Sounds like an interesting problem - could be a lot more complicated than you think.
What other sensors does the robot have?
Is the house map pre-loaded into the robot.
There are a number of ways this could be implemented.
- SLAM: seems a quite popular field at the moment, but it quite complex and non-intuitive to implement. It also requires a lot of memory - more than the arduino has.
- You could use a searching mechanism - each room would have a "beacon" of some kind so the robot knows roughly where it is and where it needs to get to. Much simpler to implement - could be done with sonar/infra-red distance sensors maybe a low res-camera driven by an external controller.