Work apparatus (100) for a limited work area (S), the apparatus comprising: - a base station (80) configured to generate a magnetic field (B) that extends at least partly through the work area； - a self-propelled robot (1) that has a normal operating mode in which it performs a work cycle in the work area and a base return mode in which it automatically returns to the base station, comprising the self-propelled robot: - means for moving (20, 20a) the self-propelled robot in the work area, depending on a motion driving signal (S_amm)； characterized in that the self-propelled robot further comprises: - a gyroscope (45) configured to generate an angular velocity signal (S_ ω) that indicates the measurement of the angular velocity of the self-propelled robot around a substantially vertical axis with respect to the plane of the area of work； - a magnetic field sensor (76) configured to generate a detection signal (S_ril) indicating a right or left position of the self-propelled robot with respect to a set of contiguous lines of force (91) of the magnetic field； - a processing unit (75) configured to control the movement of the self-propelled robot within the work area, the processing unit comprising: - a magnetic field search module (75-4) configured, during a mode search phase back to base, to generate, based on the values of the detection signal and a distance traveled signal (S_d) that indicates the estimation of the distance traveled by the self-propelled robot, the motion driving signal to move the robot self-propelled within the work area to search for the set of contiguous lines of force (91) of the magnetic field within the work area according to a defined search path (94)； - a magnetic field tracking module (75-5) configured, during a tracking phase of the back-to-base mode after the magnetic field search phase, to generate, based on the values of the detection signal, of the angular velocity signal and the distance traveled signal (S_d), the motion driving sign
