure, with the preposition dans, concerns only 45.6% of the occurrences. Even if the Internet cannot be considered as a representative corpus, it seems that the direct construction is relatively frequent. In order to test the hypothesis of the role of emotion in transitivization, I next characterized the nature of the websites containing simultaneously pêcher and rivière.

The categorization of the websites in which the occurrences were found was relatively easy. I identified ten types of websites: forum, blog, story, press, book, travel, regulations, translation, dictionary, varia. Note that no site corresponded to commercial fishing. This is probably due to the fact that to fish in a river (contrary to fish in an ocean for example) is not a commercial activity.

These websites are not specifically dedicated to angling, so, in order to refine my hypothesis, I focused on occurrences in websites that met two criteria: the site was devoted to angling, and it contained markers of subjective involvement (most of the forums and the blogs) such as first-person pronouns or an emotional lexicon. A total of 516 occurrences (35%) corresponded to these two criteria. Table 2 summarizes the distribution of the constructions in angling websites that have an emotional dimension. It is clear that in these kinds of websites, the most frequently used structure is the direct construction. This point demonstrates that the hypothesis was relevant: anglers, when speaking to each other, tend to use the direct construction. Other clues point to the same conclusion.

Analysis of other elements characterizing the objects

In this part, I examine three kinds of phenomena generally considered characteristic of objects in sentences. The first one concerns the adjective derived from the verb: pêchable (ʻfishable'), generally considered as linked to the object of the verb. The following two concerns syntactic and semantic aspects.

The case of pêchable

In relation with the verb pêcher, I also examined the adjective "pêchable"4 (fishable). Generally speaking, -able adjectives are considered as more often attributable to the object of the verb from which they are derived. This is the case, for example, in:

(5) Block purchasable: this block is available to advertise on it The underlying utterance is: You can purchase the block, in which block is the object.

I identified 583 occurrences of pêchable, among which 458 are associated with water courses or water bodies and only 125 with a fish or a crustacean. So, in 78% of the cases, the noun with which pêchable is associated does not belong to the category of the expected object of the verb, namely fish or crustacean.

(6) Le gave de Pau redevient pêchable après une fonte des neiges très précoce cette année ʻThe Gave de Pau stream has become fishable again after the very early snowmelt this year'

Another interesting point is that when pêchable concerns water courses or water bodies, it is most often modified, as in:

(7) La pluie qui tombe chaque jour conduit à voir des rivières difficilement pêchables ʻThe daily rainfall makes the rivers difficult to fish' (8) La mer est en train de tomber et devient plus pêchable. ʻThe sea level is falling, making the sea more fishable.' This gradation in "fishability", more often attributed to the water than to the fish, seems to confirm a strong link between the angler and the water.

Syntactic tests

Two tests are generally considered useful to characterize the object function: the possibility of pronominalizing and of passivating the object in sentences (ref). A few occurrences on the Internet seem to confirm the possibility of these two transformations for rivière:

(9) La Loire, je la pêche du bord ʻThe Loire, I fish it from the river bank'

In (9), it is the river-here, La Loire-that is pronominalized.

(10) La rivière est pêchée tous les jours depuis un mois. ʻThe river has been fished every day for the last month'.

In (10), rivière appears in subject position in the passive voice.

"Semantic" tests

Most semanticists accept the hypothesis of a gradation in transitivity [START_REF] Lakoff | Linguistic Gestalts[END_REF][START_REF] Dowty | Thematic Proto-roles and Argument Selection[END_REF]. In their paper, [START_REF] Hopper | Transitivity in Grammar and Discourse[END_REF] propose ten semantic elements that are useful for evaluating the transitivity of a sentence: participants, kinesis, aspect, punctuality, volitionality, affirmation, mode, agency, affectedness of O, individuation of O. Depending on the number of elements concerned and the degree of their relevance, the sentences are considered as more or less transitive.

