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ikine 4 DOF arm

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Rookie ( offline )
Posts: 23
Posted: 2008-11-01 16:19 
 Post subject: ikine 4 DOF arm
Hi all,

This topic is about anyone who is interested in inverse kinematics.
I always wanted to draw a straight line with my robot (linear motion).
I finally solved the inverse kinematics for this 4 DOF robot.
To test this linear motion I tried to draw a square.
You can see the result here:

http://cid-976b52dad42d0a1e.skydrive.li ... otics?uc=1

In this video you see that the lines are almost straight.
This difference is because that the SES arm is not a real robotic arm.
It is just a toy robot. But the mathematics are correct !

I also placed the solutions of the inverse kinematics in a PDF file.


Guru ( offline )
Posts: 2251
Posted: 2008-11-01 19:01 
 Post subject: Re: ikine 4 DOF arm
All I get with your avi files is sound and no video. Maybe youtube would be a better video site.


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Posted: 2008-11-03 10:28 
 Post subject: Re: ikine 4 DOF arm
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Posts: 9257
Posted: 2008-11-03 12:43 
 Post subject: Re: ikine 4 DOF arm
Nice videos! So the accuracy is not on par with light industrial robotic arms, but look at the repeatability! Awesome! 8)

_________________
Jim Frye, the Robot Guy
http://www.lynxmotion.com
I've always tried to do my best...


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Posts: 5
Posted: 2008-11-04 05:29 
 Post subject: Re: ikine 4 DOF arm
Nice work

On the left hand side of the front view you can see the limitations of the servo resolutions as you have a "saw tooth" line. If you could increase the servo angular resolutions then you should be able to get straighter lines.

What servos are you running in your arm?

Andy


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Posted: 2008-11-07 07:35 
 Post subject: Re: ikine 4 DOF arm
Hi Andy,

I also noticed this problem.
The servos that I used where the standard ones from Lynxmotion.
All the servo's are working on maximum resolution.

The problem here has to do with the base servo.
The base servo should have a much higher resolution than the other servo's.
What I mean here is higher resolution than 0.09 degrees/step (=180/2000 degrees/steps).

But maybe you are also right. The software range of the base servo is in [-90,90] degrees (res=0.09). So if I narrow this to [-45,45] you become a better resolution (res=0.045).
And for the square in this case, it should give a better result... 8)

On the other hand, the purpose is that you once set the range of all the servo's. Once this is done, you know the workspace of the robot. In this workspace the accuracy should be everywhere the same. :wink:


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Posts: 5
Posted: 2008-11-07 08:12 
 Post subject: Re: ikine 4 DOF arm
Just a few questions more :)

Do you control the servos from using positional control? As it looks like bigger than a 0.09 deg step although the further your arm operates from the base the wider this step is (arch opening up). How often are the commanded points on each line? Do you use just 4 points? as this may cause the step.

If you used velocity control instead you should be able to get smooth lines.

You may find this helpful next time you have to do lots of matrix multiplcations wxMaxima is a free symbolic maths tool. Once you'd set up your transformation matrices you can multiple them and it generates your result.

Andy


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Posted: 2008-11-07 11:27 
 Post subject: Re: ikine 4 DOF arm
All of the hobby servos have roughly the same resolution. Some are better than others, but the maximum for a perfect servo is 0.09°. There is no better resolution servo to put into the base. Probably the area to improve the arm performance would be to add mechanical dampening. It's sort of impossible to add mechanical dampening to the shoulder which has two servos operated in tandem. But the four new arms we are developing use a large scale servo in the shoulder position. This allows our mechanical dampening disks to be used instead of a ball bearing on the shoulder axis. Of course we are using the disks on the elbow as well. We will duplicate the "draw a box" idea with the new arms as soon as we are able. This should fix the jagged lines. Here is a view of the top secret AL5D-KT. Shown without the new light weight wrist rotate option.



Here is an image of the light weight wrist rotate bracket on the new AL5C-KT (old SES arm). It uses an HS-85 for the axis.


_________________
Jim Frye, the Robot Guy
http://www.lynxmotion.com
I've always tried to do my best...


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Posts: 2251
Posted: 2008-11-07 12:00 
 Post subject: Re: ikine 4 DOF arm
Below is some previous discussion on real world servo resolution. If you ever see the insides of the pot used in standard servos, it is pretty amazing they do as well as they do.

http://www.lynxmotion.net/phpbb/viewtop ... 2&start=45


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Posts: 170
Posted: 2008-11-07 12:43 
 Post subject: Re: ikine 4 DOF arm
hi nowis,

The videos are cool. Great work!
Have you determined the IK using Denavit hartenberg principle, i.e using DH-tables? or through the geometric approach?

