A robot is anything with a sensor, an actuator, and some smarts. Build anything you want!
I suggest looking at the website for some college engineering classes on mechatronics to see what they have been building and controlling. For instance, UC Berkeley, Cal Tech, or MIT. All you have to do is see the student projects to get an idea of what to build yourself. Maybe you want to get a degree in controls!
Look at the MAKE: webpage. One peek into MAKE: magazine, the web site, or a Maker Faire and you'll get a zillion ideas for getting started. These folks never stop at the algorithm: they want something that moves!
In the US, you may be interested in getting the controls P.E. stamp. Take the Engineer-In-Training exam right away, then try to get a job where somebody has the controls P.E. stamp, such as at any infrastructure plant like sewage, water treatment, electrical grid, etc. Then after a few years you can take the test to be a controls PE yourself.
Learn an appropriate controls code language... I've heard that C (or was it C#?) is a good one for this purpose. Try it out on a Raspberry PI or Arduino.