The first and eponymous story of the collection, "Robot Visions," seemed a little odd at first. After thinking on it for a bit, I think I figured out why.
The (unnamed) narrator of the story, a "humaniform" robot, reasons that there must be a "sad event" at some point in the future, which would completely wipe out the human race before 200 years from present time (2030). Humans are taken over by many humaniform robots (whom the time-travelling robot witness assumed to actually be human).
Enchanted with this "robot vision," the narrator takes steps to ensure that nothing done in his time will prevent this future from taking place.
Shouldn't this violate Asimov's First Law of Robotics?
A robot may not injure a human being or, through inaction, allow a human being to come to harm.
Now, to be fair, the robot does reason that telling his masters (the time-studying "Temporalists") about this might make them destroy the possibility of an all-robot future, but would not prevent the apocalypse-event from occurring, which would destroy humanity's robotic successors with no human life saved, so that was not a worthwhile path to pursue. (We find a similar line of reasoning in "Little Lost Robot," another story in the collection)
Be that as it may, there is still the possibility of action to be taken that would save the human race, which is even mentioned in the story -- instead of 200 years in the future, go 50, 100, or 150 years to find out what actually happened, and then make a plan of action based on that to save at least some (if not all) human life. After all, the second clause of the law forbids allowing humans to come to harm through inaction.
The only answer I could think of involves the Zeroth Law, the one that puts "humanity" above "human beings." The narrator makes a few references to "humanity." Referring to a plan that would prevent robots from taking over humans, but that could not save the lives of the humans themselves:
It would just prevent a replacement; stop another group of beings, made by humans and honoring humans, from carrying human aspirations and dreams through all the Universe.
And in the final paragraph:
I am the first humaniform robot, and it is on me and on those of my kind that are yet to be constructed that future of humanity depends.
However, I'm not certain that "Robot Visions" was written before the invention of the Zeroth Law, so I don't know if that will work as an answer.