Lev Smolentsev

Alexandre Krupa

Franc ¸ois Chaumette

F Chaumette

Shape visual servoing of a tether cable from parabolic features

In this paper we propose a visual servoing approach that controls the deformation of a suspended tether cable subject to gravity from visual data provided by a RGB-D camera. The cable shape is modelled with a parabolic curve together with the orientation of the plane containing the tether. The visual features considered are the parabolic coefficients and the yaw angle of that plane. We derive the analytical expression of the interaction matrix that relates the variation of the visual features to the velocities of the cable extremities. Singularities are demonstrated to occur if and only if the cable is taut horizontally or vertically. An image processing algorithm is also developed to extract in real-time the current features fitting the parabola to the cable from the observed point cloud. Simulations and experimental results demonstrate the efficiency of our visual servoing approach to deform the tether cable toward a desired shape configuration.

I. INTRODUCTION

The manipulation of Deformable Linear Objects (DLO) by a robotic manipulator is a challenging task due to the high number of DLO degrees of freedom (DOF) and the low number of robot DOF. Cable routing and cable inserting are common examples of DLO manipulation tasks in industry. Since these tasks are still mainly performed manually, their automation by robots has a great potential [START_REF] Jin | Robotic cable routing with spatial representation[END_REF], [START_REF] Galassi | Robotic wires manipulation for switchgear cabling and wiring harness manufacturing[END_REF], [START_REF] Fresnillo | An approach for the bimanual manipulation of a deformable linear object using a dual-arm industrial robot: cable routing use case[END_REF], [START_REF] Zürn | Software architecture for deformable linear object manipulation: A shape manipulation case study[END_REF]. In particular, two robot arms are used in [START_REF] Caro | Manipulating deformable objects with a dual-arm robot[END_REF] for manipulating a flexible beam in order to adapt its shape before an assembly operation. Accurately and automatically controlling the shape of a suspended cable can also be useful for Unmanned Aerial Vehicle (UAV) applications such as managing the shape of the power cable of tethered UAVs. For instance, [START_REF] Zikou | The power-over-tether system for powering small uavs: Tethering-line tension control synthesis[END_REF] proposed a device composed of a winch mounted on the ground that is controlled to maintain the power cable in a slack configuration to avoid pulling the drone or touching the ground. [START_REF] Micotra | Taut cable control of a tethered uav[END_REF] proposed an UAV controller that maintains the cable taut for canceling its oscillation and improving the flight stability. Another possible application is aerial transportation performed by a flying gripper made of two UAVs linked by a cable [START_REF] D'antonio | The catenary robot: Design and control of a cable propelled by two quadrotors[END_REF] or by cable-suspended parallel robots actuated by flying robots [START_REF] Czapalay Erskine | Wrench capability analysis of aerial cable towed systems[END_REF], [START_REF] Sanalitro | Indirect force control of a cable-suspended aerial multirobot manipulator[END_REF]. Controlling the shape of power cables linking a chain of underwater robots was also considered in [START_REF] Laranjeira | Catenary-based visual servoing for tether shape control between underwater vehicles[END_REF].

In the following, we present some works concerning the shape control of DLO using visual servoing. They are divided Firstname.Name@inria.fr into two families: model-based and model-free approaches. In the model-free branch, the DLO is usually modeled as a set of points [START_REF] Caro | Manipulating deformable objects with a dual-arm robot[END_REF], [START_REF] Lagneau | Automatic shape control of deformable wires based on model-free visual servoing[END_REF], [START_REF] Yu | Shape control of deformable linear objects with offline and online learning of local linear deformation models[END_REF] or a contour [START_REF] Qi | Adaptive shape servoing of elastic rods using parameterized regression features and auto-tuning motion controls[END_REF] that can be represented by geometrical features. The common way to control the object deformation is by minimizing the error between the current measure of these features and their desired values corresponding to the targeted shape. In [START_REF] Caro | Manipulating deformable objects with a dual-arm robot[END_REF] the considered features are the 3D positions of markers attached on the DLO while in [START_REF] Lagneau | Automatic shape control of deformable wires based on model-free visual servoing[END_REF] a set of 3D equidistant points lying on a B-spline curve fitting the shape is considered. In [START_REF] Qi | Adaptive shape servoing of elastic rods using parameterized regression features and auto-tuning motion controls[END_REF] four different cases of features are studied: contour polynomial spline coefficients, Bezier and Nurbs splines control points, and Fourier coefficients. To relate the variation of these features to the velocities of the robot end-effector that interacts with the DLO, [START_REF] Caro | Manipulating deformable objects with a dual-arm robot[END_REF] propose to estimate an approximate shape Jacobian matrix during an offline identification procedure that consists in deforming the DLO by applying open-loop step motions on each robot DOF and measuring the induced displacements of the attached markers. The shape Jacobian matrix can also be estimated online from visual data by using a Kalman filter [START_REF] Qi | Adaptive shape servoing of elastic rods using parameterized regression features and auto-tuning motion controls[END_REF] or by minimizing a quadratic objective on a sliding time windows [START_REF] Lagneau | Automatic shape control of deformable wires based on model-free visual servoing[END_REF]. More recently, [START_REF] Shetab-Bushehri | As-rigidas-possible shape servoing[END_REF] proposed a control scheme relying on a shape Jacobian that is updated online from simulations based on a geometrical deformation model [START_REF] Sorkine | As-Rigid-As-Possible Surface Modeling[END_REF]. In another way, a neural network is trained in [START_REF] Yu | Shape control of deformable linear objects with offline and online learning of local linear deformation models[END_REF] during an offline procedure for predicting the shape Jacobian matrix from the position of the cable control points. All aforementioned works allow to control the shape of the DLO without knowledge of its mechanical properties. However, the limitations of these approaches are the inability to determine possible singular configurations of the system that may cause instabilities in the control and the potential convergence of the system to local minima if the goal configuration is too far away. Moreover, the approaches that require an online estimation of the shape Jacobian are sensitive to measurement noise.

In the model-based branch of methods, a way to control the shape of a soft body consists in using a mechanical model that predicts its behavior. However, depending of its complexity, it may be difficult to run this model in realtime. The authors of [START_REF] Koessler | An efficient approach to closed-loop shape control of deformable objects using finite element models[END_REF] consider control points velocities as features and use a Finite Element Model that formulates locally the static equilibrium equations for these points to avoid real-time model simulations. In some cases the control input can be derived directly from model equations as it is done in [START_REF] D'antonio | The catenary robot: Design and control of a cable propelled by two quadrotors[END_REF] and [START_REF] Laranjeira | Catenary-based visual servoing for tether shape control between underwater vehicles[END_REF] with a catenary/chain curve.

In this work, we focus on the robotic manipulation of a suspended tether cable that is subject to gravity in order to control its shape. In that case, the cable can be slack or taut and we propose to generalize this possible set of configurations in a single and simple geometrical model: a 2 nd order polynomial curve, that is, a parabola. We show through simulations and experimental results that such approximation is sufficient. The proposed shape control approach only uses the length of the cable as a priori knowledge and the visual information provided by a RGB-D camera observing the cable. Moreover, it is capable of operating with slack and taut configurations and does not need to observe the cable extremities. In particular, the chain model considered in [START_REF] Laranjeira | Catenary-based visual servoing for tether shape control between underwater vehicles[END_REF] and in [START_REF] D'antonio | The catenary robot: Design and control of a cable propelled by two quadrotors[END_REF] does not allow to consider any taut configurations due to a singularity of the corresponding shape Jacobian, while our parabola model is not singular in this configuration apart when the cable is taut horizontally or vertically. An analytic expression of the shape Jacobian is derived for this model, thus avoiding the limitations of the model-free methods mentioned earlier. Another advantage of our solution is that it does not consider any mechanical model of the DLO and thus does not need any knowledge about its material mechanical properties. In contrast, our method relies only on an approximate geometrical model that is extracted and tracked from RGB-D data.

The paper is organized as follows: Section II presents the selected model of the tether cable and the visual features proposed for controlling its shape. The related Shape Jacobian matrix is analytically derived, from which a complete singularity analysis is performed and a classical visual servoing controller is presented. Section III describes the image processing developed to track in real-time the cable shape from the successive 3D point clouds provided by a RGB-D camera. Section IV presents simulation and experimental results of the proposed visual servoing approach. Finally, Section V summarizes the results of our work.

II. POLYNOMIAL VISUAL SERVOING A. Tether Modelling

We begin by defining Cartesian frames and 3D points necessary to model the tether shape. Coordinate frames are shown on Fig. 1. Note that both the tether frame F t and the world frame F w are defined so that their z axis is in the opposite direction of the gravity. Points p m and p f represent tether attachment points and p m is selected as the origin of F t . To be as general as possible, we consider in this section that both the 3D positions of p m and p f can be controlled.

Since the system has 3 degrees of freedom (that are the 3 components of the relative translation between p m and p f ), 3 independent parameters are sufficient to control it. Let us note that a trivial solution would be to select as visual features the relative position between p m and p f . However, these two points may not be visible. That is why the method we propose does not necessitate to measure their 3D coordinates. As already said, we use a parabola to model the shape of the cable. Its equation in the plane (x t , z t ) to which it belongs is given by z = ax 2 + bx. We thus use as first two visual features the parameters a and b that characterize the shape of this parabola. Finally and similarly to [START_REF] Laranjeira | Catenary-based visual servoing for tether shape control between underwater vehicles[END_REF], we use as third and last feature the yaw angle of the vertical plane containing the cable, i.e., the angle α between x t and x w (note that sin α was used in [START_REF] Laranjeira | Catenary-based visual servoing for tether shape control between underwater vehicles[END_REF], which induces a singularity when α = ±π/2).

