It wouldn't work and it wouldn't be cheap. With the existing level of technology, the perfect robot lawnmower already exists. It's a lightweight solar powered thing that doesn't actually navigate but just rumbles around in the garden at random. It turns another way if it hits an obstacle (and most gardens ARE full of unpredictable obstacles - garden hoses, soccer balls, garden furniture, buckets, barbecues etc). A radio-wave emitting cable can be buried to prevent it from entering plantation areas and get stuck in plants. The lawnmower is a bit slow since it is so tiny, but on the other hand it is silent and can be always working! Since it's solar powered it never needs to be recharged or refilled with gasoline.

I think this lawnmower is sold by Husqvarna in Sweden and costs about 1500 USD. I don't know if it has a theft protection system, but it would be easy to implement a code lock.

I am currently interested in robot vacuumcleaners. The same stategy can't be used there, since indoor areas are smaller and more complex. A vacuumcleaner that navigates at random, can't be trusted to clean all areas. But there are reliable and cheap solutions to that to (they are NOT radio or ultrasonic navigation, GPS or expensive computer vision). However, the brain is not a PIC.

Glenn
Sweden