Here's my two cents on some the characters that have been mentioned:
Villager:
He has all the tools in the world to shut ROB down. As stated, pocket removes gyro from play for an entire stock. That not only shuts down a ROB's camping game, but also eliminates some great on-the-floor & thrown-item gyro set ups and strings.
Without the gyro in play, ROB relies on his laser (which beats Tree) but is severely limited. Villager can use his pesky F- and B-airs to harass, and potentially KO. Additionally, ROB's inability to move for the first part of his up+B makes him a sitting duck. Villager U-air beats D-air, and usually the lower part of N-air almost all day. Villager D-air seems to outpriorize ROB's U-air (might be dependent on the number of turnips).
Furthermore, ROB is rather slow and clunky... so Villager can play keep-away rather well.
All that being said, if you rely on solely camping ROB out without mixing in a solid punish game or taking advantage of aggro options he does have the tools to be able to contend if you aren't smart about it due to being able to stick around, as well as KO at a reasonable percent with U-throw or U-smash (the latter if you decide to get stupid with Lloid tricksies).
Definitely in Villager's favor. Solidly in his favor if you take customs into account.
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Kirby:
I believe Kirby has the advantage. Yes, ROB wins at a distance & mid-range, but if the Kirby can use their multiple jumps to hover above the max angle of the laser, that move is rendered almost useless & if he can use those jumps to hang out in ROB's blindspot... that makes things significantly more difficult for him. Similar situation with the gyro... if the Kirby stays in the air, the gyro is much less effective.
A good Kirby will use their multiple jumps to bait an action from you, and then punish accordingly - typically by doing something to get him in the air. And, Kirby has the tools to punish ROB for days on end in the air. In fact, I go into any match with Kirby (as well as a host of other characters) feeling & playing as if I already have about 60% damage on me... as I know that as soon as this (and other chars) get in on ROB... he'll eat that much when at zero/low percents.
Kirby's crouch animation brings him so low to the ground that ROB actually has to somewhat space... for a grab to even connect, which decreases the U-Throw KO potential. I think Kirby's crouch goes under either ROB's jab 1, or jab 2 (not sure) so that makes a quick 'get off me jab' significantly less effective, leaving D-tilt as a ROBs only reliable CQ 'get off me' in this MU.
Again, I feel Kirby does well against ROB.... significantly more so if you take customs into account.
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Mario:
I feel that this is a pretty even MU in the current state of the game (imo), but I see it eventually going solidly in Mario's favor as things develop. His Bread & Butter combos work exceptionally well on ROB at higher percents than some of the cast. His strong, quick, U-air wrecks ROB when underneath, his U-smash is an absurd anti-air, as is his U-tilt to a somewhat lesser degree, N-air is a solid combo-buster, and depending on the timing/spacing his D-air is a solid landing move,
I feel Mario has a superior boxing game once you get into Mario's jab range, and that boxing game leads to lots of rewards. Fireballs are great to harass, to freeze up his up+B to allow for edge guarding, as a set-up to land grabs. Grabs lead into aerial strings, which Mario excels at executing and ROB utterly fails at getting out of.
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To the folks talking about Rosalina:
This is a solid MU for Rosalina, if she's competent. Solid as in "she doesn't get super shut down / not an unwinnable MU/ probably close to 50/50; could go either way +/- 5 points".
Staying at long range as ROB & trying to camp will get you virtually nowhere as Luma will eat it, or the gravitational pull will negate it. Sure, you might get some chip damage, but Rosalina is able to rack that up as well.
Rosalina has janky enough hitboxes on her aerials that fit almost perfectly in all the places ROB can not defend at all in the air. U-air chains are REAL vs. ROB. Not to mention, stage control with Luma will make landing (a task already super hard for ROB) significantly harder. This becomes increasingly true on a smaller stage (think BF... where Luma can police the one platform, Rosa can chill out underneath the other. If ROB tries to land on the top he is at risk of U-air, tries to fall through top platform and Rosa can call Luma back and hit him as he drops, and if he tries to land above the by-herself-Rosalina... she has plenty of options to harass or keep him in the air long enough to put herself in a favorable position).
Yes, ROB can remove Luma somewhat easily... but I feel that in many ways this is a moot point. People think Rosalina is TRASH w/o Luma... which is not the case. She loses many of her solid KO options, but even w/o Luma, Rosalina has decent enough aerial options that can be set up out of dash attack or grab, due to the size & shape of her hitboxes to throw plenty of damage in the event ROB gets sent airborne for any reason... usually keeping ROB in a string + resetting to neutral taking long enough for Luma to respawn.
Sure, ROB can KO her rather easily with a U-throw or U-smash. I rarely see U-smash hit on a consistent basis without a medium-hard read (unless you have something like a slip gyro custom that can set up for it).
But, if Luma is around getting this grab becomes a LOT harder if Rosa is highly aware, comfortable with using Luma on their own, and has good reaction time (as the Luma attack will break the grab). When Luma is gone, odds are Rosa will just be running away via rolls, jumps, and even up+b's which make landing that grab hard as well.
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TL;DR
Villager is an amazing pick vs. ROB.
Mario and Kirby are solid as well.
People are silly about Rosalina, she is a decently solid pick as well as long as you have a firm understanding and control of a launched Luma.