Stick in the ground
In the short term, you whack a stake in the ground and securely attach a popular petrol mower via a length of rope == the radius of your soon to be new circular lawn. Fire up and let it roll up. Later, a semi automomous triangular lawnbot with 3 auto feeding strimmers on the angles will tackle any edging issues. Orientation and navigation via any popular 9DOF IMU and a few coded IR reference LEDs around the estate for Wii mote positioning and then stand well back. Hours of fun working out the best cutting topology for a quality finish.
Paris as she loves a little triangle.