Robert is Billy's son. He is a wild kid in high school, but then he joins the Marines and straightens out. In 1968 Robert is deployed in Vietnam, but he flies home when he receives the news of Billy's plane crash and Valencia's death by carbon monoxide.
Robert doesn't have much of a character. Billy even thinks to himself that he doesn't really know Robert... if there even is much to know (8.20.2). The most significant thing about Robert is that he is a Green Beret in the Marine Corps (made famous, in part, by the movie The Green Berets starring the John Wayne that Mary O'Hare is so concerned about). Robert seems to fit that perfect army profile the way Billy didn't: a rough kid who makes good serving in the military.
At the same time, there is a weird disconnect between the generations. Even though Billy has been totally screwed up by his war experiences, he's happy that his own son is in the army.
This is one point where Billy and the narrator really differ. The narrator tells his sons that they are "under no circumstances to take part in massacres, and that news of massacres of enemies is not to fill them with satisfaction or glee" (1.16.1). Even though war has thoroughly messed Billy up, he isn't assertive or reflective enough to condemn it, or to dissuade his own son from involvement in a war that, by 1969, had come under criticism for its huge number of civilian deaths.