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Gimbal Lock (90 deg pitch singularity)

Gimbal Lock (90 deg pitch singularity)

Gimbal lock is a singularity when pitch approaches 90 or -90 deg. Because of the definition of the Euler angles, the orientation is not fully defined, which means that roll and yaw are not stable values when pitch is approaching 90 deg. The sensor fusion algorithm of the MTi does not experience gimbal lock, as the filter is completely running in quaternion mode. The resulting singularity in Euler angles representation should be addressed in another way (see below).

See below for two screenshots from MT Manager. The orientation of the MTi is almost the same, yet the roll and yaw are completely different in both screenshots.

 

Preventing the singularity

It is possible to prevent the singularity in the following ways:

  1. Choose a different orientation representation. Both quaternions and rotation matrix don’t experience the singularity
  2. Stay away from a pitch of 90 deg. If it is necessary to mount the MTi with the y-axis in the direction of gravity, apply an alignment rotation.
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