The object of research is a spherical robot with an internal platform with four classic-type omni-wheels. The motion of the spherical robot on the horizontal surface is considered and its kinematics is described. The aim of the research is to study the dynamics of the spherical robot with different levels of detailing of the contact friction model. Nonholonomic models of the dynamics of the robot with different levels of detailing of the contact friction model are constructed. The programmed control of the movement of the spherical robot using elementary maneuvers is proposed. The simulation of motion was carried out and the efficiency of the proposed control was confirmed. It is shown that at low speeds of movement of ther spherical robot, it is allowed to use a model obtained under the assumption of no slipping between the sphere and the floor. The influence of the contact friction model at high-speed movements of the spherical robot on its dynamics under programmed control is demonstrated. This influence leads to the need to develop more accurate models of the motion of a spherical robot and its contact interaction with the supporting surface in order to increase the accuracy of motion control based on these models.