Yang Tan

Darwin Lau

Mingxing Liu

Philippe Bidaud

Vincent Padois

Minimization of the Rate of Change in Torques during Motion and Force Control Under Discontinuous Constraints

Large and sudden changes in the torques of the motors of a robot are highly undesirable and should be avoided during robot control as they may result in unpredictable behaviours. One cause of large changes in torques is the presence of discontinuities in the constraints that the robot must satisfy, such as the avoidance of an obstacle or the breaking of contacts with the environment. In this paper, a model predictive control (MPC) approach to approximate constraints that can be predicted over a finite horizon is proposed to minimize the derivative of torques during robot control. The proposed method does not directly modify the desired task trajectory but the constraints to ensure that the worst case of changes in torques is well-managed. From the simulation results on the control of a Kuka LWR robot, it is shown that our approach significantly decreases the maximum derivative of joint torques for both force and acceleration task control examples.

I. INTRODUCTION

The redundancy of robots makes it possible to simultaneously execute complex tasks while satisfying constraints. These constraints can either be related to some intrinsic limitations of the system, such as joint limits and actuation capacities, or to the surrounding environment, for example obstacles to avoid and contacts to maintain. These constraints have to be accounted for when solving the control problem and thus must be monitored. More specifically constraints can be: 1) added to the control problem when needed, e.g. when a contact is established; 2) updated within the control problem, e.g. when the distance to an obstacle is updated based on some sensor information; 3) removed from the control problem, e.g. when a contact is broken.

The addition, removal or abrupt change of a constraint is a source of discontinuity for the control law and may result in large instantaneous changes in the actuation torque and unpredictable behaviours of robots. Rapid changes in the motor torques are undesired for many reasons: damage to the actuators, bad control performance or even unstable robot motion. In fact, the problem of large rate of change in the actuation torque has not yet been fully resolved.

The problem of large changes in motor torques has been related to different types of causes and studied in the literature. First, sudden changes of task target in operational space can lead to great discontinuities in joint torques. In this case trajectory planning is a proper way to solve this problem. In [START_REF] Kyriakopoulos | Minimum jerk path generation[END_REF] a minimum jerk path generation is proposed to produce a continuous Cartesian trajectory. The work [START_REF] Haschke | On-line planning of timeoptimal, jerk-limited trajectories[END_REF] introduces a time-optimal, jerk-limited online trajectory planning, complying with the maximal velocity, acceleration and jerk of joints. In [START_REF] Macfarlane | Jerk-bounded manipulator trajectory planning: design for real-time applications[END_REF] a jerk-bounded trajectory planner is used to generate continuous trajectories online. Second, changes in hierarchical priorities amongst a set of tasks can also lead to discontinuities in joint torques. A large number of works [START_REF] Petrič | Smooth continuous transition between tasks on a kinematic control level: Obstacle avoidance as a control problem[END_REF]- [START_REF] Dietrich | On continuous null space projections for torque-based, hierarchical, multi-objective manipulation[END_REF] have aimed to create a continuous null space projector that allows switches among task priorities without causing large changes in motor control torques. A generalized continuous projector is used to deal with the task transitions in [START_REF] Liu | Generalized projector for task priority transitions during hierarchical control[END_REF] with an optimization approach. Moreover, constraints can be handled by the task formulations. The method of classical artificial potential fields [START_REF] Khatib | Real-time obstacle avoidance for manipulators and mobile robots[END_REF] is widely used to achieve the avoidance of obstacles. However, when the obstacle avoidance constraint switches between inactive and active, a discontinuous control law is produced. In [START_REF] Dietrich | Integration of reactive, torque-based self-collision avoidance into a task hierarchy[END_REF] a reactive continuous null space projection is extended to prevent large changes in torques while activating/deactivating the constraints. The intermediate desired value approach [START_REF] Han | A continuous task transition algorithm for operational space control framework[END_REF] is applied to avoid large changes in torques by smoothly activating the obstacle avoidance constraints.

In addition to the previously identified causes of large rate of change in torques, discontinuities in constraints are also able to induce sudden changes in torques and have not been previously studied. When considering the discontinuity of constraints, two different situations may occur. In some situations, sudden changes in constraints cannot be known in advance and hence the controller cannot avoid the induced large change in motor torques. However, if the appearance, disappearance or sudden change of constraints can be known in advance, then the controller can handle this in a predictive manner. Changes in constraints can be known in advance in several ways, for example:

• constraint from the control scenario for the system can be anticipated, such as when a robot is about to sit on a chair or to put a foot on the ground; • constraint is sensed ahead of time, such as the detection of an obstacle using vision before the obstacle avoidance actually becomes a constraint.

Optimization is one common approach to determine the motor torques required to produce a desired motion subject to constraints. This type of formulation is starting to prevail in Robotics as it allows to properly account for constraints which are expressed as inequalities [START_REF] Kanoun | Prioritizing linear equality and inequality systems: Application to local motion planning for redundant robots[END_REF]. If the objective function is quadratic and the system is subject to linear constraints, Quadratic Program (QP) solvers can be efficiently employed [START_REF] Cheng | Obstacle avoidance for redundant manipulators using the compact qp method[END_REF]- [START_REF] Saab | Dynamic whole-body motion generation under rigid contacts and other unilateral constraints[END_REF]. In this scheme, the computed torques may exhibit sudden changes due to three different reasons: 1) if the objective function is discontinuous; 2) if the solution of the QP is on the boundary of the constraint and the constraint is discontinuous; and 3) if the solution of the QP transitions between the interior and the boundary of the feasible set.

In this paper, a predictive control scheme to minimise the rate of change in torques over time in the presence of discontinuities in constraints is proposed. Assuming that information about the evolution of constraints within a finite horizon is known, a Model Predictive Control (MPC) scheme is employed. The MPC is used to design a new constraint that results in minimised changes in joint torques compared with the original discontinuous constraints. The new constraint, which is shown to be more conservative, replaces the original constraint, and the new constraints are used within a reactive controller scheme. The effectiveness of the proposed approach is demonstrated through simulations on a Kuka LWR robot with kinematic and force constraint discontinuities. The results show a significantly lower instantaneous change in joint torques compared with the controller output if the original discontinuous constraints are used.

One key feature of this approach is that the constraints of the reactive controller are modified rather than the objective function. As such, the proposed method does not directly modify the task trajectory but ensure that the worst case torque derivative is minimised. It is a very generic approach which can be applied independently from the way the control law is formulated. Furthermore, the proposed MPC formulation provides the potential to adjust the balance between the worst case change in joint torques and the conservativeness of the new constraint.

II. CONTROL FRAMEWORK

The equation of motion of a fixed-base robot with n degrees of freedom (DoF) can be derived from the Euler-Lagrange formalism and expressed as

M (q)q + n(q, q) = τ + J c (q) T F c , (1)
where q, q, q ∈ R n are respectively the generalised coordinates, velocities and accelerations, M (q) ∈ R n×n is the generalized inertia matrix, n(q, q) ∈ R n is the vector of Coriolis, centrifugal and gravity induced joint torques, and τ is the vector of joint torques. F c is the external contact force, J c (q) T is the Jacobian at the contact point. (2)

A. Tasks

A motion task of a frame attached to the robot here is defined as the tracking of a desired trajectory in operational space. The kinematic relationship between the operational and joint spaces can be expressed as ẋ = J(q) q and ẍ = J(q)q + J(q, q) q, where J(q) and J(q, q) are the task Jacobian matrix and its derivative, respectively. The tracking error T (χ) relative to a 3D trajectory x ref can be expressed linearly as T (χ) = J(q)q + J(q, q) qẍcmd , where the task command ẍcmd is computed using a proportionalderivative (PD) controller with a feedforward term ẍref : ẍcmd = ẍref + K p (x -x ref ) + K d ( ẋẋref ), and K p and K d are the proportional and derivative gains, respectively.

When a body of the robot is expected to apply a desired force in operational space, the force error is:

T (χ) = F c - F ref c , where F ref c
is the desired value of the force.

B. Constraints

While performing the task, the robot must respect constraints, such as joint limits and collision avoidance with obstacles. It is shown in this section that different types of constraints can be expressed linearly with respect to the action variable χ in the form Gχ ≤ h .

