Vacuum Floor

Take a double floor. The top floor would be densely covered in evenly spaced tiny holes. The bottom floor would have equally placed pegs to plug the holes in the upper floor, and would rest on hydraulic or electric actuators. Once a day, actuators would lower the bottom floor, unplug the holes, and the entire floor would simply... inhale. Collecting all the dust that had gathered on it. The dust would be routed to a standard vacuum cleaner filter bag, that could be replaced when needed. Alternatively, a vacuum nozzle would sweep under the floor and vacuum dust through the holes in swathes instead of all at once. This would require a mechanical array to maneuver the nozzle, but would require a much less powerful motor than the entire floor inhaling at once.

The more holes the better, of course. They should be close to each other, the majority of the floor surface should be a hole; the mesh holding up the furniture and room occupants should be as thin as is structurally possible without collapsing. The holes should be small in diameter, to avoid the floor eating any small items accidentally dropped.

This system would vacuum around obstacles and under furniture (simply by vacuuming from underneath the floor), but would be entirely ineffectual with rugs. Rugs would still be up to you. Or a Roomba.