PROPERTIES OF SOLUTIONS IN THE DUBINS CAR CONTROL PROBLEM
TThis paper addresses the time-optimal control problem of the Dubins car, which is closely related to the problem of constructing the shortest curve with bounded curvature between two points in a plane. This connection allows researchers to apply both geometric methods and control theory techniques...
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| Format: | Article |
| Language: | English |
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Ural Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin, Krasovskii Institute of Mathematics and Mechanics
2024-12-01
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| Series: | Ural Mathematical Journal |
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| Online Access: | https://umjuran.ru/index.php/umj/article/view/844 |
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| author | Artem A. Zimovets |
| author_facet | Artem A. Zimovets |
| author_sort | Artem A. Zimovets |
| collection | DOAJ |
| description | TThis paper addresses the time-optimal control problem of the Dubins car, which is closely related to the problem of constructing the shortest curve with bounded curvature between two points in a plane. This connection allows researchers to apply both geometric methods and control theory techniques during their investigations. It is established that the time-optimal control for the Dubins car is a piecewise constant function with no more than two switchings. This characteristic enables the categorization of all such controls into several types, facilitating the examination of the solutions to the control problem for each type individually. The paper derives explicit formulas for determining the switching times of the control signal. In each case, necessary and sufficient conditions for the existence of solutions are obtained. For certain control types, the uniqueness of optimal solutions is established. Additionally, the dependence of the movement time on the initial and terminal conditions is studied. |
| format | Article |
| id | doaj-art-e4d70f1984e0438794c12d5c8ba2210c |
| institution | DOAJ |
| issn | 2414-3952 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | Ural Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin, Krasovskii Institute of Mathematics and Mechanics |
| record_format | Article |
| series | Ural Mathematical Journal |
| spelling | doaj-art-e4d70f1984e0438794c12d5c8ba2210c2025-08-20T03:19:07ZengUral Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin, Krasovskii Institute of Mathematics and MechanicsUral Mathematical Journal2414-39522024-12-0110210.15826/umj.2024.2.014218PROPERTIES OF SOLUTIONS IN THE DUBINS CAR CONTROL PROBLEMArtem A. Zimovets0Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, 16 S. Kovalevskaya Str., Ekaterinburg, 620108TThis paper addresses the time-optimal control problem of the Dubins car, which is closely related to the problem of constructing the shortest curve with bounded curvature between two points in a plane. This connection allows researchers to apply both geometric methods and control theory techniques during their investigations. It is established that the time-optimal control for the Dubins car is a piecewise constant function with no more than two switchings. This characteristic enables the categorization of all such controls into several types, facilitating the examination of the solutions to the control problem for each type individually. The paper derives explicit formulas for determining the switching times of the control signal. In each case, necessary and sufficient conditions for the existence of solutions are obtained. For certain control types, the uniqueness of optimal solutions is established. Additionally, the dependence of the movement time on the initial and terminal conditions is studied.https://umjuran.ru/index.php/umj/article/view/844dubins car, dubins problem, time-optimal control, curve with bounded curvature |
| spellingShingle | Artem A. Zimovets PROPERTIES OF SOLUTIONS IN THE DUBINS CAR CONTROL PROBLEM Ural Mathematical Journal dubins car, dubins problem, time-optimal control, curve with bounded curvature |
| title | PROPERTIES OF SOLUTIONS IN THE DUBINS CAR CONTROL PROBLEM |
| title_full | PROPERTIES OF SOLUTIONS IN THE DUBINS CAR CONTROL PROBLEM |
| title_fullStr | PROPERTIES OF SOLUTIONS IN THE DUBINS CAR CONTROL PROBLEM |
| title_full_unstemmed | PROPERTIES OF SOLUTIONS IN THE DUBINS CAR CONTROL PROBLEM |
| title_short | PROPERTIES OF SOLUTIONS IN THE DUBINS CAR CONTROL PROBLEM |
| title_sort | properties of solutions in the dubins car control problem |
| topic | dubins car, dubins problem, time-optimal control, curve with bounded curvature |
| url | https://umjuran.ru/index.php/umj/article/view/844 |
| work_keys_str_mv | AT artemazimovets propertiesofsolutionsinthedubinscarcontrolproblem |