>> Trajectory control and lookahead seems to come up as a feature-request
>> periodically..
>
> The first page looks good...
>
> That does 'S' curve (Cubic) profiles which would improve accuracy for a given
> acceleration limit. S curves will reduce that last untunable following error
> spike at the beginning and end of a trapezoidal trajectory caused by a step
> function in the servo system force. Since S curves lower the high frequency
> components in the force input to the mechanics (Which is currently a step
> function as mentioned above), they also reduce exitation of mechanical
> resonances.

Yes, AFAIK LinuxCNC now uses "bang-bang" control on the acceleration
(acceleration vs. time looks like a square wave signal).
When acceleration switches on/off that curve obviously has infinite jerk.
This then leads to a trapezoidal velocity vs. time plot.

Most of the new papers are "jerk-limited" (ha ha), where the bang-bang
control is on jerk, the acceleration plot looks trapezoidal, and the
velocity plot is a smooth "S" (combination of parabolic arcs and
line-segments I guess).
I had matlab-code from a paper for a jerk-limited exact-stop
controller a few years ago. If someone has an application where
blending isn't required then this would work.

Modifying this exact-stop jerk-limited controller so each segment has
some pre-set start velocity vs, and end-velocity ve isn't too hard.
I think the novel thing in this paper is a feedrate-scheduling step
where suitable vs and ve are calculated for each move of the NC
program, given some the machine parameters and tolerance. Their
implementation (no code in the paper, and I doubt it is available on
request) is on a TI DSP chip, and they run it at a slowish T=4ms
period.

One really needs a machine with high feedrate and accelerations where
developing something new will make a difference in order to justify
spending time on this I think...

Anders

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