By triangulating off of the two unmoved beacons the robot can know pretty exactly where the third beacon is now located.
Did you just say 'triangulating off of the two' beacons? You need at least three to triangulate
Actually, triagulation only works if you have a perfectly flat world. You would need four beacons for 3D terrain. Then a 5th to move around so that you have at least four that are stationary at all times.
I think the biggest problem with this is:
A) robot needs to decide where to move the beacons intelligently
B) moving 5 beacons means the robot needs to move back and forth 5 times, resulting in 10 times the distance needed to travel (both ways)
I think a better method would be to identify landmarks in the path, and change landmarks as the robot progresses. This is how humans navigate.