Trajectory Planner using Ruckig Lib

I'm not sure this is entirely true.
Both fanuc and siemens fit splines for high speed motion. We definitely don't need the g code to describe a spline, but it does often get used under the hood to help describe all the pointes BETWEEN your g1 end points.

Hi Arciera,

I'm afraid I can't help you with implementing the linked 3d clothoid algorithm.
I have used chat_pdf ai yesterday. This works quite good, but stops and ask's money.
However i don't understand in the page at section (23)

There is a text :
i=1,2;
for j=0,1,2,3,4 are the knots of the spline, this i understand. But do you get what i does?
Thanks.

@IhaveNoFish,
get used under the hood
Indeed.
 

Both fanuc and siemens fit splines for high speed motion

Yes. What I meant is that nobody uses splines in the Gcode they load into the controller and thus the spline-related Gcodes implemented in LinuxCNC (ie G5, G5.1, G5.2, G5.3) have really been a solution looking for a problem. That is why I say that they are pretty much useless, _unless_ the can be repurposed for something new like internal path blending.

There is a text :
i=1,2;
for j=0,1,2,3,4 are the knots of the spline, this i understand. But do you get what i does?

I haven't really looked at the paper closely but here is what I think:
If you look at formula (14) you see that the 3d clothoid has two sets (i=1,2) of four parameters (theta, kappa, c , gamma). So 'i' stands for which set of parameters we are looking at.

Hi Arciera,

This is one of the first formula's to actually solve the clothoid spline.

It looks like 1.0 is for z trajects. Then the zero is knot zero. Begin of spline.
It looks like 2.0 is for xy trajects.

It looks like 1.4 is for z trajects. Then the 4 is knot four. End of spline.
It looks like 2.4 is for xy trajects.

Then you can say i=1, j=2. You have a set for z values, and a set for xy values. Because curvature is not only
on xy plane but also in xz plane.

 

I still don't fully understand the first formula, the short one at the top.
I think its calculating the "angle start" parameter for the z component.

It looks like 1.0 is for z trajects. Then the zero is knot zero. Begin of spline.
It looks like 2.0 is for xy trajects.

It looks like 1.4 is for z trajects. Then the 4 is knot four. End of spline.
It looks like 2.4 is for xy trajects.

Yes, that is how I understand it.

Then you can say i=1, j=2. You have a set for z values, and a set for xy values. Because curvature is not only on xy plane but also in xz plane.

I would say
i=1 is the parameter set for the xz-plane
i=2 is the parameter set for the xy-plane

As for the actual formula I'll need to have a look tomorrow as I have run out of time for today.
Overall the paper seems like quite a thorough step by step presentation of the method which makes me feel somewhat optimistic.