Madgwick's sensor fusion algorithm on iOS

Question

i'm trying to run Madgwick's sensor fusion algorithm on iOS. Since the code is open source i already included it in my project and call the methods with the provided sensor values.

But it seems, that the algorithm expects the sensor measurements in a different coordinate system. The Apple CoreMotion Sensor System is given on the right side, Madgewick's on the left. Here is the picture of the different coordinate systems. Both systems follow the right hand rule. For me it seems like there is a 90 degree rotation around the z axis. But this didn't work.

I also tried to flip x and y (and invert z) axis as suggested by other stackoverflow posts for WP but this didn't work also. So do you have a hint? Would be perfect if Madgwick's alogithm output could be in the same system as the CoreMotion output (CMAttitudeReferenceFrameXMagneticNorthZVertical).

Furthermore I'm looking for a good working value for betaDef on the iPhone. betaDef is kind of the proportional gain and is currently set to 0.1f.

Any help on how to achieve the goal would be appreciated.

Answer 1

I'm not sure how to write this in objective c, but here's how I accomplished the coordinate transformations in vanilla c. I also wanted to rotate the orientation so that +y is north. This translation is also reflected in the below method.

This method expects a 4 element quaternion in the form of wxyz, and returns a translated quaternion in the same format:

void madgeq_to_openglq(float *fMadgQ, float *fRetQ) {
  float fTmpQ[4];
  // Rotate around Z-axis, 90 degres:
  float fXYRotationQ[4] = { sqrt(0.5), 0, 0, -1.0*sqrt(0.5) };

  // Inverse the rotation vectors to accomodate handedness-issues:
  fTmpQ[0] = fMadgQ[0];
  fTmpQ[1] = fMadgQ[1] * -1.0f;
  fTmpQ[2] = fMadgQ[2];
  fTmpQ[3] = fMadgQ[3] * -1.0f;

  // And then store the translated Rotation into ret:
  quatMult((float *) &fTmpQ, (float *) &fXYRotationQ, fRetQ);
}

// Quaternion Multiplication operator. Expects its 4-element arrays in wxyz order 
void quatMult(float *a, float *b, float *ret) {
  ret[0] = (b[0] * a[0]) - (b[1] * a[1]) - (b[2] * a[2]) - (b[3] * a[3]);
  ret[1] = (b[0] * a[1]) + (b[1] * a[0]) + (b[2] * a[3]) - (b[3] * a[2]);
  ret[2] = (b[0] * a[2]) + (b[2] * a[0]) + (b[3] * a[1]) - (b[1] * a[3]);
  ret[3] = (b[0] * a[3]) + (b[3] * a[0]) + (b[1] * a[2]) - (b[2] * a[1]);

  return;
}

Hope that helps!