Inverse Kinematics of Fanuc CRX-10iA and other robots with non-spherical wrist

    Hello,

    I am trying to make an analytical inverse kinematics solver for the Fanuc CRX-10iA robot. I already made such a solver for "normal" 6-axis robots with spherical wrists (spherical = axis 4-5-6 intersect in the same point), and for UR-style robots.

    For robots with spherical wrist, I use the flange->wrist offset to determine the location of the center of the wrist. The A1, A2, and A3 angles can then be found using a little geometry. A4, A5 and A6 angles are found using ZYZ Euler angles.

    The UR robot does not have a spherical wrist, but I know that A4 is parallel with A2 and that both A4 and A6 are perpendicular to A5. So I can find the A5-A6 intersection, calculate an initial angle to that one (first guess for A1), compensate for the A4 offset to get the correct A1 angle, then subtract the A4 offset to find the intersection between A4-A5. This point is then used for the formulas to derive the A1-A3 angles, and the A4-A5-A6 angles are derived using ZYZ Euler angles like I did for the robots with spherical wrists.

    But now I want to make an analytical solver for the Fanuc CRX-10iA robot. It is in many ways like a robot with a spherical wrist, only the wrist axes do not all intersect in the same point. See attached picture. Do any of you have a good idea for how to solve this using geometry? I know that I can find a solution using the jacobian method, but I want to use the analytical solver to find a good starting guess for the jacobian solver.

    Thanks in advance!

    I did some research but I cannot find analytical IK solutions for CRX type of robot, what I ended up with is IKFast. It returns multiple solutions without configuration information.

    During the analytical study, I found that paper [1] mentioned that CRX robot is cuspidal type of robot. This type of robot can pass through different configurations without going across singularities, quite difficult to imagine.
    In another paper [2], the author proposed a method for Kinova robot inverse kinematics. This Kinova is the same with CRX (Fig. 2 of [2]). They use polynomial method and provides source code. I haven't got a chance to reimplement to CRX robot.

    If you guys got an more elegant solution, I would be very much appreciate it!

    [1] A review of cuspidal serial and parallel manipulators
    [2] Kinova Gen3 Lite manipulator inverse kinematics optimal polynomial solution

    Hello

    Just letting you know there is this new paper that can solve any 6 and 7-axis robot:
    In the paper there is some examples with UR, Fanuc CRX 10iA, Kinova, Kuka and more.....

    Its very similar to the paper Be bop found.

    For the Fanuc CRX robot it can find 16 unique solutions, For a given target :smiling_face:

    The Inverse Kinematics of Lobster Arms:
    https://www.researchgate.net/publication/379147413_The_Inverse_Kinematics_of_Lobster_Arms

    It has Maple and Matlab code examples, so it is easy to replicate the code into other languages.

    Software.zip
    SACO - Servicio de Almacenamiento Compartido de la Organización - SGAI - CSIC
    saco.csic.es


    I have been playing around with it for a few weeks now, and got into C++. Working perfectly for my purpose. I can unfortunately not share the code with your guys. I got it to run relatively fast, 1ms
    :smiling_face:

    If anybody is downloading the Maple code (Use free licens). Then look for the ExampleFanuc_fast.mw file. It will compute a general polynomial, Then this polynomial can be save in a file. And once you have the target you can just use the general polynomial to sub in the target, and solve for the last unknown variable. You don't have to recompute the general polynomial every time you have a new target.

    Hope this can help anybody looking for a Fanuc solver.

    Edited once, last by GreenHigh (May 21, 2024 at 10:12 AM).

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