Optimum grasping planning for multi-fingered dextrous hands based on the asymptotical stability

The grasp stiffness and joint stiffness for the grasping system of a multi-fingered dextrous hand are characterized, and the expressions are developed for the potential energy, kinetic energy and the dissipation function in a grasp. Using a Lagrangian formula, the small displacement disturbance equation for a multi-fingered grasping system is introduced and the equation is solved by modal analysis. Based on this work, an optimum grasping planning is formulated as a non-linear programming problem so that the grasping system could have ideal asmptotical stability. An example for the BH-2 anthropoid hand grasping a cylinder-object demonstrates the applicability and effectiveness of the method.