Here's how I would do a simple, unbiased, accurate trial. Set up electric eyes and cameras to view the edges of the strike zone. That would enable us to know with certainty whether a pitch moves through any part of the zone. (This could not be done during a game, of course.) Then compare that to the calls made on those pitches, whether by robo umps or by humans. (Professional umpires and any robo ump systems should all be tested.) This would enable us to determine the accuracy of the calls.
I have not done a search of any kind to determine whether this has been done so obviously I don't have a citation for it. But I must believe that I am not the only one who has ever thought of doing this and I would be flabbergasted if this (or something very similar) has not been done. And I would be even more flabbergasted if it has been done and MLB has not been made aware of the results. Hence, I concur with minny505 that it's easy to believe that MLB is suppressing this data. If the data showed that robo umps were less accurate than humans that would be publicized.
Edited to add:
This is how all professional umpires could (and, IMHO, should) be evaluated for their ability to call pitches correctly.