Robert, the robot you keep breaking
On the Facility map you walk up to a robot named Robert. The game gives no hint about what he wants, and the most common forum question about him is some version of why he died when all you did was touch him. Players have worked out the basic choice, drawn below.
Two ways past Robert
Leaving him alone
One player spelled out the careful version: “Just walk on by, don’t click, don’t mouse over, don’t use a card on Robert.” Their result: “Then the next enemies are standard enemies.” (both in Steam discussion: Robert's family loves him) A Reddit reply in the Robert thread describes the same split between ignoring him and interacting.

That matters mostly when a run is fragile. If you are low on health heading into the Facility, skipping him keeps the next fight predictable. Players’ healing tips for the stretch between fights, including the vending machine, are in the Janitor guide.
Touching him
Any interaction seems to count. The same player, in another thread: “if you fiddle with him at all the “you gain knowledge” pop-up happens and you have to fight his friends.” (in Steam discussion: Card Unlocks?) A different player: “If you do interact, the next wave of enemies are “roberts family” instead of normal goo.” (in Steam discussion: Any insight into the robot you can interact with after camp in facility?)
People have tried to be gentle and failed. “No matter what I do it seems to kill him, not fix him??” asked one, adding “I’ve tried reveal and break on him and those both just trigger combat.” (both in Steam discussion: Love the game, hate the janitor) On Reddit the thread starter tried an ignite-and-reveal card with the same outcome, and another player reported that Robert then showed up in the next fight himself (reply). A player asking whether he can ever turn out well had tried reveal, which killed him and brought his family, and a reply added that feeding him makes his family angry too (both in Steam discussion: What does "There is more to be discovered here..." on an obstacle mean?). Break, reveal, fix and the rest of the explore verbs are explained in the beginner guide.
Everything players tried on him
Why break him on purpose
Cards. The clearest claim: “You unlock at least two packs of cards by interacting with Robert in different ways.” The same poster adds that “once you interact with him in a certain way, you don’t need to interact with him in the same way again.” (both in Steam discussion: Robert's family loves him) All of that comes from a single player, so treat it as unconfirmed. They repeat the idea in another thread: “If you check the Janitor unlocked cards, one of them is the card obtained from the Robert encounter.” (in Steam discussion: Card Unlocks?)
So a sensible pattern is to break him on healthy runs, trying a different kind of card each time, and walk past him when a run is on the edge. Where card unlocks show up for each character is on characters and unlocks, and the full pool is on the cards page.