You probably didn't specify the project well enough. It's ridiculously hard to make a robot go somewhere regardless of all obstructions in the way (unless you mean on a flat floor with obstacles, I am thinking about somewhere like a forest floor). You would need an an IMU and a very robust chassis. The IMU alone should be enough to shut the prof up (they aren't easy to make).
Even if it was just a flat floor, you are almost cheating if you just have it wandering blindly to a general destination area and then wandering around some mroe until it reaches a destination "beacon".
Your prof would probably let you do it if all the start points and destination were internally programmed (no beacons) and the distance you planned to travel was long enough. TO do that you would need accyrate dead-reckoning which would increase the complexity of your project (if not skyrocketing) to the point your prof would let you.