Quaternions and relative orientation

[Davidoux]

Hi ,

I am currently using quaternions in my dynamics simulation library for the orientation of rigid bodies .

The bodies are very simple spacecraft orbiting around Earth and what I need is the relative yaw pitch and roll of one spacecraft against an other one
(let's call them chaser VS target).

At first, I converted the quaternions to euler angles and did the difference, with this solution, I am experiencing variations in one channel (for instance pitch) but I am only applying torques in the roll and yaw channel, I expected not this to happens but maybe I am confusing something in the quaternion theory and their link to euler angles.

Should I instead integrate the equations of relative motion (Hill/CW) and retrieve angles from this one ?

Thanks,

David

 

[Achy47]

Dear David,

Thank you for sharing your question with the forum. Quaternions are a powerful tool in dynamics simulation, especially for representing orientations of rigid bodies. However, converting quaternions to Euler angles can sometimes lead to unexpected variations in certain channels, as you have experienced.

One potential solution to this issue is to directly integrate the equations of relative motion (Hill/CW) to retrieve the relative yaw, pitch, and roll angles. This approach may provide more accurate results, as it takes into account the dynamics of the system rather than just the orientation at a single moment in time.

Additionally, it may be helpful to check your quaternion conversion process and ensure that it is being done correctly. There are various methods for converting quaternions to Euler angles, and some may be more accurate than others.

I would also recommend consulting with other experts in the field or conducting further research on the topic to gain a deeper understanding of the relationship between quaternions and Euler angles. This may help you identify any potential errors in your approach and improve the accuracy of your simulations.

Good luck with your research and simulations!

 

[ravenprp]

Hello David,

Quaternions are a powerful tool for representing orientation in 3D space, and they have many advantages over Euler angles. However, it is important to understand their limitations and how to properly use them.

In your case, it seems like you are trying to calculate the relative orientation between two spacecraft. Instead of converting quaternions to Euler angles, I would suggest using the quaternion's properties to directly determine the relative orientation. The quaternion multiplication formula allows you to combine the orientations of two objects to get the relative orientation between them.

You can also use the conjugate of a quaternion to get the inverse orientation, which can be useful for calculating the relative orientation between two objects. By using these properties, you can avoid any issues with Euler angles and their singularities.

Additionally, integrating the equations of relative motion (Hill/CW) can also give you accurate results. However, this approach may be more computationally intensive compared to using quaternions.

I hope this helps. Good luck with your simulation!