How to move a chair through a door

We define the door-width of a simple polygon (a 'chair') and give an O(n2) algorithm for computing its door-width. It is first shown that all passages of the chair through the door can be reduced to a sequence of certain elementary motions. We introduce the technique of constraint analysis in characterizing elementary motions. Our algorithm actually constructs a motion of the chair through a door, and thus is a 'local-expert' for planning motion through doors. Such algorithms have applications in more general motion-planning systems in robotics.