In frame F t the coordinates p m and p f are respectively given by (0, 0, 0) and (D, 0, H) and any point belonging to the parabola that represents the tether has as coordinates:

t p =   t x 0 a t x 2 + b t x   (1)
where H = aD 2 + bD. Since F t and F w have been defined with parallel z axis, their relative pose is given by the homogeneous transformation matrix (c stands for cos, s for sin):

w H t =     cα -sα 0 w p mx sα cα 0 w p my 0 0 1 w p mz 0 0 0 1     (2)
This allows expressing any tether point in F w by:

w p = w p m +   t x cα t x sα a t x 2 + b t x   (3)
In particular, the coordinates of point p f in F w is given by:

w p f = w p m +   D cα D sα aD 2 + bD   (4)

B. Interaction matrix

As already said, the set s of visual features we consider is:

s =   a b α   (5)
We are now interested in determining the time variation of s in function of the time variation of w p m and w p f in F w for obtaining the analytical form of the interaction matrix of s.

By differentiating (4) we obtain:

w ṗf = w ṗm +   Ḋcα -sαD α Ḋsα + cαD α (2aD + b) Ḋ + D 2 ȧ + D ḃ  (6)
This equation can be rewritten as:

w ṗf -w ṗm =   0 0 cα -Dsα 0 0 sα Dcα D 2 D 2aD + b 0       ȧ ḃ Ḋ α     (7)
As D depends on a and b, it is necessary to eliminate Ḋ from [START_REF] Galassi | Robotic wires manipulation for switchgear cabling and wiring harness manufacturing[END_REF] to get a one-to-one relation between ṡ and w ṗfw ṗm .

In frame F t , D is related to a, b and the tether length L by the following equation:

L = D 0 1 + (2ax + b) 2 dx (8)
To solve this integral analytically, we choose t = 2ax + b, from which we deduce dt = 2adx and we obtain:

L = 1 2a t2 t1 1 + t 2 dt ( 9
)
where t 1 = b and t 2 = 2aD + b. Notice that this equation is not valid when a = 0 (that is, when the parabola degenerates to a straight line, in which case the tether is taut) for which:

L = D 1 + b 2 = D 2 + H 2 (10)
Since it is well known that:

1 + t 2 dt = 1 2 t 1 + t 2 + 1 2 ln t + 1 + t 2 (11)
and

ln t + 1 + t 2 = arcsinh t, t ∈ R (12)
we finally obtain the expression of the tether length:

L = f (D, a, b) = t 2 1 + t 2 2 -b 1 + b 2 (13)
+ arcsinh t 2 -arcsinh b /(4a)
Since L = 0, by differentiating (13) we get:

∂f ∂D Ḋ = - ∂f ∂a ȧ - ∂f ∂b ḃ (14)
from which we obtain:

Ḋ = k 1 ȧ + k 2 ḃ (15)
where

k 1 = 4(L -D 1 + t 2 2 )/k ( 16
)
k 2 = 2( 1 + b 2 -1 + t 2 2 )/k (17)
with

k = 4a 1 + t 2 2 ( 18
)
We can note that k = 0 when a = 0 (i.e., the tether is taut).

Fortunately, after applying a first order Taylor expansion to the term f (a) = 1 + t 2 2 = 1 + (2Da + b) 2 , we obtain

lim a→0 k 1 = -2D 2 b 1 + b 2 (19)
lim a→0 k 2 = -Db 1 + b 2 (20)
It is thus always possible to compute the terms k 1 and k 2 whatever the tether configuration. Then by injecting ( 15) into [START_REF] Galassi | Robotic wires manipulation for switchgear cabling and wiring harness manufacturing[END_REF] we obtain the following relation:

w ṗf -w ṗm = Mṡ (21)
with

M =   k 1 cα k 2 cα -Dsα k 1 sα k 2 sα Dcα n 1 n 2 0   (22)
where

n 1 = D 2 + t 2 k 1 and n 2 = D + t 2 k 2 .
The inverse of M can be analytically calculated and is given by:

M -1 = 1 Dq   -n 2 cα -n 2 sα k 2 n 1 cα n 1 sα -k 1 -qsα qcα 0   (23)
with q = Dk 2 -k 1 .

From ( 21), we finally obtain the relation:

ṡ = M -1 ( w ṗf -w ṗm ) = L s v (24)
where L s = -M -1 M -1 is the 3 × 6 shape interaction matrix that relates the variation of the visual features s to the translational velocity of p m and p f expressed in

F w : v = (v m , v f ) = ( w ṗm , w ṗf ) C. Control law
From the modelling presented in the previous section, we can immediately use the classical control law:

v = -λL + s (s -s * ) (25)
for ensuring an exponential decrease of the visual feature error e = ss * toward zero [START_REF] Chaumette | Visual servoing[END_REF]. Here s * denotes the desired value of the visual features, λ(> 0) is the control gain, and L + s is the Moore-Penrose pseudoinverse of L s . In case point p f is static (which is the case considered for our real experiments), the controller reduces to:

v m = λM(s -s * ) (26)
Note that apart the singular configurations exhibited in Section II-D, M is always of full rank 3, which ensures that the system is globally asymptotically stable in case M is correctly evaluated in (25) [START_REF] Chaumette | Visual servoing[END_REF].

As can be seen from ( 22), matrix M depends on the visual features a, b, α that are measured at each iteration of the control scheme, the tether length L that is constant and supposed to be known, and D that is varying. We thus need to estimate D. There are two ways for that: the first would be to track the attachment points p f and p m and measure their 3D position. As already said, this would not be convenient because the camera would need to have both points in its field of view, which would reduce the range of possible applications. The second method relies on estimating D from [START_REF] Micotra | Taut cable control of a tethered uav[END_REF]. Since there is unfortunately no explicit form for the solution of this equation, we propose to numerically search for a zero of (13):

D = argmin D∈R (f (D, a, b) -L) (27)
by determining D with a Newton method using the derivatives of the objective function (27). In practice, only a couple of iterations are needed to estimate the new value of D at each iteration of the control loop by using its previous value as initial guess. We used D = L/2 for the very first image.

D. Study of the singularities of L s

In the following, we present a study on the possible singularities that the interaction matrix L s may encounter. The determinant of M is given by:

det M = D 2 q = D 2 (Dk 2 -k 1 ) (28)
M and thus L s are singular when D is null, meaning that points p f and p m coincide or lay on the same vertical. This is logical since the angle α is no more defined in that degenerate case. Another singularity is reached for the condition Dk 2 -k 1 = 0. By using ( 16) and ( 17) this condition can be rewritten as:

D( 1 + tan 2 α f + 1 + tan 2 α m ) = 2L (29)
with tan α f = t 2 = 2Da + b and tan α m = b, where α f and α m are respectively the angles of the tangent of the parabola at point p m and p f (see Fig. 2).

Fig. 2: Tangent of the parabola at points p m and p f .

Since 1 + tan 2 α = 1 cos 2 α , (29) is equivalent to D | cos α f | + D | cos α m | = 2L (30)
Then, by combining (30) and ( 13), and using tan α ftan α m = 2Da, we obtain:

tan α f | cos α m | - tan α m | cos α f | = arcsinh tan α f | cos α m | - tan α m | cos α f | (31)
The singularity condition is given by the solution of (31), which exists in R if and only if

tan α f | cos α m | = tan α m | cos α f | (32)
Thus, the singularity occurs when α m = α f , meaning that the tether is taut. However, when the tether is taut, we directly obtain from ( 19) and ( 20)

q = Dk 2 -k 1 = D 2 b/(1 + b 2 ).
Apart from the previous exhibited configuration D = 0, this term vanishes only when b = 0, that is, when the tether is taut horizontally. This analysis demonstrates two singular configurations only: when p f and p m coincide, and when the parabola degenerates into a vertical or horizontal straight line. The former configuration corresponds to a pure degenerate case that cannot occur in practice. The latter can be avoided by never specifying such a desired configuration.