(3)

1) Joint limits: Bounds on the joint positions and velocities can be locally expressed with respect to the joint accelerations based on a discrete linear approximation with a time step of δt:

qmin ≤ qk + qk δt ≤ qmax , (4)
q min ≤ q k + qk δt + qk δt 2 2 ≤ q max , (5)
where q k , qk and qk are the joint positions, velocities and accelerations, respectively. Bounds on joint torques can be directly expressed:

τ min ≤ τ k ≤ τ max . (6)

Task Trajectory

Fig. 1: Description of the obstacle avoidance constraint.

2) Obstacle avoidance constraint: As shown in Figure 1, the obstacle avoidance constraint can be defined as requiring the minimum distance d = p r,k -p o,k between the robot body and the obstacle to be strictly non-zero, where p

•,k = [x •,k y •,k z •,k ]
T represents the a position in Cartesian space.

Using a discrete linear approximation with a time step of δt, the minimum distance d k+1 can be expressed as

d k+1 = d k + n T ( ṗr,k -ṗo,k )δt + δt 2 2 n T ( pr,k -po,k ) , ( 7
)
where n is the vector associated to the shortest distance from the robot to the object, which is assumed to evolve continuously in this paper. p r,k and ṗr,k are the current position and velocity of the closest point of the robot with respect to the obstacle, pr,k is the acceleration resulting from the next control action. They evolves continuously according to the continuous motion task or force task. It is worth noting that constraint [START_REF] Liu | Generalized projector for task priority transitions during hierarchical control[END_REF] relies on the knowledge of p o,k , ṗo,k and po,k which are the current position, velocity and acceleration of the obstacle. If the velocity and acceleration of the obstacle are unknown, i.e. neither measured nor estimated, [START_REF] Liu | Generalized projector for task priority transitions during hierarchical control[END_REF] assumes that the obstacle is quasi-static over a control period which can be a valid working assumption. Using the kinematic relationship between the operational space velocity/acceleration and the generalized coordinates in [START_REF] Liu | Generalized projector for task priority transitions during hierarchical control[END_REF], the obstacle avoidance constraint can be expressed linearly with respect to qk as:

d k + n T (J(q k ) qk -ṗo,k )δt + δt 2 2 n T (J(q k )q k + J(q k ) qk -po,k ) ≥ 0 . (8)
3) Contact constraint: Contact forces can be constrained according to different scenarios. For example, when there is no contact, contact force must be 0. For safety reasons, it can also be necessary to limit the maximum value of the contact force. In this case, the contact constraint can be written:

0 ≤ f n = n T f F c ≤ f max , (9)
where f n = n T f F c is the normal contact force along the normal direction to the contact surface n f , and F max is the maximum allowable force related to the scenarios.

C. Control Framework

The optimal action variable χ * can be determined through QP by minimising a weighted sum of the task error T (χ) 2 and the action effort χ 2 , while satisfying constraints:

χ * = arg min χ T (χ) 2 Q + χ 2 R subject to Aχ = b, Gχ ≤ h . ( 10
)
The notation a 2 Q is the shorthand of the form a T Qa. The weighting matrices Q and R in [START_REF] Han | A continuous task transition algorithm for operational space control framework[END_REF] allow to modulate the importance between the task objective and the regularization term. As a reactive controller, this QP is solved at each time step. Observing that (10) is a strictly convex QP problem, a unique globally optimal solution for the redundant robot can be determined. For this type of problem with constraints (4)-( 8), G and A are matrices related to the rigid body model of the system and are always continuous. So time discontinuous solutions to [START_REF] Han | A continuous task transition algorithm for operational space control framework[END_REF] can occur under following situations:

• The original task reference is discontinuous. This task discontinuity could be handled by trajectory planning and the task reference is assumed to be continuous throughout this work; Fig. 4: Due to the evolution of task reference, the inequality constraint switches from inactive to active, which can cause large instantaneous changes in joint torques.

• Equality constraints ( 2) are active at all feasible solutions 1 . Assuming that the task reference is constant and A is continuous, there are two possible cases that large instantaneous changes in joint torques may occur. 2) The dimension of b increases or decreases with additions and removals of equality constraints, which is shown in Figure 3. • Assuming G is continuous, the solution changes from being on the interior of the feasible set of (3) to the boundary, or vice versa (see in Figure 4). In other words, any of the constraints G i χ ≤ h i switches between inactive and active.

III. MPC CONTINUOUS CONSTRAINT GENERATION

The discontinuous evolution of any active constraint causes inevitably discontinuous control torques as stated in Section II, which is not desirable. Therefore, smoothing the discontinuous evolution of inequality constraints is a prerequisite to minimize the changes in joint torques. As shown in Figure 5, given the information from sensors and/or environment contexts, we can know discontinuous variations in a look ahead window of N steps with T being the time step. A continuous constraint h * i can thus be generated. Then it can replace h i in the constraint (3):

Gχ ≤ h * . ( 11
)
Horizon Future Past Time step Fig. 5: Smoothing the discontinuous evolution of inequality constraints using a receding horizon technique.

Model Predictive Control (MPC) [START_REF] Bellingham | Stable receding horizon trajectory control for complex environments[END_REF] is a good candidate to generate a smooth evolution of h * with respect to h. MPC, also known as receding horizon control [START_REF] Camacho | Model predictive control[END_REF], is based on iterative, finite horizon optimization of a dynamic model. MPC uses the current dynamic states of the system, the dynamic model, the variable targets and limits to calculate a set of future inputs. These inputs can hold variables close to their targets as well as respect their constraints in the future. At time step k, the current states are measured and a cost minimizing the tracking errors is computed for a time horizon [k, k + N ] to find a sequence of the system inputs until step k + N . Only the first step of the system inputs is fed to update the states of the system, then the calculation shifts to the next time step, yielding repeatedly a new set of system future inputs. With these properties, MPC is well qualified to generate smooth constraints evolution with respect to discontinuous constraints. The overall control framework is shown in Figure 6. MPC is used to deal with discontinuous constraints by generating a new constraint evolution that can minimise the rate of change in joint torques in the QP control framework. According to the types of constraints, two main continuous constraint generation based on MPC are presented in this section.

A. Continuous Force Constraint Generation

For the force constraint [START_REF] Dietrich | Integration of reactive, torque-based self-collision avoidance into a task hierarchy[END_REF], the goal of MPC is to generate smooth maximum allowable force f with respect to f max . Then, it can replace f max in constraint (9):

0 ≤ f n ≤ f . (12)
A discrete-time model of the force can be expressed as:

f k+1 = f k + ḟ k T , (13)
where f k is the maximum allowable forces at time step k. ḟ k is the first-order time derivative of f k . f k should be optimized according to the original profile of f max . Within the time horizon N T , the MPC for generating a optimized f can be formulated as:

ḟ * k = arg min ḟ k ,..., ḟ k+N k+N j=k f j -f max,j 2 + γ ḟ j 2 (14a) subject to f j+1 = f j + ḟ j T (14b) 0 ≤ f j ≤ f max,j (14c)
where (14c) ensures that at each time step j every solution χ * that satisfies the constraint ( 12) also satisfies the constraint [START_REF] Dietrich | Integration of reactive, torque-based self-collision avoidance into a task hierarchy[END_REF]. The coefficient γ is the weight, governing the importance between the changes of f and the deviation from the original maximum allowable force. In ( 14), ḟ * k can be computed by a Quadratic Program solver. The generated maximum allowable force is f k+1 = f k + ḟ * k T . Note that an alternative method to address this problem is to smooth the profile of f max by applying a smooth polynomial spline [START_REF] Lin | Formulation and optimization of cubic polynomial joint trajectories for industrial robots[END_REF][START_REF] Lambrechts | Trajectory planning and feedforward design for high performance motion systems[END_REF]. However, the advantage of using MPC here is to be able to handle multiple constraints in an automatic and generic way, e.g. to ensure that the optimized f is compatible with other constraints. For example, by using MPC, two contact forces can easily satisfy the following three constraints simultaneously: 1) 0 ≤ f 1 ≤ f 1,max ; 2) 0 ≤ f 1 ≤ f 2,max , and 3) f 1 + f 2 ≤ f 3,max . However, it is difficult for the polynomial to deal with this problem. Moreover, the use of a polynomial approach requires manual choose of the start and end points of the segment to be smoothed and manual tuning of polynomial parameters and may lead to oscillation problems [START_REF] Schatzman | Numerical analysis: a mathematical introduction[END_REF].

