Constrained motion of grasped objects by hybrid control

The author considers the control of an object, grasped by a multifingered hand, which is constrained (at a point) to follow some frictionless surface. Using the surface description, orthogonal position-controlled and force-controlled subspaces, together with their relevant parameters, are defined. By analyzing all the kinematic constraints on the grasped object, the author derives the dynamic equation for the total constrained system in terms of the surface parameters and force parameters. Finally, a hybrid control scheme for the hand is proposed which allows a fixed point on the object to track a prespecified position trajectory on the surface while exerting a desired normal force