You have quite a few options with embedded processors that you can use. This includes the Basic Stamp or Atom, the HC6811's, Pics, etc. which are all used for this purpose. You will not be doing any image processing with those systems though. Perhaps you may want to have a look at the mini-ITX boards that allow you to boot an OS on the robot.
No, there is no Linux version of RoboRealm.
We built a now outdated Robot called the Bucketbot about 5 years ago. Had a 386 and would boot win98. Used VNC to connect to it via a desktop and worked quite nicely except for a couple times where a keyboard and monitor were needed to change network settings.
Perhaps you want to look at the more hardware oriented solutions like the CMUCam, AVR Cam, Cognachrome, POB-EYE or Falcon systems that are meant to be interfaced to lower end embedded microcontrollers.