B. Continuous Motion Constraint Generation

According to the obstacle avoidance constraint (8), h i can be expressed as:

h i = d k (p r , p o )+n T (J(q) q-ṗo )δt+ δt 2 2
n T ( J(q) q-po ) .

(15) h i is a function of the position, velocity and acceleration of the obstacle. Considering the fact that the movement of the obstacle along any axis in operational space is independent, without loss of generality the position, velocity and acceleration along the x-axis are formulated in the following part of this paper. In this case, a linear discrete-time dynamic model of the obstacle can be created in state space form:

  x o,k+1 ẋo,k+1 ẍo,k+1   X o,k+1 =   1 T T 2 2 0 1 T 0 0 1   A   x o,k ẋo,k ẍo,k   X o,k +   T 3 6 T 2 2 T   B ... x o,k , (16)
where X o,k and ...

x o,k are the state vector of the obstacle and the control action at time k, respectively. Matrices A and B implicitly describe the linearity of the system.

Using the dynamic model ( 16) recursively, at time k, the relationships between the control action vector and state vectors over a finite time horizon N T is given by:

Xo = ÂX o,k + BU o , (17)
where, . In order to take advantage of x m o , the model predicted position information can be extracted from Xo : Xo,x = x o,k+1|k . . . x o,k+N |k T . Consequently, Âx and Bx can be extracted from  and B, respectively. Therefore, the predicted position of the obstacle over the horizon can be formulated as:

Xo =      X o,k+1|k X o,k+2|k . . . X o,k+N |k      , U o =      ... x o,k|k ... x o,k+1|k . . . ... x o,k+N -1|k      , Â =      A A 2 . . . A N      , B =      B 0 • • • 0 AB B • • • 0 . . . . . . . . . . . . A N -1 B A N -2 B • • • B      .
Xo,x = Âx X o,k + Bx U o . ( 18
)
Thus similarly to [START_REF] Salini | Synthesis of complex humanoid whole-body behavior: a focus on sequencing and tasks transitions[END_REF], the general form of the MPC problem to be solved is formulated as ... 19) is used with time step T = 0.01s, constant ratio α/β = 10 5 and time horizon N T = 2.0s. In Figure 7 Fig. 8: The resulting smooth constraint with T = 0.01s, N T = 2.0s, α/β = 10 5 and a dynamic weighting matrix Q.

x * o,k|k = min U o α Xo,x -x m o 2 + β U o 2 subject to Xo,x = Âx X o,k + Bx U o Xo,x ≤ x m o . (19
solution of x * o and the original position as well as reduces the instantaneous variation of ẍo .

It is shown in Figure 7 that there exist overshoots at t = 3.0s and t = 6.0s. These overshoots are mainly due to a relatively large weight α associated to X0 -x ref o 2 , which minimises the distance to the original reference, with respect to the weight β of the regulation term U o 2 , which reduces the instantaneous variation of ẍo . Thus a dynamic weighting matrix Q is added into (19):

...

x * o,k|k = min U o α Xo,x -x m o 2 Q + β U o 2 subject to Xo,x = Âx X o,k + Bx U o Xo,x ≤ x m o , (20)
where Q = diag(a j , a j+1 , . . . , a j+N ) is a diagonal matrix, and a j ∈ (0, 1], ∀j ∈ [k, k + N ] determines the weight associated to each sample in the time horizon. Each a j is computed with respect to the variation of x m o :

a j = max(x m o ) -x m o,j + λ max(x m o ) -min(x m o ) + λ , ( 21
)
where λ is a regulation term to avoid a division by zero. a j is dynamically changing in the time horizon

[k, k + N ]: 1) If max(x m o ) = min(x m o )
, then a j = 1.0. The relation between α and β is set to α ≥ β, which means the approximation to the reference is always more important than the minimization of U o 2) If max(x m o ) = min(x m o ), discontinuities might occur in the time horizon, then a j tends to 1.0 for large variations of the reference value and a j tends to 0 for small ones. In this case the approximation to the original reference is sacrificed to reduce variations of U o as soon as the discontinuity is previewed in the time horizon.

The results using the dynamic weighting matrix Q are shown in Figure 8, which shows that there is no overshoot on x * o and MPC begins to react to future discontinuity once the change is detected in the horizon. In Figure 8 Here, MPC works as a preprocessing of constraints before they are incorporated into the control framework. Its advantages of previewing future events and taking actions consequently make it possible to reduce large constraint variations. This can handle torque discontinuities due to discontinuous evolutions of active constraints. However, it cannot solve the problem caused by activation of the constraint (as shown in Figure 4).

C. Continuous Activation of Constraints

The discrete linear approximation over the discrete time step δt described in Section II leads to a truncation error. Indeed, with the decrease of δt, the error of h i increases dramatically. In [START_REF] Rubrecht | Constraints compliant control: constraints compatibility and the displaced configuration approach[END_REF] a constraint compliant control law is proposed to solve this problem, but it is only applied in the case of inverse kinematics. The approach in [START_REF] Salini | Dynamic control for the task/posture coordination of humanoids: toward synthesis of complex activities[END_REF] increases the discretization time step δt in the constraint (not in the control time step) properly to diminish the error for dynamic control problem. In this paper, the same method is adopted to solve discontinuities in constraint activations.

IV. SIMULATION RESULTS & DISCUSSION

The proposed methods are applied to the control of a 7-DOF Kuka LWR robot in simulation. The experiments are carried out in the robotic simulation software XDE [START_REF] Merlhiot | The xde mechanical kernel: efficient and robust simulation of multibody dynamics with intermittent nonsmooth contacts[END_REF]. The Kuka robot is actuated by joint torques to perform tasks in operational space under discontinuous force constraints and obstacle avoidance constraints. The constraint generation approach presented in Section III is applied here to reduce the instantaneous variations of τ .

A. Handling of Force Constraint

In this experiment, the end-effector force task is defined to push against a fixed object with a constant force value. Meanwhile, the force constraint on the maximum allowed contact force evolves discontinuously. The results using the proposed approach is compared with the baseline approach, which is based on the QP control framework [START_REF] Han | A continuous task transition algorithm for operational space control framework[END_REF] with the min jerk term ... q 2 W in the objective function to minimize the changes of joint torques. W is the weight of the min jerk term. In this experiment, Q is identity matrix, R = 10 -6 and W = 10 -3 .

In Figure 9, at the beginning the impact force results in a big peak on the force, which is not considered in this work. At t = 5.0s, the force constraint becomes suddenly active, causing torque discontinuities. At t 6.0s the force constraint changes discontinuously, and discontinuous torques and big torque derivative are observed. At t = 9.0s, the constraint decreases to zero suddenly, which means the contact is removed, leading to discontinuities of torques and big torque derivatives. Although the term ... q 2 W can limit changes of joint torques as a penalty, it cannot preview sudden large changes of constraint in advance. Once the sudden large changes of constraints occur, joint torques have to change largely to respect the constraints in a reactive way.

In Figure 10(a), the new generated continuous force constraint is used instead of the original one. In Figure 10(b), it is shown that the new continuous force constraint is fully respected. With this continuous force constraint, the joint torques evolve smoothly and significant decreases of torque derivatives can be observed in 10(d).