Concerning the case of pêcher la rivière, the two elements that are perhaps the least relevant are affectedness of O and particularly individuation of O. They are defined as follows: "The degree to which an action is transferred to a patient is a function of how completely that patient is affected […]. The component of individuation, however, refers both to the distinctness of the patient from the A [agent] and to the distinctness from its own background" (Hopper and Thompson 1980:253). While the individuation of a river is perhaps difficult to grasp, its affectedness is not impossible to demonstrate. In several examples, the river is presented as affected by the fishing process and even as a person:

(11) Je vais également en profiter pour ressortir ma canne à toc, mais également pêcher la rivière qui a connu mes premiers lancés ʻI'm going to take the opportunity to get out my fly-fishing rod and to fish the river that witnessed my first casts' (12) Je décide donc de pêcher une rivière qui ne m'a pas revu depuis un petit moment déja ʻSo I've decided to fish a river that hasn't seen me for quite a while'

For semanticists, "[w]hen analyzing transitivity the focus is on how events and processes are connected (or not connected) with subjects and objects" (Jørgensen and Phillips 2002:83).

Taking into account the syntactic or semantic elements I have examined, we can say that for anglers, the "connection" with the river itself is probably more important than with the fish.

Other languages, other verbs

To extend the analysis of transitivization of the locative complement, I explored the same phenomenon in other languages and other fields.

Other languages

In view of these surprising results for French, I decided to consider the issue for three other languages: English, Spanish and Italian.

Preparation of the studies

I hired three linguistics students in order to constitute the data;5 each one speaks one of the three languages considered. As I did for French, they used the Internet as a corpus and focused on all the structures involving the verb corresponding to "pêcher" in each language (to fish/pescar/pescare) and the noun corresponding to "rivière" (river/río/fiume). As I did for French also, two categories of determiners were considered between the verb and the noun: definite and indefinite. Here are the structures selected for the three languages.

English

Four structures were searched for with Google: (1) to fish in (DET) river(s); (2) to fish on (DET) river(s); (3) to fish within (DET) river(s); (4) to fish (DET) river(s). The determiners used were a and the. There were 2202 occurrences of sentences containing one of the four structures. Example (13) shows the direct construction (structure 4):

(13) If I was going to fish a river this time of year, I would only have two options […].

Spanish

For Spanish, three kinds of structures were searched for with Google, and a total of 1610 occurrences were found. The structures were: (1) pescar en (DET) río(s); (2) pescar sobre (DET) río(s); (3) escar (DET) río(s). The determiners used were el, un, and los. Example ( 14) shows an occurrence without a preposition:

(14) Por eso es que necesito saber come se debe pescar un río de aguas claras. ʻTherefore I need to know how to fish a river with clear waters.'

Italian

Three structures were examined in Italian: (1) pescare in (DET) fiume/I; (2) pescare su (DET) fiume/I; (3) pescare DET fiume/i. The determiners used were un, il, dei and i. These structures occurred in 986 different sentences. Since prepositions and determiners can be contracted in Italian, the following structures were searched for: pescar + (in un fiume, in dei fiume, nei fiumi, su un fiume, su dei fiumi, sul fiume, sui fiumi, in fiume, in fiumi, un fiume, dei fiumi, il fiume, i fiumi). Here is an example without a preposition:

(15) Intanto le trote sono diventate nervose decidiamo di iniziare a pescare il fiume ʻMeanwhile the trout became restless and we decide to start fishing the river'

As I did for French, each website in which the structures occurred was characterized according to two criteria: the domain (devoted to angling or not) and with or without subjective involvement. Note that the geographical origin of the websites (France or Quebec, Spain or Latin America, Great Britain or the USA) was not taken into account. This element may play a role in the use of the direct construction but, at this stage of the study, it is too difficult to examine. Concerning the acceptability of the direct structure by dictionaries, note that Spanish and Italian dictionaries, like French ones, do not accept the construction without a preposition, whereas English dictionaries do record it.

Results

The results are presented in Tables 3 to 8. For each language, the tables first present the distribution of the structures in all the websites and then only in the websites dedicated to angling that have an emotional dimension. At first glance, it appears that the structure without a preposition is very frequent in English (which explains why this structure is registered in dictionaries) and very rare in Italian. Table 9 shows this even more clearly. It summarizes the results for all the languages concerning occurrences without a preposition before rivière/river/fiume/rio and their distribution in websites in the whole corpus compared to the corpus of angling websites with an emotional dimension. It constitutes the contingency table used to calculate the chi2. The crucial question is that of the role of the nature of the websites (which concern angling and present an emotional dimension). Based on the raw numbers presented in Table 9, the chi-squared test showed a significant difference (p <.001) in the use of the preposition. 6 Direct constructions (without a preposition) seem to characterize websites conveying a passion for fishing. This aspect was observed for three languages: French, English and Spanish. It is not the case with Italian, where the direct construction is rare in general and not more significantly present in the websites concerning fishing that have an emotional dimension.

