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Guaranteed Manipulator Precision via Interval Analysis of Inverse Kinematics

[+] Author Affiliations
Muhammed R. Pac, Dan O. Popa

University of Texas at Arlington, Arlington, TX

Micky Rakotondrabe, Philippe Lutz

FEMTO-ST Institute, University of Franche-Comté (UFC), Besançon, France

Sofiane Khadraoui

Texas A&M University at Qatar, Doha, Qatar

Paper No. DETC2013-13033, pp. V001T09A017; 8 pages
  • ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 1: 15th International Conference on Advanced Vehicle Technologies; 10th International Conference on Design Education; 7th International Conference on Micro- and Nanosystems
  • Portland, Oregon, USA, August 4–7, 2013
  • Conference Sponsors: Design Engineering Division, Computers and Information in Engineering Division
  • ISBN: 978-0-7918-5584-3
  • Copyright © 2013 by ASME


The paper presents a new methodology for solving the inverse problem of manipulator precision design. Such design problems are often encountered when the end-effector uncertainty bounds are given, but it is not clear how to allocate precision bounds on individual robot axes. The approach presented in this paper uses interval analysis as a tool for uncertainty modelling and computational analysis. In prior work, the exponential formulation of the forward kinematics map was extended to intervals. Here, we use this result as an inclusion function in the computation of solutions to set-valued inverse kinematic problems. Simulation results are presented in two case studies to illustrate how we can go from an uncertainty interval at the end-effector to a design domain of allowable uncertainties at individual joints and links. The proposed method can be used to determine the level of precision needed in the design of a manipulator such that a predefined end-effector precision can be guaranteed. Also, the approach is general as such it can be easily extended to any degree-of-freedom and kinematic configuration.

Copyright © 2013 by ASME



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