[Singularity] how to check if a path passes through singularity?

    I am planning to implement joint space interpolation method to pass through the wrist singularity area of a six-axis robot arm.

    But here comes the first question: How to check if a path passes through its wrist singularity? If it does, where does it start and end? Only with these information, I can further plan multiple joint motions between the singularity area.

    If it is a SCARA robot, to check if a straight line path passes through its hand singularity is pretty easy, as it is happening in a 2D space.

    What about six-axis robot? I am wondering if there is a magical math equation that is able to find out the singularity entry and exit point for a path happening in a 3D space.

    I have found plenty of methods to deal with passing through singularity, but not one is to determine where the singularity it is. Or did I not try hard enough:frowning_face:. Any thoughts are appreciated!

    Quote from MOM

    You did not try hard enough.

    You have the wrist singularity when a4 and a6 are parallel.

    Do a inverse kinematics and you will find that point.

    I think that every robot manufacturer keeps his strategy secret.

    Yeah my last resort is to check multiple points on a path if their a4 and a6 are parallel. Assuming only one singularity point exists in a path, it becomes a finding local maxima problem. Just wondering if there is a better solution.

    Even most robots don't do this as a "look ahead" type of check. At the root, interpolated motions are just lots and lots of very short joint motions -- a robot making a "straight line" is actually performing a large number of tiny arcs, daisy-chained together. And most robot controllers don't look any further ahead then a half-dozen of those small moves, max.

    As such, the first warning of a singularity is often when A4 or A6 exceed their maximum rated speed while trying to pass near (not necessarily through) the singularity.

    To a first approximation, you could perhaps do a quick yes/no check. I'm just spitballing here, but... I imagine that, for most interpolated motions passing too close to singularity, the final joint position will be quite different than making a joint move between the same start/end points. If you can predict both robot end poses (which would require a strong knowledge of the robot's path planner), and they have substantial differences in the wrist axes, that would be a sign that that move needs more detailed checking for singularity.

    Beyond that... most in-built solutions I've seen robot controllers use for getting around singularities work by "relaxing" the TCP orientation en route, while keeping the TCP on the linear path. The details are almost certainly proprietary, but from observation, it seems as if the motion planner is constantly checking A5's distance to zero against the "ideal" linear path, and lets the "pressure" of A5 approaching zero "push" the orientation of the TCP for the next tiny arc.

    I've heard some brands have solutions that will actually let A5 pass through zero, but it sounds like all of those solutions tend to have some unpredictable TCP motion at the crisis point, so it's not suitable for any situation that needs path accuracy.

    The only "homebrew" solution I've ever seen for this was (for specific situations) predict a linear motion that would cause the wrist singularity, and divide that motion in a series of joint motions calculated along the same line. It worked surprisingly well, but was still only suited for "air moves" -- it wouldn't have worked for something like a paint, sealer, or continuous-weld path.

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