Robotic kinematics

JoergS5

@jtimon if you need help to understand firmware or how to address additional axes, I can help you, I have some experience now. I've created some documents about robot, starting is at https://docs.duet3d.com/User_manual/Machine_configuration/Configuring_RepRapFirmware_for_a_Robot_printer and made a tag "robot". The documents firmware and CNC 5 axis may be interesting for you about orientation.

I am constantly updating the documentation pages, when I think I have new knowledge to add.

Hangprinter may be a closed chain system, then robot kinematics will not help you much. You can check FiveBarScara, which is in the official RRF and uses closed kinematics, for additional code. I've used circle intersection in this kinematics to calculate the position of two arms without knowing the angles, this may help with wire based kinematics. Because you know the arm length (wire length), but not the angles.

JoergS5

@jtimon said in Robotic kinematics:

Wall painting seems like a cool use case.
There are plenty of small projects doing

Thank you for the links. I meant wall painting: a house wall, to save house scaffolding. But I will start in the house, a single wall. After all, most of the work is in the little nooks and crannies. These exceptions and path planning could be programmed and then executed with G-Code. A camera can control the result and repaint the locations where it is not good enough. Maybe spraying is better than painting then (a fixed orientation endpoint).

I first thought about using an industrial robot for wall painting, but long arms are a problem for high payload. But maybe one can combine hangprinter with robot: robot for orientation and placing to the correct location, hangprinter to support payload. It will be necessary to paint around corners.

JoergS5

I have a problem with understanding CNC 5 axis. If someone here has knowledge of CNC 5 axis, could you please tell me whether my understanding is correct? This is also valid for CoreXY 5 axis, Pentarod and Open5x.

I've described it in
https://docs.duet3d.com/en/User_manual/Machine_configuration/robot_5_axis_CNC
second section called "Calculation".

My main confusion was reading an article about G-Code based on IJK (using tool vectors in G-Code) versus AC. The article wrote, an advantage of IJK is the machine independence. But in my understanding, AC is also machine independent (with the exception of the axis direction of AC versus BC). If someone knows if this is correct, a confirmation would be very kind.

wieman01

Hello,

Is there a list of compatible robots somewhere on docs.duet.com? I searched but could not find anything...

Just curious what Duet will be capable of with the upcoming release (3.5).

wieman01

JoergS5

@wieman01 tested will be:

6 axis industrial robot
CNC 5 axis including CoreXY 5 axis
4 axis palletized robot

Documentation starting point is https://docs.duet3d.com/User_manual/Machine_configuration/Configuring_RepRapFirmware_for_a_Robot_printer and by the robot tag there are specialized documents for the specific types.

Other serial chain types are possible by configuring Denavit-Hartenberg parameters. With this concept, prismatic/linear and rotary axes can be combined in any combination, as long as they are in series. The current limit is 7 axes, but this is just a fixed variable.

wieman01

@joergs5 said in Robotic kinematics:

@wieman01 tested will be:

6 axis industrial robot
CNC 5 axis including CoreXY 5 axis
4 axis palletized robot

Documentation starting point is https://docs.duet3d.com/User_manual/Machine_configuration/Configuring_RepRapFirmware_for_a_Robot_printer and by the robot tag there are specialized documents for the specific types.

Other serial chain types are possible by configuring Denavit-Hartenberg parameters. With this concept, prismatic/linear and rotary axes can be combined in any combination, as long as they are in series. The current limit is 7 axes, but this is just a fixed variable.

Thank you, @JoergS5. So the supported hardware isn't restricted to certain manufacturers, but to the design of the robot. That makes sense. I'll look into it. And really big thanks for your contribution here!

JoergS5

@wieman01 your're welcome. Don't hesitate to post your hardware setup here to discuss how to configure it, if you need help. I'll try to offer as much example configs and explanations as possible, but some questions may remain unanswered.

JoergS5

I am starting a new topic now in the "My Duet controlled machine" to apply the robot kinematics to robot prototypes of different kinds. You're invited to join the process of building:

CNC 5 axis for abrasive drilling (with iHSV servos and 6XD) and CoreXYAC 5 axis for additive 3D printing
4 axis palletized for 3D printing (only for proof of firmware working)
6 axis industrial robot (later)

The next steps are:

prototypes and verify robot kinematics in real life
improve RobotViewer DWC plugin
find or develop a free software solution to create 5 axis G-Code

I will concentrate on CNC. Some users plan to create CoreXY 5 axis printing, so for 3D printing, the 3D printer prototypes are mainly meant to help solving problems.

