The mathematical model and control method of a mobile robot moving due to the rotation of an internal mass (one or more bodies inside the robot body) around a vertical axis, and alternately coming into contact with a flat support surface of struts located on the robot body are considered. During the movement process, holonomic liaisons are periodically applied or removed on the support struts, allowing the body to perform in-plane motion. The mathematical model accounts for discrete interaction of the support with the surface and control of the rotation of the internal mass relative to the body. The motion of the mobile robot is considered, which is realized due to the coordinated alternating contact of the supports with the surface while the rotation speed of the internal mass is constant. The main condition of the programme motion is the absence of impact at the moment of changing the struts.