B. Handling of Obstacle Avoidance Constraint

In this experiment, the end-effector is tracking a sinusoid trajectory as shown in Figure 11 and the robot has to avoid collision with a moving object. While the robot is performing the tracking task, the obstacle moves suddenly towards the robot and thus the tracking task has to be stopped to avoid the obstacle. After a while, the object moves away from the robot. During the whole process, the robot should respect the discontinuous obstacle avoidance constraint and handle the discontinuities due to its activation and deactivation. In order to demonstrate the effectiveness the proposed methods, different experiments are carried out where:

(i) only the QP control framework [START_REF] Han | A continuous task transition algorithm for operational space control framework[END_REF] with the original discontinuous obstacle avoidance constraint is used; (ii) the new continuous obstacle avoidance constraint is generated by the proposed approach [START_REF] Lin | Formulation and optimization of cubic polynomial joint trajectories for industrial robots[END_REF] with time horizon N T = 1.5s and α/β = 10 5 before being incorporated into the QP control framework (10); (iii) the new continuous constraint is calculated based on the proposed approach (20) with the same time horizon and ratio as the experiment (ii); (iv) the control framework is the same as the experiment (iii) but with a different ratio α/β = 10 3 . Figure 12 shows the resulting trajectory of the robot, the position of the obstacle, evolution of joint torques and evolution of torque derivatives. In Figure 12(a), at t = 3.8s and t = 5.8s the obstacle moves suddenly and big peaks of joint torques and torque derivatives are clearly observed. The chattering of joint torques can be clearly observed The weighting matrix Q is used to reduce the variation of the constraint itself in order to lower the rate of change on joint torques. Its effectiveness is demonstrated by the evolution of torque derivatives shown in Figure 12(c) compared with that in 12(b).

The ratio α/β determines the relative importance of minimization of the error between the new constraint and the original constraint over the minimization of instantaneous variation of the new constraint. A relative large α/β means that the new constraint is closer to the original one with relative large variations. Conversely, the distance to the original constraint is sacrificed to reduce variations with a relative small α/β. The influences of the ratio α/β are clearly shown in Figure 12(c) and 12(d): A larger α/β means the new continuous constraint is much closer to the original constraint with a much larger variation. This consequently leads to much bigger torque derivatives by comparing the maximal torques and torque derivatives in Table I with experiment (i) and (ii).

V. CONCLUSION In this paper, a MPC-based constraint smoothing approach is proposed, which is applied to design a new constraint trajectory that results in minimised changes in joint torques compared with the original discontinuous constraints. Experiments involving a force constraint and an obstacle avoidance constraint show that the generated continuous constraints can successfully minimise instantaneous variations of joint torques caused by discontinuous constraints.

One key feature of this approach is that the constraints of the reactive controller are modified rather than the objective function. Therefore, the proposed method does not directly modify the task trajectory but ensure that the worst case torque derivative is minimised. As such, it is a very generic approach which can be applied independently from the way the control law and objective function is formulated.

Future work will focus on the application of this very general approach to the case of humanoids making and breaking contacts with their environment in simple activities such as walking, sitting, standing or leaning over an object.

  Defining the action variable as χ = qT τ T F T c T allows the equation of motion (1) to be represented linearly as Aχ = b .

Fig. 2 :

 2 Fig. 2: The change of b i in equality constraints can cause change in joint torques. The solution always lies on the constraint Aχ = b.

Fig. 3 :

 3 Fig. 3: The change of the dimension of b can cause change in joint torques. A new equality constraint is added at t k+1 and then is removed at t k+2 . The solution χ may undergo a large change.

1 )

 1 Any b i in b = [b 1 . . . b m ] ∈ R m has large instantaneous changes. For example, in Figure 2, the large change of b i can cause large change in joint torques.

Fig. 6 :

 6 Fig. 6: Block diagram of the control framework.

  Over the time horizon, only the position of the obstacle is measured by scenarios in advance, which is x m o

  (a), the generated x * o is continuous compared with the original position x m o . Moreover MPC also generates continuous ẋ * o and ẍ * o in Figure 7(b). With the constant ratio of α/β, MPC minimizes the error between the

Fig. 7 :

 7 Fig. 7: The optimized constraint with = 0.01s, N T = 2.0s and α/β = 10 5 .

  (b) the max values of ẋ * o and ẍ * o are much less than those in Figure 7(b).

Fig. 11 :

 11 Fig. 11: The end-effector avoids a moving obstacle while performing the task.

Fig. 9 :

 9 Fig. 9: Simulation results of the discontinuous force constraint with the minimum jerk term. The large torque derivatives are clearly observed in (d).

Fig. 10 :Fig. 12 :

 1012 Fig. 10: Simulation results of the discontinuous force constraint with MPC smoothing. (d) The maximum of torque derivatives are significantly reduced.

TABLE I :

 I Maximum of joint torques and torque derivatives

	Experiment	(i)	(ii)	(iii)	(iv)
	Maximum of τ [N m]	308.6	19.4	16.3	10.2
	Maximum of τ [N m/s] 32358	1244	531	339

Yang Tan, Darwin Lau, Mingxing Liu, Philippe Bidaud and Vincent Padois are with: -Sorbonne Université, UPMC Univ Paris 06, UMR 7222, Institut des Systèmes Intelligents et de Robotique, F-75005, Paris, France -CNRS Centre National de la Recherche Scientifique, UMR 7222, Institut des Systèmes Intelligents et de Robotique, F-75005, Paris, France Email:{tan,lau,liu,bidaud,padois}@isir.upmc.fr

Philippe Bidaud is with the ONERA, 91123 Palaiseau, France Email:philippe.bidaud@onera.fr

If χ is feasible and G i χ = h i , we say the ith inequality constraintG i χ ≤ h i is active at χ. If G i χ < h i , we say the constraint G i χ ≤ h i is inactive[16, p. 128].

ACKNOWLEDGMENT

This work was partially supported by the China Scholarship Council, and by the RTE company through the RTE/UPMC chair Robotics Systems for field intervention in constrained environments held by Vincent Padois.


Martine Gautier
email: martine.gautier@loria.fr

Brigitte Wrobel-Dautcourt
email: brigitte.wrobel-dautcourt@loria.fr

Brigitte Wrobel

artEoz -dynamic program visualization

Keywords: Dynamic program visualization, object programming, education, graphic object representation, memory diagram, software

published or not. The documents may come

Contents and practical implementation

The tutorial will introduce the basic usage of artEoz : visualize the execution of your program code written in Java or Python.

Sequences of exercises will address:

○ the basic mechanisms: assignment, instantiation, instantiation per copy, cloning, ... ○ more complex paradigms: ■ collections management: arrays, tables, lists, stacks, hash tables, trees, ... ■ memory management: unreferenced objects ■ function calls: parameters, receiver, return value, call stack, recursion, … ■ declaration scopes, nesting scopes, … ■ inheritance, dynamic binding About 20 sequences of exercises are currently available.They can be customized to fit different students' needs. These sequences were developed, tested and progressively improved during our courses (2nd year undergraduate students in computer science, engineering school, ...) and workshops (secondary school teachers). Some are freely available on arteoz.loria.fr website. Alternative / new ideas will be proposed during the workshop based on questions / wishes / goals from participants.

The objectives of this workshop are to show the possibilities of artEoz software. In particular, it will emphasize its ease of use to teach beginners students. Also, we will show how to create educational sequences adapted to the learners' profiles and teacher's objectives. artEoz can either be used in a classroom or independently for selflearning.

Duration

Between 45 minutes and 2 hours, depending on the application and the participant objectives. Anyone can create their own teaching sequence using artEoz educational tool.

Targeted audience

• code programming teachers, who wish to use artEoz as an educational tool during their lessons for beginners or for more experienced students; • and more generally, anyone curious of how this software works.

Resources

Each participant must have a personal laptop computer with administrator rights ( artEoz install) and internet access.

However, a web version of artEoz is currently under active development. artEoz will be available for use via an internet browser.

Notes

artEoz software is currently available in two languages: English and French. The website arteoz.loria.fr is in French, and partly in English. The English translation will be completed by September 2016.

Biographies

Martine Gautier , assistant professor, Université de Lorraine. Her works are focused on the development of educational tools.

Brigitte WrobelDautcourt , assistant professor, Université de Lorraine, LORIA (Laboratoire lorrain de recherche en informatique et ses applications). Her teaching in computer science and educational involvement are behind the creation of artEoz .


Marianne Doury
email: marianne.doury@cnrs.fr

Pascale Mansier
email: pascale.mansier@yahoo.fr.

The psychiatrization of the opponent in polemical context

Keywords: ad hominem argument, disqualifying strategies, mental pathologies

This paper deals with a variant of the ad hominem argument that challenges the opponent's mental health. Semi-technical terms borrowed from psychiatric paradigms (such as autistic, paranoiac, hysterical) are thus appealed to in order to disqualify the opponent. Based on three examples from polemical discussions on political issues, we investigate what kind of behavior triggers such accusations, how they are justified, and how they are handled by the speaker to whom they are addressed.

