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ESAIM: Control, Optimisation and Calculus of Variations (1)

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On complexity and motion planning for co-rank one sub-Riemannian metrics
Cutberto Romero-Meléndez, Jean Paul Gauthier, Felipe Monroy-Pérez
Journal:

ESAIM: Control, Optimisation and Calculus of Variations / Volume 10 / Issue 4 / October 2004

Published online by Cambridge University Press:

15 October 2004, pp. 634-655

Print publication:

October 2004
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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 [CITE]), 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.