Synthesis of Robust Algorithms of Program Motion Stabilization for an Omni-Wheel Mobile Robot by the Method of Lyapunov Vector Functions

In recent years the problem of a mobile wheeled robot control has received great attention and lots of solutions have been found. The dynamical model of a mobile wheeled robot includes the mass-inertial parameters, which are customary, as a rule, unknown and time varying. It is difficult to select an exact dynamical model of a wheeled mobile robot for the design of a model-based control. In order to handle such unknown parameters many control strategies were proposed, including sliding-model control and adaptive control. The problem of dynamics of the controlled motion of the mobile robots with omni-directional wheels is of interest to many researches. Such mobile robots are characterized by a full omni-directionality with simultaneous and independently rotational and translation motion capabilities. Therefore, such types of the wheeled robots can implement complicated tasks in a narrow space. An independent control of the rotation of each omni-wheel leads to the inevitable slipping in motion along the motion surface. Therefore, considering slipping between the wheels and the motion surface, a dynamic model of an omnidirectional wheeled mobile robot is of great interest to many researches. The sliding friction occurs both in the direction along the surface of the wheel and transversely to it. It is important to design a motion control, which has no hard performance and allows us to take into account the sliding friction and the inaccuracy of the dynamical model. The aim of this paper is to solve the problem of a non-stationary trajectory tracking control of a mobile robot with four omni-wheels and inaccurately known inertia matrix, taking into account the wheel slip. On the basis of Lyapunov vector functions the discontinuous and continuous control laws were obtained. The results of the numerical simulation are presented.

колесный мобильный робот, управление, проскальзывание, стабилизация, программное движение, омни-колесо, вектор-функция Ляпунова, динамическая модель, система сравнения, wheeled mobile robot, control, slip, stabilization, program motion, omni-wheel, Lyapunov vector function, dynamical model, comparison system

1. Мартыненко Ю. Г., Формальский А. М. О движении мобильного робота с роликонесущими колесами // Известия РАН. Теория и системы управления. 2007. № 6. С. 142-149.

2. Мартыненко Ю. Г. Устойчивость стационарных движений мобильного робота с роликонесущими колесами и смещенным центром масс // ПММ. 2010. Т. 74, Вып. 4. С. 610-619.

3. Зобова А. А., Татаринов Я. В. Динамика экипажа с роликонесущими колесами // ПММ. 2009. Т. 73, Вып. 1. С. 13-22.

4. Борисов А. В., Килин А. А., Мамаев И. С. Тележка с омни-колесами на плоскости и сфере // Нелинейная динамика. 2011. Т. 7, № 4. С. 785-801.

5. Караваев Ю. Л., Трефилов С. А. Дискретный алгоритм управления по отклонению мобильным роботом с омни-колесами // Нелинейная динамика. 2013. Т. 9, № 1. С. 91-100.

6. Килин А. А., Караваев Ю. Л., Клековкин А. В. Кинематическая модель управления высокоманевренным мобильным сферороботом с внутренней омни-колесной платформой // Нелинейная динамика. 2014. Т. 10, № 1. С. 113-126.

7. André S. Conceição, A. Paulo Moreira, Paulo J. Costa. A Practical approach of Modeling and Parameters Estimation for OmniDirectional Mobile Robots // IEEE-ASME TRANSACTIONS ON MECHATRONICS. 2009. Vol. 14, N. 3. P. 377-381.

8. Lins Barreto S. J. C., Scolari Conceicao A. G., Dorea С. Е. Т., Martinez L., De Pieri E. R. Design and Implementation of Model-Predictive Control With Friction Compensation on an Omnidirectional Mobile Robot // IEEE-ASME TRANSACTIONS ON MECHATRONICS. 2014. N. 2. P. 467-476.

9. Yanwen Huang, Qixin Cao and Chuntao Leng. The Path-Tracking Controller Based on Dynamic Model with Slip for One Four-Wheeled OMR // Industrial Robot: An International Journal. 2010. Vol. 37, N. 2. P. 193-201.

10. Huang H. C., Tsai C. C. Adaptive Trajectory Tracking and Stabilization for Omnidirectional Mobile Robot with Dynamic Effect and Uncertainties // Proc. of the 17th World Congress The International Federation of Automatic Control Seoul, Korea, July 6-11, 2008. 2008. P. 5383-5388.

11. Метод векторных функций Ляпунова в теории устойчивости / Под ред. А. А. Воронова и В. М. Матросова. М.: Наука, 1987. 312 с.

12. Халил Х. К. Нелинейные системы. М.-Ижевск: НИЦ "Регулярная и хаотическая динамика", Институт компьютерных исследований, 2009. 832 с.