Аннотация:
The paper discusses the dynamics of systems with Béghin's servoconstraints where the constraints are realized by means of controlled forces. Classical nonholonomic systems are an important particular case. Special attention is given to the study of motion on Lie groups with left-invariant kinetic energy and left-invariant constraints. The presence of symmetries allows one to reduce the dynamic equations to a closed system of differential equations with quadratic right-hand sides on a Lie algebra. Examples are given which include the rotation of a rigid body with a left-invariant servoconstraint — the projection of the angular velocity onto some direction fixed in the body is equal to zero (a generalization of the nonholonomic Suslov problem) — and the motion of the Chaplygin sleigh with servoconstraints of a certain type. The dynamics of systems with Béghin's servoconstraints is richer and more varied than the more usual dynamics of nonholonomic systems.
Ключевые слова:
servoconstraints, symmetries, Lie groups, left-invariant constraints, systems with quadratic right-hand sides.
E. A. Mikishanina, P. S. Platonov, “Control of a Wheeled Robot on a Plane with Obstacles”, Mehatronika, avtomatizaciâ, upravlenie, 25:2 (2024), 93
Sergej Čelikovský, Milan Anderle, “Feedback equivalence of the chained mechanical system to the almost linear form and its use for the sustainable multi-step walking design”, Journal of the Franklin Institute, 2024, 107086
E. A. Mikishanina, “Two Ways to Control a Pendulum-Type Spherical Robot on a Moving Platform in a Pursuit Problem”, Mech. Solids, 59:1 (2024), 127
E. A. Mikishanina, “Control of a Spherical Robot with a Nonholonomic Omniwheel Hinge Inside”, Rus. J. Nonlin. Dyn., 20:1 (2024), 179–193
E. A. Mikishanina, “Two Ways to Control a Pendulum-Type Spherical Robot on a Moving Platform in a Pursuit Problem”, Izvestiâ Rossijskoj akademii nauk. Mehanika tverdogo tela, 2024, № 1, 230
Е. А. Микишанина, “Омниколесная реализация задачи Суслова с реономной связью: динамическая модель и управление”, Вестник российских университетов. Математика, 29:147 (2024), 296–308
Е. А. Микишанина, “Принципы реализации сервосвязей в неголономных механических системах”, Вестн. Томск. гос. ун-та. Матем. и мех., 2024, № 89, 103–118
G. K. Tolokonnikov, Lecture Notes on Data Engineering and Communications Technologies, 158, Advances in Intelligent Systems, Computer Science and Digital Economics IV, 2023, 126
Chuan Min, Yongjun Pan, Wei Dai, Ibna Kawsar, Zhixiong Li, Gengxiang Wang, “Trajectory optimization of an electric vehicle with minimum energy consumption using inverse dynamics model and servo constraints”, Mechanism and Machine Theory, 181 (2023), 105185
Jiaming Xiong, Ruihan Yu, Caishan Liu, “Steering control and stability analysis for an autonomous bicycle: part I—theoretical framework and simulations”, Nonlinear Dyn, 111:18 (2023), 16705
E. A. Mikishanina, “Motion Control of a Spherical Robot with a Pendulum
Actuator for Pursuing a Target”, Rus. J. Nonlin. Dyn., 18:5 (2022), 899–913
Е. А. Микишанина, “Динамика качения сферического робота с маятниковым приводом, управляемого сервосвязью Билимовича”, ТМФ, 211:2 (2022), 281–294; E. A. Mikishanina, “Rolling motion dynamics of a spherical robot with a pendulum actuator controlled by the Bilimovich servo-constraint”, Theoret. and Math. Phys., 211:2 (2022), 679–691
I. A. Bizyaev, V A. Borisov, V. V. Kozlov, I. S. Mamaev, “Fermi-like acceleration and power-law energy growth in nonholonomic systems”, Nonlinearity, 32:9 (2019), 3209–3233
Р. Г. Мухарлямов, “Управление динамикой системы с дифференциальными связями”, Изв. РАН. Теория и системы управления, 2019, № 4, 16–28; R. G. Mukharlyamov, “Control of the dynamics of a system with differential constraints”, J. Comput. Syst. Sci. Int., 58:4 (2019), 515–527
Sergej Celikovsky, Milan Anderle, 2019 IEEE 15th International Conference on Control and Automation (ICCA), 2019, 1289
B. I. Adamov, “A Study of the Controlled Motion of a Four-wheeled Mecanum Platform”, Nelin. Dinam., 14:2 (2018), 265–290
R. G. Mukharlyamov, “Modelling of dynamics of mechanical systems with regard for constraint stabilization”, Fundamental and Applied Problems of Mechanics-2017, IOP Conference Series-Materials Science and Engineering, 468, IOP Publishing Ltd, 2018, 012041
Sergej Čelikovský, Milan Anderle, “Stable walking gaits for a three-link planar biped robot with two actuators based on the collocated virtual holonomic constraints and the cyclic unactuated variable”, IFAC-PapersOnLine, 51:22 (2018), 378
Sergej Čelikovský, Milan Anderle, Lecture Notes in Electrical Engineering, 465, AETA 2017 - Recent Advances in Electrical Engineering and Related Sciences: Theory and Application, 2018, 554
А. В. Борисов, И. С. Мамаев, И. А. Бизяев, “Динамические системы с неинтегрируемыми связями: вакономная механика, субриманова геометрия и неголономная механика”, УМН, 72:5(437) (2017), 3–62; A. V. Borisov, I. S. Mamaev, I. A. Bizyaev, “Dynamical systems with non-integrable constraints, vakonomic mechanics, sub-Riemannian geometry, and non-holonomic mechanics”, Russian Math. Surveys, 72:5 (2017), 783–840
Цитирование в формате AMSBIB
Обратная связь: