Синтез робастных алгоритмов стабилизации программных движений мобильного робота с омни-колесами методом вектор-функций Ляпунова

Abstract

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.