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Stability of •gblind grasping•h of a 2-Dimensional (2-D) rigid object by a pair of multi-DOF planar robot fingers with hemispherical ends is analyzed on the basis of Lagrange's equation of motion of the overall fingers-object system subject to point contact constraints and rolling constraints. It is assumed that motion of the fingers and object is confined to a vertical plane and hence it is affected by the gravity. Blind grasping is defined as a manner of grasp when 1) the control signal is constructed on the basis of finger kinematics and measurement data on finger joints without knowing object kinematics or using external sensings such as visual or tactile sensing and 2) at the same time the closed-loop dynamics converges to a state of force/torque balance. In fact, human can grasp an object even if they close eyes, provided the hand is preshaped toward the object placed on a table. Stability is defined on a constraint manifold and also the new concept called •gEP-manifold•h (EP: Equilibrium Point) is introduced when the overall fingers-object system is redundant in DOF. It is shown that any solution of the closed-loop dynamics lying on the constraint manifold converges to a low-dimensional EP-manifold satisfying force/torque balance and the speed of convergence is exponential in time.

Stability on a Manifold for 2-D Object Grasping by a Pair of Robot Fingers