The invention relates to an automated home apparatus (10) that is provided with at least one rotary actuator (28) comprising a first portion (30) which is secured to a winding tube (22) of a canvas (18) of a movable screen (12A, 12B), and a second portion (32) secured to a balancing member (34), the first portion turning in relation to the second portion about a reference geometric axis (26) of the winding tube (22) for winding and unwinding the canvas (18), the winding tube (22) being suspended from the canvas (18) such that the reference geometric axis (26) moves vertically and perpendicularly relative to itself between a high position and a low position during the winding and unwinding of the canvas (18). The actuator (28) is controlled by a control unit (44) which is stationary in relation to the rotating actuator (28) and/or in relation to the balancing member (34) and connected to one or more inertial sensors (42, 60) that are stationary in relation to the balancing member (34), which can include an inclination sensor (42) or an accelerometer in particular. The signals of the inertial sensors can be used in particular for detecting an end-of-stroke position or the immediate position of the tube, in order to detect any malfunction of the apparatus, to initiate the start of a learning mode or to facilitate the setting of other actuators connected to other screens of the apparatus (10).
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