Manipulation of 3D enveloped object

This paper discusses the manipulation of 3D enveloped object. By assigning all fingers as either the position controlled finger (P-finger) or the torque controlled finger (T-finger), we propose a method for letting the object to move in the desired direction along the surface of the P-fingers. For this purpose, we obtain the joint torque command for the T-fingers. The formulation of the total force/moment set can be applied to general 3D enveloping grasp. Also, we newly provide a sufficient condition for the total force/moment set of the object moving toward the desired direction, where it can be applied to general 3D contact configurations between the object and the P-fingers.