Doors – improvise to slowly close a door

I am going to make the assumption that this condition has developed over time, rather than been this way since built. I am also assuming you meant an interior door, not an exterior door, since it is to a laundry area, not an entry door.

The easy answer would be to trim the door to fit better. But before we go that route, let's try to determine why the door has sagged. Open the door half way, stand in front of the handle edge, grab the knobs on both sides and try to lift the door. Is there any give? If you are able to lift the door, which would effectively close the gap you described in your question, then we have a hinge or frame issue. If you are able to lift the door to a point where the door would close properly and notice any give to the frame, here is a fix. Remove the center screw from the jam side of the top hinge. Use a 3 to 4 inch screw of similar finish to replace the one removed. This screw should reach the jack stud and can be used to move the top of the door frame closer to the jack stud, evening out the gap on the top of the door. Adjust this screw until you get the proper fit.

If the above mentioned technique doesn't work in your case, then trimming the door may be necessary. If so, carefully measure how much needs to be trimmed off, scribe a straight line on both sides of the door. Remove the door, secure it on it's side (just so it is easier to reach and work on,) and use a belt sander, plane, or DA sander to remove material just up to the scribed line. This will give you a nice straight edge. Re-hang your door and enjoy!

The best approach would be gravity self closing hinges such as these

These are designed to close the door, regardless of the angle of position.

What you need is the same type of device, but one where the high point of the lower section is at the midpoint of the swing. On one side of the midpoint, the door would swing in, on the other swing out.

As far as I know, no such versions are commercially avaialble. If you are handy and have the tools, you could gring the adjoining faces of such hinges down to create the right "tip point". Note that the door needs to rise and fall a small amount to make this happen.