A riemannian-geometry approach for dynamics and control of object manipulation under constraints

Suguru Arimoto, Morio Yoshida, Masahiro Sekimoto, Kenji Tahara

Research output: Chapter in Book/Report/Conference proceedingConference contribution

5 Citations (Scopus)

Abstract

A Riemannian-geometry approach 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 multijoint 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 spanned from the constraint gradient can be regarded as a lifting in the direction orthogonal to the kernel space. 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. A control signal called "blind grasping" is defined and shown to be effective in stabilization of grasping without using the details of information of object shape and parameters or external sensing. The concept of stability of the closedloop system under constraints is renewed in order to overcome the degrees-of-freedom redundancy problem. An extension of Dirichlet-Lagrange's stability theorem to a system of DOFredundancy under constraints is presented by using a Morse- Lyapunov function.

Original languageEnglish
Title of host publication2009 IEEE International Conference on Robotics and Automation, ICRA '09
Pages1683-1690
Number of pages8
DOIs
Publication statusPublished - Nov 2 2009
Event2009 IEEE International Conference on Robotics and Automation, ICRA '09 - Kobe, Japan
Duration: May 12 2009May 17 2009

Publication series

NameProceedings - IEEE International Conference on Robotics and Automation
ISSN (Print)1050-4729

Other

Other2009 IEEE International Conference on Robotics and Automation, ICRA '09
Country/TerritoryJapan
CityKobe
Period5/12/095/17/09

All Science Journal Classification (ASJC) codes

  • Software
  • Control and Systems Engineering
  • Artificial Intelligence
  • Electrical and Electronic Engineering

Fingerprint

Dive into the research topics of 'A riemannian-geometry approach for dynamics and control of object manipulation under constraints'. Together they form a unique fingerprint.

Cite this