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

Abstract

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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.

How to cite

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Romero-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 -

References

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  12. [12] F. Jean and E. Falbel, Measures and transverse paths in Sub-Riemannian Geometry. J. Anal. Math. 91 (2003) 231-246. Zbl1073.53046MR2037409
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