III. FEATURES EXTRACTION

In practice, the tether shape is estimated from RGB-D data. In particular, its RGB image together with the depth are used to fit a parabola into the observed point cloud of the tether. The image processing pipeline consists in first applying an HSV threshold on the RGB image to segment the cable in the image from its color (yellow in our case). A thinning algorithm [START_REF] Zhang | A fast parallel algorithm for thinning digital patterns[END_REF] is then applied for determining the middle line of the cable in the image. The 3D coordinates of the N points belonging to this middle line are first expressed in the camera frame F c thanks to the depth data (see Fig. 3) and then in the world frame F w thanks to the knowledge of the transformation matrix w H c (determined offline using a classical hand-eye calibration technique [START_REF] Tsai | A versatile camera calibration technique for high-accuracy 3d machine vision metrology using off-the-shelf tv cameras and lenses[END_REF]). Using these 3D points w p 1 . . . w p N , the parameters w n and w d of the cable plane equation w n T w p + w d = 0 in F w are estimated by using a robust least square method [START_REF] Comport | Robust model-based tracking for robot vision[END_REF] for eliminating potential outliers due to depth measurement errors. Notice that we impose the z-component of the normal w n to w n z = 0 during the estimation process since the plane is always vertical in F w due to the gravity. The angle α is then directly given by:

α = arctan(-w n x / w n y ) (33)
Afterwards, we use the cable plane equation expressed in the camera frame F c : c n T c p + c d = 0 to reconstruct the 3D coordinates c p i of each point belonging to the middle line of the cable from its observed image coordinates p im = (x i , ỹi , 1). Indeed, we have:

c p i = (x i z i , ỹi z i , z i ) (34)
with

z i = - c d c n T p im (35)
This process allows considering a new set of N 3D points that are less tainted by the sensor depth measurement noise. Note that c n T p im = 0 in (35) if and only if the cable plane is orthogonal to the image plane, which is a degenerate case we do not consider. Finally, the parabolic features a and b are estimated using a classical least squares method from this set of N points expressed in F t . For doing that, the points are expressed in F t using the transformation t H c = t H w w H c where t H w is the inverse of the homogeneous transformation (2) that is computed using the estimated α and the 3D position of p m in F w provided by the robot odometry. Furthermore, a and b are given by solving a t x 2 i + b t x i = t z i , i = 1, . . . , N whose solution is given by: Note that at least two points are necessary to obtain a and b, but the more the better.

a b =   t x 2 1 t x 1 . . . . . . t x 2 N t x N   +   t z 1 . . . t z N   (36)

IV. RESULTS

In a first part, we test our control approach in a simulation framework by using a continuous mechanical model of the tether cable to simulate its deformation. The accompanying video shows simulations where the position of the two cable extremities are controlled. In a second part, we present experimental results obtained for the real system and show that our method is robust to the approximation of the tether by a parabolic curve. Note that there is no difference between eye-in-hand and eye-to-hand setups in our case since the pose of the camera frame F c with respect to the world frame F w is constant and known from hand-eye calibration for the eyeto-hand setup while this now varying pose is obtained from hand-eye calibration and robot odometry for the eye-in-hand setup.

A. Simulation framework

A simulation framework has been implemented for validating the control approach developed in Section II. The overall pipeline of the simulation is presented by Algorithm 1 where dk is the simulation time step. For simulating a realistic cable deformation, the shape of the tether is expressed following the extensible catenary model presented in [START_REF] Yuan | Static and dynamic stiffness analyses of cable-driven parallel robots with non-negligible cable mass and elasticity[END_REF]. For using this model, we set arbitrary values for the Young's modulus E, the tether cross-section A and the tether mass per unit length ρ. These parameters correspond to the mechanical parameters of the cable that are required for the physicsbased model [START_REF] Yuan | Static and dynamic stiffness analyses of cable-driven parallel robots with non-negligible cable mass and elasticity[END_REF]. From the known position of the two tether extremities, the corresponding external force f with components (f x , 0, f z ) in F t to be applied to the extremity point p m is first estimated (see Fig. 3). Then, the solution at static equilibrium of the forces applied to the tether, that is, the external force f and the gravity g, allows determining the shape of the cable, from which a Point Cloud (PC) is generated. The coefficients (a, b) of the parabola are then determined using the least squares method described in Section III and a next iteration of the control loop can be achieved. We use ViSP [START_REF] Marchand | Visp for visual servoing: a generic software platform with a wide class of robot control skills[END_REF] for the implementation of the overall simulation.

The results of two shape servoing tasks are illustrated on Fig. 4. The first one is such that s * = [0, -0.7, 0], which means we want to reach a taut configuration, while the second one is such that s * = [3.6, -1, -30 o ], which corresponds to a general configuration. In both cases, the initial configuration of the tether is set to s

0 = [1.2, -1.4, 75 • ].
We can see the perfect exponential decrease of the error on Fig. 4c and4d. The three translational velocities of p m depicted on Fig. 4e and 4f also show a nice behavior without any instabilities when the tether becomes taut. These simulation results demonstrate that our control solution based on an approximation of the tether shape with a parabola can accurately perform the task, whatever the desired configuration of the cable.

B. Experimental validation

The experimental setup is composed by an Omron © 6 DOF articulated robot Viper650 (see Fig. 5a). The left extremity of a 86 centimeters length cable is attached to the robot end-effector and the right one is fixed to a tripod. A remote Intel © D435 RGB-D with a resolution of 1280x720 pixels for both data streams is mounted on a second fixed tripod and observes the scene.

To validate our method two different tasks were tested: the first is to stretch the tether by setting s * = [0, -0.4, -30 • ] and the second is to move it back to a slack configuration with s

* = [1.5, -1.4, -15 • ]. The initial state is such that s 0 = [1, -1.1, -17 • ].
The robot control sampling frequency is set to the camera frame rate (30 Hz) and the control gain to λ = 0.5. Typical RGB and depth images acquired by the camera are presented in Fig. 5. The temporal evolution of the features error together with the control velocity applied on point p m are shown on Fig. 6 (see also the accompanying video). One can see in Fig. 6a and 6b the exponential decoupled decrease of the features error to zero, which demonstrates the efficiency of the proposed approach. We can note on Fig. 6c and 6d that the noise on the estimated value of α, which is due to the low accuracy of the depth measurements, induces some noise on the v x and v y components of the end-effector velocity, but without destabilizing the system. These results show that even if our approach is based on a coarse modelling of the tether cable by a parabolic curve, it can efficiently perform the shaping task thanks to the robustness of the shape servoing closedloop control scheme.

V. CONCLUSION

In this paper, we addressed the automatic manipulation of a suspended tether cable. We proposed three visual features from a simple parabolic geometric model to control the translational velocities of its extremities. The analytical form of the related interaction matrix has been determined, allowing to demonstrate the absence of singularities apart when the tether is taut vertically or horizontally. Simulations together with real world tests have shown the efficiency of our method that does not require any knowledge of material mechanical properties. In comparison to model-free methods, the proposed approach has the advantage to provide a complete study of potential singular configurations and it gets rid of an online estimation of the shape Jacobian. Moreover it does not require any path planning for local minima avoidance and allows to bring the cable to taut configurations, which was not possible before.

In future work, we plan to extend this approach for controlling two quadrotors holding together a tether cable with the objective to grasp and manipulate objects for transport applications.

Fig. 1 :

 1 Fig. 1: Tether (green curve) and its parabola model (red curve): D > 0, H < 0 in this configuration.

Fig. 3 :

 3 Fig. 3: The tether cable setup used for the simulations and the experiments. The external forces used in the simulation are depicted in red.

Fig. 4 :

 4 Fig. 4: Simulation results. Cable configuration at the beginning and at the end for the first task (a) and for the second task (b) (parabola depicted in red and catenary in green). Evolution of the visual features error (c),(d) and velocity applied to point p m (e),(f) during the first and the second tasks respectively.

Fig. 5 :Fig. 6 :

 56 Fig. 5: (a) RGB image of the experiment during the first task. The fitted parabola, F w and F t frames are depicted in red. (b) Depth image with the first task target shape overlaid in yellow.

  while ||e k || > ϵ do e k = s k -s * compute D from (27) compute M(s k , D, L) from (22) v m = λMe k w p m(k+dk) = w p m(k) + v m dk compute αfrom w p m(k+dk) and w p f compute w H t from (2) f = simulator.estimateF( t p m , t p f , E, A, ρ)

	cable PC = simulator.sampleCatenary(f , E, A, ρ)
	compute a, b from cable PC
	s k = (a, b, α)
	end
	Algorithm 1: Simulation of the proposed visual servoing

VI. ACKNOWLEDGEMENTS

The authors would like to thank Sébastien Briot who suggested to use the catenary model for simulations, as well as Isabelle Fantoni for useful discussions.

This work carried out in the MAMBO project has received a French government support granted to the Labex CominLabs excellence laboratory and managed by the National Research Agency in the "Investing for the Future" program under reference ANR-10-LABX-07-01

Experiments presented in this paper were carried out thanks to a platform of the Robotex 2.0 French research infrastructure


Zoé Bollen
email: zoe.bollen@uclouvain.be

Louise Kauffmann

Nathalie Guyader

Carole Peyrin

Pierre Maurage

Uclouvain

Does alcohol automatically capture drinkers' attention? Exploration through an eye-tracking saccadic choice task

Keywords: attentional bias, binge drinking, saccadic choice task, saccadic response, alcohol use disorder

Rationale: Dominant theoretical models postulate the presence of an automatic attentional bias (AB) towards alcohol-related stimuli in alcohol use disorder, such AB constituting a core feature of this disorder. An early alcohol AB has been documented in subclinical populations such as binge drinking (i.e. a drinking pattern prevalent in youth and characterized by repeated alternation between alcohol intoxications and withdrawals, generating cerebral consequences). However, the automatic nature of AB remains to be established.

Objectives:

We investigated the automatic nature of AB in binge drinkers through the saccadic choice task. This eye-tracking paradigm consistently highlights the extremely fast and involuntary saccadic responses elicited by faces in humans, relative to other object categories. Through an alcohol-related adaptation of the saccadic choice task, we tested whether the early and automatic capture of attentional resources elicited by faces can also be found for alcohol-related stimuli in binge drinkers, as predicted by theoretical models.

Methods: Forty-three binge drinkers and 44 control participants performed two versions of the saccadic choice task. In the original version, two images (a face, a vehicle) were displayed on the left and right side of the screen respectively. Participants had to perform a saccade as fast as possible towards the target stimulus (either face or vehicle). In the alcohol-related version, the task was identical but the images were an alcoholic beverage and a non-alcoholic stimulus.

