As nice as home robots look, and as much as I personally love them (I have a faint memory of watching a video about Jibo at 3 in the morning and just like, crying for twenty minutes) I don't think they'll quite take off - they're too expensive, too limited, and the AI is far from being there yet.
The real "robot takeover" will not be machines running around killing people - it'll be the use of artificial intelligences in every field, for every specialty. I think what we're going to see first and foremost is AIs like Alexa and Siri getting smarter and smarter. We're going to be seeing beings just short of HAL, most likely - limited both in capability and speech capacity, but able to emulate human emotion and interaction to a very realistic degree. Most likely these will be mobile AIs stored on servers and connected to from elsewhere. Carrying around that much information in a physical body just isn't that feasible. Plus, we love our mobile devices, and that culture doesn't seem to be going anywhere.
Of course, those will always be limited by the problem of strong AI, which, the less idealistic I get, the less I feel we're going to be able to solve with machines alone. I mean, I wouldn't be surprised if we eventually figure it out, but brains are really damn complicated, on a level no computer has even begun to approach.
I think the first truly intelligent AIs will actually be human-AI hybrids - people using augmentations to think faster, to store more memories, to eventually upload their minds. Emulating a human brain is beyond tricky, but once we figure it out, it'll allow for strong AI without the need to build a thinking machine from the ground up. It's the natural next step. We're getting closer and closer to our AI, might as well just merge with it and finish the job. Of course, then you get into all the speculative discussion about the future of the species, which is fine and dandy, but we're going to have to not extinct ourselves before then.
