Quasiperiodic oscillations in robot dynamics

G. Stépán, G. Haller

Research output: Contribution to journalArticle

53 Citations (Scopus)

Abstract

Delayed robot systems, even of low degree of freedom, can produce phenomena which are well understood in the theory of nonlinear dynamical systems, but hardly ever occur in simple mechanical models. To illustrate this, we analyze the delayed positioning of a single degree of freedom robot arm which leads to an infinite dimensional dynamical system. Restricting the dynamics to a four dimensional center manifold, we show that the system undergoes a codimension two Hopf bifurcation for an infinite set of parameter values. This provides a mechanism for the creation of two-tori in the phase space and gives a theoretical explantion for self-excited quasiperiodic oscillations of force controlled robots. We also compare our results with experimental data.

Original languageEnglish
Pages (from-to)513-528
Number of pages16
JournalNonlinear Dynamics
Volume8
Issue number4
DOIs
Publication statusPublished - Dec 1995

Fingerprint

Robot Dynamics
Robot
Robots
Oscillation
Degree of freedom
Infinite Dimensional Dynamical System
Nonlinear dynamical systems
Hopf bifurcation
Center Manifold
Nonlinear Dynamical Systems
Degrees of freedom (mechanics)
Hopf Bifurcation
Codimension
Positioning
Phase Space
Torus
Dynamical systems
Experimental Data
Model

Keywords

  • Codimension two bifurcation
  • force control
  • sampling
  • time delay

ASJC Scopus subject areas

  • Mechanics of Materials
  • Mechanical Engineering
  • Computational Mechanics

Cite this

Quasiperiodic oscillations in robot dynamics. / Stépán, G.; Haller, G.

In: Nonlinear Dynamics, Vol. 8, No. 4, 12.1995, p. 513-528.

Research output: Contribution to journalArticle

Stépán, G. ; Haller, G. / Quasiperiodic oscillations in robot dynamics. In: Nonlinear Dynamics. 1995 ; Vol. 8, No. 4. pp. 513-528.
@article{00e3987d4a3d43d68a987174f3294d6c,
title = "Quasiperiodic oscillations in robot dynamics",
abstract = "Delayed robot systems, even of low degree of freedom, can produce phenomena which are well understood in the theory of nonlinear dynamical systems, but hardly ever occur in simple mechanical models. To illustrate this, we analyze the delayed positioning of a single degree of freedom robot arm which leads to an infinite dimensional dynamical system. Restricting the dynamics to a four dimensional center manifold, we show that the system undergoes a codimension two Hopf bifurcation for an infinite set of parameter values. This provides a mechanism for the creation of two-tori in the phase space and gives a theoretical explantion for self-excited quasiperiodic oscillations of force controlled robots. We also compare our results with experimental data.",
keywords = "Codimension two bifurcation, force control, sampling, time delay",
author = "G. St{\'e}p{\'a}n and G. Haller",
year = "1995",
month = "12",
doi = "10.1007/BF00045711",
language = "English",
volume = "8",
pages = "513--528",
journal = "Nonlinear Dynamics",
issn = "0924-090X",
publisher = "Springer Netherlands",
number = "4",

}

TY - JOUR

T1 - Quasiperiodic oscillations in robot dynamics

AU - Stépán, G.

AU - Haller, G.

PY - 1995/12

Y1 - 1995/12

N2 - Delayed robot systems, even of low degree of freedom, can produce phenomena which are well understood in the theory of nonlinear dynamical systems, but hardly ever occur in simple mechanical models. To illustrate this, we analyze the delayed positioning of a single degree of freedom robot arm which leads to an infinite dimensional dynamical system. Restricting the dynamics to a four dimensional center manifold, we show that the system undergoes a codimension two Hopf bifurcation for an infinite set of parameter values. This provides a mechanism for the creation of two-tori in the phase space and gives a theoretical explantion for self-excited quasiperiodic oscillations of force controlled robots. We also compare our results with experimental data.

AB - Delayed robot systems, even of low degree of freedom, can produce phenomena which are well understood in the theory of nonlinear dynamical systems, but hardly ever occur in simple mechanical models. To illustrate this, we analyze the delayed positioning of a single degree of freedom robot arm which leads to an infinite dimensional dynamical system. Restricting the dynamics to a four dimensional center manifold, we show that the system undergoes a codimension two Hopf bifurcation for an infinite set of parameter values. This provides a mechanism for the creation of two-tori in the phase space and gives a theoretical explantion for self-excited quasiperiodic oscillations of force controlled robots. We also compare our results with experimental data.

KW - Codimension two bifurcation

KW - force control

KW - sampling

KW - time delay

UR - http://www.scopus.com/inward/record.url?scp=0029486988&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0029486988&partnerID=8YFLogxK

U2 - 10.1007/BF00045711

DO - 10.1007/BF00045711

M3 - Article

AN - SCOPUS:0029486988

VL - 8

SP - 513

EP - 528

JO - Nonlinear Dynamics

JF - Nonlinear Dynamics

SN - 0924-090X

IS - 4

ER -