How does it handle moves where pieces might accidentally hit each other like https://en.wikipedia.org/wiki/Castling and knight moves?
It's in here, but not for the faint-hearted: https://github.com/jes/autopatzer/blob/master/mojo/lib/Autop...
I did try giving it an accurate model of the acceleration curve of the stepper motors, so that it would do the set of moves that actually took the least time, but that led to strange motions where it would deliberately move pieces too far, and then back again at a diagonal, just to minimise the number of corners it needs to turn, so I instead just made it do a simple shortest-path, because it looks more natural to a human observer.
I.e. instead of going 2 squares right, then 2 squares up, then 1 square diagonal up-left, it would prefer to go 4 squares right, then 3 squares diagonal up-left. It takes less time, but looks stupid.
The problem I faced was that when I had magnets that were strong enough to be reliably grabbed by the electromagnet, they were strong enough to repel each other if they got too close! I went through quite a large selection of different magnet sizes before I settled on the final one (which is 6mm diameter, 6mm tall, neodymium cylinders). They're strong enough to be grabbed by the electromagnet, and weak enough that 2 pieces can be in the centre of a square and a corner of the square without moving apart, but unfortunately still not weak enough that a piece can slide in a straight line past another piece.
When there is a piece in the way, it works out whether it would be shorter to move a piece out of the way, or to route the long way around, and picks whichever is shorter.