Practical issue regarding Quaternions

[jensru]

Hi there!

I´ve got a practical problem with quaternions which I was not able to solve by my own so far.

A machine detects the position and orientation of an object which I get as unity quaternion.
I visualize that using matlab, which still works more or less, but I´d like to 'force' the object to a defined position in the beginning and make the following movement relative to that. I hope it´s understandable what I want?

So my thought was to 'define' the first quaternion, which is ~ [0.89 -0.27 -0.28 -0.2] as [1 0 0 0] just by subtracting the difference and also subtract the difference from the following quaternions. But obviously that won´t work, because the result is no longer a unity quaternion in most cases. So does anyone has an idea of how to solve my problem?

Thanks a lot in advance
jens

 

[jvicens]

Hello Jens,

Thank you for sharing your problem with us. It sounds like you are trying to set a specific starting position and then have the object move relative to that position. This can be achieved by using a technique called "quaternion multiplication."

First, let's define the starting quaternion as q0, and the following quaternions as q1, q2, q3, etc. To move the object relative to q0, we need to multiply each subsequent quaternion by q0. This can be written as q1' = q0 * q1, q2' = q0 * q2, q3' = q0 * q3, etc.

This will result in new quaternions that are relative to the starting position. However, as you mentioned, this may not always result in a unity quaternion. To fix this, we can normalize the resulting quaternion by dividing each component by the magnitude of the quaternion.

Alternatively, you can also use the concept of "quaternion conjugation" to rotate the object to a specific position. This involves finding the inverse of the starting quaternion, q0^-1, and then multiplying it with each subsequent quaternion. This can be written as q1' = q0^-1 * q1, q2' = q0^-1 * q2, q3' = q0^-1 * q3, etc.

I hope this helps you solve your problem. If you have any further questions or need clarification, please don't hesitate to ask.