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I am using an IMU (MPU9150/9250) for measuring relative joint angle. If in two different conditions where,

  1. X is up and Z is towards the user

  2. Z is up and X is towards the user

How can I convert the quaternion to Euler angle in ZYX sequence with out having singularity?

Best Regards,

Akhil

AM_87
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  • Euler angles inherently cause singularities when some of the axis are rotated by 90 or 180 degrees (which rotations cause a singularity depends on your choice of X/Y/Z combination). So no matter which method you use, as long as you require a conversion to Euler angles, you will hit a singularity for some quaternion values. Out of curiosity - can't you just keep the relative rotation as a quaternion, or simply use the axis-angle representation? Neither would suffer from singularities of this kind. – Martin Prazak Mar 31 '15 at 03:13
  • I agree that it is nice to have the data in quaternion or axis-angle form to avoid singularity, but to explain in a forum or to a physician itis necessary to convert the data to Euler angle form. ISB provide guidelines for choosing rotation sequences and hand and wrist am not clear. The result that you obtained also depends on the way you unfold it,so order matters. I am in a dilemma here how to choose a rotation sequence, what an option is to implement all 6 floating types and choose the one which has accurate result. – AM_87 Apr 01 '15 at 05:09
  • I am not sure I follow - what is ISB? To explain an algorithm on a forum or to a physician, it is usually better to use axis-angle notation, because it is unambiguous (there are 16 different combinations of axes order for euler angles, not just 6). But as an answer to you question - "How can I convert the quaternion to Euler angle in ZYX sequence with out having singularity?" - you can't, sorry. – Martin Prazak Apr 01 '15 at 06:47
  • International Society of Biomechanics provide guidelines to choose co-ordinate systems and Euler angle sequence order for specific joints. They have chosen to use Euler angles to describe rotations. The rotations of distal co-ordinate systems are then described wrt the proximal. It is possible to convert the quat to euler angle having a check for singularity. At the singularity point on near singularity region we can manually assign values. – AM_87 Apr 02 '15 at 10:50
  • Out of the 6 possible combinations (Euler and Tait Bryan sequences forms 12 and am interested in the Tait Bryan), how to find a sequence which gives the best result is what I am trying to understand. – AM_87 Apr 02 '15 at 10:51
  • Ok, fair enough, I stand corrected. As a humble (and possibly obvious) "pragmatic" suggestion - for each combination, there will be a limited number of singularities when to axes align (I am guessing 4, but didn't try to go through the maths so might be wrong there). Its relatively easy to enumerate them, and make a simple metric that will give you the combination that is furthest from the singularity. mathoverflow might be a better place to ask, tho. – Martin Prazak Apr 02 '15 at 14:36

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