Trajectory Planner using Ruckig Lib

One possibility that comes to mind is to
1. smooth the tool position trajectory (ie XYZ) as Grotius has been doing
2. create a second 3d trajectory that is offset from the tool position trajectory by a fixed distance along the tool orientation vector
3. smooth this second trajectory using the same method as in step 1
4. calculate the smoothed tool orientation vectors
5. calculate the smoothed orientation angles (ABC) from the smoothed tool orientation vectors.


I found a paper that may describe the method above but I do not have access to the full text:
www.researchgate.net/figure/3D-clothoid-...ector_fig3_361356637

@Automata,

Nice document.
There is a video link from andy, in the video they show curvature.

@Arciera,
I think also a graphical representation of the abc optimalistion will be much easyer to do. For sure in opencascade.
If i draw the tool orientation vector lenght:10mm at each gcode line. Or at each known position.

Then i connect these tool orientation's at the top with a poly line.
Then create fillets inbetween the polylines? Then set tool orientation vector to touch the fillets?

Maybe a scetch would help to verify the steps.
 

If i draw the tool orientation vector lenght:10mm at each gcode line. Or at each known position.

Then i connect these tool orientation's at the top with a poly line.
Then create fillets inbetween the polylines? Then set tool orientation vector to touch the fillets?

Yes, that is what I'm thinking.

This image is from the preview of the paper linked above. The tool position is the curve in red and the tool orientation is the curve in blue. The blue curve would be the G2 continuous representation of the polyline that connects the green dots marked 'Knot of TA'.

 

Mind you, I have not really thought about what a particular machine's kinematic restriction will mean when using this approach. If we have a machine with only an A-rotary then we may not be able to orient the physical tool to the calculated (smoothed) 3D angles (ABC).

Hi Arciera,

I'm still a little confused how to solve this 5 axis geometry. Especially caluclating the inbetween TA knots.

If knot Tcp.0 to Tcp.1 = 100mm.
if knot Ta.0 to Ta.1 = 150mm.
Then tcp 50% = 50mm, then ta=75mm? This should be the interpolation.

Should it be like above?

For only "a" axis, i think just interpolate this. And make it a master move when "a" axis need more time then xyz.

For halcore the progress is running a program with scurve now.
It can start from line, motion fwd, motion reverse. It has a scope for the trajectory planner.

I'm still a little confused how to solve this 5 axis geometry. Especially caluclating the inbetween TA knots.

say we have a gcode line:

G1 X1 Y2 Z3 A10 C20

for the end of each segment we have the toolposition (TCP knot in XYZ coordinates) and the tool orientation vector (using the A and C angles in this example or by whatever angle(s) the kinematic for the particular machine uses eg A, AB, BC ..)
The corresponding TA knot is offset from the TCP knot by a fixed distance (say 10mm) along the tool orientation vector.

This is another image from the link:
 

The current tool position XYZ (ie the TCP knot) is at the center of the sphere.
The current  tool orientation  (black arrow)  is defined by angles 'A' and 'C' in red (ie this would be an XYZAC kinematic), the vector points to the corresponding TA knot (green dot, here called 'TO' knot) a certain fixed distance away.

The other two green dots would represent the previous and the next TA/TO knot for the previous and the next TCP knots.