Quote
nicholas.seward
Also noteworthy, I am unaware of any firmware that tries to keep discontinuities out of the acceleration graph. In fact, the graph would usually be a bunch of discontinuous horizontal lines. I wonder how useful it would be to smooth this out. It is worth an experiment.
I have been experimenting with this recently based on this paper I ran across:
Exponential Trajectory Generation for Point to Point Motions
It presents a velocity planning formula which is designed to offer continuous jerk as well as acceleration. I've done quite a few mathematical models with it now, and it looks quite promising. I'm getting closer to implementing it in firmware using a simple linear approximation of the normalized velocity curve. I don't have any real-world results with it yet, but I'm happy to share when I do.