Grasp planning for multifingered robot hands

The grasping stiffness and the contacting stiffness for the grasping system of a multifingered robot hand are characterized. Using a Lagrangian formulation, the authors develop the small displacement vibration equation of the grasping system. Based on the features of a grasping state, they characterize object stability, contact stability, contact position, and uniaxial fingertip force constraints for grasp planning. From the asymptotical stability of the vibration system, a quality measure is defined that is used as an objective for grasp planning, and grasp planning is formulated as a nonlinear programming problem. An example for a three-fingered robot hand grasping a spherical object demonstrates the applicability and effectiveness of this approach. Numerical results using a constrained conjugate direction descent technique are described