## 1 Introduction  
The expanding possibilities of wheeled mobile robots (WMR), such as maneuverability, communication, battery life, and the possibility of using sensors that enable data collection from the environment, has led to a growing interest in their industrial, medical, and scientific applications. The challenge is in designing robots for a dynamic work environment and meeting the required safety, accuracy, reliability, and maneuverability. Solutions such as mecanum wheels [1], which enable freedom of movement and advanced intelligent control systems such as artificial neural networks (NNs) [2; 3; 4; 5; 6] that provide real-time approximation of nonlinearities in a mathematical model of a robot using network weight adaptation, may prove helpful in this process. The use of omnidirectional wheels, such as mecanum wheels, in the construction of a robot allows direct control of all degrees of freedom, which leads to its classification as a holonomic object. A description of a kinematics model of a holonomic robot with mecanum wheels can be found, inter alia, in [7; 8; 9; 10; 11; 12; 13; 14] These previous studies have resolved the inverse kinematics problem, determining the angular velocities of the wheels based on the set velocity of the characteristic point of the robot's platform in relation to a stationary reference system [7; 8], and in relation to a moving coordinate system [9; 10]. The next stage of the mathematical analysis of an object has involved describing its dynamics [15; 16; 17; 18; 19; 20]. This task was performed in [15; 16; 17], using Lagrange equations of the second kind [15] and Lagrange equations of the second kind with multipliers [16; 17]; as a result, the simple and inverse dynamics problems of the WMR were solved. In [21], a description of a WMR dynamics model using Lagrange equations of the second kind was identified with the use of a real object. It was confirmed that the WMR could map a desired motion path based on the values of the wave forms of the driving moment determined by solving the inverse dynamics problem. The effect of losing control over the robot was also considered under conditions of a low friction coefficient, which led to skidding, which has been a typical problem for the control of vehicles equipped with mecanum wheels. The control of mechatronic objects had been widely studied [22; 23; 24; 25; 26]. Traditional mechatronic systems have commonly used intelligent control methods [27; 28; 29; 30; 31; 32; 33; 34; 35; 36; 37], while for holonomic mobile robots, traditional control algorithms have often been used [38; 39; 40; 41; 42; 43]. A small number of studies have combined both topics by presenting intelligent control algorithms for holonomic (mecanum) mobile robots [44; 45; 46; 47; 48; 49; 50]. The use of intelligent control enables the synthesis of a control law with the adaptation of the control system parameters. The implementation of such functionality has been possible due to the use of an NN, which is a universal approximator of function [51; 52]. The studies in [53; 54] presented the concept of WMR control based on a neuro-fuzzy control system with wavelet networks. A numerical simulation was conducted to confirm that a WMR could implement the desired motion path. However, these works did not provide information on the quality of control expressed by the tracking errors or the adopted quality indicators. In addition, the control method was not compared with other known robot control algorithms. For this reason, it was not clear to what extent the proposed method differed from known control algorithms. The study in [55] presented an adaptive sliding control system containing a radial basis function (RBF) network. The nonlinear function, which is part of the robot dynamics description, was approximated using a three-layer radial NN. Based on the analysis of the Lyapunov stability, the law of network weight adaptation was determined. Numerical simulations and tests were conducted on a real object.