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Outils algébriques pour la résolution de problèmes géométriques et l'analyse de trajectoire de robots parallèles prévus pour des applications à haute cadence et grande précision

Abstract : Parallel robots have been introduced in flight simulators because of their high dynamics. Research is now focused on their application as machine tools. The requirements on accuracy are more stringent. The first objective is to find a resolution method to kinematics problems. Only a few implementations have succeeded to solve the general case (Gough platform). We have cataloged 8 algebraic formulations for the geometric model. The selected exact method is based the computation of Gröbner bases and the Rational Univariate Representation. The method is too slow for trajectory pursuit. The 2nd objective is the realization of a certified numeric iterative method (Newton) based on the Kantorovich theorem and interval arithmetic. The 3rd objective is milling task feasibility. A trajectory simulator includes tool accuracy estimations with given federate. One can determine the impact of a given architecture, selected sensors and the controller. This thesis terminates by a trajectory certification method, verifying if the tool can follow a trajectory included in a zone around the nominal trajectory. A convergence theorem is applied to insure that the forward kinematics model can be solved everywhere in the tube.
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Theses
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http://docnum.univ-lorraine.fr/prive/SCD_T_2003_0180_ROLLAND.pdf
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https://hal.univ-lorraine.fr/tel-01746839
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Submitted on : Thursday, March 29, 2018 - 10:45:52 AM
Last modification on : Thursday, September 24, 2020 - 2:52:03 PM

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  • HAL Id : tel-01746839, version 1

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Luc Hugues Rolland. Outils algébriques pour la résolution de problèmes géométriques et l'analyse de trajectoire de robots parallèles prévus pour des applications à haute cadence et grande précision. Autre [cs.OH]. Université Henri Poincaré - Nancy 1, 2003. Français. ⟨NNT : 2003NAN10180⟩. ⟨tel-01746839⟩

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