On the codimension one motion planning problem
type: Item
instance of: scholarly article
title: On the codimension one motion planning problem
zbMATH Open document ID: 1079.53049
published in: Journal of Dynamical and Control Systems
publication date: 2005-05-17T00:00:00Z
review text: The paper under review deals with the problem of motion planning for co-rank one sub-Riemannian metrics. The results are obtained in a constructive way, i.e., by computing metric complexity and finding asymptotic syntheses. The main results of the paper are as follows: For the 3-dimensional case an explicit exact expression of the metric complexity together with a corresponding asymptotic optimal synthesis is obtained. For other dimensions the results presented in the paper are deeper then in literature. For instance, the motion planning problem in the \(C^{\infty}\) category outside of a set of infinite co-dimension is solved here.
reviewed by: Adrian Sandovici
Mathematics Subject Classification ID: 53C17
Mathematics Subject Classification ID: 34H05
zbMATH DE Number: 2168272
zbMATH Keywords: sub-Riemannian geometry
zbMATH Keywords: robotics
zbMATH Keywords: motion planning
author: Jean-Paul Gauthier
author: V. M. Zakalyukin
MaRDI profile type: Publication
full work available at URL: s10883-005-0002-6
OpenAlex ID: W1969916170
cites work: Q4258204
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cites work: Complexity of nonholonomic motion planning
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cites work: Q5526485
DOI: 10.1007/S10883-005-0002-6
description: scientific article; zbMATH DE number 2168272