outdoor ultra sound positioning system robotic lawn mower
Things you might need to consider:


Ultrasonic frequency can be heard by dogs and other animals and insects. It might affect them.
This approach will work best in open areas with no obstructions such as walls in between or trees because they will affect the received signal in a weird way.
You will have to use at least three different frequency speakers for a proper triangulation. Most probably three separate mics as well for easy implementation.
Accuracy will depend on the quality of hardware as well as weather conditions which might be difficult to compensate easily.


Here is what I suggest:

Use GPS modules for positioning. You can easily get GPS modules with 2-3 meters of accuracy. Program the mower in such a way that it stays at a safe distance from any structure/tree. Once it does it's job, someone can manually cut the remaining grass near the structures.

GPS will also save you from the trouble of putting 3-4 speakers in the corners of field and laying wires for them. These days drones are equipped with GPS and they are working well so I believe it might work for you as well.

Modification for lawn mower:

I haven't used one but I feel that small stones or pebbles might damage the blade if they get into it. If someone is manually mowing, then they can tackle the situation but when it's running automatically then I guess you need to take precautions. 

You can modify the mower to use a rotating wire similar to this machine:



It uses a plastic wire attached to the rotating head to cut down grass.