How to get something to follow you

I am working on a project at school where our task is to get an electric golftrolley to follow the golf player using arduino. How would you solve this problem? What equipment would you use to do this as easy and cheap as possible?

Thanks in advance!

Have the golfer wear an IR beacon, have the "golftrolley" scan and lock on to the beacon, and use a ultrasonic sensor to have the trolley stop moving when it gets close enough.
As a golfer, I don't know if I'd want a robot following me around, tipping over on uneven terrain, struggling to get up hills, or getting stuck on ruts, tree roots, etc. A trolley on New England terrain would have difficulty.