# Moving Sofa Problem with the help of 'Potential Field Method' and 'Navigation Functions'

I would like to move a piano. Having a mathematical background, I was trying to figure out whether I can get it into the new apartment. In my research I stumbled upon the already explored "moving sofa problem" as illustrated below:

Now, my question is:

Is there a computational model that is able (or at least tries) to find solution for this problem for any (or at least some) arbitrary shape? By solution I mean a path along the object can be moved that brings it around the corner.

I stumbled on some interesting concepts in motion planing. Most importantly on: "Potential field method" in motion control and navigation functions

Now to my two new subquestions:

• Exists a publicly available "Potential field model" for arbitrary movable object shapes, or something similiar?
• Is there a method that lets me construct an (optimal) navigation function if I know the potential field and the shape of the movable object?

Keep in mind that my special interest is in cases where there is almost no "free space". Hence, where it is hard to move it around the corner.

Thank you!