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 case, we study some non-generic generalizations in the analytic case.
Mots-clés : motion planning problem, metric complexity, normal forms, asymptotic optimal synthesis
@article{COCV_2004__10_4_634_0,
author = {Romero-Mel\'endez, Cutberto and Gauthier, Jean Paul and Monroy-P\'erez, Felipe},
title = {On complexity and motion planning for co-rank one sub-riemannian metrics},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {634--655},
publisher = {EDP-Sciences},
volume = {10},
number = {4},
year = {2004},
doi = {10.1051/cocv:2004024},
mrnumber = {2111085},
zbl = {1101.93030},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/cocv:2004024/}
}
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 SP - 634 EP - 655 VL - 10 IS - 4 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv:2004024/ DO - 10.1051/cocv:2004024 LA - en ID - COCV_2004__10_4_634_0 ER -
%0 Journal Article %A Romero-Meléndez, Cutberto %A Gauthier, Jean Paul %A Monroy-Pérez, Felipe %T On complexity and motion planning for co-rank one sub-riemannian metrics %J ESAIM: Control, Optimisation and Calculus of Variations %D 2004 %P 634-655 %V 10 %N 4 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv:2004024/ %R 10.1051/cocv:2004024 %G en %F COCV_2004__10_4_634_0
Romero-Meléndez, Cutberto; Gauthier, Jean Paul; Monroy-Pérez, Felipe. On complexity and motion planning for co-rank one sub-riemannian metrics. ESAIM: Control, Optimisation and Calculus of Variations, Tome 10 (2004) no. 4, pp. 634-655. doi : 10.1051/cocv:2004024. http://archive.numdam.org/articles/10.1051/cocv:2004024/
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