A stability theory of a manifold: concurrent realization of grasp and orientation control of an object by a pair of robot fingers

Abstract

2003). A stability theory of a manifold: concurrent realization of grasp and orientation control of an object by a pair of robot ngers. SUMMARYThis paper is concerned with a stability theory of motion governed by Lagrange's equation for a pair of multi-degrees of freedom robot fingers with hemi-spherical finger ends grasping a rigid object under rolling contact constraints. When a pair of dual two d.o.f. fingers is used and motion of the overall fingers-object system is confined to a plane, it is shown that the total degree of freedom of the fingers-object system is redundant for realization of stable grasping though there arise four algebraic constraints. To resolve the redundancy problem without introducing any other extra and artificial performance index, a concept of stability of motion starting from a higher dimensional manifold to a lower-dimensional manifold, expressing a set of states of stable grasp with prescribed contact force, is introduced and thereby it is proved in a rigorous way that stable grasp in a dynamic sense is realized by a sensory feedback constructed by means of measurement data of finger joint angles and the rotational angle of the object. Further, it is shown that there exists an additional sensory feedback that realizes not only stable grasp but also orientation control of the object concurrently. Results of computer simulation based on Baumgarte's method are presented, which show the effectiveness of the proposed concept and analysis.

Stable pinching by controlling finger relative orientation of robotic fingers with rolling soft tips

“…[32][33][34] This class of controllers achieves stable grasping and fine manipulation without any force and contact sensing requirements for objects with flat surfaces and arbitrary shape for both the 2D and 3D cases. 7,[35][36][37][38][39][40][41] As the initial finger-object pose and contact positions must not necessarily correspond to an equilibrium state, perception and execution errors can be accommodated.…”

A Simple Control Method Coping With a Kinematically Ill-Posed Inverse Problem of Redundant Robots: Analysis in Case of a Handwriting Robot

“…Instead, a novel concept named "stability on a manifold" is introduced and it is shown that there exists a sensory feedback based on measurements of physi-cal variables of task description and this sensory feedback signal enables the overall closed-loop system naturally and coordinately to converge to a lower-dimensional constraint manifold that describes a set of joint states fulfilling a target given task. The original idea of "stability on a manifold" was first introduced in control of multi-fingered hands for stable grasp and object-manipulation [7][8][9]. In this paper, typical robotic tasks of handwriting [10] under DOF redundancy are treated.…”

Bimanual regrasping from unimanual machine learning

“…Their solution is not general, since they solve it specifically for two 2-link planar arms and assume rectangular objects. A previously-published grasp algorithm [1] is rendered computationally efficient by empirically determining, using numerical simulations, a quasi-linear relationship between the object's orientation and the manipulator's initial contact positions. This relationship is then exploited to calculate regrasping phases that will change the object's orientation.…”