What level of engineering student are you? And again, what research have you done? Show us where you are confused in the things you are reading and maybe we can help.
But getting a sense of the level of course will help me figure out what caliber of robot they are looking for.
You could get something very very basic going by just building the $50 robot and using timers to control the motors. It is almost guaranteed to fail but it sounds like you don't have much experience so this may be one of those exercises where the instructor is trying to make a point about how awful dead reckoning is.
But if there are more specifications you are not telling us, like markings of the course, then you can do more.
But again, show us the things you have looked at in your research of this project, tell us what you don't understand and we can probably do more for you.