DerAndere

@JoergS5 Re: "My main confusion was reading an article about G-Code based on IJK (using tool vectors in G-Code) versus AC. The article wrote, an advantage of IJK is the machine independence. But in my understanding, AC is also machine independent (with the exception of the axis direction of AC versus BC). If someone knows if this is correct, a confirmation would be very kind."

Answer:
AFAIK, there is no international standard beyond 3 axis CNC G-code (ANSI/EIA RS-274D, ISO 6983-1:2009)

XYZIJK notation is usually not interpreted by the CNC controller. It is usually used in an intermediate format of the CAM software. A post processor is used to convert it to the correct NC language for the selected machine.

There are two ways how G-code axis codes XYZABC can be interpreted.
a) direct joint control: each G-code axis is directly mapped to one joint/motor and controls only its position.
b) Tool center point control (TCPC): inverse kinematics are applied so that other joints compensate changes in the commanded position of the rotational axes.This way, G-code axes XYZ control the tool center point (TCP) position and axes ABC control the tool angle/orientation.

LinuxCNC is based on "NIST RS274NGC interpreter, Version 3". It cannot interpret the XYZIJK notation. LinuxCNC by default uses identity kinematics ("trivkins") which means direct joint control. it can (should) be configured to use kinetics that match the machine geometry, e.g. by adding this section in the config INI file:

[KINS]
KINEMATICS = xyzac-trt-kins

Then, at startup, it applies the correct inverse kinematics to allow TCPC. You can change to direct joint control mode at runtime using a combination of M66 and M68 commands.

For added confusion, LinuxCNC can be configured to start in direct joint control mode at startup:

[KINS]
KINEMATICS = xyzac-trt-kins sparm=identityfirst

Source: https://linuxcnc.org/docs/devel/html/motion/switchkins.html

Siemens Sinumeric controllers cannot interpret XYZIJK or XYZABC notation, only their own formats: https://www.manualslib.de/manual/134235/Siemens-Sinumerik-840Di.html?page=69#manual

Haas
direct joint control mode: G49 (default)
TCPC mode: G234
XYZIJK notation: no

Fanuc:
direct joint control mode: G49 (default)
TCPC mode: G43.4
XYZIJK notation: G43.5 (RTCP type II)

JoergS5

@DerAndere I wanted to use IJK, but then searched for alternatives, because IJ has a conflict with G2/G3 parameters. That's the reason why I changed to AC/BC and quaternions for full orientation. There is no G-Code standard for quaternions, so I use an artificial currently, until someone tells me which standard to use...

I am using the b) method which supports the RTCP mode mentioned and explained e.g. in the links (the beckhoff one gives the fastest overview):

https://www.cnclathing.com/guide/what-is-5-axis-cnc-machine-and-rtcp-function-advantages-of-5-axis-machining-cnclathing

https://www.cnczone.com/forums/uncategorised-cam-discussion/413638-cnc-mastercam.html

https://infosys.beckhoff.com/index.php?content=../content/1031/tccncprogramming/html/rotationtoolcenterpointrtcp.htm&id=

This method has the advantage that you can configure the robot to calibrate any inexactness of axes, e.g. between X and Y. The kinematics will calculate the true rotations and positions. The idea is to measure the endpoints and calculate back to the config parameters.

LinuxCNC is a great software and I'm taking it as reference sometimes how to propose parameters. It has however only experimental nurbs and bspline support, that's the next topic I want to address.

The Fanuc has IJK support, but they need to change modes before using it (probably because of the G2/G3 problem), so it's a proprietary solution. Fanuc has good manuals. I find only few information about 5 axis CNC, so it's a valuable additional information source.

JoergS5

The current status is that I changed internal calculations to skew symmetric matrices, but there were differences to the quaternion based calculations. The formulae in the internet are inexact (the rotation angle is set to 1), I've found the solution yesterday to get correct results now. Unfortunately from skew to rotation, there are also two solutions(!). As I said, orientations are a beast. I always use forward-inverse algorithms to calculate roundtrip calculation with random parameters. stackexchange and stackoverflow are very valuable information sources!