Results:

We replicated the automatic attraction toward faces in both groups, as faces generated higher saccadic accuracy, speed and amplitude than vehicles, as well as higher corrective saccade proportion. Concerning the alcohol-related adaptation of the task, groups did not differ for the accuracy, speed and amplitude of the first saccade towards alcohol.

However, binge drinkers differed from controls regarding the proportion of corrective saccade towards non-alcoholic stimuli after an error saccade towards alcohol, suggesting the presence of an alcohol disengagement bias specific to binge drinkers.

Conclusions:

Alcohol-related AB in binge drinkers is not characterized by an early and automatic hijacking of attention towards alcohol. This AB rather relies on later and more controlled processing stages, namely a difficulty to disengage attentional resources from alcohol-related stimuli.

Introduction

Attentional bias (AB) refers to the tendency to preferentially orient one's attentional resources towards salient or behaviorally-relevant stimuli when presented in the environment. Prominent addiction models [START_REF] Bechara | Decision making, impulse control and loss of willpower to resist drugs: A neurocognitive perspective[END_REF][START_REF] Wiers | Automatic and controlled processes and the development of addictive behaviors in adolescents: A review and a model[END_REF] suggested that alcohol-related stimuli would hijack the attention of individuals with alcohol use disorder (AUD) through associative learning, ending up in an AB towards alcohol. The influential incentive-sensitization theory [START_REF] Robinson | Development of the Alcohol Use Disorders Identification Test (AUDIT): WHO collaborative project on early detection of persons with harmful alcohol consumption-II[END_REF] notably posits that repetitive alcohol exposures sensitize the reward system, thus enhancing the motivational properties (i.e. incentive salience) of the stimuli associated with alcohol use. Becoming more salient, these alcohol-related stimuli automatically and rapidly grab drinker's attention and result in AB. This theory was then refined by a psychopharmacological model [START_REF] Franken | Drug craving and addiction: Integrating psychological and neuropsychopharmacological approaches[END_REF], suggesting that, when alcohol-related stimuli are present in the environment, they increase the dopaminergic response in the reward circuit, which in turn serves to automatically capture one's attention toward those stimuli. Such alcohol AB is thought to have clinical consequences, as it would increase craving (i.e. the intense urge and desire to consume alcohol), favor increased alcohol consumption, and enhance relapse risk. Hence, AB would play a crucial role in the onset and persistence of AUD, and is now considered as a key process in this disorder. Indeed, current prominent models postulate that the over-sensitivity of the reward system, caused by repeated alcohol use, makes the user highly reactive to alcohol-related stimuli, this AB being considered as an early, automatic and uncontrollable hijacking of attentional resources.

However, the empirical evidence supporting such strong theoretical assumptions remains limited in AUD. Previous behavioral studies showed very heterogeneous findings regarding the presence and extent of AB in the classical population of interest, namely recently detoxified patients with severe AUD (for a review, see [START_REF] Bollen | Attentional bias in alcohol drinkers: A systematic review of its link with consumption variables[END_REF]. Indeed, some findings revealed the presence of AB in this clinical population (e.g., [START_REF] Müller-Oehring | Brain activation to cannabis-and alcohol-related words in alcohol use disorder[END_REF], but others rather revealed an avoidance pattern (e.g., [START_REF] Townshend | Avoidance of alcohol-related stimuli in alcoholdependent inpatients[END_REF], and most did not show any difference in the attentional processing of alcohol-related stimuli compared with control individuals presenting low/moderate alcohol consumption (e.g., [START_REF] Field | Attentional biases in abstinent alcoholics and their association with craving[END_REF][START_REF] Wiers | Comparing three cognitive biases for alcohol cues in alcohol dependence[END_REF]. These disparate findings might be partly explained by the heterogeneity (e.g., various stimuli presentation times) and low reliability (due to reaction time measures; [START_REF] Ataya | Internal reliability of measures of substance-related cognitive bias[END_REF] of the AB paradigms used, as well as by the lack of inclusion criteria (e.g. alcohol doses per week) for recruiting healthy controls. The presence of alcohol-related AB appears more consistent in subclinical populations (i.e. individuals presenting excessive alcohol consumption but who do not present the diagnosis of severe AUD), since AB was positively related with alcohol use intensity in most studies conducted among social drinkers [START_REF] Albery | Testing a frequency of exposure hypothesis in attentional bias for alcohol-related stimuli amongst social drinkers[END_REF][START_REF] Field | Alcohol expectancy moderates attentional bias for alcohol cues in light drinkers[END_REF], and was found to be stronger in more specific drinking patterns (e.g., heavy or binge drinkers) compared to light drinkers [START_REF] Depalma | Attentional blink to alcohol cues in binge drinkers versus non-binge drinkers[END_REF][START_REF] Tibboel | Reduced attentional blink for alcohol-related stimuli in heavy social drinkers[END_REF], especially in the presence of high subjective craving [START_REF] Bollen | Craving is everything: An eye-tracking exploration of attentional bias in binge drinking[END_REF]. Nevertheless, the inter-studies comparison is dampened by a lack of coherence regarding the terminology and inclusion criteria to characterize these drinking patterns. To address this issue, we will focus on binge drinking, because it constitutes a clearly defined and specific drinking pattern [START_REF] Maurage | What we talk about when we talk about binge drinking: Towards an integrated conceptualization and evaluation[END_REF], and because it has been repeatedly associated with alcohol AB [START_REF] Elton | Acute depletion of dopamine precursors in the human brain: Effects on functional connectivity and alcohol attentional bias[END_REF][START_REF] Langbridge | A neurophysiological and behavioral assessment of interventions targeting attention bias and sense of control in binge drinking[END_REF], thus constituting the ideal population to reliably test the features of AB in a subclinical population. Popular in youth, binge drinking is characterized by intense alcohol consumptions in short periods of time to reach drunkenness [START_REF] Lannoy | What is binge drinking? Insights from a network perspective[END_REF]. The repeated alternation between intense intoxications and withdrawal periods appears particularly harmful for the brain, leading to well-established neuropsychological and cerebral negative effects [START_REF] Crego | Binge drinking affects attentional and visual working memory processing in young university students[END_REF][START_REF] Lannoy | Behavioral and cerebral impairments associated with binge drinking in youth: A critical review[END_REF]López-Caneda et al., 2013). The definition criteria for binge drinking usually relies on the computation of a binge drinking score evaluating the key characteristics of this habit: consumption speed, drunkenness frequency, and drunkenness ratio per drinking occasions [START_REF] Townshend | Patterns of alcohol drinking in a population of young social drinkers: A comparison of questionnaire and diary measures[END_REF].

As mentioned above, a key models' assumption is that AB towards alcohol is early, involuntary and automatic. To date, studies focusing on the time course of AB in subclinical populations revealed, however, that it mostly appears at later and more controlled attentional stages [START_REF] Bollen | Attentional bias in alcohol drinkers: A systematic review of its link with consumption variables[END_REF]. For example, [START_REF] Field | Attentional biases for alcohol cues in heavy and light social drinkers: The roles of initial orienting and maintained attention[END_REF] reported an alcohol-related AB (i.e., shorter reaction times for probes appearing on the side of the screen previously occupied by alcohol-related stimuli) in heavy drinkers (compared to light drinkers) when using the visual probe task, but only for stimuli with longer presentation duration (i.e. 500-2000ms versus 200ms). The maintenance of attention towards alcohol was also reflected by specific assessment of disengagement processes of AB through alternative paradigms (see [START_REF] Bollen | Attentional bias in alcohol drinkers: A systematic review of its link with consumption variables[END_REF] for a detailed description): the spatial cueing task, the Odd-One-Out task and the selective attention/action-tendency task [START_REF] Gladwin | Medial parietal cortex activation related to attention control involving alcohol cues[END_REF][START_REF] Heitmann | Attentional bias for alcohol cues in visual search-Increased engagement, difficulty to disengage or both?[END_REF][START_REF] Sharbanee | Alcohol-related biases in selective attention and action tendency make distinct contributions to dysregulated drinking behaviour: Alcohol-biases in selective attention and action tendency[END_REF]. Such findings suggested that AB would be characterized by a difficulty to disengage attention from alcohol-related stimuli once detected, potentially caused by the disrupted activity of higher-level and controlled processes (i.e. inhibitory control, executive functions; [START_REF] Carbia | A systematic review of neuropsychological studies involving young binge drinkers[END_REF][START_REF] Lees | Neurobiological and Cognitive Profile of Young Binge Drinkers: A Systematic Review and Meta-Analysis[END_REF][START_REF] López-Caneda | Impact of Alcohol Use on Inhibitory Control (and Vice Versa) During Adolescence and Young Adulthood : A Review[END_REF]. The automaticity in AB, postulated by dominant models, thus appears questionable in these populations. Some discrepancies were however found regarding the time course of AB when focusing on binge drinkers. Indeed, binge drinkers showed delayed interferences for color-naming alcohol-related words in an alcohol Stroop task, reflecting an AB at later and more controlled stages of processing [START_REF] Hallgren | Interference in the alcohol Stroop task with college student binge drinkers[END_REF], but were more efficient to process alcohol-related cues at early encoding levels in an attentional blink task, reflecting more automatic AB processes [START_REF] Depalma | Attentional blink to alcohol cues in binge drinkers versus non-binge drinkers[END_REF][START_REF] Elton | Acute depletion of dopamine precursors in the human brain: Effects on functional connectivity and alcohol attentional bias[END_REF]. A major limitation of these previous studies is that they exclusively relied on behavioral measures (i.e. manual reaction time) showing very low reliability [START_REF] Ataya | Internal reliability of measures of substance-related cognitive bias[END_REF]. Beyond the issue that such measures relied on hand movements and could thus be biased by potential deficits in motor responses, inferring AB through manual reaction time raises concerns since it only provided information about where participants focused their attention at the specific time of probe onset, without indexing the global stream and successive steps of attentional processing involved in AB (Field and Cox, 2008). Therefore, their methodology did not allow determining whether this bias relies on a genuine automatic hijacking of the attentional resources by alcohol or whether it is rather characterized by an increase in the controlled processing of alcohol-related stimuli when consciously perceived.

