Many older square dance calls use the language "Sashay round your corner, Sashay round your own." It is kind of a Dosido movement, but sometimes shoulders vary.
In Modern Western Square Dance, a move similar to 1/2 of a Mad Robil is called a Half Sashay. If you do a half Sashay twice, it is a Mad Robin.
In the contra application, you could call, Sashay round your partner, or Sashay round your Neighbor, and this terminology would be consistent with both older square dance and MWSD. Since the Sashay movement is a sideways slide, Sashay Round would be a slide around the appropriate dancer, whereas Sashay Down, would mean down the set.
Rich Sbardella
Stafford Springs, CT