The invention relates to an apparatus for cleaning a surface which is immersed in a liquid, comprising a hollow body, members which are integral with the hollow body and which come into contact with the immersed surface, a filtration chamber, at least one electric motor which is carried by the hollow body, and a control unit which is configured to control the motor. For at least one movement configuration of the apparatus, at least one non-steering non-driving rolling member in contact with the immersed surface is arranged relative to the instantaneous drive orientation so as to apply a gyration torque of the apparatus only due to such an arrangement.