Stiffness modeling for multi-fingered grasping with rolling contacts

The stiffness control of an object grasped by a multi-fingered robot hand requires the modeling of the elastic behavior of the object, caused by the stiffness of the fingers. Because of the presence of rolling contacts between the fingers and the object, such a modeling is not a trivial issue, and a very different one from the case of simpler parallel manipulators. We provide here a first expression of the cartesian stiffness matrix produced on the object, as a function of the cartesian stiffness matrices of the fingers, in the case that the contacts are non-sliding point contacts that may freely roll (on the tangent plane) and twist (around the contact normal). We show that this expression of the object-level cartesian stiffness matrix depends also on the contact forces and on the local geometries of the contacting surfaces.