Mathematicians have proven that there are true statements that can not be concluded to be true by following a set of rules or axioms.
Turing machine based robots will get stuck until the end of time stuck in infinite loops that humans are able to easily step out of. This is one of the requirements for understanding, so examples of robots aren’t very illuminating.
There are ways to detect that to an extent and abort in machine systems, and for humans you can see kind of analogous attacks against the immune system (it gets really, really crazy in there, real arms race stuff), but in general why do you expect humans to be specially invulnerable to Godel attacks? To the extent they're hard to attack, it's because they don't actually execute math.
Turing machine based robots will get stuck until the end of time stuck in infinite loops that humans are able to easily step out of. This is one of the requirements for understanding, so examples of robots aren’t very illuminating.