Foxconn is almost on their doubling the current level of industrial robots by 2014. If other manufacturing companies in China follow then we could see ten times or more the number of industrial robots by 2015. Heartland Robotics has talked about bringing automated robotics to a far lower price point. Instead of $20,000 to 100,000 down to $1000-5000.
Also, there is the construction of a lot of higher performance personal robots using tablets like the Ava Robot Tablets for the head and enlarged Roombas on the bottom with a 3 foot neck.
Finally making the move to the popularity growth pattern of PCs in the 1980s. Ten Million IBM PCs in 1983 after being introduced about 3 years earlier.
Gartner projects that the number of tablets will increase from about 17 million at the end of 2010 to 294 million (over 16 times more) by 2015. If those tablets were levels were used for Robots with a three year lag, then their could be 300 million tablet leveraging robots with cheap Heartland Robotic (and Chinese knockoff) arms by 2020.
By the end of 2020, there will be over ten million professional service and manufacturing robots.
By the end of 2025, there will be over one hundred million professional service and manufacturing robots.
The Korean government has already a stated goal of one robot in every Korean Kindergarten by 2013 and one robot in every home by 2020. There are currently 16 million South Korean households out of a population of nearly 49 million.
However, my upside scenario for robots is 1 billion robots by 2020, mainly tablets used for the head and processing. The wheels, mobility and arms become $200-1000 upgrade accessories for the tablet. The 2020 tablets could have 1000 to 10,000 times the processing power of todays tablets.
I make predictions with some margin for things not going as well as I expect. I think that things can come together for 1 billion robots by 2020.