I'm growing a bit tired of making browsers do things, and think it would be fun to make robots do things. I've messed around with Arduino, but nothing beyond that. Where should I start?
Robotics with capital R comes with mechanics, algebra and control theory, my flatmate was building robots. They are super expensive though. I think an arrival point to go to "career" could be to stabilize a body standing still on top of a sphere or over two wheels.
If you want to get serious/make a career of it, there's no getting around the math. Even an embedded controls engineer needs to understand signals and timing.
What you do really depends on what focus area you want to start diving in to. Try making a simple drone fly around for awhile automatically, you will learn all sorts of nifty things about control theory, mechanical models, digital signal processing, machine learning, telemetry and more.
Robotics as a field is quite large. There's all sorts of Robotics out there really.
JavaScript probably isn't the language of choice for Robotics though... C/C++ most definitely are a lot more widely used considering you want low latency with hard time limit control loops. Imagine if your robotics software suddenly decided it needed to garbage collect or JIT some code when it should've been making a decision to avoid collisions...
Thanks for the advice. Do you have any suggestions on a drone platform that would be good for a beginner?
I notice that the first thing that pops up on google for 'programming drones' is http://www.nodecopter.com/ which seems right up my alley, but I think you have a good point about learning C/C++
Another good place to start would be OpenCV, a library for computer vision. It'll come in handy if you wish to build robots that are aware of their environment.
Pick a framework and order some devices / components. I was attempting to get into this but never got beyond toying around with GPIO on the Beaglebone. You just have to start getting the equipment and dive into it.