To address this issue, recent studies used neuroscience tools to determine the neural activation underlying the different processes of alcohol-related AB. For example, the study of brain electrical activity through electroencephalogram (EEG) allows to measure the neurofunctional brain response evoked by alcohol-related stimuli with high temporal resolution, thus providing major insights on the early brain processes involved when exposed to alcohol-related stimuli [START_REF] Almeida-Antunes | It's a beer! »: Brain functional hyperconnectivity during processing of alcohol-related images in young binge drinkers[END_REF]. Most EEG studies reported consistent findings by showing higher alcohol-related cue-reactivity and altered inhibitory processes (e.g., [START_REF] Blanco-Ramos | Electrophysiological Correlates of an Alcohol-Cued Go/NoGo Task: A Dual-Process Approach to Binge Drinking in University Students[END_REF][START_REF] Petit | Alcohol-Related Context Modulates Performance of Social Drinkers in a Visual Go/No-Go Task: A Preliminary Assessment of Event-Related Potentials[END_REF][START_REF] Ryerson | Attenuating the alcohol allure: Attentional broadening reduces rapid motivational response to alcohol pictures[END_REF]. Nevertheless, this method does not allow to investigate the specific processes involved in the preferential allocation of attentional resources towards alcohol-related stimuli when confronted with neutral ones. Recent studies thus used eye-tracking measures to directly and precisely assess and distinguish the successive cognitive processes underlying AB, by detecting eye movements and gaze positions with a high temporal and spatial resolution throughout the task [START_REF] Popa | Reading beyond the glance: Eye tracking in neurosciences[END_REF]. Whereas manual reaction times only offer an indirect AB measure (i.e. the final processing output), eye-tracking allowed deepening the understanding of the time course and core mechanisms of AB and enhancing the reliability of its assessment [START_REF] Bollen | Craving is everything: An eye-tracking exploration of attentional bias in binge drinking[END_REF][START_REF] Christiansen | Internal reliability of the alcohol-related visual probe task is increased by utilising personalised stimuli and eye-tracking[END_REF]. Eye-tracking findings suggested the presence of alcohol-related AB in subclinical populations (e.g. heavy or regular drinkers) at later processing stages, as indexed by longer dwell times (i.e. overall fixation time) or higher number of fixations towards alcohol-related stimuli (e.g., [START_REF] Mcateer | Alcohol attention bias in adolescent social drinkers: An eye tracking study[END_REF][START_REF] Mcateer | Age-related differences in alcohol attention bias: A cross-sectional study[END_REF][START_REF] Monem | Measuring heightened attention to alcohol in a naturalistic setting: A validation study[END_REF]. While these studies did not index any early AB (e.g., alcohol preference in the first fixation), they used free exploration tasks with relatively long presentation times and without any "attentional task" per se, which does not make them suitable for measuring the early and automatic capture of attention towards alcohol-related stimuli. To date, only one study [START_REF] Bollen | Craving is everything: An eye-tracking exploration of attentional bias in binge drinking[END_REF] has explored the time course of AB in a specific population of binge drinkers, by combining the visual probe task with eye-tracking.

They documented an AB among binge drinkers with high current craving, this bias being related to late controlled attentional stages (i.e. longer dwell times for alcohol-related stimuli compared to neutral ones). However, the visual probe task is usually characterized by long stimuli presentation duration before the appearance of the probe, with participants not receiving any specific instruction on how to process these stimuli, thus potentially masking the early processing stages of AB. The present study will overcome this limit through a paradigm specifically dedicated to the exploration of early and automatic AB, namely the saccadic choice task, which will allow the first specific exploration of AB automaticity.

This paradigm was initially developed to explore the speed of visual processing [START_REF] Kirchner | Ultra-rapid object detection with saccadic eye movements: Visual processing speed revisited[END_REF] and was later adapted to address the speed of face processing [START_REF] Crouzet | Fast saccades toward faces: face detection in just 100 ms[END_REF]. Indeed, human faces are naturally salient stimuli automatically capturing attention at very early processing stages. In this saccadic choice task, two images, a target (e.g., a face) and a distractor (e.g., a vehicle) are simultaneously displayed on the left and right of the screen. Participants have to perform a saccade as fast as possible towards the target stimulus. Studies have repeatedly reported shorter saccadic latencies when the target is a face (minimum saccadic reaction times of 100-120ms for face targets vs. 130-150ms for other target categories e.g., vehicles), demonstrating the presence of a very strong automatic bias for faces compared to other stimuli [START_REF] Crouzet | Fast saccades toward faces: face detection in just 100 ms[END_REF][START_REF] Guyader | Do low spatial frequencies explain the extremely fast saccades towards human faces?[END_REF]Kauffman et al., 2019;2021). Furthermore, they also reported that participants made more error saccades (i.e. saccades toward the distractor) when the distractor was a face than when it was another stimulus. These experimental results suggest that fast saccades toward attention-grabbing stimuli (i.e. faces) are automatic and beyond voluntary control. It should however be noted that other paradigms that directly involved more controlled processes (e.g., the antisaccade task) led to different results, notably reporting that facial stimuli are easier to avoid (i.e. generate stronger inhibitory control) than circles or scrambled facial stimuli [START_REF] Hoffmann | Do emotional stimuli interfere with response inhibition? Evidence from the antisaccade paradigm[END_REF]. The saccadic choice task thus constitutes an ideal paradigm to explore the early preferential processing of specific stimuli. This is further illustrated by the fact that, after an error saccade in this task, participants present more frequent and faster corrective saccades (i.e. second saccades directed towards the target when first saccades were directed towards the distractor) when the target is a face (indexing a re-engagement bias towards faces) than when it is another stimulus (indexing a disengagement bias from faces, [START_REF] Kauffmann | Face perception influences the programming of eye movements[END_REF]. Finally, they explored the amplitude (i.e. distance between the saccadic starting and ending points) of the saccade and observed larger saccades directed towards faces (either as target or distractor; [START_REF] Kauffmann | Face perception influences the programming of eye movements[END_REF], suggesting that the content of the stimuli influences the programming of saccade amplitude prior to its execution. As a whole, the saccadic choice task constitutes a powerful paradigm to test the early, automatic and involuntary capture of attentional resources by salient stimuli, and thus the presence of an AB towards such stimuli.

We thus used an adapted version of the saccadic choice task with alcohol-related stimuli to explore the automatic aspects of alcohol-related AB. If theoretical models' assumptions are correct, alcohol-related stimuli should hijack attentional resources and generate the same response pattern than the one reported above for faces (i.e., shorter saccadic latencies, increased error saccades when alcohol-related stimuli are the distractor, re-engagement and disengagement biases). We investigated this assumption in binge drinkers, since the presence of AB has been more consistently reported in subclinical populations than among patients diagnosed with severe AUD. The advantages of the saccadic choice task are multiple. First, it is combined with eye-tracking, thus offering more reliable AB measures than manual reaction times. Second, it uses very short stimuli presentation times, thus forcing participants to perform their saccade towards stimuli as fast as possible and providing more insights regarding the early processes of AB compared to paradigms with longer presentation times. Finally, the assessment of the first saccades and the corrective ones offer important insights on the engagement, disengagement and reengagement aspects of AB. We firstly administered the original version of the saccadic choice task to all participants to ensure the absence of any attentional dysfunction for the detection of highly salient stimuli in binge drinkers. The simultaneous use of both the original and the adapted alcohol version of the task led to two hypotheses: (1) binge drinkers and control participants will present the classical automatic capture of attention by universally salient stimuli (i.e. faces); (2) this automatic AB will also be present for alcohol-related stimuli among binge drinkers (but not among control participants), as these stimuli are supposed to acquire incentive salience in these populations [START_REF] Robinson | Development of the Alcohol Use Disorders Identification Test (AUDIT): WHO collaborative project on early detection of persons with harmful alcohol consumption-II[END_REF].

Methods

Participants

We recruited participants via an online screening survey sent through social networks to students from UCLouvain (Belgium). Participants had to fill in questionnaires assessing alcohol-related disorders (Alcohol Use Disorders Identification Test, AUDIT;[START_REF] Robinson | Development of the Alcohol Use Disorders Identification Test (AUDIT): WHO collaborative project on early detection of persons with harmful alcohol consumption-II[END_REF]French validation: Gache et al., 2005), binge drinking habits [i.e. consumption speed, drunkenness frequency and ratio, number of binge drinking episodes (i.e., drinking more than 6 units) per week], socio-demographic (e.g., age, sex) and other alcohol consumption variables (i.e. number of alcohol units consumed per week, number of units per occasion, number of drinking occasions per week). Before completing them, they were provided with information about equivalences in terms of the number of alcohol units per type of alcoholic beverages (an alcohol unit corresponding to 10 gr of pure ethanol in Belgium). To be included in the study, they had to meet the following criteria: absence of parental history of severe AUD, absence of current or past psychological or neurological disorders, normal or lens corrected vision.

