Since I, Robot is a collection of short stories, we're going to try something a little different here. Here, we're going to look at "Runaround" and see how it doesn't exactly fit with the "Overcoming the Monster" plot. Why? Largely because many robot stories fit into that plot. (For more on Booker's Seven Basic Plots, check here or search Shmoop for examples.)
Anticipation Stage and Call
Stage Identification: Robot Speedy isn't working properly and the environment of Mercury could kill Powell and Donovan soon.
Explanation/Discussion: This stage introduces the monster. But notice that the "monster" in "Runaround" isn't an actual monster. It's not like there's a dragon on Mercury or robots planning a revolution. No, the problem here is Mercury itself—if Powell and Donovan don't do anything, it's Mercury that's going to kill them.
Stage Identification: Powell and Donovan travel through the mines and see the wonders of Mercury.
Explanation/Discussion: The Dream Stage is the part of the adventure when everything is going reasonably well. Powell and Donovan certainly have problems here—like the fact that they have old robots that need to be ridden. But overall, their quest to overcome Mercury's environment seems to be going OK. They can't be on the surface for too long, but they've got mines to travel through. This part also includes the dream-like imagery of absolute shadow in the shade and a glittering plain of crystal in the sunlight (86). Mercury is dangerous, but it can be beautiful.
Stage Identification: Speedy is drunk and Powell and Donovan can't scare him back to them.
Explanation/Discussion: The Frustration Stage is all about how the plan to defeat the monster falls apart. Here, Powell and Donovan can't get to Speedy because he's acting funny. And when they cleverly figure out a plan to use chemistry, even that doesn't work (192). And if chemistry doesn't work, what hope is there? This is so frustrating that it might shade into the next stage.
Stage Identification: Powell runs out to get Speedy—even though he might die. And he almost gets rescued by the wrong robot.
Explanation/Discussion: The Nightmare Stage is when things are at their lowest, when the monster is about to kill the protagonist. Here, in order to snap Speedy out of his dilemma between the Second and the Third Law, Powell rushes out into the full heat of the Sun. But what really makes this a nightmare is that one of the older robots goes to help him first (222-224), which a) messes up the plan to get Speedy and b) would kill Powell anyway because the older robots move so slowly. So, if the older robot "saves" Powell, then both Powell and Donovan are dead men.
Thrilling Escape from Death
Stage Identification: Speedy saves everyone.
Explanation/Discussion: Luckily, just in time, Speedy snaps out of his drunkenness, saves Powell, and gets the element they need to overcome the danger of Mercury's environment. That's kind of the definition of a thrilling escape from death.
Now, if you look at "Runaround" as a story about "Overcoming the Monster," it's a little strange, because it's hard to locate the monster: it's mostly the environment of Mercury, but it's also (at least a little bit) the problem in Speedy's programming. And this story is probably the story that best fits this Basic Plot. (Where's the monster in "Reason" when Cutie takes over the space station and does a good job of running it? Or "Escape!" when Brain temporarily kills Powell and Donovan so that they can travel through hyperspace?) "Overcoming the Monster" is a pretty common story in science fiction (Frankenstein might fit this, and that's a classic "dangerous creation" story). But Asimov's robot stories only fit this Basic Plot if you squint. And then what we see is that the monster is usually not the robot, but something else (a conflict in the Three Laws, a poorly-given order, the temperature on Mercury).