On complexity and motion planning for co-rank one sub-riemannian metrics
ESAIM: Control, Optimisation and Calculus of Variations, Tome 10 (2004) no. 4, pp. 634-655.

In this paper, we study the motion planning problem for generic sub-riemannian metrics of co-rank one. We give explicit expressions for the metric complexity (in the sense of Jean [10, 11]), in terms of the elementary invariants of the problem. We construct asymptotic optimal syntheses. It turns out that among the results we show, the most complicated case is the 3-dimensional. Besides the generic ${C}^{\infty }$ case, we study some non-generic generalizations in the analytic case.

DOI : https://doi.org/10.1051/cocv:2004024
Classification : 34H05,  49J15,  53C17
Mots clés : motion planning problem, metric complexity, normal forms, asymptotic optimal synthesis
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title = {On complexity and motion planning for co-rank one sub-riemannian metrics},
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Romero-Meléndez, Cutberto; Gauthier, Jean Paul; Monroy-Pérez, Felipe. On complexity and motion planning for co-rank one sub-riemannian metrics. ESAIM: Control, Optimisation and Calculus of Variations, Tome 10 (2004) no. 4, pp. 634-655. doi : 10.1051/cocv:2004024. http://www.numdam.org/articles/10.1051/cocv:2004024/

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