INTRODUCTION

The present paper proposes an exploratory introduction to a research program aiming at contributing to highlight how mental illness is perceived in our modern societies -and specifically, in France. In order to answer this question, some studies have been conducted, based on surveys and questionnaires on the perception of mental health 1 . The way we chose to proceed is different. We focused on the use of various terms originating in esoteric bodies of knowledge pertaining to psychiatry, and that have been disseminated beyond their technical use in expert fields to ordinary discourses, in the political domain as well as in everyday conversations. Examples of such terms are "paranoid", "schizophrenic", "autistic", "hysterical", "psychotic" or "mythomaniac". In their technical use, these terms designate specific mental pathologies. As such, they do not convey any negative judgment 2 . When used in ordinary interactions, they nevertheless often serve as pejorative attributes aiming at disqualifying a person. This paper focuses on three of these items: "hysterical", "paranoid", "autistic"3 . We will first briefly evoke their possible use as insults in French, owing to their insertion in discursive patterns such as "espèce de..." or "sale...". Beyond the use of these terms as mere insults, we will examine examples in which they fulfill an argumentative function, as part of ad hominem arguments. We will indicate what we mean by "ad hominem argument", and justify our categorizing the examples we will account for as pertaining to this argument scheme. We will then identify the specific argumentative functions that may be achieved by the adjectives "hysterical", "paranoid" and "autistic" in polemical contexts. We will correlate these specific argumentative functions with the technical definitions of "hysteria", "paranoid disorder" and "autism". We will conclude on what such argumentative uses of terms labelling mental pathologies tell us about the perception of mental disease in our society, and on how they contribute to stigmatizing persons suffering from mental troubles.

FRENCH "PARANO" OR "AUTISTE" AS INSULTS

We have just stated that the sort of items that are examined here often serve as pejorative means aiming at disqualifying a person, and even as insults. Some linguistic devices are characteristic of this insulting use. French offers specific discursive patterns which may change almost any item into an insult. Thus, in "espèce de X" and "sale X"4 , X has an offending dimension because of its insertion within such phrases, whatever its initial meaning may be. Even a neutral, descriptive word may work as an insult when obeying such a pattern. However, although any word may be turned into an insult owing to such discursive patterns, the words that are intrinsically marked as pejorative are much more likely to be used in that way.

Searching Google in order to investigate the frequency of phrases like "espèce de parano" or "sale autiste", shows that they are quite common. Examples 1 and 2 illustrate such offensive uses of these terms. In example 1, the administrator of a blog reacts to a participant accusing him of committing censorship unduly by calling him "espèce de parano":

(1) On se calme le Bauju, pas la peine de monter sur tes grands chevaux, il n'y a pas de censure […] Ton commentaire n'avait plus lieu d'être, espèce de parano, alors je l'ai scratché. Tu ne l'avais pas vu?5 Let's calm down Bauju, there is no use getting mad, there was no censorship […] Your commentary was pointless, you paranoid, so I erased it. Didn't you see it?

In example 2, a teenager expresses his hatred for one of his teachers, calling her autistic:

(2) Il etait une fois , dans ce qu'on ose appeler un lycee , une prof de sciences economiques et sociales […] Once upon a time, in what they dare call a high-school, an economics teacher […] who was bizarre… this thing-oups, woman (let's call her that way) had little manias: [she would] put her finger into her nose, lick them, she also gets dressed in a strange way with a small blue woolly hat […] and when she speaks she has to rephrase her sentence at least ten times before getting the right version: she's a fucking shitty autistic! […] you autistic you, you'd better give me 12 for my exam otherwise I will steal your shitty trolley.. In both cases, the use of the qualifications "paranoid" or "autistic" is supported by the mention of types of behavior (hastily interpreting an action as censorship, wearing a blue woolly hat) presented as characteristic of the corresponding pathologies7 . In these sequences "paranoid" and "autistic" obey an offensive objective. They aim at hurting, humiliating, devastating the person they aim to disqualify. We will now turn to examples where the target of the attack, beyond the person, is the claim he or she advances: we will then consider that "hysterical", "paranoid" or "autistic" are part of an ad hominem argument. .

AD HOMINEM ARGUMENT

Ad hominem arguments are generally defined as attempts at disqualifying a claim by attacking the person who advances it, or some circumstance attached to this person. 8Scholars distinguish between two [START_REF] Govier | Problems in Argument Analysis and Evaluation[END_REF][START_REF] Walton | The Ad Hominem Argument as an Informal Fallacy[END_REF], Woods & Walton 1989[START_REF] Krabbe | It's All Very Well for You to Talk!" Situationally Disqualifying Ad Hominem Attacks[END_REF], three [START_REF] Eemeren | Relevance reviewed: the case of Argumentum ad hominem[END_REF], four [START_REF] Walton | The Place of Emotion in Argument[END_REF][START_REF] Macagno | Strategies of Character Attack[END_REF]), up to seven [START_REF] Rolf | Credibility. The art of being trustworthy[END_REF] subtypes of ad hominem arguments. Whatever the sub-classification may be, there seems to be a consensus on the abusive ad hominem type, which consists in attacking a claim by denigrating "the other party's expertise, intelligence or good faith" (Eemeren & Grootendorst 1992: 153): this is the ad hominem subtype we are interested in here.

We shall retain that first and foremost, an ad hominem argument is… an argument. In the examples that we will analyse, calling the opponent "hysterical", "paranoid" or "autistic" does not necessarily support any explicit conclusion. But even when no reasoning of the type:

X claims that p. X is schizophrenic / autistic / hysterical Hence, p should not be accepted.

is made explicit, we consider that the disqualification of the opponent that these adjectives achieve has an argumentative function for contextual reasons.

The three examples we will examine pertain to political discourse. They appear within what Christian [START_REF] Plantin | Les instruments de structuration des séquences argumentatives[END_REF] would call an "argumentative situation". According to Plantin, an argumentative situation is governed by an argumentative question ("should the government implement Measure M?", for instance) which may receive opposing answers, each of them being supported by arguments ("I'm for M because arg.1, arg.2…"), or ("I'm against M because arg.3, arg.4…"). In an argumentative situation, any statement should be understood as part of an answer to the argumentative question which structures the discussion, whether it is presented as such or not. The question, writes Plantin, should be seen as an interpretative magnet which polarizes all the contributions that fall into its attraction field (2010: 33; translation is ours). In this perspective, the three adjectives which appear in the examples we will focus on are to be interpreted as personal attacks aiming at disqualifying, beyond the person of the opponent, the thesis that he supports. Hence they embody abusive ad hominem arguments.

We consider the use of terms issued from psychiatry, like "hysterical", "schizophrenic", "autistic", as a subtype of a more general type of abusive ad hominem arguments, aiming at presenting the opponent as belonging to a debased fraction of humanity. Of course we do not assume that this fraction really is debased, but rather that the use of such qualifications as personal attacks suggests that for the arguer, in some way, it is. Other variants of this general scheme consist in some cases in designating the adversary as an animal 9 , as a female (when addressing a man 10 ), as or a child or a teenager (when addressing an adult 11 ).

Example 3 simultaneously displays some of these disqualifying strategies. It is drawn from a French political newsgroup, and it combines the psychiatric and the animalistic variants of the ad hominem disqualifying strategy:

(3) Ce forum est essentiellement un exutoire pour une poignée d'autistes qui y déversent leurs délires d'illuminés, leurs élucubrations psychotiques ou leurs éructations de primates. 12 This newsgroup is mainly an outlet for a handful of autistic individuals who pour in their cranks' deliriums, their psychotic pipe dreams or their primates' eructations.

HYSTERICAL

9 As when Anne-Sophie Leclère, a National Front candidate for the 2014 local elections, compared French Attorney General, Christiane Taubira, to a baboon. 10 Contesting the manliness of the opponent is a very common disqualifying strategy. It transpires from the revolting but nonetheless frequent injunction addressed to a boy in tears: "Don't cry, you look like a girl!" 11 As when, during the "Gayet Gate", Manuel Valls suggested that "François Hollande behaved like a retarded teenager"; https://fr.news.yahoo.com/closer-fran%C3%A7ois-hollande-agi-quot-ado-attard%C3%A9-quot-103503108.html

The first term originating in psychiatry we will examine in this paper is the adjective "hysterical". "Hysterical" is frequently used in polemical contexts in order to qualify a whole debate, the communicative behavior of one participant in the discussion, or the discussant himself. In context, "hysterical" refers to heated exchanges, characterized by a highly emotional tone.

