I feel left out in the coming 'robotics revolution'. I am planning to take a couple of years off from work and switch careers into something robotics. I've been building my math base past couple of months, but I am utterly clueless as to where to even start with robotics.
So depending on where you find yourself most comfortable consider focusing on that part of the problem. Could be algorithms (software focus), could be mechanics, could be 'mechatronics' (which is the term the local community college uses for a combined electronics/mechanical engineering sort of curriculum).
For embedded hardware, I'm a big fan of the BeagleBone Black. People talk a lot about the Raspberry Pi, but the BeagleBone makes a bit more sense. Look at the OpenROV project as a good example of that.
Lower level, there is a lot of stuff related to feedback controlled (closed loop) motor controllers that is key.
Higher level, pathfinding AI is interesting. Even things like inverse kinematics, thought that is largely a solved problem.
Some of my favorite books are Probabilistic Robotics for the theoretical stuff, and Robot Builders Bonanza for the really practical hobbyist stuff.
With an EE, CS, or ME degree? Minor in biology. Nature has made by far the best robots. Definitely useful to learn from it.
Edit: Found it: http://www.smithsonianmag.com/science-nature/this-insect-has...