It is easy to follow light, if you turn all the rest of the lights in the room off.
How reliable does this thing have to be ? Work outdoors, or indoors only ? Can you guarantee that there
will be no other "red" things in the room for it to home in on ?
Arduino is not really capable of real "machine vision" capability.
One idea, might to be make your led blink at some specific and unusual frequency ( not necessarily visible),
and set up an antenna on the robot which is going to notice that specific frequency and home in on it.