English

This result seems surprising and at the moment I have no explanation for it. Apart from Italian, it is clear that the possibility of transitivizing the locative complement may be connected to some extra-linguistic characteristics at least in some Romance or Anglo-Saxon languages; it will probably be different in other kinds of languages (see for example [START_REF] Lazard | L'actance[END_REF].

I would argue, however, that this phenomenon tells us something about the activity of fishing for anglers. Again, we can consider that, for them, the most important aspect is not to catch fish but rather to be in contact with the river. By expressing the link between the verb and the location directly (probably in an unconscious way) they express their proximity to the river. The fact that this phenomenon exists in different languages is a strong indication that it belongs to a cognitive process, partly independent of language.

Other verbs

What about other verbs? If my hypothesis is valid, other verbs may allow the same transitivization. Indeed, transitivization of the locative complement is fairly common in sport or hobbies. I tested some verbs on the Internet and easily found other examples in the three languages considered:

(16) A partir de quand peut-on skier le Mont Blanc?

ʻWhen can one start skiing the Mont Blanc?' However, some verbs that appear similar to pêcher do not occur (or only very rarely) without a preposition before the locative complement. This is the case for chasser (to hunt). In French, the direct construction with the locative complement is in fact very rare.

(24) A la fin du lâcher, on peut chasser les bois et prairies environnantes, à l'aide de son chien d'arrêt ʻAt the end of the release, you can hunt the surrounding woods and fields with your pointer.'

It is also the case for Spanish (25) Cazar el bosque para todo tipo de animales y ser conscientes de que no todo obtener buenos puntos 'Hunting woods for all sorts of animals and being aware that getting good shots is not everything.'

It seems a little more frequent in English, however:

(26) I went out to hunt the forests surrounding the canyon.

In order to explain what appears to be an important difference between to fish and to hunt, it would probably be necessary to take into account the nature of the location. A river is perhaps more limited an area than a forest or fields, and it provides a real resistance (a force in Talmy's terminology [START_REF] Talmy | Toward a Cognitive Semantics[END_REF]). This hypothesis will be examined in further studies.

Cognition, emotion and specialized languages

This study conducted on fishing contributes to the development of new considerations in terminology that take into account the role of the body and of emotions, thereby bringing terminology closer to cognitive linguistics. I will examine this issue first by discussing studies dealing with cognitive linguistic aspects, and then those dealing with the notion of embodiment. Finally, I inquire how this kind of variation could be registered in terminological databases.

Cognition, terminology, frames

Like the lexicon in formal or generative approaches, terms in the Wüsterian point of view are considered as being remote from emotion. The prescriptive Wüsterian approach argues that normalization contributes to the clarity of language and considers communication as the equivalent of information transmission. This point of view seems too reductive for linguists. These situations are assumed to correspond to technical or scientific contexts. However, specialized fields cannot be reduced to these situations, and even scientific and technical situations may generate emotions (stress, enthusiasm, apprehension, etc.). For terminologists, the problem is to analyze how terms work in emotional situations. If the way they work is regular enough, it must be included in term banks.

The problem is that looking for and describing such phenomena may be very time-consuming. One of the important concepts in cognitive linguistics is that of frame. Frames are defined by Evans and Green (2011:166) as "detailed knowledge structures or schemas emerging from everyday experiences." The notion of frame comes from Fillmore's work on semantic grammar [START_REF] Fillmore | The Case for Case Reopened[END_REF]. Fillmore defined a semantic frame as a "schematic representation of the conceptual structures and patterns of beliefs, practices, institutions, images, etc. that provide a foundation for meaningful interaction in a speech community" (Fillmore et al. 2003:235).

