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I would like to reset/remove offset quaternion data from real-time IMU sensor recordings. E.g. I get [-0.754, -0.0256, 0.0321, 0.324] (XYZW) when I start recordings. I would like to reset this to be [0, 0, 0, 1] when I start recording, as I am using it to rotate a 3D object which initial quaternion values are [X: 0, Y: 0, Z: 0, W: 1].

I tried subtracting all quaternion data from the first as so:

counter = 0

quat = getting_sensor_data_from_somewhere()
while True:

   if counter == 1:
      offset = quat

   calib_data = [x1 -x2 for x1, x2 in zip(quat, offset)

However, it doesn't seem to be the right solution. I am a bit confused of why W should be 1. Can you help me?

The 3D model are from ThreeJS libraries.

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2 Answers 2

Reset to default
3

Try this out:

def quaternion_multiply(quaternion1, quaternion0):
    import numpy as np
    w0, x0, y0, z0 = quaternion0
    w1, x1, y1, z1 = quaternion1
    return np.array([-x1 * x0 - y1 * y0 - z1 * z0 + w1 * w0,
                     x1 * w0 + y1 * z0 - z1 * y0 + w1 * x0,
                     -x1 * z0 + y1 * w0 + z1 * x0 + w1 * y0,
                     x1 * y0 - y1 * x0 + z1 * w0 + w1 * z0], dtype=np.float64)

glob_quat = [1,0,0,0]
counter = 0

quat = getting_sensor_data_from_somewhere() # W,X,Y,Z order
while True:

   if counter == 0:
       quat_first = [quat[0], -quat[1], -quat[2], -quat[3]]
       offset = quaternion_multiply(glob_quat, quat_first)

   quat_calib = quaternion_multiply(offset, quat)
   
   # Now first quat will always be [1, 0, 0, 0]
   # Shift places if W is at the end instead of in the start
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2 Comments

isn't glob_quat just the identity quaternion? If so, wouldn't quaternion_multiply(glob_quat, quat_first) just be equal to quat_first (which is the conjugate of quat)?
from testing it seems like my comment is correct. I suppose if glob_quat was not the identity quaternion, then maybe that extra multiplication would be necessary. also as a general comment you never increment counter. Thanks!
0

Nice description of usage of equation rotation about axis set as quaterion can be found here:
http://wiki.alioth.net/index.php/Quaternion

quote

A quaternion is a set of four values (W X Y Z) that are used in Oolite to specify a rotation in 3D space. To specify a particular rotation you need to think about the axis about which the rotation is made and the angle or amount by which the model is to be rotated.

For a given axis (x y z) and angle (α), the quaternion representing a rotation of a degrees around the axis from the origin (0,0,0) to (x,y,z) is:

W = cos (0.5 × α)
X = x × sin (0.5 × α)
Y = y × sin (0.5 × α)
Z = z × sin (0.5 × α)

So a rotation of 90 degrees about the z axis (0 0 1) would be:

W = cos 45 ° = 0.707…
X = 0 × sin 45 ° = 0
Y = 0 × sin 45 ° = 0
Z = 1 × sin 45 ° = 0.707…

That mean You need to select different axis to achieve the setting to [0,0,0,1] as desired.

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1 Comment

I am not trying to rotate quaternions to a specific angle but thanks for the answer

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