CONTROL OF 3 SERVOMOTORS KINETIX TO FILL AREA

[KarajoSoft]

It's good to do research, as we all do, but best of luck!

The mechanical engineering could be better suited for the controls task at hand, but it's a retrofit of a manual operation, so you have to deal with that.

You should probably Engineer a new system that covers everything.

You may need to think about this for a bit.

My comment is that Magna is ruthless towards OEM's if they can't deliver. And you, being a contractor for the OEM... If **** hits the fan, you are SOL.

That's really the gist of my comments.

Dear Padees,

you are talking without knowing, just guessing. we are directed involved with Magna (the maximum responsible of the corporative group) and their engineering team (mechanical) and all departments. We are not trying to do anything wrong. It is not retroofit is a new machine, just wanna learn more about kinematics and we are goin to achieve with specialist guys.

Asking in forum to get some more knowledge is always welcome, we are in many forums (helping a lot) and normally we find nice and polite colleagues that try to help not try to guessing who is that colleague, which kind of relation or contract has with his client and so on so so on.

We are quiet, professionaly and just trying to learn from the best to be able to develop this projects and many many others in the way.

best regards,

 

[padees]

Like I said, Best of luck!

 

[KarajoSoft]

Like I said, Best of luck!

thank you and same for you

 

[Peter Nachtwey]

dear Peter,

thank you for your comments and help. Honestly this level of knowledge is out of my range currently. First time i hear "jacobians" hehe.

about solution of 2 links, can i use "SCARA INDEPENDENT" motion planner directly? Can you advise please?

about third link i see that is super complicated and maybe here the solution is putting a robot instead machine controled by servos. According your experiencie what do you recommend?

EDIT: is it possible to share your example with 2 links?

many many thanks!

I have an example but I did it for myself. I worked through a few iterations to make sure my positions, and velocities calculated using a Jacobian matched the perfect solution. There are not enough comments to begin to explain Jacobian and how to use it. I have provided a link. Go down to example one

Jacobian matrix and determinant - Wikipedia

en.wikipedia.org

The link explains what a Jacobian is but not really how to use it.

Basically, you need to know how the angle need to change as a function of the end effector's rate of change. To move the end effector around the area you need to generate a path which could be a curve or series of points for the end effect-or to move through. A rate needs to be specified that also determines the rate of change of the x and y position. So far this is the job of what I call the target generator. The there will be a set of equations for each cell of the Jacobian that must be updated every iteration and then the Jacobian is used to calculate the rate of change in the angles alpha and beta so x and y change at the desired rate of change.

Jacobians are used not only for computing motion for robots, they are use to minimize cost function. This is used in auto tuning algorithms and optimizing neural net weights. The auto tuning software in our RMCTools uses the Levenberg-Marquardt alorithm and that uses Jacibians to find how to modify parameters that minize a sum of squared error

Again, if there are perfect solutions for only two links and Jacobians are not necessary. Scara type robots are relatively easy. Robots wih more links need to use Jacobians. Some even use Hessians which are the second derivatives. I personally know the math and because my target generator generates positions, velocity and accelerations, I would use the Hessians and the target acccelerations to.

Hessian Matrix | Brilliant Math & Science Wiki

The Hessian Matrix is a square matrix of second ordered partial derivatives of a scalar function. It is of immense use in linear algebra as well as for determining points of local maxima or minima. The above Hessian is of the the function ...

brilliant.org

My advice is to stick to only two links unless you want to learn a lot of math.

I deal with gradients and Jcobians all the time. I can easily generate these using a symbolic math package such as wxMaxima, Mathematica, Mathcad, Octave and Maple.

 

[KarajoSoft]

I have an example but I did it for myself. I worked through a few iterations to make sure my positions, and velocities calculated using a Jacobian matched the perfect solution. There are not enough comments to begin to explain Jacobian and how to use it. I have provided a link. Go down to example one

Jacobian matrix and determinant - Wikipedia

en.wikipedia.org

The link explains what a Jacobian is but not really how to use it.

Basically, you need to know how the angle need to change as a function of the end effector's rate of change. To move the end effector around the area you need to generate a path which could be a curve or series of points for the end effect-or to move through. A rate needs to be specified that also determines the rate of change of the x and y position. So far this is the job of what I call the target generator. The there will be a set of equations for each cell of the Jacobian that must be updated every iteration and then the Jacobian is used to calculate the rate of change in the angles alpha and beta so x and y change at the desired rate of change.

Jacobians are used not only for computing motion for robots, they are use to minimize cost function. This is used in auto tuning algorithms and optimizing neural net weights. The auto tuning software in our RMCTools uses the Levenberg-Marquardt alorithm and that uses Jacibians to find how to modify parameters that minize a sum of squared error

Again, if there are perfect solutions for only two links and Jacobians are not necessary. Scara type robots are relatively easy. Robots wih more links need to use Jacobians. Some even use Hessians which are the second derivatives. I personally know the math and because my target generator generates positions, velocity and accelerations, I would use the Hessians and the target acccelerations to.

