System consisting of a mowing robot and a base station, the mowing robot comprising: 1.1. at least one cutting mechanism, 1.2. a controllable running gear having a control apparatus, 1.3. at least one motor for driving the cutting mechanism and running gear, 1.4. a receiving and transmitting device for radio signals, to produce a radio connection between the mowing robot and a stationary base station associated with the mowing robot, 1.5. a means for determining the orientation of the mowing robot for the purposes of two- or three-dimensional alignment, 1.6. the receiving and transmitting device of the mowing robot has an antenna for radio communication (A, E), 1.7. wherein the base station has an antenna for radio communication (A, E), 1.8. the mowing robot and the base station are connected to at least one processor system having program and data memory, including program code for processing mowing-robot-related data and signals, 1.9. at least one of the two antennas for radio communication of the base station and the mowing robot is in the form of an antenna array for detecting phase differences in incoming radio signals of a determined frequency, 1.10. wherein the program code of a processor system is in a form such that: - use of at least one antenna array, - applying two determinations of direction - and applying one determination of distance, - identifies the position and orientation of the mowing robot relative to a base station, - at least one of the two determinations of direction results in the phase relationships of the exchanged radio signals between an antenna for radio communication (E, A) and an antenna array for detecting phase differences in incoming radio signals of a determined frequency being evaluated, - and the determination of distance results in the intensity of the received radio signals being evaluated, - in order to use the known position and orientation of the mowing robot to guide the mowing robot. 1.1. at least one cutting mechanism, 1.2. a controllable running gear having a control apparatus, 1.3. at least one motor for driving the cutting mechanism and running gear, 1.4. a receiving and transmitting device for radio signals, to produce a radio connection between the mowing robot and a stationary base station associated with the mowing robot, 1.5. a means for determining the orientation of the mowing robot for the purposes of two- or three-dimensional alignment, 1.6. the receiving and transmitting device of the mowing robot has an antenna for radio communication (A, E), 1.7. wherein the base station has an antenna for radio communication (A, E), 1.8. the mowing robot and the base station are connected to at least one processor system having program and data memory, including program code for processing mowing-robot-related data and signals, 1.9. at least one of the two antennas for radio communication of the base station and the mowing robot is in the form of an antenna array for detecting phase differences in incoming radio signals of a determined frequency, 1.10. wherein the program code of a processor system is in a form such that: - use of at least one antenna array, - applying two determinations of direction - and applying one determination of distance, - identifies the position and orientation of the mowing robot relative to a base station, - at least one of the two determinations of direction results in the phase relationships of the exchanged radio signals between an antenna for radio communication (E, A) and an antenna array for detecting phase differences in incoming radio signals of a determined frequency being evaluated, - and the determination of distance results in the intensity of the received radio signals being evaluated, - in order to use the known position and orientation of the mowing robot to guide the mowing robot. - use of at least one antenna array, - applying two determinations of direction - and applying one determination of distance, - identifies the position and orientation of the mowing robot relative to a base station, - at least one of the two determinations of direction results in the phase relationships of the exchanged radio signals between an antenna for radio communication (E, A) and an antenna array for detecting phase differences in incoming radio signals of a determined frequency being evaluated, - and the determination of distance results in the intensity of the received radio signals being evaluated, - in order to use the known position and orientation of the mowing robot to guide the mowing robot.