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Time Minimization During Simultaneous Longitudinal and Rotational Motion of a Chaplygin Sleighстатья
- Авторы: Obradovich A., Selyutskiy Yu D., Cherkasov O.Yu
- Журнал: Journal of Computer and Systems Sciences International
- Том: 64
- Номер: 5
- Год издания: 2025
- Издательство: Maik Nauka/Interperiodica Publishing
- Местоположение издательства: Russian Federation
- Первая страница: 735
- Последняя страница: 747
- Аннотация: The problem of minization of the time of motion of a Chaplygin sleigh in the horizontalplane is analyzed. The force directed along the linear velocity vector and the torque are considered ascontrol inputs. The use of the Pontryagin maximum principle allows for establishing that three typesof control are possible: regular control, taking the boundary values (bang-bang) for the force and thetorque, first-order singular control for the force, and second-order singular control for the torque. Ifthe control is singular for the force on the entire interval, the solution of the optimization problem isnot unique. The second-order control segment can be connected with nonsingular control only bymeans of the “chattering” regime. A simpler suboptimal control is proposed that contains a finitenumber of switchings. Examples are considered for the specified end states and partially specified endstates. Analysis of possible combinations of singular and regular arcs of the trajectory is performed.
- Добавил в систему: Черкасов Олег Юрьевич