I don't know how you'd represent your map, but if it's just a 2D grid of occupied/clear cells then you're going to need large amounts of data to get anything worth while. Are you planning to put it on an SD card, or something?
Calculating position by dead reckoning is not going to be very accurate and trying to use the previously-discovered map results to tell you where you are I think would actually be very hard to do effectively.
If any of the obstructions in the room/maze are moving/moveable, all bets are off.