The bottom layer of this floor would consist of a floor-wide space for water about half an inch thick. One side of the room would have a water/soapy water dispenser and the other would have a dirty water collector and drain.
Above this there would be a fluffy carpet formed around rollers. These would be as wide as the room. They would be small, strong, and closely packed enough to support people walking on them.
At the push of a button a wash cycle would start. First clean water would be dispensed along the bottom. Then the rollers would all turn, and the friction between them would create a scrubbing action. The bottom of the rollers would pick up water and drop dirt into the water. Then soap would be added to the water. A rinse cycle would remove most of the soap. If desired the luxury version also blows hot dry air under the carpet for a fast dry.-- Voice, Dec 07 2019random, halfbakery