“Private” isn’t describing the spacecraft per se, but the ownership of the spacecraft. “Privately-owned robotic spacecraft” is the “full” phrase, of which we elide part of the adjective.[0] Here, “privately-owned” is ORIGIN in that list, which puts it before TYPE.

[0] “Privately owned”, while on its own an adverb and verb, is functioning as a singular adjective in the larger phrase.

Edit: Previously said “funded”, not “owned”