ICRA'09 Paper Abstract

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Paper FrA5.1

Arimoto, Suguru (Ritsumeikan University), Yoshida, Morio (RIKEN), Sekimoto, Masahiro (Ritsumeikan University), Tahara, Kenji (Kyushu University)

A Riemannian-Geometry Approach for Dynamics and Control of Object Manipulation under Constraints

Scheduled for presentation during the Regular Sessions "Grasping - I" (FrA5), Friday, May 15, 2009, 08:30−08:50, Room: 403

2009 IEEE International Conference on Robotics and Automation, May 12 - 17, 2009, Kobe, Japan

This information is tentative and subject to change. Compiled on January 24, 2022

Keywords Grasping, Dynamics, Redundant Robots

Abstract

A Riemannian-geometry appraoch for control and stabilization of dynamics of object manipulation under holonomic or non-holonomic (but Pfaffian) constraints is presented. First, position/force hybrid control of an endeffector of a multi-joint redundant (or nonredundant) robot under a nonholonomic constraint is reinterpreted in terms of "submersion" in Riemannian geometry. A force control signal constructed in the image space of the constraint gradient can be regarded as a lifting in the direction orthogonal to the kernel space of that. By means of the Riemannian distance on the constraint submanifold, stability on a manifold for a redundant system under holonomic constraints is discussed. Second, control and stabilization of dynamics of two-dimensional object grasping and manipulation by using a pair of multi-joint robot fingers are tackled, when a rigid object is given with arbitrary shape. Then, it is shown that rolling contact constraint induce the Euler equation of motion in an implicit function form, in which constraint forces appear as wrench vectors affecting on the object. The Riemannian metric can be introduced in a natural way on a constraint submanifold induced by rolling contacts. The concept of stability of the closed-loop system under constraints is renewed to overcome the DOF redundancy problem. An extension of Dirichlet-Lagrange's stability theorem to a system of DOF-redundancy under constraints is presented by using a Morse-Lyapunov function.

 

 

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