How do you guys play vs ROB/Robin/other projectile characters
Usually against projectile heavy characters, it's important to watch out for the timings of their projectiles and react accordingly with a roll, dash attack or dash grab. Dimensional Cape also works for hard reads at higher percents.
Our burst movement can sometimes catch them just as they're going to throw out a projectile e.g.

's Lloid Rocket or a well timed roll through can allow us to get through the projectile and catch them whilst they're recovering e.g.

/

's Arcfire.
Apart from that, a lot of it is match-up specific. I'll take

and

/

for example since you mentioned them.
Against

, dtilt or jab to stop his gyro from spinning and then either throw it up or use it against him.
Throwing it up against him is good since it limits his zoning to chucking out laser instead which has a charge time and that allows you to play neutral more against him. Since he can't throw out another Gyro whilst one is already active. Just be ready to re catch the gyro and throw it up again when it comes back down.
Using it against him also works; we have a good set of special moves to keep the Gyro in our hand and can use his own ledge trap against him as well as get follow-ups off of it.
Video Examples of Gyro Follow-ups
https://youtu.be/apw6xd5Ah2Q?t=3m37s MK Gyro Stuff vs ROB
https://www.youtube.com/watch?v=gKSYSHeDbfc ROB Ledge Trap
^ Although the above is for ROB we can also do this with our up smash and to an extent fsmash whilst we have the Gyro in our hand as well.
Against

/

, walking and shielding is essential to not getting clipped by arcfires and all of their other projectiles. They can pressure us with Arcfires, Thunders, ElThunders and to an extent ArcThunders in Dash Attack/Dash Grab range too.
Rolling through arcfires are useful if you can predict one and you can punish it well considering its recovery time isn't really that great in comparison to their other projectiles. They get 6 arcfires until they have to recharge during which they can pick up the empty book and use it as a fairly strong kill move.
For thunders, it's best to watch the level of charge they have whilst they're charging. The bigger the spark, the greater the level of projectile, they're gonna throw out.
Level 1 Thunders can be rolled through and they're good in around our optimal ranges but they don't do a lot of damage. It's best to stay in the air against them and see what they do afterwards. They get 20 level one thunders before they have to reload.
Level 2 Thunders are similar but the recovery on them is a little worse but you don't wanna be caught shielding vs Level 3 Thunders (ArcThunder) since due to the shield stun, they're able to run up and grab you from a good half of FD. They get 7 level 2 thunders before they have to reload iirc and 4 level 3 thunders (ArcThunder)
Level 4 Thunders (Thoron) are useful whilst at range. It has greater knockback the closer you are to Robin but it can still kill us around 130-140% with some rage. They get 3 level 4 thunders before they have to recharge.
There are also certain combinations of Thunder they can use before they have to get rid of the books. I'd suggest going through them in training mode when you have the chance in order to know when to attack.
After 4 Nosferatu spells (Down B) the book can be used to kill and they get 8 swings of the Levin Sword before it becomes a throwable item.
As for jabs, any jab involving the fire spell takes away one arcfire spell and their rapid jab drains their elwind spell. Usually against, their rapid jab, it's best to Down B it if they're whiffing it in neutral or just let it run out if they wanna just let it run out since they could lose their Elwind (up B) when they need it the most. We can also shield grab in between jab 1 and jab 2 if we're close enough.
You also want to have Down B on lock for if they try their zoning game at higher percents to punish poorly timed projectile placement. Camping them also helps when we're in the lead since Robin's mobility is limited in comparison to ours.
These were only two match-up examples but overall against projectile happy characters, you'll wanna mentally keep track of what they resources they have and how they use them against you so you can make reads with timed rolls, dash attacks or dash grabs. Being patient with our multiple jumps as well as walking around also helps.

's got a good walk speed. We don't need to be running from one side of FD to the other with a Dash Attack just to get in.
Hope this helps. I struggle against zoning characters myself personally but I've been trying to find ways around it.