Xiaomi Mi Robot
Robot vacuum
Xiaomi Mi Robot
Robot vacuum
We don't have any pets, so I can't say anything about long hair. The robot drives over thicker carpets without any problems and can in principle also drive over a small threshold. However, the threshold should have a small ramp and not a hard edge, otherwise the bumper will be triggered and the robot will turn around.
The Mi Robot can hardly "eliminate" the threshold, but if "overcome" is meant, what VolkerD said applies. I have a short-haired dog and the device is extremely effective. Hair over 6 cm will wrap around the roller, but can be removed with a little effort.