From these two definitions, two elements stand out. First, cognition is based on everyday experience. And experience involves actions or thoughts in which the body (that is, perceptions) is involved. Even in scientific or technical domains, it seems very difficult to argue that only rationality is involved. And in sports or hobbies, it is obvious that the entire body is involved. The role of emotion in terminology has been examined in a recent neurolinguistic study carried out by Faber's team [START_REF] Benítez | Neural Substrates of Specialized Knowledge Representation: An fMRI Study[END_REF], based on brain-imaging techniques. In a paper relating this experiment, Faber and her team show that, in a task associating words with more generic words and terms with more generic terms, experts and non-experts do not use exactly the same part of their brain:

The amygdala is said to facilitate the integration of emotive and cognitive function. Our results seem to confirm that lexical decisions were more accurate for terms with an emotional valence because their semantic representations stored in a distributed network of cortical regions in the temporal cortex received reciprocal feedback from the amygdale. (Faber et al. 2014:27) They also note that the amygdala is "interconnected with the other frontotemporal components implicated in autobiographical memory." In other words, when experts are involved in a linguistic process implying their domain knowledge, they use their perceptive and emotive experience of the objects denominated by the nouns and not only a rational perception. In the case of fishing, we can establish a similarity between the neurolinguistics experiment and the possibility of transitivizing the location by saying that anglers, who are experts in their domain, use the perceptions they experience when fishing to authorize themselves to infringe the code and give the river the role of object. The quotation from Fillmore points out the importance of the speech community in meaningful interaction. In the case of fishing, experts (the anglers) restrict infringements of the code mainly to situations in which they assume that the readers are also experts, that is to say that they share the same bodily experience of being in the water when fishing.

Embodied cognition

In cognitive approaches, the role of the body (perceptions and emotion) is usually addressed under the term embodied cognition. The quote from Johnson below highlights the role of the body not only in cognition but also in understanding:

On the view developed here, the key notion is embodied understanding. We are never separated from our bodies and from forces and energies acting upon us to give rise to our understanding (as our "being-in-the world"). (Johnson 1987:205) Johnson's remark concerning the role of the body in understanding can probably also be extended to speaking. The position of [START_REF] Varela | The Embodied Mind, Cognitive Science and Human Experience[END_REF] is very close to that of Johnson, but it also underlines the link with cultural context:

Let us explain what we mean by this phrase embodied action. By using the term embodied we mean to highlight two points: first, that cognition depends upon the kinds of experience that come from having a body with various sensorimotor capacities, and second, that these individual sensorimotor capacities are themselves embedded in a more encompassing biological, psychological and cultural context. (Varela et al. 1993:175) So, when fishing, we can consider that anglers are engaged with their whole body in the activity (perceiving water, battling the natural elements, etc.) with the result that this engagement is linguistically expressed, at least when among other anglers, by the transitivization of the locative complement.

Taking the emotional dimension into account in terminology

Taking the emotional dimension into account in terminology raises two main issues. First, it is necessary to provide models that account for the type of variation that is linked to the emotional dimension. This seems possible with database models in which more than one frame can be associated with a word. As noted by Faber and Pizzaro (2012:5), "Until now, frames have only been applied to general language and not to specialized languages." But now, some new models based on frames are being designed in order to describe terminological variation. This is the case of FrameNet, developed by Fillmore and his team [START_REF] Fillmore | Background to FrameNet[END_REF]. However, it is not easy to tackle the fact that several entries for the same word may or may not concern different meanings. Can we consider that pêcher in the two constructions pêcher un poisson and pêcher une rivière has the same meaning or not? Such a question allows to link terminology studies with cognitive semantics issues. This appears a very promising perspective. But, fundamentally, this very interesting theoretical question has probably no consequence on the chosen model itself. Nonetheless, it is important to decide whether it is acceptable to register a verb, generally constructed with a direct argument belonging to a certain semantic class, with a direct argument belonging to another semantic class, generally represented by a complement (locative argument in the case of pêcher). If the answer is "yes," the problem is then to find the best way of registering it: for each individual verb or for a verb class? Whatever the answer, the important point is that the variation between the two constructions is linked to the nature of the communicative situation (with or without emotion). In the future terminological bases, it will be probably possible to take this element into account.

The second issue raised is the problem of identifying the linguistic phenomena, on the one hand, and, on the other, of identifying the kind of situation that may generate the emotion, in order to link linguistic phenomena and situational characteristics. Every type of linguistic variation may be difficult to identify, but with regard to emotional variation, the two aspectslinguistic and situational-may be particularly difficult to single out. In the case of fishing, for example, locating the transitivization phenomenon was a question of chance, and its description, based on real usage, was very timeconsuming. As we have seen, if some verbs (ski, paddle, surf, etc.) seem to have the same characteristics, it is not the case with others such as chasser (to hunt). So, it is not yet possible to generalize the description to all verbs. Further research is necessary in order to describe precisely the situational characteristics that allow this phenomenon.