In the context of a political discussion, pointing to the emotional dimension of one's contribution amounts to disqualifying it as irrational and potentially biased.

Even if the originally Freudian meaning of "hysterical" seems to be somewhat remote from its present uses in political discussions, accusing the opponent of being hysterical still suggests that he has lost control over his own communicative behavior. Hence the conditions for a rational discussion are not fulfilled, and the opponent's argument does not deserve any serious examination.

Furthermore, the accusation of loss of control is not the only vector of disqualification of the opponent. The adjective "hysterical" is deeply marked by the specific historical situations in which it was used, as the analysis of example 4 will show.

Example 4 is drawn from the French debate that preceded the adoption of the socalled "mariage pour tous" law, opening the marital institution to same-sex persons. During a particularly heated parliamentary session, Christian Jacob, who opposes the law, accuses Sergio Coronado, who supports it, of being hysterical 13 :

(4) M. Christian Jacob. J'pense qu'on pourrait: profiter/ euh je le: dis à mes (.) mes collègues de la majorité/ qui pourraient profiter (.) agréablement de la: coupure du dîner/(.) pour reprendre/ (.) un peu leurs le leurs esprits/ (..) [protestations dans l'Assemblée] 'ttendez\ (.) les les les attaques (..) qui ont été les vôtres/ vous savez/ (.) on peut avoir de vrais di-différences/ (.) et: et d'ailleurs j'ai apprécié le ton/ avec lequel Patrick Bloche (.) s'est exprimé tout à l'heure/ (.) nous sommes en désaccord/ (.) Total\ XX (.) MAIS/ (.) il l'a fait avec euh beaucoup de dignité/ avec des CONvictions qui sont les siennes/ (.) et qu'on accepte que l'on puisse s'exprimer d'la même façon/ (.) sans êt' soumis (.) à des invectives voire à de l'HYStérie/ (.) à de l'HYStérie/ (.) de par certains collègues/ je pense à vous [montrant SC de la main] (.) mon cher collè/gue (.) mais si/ (.) ces propos (.) vous n'apportez (.) RIEN au débat/ (.) vous n'avez pas/ d'argument/ (.) vous z'hurlez/ vous êtes dans l'hystérie totale/ (.) et je pen/se qu'il faut profiter du moment du déjeuner/ pour se calmer\ (.) je-du dîner\ (.) [puis s'adresse à Mme la Ministre] I think we could take advantage of… -I'm addressing my colleagues in the majority who could pleasantly take advantage of the dinner break to come to their senses [protests in the Assembly]. Wait, you were the ones who made these attacks, you know, people may have important differences of opinion, and by the way, I appreciated the way Patrick Bloche expressed his position a few minutes ago, we deeply disagree but he expressed his convictions with much dignity, and people should accept that we express ourselves in the same way, without suffering abuses or even hysteria, hysteria from some colleagues, I'm thinking of you [pointing to Sergio Coronado] my dear colleague, yes yes, these words, you make no valuable contribution to the discussion, you have no argument, you're just yelling, you're totally hysterical, and I think one should take advantage of the dinner break to calm down.

Nothing, in Sergio Coronado's offensive turn accounts for such an attack, either in what is said, or in the tone in which it is said: it is by no way more emotional or heated than the contributions of the other participants, Yet Jacob accuses his of being hysterical.

Regardless of its factual adequacy, Christian Jacob's attack may be understood, as suggested before, as a strategy aiming at shifting the discussion from the criticism of the opponent's arguments to his very person. Such a strategy may prove useful when no simple refutation is available. It may also be seen as obeying another logic, in connection with the history of the usage of the terms "hysteria" and "hysterical" in various contexts in France. This is indeed what Sergio Coronado suggests, when reacting to Jacob's charge with hysteria as follows:

(5) Sergio Coronado: en fin d'séance tout à l'heure/ (-) euh le président euh Jacob/ m'a::: (.) se dirigeant vers moi/ m'a qualifié/ d'hystérique\ […] (..) […] (.) les invertis\ (..) les invertis\ (..) alors (.) cher/ président Jacob\ (.) vous auriez pu êt' plus franc/ (.) et faire co:mme dans les cours d'éco/le me traiter d'pé/dé\ (..) voilà/ (.) cette inju/re (.) qui fait tant de mal notamment aux jeunes qui découvrent leur sexualité/ (.) je tiens à vous rassurer\ (.) cher président Jacob (.) j'assu/me (.) j'en suis fier/ (.) et je n'ai pas (.) du tout (.) envie d'raser les murs/ (.) malgré/ (.) vos/ (.) injures\ (..) j'aimerais simplement dire (.) au président Jacob/ (.) que ce type d'invectives (.) au sein d'cette assemblée/ (.) n'honore (.) ni vot' grou/pe (.) ni les travaux (.) aujourd'hui (.) de l'Assemblée Nationale/ (.) j'ai hon/te (.) pour ceux/ (.) qui profèrent ce ty/pe (.) de propos (.) c'est vrai que l'heure est un peu tardi/ve et j'ai l'impression/ (.) que vos nerfs commencent à lâcher\ (.) merci Sergio Coronado: earlier at the end of the session, President Jacob, addressing me, called me hysterical. […] I wondered, "why did he call me hysterical?", and as I am fond of history, I remembered that the word "hysterical" was used to disqualify people in troubled circumstances, for instance it was used to denigrate suffragettes by those who opposed women's right to vote; it was used to denigrate Simone de Beauvoir when she published Le deuxième sexe; or it was used to denigrate the three hundred and forty three bitches when they published the manifesto for the right to abortion. And I wonder, why did Jacob call me hysterical, since I am neither a suffragette, nor Simone de Beauvoir or a woman claiming the right to abortion. So I went back to nineteenth century […] and I remembered the clinical works in the tradition of Charcot, and in fact I remembered -and I think that's what Jacob was referring to -that at that time, the word "hysterical" was addressed to all women -as you know, all women are potentially hysterical, you know that, dear colleague -and "hysterical" was also applied to a certain category of men, namely, homosexuals; yes, homosexuals. So, dear President Jacob, you could have been more frank, and, as children do in the schoolyard, you could have called me a fag. Here it comes, this insult that causes so much pain to young people who discover their sexual orientation. I want to reassure you, dear President Jacob, I assume my sexual orientation, I am proud of it, and I don't feel like hugging the walls despite your insults. I just want to tell President Jacob that such invectives, within this Assembly, do not honor either your group, or the work that the National Assembly has been doing today. I feel ashamed for those who utter such words. True, it is late, and I feel you're losing your nerves.

Puzzled by the adjective "hysterical", the use of which he deems unfounded, Coronado connects it with former uses: it was used against the "suffragettes", that is, the feminist supporters of women's right to vote, to disqualify them; it was used against Simone de Beauvoir as she published her book Le deuxième sexe, which was considered a feminist manifesto; it was used against the feminine activists who claimed the right to abortion. Sergio Coronado finally mentions that the diagnosis of hysteria was made for a specific category of male individuals, namely, homosexuals. On that ground, he suggests that Jacob's accusation of hysteria amounts to calling him a fag: "vous auriez pu êt' plus franc/ (.) et faire co:mme dans les cours d'éco/le me traiter d'pé/dé".

The accusation by Christian Jacob of being hysterical, as well as its analysis by Sergio Coronado, can be further analysed by examining some features of the technical definition of hysteria. Although hysteria (meaning matrix in Greek) has been described at length by Hippocrates, two main medical figures are more commonly associated with the trouble, both in the nineteenth century: Charcot who became famous for his public presentations of women in « full hysterical crisis », and Freud for whom hysteria was the turning point for the modern psychiatry and the psychoanalysis theory. After numerous controversies on hysteria in the 1960s, the term has now disappeared in the latest versions of both ICD14 and DSM15 , to be replaced by the concepts of conversion or dissociative disorders.

