In this paper a review of a mobile transport robot with mecanum wheels has been made. The robot control hardware is described. The research and development of methods for remote control and autonomous control are presented. Software algorithms have been developed for implementation of the described methods. Experiments have been conducted related to remote control and autonomous mode of a transport mobile robot in real time, using an educational mobile robot with mecanum wheels. The results of the conducted experiments are presented. The results show that the proposed methods and algorithms are able to provide tele-operation of the robot and autonomous movement.