For each participant, we then computed the binge drinking score [START_REF] Townshend | Binge drinking, cognitive performance and mood in a population of young social drinkers[END_REF]) by using the following formula: (4 x consumption speed) + drunkenness frequency + (0.2 x drunkenness ratio). We recruited 44 binge drinkers (BD; AUDIT score ≤ 20; binge drinking score ≥ 24; 2-4 drinking occasions per week; binge drinking episodes per week ≥ 1) and 45 control participants matched on gender (CTL; AUDIT score ≤ 8; binge drinking score ≤ 16; units per week ≤ 10; units per occasion ≤ 3; no binge drinking episodes). Regarding the sample size determination, no reliable a priori power computation was possible as this study constituted the first using the saccadic reaction time with alcoholrelated stimuli in a subclinical population. We thus decided to include a larger sample size per group than all previous studies using this paradigm with facial stimuli among healthy populations [START_REF] Kauffmann | Face perception influences the programming of eye movements[END_REF]2021), to increase our ability to detect smaller effects of alcohol-related stimuli in the second task.

All participants provided their informed written consent before taking part in the study and were not aware of the hypotheses tested. We performed the study protocol in accordance with the ethical standards established by the Declaration of Helsinki for experiments involving humans and the Ethics Committee of the Psychological Sciences Research Institute (UCLouvain) approved it.

We asked participants to refrain from consuming alcohol during the day preceding the experimental session and we questioned them about their recent consumption before starting the experiment 1 . Before performing the two experimental tasks, we asked participants to fill in questionnaires using Qualtrics software (Qualtrics, LLC), assessing state anxiety (STAI-A) and current alcohol craving [Alcohol Craving Questionnaire Short Form 1 We performed correlations between alcohol consumption the day before the experiment (i.e. number of alcohol units) and alcohol-related AB, since previous studies showed that acute alcohol consumption could induce alcohol-related AB in social drinkers (Duka & Townshend, 2004). Finally, a previous study comparing face with flower pictures in a saccadic choice task showed that they were appropriate neutral stimuli as they elicited similar saccadic performance than vehicle pictures and did not contain features salient enough to capture attention like faces [START_REF] Kauffmann | Isolated face features are sufficient to elicit ultra-rapid and involuntary orienting responses toward faces[END_REF]. All pictures were matched on size (600×600 pixels; 11x11° visual angle) and spatial position of the main object in the picture.

Procedure

Stimuli were displayed using the Psychtoolbox [START_REF] Brainard | The Psychophysics Toolbox[END_REF][START_REF] Pelli | The VideoToolbox software for visual psychophysics: Transforming numbers into movies[END_REF] implemented in MATLAB R2021a (MathWorks, Natick, MA, USA) against a gray background (luminance of 0.44). Participants seated on a desk chair placed 60cm away from an Asus Display Laptop PC equipped with a 17.3-inch FHD screen (resolution 1080 × 1920 pixels; refresh rate 120 Hz) and facing an eye tracker camera. We used a chinrest to stabilize participants' head position and we recorded eye movements using the pupil-corneal reflection and remote mode of an EyeLink Portable Duo eye-tracker (SR Research, Canada;

sampling rate of 1000 Hz; average accuracy range 0.25°-0.5°, gaze tracking range of 32° horizontally, 25° vertically). Eyelink software automatically detected saccades with the following thresholds: speed >30°/s, acceleration >8000°/s2, and saccadic displacement >0.15°. Blinks were detected during partial or total occlusion of the pupil. A 9-point calibration of participant's eye gaze position was set up at the beginning of each block.

All participants completed two experimental phases consisting of the faces vs.

vehicles saccadic choice task and the alcohol vs. flowers saccadic choice task. They received verbal instructions to perform the tasks, without being informed about their rationale. All participants systematically started by performing the faces vs. vehicles saccadic choice task, which was replicated from [START_REF] Kauffmann | Face perception influences the programming of eye movements[END_REF][START_REF] Kauffmann | Isolated face features are sufficient to elicit ultra-rapid and involuntary orienting responses toward faces[END_REF] and [START_REF] Guyader | Do low spatial frequencies explain the extremely fast saccades towards human faces?[END_REF]. The task comprised two blocks, one for which the targets were images containing human faces (the distractors being vehicle images) and the other one for which the targets were images containing vehicles (the distractors being human face images). In a second phase, participants underwent the alcohol vs. flowers saccadic choice task, with one block presenting alcoholic beverages as targets (and flowers as distractors), and the other block presenting flowers as targets (and alcoholic beverages as distractors). We asked participants to make a saccade as fast as possible toward the target image. We counterbalanced the order of blocks within the tasks to avoid potential learning and/or training effects.

At the beginning of each trial, a white fixation cross subtending 0.73° of visual angle was displayed centrally on a gray background screen (mean luminance of 0.5 for pixel intensity values between 0 and 1). We used the fixation cross as drift check to confirm the reliability of the eye-gaze calibration. This instruction ensured that participants initially focused their visual attention at the center of the screen in each trial. We carried out a drift correction every ten trials. The fixation cross was followed by a gap (mean gray-level screen) of 200ms. Two images (a target and a distractor) were then simultaneously displayed on the left and right side of the central fixation cross for 400ms. The center of each image was lateralized at 8° from the screen center. The inter-trial interval (uniform gray background) was fixed at 1000ms (Fig. 1). Each block comprised 64 trials, with each image being presented twice, once on the left and once on the right side, randomly. Each block lasted approximately 5 minutes and the total experimental task 20 minutes.

Fig. 1 Time course of a trial in the face vs. vehicle (Fig. 1a) and alcohol vs. flower (Fig. 1b) saccadic choice task.

Statistical analyses

We performed the same data reduction procedure than Kauffmann et al. ( 2021) by removing trials in which (1) a blink occurred during stimulus presentation, (2) saccadic reaction time (SRT) was shorter than 50ms, (3) saccades were initiated from more than 2° around the fixation cross, (4) saccades had an amplitude below 1° or (5) saccades duration were above 100ms. These criteria were based on the distributions of eye movement parameters consistently reported in the literature (e.g., [START_REF] Devillez | The bimodality of saccade duration during the exploration of visual scenes[END_REF]. This procedure resulted in removing two participants (1 BD,1 CTL), as more than half of their trials were invalid (due to poor calibration), and discarding 8.38% of the trials from the remaining participants. It should be noted that the percentage of remaining trials was similar between groups (BD: 92.59±0.06%; CTL: 90.68±0.08%; t 85 =1.219, p=.226) and was higher than those reported in previous studies using the same paradigm, thus ensuring the validity of our experimental procedure. We performed all statistical analyses using MATLAB R2021a (MathWorks, Natick, MA) and R (R Core Team, 2021).

We performed between-group comparisons (i.e., independent t-tests) on demographic, psychopathological characteristics and alcohol consumption variables. We analyzed the error rate (percentage of erroneous saccadic movement), latency (in milliseconds from the onset of stimuli -also called saccadic reaction time, SRT) and amplitude (distance between the positions of the start and the end of saccades, in degrees of visual angle) of the first saccade. We also examined whether erroneous first saccades were followed by corrective saccades. When applicable, we analyzed the percentage (%)

and SRT of corrective saccades. Second, we considered saccades as corrective if they ended on the target side of the display. For both tasks (face versus vehicle, alcohol versus flower), we performed analyses of covariance (ANCOVAs) with Target (alcohol or face, flower or vehicle) as within-subject factor, Group (BD, CTL) as between-subject factor and Age as covariate (as age differed across groups, see below). We performed them on eyetracking measures related to the first saccade (accuracy, SRT, amplitude) and the corrective saccade (proportion, SRT) when applicable. We conducted Post-Hoc tests (independent samples t-tests) for the interpretation of significant Target x Group interactions. We estimated effect sizes by calculating partial eta-squared (η p 2

) for ANCOVAs and Cohen's d

for Post Hoc t-tests. We also reported in Supplementary material (1) results for the alcohol vs flower task when including only control participants with AUDIT score ≤ 4 to exclude any women participants with potential risky drinking, (2) methods and results regarding the minimum SRT for both tasks and (3) methods and results for the exploratory correlations between eye-tracking measures (i.e. accuracy and SRT of the first saccade, proportion of corrective saccades) and alcohol consumption (i.e. AUDIT and binge drinking score, craving).

Results

Demographic, psychopathological, and alcohol-related measures

As showed in

BD (N=43) CTL (N=44) t or χ 2 p-value

Table 1. Group differences on demographic, psychopathological and alcohol consumption measures (mean ± standard deviation) between binge drinkers (BD) and control participants (CTL).

Face vs vehicle Saccadic Choice Task

Accuracy. The 2x2 ANCOVA on mean error rates for the first saccade revealed a main effect of Target (F 1,84 =88.78, p<.001, η p 2 =.514). Participants made significantly less error saccades when the target stimulus was a face (14.05±8.96%) than when it was a vehicle (24.61±12.94%). We observed neither Group effect (p=.644), nor interaction between Group and Target (p=.589).

