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Modélisation dynamique des systèmes non-holonomes intermittents : application à la bicyclette

Abstract : This thesis deals with the dynamic modelling of intermittent non-holonomic systems andits application to the Whipple 3D bicycle. To that end, we relied on a set of tools in geometric mechanics (mainly Lagrangian reduction and the projection in the kernel of the kinematic constraints). In the first instance, we have addressed the case of the bicycle subjected to persistent contacts. By defining the space of the bicycle configurations as a principal fibre bundle with SE(3) as structural group, we obtained a model of the contact points and of the constraints free of any non-linearities associated with a generalized coordinate type configuration. This formulation allowed us to obtain the kernel of the constraints in a symbolic form without singularity. We then produced a symbolic model of the dynamics ofthe bicycle subjected to persistent contacts using the projection reduction method of its free dynamics in the subspace of its permissible speeds. This approach extends the general framework developed in recent years for bio-inspired locomotion. Taking advantage of the structure of SE(3), a model of the intermittent bicycle was proposed as part of an event-driven approach. Moreover, the adoption ofthe physical model of plastic impact has allowed us to extend the projection reduction method to the intermittent case. We then compared our "reduced" approach to the conventional approach and showed that they shared a common geometric interpretation. These tools were finally applied to the simulation of the intermittent bicycle to illustrate its rich dynamics.
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  • HAL Id : tel-02940450, version 1

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Johan Raphaël Mauny. Modélisation dynamique des systèmes non-holonomes intermittents : application à la bicyclette. Automatique / Robotique. Ecole nationale supérieure Mines-Télécom Atlantique, 2018. Français. ⟨NNT : 2018IMTA0113⟩. ⟨tel-02940450⟩

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