[SOLVED] Maths: Euler angles + robots: how to calculate?

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Hello all,

My math skills are not the best in the world... :~

The problem here is that I have a robot and I need to calculate different points mathematically.

The main idea here is that I have two points in the space with different orientations:

XYZ is the position in the space.
ABC is the euler angle.

P1 = {XYZABC}
P2 = {X'Y'Z'A'B'C'}

The problem here is that if I send the robot from P1 to P2 the robot makes the movement automatically without any problem.

But what I de need is to divide the movement in segments in order to make an oscillation. This means that I need to be able to calculate not only the XYZ position here (something that we got soon) but the orientation in each of the points...

Getting the orientation is where we are having problems...

Any tip from someone?

Thank you in advance.

Posted 18-Mar-10 22:06pm

Joan M

Updated 8-Jul-10 12:03pm

William Winner

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Nelek · Answer 1 · 2010-03-18T23:01:00

The ABC angles have to be considered as (note the capital letters):
XYZ = base coordinates
xyz = tool coordinates

If you get Z and twist the XY-Plane, you get X'Y' where A is the angle between X and X'

If you now get the new Y' and twist the X'Z plane, you will get X''z-Plane where B is the angle between Z and z

If you now get the new z axis and twist the X''Y' plane, then you get xy, where C is the angle between X'' and x

But I don't really understand you when you say "oscilations" between P1 and P2, is there any risk of collision? or what do you mean?

Anyways... the ABC are angles of the relative position of the tool considering the start point at the basis of the robot. So it is very, very, very dependant on how the scenario looks like to move safely from P1 to P2.
I would recommend you to go from P1 to the origin and from origin to P2, is that possible in you case? or do you MUST go directly from P1 to P2?

If the last option... I would try to find the middle points so that from one position to the next one you move ONLY one of the tool-relative axis. And then configure the robot to interpolate the ways in order to make the movement constant and even starting to move to the next position before getting the actual movement ended.

Joan M · Answer 2 · 2010-07-08T10:18:00

Solution 2

Solved: First I have needed to go from EULER to QUATERNIONS and then calculate the interpolations. After that I've passed the results (in quaternions) back to EULER angles.

Posted 8-Jul-10 10:18am