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Нелинейная динам., 2020, том 16, номер 1, страницы 115–131 (Mi nd701)  

Nonlinear physics and mechanics

On Global Trajectory Tracking Control for an Omnidirectional Mobile Robot with a Displaced Center of Mass

A. S. Andreev, O. A. Peregudova

Ulyanovsk State University, ul. Lva Tolstogo 42, Ulyanovsk, 432000 Russia

Аннотация: This paper addresses the trajectory tracking control design of an omnidirectional mobile robot with a center of mass displaced from the geometrical center of the robot platform. Due to the high maneuverability provided by omniwheels, such robots are widely used in industry to transport loads in narrow spaces. As a rule, the center of mass of the load does not coincide with the geometric center of the robot platform. This makes the trajectory tracking control problem of a robot with a displaced center of mass relevant. In this paper, two controllers are constructed that solve the problem of global trajectory tracking control of the robot. The controllers are designed based on the Lyapunov function method. The main difficulty in applying the Lyapunov function method for the trajectory tracking control problem of the robot is that the time derivative of the Lyapunov function is not definite negative, but only semidefinite negative. Moreover, the LaSalle invariance principle is not applicable in this case since the closed-loop system is a nonautonomous system of differential equations. In this paper, it is shown that the quasi-invariance principle for nonautonomous systems of differential equations is much convenient for the asymptotic stability analysis of the closed-loop system. Firstly, we construct an unbounded state feedback controller such as proportional-derivative term plus feedforward. As a result, the global uniform asymptotic stability property of the origin of the closed-loop system has been proved. Secondly, we find that, if the damping forces of the robot are large enough, then the saturated position output feedback controller solves the global trajectory tracking control problem without velocity measurements. The effectiveness of the proposed controllers has been verified through simulation tests. Namely, a comparative analysis of the bounded controller obtained and the well-known “PD+” like control scheme is carried out. It is shown that the approach proposed in this paper saves energy for control inputs. Besides, a comparative analysis of the bounded controller and its analogue constructed earlier in a cylindrical phase space is carried out. It is shown that the controller provides lower values for the root mean square error of the position and velocity of the closed-loop system.

Ключевые слова: omnidirectional mobile robot, displaced mass center, global trajectory tracking control, output position feedback, Lyapunov function method

Финансовая поддержка Номер гранта
Российский фонд фундаментальных исследований 18-01-00702
The work was supported by the Russian Foundation for Basic Research under Grant [18-01-00702].


DOI: https://doi.org/10.20537/nd200110

Полный текст: PDF файл (947 kB)
Список литературы: PDF файл   HTML файл

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Тип публикации: Статья
MSC: 93C10, 93D15, 93D30
Поступила в редакцию: 17.09.2019
Принята в печать:11.02.2020

Образец цитирования: A. S. Andreev, O. A. Peregudova, “On Global Trajectory Tracking Control for an Omnidirectional Mobile Robot with a Displaced Center of Mass”, Нелинейная динам., 16:1 (2020), 115–131

Цитирование в формате AMSBIB
\RBibitem{AndPer20}
\by A. S. Andreev, O. A. Peregudova
\paper On Global Trajectory Tracking Control for an Omnidirectional Mobile Robot with a Displaced Center of Mass
\jour Нелинейная динам.
\yr 2020
\vol 16
\issue 1
\pages 115--131
\mathnet{http://mi.mathnet.ru/nd701}
\crossref{https://doi.org/10.20537/nd200110}
\elib{https://elibrary.ru/item.asp?id=43279236}


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  • http://mi.mathnet.ru/rus/nd/v16/i1/p115

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