Latency and amplitude of the correct first saccade. The 2x2 ANCOVA on mean SRT for the correct first saccade showed a main effect of Target (F 1,84 =139.22, p<.001, η p 2 =.624).

Participants initiated their correct first saccade faster when the target stimulus was a face (180±20ms) than when it was a vehicle (203±26ms). We observed neither Group effect (p=.578), nor interaction between Group and Target (p=.657). The 2x2 ANCOVA on mean amplitude for the correct first saccade showed a main effect of Target (F <.001 face (7.62±0.53°) than when it was a vehicle (7.03±0.72°). We observed neither Group effect (p=.237), nor interaction between Group and Target (p=.986).

Proportion and latency of the corrective saccade. The 2x2 ANCOVA performed on proportion of corrective saccade revealed a main effect of Target (F 1,82 =5.08, p=.027, η p 2 =.058). Participants made significantly more corrective saccades when the target stimulus was a face (89.97±17.73%) than when it was a vehicle (83.72±15.27%). We observed neither Group effect (p=.404), nor interaction between Group and Target (p=.775). The 2x2 ANCOVA performed on mean SRT for the corrective saccade revealed a main effect of Target (F 1,82 =20.41, p<.001, η p 2 =.201). Participants initiated their corrective saccade faster when the target stimulus was a face (110±23ms) than when it was a vehicle (122±19ms).

We observed neither Group effect (p=.737), nor interaction between Group and Target (p=.064). (p=.971) or interaction between these two factors (p=.815).

Discussion

Dominant theoretical models hypothesized the presence of an automatic AB towards stimuli with acquired salience (e.g. alcoholic beverages) in chronic drinkers. Such bias is not consistently documented in the literature, since previous studies showed heterogeneous findings among individuals with severe AUD [START_REF] Bollen | Attentional bias in alcohol drinkers: A systematic review of its link with consumption variables[END_REF]. While the literature is more consistent in subclinical populations, most studies showing the presence of an alcoholrelated AB, its automaticity remains to be proven. We thus applied the saccadic choice paradigm, commonly used to evaluate AB towards faces, in a population of binge drinkers and matched controls to investigate the automatic aspects of the alcohol-related AB.

First, we replicated previous findings regarding AB towards faces, since both groups processed these stimuli more rapidly and efficiently compared to vehicles [START_REF] Guyader | Do low spatial frequencies explain the extremely fast saccades towards human faces?[END_REF][START_REF] Kauffmann | Face perception influences the programming of eye movements[END_REF]2021). Indeed, they made less incorrect saccades and performed quicker and larger first saccades when the target was a face than when it was a vehicle. Corrective saccades were also more frequent and rapid when faces were the targets. By replicating these findings in both binge drinkers and control participants, we showed that (1) saccadic choice task constitutes a valid eye-tracking paradigm to evaluate the automatic nature of AB, and (2) binge drinkers have an automatic preference for processing faces similar to control participants, and do not present any generalized dysfunction of the impulsive/reward system responsible for the detection of salience [START_REF] Franken | Drug craving and addiction: Integrating psychological and neuropsychopharmacological approaches[END_REF]. The similar performance between groups is in line with [START_REF] King | Alcohol-induced performance impairment in heavy episodic and light social drinkers[END_REF], who showed that heavy drinking habits did not impact the saccadic latency and velocity measured in a prosaccade task.

Second, in contradiction with theoretical models' predictions, we found no early, automatic and involuntary hijacking of attention provoked by alcohol-related stimuli (indexed by the accuracy and latency of the first saccade) specific to binge drinkers, since our findings revealed shorter SRT for alcohol-related stimuli in both groups. Whereas our findings regarding facial stimuli clearly demonstrate the saccadic choice task as an appropriate measure of the automatic hijacking processes related to AB, further research could explore the involuntary aspects of attentional processing by using other paradigms and/or measures.

For example, other saccadic paradigms are known to explicitly request to inhibit saccadic responses towards alcohol when no second stimulus is on the target side of the screen, thus directly involving both automatic and controlled processes (e.g., antisaccade task ;[START_REF] Hoffmann | Do emotional stimuli interfere with response inhibition? Evidence from the antisaccade paradigm[END_REF]. In the same line, recent studies investigated the interaction between automatic (e.g., alcohol cue-reactivity) and controlled (e.g., inhibition abilities) processes in binge drinkers at the electrophysiological level, thus providing important insights on the underlying processes of mechanisms related to AB (i.e., alcohol-related cue-reactivity; [START_REF] Almeida-Antunes | It's a beer! »: Brain functional hyperconnectivity during processing of alcohol-related images in young binge drinkers[END_REF][START_REF] Blanco-Ramos | Electrophysiological Correlates of an Alcohol-Cued Go/NoGo Task: A Dual-Process Approach to Binge Drinking in University Students[END_REF]Lannoy et al., 2018). Beyond these perspectives, our findings already showed that binge drinkers had more difficulty to disengage from alcohol-related stimuli when their gaze was erroneously directed towards alcohol. Indeed, they corrected less frequently their saccade than control participants after having performed an error first saccade towards alcohol-related stimuli when the target was a flower, revealing the presence of a late and controlled disengagement bias related to alcohol cues. While the presence of a disengagement bias in subclinical drinkers was already demonstrated in previous studies [START_REF] Gladwin | Medial parietal cortex activation related to attention control involving alcohol cues[END_REF][START_REF] Heitmann | Attentional bias for alcohol cues in visual search-Increased engagement, difficulty to disengage or both?[END_REF][START_REF] Sharbanee | Alcohol-related biases in selective attention and action tendency make distinct contributions to dysregulated drinking behaviour: Alcohol-biases in selective attention and action tendency[END_REF], we strengthen these findings through the use of an eye-tracking paradigm in a specific population of binge drinkers.

These joint results thus demonstrate that AB in binge drinkers is not characterized by an automatic capture of attention by alcohol-related cues, but by an increased willingness to process these cues once detected. In line with previous studies [START_REF] Field | Attentional biases for alcohol cues in heavy and light social drinkers: The roles of initial orienting and maintained attention[END_REF][START_REF] Hallgren | Interference in the alcohol Stroop task with college student binge drinkers[END_REF], we thus suggest that alcohol-related AB relies on late and controlled processes rather than early and automatic ones. The different effect between faces and alcoholic beverages might be partly explained in terms of differential exposure and behavioral relevance between these two classes of stimuli during life. Faces stimuli are salient for humans since the very beginning of life, as the human brain requires to quickly detect and preferentially process those socially relevant stimuli to interact with the social world. Conversely, the increased salience properties of alcohol-related stimuli would result from repeated alcohol exposures and are thus acquired through alcohol-related experiences [START_REF] Robinson | Development of the Alcohol Use Disorders Identification Test (AUDIT): WHO collaborative project on early detection of persons with harmful alcohol consumption-II[END_REF]. As we tested young binge drinkers who have been usually

drinking for a few years only, alcohol-related AB might thus have not achieved an automatic stage yet. Future research should test the automatic aspects of alcohol-related AB in individuals with severe AUD, since this population has been exposed to excessive and chronic alcohol consumption for a longer time and might thus have developed an automatic capture of attention for alcohol-related stimuli. Nevertheless, this remains to be established as most previous studies did not show any strong and stable AB among patients with severe AUD compared to light drinkers, some of them even revealing an avoidance AB [START_REF] Bollen | Attentional bias in alcohol drinkers: A systematic review of its link with consumption variables[END_REF]. While the aim of this study was to determine whether the automatic AB for faces could be also found for alcohol-related stimuli in binge drinkers, future studies should also directly compare the attractiveness of faces versus alcoholic beverages by confronting these two types of stimuli in different populations of drinkers. Indeed, alcohol-related stimuli could reduce or counter the AB towards faces, although our results suggest that the incentive salience of alcohol is much lower than faces in binge drinkers.

Limitations

First, whereas the number of trials per block chosen in previous studies using the saccadic choice task [START_REF] Guyader | Do low spatial frequencies explain the extremely fast saccades towards human faces?[END_REF][START_REF] Kauffmann | Face perception influences the programming of eye movements[END_REF]2021) was sufficient to explore AB towards highly attractive stimuli like faces, it might have been too small to detect smaller effects from less salient stimuli like alcoholic beverages. Second, the shorter SRT for alcohol-related stimuli in both groups could be partly explained by the higher luminance of the alcohol-related stimuli compared to flower stimuli. Moreover, while the size of the pictures was standardized, we did not control for the size of the main object within the alcohol-related and flower pictures, although bigger stimuli are known to be detected easier and faster [START_REF] Hoffmann | Do emotional stimuli interfere with response inhibition? Evidence from the antisaccade paradigm[END_REF]. Finally, the use of flower rather than non-alcoholic beverages as neutral stimuli, although justified by physical aspects, did not allow for dissociating the alcohol-related and appetitive nature of alcoholic beverages pictures.

Nevertheless, these potential effects should be found in all participants, and thus would not impact the Target x Group interactions we were interested in to detect the presence of an automatic alcohol-related AB specific to binge drinkers.

Conclusion

The present study demonstrates that, while binge drinkers present a preserved early salience processing (as confirmed by the replication of the effects previously established for faces), the AB towards alcohol-related stimuli in binge drinking is not characterized by an automatic capture of attention but rather appears on later and more controlled attentional processing stages.

