In robotics, when the demands for dexterity and versatility are high, traditional end effectors quickly show their limits and humanoid robot hands look like an appealing alternative. Unfortunately, although such hands can be built nowadays that are mechanically satisfactory, using them still remains problematic because their control is difficult. In this thesis, we have investigated three problems related to the control of humanoid robot hands: controlling the motion of the grasped object and the forces it is subject to, keeping hold of the object in case of external disturbances, and calculating the stiffness of the grasp, that is to say its elastic behavior. To manipulate the object, we propose a new control law, based on mathematical programming, that has the advantage of returning control torques which realize a trade-off between the different setpoints, possibly incompatible or unfeasible, and also respect the constraints due to physics and to the mechanics of the robot. To keep hold of the object when a disturbance happens, we propose a method to compute the tightening forces that make the grasp withstand the largest possible disturbance, in the direction where this largest possible disturbance is the smallest: a kind of critical disturbance for the grasp. Finally, we model the stiffness of the object as a function of the stiffness of the fingers, in the case when a relative rolling motion is possible between the fingers and the object. We prove that this stiffness is also function of the contact forces and the curvatures of the contacting surfaces.
