I don't have a real robotics background, but I do work in automation, so I have a pretty decent grasp on machines that do things. I'd put this at a 9 on the impossibility scale. I base this mostly on the fact that robotics and automated machinery is usually very specific to a certain task. However, if you change your thinking from "a robot that cleans for me" to "machines that clean different surfaces" then the problem becomes much easier, probably around a 5 on your scale. Think a Roomba for the floor, an automatic shower cleaner for the shower, etc. It's a lot easier to make machines that do one very specific, repeatable task rather than a general purpose robot (which is probably why they aren't very common). Microcontrollers are dirt cheap and easily programmable, so I see your best route to getting a cleaner bathroom to break up the specific tasks to dedicated machines. That also has the benefit of breaking the development into smaller and more easily managed chunks.