A robot with only a charging dock is the cheapest and smallest way to have your floor vacuumed daily. You empty the bin yourself, every few days in an average home, and if the robot mops you clean the cloth yourself. The dock is no bigger than a book and fits anywhere.
With these robots, look mainly at navigation (laser is more accurate than a camera), suction on carpet and the size of the bin. Many models also exist in a version with a self-emptying station, usually with a plus in the name, for a little more. The order below comes from the tests of 5 independent sources. The price is today's lowest including shipping.
Models without a station
Score: consensus of the positions in 5 test sources, 100 = top of every source. Every model on this list is recommended by at least one test source. The bottom of a top list is still worth half the points, and a model named by only one source cannot score above 50. Only models sold in the United States count. Method.