My guy, robot mowers have been around for some time now. The catch is you need to bury a guide wire around the perimeter of the area the mower is meant to cut. Or at least that was the case the last time I looked into getting one.
There are some which are guided via gps now. However, i won't trust them being so precise.
For me/us burying a guide wire was the better solution. Some manufacturers even claim, that you dont have to burry the line cos it will be overgrown by grass after a short amount of time.
GPS will only ever be accurate within 5 meters, which won’t cut it for small yards where even 1 meter over the line may send it down a hill or into the neighbors yard
Linus Tech Tips reviewed one that came with a little radio tower it used for position (guessing it used a combination of many sensors). Seemed to work OK in his flat little backyard.
My Roomba vacuums in a pattern. It finds the edges of the room, finds obstacles, and then goes ||||| across the middle of the room, doing little circles around table legs.