Computation of Marginal External Force Space of Power Grasp Using Polyhedral Convex Set Theory

Abstract

This paper describes an efficient computation algorithm of the marginal external force space of the power grasp. A general computational algorithm of the space is provided for the 3-dimensional grasp with multiple contacts including defective contacts by a multi-fingered robot hand. Evaluation of the marginal external force space requires the computation of convex hull in a 6-dimensional space, which is known to have O(n^{⌊(d+1)/2⌋}) computational complexity. For more realistic evaluation, we propse to compute the 3-dimensional section of the marginal external force space, and establish its computational scheme. Numerical examples, for 3-dimensional grasp by a 3-fingered robot hand, illustrate the efficiency and usefulness of the proposed algorithms.