Hello and great question.
I haven’t done a lot of research on vacuums yet. Generally, from the studies I’ve read, the most important factor is to ensure the vacuum has a beater-bar. The beater-bar picks up eggs, larvae, and pupae, and also vigorously agitates the carpeting. This agitation causes heat and pressure, which the fleas perceive as a host. These host cues trigger pre-emerged adults to emerge. The agitation may also cause larvae to pupate without cocoons (naked). Naked pupae are easier to remove from carpeting, plus they can’t enter into a dormant-like state.
The process of being vacuumed up will kill all flea stages, regardless of the specific vacuum. However, some vacuums are obviously more effective at removing debris than others. The vacuums I put on the vacuum page are highly-rated beater-bar styles specifically designed for pet-hair.
To answer your question, no, I haven’t read anything about, or had experience with, robotic vacuums. However, I assume they’d work as long as they have a beater-bar. As an added benefit, the movement of the vacuum may attract more fleas, ultimately leading to more getting sucked up. Read more about the attraction stimuli of fleas.
If you own a robotic vacuum, I’d say give it go. Run the vacuum at least every other day. After a week or two, if you still notice numerous adult fleas emerging from the carpets, it’s probably a good idea to switch to an upright with more suction power. (The key word is ‘numerous’ here. Even the best vacuum won’t remove all the fleas from carpets.)
Hope this helps!