[R2K2D2]

This seems like a really really unique project, I think it would be tons of fun to work on. I am gonna toss in my two cents here, and hopefully it will be of some help.

This is how I would select a plan of attack for this problem. Use rotary encoders on your drive wheels or whatnot, this will account for the lateral distance you travel. Then, use a gyro-chip to account for turning and what not. If you couple these things together, you can maneuver around in an autonomous fashion very well. Basically, you will account for any error using these sensors. For example drift and whatnot, you can have the software tell the robot to get back on path. I think this would also be a neat way to do your error fixing. Place an IR Sensors on a sweeping turrett which rotates a certain angle amount. Then, what you can do is put IR Beacons near the pictures and around the room. Then, when the robot jumps off the path, it'll get the IR signal and you can use that to put the robot back on track. I think that is a neat and good way to do things for this part of the task.