Roll-pitch-yaw singularity

1. What is singularity in rotation?
2. Is gimbal lock a singularity?
3. Do rotation matrices have singularities?
4. How do you prevent singularity in Euler angles?

What is singularity in rotation?

Question 1A singularity occurs when the middle rotation in the sequence makes the rotation axes of the first and third rotations parallel.

Is gimbal lock a 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.

Do rotation matrices have singularities?

The Direction Cosine Matrix (DCM) is a rotation matrix that transforms one coordinate reference frame to another. Rotation matrices are a complete representation of a 3D orientation, thus there is no singularity in that model.

How do you prevent singularity in Euler angles?

To avoid singularity of Euler angle, a new heading estimation parameter is introduced and a filter mode switching algorithm is proposed. The experimental results indicated that the proposed system performed better than a quaternion algorithm based on magnetometer disturbance.