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IMU User Guide revision 3.1 SMC Ship Motion Control www.shipmotion.eu
In the SMC motion sensors, the coordinate system can be defined by a setting option in the SMC
configuration software that is included with the motion sensor. The user can choose between the
IMU coordinate system and the Earth Coordinate system.
The default setting for the SMC motion sensor is Earth Coordinates without earth G in Acc.
The SMC motion sensor defines its body axis from the Tait-Bryan (z-y-x) angles in the order yaw,
pitch, roll to describe the orientation of a vessel.
In the Earth Coordinate system positive Z is vertical with reference to the earth horizon. The X-axis in
the earth coordinate system has the same direction as the X-axis of the IMU coordinate system
projected onto the horizontal plane of the earth. The Y-axis is horizontal and is perpendicular with
respect to the earth fixed X-axis and has close to the same direction as the IMU coordinate Y-axis.
To obtain the accelerations in the IMU coordinate system the accelerations measured by the motion
sensor are rotated with a three-dimensional calculation with respect to the mounting angles offsets.
To obtain the accelerations in the earth fixed system the accelerations measured in the motion
sensor in the IMU coordinate system are rotated with a three-dimensional calculation with respect to
the current value of the roll and pitch angles and their offsets.
The accelerations are in sent in the selection for the IMU coordinate system and is not related to the
selection of the Heave, surge and sway output selection in the motion sensor.
Heave, surge and sway motions are calculated in the earth
fixed coordinate systems as default. The calculations of these
linear motions are done by taking the accelerations in the
Earth Coordinate system and double integrate these to obtain
surge, sway and heave positions.
If the IMU coordinates is selected for the Surge, sway and
heave in the IMU configuration software these values are
calculated three-dimensional using the roll and pitch angular
data before being output.
The surge, sway and heave velocities are the derivatives of
the surge, sway and heave positions.
For the Roll, Pitch and Yaw calculations when using the earth coordinate system selection, the three-
dimensional rotation corresponding to the motion sensor readings is composed (conjugated) with
the three-dimensional rotation of the mounting offsets.
After the internal measured data in the IMU coordinate system has been rotated into the earth
coordinate system the Roll, Pitch and Yaw angles are calculated.
The roll, pitch and yaw velocities being output in the earth coordinate system are the derivatives of
the corresponding angular values.