Going from KUKA Euler angles to transformation matrix.

    Hi.

    I've recently run a series of tests on a KR-60 Robot using a KRC2 controller.

    I have position data at the tool center point, in the tool frame and I'm interested in getting position data from a DIFFERENT point on the tool for which I have the coordinates in the tool frame.

    I've created a 4x4 transformation matrix that represents the motion of the tool during the test, and I will multiply the vector of the point I'm interested in by that matrix to get its final position.

    The only thing I'm a bit confused about is the KUKA representation of Euler angles, and I'd like to make sure I'm doing the right thing since we will be publishing this data in a scientific journal.

    I'm under the impression that the angles are represented as INTRINSIC X''Y'Z Euler angles starting with Z (A), then Y (B), then X (C)

    So, to construct a rotation matrix from thos angles I need the matrix
    R=X''Y'Z which would be equivalent to R=ZYX where

    X=[1 0 0
    0 cos(C) -sin(C)
    0 sin(C) cos(C)]

    Y=[cos(B) 0 sin(B)
    0 1 0
    sin(B) 0 cos(B)]

    Z=[cos(A) -sin(A) 0
    sin(A) cos(A) 0
    0 0 1]

    Is this the correct way to compute a rotation matrix from the KUKA euler angles A,B,C?

    Thanks for your help.

    you have mistake for rotation matrix Ry(B). There sin(B) in lower left corner should be negative.
    Once you multiply those three 3x3 elementary rotation matrices, you will get single 3x3 matrix R=Rz(A)*Ry(B)*Rx(C)

    https://en.wikipedia.org/wiki/Rotation_matrix

    1) read pinned topic: READ FIRST...

    2) if you have an issue with robot, post question in the correct forum section... do NOT contact me directly

    3) read 1 and 2

    I wrote a set of Linear algebra routines for KUKA.
    Computing a matrix from ABC Euler angles:
    public static double[][] matrix(double aDeg, double bDeg, double cDeg) {
    //ABC: Euler angles, A: round z-axis B: round y-axis C: round y-axis
    double a = -aDeg * PI / 180;
    double b = -bDeg * PI / 180;
    double c = -cDeg * PI / 180;
    double ca = Math.cos(a);
    double sa = Math.sin(a);
    double cb = Math.cos(b);
    double sb = Math.sin(b);
    double cc = Math.cos(c);
    double sc = Math.sin(c);
    double[][] tt = new double[3][];
    tt[0] = new double[] { ca * cb, sa * cc + ca * sb * sc, sa * sc - ca * sb * cc };
    tt[1] = new double[] { -sa * cb, ca * cc - sa * sb * sc, ca * sc + sa * sb * cc};
    tt[2] = new double[] { sb, -cb * sc, cb * cc };
    return tt;
    }

    applying the matrix: a is the rotation marix, b is the vector
    public static double[] mul(double[][] a, double[] b) {
    double[] re = new double[3];
    int len = a[0].length;
    if (len == 4) { // matrix a[][] includes both rotation and the position of the current frame
    for (int i = 0; i < 3; i++)
    re[i] = a[i][0] * b[0] + a[i][1] * b[1] + a[i][2] * b[2] + a[i][3];
    }
    else if (len == 3) { // only rotation
    for (int i = 0; i < 3; i++)
    re[i] = a[i][0] * b[0] + a[i][1] * b[1] + a[i][2] * b[2];
    }
    return re;
    }

    Very often, one computes the matrix from both Euler angles (ABC) and the position (XYZ) of the current frame as:
    public static double[][] matrix(double x, double y, double z, double aDeg, double bDeg, double cDeg) {
    double a = -aDeg * PI / 180;
    double b = -bDeg * PI / 180;
    double c = -cDeg * PI / 180;
    double ca = Math.cos(a);
    double sa = Math.sin(a);
    double cb = Math.cos(b);
    double sb = Math.sin(b);
    double cc = Math.cos(c);
    double sc = Math.sin(c);
    double[][] tt = new double[3][];
    tt[0] = new double[] { ca * cb, sa * cc + ca * sb * sc, sa * sc - ca * sb * cc, x };
    tt[1] = new double[] { -sa * cb, ca * cc - sa * sb * sc, ca * sc + sa * sb * cc, y };
    tt[2] = new double[] { sb, -cb * sc, cb * cc, z };
    return tt;
    }
    Hope it’s helpful.

    Edited once, last by whitegreen (December 16, 2015 at 7:09 AM).

    Great, thanks for the clarification everyone.

    Panic mode: Good catch, and thanks for confirming that I am multiplying the matrices in the correct order.

    Fubini, for future tests I'll definitely have a look at that. For now it's too late since we already have all the data but that's a great tip, I can use it to check my own matrix calculation vs the built-in one.

Advertising from our partners