The first thing you can do to stabilize a multi-panel room divider is to make sure that it’s unfolded in such a way that its weight is distributed evenly across the panels. Rolling dividers can be locked into place. If your room divider is held together by hinges, check to see that they haven’t come loose from opening and closing the divider, and tighten as necessary. And to take things a step further you can add stabilizing brackets to the room divider base, or secure one side of the room divider itself to a wall stud with a hinge.