Rolling apparatus for cleaning a submerged surface, comprising: - a hollow body designed to be driven in movement over the submerged surface at least in one sense of forward travel and in one main direction of forward travel, known as the longitudinal direction, - rolling members (2, 3, 4) that have regions of contact with the submerged surface defining a rolling plane for the hollow body on the submerged surface, - a filtration chamber that is formed in the hollow body and has: · at least one inlet for liquid into the hollow body, said inlet being situated at the base of said hollow body, · at least one outlet for liquid out of the hollow body, said outlet being situated at a distance from the base of said hollow body, · at least one hydraulic circuit for liquid to flow between said at least one liquid inlet and said at least one liquid outlet through at least one filtering device, - at least one motorized pumping device (12, 13, 14) that is interposed at least partially in said hydraulic circuit and is designed to generate a liquid flow between each liquid inlet and each liquid outlet that are connected by said hydraulic circuit, - a flow guide mounted on a liquid outlet, known as the propulsion outlet, said flow guide having a movable deflecting member for orienting the current of liquid that escapes via this propulsion outlet through this flow guide such that it creates by reaction, at one outlet of the flow guide, forces, the resultant of which, known as the hydraulic reaction force, has a non-zero component driving the apparatus parallel to the rolling plane, known as the horizontal component, - a drive actuator for said movable deflecting member of said flow guide, - a control unit for said actuator, characterized in that said actuator is designed to orient and keep said movable deflecting member in at least three distinct positions that correspond to three horizontal components with distinct directions that are able to drive the apparatus in at least three distinct directions, at least one of which corresponds to the longitudinal direction, and another of which is different from both the longitudinal direction and the opposite direction to the longitudinal direction. - a hollow body designed to be driven in movement over the submerged surface at least in one sense of forward travel and in one main direction of forward travel, known as the longitudinal direction, - rolling members (2, 3, 4) that have regions of contact with the submerged surface defining a rolling plane for the hollow body on the submerged surface, - a filtration chamber that is formed in the hollow body and has: · at least one inlet for liquid into the hollow body, said inlet being situated at the base of said hollow body, · at least one outlet for liquid out of the hollow body, said outlet being situated at a distance from the base of said hollow body, · at least one hydraulic circuit for liquid to flow between said at least one liquid inlet and said at least one liquid outlet through at least one filtering device, · at least one inlet for liquid into the hollow body, said inlet being situated at the base of said hollow body, · at least one outlet for liquid out of the hollow body, said outlet being situated at a distance from the base of said hollow body, · at least one hydraulic circuit for liquid to flow between said at least one liquid inlet and said at least one liquid outlet through at least one filtering device, - at least one motorized pumping device (12, 13, 14) that is interposed at least partially in said hydraulic circuit and is designed to generate a liquid flow between each liquid inlet and each liquid outlet that are connected by said hydraulic circuit, - a flow guide mounted on a liquid outlet, known as the propulsion outlet, said flow guide having a movable deflecting member for orienting the current of liquid that escapes via this propulsion outlet through this flow guide such that it creates by reaction, at one outlet of the flow guide, forces, the resultant of which, known as the hydraulic reaction force, has a non-zero component driving the apparatus parallel to the rolling plane, known as the horizontal component, - a drive actuator for said movable deflecting member of said flow guide, - a control unit for said actuator, characterized in that said actuator is designed to orient and keep said movable deflecting member in at least three distinct positions that correspond to three horizontal components with distinct directions that are able to drive the apparatus in at least three distinct directions, at least one of which corresponds to the longitudinal direction, and another of which is different from both the longitudinal direction and the opposite direction to the longitudinal direction.