  For the alcohol vs flower task, results showed no correlation with the accuracy of the first saccade (r=.180, p=.103), the proportion of corrective saccade(r=.148, p=.183), the latency of the first saccade(r=- .087, p=.432) or the latency of the corrective saccade(r=.113, p=.307).Revised, ACQ-SF-R and Craving Visual Analogue Scale, C-VAS: "Indicate how much you want to drink alcohol right now (from 0 = not at all, to 100 = terribly wanting)"]. To control for psychopathological comorbidities, they filled in other questionnaires between the tasks assessing depressive symptoms(Beck Depression Inventory, BDI-II; French validation: Beck et al., 1998) and anxiety (State-Trait Anxiety Inventory, STAI A-B; French validation:[START_REF] Bruchon-Schweitzer | Adaptation francophone de l'inventaire d'anxiété Trait-Etat (Forme Y) de Spielberger[END_REF]. At the end of the experiment, we debriefed participants, who received financial compensation.StimuliStimuli were 128 colored pictures depicting human faces, vehicles, alcoholic beverages or flowers with context (32 pictures of each category), extracted from the freefrom copyright "Pixabay" stock image base (https://pixabay.com/) under CC0 License. We chose the faces, vehicles and flowers pictures from the stimuli used inKauffman et al. (2019; 2021) that were matched on perceptual features such as luminance and RMS contrast 2 .Faces were presented with vehicles pictures to replicate the version of the saccadic choice task used in[START_REF] Kauffmann | Face perception influences the programming of eye movements[END_REF]. In the alcohol saccadic choice task, we chose flower pictures as neutral stimuli instead of non-alcoholic beverages pictures since they sufficiently differ from alcoholic beverages in terms of shape and are not related with alcohol through associative learning, contrarily to non-alcoholic beverages (e.g., orange juice might hijack attentional resources through its visual similarity with alcoholic cocktails). Moreover, we conducted preliminary tests showing that the use of flower stimuli compared with alcohol stimuli facilitated the categorization of the two stimuli, resulting in a similar level of difficulty than the initial face versus vehicle task, thus increasing the comparability across tasks.

Fig. 2

 2 Fig. 2 (a) Mean accuracy (in percentage of correct saccadic responses) of the first saccades, (b) mean latency or saccadic reaction time (in milliseconds) of the first correct saccades, (c) mean amplitude (in degrees) of the first correct saccades, (d) mean proportion of corrective saccades and (e) mean latency or saccadic reaction time (in milliseconds) of corrective saccades according to the Target category (Face, Vehicle) and the Group (BD, CTL). Error bars correspond to ± 1 SE.

  vehicle targets corresponded to the 140-ms bin in controls and the 170-ms bin in binge drinkers.Alcohol vs flower Saccadic Choice Task. The analyses of minSRT showed that the fastest saccades correctly initiated towards alcohol targets were in the 150ms bin in binge drinkers and the 140ms bin in controls. The fastest saccades correctly initiated towards flower targets corresponded to the 160ms bin among binge drinkers and the 170ms bin among controls.

Table 1

 1

	, binge drinkers were younger (t 85 =2.288, p=.025, d=.491) and
	reported higher craving as assessed through VAS (t 84 =3.096, p=.003, d=.668) or ACQ
	(t 84 =4.156, p<.001, d=.896) than controls. Groups did not significantly differ regarding gender
	ratio (χ 2 2,87 =.988, p>.500), state anxiety (p=.580), trait anxiety (p=.087) and depression
	(p=.295).

  1,84 =124.95, p<.001,

	Demographic measures
	Sex ratio (male/female)	24/19	24/20	.989	.610
	Age	20.88 ± 1.94	22.07 ± 2.80	2.298	.024
	Psychopathological measures
	Beck Depression Inventory	5.21 ± 4.26	4.28 ± 3.92	1.054	.295
	State Anxiety Inventory	33.53 ±	32.44 ± 8.15	.555	.580
	Trait Anxiety Inventory	10.02	39.86 ± 9.54	1.731	.087
		43.56 ±
		10.26
	Alcohol consumption measures
	Alcohol Use Disorder Identification	15.65 ± 6.02	3.36 ± 2.10	12.645	<.001
	Test	43.27 ±	5.64 ± 4.13	11.419	<.001
	Binge drinking score	21.22	7.58 ± 13.04	3.096	.003
	Craving (Visual Analogue Scale)	18.30 ±	22.63 ± 9.06	4.156
	Craving (Alcohol Craving	18.59
	Questionnaire)	31.77 ±
		11.22
	η p 2 =.598). Participants performed a longer correct saccade when the target stimulus was a

Alcohol-related pictures presented higher luminance (0.51±0.12 vs 0.42±0.12; t 62 =2.943, p=.005, d=.736) than flower pictures but they were matched on RMS contrast (p=.394). This resulted in 72% of trials containing a pair of stimuli with alcohol-related pictures showing higher luminance than flower pictures. This difference however did not interfere with participants' performance, as saccadic reaction time of the first saccade did not correlate with the luminance of the picture fixated (r=-.060, p=.576).

Pierre Maurage (Senior Research Associate) and Zoé Bollen (Junior Research Associate) are supported by the Belgian Fund for Scientific Research (F.R.S.-FNRS). This work has been supported by CerCoG IDEX of the University of Grenoble Alpes in the framework of the "Investissements d'avenir" program of the French National Research Agency (grant number ANR-15-IDEX-02).

Alcohol vs flower Saccadic Choice Task

Accuracy. The 2x2 ANCOVA on mean error rates for the first saccade revealed no main effect of Target (p=.276), Group (p=.599) or interaction between these two factors (p=.849).

Latency and amplitude of the correct first saccade. The 2x2 ANCOVA on mean SRT for the correct first saccade showed a main effect of Target (F 1,84 =7.51, p=.007, η p 2 =.082).

Participants initiated their correct first saccade faster when the target stimulus was an alcoholic beverage (191±26ms) than when it was a flower (197±27ms). We observed neither Group effect (p=.573), nor interaction between Group and Target (p=.987). The 2x2 ANCOVA on mean amplitude for the correct first saccade showed no main effect of Target (p=.726), Group (p=.194) or interaction between these two factors (p=.157).

Supplementary material

Alcohol vs flower Task (with CTL participants ≤ 4 on AUDIT score)

Accuracy. The 2x2 ANCOVA on mean error rates for the first saccade revealed no main effect of Target (p=.158), Group (p=.623) or interaction between these two factors (p=.802).

Latency and amplitude of the correct first saccade. The 2x2 ANCOVA on mean SRT for the correct first saccade showed a main effect of Target (F 1,73 =7.99, p=.006, η p 2 =.099).

Participants initiated their correct first saccade faster when the target stimulus was an alcoholic beverage (190±26ms) than when it was a flower (197±27ms). We observed neither Group effect (p=.432), nor interaction between Group and Target (p=.705). The 2x2 ANCOVA on mean amplitude for the correct first saccade showed no main effect of Target (p=.893), Group (p=.223) or interaction between these two factors (p=.148).

Proportion and latency of the corrective second saccade. The 2x2 ANCOVA performed on proportion of corrective saccade revealed a significant interaction between Target and Group (F 1,73 =4.18, p=.045, η p 2 =.054). Post-Hoc independent sample t-tests showed that binge drinkers made fewer corrective saccades than controls when the target stimulus was a flower (BD: 63.15±22.22%; CTL: 74.88±16.42%; t 74 =2.647, p=.010) but groups did not differ when the target stimulus was an alcoholic beverage (p=.556). We observed neither Target (p=.314) or Group (p=.153) effects. The 2x2 ANCOVA performed on mean SRT for the corrective saccade revealed no main effect of Target (p=.422), Group (p=.696) or interaction between these two factors (p=.842).

Minimum saccadic reaction time

We computed the minimum saccadic reaction times (minSRT) for each Target condition in each group. The minSRT corresponds to the minimum SRT leading to significantly more correct than error saccades. We computed the distributions of SRT separately for correct and error saccades, taking all saccades of participants from each group. We grouped SRTs into 10ms bins (e.g., the 120ms bin contained SRT comprised between 115 and 124ms). For each bin, the proportion of correct saccades was compared to the one of error saccades using a χ 2 test. If there was significantly more correct than error saccades in five consecutive bins, the first bin was then defined as the minSRT (for a similar procedure, see [START_REF] Crouzet | Fast saccades toward faces: face detection in just 100 ms[END_REF][START_REF] Guyader | Do low spatial frequencies explain the extremely fast saccades towards human faces?[END_REF]Kauffman et al., 2021).

Face vs Vehicle Saccadic Choice Task. The analyses of minSRT showed that the fastest saccades correctly initiated towards face targets were comprised in the 120-ms bin (i.e. SRT between 115 and 124ms) in both groups, while those correctly initiated towards

Correlations

We performed exploratory Pearson's correlations to investigate the influence of alcohol-related variables on the first and corrective saccades in the alcohol vs. flower saccadic choice task. To do so, we performed correlations on the difference score between blocks with alcohol as target and blocks with flower as target for accuracy and SRT of first saccades as well as the proportion of corrective saccades, leading to a positive score when alcohol was detected more correctly and faster than flower. The difference score on the accuracy of first saccades did not correlate with AUDIT score (r=-.009, p=.933), binge drinking score (r=-.090, p=.406) or craving assessed through ACQ (r=.141,p=.195)