Perimeter wire - toggle between different routes.

It isn't clear to me what you want.

Do you have a robo mower that has selector switches on it and you want the Arduino to control the switches? The easiest way is to wire relays in parallel with the switches.

Do you have a robo mower with a wire perimeter following robo mower and you want it to follow one set of wires for a period of time and then follow a different set of wires? It might be possible to hack the perimeter fences to operate at different frequencies and hack the mower to switch frequencies, but that will probably not be easy and will be very specific to the brand. It would be easier to only power one zone at a time. Again an Arduino can control 3 relays that supply power to the zones.

Do you want to make a robo mower from scratch? That would not be trivial, but should be doable. I would recommend start with an AM transmitter and receiver and get the ability to detect the AM signal strength.