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http://elar.urfu.ru/handle/10995/90710
Название: | Analytic description of a reachable set for the Dubins car |
Авторы: | Patsko, V. S. Fedotov, A. A. |
Дата публикации: | 2020 |
Издатель: | Krasovskii Institute of Mathematics and Mechanics |
Библиографическое описание: | Patsko, V. S. Analytic description of a reachable set for the Dubins car / V. S. Patsko, A. A. Fedotov. — DOI 10.21538/0134-4889-2020-26-1-182-197 // Trudy Instituta Matematiki i Mekhaniki UrO RAN. — 2020. — Vol. 1. — Iss. 26. — P. 182-197. |
Аннотация: | A three-dimensional reachable set at an instant is considered for the controlled object "Dubins car" (also known as unicycle). We study the case when turns to both sides are possible. For this case, the authors earlier specified, based on the Pontryagin maximum principle, six types of piecewise constant open-loop controls; one can restrict oneself to these controls when studying the boundary of the reachable set G(tf) at a given time tf. These controls were used for the numerical construction of the reachable set and for its visualization. However, no analytic description of the boundary of the set G(tf) was obtained. In the present paper, we derive formulas for the generally nonconvex two-dimensional sections of the set G(tf) with respect to the angular coordinate. The structure of the sections is analyzed. For the dynamics in the normalized coordinates, an analytic description is obtained under the assumption that tf= 2π. For this case, a theorem is formulated on necessary and sufficient conditions for transferring a motion to the boundary of G(tf). The case tf> 2π is not covered by the analytic description because of the more complex structure of the sections, in particular, due to the loss of connectivity of G(tf) for some values of tf © 2020 Krasovskii Institute of Mathematics and Mechanics. All rights reserved. |
Ключевые слова: | ANALYTIC DESCRIPTION OF THE SECTIONS DUBINS CAR EXTREMAL PIECEWISE CONSTANT CONTROL PONTRYAGIN MAXIMUM PRINCIPLE SECTIONS OF THE REACHABLE SET ALONG THE ANGLE COORDINATE THREE-DIMENSIONAL REACHABLE SET TWO-SIDED TURNS |
URI: | http://elar.urfu.ru/handle/10995/90710 |
Условия доступа: | info:eu-repo/semantics/openAccess |
Идентификатор РИНЦ: | 42492203 |
Идентификатор SCOPUS: | 85090537477 |
Идентификатор WOS: | 000544884900014 |
Идентификатор PURE: | 12459194 |
ISSN: | 0134-4889 |
DOI: | 10.21538/0134-4889-2020-26-1-182-197 |
Располагается в коллекциях: | Научные публикации ученых УрФУ, проиндексированные в SCOPUS и WoS CC |
Файлы этого ресурса:
Файл | Описание | Размер | Формат | |
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10.21538-0134-4889-2020-26-1-182-197.pdf | 485,48 kB | Adobe PDF | Просмотреть/Открыть |
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