That's a complicated question with no clear answer. People have been talking about Moore's Law and the implication of exponential growth applied to robotics for decades, but we've yet to see so much as a believable path towards a true general A.I., so I believe a healthy amount of skepticism is recommendable - in other words, for robots to take over humanity as a dominant species they first need to be capable of interaction with humans as equals, both in physical mobility and in overarching, non-single-minded intelligence, and neither of those things has been achieved yet. If you've got the time, authors I'd recommend relating to the topic include Hans Moravec and Nick Bostrom, off the top of my head.
And, well, if you want my personal, biased opinion, putting aside facts for a little bit: yes, god I hope so, and preferably within the next 50 years.
i believe, if we can transfer our consciousness, or that "we dont know what" factors we humans seem to have, to a robot, by computer transfering or creating/programing a sentient robot or by something quantic, idk, we would just evolve. our mind, our creativity our emotions all of what makes us us would just live inside a body that is made from metal or ethernal plastics. i think is evolution. i think is also a matter of time for us to have real conversations about phylosophy with ravens or dolphins, give them 75.000 years and they will catch us up. cats and dogs too.
Well, no amount of technology can accurately predict this future, the game is all about Probability taking preventive measures will help us per. To take humans under control Robots with effective Intelligence will be needed to be backed by several dangers to humans. AI in itself is very tempting for humans to use as a weapon, and is already used to manipulate wars and engineer cognitive human behavior. Once this is learned by AI (which they certainly will) it is a matter of time for humans.
We all know every Civilization has a threshold, which when not handled carefully is known to create disaster. today's generation is driven by Technology at an Exponential such that humans are not able to have a perfect hold on it and no policies or care is taken by Global leaders on it, if such is the case, we will be heading to disaster one or the other way.