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

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

ESAIM: Control, Optimisation and Calculus of Variations (2004)

- Volume: 10, Issue: 4, page 634-655
- ISSN: 1292-8119

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topRomero-Meléndez, Cutberto, Gauthier, Jean Paul, and Monroy-Pérez, Felipe. "On complexity and motion planning for co-rank one sub-riemannian metrics." ESAIM: Control, Optimisation and Calculus of Variations 10.4 (2004): 634-655. <http://eudml.org/doc/246067>.

@article{Romero2004,

abstract = {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.},

author = {Romero-Meléndez, Cutberto, Gauthier, Jean Paul, Monroy-Pérez, Felipe},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {motion planning problem; metric complexity; normal forms; asymptotic optimal synthesis},

language = {eng},

number = {4},

pages = {634-655},

publisher = {EDP-Sciences},

title = {On complexity and motion planning for co-rank one sub-riemannian metrics},

url = {http://eudml.org/doc/246067},

volume = {10},

year = {2004},

}

TY - JOUR

AU - Romero-Meléndez, Cutberto

AU - Gauthier, Jean Paul

AU - Monroy-Pérez, Felipe

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

JO - ESAIM: Control, Optimisation and Calculus of Variations

PY - 2004

PB - EDP-Sciences

VL - 10

IS - 4

SP - 634

EP - 655

AB - 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.

LA - eng

KW - motion planning problem; metric complexity; normal forms; asymptotic optimal synthesis

UR - http://eudml.org/doc/246067

ER -

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