Conclusion

This contribution has attempted to show that the emotional dimension cannot always be eliminated from a terminological perspective. It can play a role in scientific or technical domains, and above all, it is essential in domains belonging to hobbies or sports. Emotion may have a major impact on the way terms work. With the example from fishing, we saw that when anglers are emotionally involved, they may transitivize the locative complement and give it the status of object. The study, first carried out for French by using the Internet as a corpus, was then conducted for English, Spanish and Italian. Of the four languages, there is only one, Italian, in which the link between the absence of a preposition before the locative complement and the nature of the website (dedicated to fishing and with an emotional dimension) is not statistically significant. These results are promising in different ways.

First, and this was my starting point, it seems necessary to develop studies on the role of the emotional dimension in terminology. Needs concerning terminology are changing. They do not concern only canonical situations in science or technology but also those domains where emotion may play a role, mainly in oral communication, as well as domains involving specialized knowledge that have a strong emotional engagement such as sports or hobbies. As we have seen, tackling this emotional dimension is not straightforward. Several elements have to be examined: -It is necessary to design terminological models able to take the emotional dimension into account. The model proposed by the FrameNet project appears able to do that [START_REF] Fillmore | Background to FrameNet[END_REF]). -Only linguistic phenomena regularly observed in speech communities (and not generated by a single speaker), associated with certain emotions should be considered. -It may be difficult to determine which phenomena are relevant and which speech community they are related to. A corpus linguistic approach to the description of the grammar of genres will be useful for the latter two points.

Second, the results from the fishing domain bring terminology closer to cognitive linguistics. Like several researchers in cognitive semantics, I assume that the relationship between a subject and an object in an utterance is quite strong. So, when anglers choose to put a locative complement in the object position, even unconsciously, this indicates something about the relationship they have with this location. The embodied cognition may be a good approach to describe this phenomenon. Indeed, it is necessary to understand the circumstances in which the transitivization of the locative complement is possible in order to generalize the description. While it seems clear that the emotional dimension is crucial in explaining this phenomenon, it does not seem sufficient to explain why this transitivization is very rare for some other verbs in French such as chasser (to hunt). In this specific case, the notion of force dynamics proposed by [START_REF] Talmy | Toward a Cognitive Semantics[END_REF] could be relevant.

Extensive studies are necessary in order to describe this phenomenon of transitivization and, more generally, to analyze how this kind of phenomenon may be first detected, then explained and finally described in terminological databases.

Table 1 .

 1 Distribution of the four French structures in all the websites (in percentages)

	Pêcher dans DET	Pêcher en rivière(s) Pêcher sur (DET)	Pêcher DET
	rivière(s)		rivière(s)	rivière(s)
	45.6	27.5	9.2	17.7

Table 2 .

 2 Distribution of the four French constructions in angling websites that have an emotional dimension (percentages)

	Pêcher dans DET	Pêcher en rivière(s) Pêcher sur (DET)	Pêcher DET
	rivière(s)		rivière(s)	rivière(s)
	36	21.7	4	38.2

Table 3 .

 3 Distribution of the English structures in all the Internet data (percentages)

	To fish in (DET)	To fish on (DET)	To fish within	To fish (DET)
	river(s)	river(s)	(DET) river(s)	river(s)
	29.2	17.7	2.8	50.3

Table 4 .

 4 Distribution of the English structures in angling websites that have an emotional dimension (percentages)

	To fish (DET)	To fish on (DET)	To fish within	To fish (DET)
	river(s)	river(s)	(DET) river(s)	river(s)
	9.9	16.5	4.4	69.2
	Spanish

Table 5 .

 5 Distribution of the Spanish structures in all the Internet data (percentages)

	Pescar en (DET) río(s)	Pescar sobre (DET) río(s)	Pescar (DET) río(s)
	72	4.2	23.8

Table 6 .

 6 Distribution of the Spanish structures in angling websites that have an emotional dimension (percentages)

	Pescar en (DET) río(s)	Pescar sobre (DET) río(s)	Pescar (DET) río(s)
	64	4.7	31.3
	Italian

Table 7 .

 7 Distribution of the Italian structures in all the Internet data (percentages)

	Pescare in (DET) fiume	Pescare su (DET) fiume	Pescare DET fiume
	73.9	23.5	2.6

Table 8 .

