Stiffness Modeling of the Soft-Finger Contact in Robotic Grasping

This paper investigates the soft-finger contact by presenting the contact with a set of line springs based on screw theory, reveals the rotational effects, and identifies the stiffness properties of the contact. An elastic model of a soft-finger contact is proposed and a generalized contact stiffness matrix is developed by applying the congruence transformation and by introducing stiffness mapping of the line springs in translational directions and rotational axes. The effective stiffnesses along these directions and axes are hence obtained and the rotational stiffnesses are revealed. This helps create a screw representation of a six-dimensional soft-finger contact and produce an approach of analyzing and synthesizing a robotic grasp without resorting to the point contact representation. The correlation between the rotational stiffness, the number of equivalent point contacts and the number of equivalent contours is given and the stiffness synthesis is presented with both modular and direct approaches. The grasp thus achieved from the stiffness analysis contributes to both translational and rotational restraint and the stiffness matrix so developed is proven to be symmetric and positive definite. Case studies are presented with a two-soft-finger grasp and a three-soft-finger grasp. The grasps are analyzed with a general stiffness matrix which is used to control the fine displacements of a grasped object by changing the preload on the contact.

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