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| HAL: hal-00712792, version 1 |
| arXiv: 1206.6645 |
| Detailed view |  Export this paper |
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| A Global Steering Method for Nonholonomic Systems |
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Yacine Chitour 1Frédéric Jean 2 |
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| (2012-06-28) |
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| In this paper, we present an iterative steering algorithm for nonholonomic systems (also called driftless control-affine systems) and we prove its global convergence under the sole assumption that the Lie Algebraic Rank Condition (LARC) holds true everywhere. That algorithm is an extension of the one introduced in [21] for regular systems. The first novelty here consists in the explicit algebraic construction, starting from the original control system, of a lifted control system which is regular. The second contribution of the paper is an exact motion planning method for nilpotent systems, which makes use of sinusoidal control laws and which is a generalization of the algorithm described in [29] for chained-form systems. |
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| 1: | Laboratoire des signaux et systèmes (L2S) |
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UMR8506 CNRS – SUPELEC – Université Paris XI - Paris Sud |
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| 2: | Unité de Mathématiques Appliquées (UMA) |
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ENSTA ParisTech |
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| 3: | Centre de Mathématiques Appliquées - Ecole Polytechnique (CMAP) |
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Polytechnique - X – CNRS : UMR7641 |
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| Division Systèmes |
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| Subject | : | Mathematics/Optimization and Control |
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| Nonholonomic systems – motion planning – sub-Riemannian geometry |
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| hal-00712792, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00712792 | |
| oai:hal.archives-ouvertes.fr:hal-00712792 | |
| From: Frédéric Jean | |
| Submitted on: Thursday, 28 June 2012 10:43:35 | |
| Updated on: Thursday, 28 June 2012 14:05:52 | |
