A Riemannian-Geometric Approach for Intelligent Control and Fingertip Design of Multi-fingered Hands

摘要

Based upon the analysis of modeling and control of two-dimensional (2-D) grasping and manipulation of arbitrary rigid objects under rolling contact constraints, geometrical conditions for the design of desired fingertip shapes of robot fingers are discussed from the Riemannian-geometric standpoint. A required condition is given as an inequality expressed in terms of quantities of the second fundamental form of fingertip contour curves, although the quantities do not enter into the Euler-Lagrange equation of motion of the overall fingers/object system. Satisfaction of the inequality is necessary for stabilization of grasping by using fingers-thumb opposable control signals without use of external sensings or knowledge of an object to be grasped. At the same time, asymptotic convergence of a solution to the closed-loop dynamics of 2-D precision prehension by a pair of multi-joint robot fingers is proved under rolling contact constraints and the existence of redundancy in the system's degrees of freedom. This is regarded as an extension of the Dirichlet-Lagrange stability theorem to a dynamical system with redundancy and geometric constraints.