A formulation of the linear discrete Coulomb friction problem via convex optimization

Vincent Acary 1 Florent Cadoux 1 Claude Lemaréchal 1 Jérôme Malick 1
1 BIPOP - Modelling, Simulation, Control and Optimization of Non-Smooth Dynamical Systems
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, INPG - Institut National Polytechnique de Grenoble
Abstract : This paper presents a new formulation of the dynamical Coulomb friction problem in finite dimension with discretized time. The novelty of our approach is to capture and treat directly the friction model as a parametric quadratic optimization problem with second-order cone constraints coupled with a fixed point equation. This intrinsic formulation allows a simple existence proof under reasonable assumptions, as well as a variety of solution algorithms. We study mechanical interpretations of these assumptions, showing in particular that they are actually necessary and sufficient for a basic example similar to the so-called ''paradox of Painlevé''. Finally, we present some implementations and experiments to illustrate the practical aspect of our work.
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Vincent Acary, Florent Cadoux, Claude Lemaréchal, Jérôme Malick. A formulation of the linear discrete Coulomb friction problem via convex optimization. ZAMM, Wiley-VCH Verlag, 2011, 91 (2), pp.155-175. 〈10.1002/zamm.201000073〉. 〈inria-00495734〉

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