Question: is there an agreed upon starting position of the pieces when having these types of competitions? Ie, both the robot and the human had to solve the exact same problem?
I would assume in these cases it is not the same starting position. A competition like that could be done, but the reality is that it doesn't matter. The way this robot and the fastest human speedcubers solve the cube is most likely very similar and either based on the ZB[1] or original Fridrich method (sometimes refereed to as F2L)[2] method of solving which requires the use of 100s of different algorithms. Because of this, solutions will usually take a similar amount of time and require a similar number of moves to solve the cube.
In Rubik's cube competitions I think you solve the cube 10 times, and then the fastest and slowest times are dropped and the remaining 8 are averaged together, and that's how they get those times. It's not perfectly fair, since the starting permutations are different for different contestants, but it does a good job at figuring out who the fastest solvers are.
Thanks