I haven't dug into any of your code or (potential) documentation. In the quadrotor world a common approach is to do minimum-snap trajectories. That derivation shakes out from the fact that the aircraft itself has non-holonomic constraints: you can control force in the local Z axis (accelerating or decelerating all four motors simultaneously), and can control attitude (roll/pitch/yaw) by accelerating a pair of motors and decelerating the other pair of motors. When you go all the way down through the derivation you eventually can show that a minimum-snap trajectory results in smooth torque (aka current) commands for the motors themselves.

Is your 5th-order model derived from something like that? Or was it more of a "everything is really smooth if we have bounded crackle" kind of situation? Either way I'm really happy to see higher-order motion control coming to open-source firmware like this that doesn't require a host like Klipper does.

Thanks! Is the 6th derivative called a pop? XP

Edit: yes, apparently it is :D

After that it goes drop, lock, slam, thump

Wow - i didn’t know that the 5th derivative was covered. Is it standard in electronic devices these days ?

There are motion planners for six axis arms that go up to 11th order.