a robot that cuts a design in grass?

There are one or two robotic grass cutters around, they aren't cheap. You could hack one of those to cut patterns, with a lot of work.

Leon

You haven't been looking very hard have you? Jeesh, those things have been around for at least 3 years now! The more modern ones have sentience, plasma-tronic brains and omega-lithium batteries that recharge on ambient light. You can program them by sketching out your desired design on a used paper napkin, hold it up to an array of scanning optical sensors, then off it goes! Most of them incorporate side-scanning LIDAR to avoid objects and can maitain a pattern tolerance of 5 or 6 attometers.

Try these sites:

Good luck!