Dynamics and Stability of Blind Grasping of a 3-Dimensional Object under Non-holonomic Constraints

A mathematical model expressing the motion of a pair of multi-DOF robot fingers with hemi-spherical ends, grasping a 3-D rigid object with parallel flat surfaces, is derived, together with non-holonomic constraints. By referring to the fact that humans grasp an object in the form of precision prehension, dynamically and stably by opposable forces, between the thumb and another finger (index or middle finger), a simple control signal constructed from finger-thumb opposition is proposed, and shown to realize stable grasping in a dynamic sense without using object information or external sensing (this is called blind grasp in this paper). The stability of grasping with force/torque balance under non-holonomic constraints is analyzed on the basis of a new concept named stability on a manifold. Preliminary simulation results are shown to verify the validity of the theoretical results.