What you want to do is not simple. Outdoors and over longer distances you would use GPS.
If you want to track the position of something within a single room maybe a ceiling mounted camera and image recognition software would work - but that is far beyoned the capability of an Arduino.
Another approach, which an Arduino could manage, would be to have 3 light beacons and have a direction-sensitive scanner on the robot that can identify the angle to each beacon and work out its position from that - like the way ships used to use navigation lights and lighthouses.
If you want to be able to track it through multiple rooms I can't think how that could be done other than with a similar setup in each room.
All in all this sounds like more trouble than it would be worth.
...R