Why does Kuka and other robots use Euler angle convention when it suffers from Gimbal Lock? Is the Euler angle convention responsible for Singularity in Kuka? ABB uses quaternions; Does that make it singularity free. How to choose Euler angle convention for a Robot?
Representing Orientation
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kamalakshat -
December 15, 2012 at 1:53 PM -
Thread is marked as Resolved.
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I'm considering moving this topic over to the Geometry&Math sub-forum -- it's probably more appropriate there.
But in the meantime... in my experience, at least, the "gimbal lock" that industrial robots suffer from is not mathematical, but mechanical. Modern path planners in general seem to handle the mathematical singularities involved with Euler quite well. Mechanical singularities, however, are something all industrial robots suffer from, except for some specific cases involving unique mechanical designs or limited motion envelopes. ABBs are no more immune to this than any other brand, from what I've seen.
The standard 3-axis wrist, with the axes of all three joints intersecting (normally a "bending" axis sandwiched between two "rotation" axes), suffers from a speed limitation during interpolated motions as the first and third wrist axes (normally the 4th and 6th axes on a typical industrial articulated robot arm) approach a colinear condition. The closer these two axes come to being in parallel, the faster they have to turn in order to maintain a given linear velocity for the TCP, and it becomes quite easy to hit the maximum velocity for those axes. In practice, this is usually overcome by intelligent tool design and path programming, to avoid approaching that condition during any critical interpolated motions.
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"Gimbal lock" is a manifestation of a mathematical problem with Euler angles. In a Kuka robot where Euler ZYX rotations are used, having the Y rotation (B angle) at +/-90 degrees effectively rotates the Z axis onto the X axis which sort of screws things up. It actually causes a singularity in the maths (meaning that there is no way to get a unique solution to the inverse problem), which is subtly different from what most robot people understand by the term singularity. Anyway, it doesn't really cause any problems for the robot since internally all rotations used for motion planning are stored as quaternions or rotation matrices.
@kamalakshat. The singularity that you talk about, I'm guessing, is where axis 5 is at 0 degrees. This makes axes 4 and 6 co-linear, effectively turning the robot into a 5 axis device at that point. It's a geometric "feature" of the robot that has nothing to do with the rotation convention used in a particular robot controller.
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Here is an iOS app that my colleague and I created for guys like you who want to learn more about orientation representation: https://itunes.apple.com/us/app/eulerangles/id584911325?mt=8
Ilian