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ISSN 2079-6900 (Print)

ISSN 2587-7496 (Online)

Middle Volga Mathematical Society Journal

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MSC2010 45K05

Robust trajectory tracking control of omni-mobile robot with slipping of the wheels

A. S. Andreev1, O. A. Peregudova2

AnnotationIn this paper we consider the problem of constructing a robust controller to track the trajectory of a mobile robot with three omni-wheels moving on a horizontal surface. A dynamic model of the robot has been constructed such that the center of mass of the circular platform is offset from its geometric center and the wheel slippage occurs during braking. The motion control of the wheeled robot is carried out by using three independent DC motors. The torques developed by the engines are linear with respect to voltage supplied to the engine and to angular velocity of the rotor. Basing on the Lyapunov function method we construct a bounded controller without velocity measurement that solves the robust trajectory tracking problem. This means that for all initial deviations the robot's trajectory falls into a given neighborhood of the tracked trajectory after some time and remains there forever. Theorem on an ultimate boundedness of a closed system is proved. The results of numerical simulation are presented confirming the effectiveness of the proposed controller.
Keywordswheeled mobile robot, omni-wheel, slipping, trajectory tracking control, Lyapunov function, dynamical model

1Aleksandr S. Andreev, Head of Department of Information Security and Control Theory, Ulyanovsk State University (42 Lev Tolstoy St., Ulyanovsk 432017, Russia), D.Sc. (Physics and Mathematics), ORCID: https://orcid.org/0000-0002-9408-0392, asa5208@mail.ru

2Olga A. Peregudova, Professor, Department of Information Security and Control Theory, Ulyanovsk State University (42 Lev Tolstoy St., Ulyanovsk 432017, Russia), D.Sc. (Physics and Mathematics), ORCID: https://orcid.org/0000-0003-2701-9054, peregudovaoa@gmail.com

Citation: A. S. Andreev, O. A. Peregudova, "[Robust trajectory tracking control of omni-mobile robot with slipping of the wheels]", Zhurnal Srednevolzhskogo matematicheskogo obshchestva,21:1 (2019) 13–23 (In Russian)

DOI 10.15507/2079-6900.21.201901.13-23