Christopher Booker is a scholar who wrote that every story falls into one of seven basic plot structures: Overcoming the Monster, Rags to Riches, the Quest, Voyage and Return, Comedy, Tragedy, and Rebirth. Shmoop explores which of these structures fits this story like Cinderella’s slipper.
Plot Type : Comedy
Booker's plot analyses don't really work very well for robots, as it turns out. Among other things, most of Booker's plots focus on one character as the main focus of the plot. But R.U.R. kills off its main characters, Domin and Helena, before it gets to the end of the run time. (Yes, it's careless of R.U.R. to do that, but what can you do?)
Rather than shoving the play into Booker's boxes, it might be more useful to see it as deliberately mixing and matching some of the most common plot types:
Comedy
The prologue is essentially a comedy, complete with mistaken identity (are you a robot or a human, good sir?) and a marriage at the end. It's an uncomfortable comedy, though (sort of like Shakespeare's problem plays) in that Helena and Domin don't seem like a very good match. Domin's a jerk, and Helena never really looks like she wants to marry him.
Tragedy
That ominous comedy ending leads on to Act 1 and 2, set ten years later. This is a tragedy; miscommunication leads to dire results and finally everybody on earth is dead. Shakespeare's tragedies have nothing on this here mess.
Comedy (again)
The final act, Act 3, is set some time later again, and again ends with a marriage—this time of the robots Primus and Helena. This seems like it's supposed to be a happier end overall. Helena and Primus do seem to love each other, so they've got that going for them, at least, even if they're the only loving robots on the planet. Also, Alquist manages to create the formula for the secret of life, or rediscover it, or something. Anyway, Helena and Primus should be able to reproduce somehow, which is a good thing, Alquist thinks.
So R.U.R. goes: comedy, tragedy, comedy. It's more like three set pieces than like a unified play, which is maybe why Booker couldn't quite make sense of it. (Or maybe Booker just never dealt with robots. That's possible too.)