Abnormal extremals in the sub-Riemannian problem for a general model of a robot with a trailer-Reference-Cited by-同舟云学术

Abnormal extremals in the sub-Riemannian problem for a general model of a robot with a trailer

Published:2023 Issue:10 Volume:214 Page:1351-1372
ISSN:1064-5616
Container-title:Sbornik: Mathematics
language:en
Short-container-title:Sb. Math.

Author:

Ardentov Andrei Andreevich¹,Artemova Elizaveta Markovna²

Affiliation:

1. Ailamazyan Program Systems Institute of Russian Academy of Sciences, Ves'kovo, Pereslavl' district, Yaroslavl' oblast', Russia

2. Ural Mathematical Center, Udmurt State University, Izhevsk, Russia

Abstract

A symmetric mathematical model of a wheeled robot with a trailer is considered for various types of coupling between the robot and the trailer. It is shown that for fixed coupling parameters and fixed initial position of the robot with trailer there are two symmetric abnormal extremals. In motion along these trajectories the robot and the trailer traverse normal extremal trajectories for the sub-Riemannian problem on the group of motions of the plane; the coupling point always draws an inflectional elastica or a straight line. Bibliography: 33 titles.

Funder

Russian Science Foundation

Ministry of Education and Science of the Russian Federation

Mobius Contest

Publisher

Steklov Mathematical Institute

Reference33 articles.

1. Abnormal Optimal Controls and Open Problems in Nonholonomic Steering

2. Sub-Finsler Structures from the Time-Optimal Control Viewpoint for some Nilpotent Distributions

3. Abnormal Extremals of Left-Invariant Sub-Finsler Quasimetrics on Four-Dimensional Lie Groups

4. Abnormality of trajectory in sub-Riemannian structure

5. A cornucopia of four-dimensional abnormal sub-Riemannian minimizers