For starters, Robotech is actually three anime series from the early eighties. It includes Super Dimensional Fortress Macross, Super Dimensional Army of the Southern Cross, and Genesis Climber Mospeada. However, this page only deals with the Macross Saga portion of Robotech.
The story is like this: In the year 1999, as Earth fights the Global War (Shouldn't that be WWIII?), an alien starship crash lands on a deserted and fictional Pacific Ocean isle of Macross. Fearing an alien attack, the UN reforms itself and the war is stopped. For ten years, teams of scientists led by Emile Lang, worked to reverse engineer the ship's technology and to repair and refit the ship for human use. Then in 2009, the ship which had been named Super Dimensional Fortress One or SDF-1 for short was just about ready for launch when... The Zentraedi came! They came looking for the SDF-1 and were intent on getting it no matter what. This results in the first Robotech War. The battle for SDF-1!
In the episode, Force of Arms, Studio Nue gave everyone a sneak preview of the series they'd do after Macross by inserting the name sake of the new series in a shot as a destroid. The mecha in question is the Orguss. Name sake of the series, Super Dimension Century Orguss. The Orguss also supposedly makes an appearance in the episode, To The Stars, though, I haven't found it yet. Above is a picture of the Orguss' appearance in Force of Arms. The other picture is from the Orguss episode, Vanishing Point, and depicts the Orguss escaping a Dimensional Shift and clutching the little-girl-like Med Droid, Mome.