Underwater Navigation System for AUVSI Sub
Rigid Body Orientation Visualization (1st Method: Euler
angles)
The team decided to use Euler angles to determine the rigid body
orienation of the Sensortag, the main reason being the easy
conceptualization of Euler angles. The team decided to calculate the
roll, pitch, and yaw angles from the static accelerometer and
magnetometer data. Roll and Pitch angles can be calculated from the
static accelerometer data alone. The equations for the roll and pitch
angles are shown below. Notice the difference between the same angles
in the equations. This is because the rotation sequence that is used is
crucial, and the sequence of rotations is not communitive.
The problem with the use of Euler angles to determine rigid body
orientation is the encounter of Gimbal lock. This phenomena is the loss
of a degree of freedom, which an axis of rotation locks with another,
and cannot be calcualted once this occurs. Two graphical examples of
Gimbal lock are shown below. Since a main design goal was to create a
robust navigation system no matter the orientation of the IMU, the team
decided to look at other options for determining rigid body orientation.