The main symptoms that define hysteria (or conversion disorders) are the following:

The patients are prone to exaggeration and the need to be heard and believed, including for their physical symptoms which become obsessive;

The mental trouble is often associated with physical and not feigning symptoms for which no physical illness cannot be found; Because of their physical impairment and the inability for doctors to explain them, the patients become extremely preoccupied by their ill-health and very often accuse the medical professionals of lying on purpose.

The patients truly and greatly suffer from their troubles which cannot be treated or attenuated by prescription medicine.

It seems that the ad hominem use of the "hysteria" charge relies on a single semantic feature issued from the technical definition: the tendency to "exaggerate". The emotional tone of a person, which seems to trigger the charge of being hysterical in ordinary contexts, is not part of the psychiatric meaning of the term. Accusing the opponent of being hysterical is a way of disqualifying his contribution to the discussion as not fitting reality (as it is "exaggerate") and as irrational (as it is highly emotional). In addition, the fact that Charcot's study on hysteria was focused on women's accounts for the fact that later uses of the adjective "hysterical" address women ("suffragettes" or feminine activists), and, in the present case, supports Coronado's suspicion that Christian Jacob is homophobic (he accuses Coronado of being hysterical because, as a homosexual, Jacob equates him with a woman). In the context of a discussion on a law that opens marriage to same-sex persons, charging someone with homophobia is a way of bluntly disqualifying his contribution to the debate as irretrievably biased.

Example 4 is interesting in that it illustrates how the "hysterical" qualification, when applied to an opponent in a polemical discussion, may be a means of disqualifying this opponent's position as emotional and biased. Example 5 shows how a specific context (here, the discussion of the law opening marriage to same-sex persons) may activate some semantic features associated to "hysterical" in what Sophie [START_REF] Moirand | Les discours de la presse quotidienne[END_REF] would call a collective discursive memory (the reference to "suffragettes", to feminist activism).

PARANOID

French "paranoïaque" (and its shorter version "parano"), or English "paranoid", is another term issued from psychiatry, and entering some ad hominem attacks.

Example 6 is part of an interview of Marine Le Pen, an extreme-right politician, by the left-wing journalist Pascale Clark on France-Inter radio station. At the end of the interview, by way of closing, Pascale Clark always broadcasts a musical piece chosen by her guest. Marine Le Pen chose a song by Laurent Voulzy, the lyrics of which were written by Alain Souchon, entitled "Jeanne". This song is about a contemporary man who claims his love for a medieval woman named "Jeanne". The song does not explicitly refer to Jeanne d'Arc, but irresistibly evokes her. Whereas the interview should end with the song, Pascale Clark takes the floor and cites the lyrics of "Belle-Ile en mer", another song by Voulzy/Souchon, and specifically, a brief sequence which evokes Voulzy's feeling of rejection as a mixed-race child grown up in France16 . Though Pascale Clark does not explicitly charge Marine Le Pen with racism, it clearly is the way the latter interprets the quotation by Pascale Clark of "Belle-Ile-en-mer"'s lyrics. She then strives to force the journalist into avowing what she intended by quoting this song. Pascale Clark resists, calling Marine Le Pen paranoid 17 :

(6) MLP: ouais (.) non non mais attendez madame (.) moi/ (.) très objectiv'ment\ (.) I'm not accusing you of anything. MLP: oh yes you are, I saw your stiff face, meaning "I feel pleased with myself, I had a little dig at her" PC:

stop that, you paranoid! You paranoid, the whole world is against you… I'm just evoking some lyrics, that's all Example 6 is typical of the use of the adjective "paranoid" as a disqualifying means. It enables Pascale Clark to suggest that Marine Le Pen is wrong in suspecting that the quotation of "Belle-Ile-En-mer"'s lyrics was an indirect way of accusing her of being a racist. Beyond that, "parano" suggests that this faulty interpretation of Pascale Clark's intention by Marine Le Pen is due to a mental pathology ("you are parano"), which leads her into interpreting innocent words as personal attacks ("the whole world is against you").

The use of the adjective "paranoid" in ad hominem arguments such as exemplified above seems to match some aspects of the technical definition of paranoid disorders. DSM 5 considers the paranoid disorder as a subtype within "personality disorders" 18 :

The Paranoid Personality Disorder is characterized by a pervasive distrust and suspiciousness of other people. People with this disorder assume that others are out to harm them, take advantage of them, or humiliate them in some way. They put a lot of effort into protecting themselves and keeping their distance from others. They are known to preemptively attack others whom they feel threatened by. They tend to hold grudges, are litigious, and display pathological jealousy. Distorted thinking is evident. Their perception of the environment includes reading malevolent intentions into genuinely harmless, innocuous comments or behavior, and dwelling on past slights. For these reasons, they do not confide in others and do not allow themselves to develop close relationships. Their emotional life tends to be dominated by distrust and hostility (DSM 5) When accusing Marine Le Pen of being paranoid, Pascale Clark suggests that she is over-suspicious, that Marine Le Pen reads "malevolent intentions" into her "genuinely harmless, innocuous comments or behavior" and that she suffers "distorted thinking"which obviously is a way of discarding Pascale Clark's accusation that she is a racist as a symptom of mental illness.

More generally, the diagnosis of paranoia applied to the opponent gives clearance to the speaker of the personal attacks he may make: he does not have to answer for them while taking advantage of their devastating potential.

However in this specific case, the strategy fails. If you want to rebut your opponent's accusation of your having committed a personal attack by suggesting that he is paranoid, you should be able to propose an alternative credible interpretation for what you said. Here, there is no doubt that Pascale Clark's alternative interpretation of what she did (I'm just evoking the lyrics of a beautiful song) is a poor one, and cannot support Marine Le Pen being charged with paranoia (the host of the radio broadcast is not supposed to express his / her aesthetic preferences).

AUTISTIC

The last case we will handle briefly here is the use of "autistic" and more specifically, its use to qualify the government. In such cases, "autistic" often works as a quasi-synonym for "deaf". Example 7 is from Thierry Lepaon, the General Secretary of a left-wing tradeunion (the CGT). Lepaon criticizes Hollande's government for not defending the interests of the working classes 19 .

(7) Les patrons ont pris l'offensive, ils ont l'oreille de ce gouvernement. Plus il cède aux patrons, moins les salariés sont audibles. Ce gouvernement est autiste de son oreille gauche, il entend bien à droite.

Bosses have taken the offensive, they caught the government's ear. The more the government lets them have what they ask, the less audible the workers are. This government is autistic on the left ear, it hears perfectly well on the right side.

On the same day Lepaon made this statement, a commentator criticized the French government in similar terms in a French magazine's blog 20 : More generally, the adjective "autistic" is applied to any opponent that you fail to win over to your cause and who resists the arguments you have addressed. This strategy also appears in example 9 by Jean-Claude Gaudin, Marseille City's Mayor, who deems the government to be autistic because it does not satisfy his claims on the reform of school timetables 21 : (9) Le gouvernement est autiste. La Ville de Marseille a demandé un moratoire sur les rythmes scolaires. Il a été refusé. Elle a proposé un plan de développement du soutien scolaire. Il a été refusé.

The government is autistic. Marseille city asked for a moratorium on the reform of school timetables. Its demand was rejected. It proposed a plan for developing support classes. Its demand was rejected.

Gaudin's declaration elicited reactions on Twitter pointing to the adjective "autistic", the pejorative use of which is considered inelegant in the following tweets:

(10) Tweet 1: mother of an autistic child and hearing the word autistic all day long used by politicians and in schoolyards: STOP! Tweet 2: perhaps autistic is not the most delicate word… Tweet 3: You could say…deaf, but it's also a handicap. Tweet 4: Using the handicap as an insult. Elegant.

