Hi All,
I have an annoying problem: given a time series of quaternions that describe the orientation of a body in 3D space I'd like to estimate the angular velocity and the rotational axis.
In some successive quaternions 'flipping occurs (the quaternion id very close tot the negative value of the previous one) resulting in outliers in the estimated angular velocity. I was not able to construct or find an algorithm that 'deflips' such quaternions while preserving the handedness of the 3D space as defined in my problem. Can anybody provide me some reference/algorithm/code to fix this issue?
For illustration I've added a video showing 50 successive rotations from a smooth moving object (i.c. an Ellipsoid).
Thanks in advance
Francois Clemens
In two dimensions there’s one axis of rotation, so there can’t be any issue. In three dimensions things are more complicated. Thst’s when quaternions are really useful.
Could you attach a small sample where that phenomenon occurs? A list of 10-12 elements would suffice (that is for the purpose of seeing in which format do you store the quaternions)...
Hi Jose,
see attached examples, these are the results of two successive videoframes, in the first one t=0.6 s the coordinate systems defined in the body is left-handed after rotation with the quaternion , in the next frame (t=0.6125 s) the systems is right-handed after rotation with the quaternion , the orientation of the object is in line with the observations, but when estimating the angular velocity from the difference between the two frames, the 'flipped' representation causes spurious results, so the question is how to recognise the flipped situation in frame 2 (rel. to 1) and how to find the quaternion that preserves the orientation (6 possibilities for this symmetric body) and avoids the flip that causes issues with the angular velocity.
OK, I get the idea. I would like to give it a try with actual data, so it would be useful to have a set of values to work with. Can you send me the data corresponding to the two quaternions in the videoframes?
Are you representing quaternions as lists? matrices? I think your observed behavior is an example of what is called a gimbal lock, it is usually present when quaternions are parametrized as matrices, in terms of Euler angles. Is that the case?
Hi Jose,
I use a simple vector representation q=(a,x,y,z), with a the scalar part and x,y and z as the vector part (attached an example holding a sequence of 50 successive values). The quaternions are not extracted from Euler angles, but the result of post processed raw data in which a.o. non lineair optimisation is applied wih the quaternion as one of the results.
hope you can help me out..
kind regards
Francois
- Badges
- Science topic
- Similar topics
- Mathematics