As in - "call a student up to the front of the class"?
If 'yes', then my first guess is that "up" is conveying physical movement - its literal meaning. "up" as in in the sky. I could be wrong however... I'm quite tired :-) But I don't think it's "completion", nor "inception".
an idiomatic phrasal verb, with the meaning relying on the literal "space" meaning of "on". Maybe to explain: your call for somebody lands on a student.