This article concerns the use of an integrated RFID system with a mobile robot for the navigation and mapping of closed spaces. The architecture of a prototype mobile robot equipped with a set of RFID readers that performs the mapping functions is described. Laboratory tests of the robot have been carried out using a test stand equipped with a grid of appropriately programmed RFID transponders. A simulation model of the effectiveness of transponder reading by the robot has been prepared. The conclusions from measurements and tests are discussed, and methods for improving the solution are proposed.