Yo damn, I actually can help with this pretty well since one of my friends actively play ROB.
First off, as far as he plays it, he plays it pretty campy and keep-away, and as far as I see it you have to be pretty on-point with ROB once you get in. Getting in, however, is the hard part! ROB will keep shooting gyros which come out extremely fast and lasers will disrupt you, and if he gets a hold of that Gyro again it'll just be trouble. Gyro disappears on shield hit, so if you can help it, dash in and shield when you see or anticipate if he's going to throw it. If you can catch it? Use the item against him, or throw it straight up. No joke, throw it up; he won't be able to use it for a while after that, and all he'll have is laser to stop your approach.
Now, once you DO get in, you have to be on-point as I said. ROB's grab range is pretty good and if he shields any of your aerials, that's a free grab for him, which in early percentage is going to be dthrow to uair to build damage. Choose whether you think a dash attack or a grab will hit, or jump at him with any of your aerials if you think they can hit. If you think he's going to roll away, dash attack. If you think he's going to spot dodge, try shorthop Nair or pivot grabbing. You can also stop with your shield and poke him down with your tilts as well, because tilts are going to be important in this matchup.
A lot of this matchup is patience. Reckless aggressiveness will be the end of you if you don't approach carefully, you have to sort of slow down a bit, which is kind of a pain to say as a Falcon player. Be smart when you're aggressive, and stay in. ROB has pretty good defenses even when close, which includes his dtilt, dsmash, ftilt, and grab. Keep in mind of what ROB can do.
When in dodge roll wars, he can do Dsmash to disrupt the flow of it. If you feel you can catch ROBs rolling around a lot, do charged Dsmashes to catch him, or ground Falcon Kick to cover all the options. I wouldn't recommend Raptor Boost unless you really think you can get it.
Now, when it comes to killing, ROB only has a few options. Upsmash, Fsmash, and Dsmash can kill, but he has to get you at pretty high percentages, especially if you are vectoring correctly. The most ideal situation for my friend is to grab and Uthrow me to death, or gimp me from the edge with the Gyro Peach-style from Melee. Falcon, on the other hand, has so many ways to kill, but getting to him will be a little tough. If I actually wanted to be honest, I don't get enough knees during the matchup, but if you can find them? Get them. The best situations to get them is if he Side-Bs, Usmashes, Dsmashes, but if they're smart, they won't leave those gaps open. I think the most ideal position Falcon can be with ROB when he wants to kill him is when ROB needs to recover, because his recover is rather pitiful.
This means jumping off the stage and spiking him with Dair. Be careful, however, because he can disrupt you with lasers if you're traveling towards the edge to cover his recovery. If you do jump off, he can stop and do Uair, but if you're patient and can see the opportunity, send him to the depths and spike him. You can also attempt to stage spike him, or just knock him back more by jumping off the stage. Generally, you want to be off the stage a lot if you want to guarantee he runs out of gas before he makes it back.
Some information about ROB and grabbing him: Dthrow to Knee will not work; you have to do Dthrow to Uair to Knee in order to guarantee a knee after a dthrow. ALSO, a thing that is exclusive to ROB and some heavy characters is that you can juggle him with Nair. If you are quick with the fast falls, you can land a 8-10 hit combo on ROB with a dthrow and several consecutive Nairs, which can also lead up to a Uair if you please it. This racks up a lot of damage early if you can get the Nair or grab on him, and this also carries him really far. It basically carries him to one side of FD to the other.
A lot of the matchup problem for me is punishing dodges, but elbow is pretty solid idea as Patrick Ray stated. Pivoting is pretty good for this matchup, as is just overall patience.
I don't exactly want to say this is a disadvantageous matchup for Falcon, but I think it's at most 5.5:4.5, maybe 6:4 in ROB's favor. Best stages to fight ROB on is Battlefield and Yoshi's Island, and FD is more on ROB's side, but it's not too horrible.
Anyway, I hope this post helps! Good luck with the ROB matchup.