Thanks,
umar


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Posted: 2008-11-07 13:26 
 Post subject: Re: ikine 4 DOF arm
It might be interesting to draw a series of verticle lines starting in a center position and progressivly moving to the right and left and redrawing the lines. This would show if the loss of precision is consistant or if it might be a rough place on the pot wiper surface. Very accurate all things considered.


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Posts: 5
Posted: 2008-11-10 04:09 
 Post subject: Re: ikine 4 DOF arm
Hi pyrrhicpk
If you follow the link in the first post you can see his calculations in a PDF.
He's used the D-H configuration of the arm to derive the transformation matrix for each joint. Then using matrix maths you can do the forward and inverse kinematics for the arm. Once you've solved the problem analytically the calculations can be pretty much be reduced to a line of code per joint.

Regards
Andy


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Posts: 170
Posted: 2008-11-10 11:45 
 Post subject: Re: ikine 4 DOF arm
Quote:
Hi pyrrhicpk
If you follow the link in the first post you can see his calculations in a PDF.
He's used the D-H configuration of the arm to derive the transformation matrix for each joint. Then using matrix maths you can do the forward and inverse kinematics for the arm. Once you've solved the problem analytically the calculations can be pretty much be reduced to a line of code per joint.

Regards
Andy


Hi andy,
Thanks for the response. Actually i tried looking into the details in that pdf, but am unable to understand it thoroughly. Still i will give it another look. I am also deriving the equations for FK and IK using DH tables. here are my findings

http://www.lynxmotion.net/viewtopic.php?t=4115&start=90

FK is complete, but i am stuck with some IK equations, thats why i wanted someone to look into my details or to look into someone's. Do give them a look if you get some spare time :)

Thanks
umar


Rookie ( offline )
Posts: 23
Posted: 2008-11-10 17:42 
 Post subject: Re: ikine 4 DOF arm
Hi all,

Sorry for the late reply. I have been busy :wink:

I will try to answer all the questions.

question 1: Do you use positional control or velocity control ?

I use positional control. But the data that is used makes sure that all the movements are smooth. You can check the data (squaredat) here:
http://cid-976b52dad42d0a1e.skydrive.li ... otics?uc=1

I also put some comments there. This reads more easily. As you see there are enough datapoints (+-600 points). So there is no way that there is loss of accuracy in the software. Like I said, the mathematics are correct.

I also put an excel file "Cubic Segments" to show this principle of smoothness. This smoothness is based on a differential equation of the second degree. So you have to give 4 conditions: the start and end angle. And the speed of this start and end angle. This macro calculates a smooth path between those points according to the 4 conditions. The whole software uses this principle.

question 2: Do you use matrix calculations ?

Yes, because the DH transformations are matrices. The forward tranformations are just DH matrices multiplied after each other. All the datapoints are also stored in matrices. I programmed this robot with Visual Basic 6. I made a class matrix. With these matrices I can do addition, multiplication, determinant and inverse calculations.

question 3: how are the IK calculated ?

The IK is done like Andy said. I use DH transformation to do the forward kinematics.
The inverse kinematics are done with the formula's in the PDF file. I derived them myself. You can look at these as an exercise :wink:
The last page of the PDF file is what this is all about.
I have put them for those who are interested to program it yourself.
You can just use these formula's in your application 8)

The forward kinematics are the easy part. :wink: This is just matrix multiplication. The real stuff is in the inverse kinematics :twisted: . Because here you have multiple solutions of the robot configuration for each point in space...
But all this, is a lot to explain. I would rather refer to the following book where I learned all this stuff.

Robotics: Basic Analysis and Design
William A. Wolovich
Brown University

ISBN: 0-03-006119-9
This is really a great book because it starts from zero. Each chapter has some
exercises.

So this was it. I hoped helping you all out.
Let me know if there are more questions :wink:


Rookie ( offline )
Posts: 18
Posted: 2008-11-18 03:19 
 Post subject: Re: ikine 4 DOF arm
hey nowis
thank you very much for the study on 4-dof. I think it's gonna be real helpful. I've also been studying on 4-dof construction. but mainly on dynamics. I2m just gonna print your pdf and study on it too. you've done for me something real good:-)

wish you success...


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