Computing 3-D optimal form-closure grasps

We address the problem of computing optimal fingertip locations yielding n-finger form-closure grasps of polyhedral objects. Given grasping points of m fingers not in form-closure, we show that the calculation of optimal grip points for the n-m fingers can be viewed as a nonlinear programming problem. We propose a sufficient and necessary condition for the n-m fingers to achieve an n-finger form-closure grasp with the m fingers given. Based on this condition, we derive a set of nonlinear constraints for the nonlinear programming problem. Furthermore, we give a performance index serving as an objective function which measures the distance between the center of mass of the grasped object and the contact points to be determined. In addition, the algorithm proposed can be applied to the frictionless grasp. We have implemented the algorithm and verified its efficiency by two examples.