Linkon, Very good points.
The human populace being overwhelmed would not make for a good movie normally but that is exactly what would happen. I read the Battlefield Earth book by L. Ron Hubbard before I even knew he invented scientology . It was a 1000 page book with the premise being that aliens came to earth about now (1980ish actually) in our technological development. They came in large ships with no warning, gassed the earth with something that only killed humans, our population went from 5 billion to perhaps 50, 000 spread over various remote areas of the planet in a day, game over. Fast forward 1000 years and the story starts with aliens firmly in control and the few humans remaining doing their best to avoid all contact with the flying beasts having lost writing and all memory of civilization. They were basically a few tribes of stone age folk.
The robots will evolve to be a swarm of small units by our hands or their hands. I am not a fan of sentient robots being possible until some breakthrough occurs that is more than just more megahertz or more storage. I’ve spent a fair bit of time in university on the topic of sentient software, it’s been 5-6 years away for 30 years now. It is however a fascinating topic for a geek like me.
No need to create millions of robots, one specific virus tailored to humans would be a much more efficient way to go or gas like you suggested. Self replication is the holy grail and could spawn a million interesting story lines. I’ve come across some stories along this line I will dig up…
http://www.tested.com/tech/3d-printing/453768-nasa-3d-printing-future-rocket-parts-lasers/
http://www.rawstory.com/rs/2013/01/22/company-plans-to-mine-asteroids-with-first-fireflies-spacecraft/
Doing so in space is the way to go and it could occur in a generation. The power of doubling is mind-boggling. If we can build a machine that could duplicate it self once every 2 years it would not be terribly impressive to most people…2 years! But in 40 years there would be a million of them in orbit. In 60 years a trillion and in 100 years perhaps not enough raw materials in the solar system to create a million trillion of them…If I am wrong by a few years lets move out to 200 years where its a million trillion million trillion…30 zeros is a big big number!