I hate to plant this seed in someone's brain, but it MIGHT be possible to have a robot go from (x1, y1) to (x2, y2) using just an accelerometer. It is something I am investigating in my lab at college. Basically you construct the problem in terms of acceleration and the robot learns how to make the accelerometer read that acceleration. The idea is that if the robot gets so good at going x ft/sec^2 for any possibly x and can adjust from it's current acceleration a - > x in a reasonable time, then it is possible. However, as others have pointed out in this thread, error accumulates extremely quickly. This program will have to be flawless in its transitions.
It is a deeper investigation in my original project with a robot teaching itself how to follow a path given
velocities. I am without a robot until I go back to college in August, however.
This project should be finished by next fall....with a paper submitted for publication sometime late next year.