HI - i just recently purchased an amicus advance table tennis robot.
What is the best ball to use with it?
The better the ball, the more consistent the robot can deliver the ball. So if consistency is what you want from your robot, then use 3-star balls.
If your robot does not have random controls to vary the placement slightly (so the robot's throws are more human-like), then some players prefer to use cheaper, less consistent balls so ball delivery is less predictable.
If your robot allows slight randomization of placement, speed, and/or trajectory (I believe your Amicus Advance does), then I'd recommend getting the most consistent ball you can get and then use your robot's controls to produce randomization while still retaining the ability to turn off randomization and get more precise throws when desired, especially when first learning a new skill.
As a whole, celluloid balls are more consistent than poly (plastic) balls. If you are going to play in tournaments or leagues that use poly balls, then it would be beneficial to use poly balls in your robot. But if you only play recreationally, why not use celluloid? If you compare one grade (1-star, 2-star or 3-star) to another, celluloid will almost always be more consistent and less expensive.
Again, talking generically, most 1-star and 2-star poly balls are really bad, meaning out of round and inconsistent from one ball to the next. I'd avoid them at all costs, unless what you want is a lot of strange bounces and trajectories.
Poly balls come in two general categories--seamed and seamless. It seems to hold true that many seamed poly balls are not very durable and crack fairly quickly. Seamless poly balls tend to fare better, especially stocks produced from about Fall 2015 onward. Celluloid balls are all seamed and tend to be much more durable compared to any poly ball.
Of the poly balls, I think one of the best values, and a ball that is remarkably consistent and durable for poly balls, is the Gambler seamless 3-star from ZeroPong:http://www.zeropong.com/index.php?main_page=product_info&cPath=44&products_id=318&zenid=86d6b93431c9b960106c85d7e948c040
For celluloid balls, most all major brand celluloid balls are very good. My particular favorites were Nittaku and TSP. You should still be able to find them at many online TT shops, but I have heard that Nittaku is no longer manufacturing celluloid balls, so, if true, their supply will gradually dwindle as stocks are used up.
There's one caveat to celluloid balls. Do not fall for 4-star, 5-star, or similar claims--they're all marketing ploys to make their ball sound better than what it is. The only grade quality you can rely on is a 3-star grade, and it must carry an ITTF approval stamp. The highest grade that ITTF awards is 3-star, which means that ball meets certain criteria for approval. If the ball is not an ITTF-approved 3-star ball, the manufacturer of that ball can put anything they want on that ball and there's no guarantee of quality.
Also, is it OK to mix balls? ie. use both the butterfly and the xushaofa balls in the machine at once or is that not advisable?
Certainly, mixing balls should cause no harm to your machine. However, it all comes down to how consistent you want your robot's throws to be. I'd always recommend using the same brand and model (and 3-star quality) if you want consistent throws.
With that said, however, many brands of poly balls come out of the same factory, and simply carry different logos. I believe it's widely recognized that all seamed poly balls manufactured in China are produced in either the DoubleFish or Double Happiness factories. And all seamless Chinese-made balls come out of the Xu Shaofa factory. The outliers are the highly regarded Nittaku Premium 40+ made in Japan (not
their SHS model, made in China), and I seem to recall that a seamless ball is now being shipped from Germany (although I've never seen one and don't know much about them).
Now, what do I recommend? First decide poly or celluloid. If celluloid, most all major brand celluloid balls, particularly the 3-star grades, are pretty good, especially for robot play. If you want to use poly, I think the Gambler seamless is about as good as you can get right now. Nittaku Premium 40+ would also be recommended, but at 3 times the cost of the Gambler ball, and decidedly less durable.
Hope this helps.