Nonlinear bifurcation analysis of a robotic arm subject to digital position control

Giuseppe Habib, Giuseppe Rega, Gabor Stepan

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

Abstract

Precision and stability in position control of robots are critical parameters in many industrial applications where high accuracy is needed. It is well known that digital effect is destabilizing and can cause instabilities. In this paper, we analyze a single DoF system and we present the stability limits in the parameter space of the control gains. Furthermore we introduce a nonlinearity relative to the saturation of the control force in the model, reduce the dynamics of the nonlinear map to its local center manifold, study the bifurcation along the stability border and identify conditions under which a supercritical or subcritical bifurcation occurs. The obtained results explain some of the typical instabilities occurring in industrial applications. We verify the obtained results through numerical simulations.

Original languageEnglish
Title of host publicationASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2011
Pages483-492
Number of pages10
EditionPARTS A AND B
DOIs
Publication statusPublished - Dec 1 2011
EventASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2011 - Washington, DC, United States
Duration: Aug 28 2011Aug 31 2011

Publication series

NameProceedings of the ASME Design Engineering Technical Conference
NumberPARTS A AND B
Volume4

Other

OtherASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2011
CountryUnited States
CityWashington, DC
Period8/28/118/31/11

Keywords

  • Bifurcation
  • Center manifold reduction
  • Chaos
  • Digital position control
  • Discrete time
  • Robots

ASJC Scopus subject areas

  • Modelling and Simulation
  • Mechanical Engineering
  • Computer Science Applications
  • Computer Graphics and Computer-Aided Design

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  • Cite this

    Habib, G., Rega, G., & Stepan, G. (2011). Nonlinear bifurcation analysis of a robotic arm subject to digital position control. In ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2011 (PARTS A AND B ed., pp. 483-492). (Proceedings of the ASME Design Engineering Technical Conference; Vol. 4, No. PARTS A AND B). https://doi.org/10.1115/DETC2011-47832