Before I post on Lylat
I actually like Pictochat a lot, ROB's throws are amazing for throwing opponents into hazards. I feel like the lagless dair becomes a little more viable here because of the really high lower blast zone. This is a good level for camping, and once you get used to the hazards, ROB can abuse them fairly well. Plus, Upstate New York has some crazy stage lists, so this is actually an option for me lol.
@ Lylat
I personally love tourneys where this is a neutral, because I think this one gives ROB so many advantages when compared to the others (except maybe FD depending on matchup) Like Buenob mentioned, you can use the platform cancel here, which I feel gives ROB some good options, (Im actually really considering practicing this tech the more I think about it.) Although, keep in mind that the platforms occasionally count as still(as opposed to moving) so the platform cancel doesnt work...
Thin floor allows ROB to poke shields with Uair and get some surprise kills with nair. The platforms on this stage are all optimal height for u-tilt pressure, and theoretically i think that would make them viable for the usmash into shield>dtilt lock (although the stage tilting may interfere).
Gyro can be difficult to pick up at certain times because of the tilting, but I feel this hinders your opponent more than it does you, because you should have a better idea which slants make it harder to pick it up. And I second what buenob said about being able to predict the landing of the gyro, once you play the stage enough, you really get a feel for where its going, definitely more so than an opponent who doesn't have as much experience vs ROB on this stage.
High blast zone gives ROB a little more protection if his weak spot beneath him is being abused as he can survive much longer. If you're having trouble climbing onto the stage, you can fly underneath to the other side. Overall, it's much more likely that an opponent's recovery is going to get messed up by this stage than ROBs will. Just be careful, if you accidentally miss the ledge and go underneath, it can take a little bit of time to correct and re-grab the ledge, which gives ballsy opponents an opportunity to go for a stage spike.