[DonRotolo]

Velocity relative to what? Whatever your answer, that (thing) needs to be part of the solution.

Even the carpet can slip if you push hard enough.

If a contact solution isn't desired, then contactless means optical of some type, or maybe ultrasonic.

Astral navigation would work, but what a pain to do. It would have to adapt to the current lighting setup no matter where. I have a "Mint" floor cleaner, it uses something like that, but the pattern is fixed. (It sends an IR pattern to the ceiling, which the Mint uses for navigation). This is still optical though...