Here's a website with a creative non-electrical solution to the robotic lawn mower idea:
http://www.execpc.com/~dsmith/HomeAuto/Mower/
This guy took a large spool of rope, and let a walk-behind self-propelled mower just go in circles around it, with the spool taking in the rope as it went. He matched the width of the spool to that of the mower deck, so that there was minimal overlap.