Robinson, 28, has been the Dons club captain for the past two seasons, skippering them to the Championship 1 league leader’s shield and Grand Final trophy in 2012.
Edwards, 26, has made 53 appearances since joining from Sheffield in 2010, and was previously at Castleford.
Dons player-coach Paul Cooke said: “Both Grant and Craig have played instrumental parts in the success that the club has enjoyed over the last couple of seasons and fully deserve their new contracts.
“They give their all when they put on a Dons shirt and have proved to be important and valued members of the squad.
“We have spoken about the importance of continuity and I believe we have this in abundance with so many of our players opting to stay at the club for at least another year.”
Cooke now has 14 players signed up for next season, which includes his only new face to date – centre Liam Welham, who joins from Hunslet.