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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 — 2004

ESAIM: Control, Optimisation and Calculus of Variations

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.

On complexity and motion planning for co-rank one sub-Riemannian metrics

Cutberto Romero-Meléndez;  Jean Paul Gauthier;  Felipe Monroy-Pérez — 2010

ESAIM: Control, Optimisation and Calculus of Variations

In this paper, we study the 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 case, we study some non-generic generalizations in the analytic case.

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