# 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 (2010)

- 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 (2010): 634-655. <http://eudml.org/doc/90748>.

@article{Romero2010,

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
[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.
},

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.; motion planning problem; normal forms; asymptotic optimal synthesis},

language = {eng},

month = {3},

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/90748},

volume = {10},

year = {2010},

}

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

DA - 2010/3//

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
[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.

LA - eng

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

UR - http://eudml.org/doc/90748

ER -

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