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Evaluation of Complementarity Techniques for Minimal Coordinate Contact Dynamics

[+] Author Affiliations
Harshavardhan Mylapilli

University of Southern California, Los Angeles, CA

Abhinandan Jain

Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA

Paper No. DETC2014-34322, pp. V006T10A010; 13 pages
doi:10.1115/DETC2014-34322
From:
  • ASME 2014 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 6: 10th International Conference on Multibody Systems, Nonlinear Dynamics, and Control
  • Buffalo, New York, USA, August 17–20, 2014
  • Conference Sponsors: Design Engineering Division, Computers and Information in Engineering Division
  • ISBN: 978-0-7918-4639-1
  • Copyright © 2014 by ASME

abstract

In this article, the non-smooth contact dynamics of multi-body systems is formulated as a complementarity problem. Minimal coordinates operational space formulation is used to derive the dynamics equations of motion. Depending on the approach used for modeling Coulomb’s friction, the complementarity problem can be posed either as a linear or a nonlinear problem. Both formulations are studied in this paper. An exact modeling of the friction cone leads to a nonlinear complementarity problem (NCP) formulation whereas a polyhedral approximation of the friction cone results in a linear complementarity problem (LCP) formulation. These complementarity problems are further recast as non-smooth unconstrained optimization problems, which are solved by employing a class of Levenberg-Marquardt algorithms. The necessary theory detailing these techniques is discussed and five schemes are implemented to solve contact dynamics problems. A simple test case of a sphere moving on a plane surface is used to validate these schemes, while a twelve-link pendulum example is chosen to compare the speed and accuracy of the schemes presented in this paper.

Copyright © 2014 by ASME

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