There is no way robots could take over the world. Robots are not human beings. Robots would have to be made perfect , be able to function independent of human beings and overcome human failings.
Robots are after all just machines made by human beings. Honestly , can you tell me anything made by man that is perfect? Just look at modern aircraft. There are all sorts of robotics built in to the modern aircraft but they are by no means perfect. What goes up must come down. Hopefully you are on the flight that ninety nine point nine percent of the time comes down safely. We have our fingers crossed that aircraft inspections on the ground rule out the point one percent where an accident could occur.However there is absolutely nothing that I can think of made by man that doesn't have some flaw. Sometimes I think the flaw has deliberately been built in to present day machines such as dishwashers , washing machines etc that also have a fair amount of robotics built in, so it does break down eventually.
I have to admit robotics have come along way since the concept of a robot was first thought of.However a truly independent robot capable of taking over the world is a long way off. You have to bear in mind that the human being is far more complex than a robot and there are huge problems to be overcome when building a robot.
Supposing we did build a robot capable of understanding speech. The big problem with robotic comprehension is that no person enunciates speech. Instead of speaking clearly for instance "I am going to do it now" a human being most likely sound like " Arm gunna doowit now" I figure it will take centuries to program a robot to sort out the various slurring of words, accents, slangs and nuances people use in everyday conversation.
The human being is far more agile than a robot. The day a robot can play baseball, gridiron, tennis any sport for that matter seems like centuries away. I doubt if I will ever see a robot take part in a swimming event . I don't think waterproofing a robot has even been considered.
At the moment the human being can out perform a robot. Granted there are computer games which can better some human beings but not all. The computer games are still written by human beings. I do believe there was some attempt to have a computer compose a story by itself. All the data was fed in so that the computer could write a "Western." Needless to say while the computer was able to out think a chess player it wasn't capable of making sense when it came to the "Western." The story it concocted sent the programmers well and truly back to the drawing board.
If robots were developed to the point where they became almost indistinguishable from human beings I would hope that the robots would not have emotions as part of their make up. Lack of emotions would be the one thing that would stop robots taking over the world. The human being is capable of showing various emotions which I would not like to see built into a robot.
One of the most powerful emotions that human beings have is fear. When humans express fear of the unknown and what they cannot understand they react in a certain way. They tend to smash everything until it is no longer a threat. I would think that long before the possibility of robots taking over the world became reality human nature would assert itself one way or another.