Geodesic
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

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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 ∞ case, we study some non-generic generalizations in the analytic case.

DOI : 10.1051/cocv:2004024
Classification : 34H05, 49J15, 53C17
Keywords: 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},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {634--655},
     publisher = {EDP-Sciences},
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     zbl = {1101.93030},
     language = {en},
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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

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