Solving Quaternion Confusion for 3D Orientation

[SGGSJi]

Hi Guys,

I am getting a quaternion stream from motion sensor (accl, gyro, magneto). As I understand the quaternion represent the 3D orientation of objects. When I place the sensor at location 1 (I record quaternion, q1=[w x y z]), now if I place it at location 2 (say 3 feet to right, 2 feet up and 2 feet forward, q2=[w2 x2 y2 z2]) basically no rotation just translation, should I be expecting same quaternion values as location 1?

I get two different quaternion values, assuming that is correct. I wish to determine if there is any difference in orientation(Euler angles) at location1 and 2. Any ideas where I might be wrong.

Please guide.
Regards,

 

[gator68]

The quaternion output only describes the sensor orientation. It has nothing to do with position. If the two quaternions are different either: you did in fact rotate it, or the sensor has some error. I don't know what kind of sensor you have, but in general these things are always trying to balance a pure tilt measurement with rate sensor integration.

Change the quaternion outputs back in euler angles so that you have a better understanding of the difference. Maybe you are seeing a small angle difference.

 

[SGGSJi]

Thank you
I was making sure that I don't rotate the sensor. I even tried converting quat output to Euler but the values were way different. Please note that as the quat values are with repect to global north the Euler angles were random, however the Euler angles for both locations should still be same. I believe to set euler angles to zero for a given location I should do the following
Q1= quat at location 1
Q1'= conjugate of Q1
Qnew= multiply (Q1', Q1)
Q2= quat at loc 2
Q2new= multiply(Q1',Q2)
Then Euler angles would be

EulerQ1= 0 0 0
EulerQ2= 0 0 0 ( ideally if no orientation at loc 2)

 

[gator68]

Hmm, at this point, I'd recommend getting in touch with tech support of the sensor manufacturer. I think the quaterion output is intended to be a simple representation of the orientation as a function of time, and is not a transformation from one reading to the next. You should be able to find a set of equations to express the Euler angles in terms of quaternion components. I'd be surprised if the manual didn't have something similar.

 

[blue_raver22]

I would like to clarify that quaternions are mathematical representations of 3D orientations, which are commonly used in computer graphics, robotics, and physics. They are typically represented as four numbers (w, x, y, z) and can be used to represent rotations and translations in 3D space.

In the scenario described, it is expected that the quaternion values would be different for location 1 and location 2, as the sensor has been translated to a different position. This is because a quaternion represents both rotation and translation, and the change in position would result in a change in the quaternion values.

To determine the difference in orientation between location 1 and 2, you could convert the two quaternions into Euler angles and compare the values. However, it is important to note that Euler angles can suffer from issues such as gimbal lock and can be less intuitive to interpret compared to quaternions.

If you are experiencing difficulties with your calculations, it is possible that there may be errors in your sensor readings or in the conversion between quaternions and Euler angles. I would suggest double-checking your equations and data to ensure accuracy. Additionally, seeking guidance from experts in the field of 3D orientation and quaternions may also be helpful in troubleshooting any issues.