This paper presents a novel approach to the problem of controlling mechanical objects of unspecified description, considering variable operating conditions. The controlled object is a mobile robot with mecanum wheels (MRK M). To solve the control task, taking into account compensation for nonlinearity and the object variable operating conditions, the Lyapunov stability theory is applied, including the Hamilton-Jacobi (HJ) inequality. A neural network with basic sigmoid functions is used to compensate for the nonlinearity and variable operating conditions of the robot. A simulation example is provided in order to evaluate the analytical considerations. The simulation results obtained confirmed high accuracy of the predicted robot motion in variable operating conditions.