Compared with "hysterical" and "paranoid", the ad hominem use of "autistic" departs even more spectacularly from the technical definition of the corresponding mental disease. Criteria for diagnosing autism are:

A. Persistent deficits in social communication and social interaction across multiple contexts [...]): (1) Deficits in social-emotional reciprocity, ranging, for example, from abnormal social approach and failure of normal back-and-forth conversation; to reduced sharing of interests, emotions, or affect; to failure to initiate or respond to social interactions; (2) Deficits in nonverbal communicative behaviors used for social interaction, ranging, for example, from poorly integrated verbal and nonverbal communication; to abnormalities in eye contact and body language or deficits in understanding and use of gestures; to a total lack of facial expressions and nonverbal communication; (3) Deficits in developing, maintaining, and understanding relationships, ranging, for example, from difficulties adjusting behavior to suit various social contexts; to difficulties in sharing imaginative play or in making friends; to absence of interest in peers.

B. Restricted, repetitive patterns of behavior, interests, or activities [...]: Stereotyped or repetitive motor movements, use of objects, or speech [...]; Insistence on sameness, inflexible adherence to routines, or ritualized patterns or verbal nonverbal behavior [...]; Highly restricted, fixated interests that are abnormal in intensity or focus [...]; Hyper-or hyporeactivity to sensory input or unusual interests in sensory aspects of the environment (e.g., apparent indifference to pain/temperature, adverse response to specific sounds or textures, excessive smelling or touching of objects, visual fascination with lights or movement). [...] From above, one can see that the second order criterion (the existence of restricted, repetitive patterns of behavior makes no sense with regard to the ad hominem accusation of autism; and the "deficits in social communication and social interaction" are reduced to a unilateral incapacity to hear, equated with a mere physical handicap (in the phrase "autistic from the left ear", "autistic" stands for "deaf").

CONCLUSION

To sum up, in polemical contexts, integrating adjectives issued from psychiatry into ad hominem attacks may be shown to fulfill specific argumentative functions. These functions are partly determined by the semantic features issued from the technical definition of these adjectives that may be activated in their ad hominem use. Accusing the opponent of being hysterical is a way of disqualifying his position as emotionally biased, and enables one to dismiss a conflicting view without having to discuss it. Accusing the opponent of being paranoid enables one to make a personal attack without assuming the responsibility for such a disputable argumentative move, while taking advantage of the devastating effect it may have. Finally, calling the opponent autistic when he does not come to meet your point is a way of dismissing his resistance to your arguments as being a mere symptom of a mental pathology, which enables you not to acknowledge your argumentative failure.

Whereas such qualifications undoubtedly serve disqualifying strategies, they are somehow toned down by the fact that they do not claim that the opponent is motivated by malevolent intentions: if he is wrong, it is not his fault, because he is mentally disabled, in one way or another.

This preliminary study also opens some lines of reflexion on the perception of mental illness. Our post-modern society is considered to be biologically and geneticallyoriented. In parallel, one's mental health is often questioned and analyzed. For some authors, policy-makers lean heavily and wrongly upon psychiatry to define norms and pseudo-relevant behavior [START_REF] Gori | Exilés de l'intime[END_REF]. For others, emotions are being used for economical purposes by pharmaceutical firms [START_REF] Lane | Comment la psychiatrie et l'industrie pharmaceutique ont médicalisé nos émotions[END_REF]. Whatever the reasons, the number of mental disorders medically recognized has been steadily increasing over the years 22 . Mental illness terms -outside the medical field-are not only applied to individuals but are also used to characterize concepts or theories: for example, it was said that economy was autistic 23 or that the French society was schizophrenic 24 .

Such uses outside the medical field are paradoxical, because of the many public campaigns aiming at de-stigmatizing persons suffering from mental disorders. For the past twenty years, most Western countries, including France, have launched media campaigns to emphasize that people suffering from mental disorders are "normal" persons. To name a few of these de-stigmatization campaigns, the World Psychiatric Association has launched "Open the doors" about schizophrenia 25 worldwide; "Time to change" claims to be "England's biggest programme to challenge mental health stigma and discrimination" 26 ; in France, the FondaMental association aims at explaining mental illnesses to the lay man 27 . However, all these initiatives have not prevented the use of psychiatric terms to depreciate one's opponents.

  Le gouvernement du Parti Schizofrène est devenu autiste de l'oreille gauche et n'écoute qu'avec celle de droite le Medef, le Cac 40, et les agences de notations Standard & Poor's et Cie... The Schizophrenic Party Government became autistic in its left ear and listens only with its right ear to Medef [right-wing union], to the CAC 40 [Paris Stock Exchange], to rating agencies Standard & Poor's and Co…

EST UNE PUTAIN D AUTISTE DE MERDE

  qui etait bizare....cette chos.. heu , femme ( on va dire ca comme ca..) avait des petites manies: se mettre les doigts dans le nez , se les lecher , puis elle s'habille bizarement avec un petit bonnet bleu en laine […] ....pi lorsqu'elle parle , elle doit reformuler sa phrase au moins 10 fois avant d'en sortir le bon exemplaire: C

	!!! […]:
	SALE AUTISTE DE MES DEUX T'AS INTERET A ME METTRE 12 A MON DST SINON JE TE
	VOLE TON SAC A ROULETTE DE MERDE 6

  mais j'me suis interrogé\ pourquoi m'a-t-il qualifié d'hystérique puisque: (.) j'fais un peu d'histoi/re(.) et j'me suis rapp'lé/ en effet/ que (.) le mot hystéri/que servait à qualifier/ euh (.) notamment en période de trou/ble pour les dénigrer/ (.) euh par exemple: les suffragettes/ (..) par celles et ceux qui étaient opposés euh (.) au droit d'vote des femmes/ (.) ça a servi à qualifier euh Simone de Beauvoir/ au moment d'la publication du deuxième sexe/ (..) ou enco/re les trois cent quarante troissalo/pes (.) lors euh de la publication du manifes/te pour le droit à l'avortement\ (..) j'me suis dit pourquoi être qualifié par ce terme/ (.) alors que je n'suis NI une suffragette/ ni Simone de Beauvoir/ (.) ni encore/ une fem/me demandant le droit/ à l'avortement\ (.) alors je (.) je suis rev'nu/ euh (.) euh au dix-neuvième siè/cle […] notamment aux travaux clini/ques (.) dans la foulée d'Charcot/ et je me suis rapp'lé en effet (.) et je pense que (.) c'est à ça que faisait référence sans doute le président Jacob/ (.) qu'à l'époque/ (.) à l'épo/que le mot d'hystérique servait (.) servait évidemment de (.) à qualifier TOUtes les femmes/ (.) toutes les femmes sont potentiellement hystéri/ques vous l'savez (.) cher collè/gue (.) hein/ (.) et une catégorie très particulière d'hommes\

  19 Thierry Lepaon, General Secretary of the CGT, on RMC radio station, 29th October 2013.20 Dingo 117, 29th October 2013, www.marianne.net 21 La Provence, 12 th June 2014. Tweet 1: mère d'enfant autiste et entendre le mot autiste à tout va au gouvernement et ds les cours d'école: STOP! Tweet 2: autiste n'est peut être pas le mot le plus délicat .... Tweet 3: On pourrait dire... sourd, mais c'est aussi un handicap. Tweet 4: L'utilisation du handicap comme une injure. Classe.

Due to the exploratory dimension of the research presented in this paper, we will confine ourselves to these three words, which we deemed representative of this psychiatric lexicon that spread out of its original specialized field throughout political discussions or everyday conversations.

English "you X you" or "you fucking / dirty / lousy X" may be considered as rough equivalents for "espèce de X" or "sale X".

http://parapentesaintevictoire.blogspot.fr/2014/05/panneau-retour.html

http://www.tromal.net/conte/view.php?urlHistoCount=3623

Technical definitions of "hysteria", "paranoid disorder" and "autism" are proposed respectively in section 4, 5, 6 below.

See for instance[START_REF] Walton | The Ad Hominem Argument as an Informal Fallacy[END_REF], "the ad hominem argument […] criticizes another argument by questioning the personal circumstances or personal trustworthiness of the arguer who advanced it." (p.317)

ICD stands for International Classification of Diseases, a diagnostic tool for epidemiology, health management and clinical purposes established by the World Health Organization.

DSM (Diagnostic and Statistical Manual of Mental Disorders) is a manual for diagnosing mental disorders published by the American society of psychiatry.

«Moi des souvenirs d'enfance / En France / Violence / Manque d'indulgence / Par les différences que j'ai»

Therefore our study provides a key for understanding how French society is mentallyoriented, specifically in political interactions.