JoergS5

@DerAndere the different configurations of Haas and Fanuc shows imho that every manufacturer made his proprietary solution in the past. Worse, to get some advanced capabilities, one had to pay for those "options" additionally.
Some combinations were not possible, e.g. changing the tool length for Fanuc prohibited using some special modes afterwards. robot kinematics uses the G10 offset settting of the current tool, so tool change should be no problem.

The second problem is that there is no free software to support 5 axis. There are plugins in Blender and FreeCad, but to my knowledge not advanced ones. Currently I think, best would be to develop an own solution based on OpenNurbs, which is an open library developed by Rhino. Rhino itself is a bit expensive if one wants to use it noncommercial as hobby. (Hobby, non-commercial, being not a student => 1000$).

DerAndere

@JoergS5 List of open source CAM software for multi axis FDM (tool path- and G-code generators). I did not test them yet:

https://github.com/GuoxinFang/ReinforcedFDM (uses Rhino IIRC)
https://github.com/zhangty019/MultiAxis_3DP_MotionPlanning
https://github.com/Spiritdude/Slicer4RTN
https://xyzdims.com/vgcodectl/ : source code release planned

T3P3Tony

@DerAndere thanks for posting these here. two of them are @xyzdims work!
Also not sure if you saw but the zhangty019 work is been built on further:
https://dl.acm.org/doi/10.1145/3550454.3555516

DerAndere

@T3P3Tony Hi Tony! Thanks for the update. As a reminder for my future self, here is the source code related to the publication you mentioned: https://github.com/zhangty019/S3_DeformFDM

JoergS5

@DerAndere thanks for the links, I'll check them!

JoergS5

@T3P3Tony this is a very promising article and slicer.
robot kinematics is based on quaternions, this fits.

JoergS5

I rediscovered a book about screw theory (another name is: exponential coordinates), about robotics by Lynch/Park 2017. I had refused it, because the examples are without solutions (students shall not know the solutions if a teacher uses the tasks). But after review, the rest of the book is very good. I had problems understanding the book of Murray/Li/Sastry about the same topic. Both books together, all became much clearer.

Screw method is an alternative method to Denavit-Hartenberg and is faster than this method. I will change all internal methods to this new method, but let the configuration parameters at Denavit-Hartenberg as is. I will add an additional optional input method for screw parameters with the M669 R C parameter (S is unfortunately not free...).

Screw method allows more precalculation of the configuration values, so calculation of specific positions is faster. The whole is based on Rodrigues formula and the screws are very similar (and can be transferred to/from) quaternions.

The name screw comes from the similarity of a screw: each actuator's movement is described by a rotation and a translation, like a screw. Forces/torque calculations are also described with this method.

http://hades.mech.northwestern.edu/index.php/Modern_Robotics provides information about the Lynch/Park book. The free preprint version is there also as pdf.

Little update: the following books are about screw theory:

Lynch/Park 2017 as mentioned above
Murray/Li/Sastry
Peter Corke, Robotics, Vision and Control => Matlab extensions, visision analyzing code
Pardos-Gotor, Screw Theory for Robotics. An illustrated handbook. *)

*) there is a book of the same author named Screw Theory in Robotis, being more expensive. It seems to be similar (I don't know for sure).

I'll use the Corke book to extend the robot kinematics into two directions: improving path planning for smooth curvature (nurbs etc) and to improve quality by camera analysis with help of OpenCV.

Little update Jan 3:
I'll concentrate on implementing the closed form Paden-Kahan subproblems now, which allows direct algorithmic solutions instead of iterating. The subproblems are explained in the Pardos-Gotor book.

I've created a documentation page about screw theory now at https://docs.duet3d.com/en/User_manual/Machine_configuration/robot_screw_theory and will fill it with content.

Happy new year!

JoergS5

I'm currently converting the subproblem code from Matlab of Pador's book into C++ code for the firmware, with performance optimizing.

The results are very promising with respect to speed and quality (all solutions of inverse kinematics are provided), so I'll concentrate on screw theory now and will push back Denavit-Hartenberg (DH).

I'll remove documentation for DH next week and reorganize documentation, so if someone needs it, please back it up. I'll try to write a converter for DH->screw parameters, but this is low priority. The screw based setup is easier than DH parameters.

The first implemented robot types will be:

6 axis industrial robot
serial scara
CNC, CoreXY, Prusa like 5 axis

T3P3Tony

@JoergS5 said in Robotic kinematics:

remove documentation for DH next week

rather than removing it, could you update it to say tis not currently being used. You have put a lot of useful information in there, maybe some else will need to use DH in the future.