Fukitorimushi (literally, "wipe-up bug") accomplishes this household miracle while crawling along on your floor like an inchworm. "Feelers" of blue-white light search your floor for unwanted detritus. Upon discovering that ancient scourge - grime - Fukitorimushi emits a red light and puts its nanofiber belly to the floor and starts picking up dirt.
Watch the Fukitorimushi video.
(Fukitorimushi robot video)
Fukitorimushi’s body is covered in Teijin’s Nanofront cloth, which is made of polyester filament fibers measuring 700 nanometers in diameter (about 7,500 times thinner than the average human hair). The nanofibers significantly increase the fabric’s surface area and porosity, giving it superior wiping characteristics and the ability to absorb oil and ultra-fine dust particles less than one micron in diameter. The large surface contact area also increases the fabric’s friction with the floor and makes it resistant to sliding. The robot relies on this increased friction to push itself forward while wiping the floor.
As far as science fiction is concerned, I don't think that Fukitorimushi is what Robert Heinlein had in mind when he wrote about the hired girl robot in his 1956 novel The Door Into Summer. It's probably closer to the idea of the tiny robot mice cleaners that Ray Bradbury wrote about in his 1950 short story There Will Come Soft Rains.
Lest you think that we are the only generation of humans who have wanted floor-dwelling, autonomous cleaning robots, behold this 1959 "mechanical maid" prototype from Mechanix Illustrated.