Learning and generalizing force control policies for sculpting

Humans exhibit exceptional skills in using tools and manipulating objects of their environment by skillfully controlling exerted force and arm impedance. One of the basic components of this mechanism is the generation of internal models which associate kinematic variables with applied force. On the other hand, making robots capable of skillfully using tools and adapting their motor behavior to new environmental conditions is rather complex. In the present paper, we investigate learning of force control policies for robotic sculpting given multiple task demonstrations. These policies express the relationship between constrained motions and exerted force and are learned in Cartesian space where the coupling of dynamics between different directions of motion is also taken into account. In addition, a novel algorithm is proposed to generalize these policies to new motion tasks, executed in a sufficiently homogeneous environment, same with that in demonstrations, but in presence of new motion-dependent external forces. To this aim, a differential calculus approach is proposed where not only the mapping from motion to force but also from difference in motion to difference in force is learned to generalize the policies to new contexts. This is achieved by learning apart from a set of policy parameters, some newly introduced quantities, so called weight differentials, which express the rate of change of the policy parameters. The proposed approach is validated in simple real-world sculpting experiments by using a two degrees-of-freedom haptic device.