The control device includes a switch (12) controlling the power supply to the motor and an actuator which actuates this switch by rotatably reacting against the moving object being restrained so as to cause said switch to be opened and to cut off the power supply to the motor. This actuator consists of a bistable mechanical device (11) capable of taking up a first state in which the switch (12) is closed and a second state in which the switch is open. The actuating device also includes a cable (17) for putting the actuating device into its first state, this device being brought into its second state by reacting against the moving object.