Today's rigid industrial robots have good repeatability, which is in the order of a hundredth of a millimeter at the end of the effector, and high dynamics of the drive chain. Its bandwidth can then reach several tens of Hz Khalil02. These characteristics make it possible to obtain fast and precise movements of the robots. It is then possible to extend the applications of these robots to cobotics and teleoperation thanks to the haptic feedback. The drive chains of these robots generally include mechanical reducers, mechanical coupling systems between several drive chains, or motion conversion mechanisms. All these mechanical systems introduce friction that can absorb up to 80\% of the mechanical power. These frictions depend on the temperature, the humidity of the environment, the mechanical constraints applied to the robot. Finally, these drive chains are often not very transparent. This means that an external force applied to the effector must be high to obtain a movement of the robot.These technological characteristics mean that a fine control of the robot's force on its environment or a co-manipulation control are not possible by simply measuring the motor currents. The addition of a force sensor is necessary to take into account the interaction robot/environment or man/robot. The contribution of this work is the definition of a haptic feedback for the parallel robot, called Orthoglide. This robot has three prismatic joints that allow high Cartesian accelerations of the effector as well as uniform precision in the work area. Its effector is equipped with a force sensor. Its output rate is equal to 7000~Hz. Two feedback controls are defined for Orthoglide. The first one, which controls the joint variables, is performed with a linearizing control law, the well-known "computed torques" method. The new input consists of the addition of a desired acceleration and a correction in position, velocity in order to asymptotically cancel the position error, whose behavior is governed by a linear differential equation. Disturbances such as an unknown stiffness of the environment are mainly rejected by the feedback control of the joint variables. Unexpected collisions of the robot with the environment must also be managed by this feedback controls of the joint variables. It must therefore be able to trigger an emergency stop. The second feedback control is dedicated to haptic feedback. It includes the effector, the sensor and the environment or user with whom it interacts. The bandwidth of this haptic feedback control is lower than that of the feedback control of the joint variables. The bandwidths of the joint control as well as the internal current loop of the drives are such that their actions can be considered equivalent to that of gain compared to the haptic feedback. For the haptic feedback control the input is the desired force, the output is the force measured by the force sensor. The difference between these two forces is converted into a Cartesian acceleration by applying the equivalence, force / (mass acceleration) with a variable gain. This Cartesian acceleration is integrated to define a velocity and position references in the operating space. These reference trajectoriee for the active linear joints are projected into the articular space to obtain the acceleration, velocity and position references of the feedback control of the joint variables. Different applications can be considered for the haptic feedback such as collaboration task or force control.

The perspective of this work is to perform a teleoperation task between Orthoglide and another parallel robot with three prismatic joints and a cardan link composed of the revolute joints