Hessian Matrix | Brilliant Math & Science Wiki

The Hessian Matrix is a square matrix of second ordered partial derivatives of a scalar function. It is of immense use in linear algebra as well as for determining points of local maxima or minima. The above Hessian is of the the function ...

brilliant.org

My advice is to stick to only two links unless you want to learn a lot of math.

I deal with gradients and Jcobians all the time. I can easily generate these using a symbolic math package such as wxMaxima, Mathematica, Mathcad, Octave and Maple.

Dear Peter,

thank you so much to share your expertise which looks quite wide and deep in maths. I'm wondering all that motion controll and jacobians calculation are done by Rockwell CPU? AB CPU's support this kind of computation? Just for curiosity. Tomorrow we will meet a motion specialist guy and see what we can do with 3 links option, Many thanks!

 

[Peter Nachtwey]

I'm wondering all that motion controll and jacobians calculation are done by Rockwell CPU?

The Rockwell Controller can probably do the computations for a Scara or two link robot.
There are "perfect" solutions ( mathematical formulas ) for the two link robots.
These don't require calculating Jacobians since the formulas can be differentiated.
I want to emphasize that going to 3 links is MUCH MORE DIFFICULT.
There is no formula for the 3 link robot. The calculations must be done iteratively using Jacobians. I doubt the Rockwell Controller does this as the calculations are very complex and CPU intensive.

This project was done by forum member rwatson. At the time he worked for a company called Clansman in Scotland.
It is a grinding applications. The robot arm is much more complex. It touches the metal work piece in 3 places to get 3 x,y,z points. This defines a plane.
The grinder can not grind below the plane.
After that the robot is in auto mode and robot grinds the pour spot flat.
Touching the metal in 3 places also lets the robot compensate for the changing diameter of the grinding wheel.

RWatson did all the math himself on a RMC150.

https://deltamotion.com/peter/Videos/Clansman%20App%20-%20Light%20Bkgd.mp4

This is the robot in action.

https://deltamotion.com/peter/Videos/Grinding%20Arm.mp4

I am retired now but I was president and head engineer of Delta Motion.
I wrote firmware for the motion controllers.

Delta Motion

deltamotion.com

 

[KarajoSoft]

The Rockwell Controller can probably do the computations for a Scara or two link robot.
There are "perfect" solutions ( mathematical formulas ) for the two link robots.
These don't require calculating Jacobians since the formulas can be differentiated.
I want to emphasize that going to 3 links is MUCH MORE DIFFICULT.
There is no formula for the 3 link robot. The calculations must be done iteratively using Jacobians. I doubt the Rockwell Controller does this as the calculations are very complex and CPU intensive.

This project was done by forum member rwatson. At the time he worked for a company called Clansman in Scotland.
It is a grinding applications. The robot arm is much more complex.

I am retired now but I was president and head engineer of Delta Motion.
I wrote firmware for the motion controllers.

Delta Motion

deltamotion.com

Dear Peter,

i've appreciate your time to share your deep knowledge even been retired, thank you so much. Tomorrow we are going deeper, as you mentioned 2 links seems reachable and 3 links we will see how we can do it.

Many many thanks and wish you long and joyful retirement

 

[Ken Roach]

I can think of a handful of ways to try to accomplish this kind of project with the 2-link SCARA that I know ControlLogix can do, maybe by executing a transform after moving the main boom a fixed distance then performing the fill-in within the work envelope of the last 2 links. But I don't think that ControlLogix does 3-link SCARA natively.

I know there are other platforms that do; CoDeSys SoftMotion can do 2-link or 3-link SCARA planar manipulators; there's a nice visual demonstration of the Rexroth controller making moves like that on YouTube: ctrlX CORE – CODESYS SoftMotion – SCARA robot kinematics

 

[KarajoSoft]

I can think of a handful of ways to try to accomplish this kind of project with the 2-link SCARA that I know ControlLogix can do, maybe by executing a transform after moving the main boom a fixed distance then performing the fill-in within the work envelope of the last 2 links. But I don't think that ControlLogix does 3-link SCARA natively.

I know there are other platforms that do; CoDeSys SoftMotion can do 2-link or 3-link SCARA planar manipulators; there's a nice visual demonstration of the Rexroth controller making moves like that on YouTube: ctrlX CORE – CODESYS SoftMotion – SCARA robot kinematics

thanks Ken,

i will check first 2 link from motion planer from contrologix and see how we can adapt to my only movements XY since that predefined has another movement Z.

we will back to here once i get the solution or final decision from specialists guys.

thanks again for all the comments and suggestions, helped me a lot to be abble to argue and understand what specialist guy will teu us.

thanks!