The work presents the dynamic equations of motion of a wheeled mobile robot with mecanum wheels derived with the use of Lagrange equations of the second kind. Mecanum wheels are a new type of wheels used in wheeled mobile robots and they consist of freely rotating rollers attached to the circumference of the wheels. In order to derive dynamic equations of motion of a wheeled mobile robot, the kinetic energy of the system is determined, as well as the generalised forces affecting the system. The resulting mathematical model of a wheeled mobile robot was generated with the use of Maple V software. The results of a solution of inverse and forward problems of dynamics of the discussed object are also published.

In this paper, we propose a new application of the adaptive critic methodology for the feedback control of wheeled mobile robots, based on a critic signal provided by a neural network (NN). The adaptive critic architecture uses a high-level supervisory NN adaptive critic element (ACE), to generate the reinforcement signal to optimise the associative search element (ASE), which is applied to approximate the non-linear functions of the mobile robot. The proposed tracking controller is derived from Lyapunov stability theory and can guarantee tracking performance and stability. A series of computer simulations have been used to emulate the performance of the proposed solution for a wheeled mobile robot.

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