 8 Distribution of the Italian structures in angling websites that have an emotional dimension (percentages)

	Pescare in (DET) fiume	Pescare su (DET) fiume	Pescare DET fiume
	71	26.5	2.4

Table 9 .

 9 Contingency table of the occurrences with/without prepositions calculated for i) non-angling websites without an emotional dimension and ii) angling websites with an emotional dimension

	Non-fishing domain and	Fishing domain and
	without an emotional	with an emotional	TOTAL
	dimension	dimension

I would like to thank E. Rowley-Jolivet for this quote.

Note that in the Trésor de la langue française informatisé (http://atilf.atilf.fr/tlf.htm), the only case in which the direct construction between ʻpêcher' and ʻplan d'eau' is used is in an example such as: Vider (un étang, une pièce d'eau) pour prendre les poissons, la vider de tous ses poissons.

Even if pêcher has two meanings, only one of them can take an object.

As noted by[START_REF] Hathout | Enquête sur les dérivés enable[END_REF], pêchable is not identified by the TLFi.

I am very grateful to H. Chatelier, C. Orihuela and M. Cagliani for their help in this study.

I warmly thank Basilio Calderone for his help in this part of the study.


Philip-Dylan Gleonec
email: philip-dylan.gleonec@wi6labs.com

Jeremy Ardouin
email: wi6labsjeremy.ardouin@wi6labs.com

Matthieu Gautier
email: matthieu.gautier@irisa.fr

Olivier Berder
email: olivier.berder@irisa.fr

Demo Abstract: Multi-source energy management for Long Range IoT nodes

Energy harvesters are used in Internet of Things (IoT) networks to provide more energy to the nodes and enhance their autonomy. However, the nodes must adapt their consumed energy to variable energy harvesting conditions. Typically, an energy budget estimation (EBE) algorithm is used to calculate an energy budget based on the current energy capabilities. In this demonstration, we show an implementation and a comparison of multiple EBE algorithms on a real world LoRaWAN platform powered by different energy sources.

I. INTRODUCTION

IoT networks are usually powered by non rechargeable batteries, which limit their autonomy and require maintenance. As an alternative, the use of energy harvesting devices has been considered, which enables each node to scavenge its energy from its environment.

Most energy harvesting sources are variable, which requires the node to manage its energy to avoid power failure. To this purpose, energy management algorithms have been developed. These can be divided in two units : an EBE which calculates the best energy budget based on the node energy capabilities, and an energy allocator which decides how to spend this energy. In particular, model-free EBE algorithms, such as LQtracker [START_REF] Vigorito | Adaptive Control of Duty Cycling in Energy-Harvesting Wireless Sensor Networks[END_REF] or Fuzzyman [START_REF] Aoudia | Fuzzy Power Management for Energy Harvesting Wireless Sensor Nodes[END_REF], are generic and can be used regardless of the energy source.

In this demonstration, we show a comparison of such algorithms, implemented on a real-world LoRaWAN IoT node powered by a multi-source energy harvesting board [START_REF] Gleonec | Architecture of Multi-source Energy Harvesting for IoT nodes[END_REF]. All algorithms are implemented in a cross-platform library, which enables both real-world implementation and simulation.

II. TESTBED AND DEMONSTRATION

This demonstration is implemented on a LoRaWAN node platform, shown in Fig. 1, composed of a STM32L0 microcontroller and a SX1272 LoRa transceiver. The node is powered by a solar panel which provides up to 5 V and 40 mA. The solar energy is harvested by a multi-source energy harvesting board which can accept up to three simultaneous energy sources. This board uses SPV1050 converters from STmicroelectronics, and is used to charge a 7.5 F supercapacitor.

Four algorithms are compared in this demonstration. LQtracker takes the residual energy in storage E R as input, and determines the best energy budget E B using a linear regression algorithm. Fuzzyman takes E R and the harvested energy E H

III. CONCLUSION

This document presents a demonstration of a real-world implementation of energy budget estimation algorithms. These algorithms are used to control the duty cycle of LoRaWAN IoT nodes, and enable a theoretically infinite battery life. Future work will focus on improving the energy allocation, especially in the context of multiple tasks.

Fig. 1 :

 1 Fig. 1: Hardware evaluation platform.