Systems and methods for double shifter sorting

A method of sorting a vertically-stored stack of boxes, the method comprising:

• lifting a first box immediately above a target box from the stack of boxes using a first aperture of a lifting frame, the stack without the first box creating a first remaining stack, wherein the lifting frame has a contiguous border surrounding the first aperture and a second aperture, wherein the first aperture has a first aperture length and a first aperture width, wherein the second aperture has a second aperture length and a second aperture width, wherein the first aperture length is collinear with the second aperture length on the lifting frame, wherein the first aperture width is parallel to the second aperture width on the lifting frame, and wherein the first aperture and the second aperture move together;
• shifting the first remaining stack to below the second aperture of the lifting frame using a shuttle robot;
• lifting the target box from the first remaining stack using the second aperture, the first remaining stack without the target box creating a second remaining stack;
• shifting the second remaining stack to below the first aperture;
• releasing the first box onto the second remaining stack, the first box added to the second remaining stack creating a third remaining stack;
• shifting the third remaining stack to below the second aperture;
• and
• releasing the target box onto the third remaining stack, the target box added to the third remaining stack creating a sorted stack.