Autonomous Robot Navigation - Mapping

Good day...
I have been searching for awhile but just haven't found what I'm looking for.
Building a robot to cut my lawn - hot here in Houston so to save a lot of sweat and fun to learn.
I will be using a number of sensors such as GPS, Compass, Sonic range finders, IR and encoders to construct a bot that will cut my lawn effectively.
I'm looking for a technique that the bot can learn the environment (record it on a SD card) and then cut the lawn using the data each time. Perhaps learn again and optimize the cut pattern. Using xbee to send the data to my laptop...visual display or just display the data.
I have looked at SLAM, polar $ cartestian coorindinates for example.
Maybe use a grid...waypoints.

Anyone aware of a good algorithm, code or techniques to achieve this goal?
I was looking at laser for better resolution but too expensive.
Thanks

Maybe use a grid...waypoints.

that is one of the POSSIBLE and good methods i've previously tried this but just ended up with a bot that just knows where to go but not learning
you could probably use ir emitters sending some details over to the bot in a grid ( make it a point to compare encoder and beacon readings so as to get a better resolution )