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

In 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.