Best posts made by Larzarus

So, FWIW, I'll throw in my two cents. Three years ago I did some experiments with implementing s-curve / sinusoidal jerk in a Marlin based firmware (UM2) (I used a lookup table instead of calculating it). Let's see how much I remember...

I found it did not really improve print quality, at least not in any way I could see with the naked eye. But it did allow for faster usable movement without shaking the machine or wild oscillations. Especially non-printing moves, as my printer is mostly limited in printing speed by the extruder design. I was printing with good quality at 120mm/s, infill at 250mm/s, and non-printing moves in the 450-550mm/s range. Those are max speeds, but net average speed was within 80-90% of the max speed (depending on segment length mostly). I put up some videos (and a link to the code) here: https://www.youtube.com/watch?v=D9tGB-FtyJQ and a high speed non-printing movement / wobble test here https://www.youtube.com/watch?v=-L8scUiasVg (without S-curve, it was much more violent and that pen would fall over at less than half the max speed)

The main benefit of s-curves was I could use much much higher acceleration values. In theory I could get to those same speeds without s-curve, but I would have to keep the acceleration values low to prevent the machine shaking itself apart when it changed direction... but a high max speed with low acceleration doesn't help because the head would only reach those speeds on very long movement segments. The improvement to acceleration is what made those speeds achievable / beneficial, even on shorter movement segments.

550mm/s was pretty much the upper limit of my machine's design (belts, motor current, the rate at which the CPU could generate pulses, etc). Even then I had to make some dynamics optimizations to the Marlin movement stepper pulse generator code to move at that speed. But it would very very rarely skip steps. Like maybe once every couple hours; enough to mess up a print (it was an issue with the i2c comm interrupt blocking the stepper movement interrupts). Ultimately I think it came down to pushing hard against the limits of that 8 bit CPU. If I limited the speed to under 300mm/s, it was pretty rock solid.

I gave up on further code development when I switched to the Duet Wifi from the AVR based UM2 motherboard.

It's been three years since I did this code, so I've forgotten many of the implementation details, and I do not have the desire to debate. I am relaying my personal experience implementing this on a real world printer, with real world testing. I found the s-curve was well worthwhile in reducing oscillations, violence, noise, etc. and far less computational taxing than true 5-6th order calculations. I agree it should be optional.

I'll add that since I switched the the Duet and no longer use s-curve motion, I don't really miss it that much. Yes, it allowed faster net printing, but I'm still extruder-limited most of the time anyway.

@carlosspr Take a look at this article: https://pdfs.semanticscholar.org/6539/02c3dbd1aa7afe4d5f3538524de149d4ecb2.pdf It explains how to achieve the desired 0 jerk / 0 accel at the crossover points. It's also got some empirical data on resulting forces and movement execution time, showing the benefit in quantifiable terms. It's worth the read.

@dc42 said in 6th-order jerk-controlled motion planning:
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So at present I favour traditional S-curve motion (3rd order motion profile). See https://pdfs.semanticscholar.org/a229/fdba63d8d68abd09f70604d56cc07ee50f7d.pdf. But before I make a decision, is anyone reading this thread aware of any evidence that higher order motion profiles are advantageous?

@dc42 I'm gonna throw in this quote from the paper I linked to:

...the trigonometric S-curve trajectory is:
• simple as 3rd order polynomial model and
• capable of producing smooth trajectory as good as 5th order polynomial S-curves and quintic splines

That's what drew me to this solution in my testing -- a close approximation of 5th order with only 3rd order effort, by replacing this angular jerk curve:

with a sinusoidal jerk curve -- I mean look at it, it's beggin' for it! If you're considering limiting the implementation to 3rd order to keep it simple / maintain performance, this may be something easy and worth adding?

Honestly, anything that get us away from instantaneous jerk is going to be the largest single improvement (even the simplest 3rd order will help).

Beyond that, the debate over what's the best way to shape higher orders (splines, trig, polynomials, etc) can go on forever, and no answer will please everyone. I don't know how reasonable it is, as this is deeply tied into everything motion planning, but maybe consider if it's possible to encapsulate that shaping math enough that others can plug in their favorite method? You know, to get people off your back.