mathematics - Swapping knights

On a $3\times3$ grid we have:

with $8$ moves needed to swap the red and blue knights.

What is the minimum numbers of moves to swap the knights on a $4\times4$ grid?

Answer

It will take:

20 moves to swap the knights

This can be done as follows:

All credit goes to @klm123 for demonstrating a good way to visualize this in a similar puzzle.