No, the title does not refer to the forces of good versus those of evil. Nor
am I referring to my stance when chopping firewood with an axe. Instead,
let’s see if we can straighten out some of the terminology that
you’ll hear when people start to talk about sensors. Even folks in the
business sometimes get it wrong, so here is my attempt to establish a common
Degrees of Freedom – AKA DOF, this term gets misused
more than any I can think of. It is often confused with “number of
axes”, which I’ll discuss below. But if you consult any text on
the dynamics of rigid bodies, you will quickly learn that any movement of any
rigid body from point A to point B can be characterized as a translation plus
It takes six numbers to characterize that movement: change in X, Y and Z and
rotations about X, Y and Z axes. Notice that we’re talking about the
minimum set of numbers required to unambiguously specify a given movement. We
are NOT talking about the number of sensors required to measure that movement.
So now, let’s talk about sensors. A basic
3-axis accelerometer returns values for linear acceleration
in each of 3 orthogonal directions.
There’s an important thing you should consider about accelerometers at
rest. When one of the axes associated with the sensor frame of reference is
parallel to the gravity vector, as it is in the figure above, you will get no
additional information from the other two acceleration numbers. They will both
be zero, and you will be unable to tell if the accelerometer is rotated about
the axis parallel to gravity.
The next device in our toolbox is the gyro which returns rates of rotation
about each of the 3 sensor axes. Notice that I’m talking about
sensor axes here. As the sensor rotates, so does its frame of
reference for the next measurement.
A 3-axis magnetometer will return the X, Y and Z components of the ambient
magnetic field. This is nominally the earth field for many applications, but
may include significant offsets and distortions due to hard/soft iron effects.
The magnetometer is subject to the same issue as an accelerometer – if
one of the sensor axes is parallel to the ambient magnetic field vector the
other two sensor axes will return values of zero. The good news is that since
the earth magnetic field and gravity are never colinear, between our
accelerometer and magnetometer, we have enough information to figure out the
current device orientation, regardless of how we rotate the sensor.
Our 1st three sensors each returned a 3-dimensional vector. But the pressure
sensor returns just a single scalar value. As discussed in previous postings,
pressure can be used to infer changes in altitude, which adds another source
of information when computing vertical locations.
Combine an accelerometer with a gyro and you get a 6-axis Inertial Measurement
Unit, or IMU.
Add a magnetometer to an IMU, and you have a
MARG (Magnetic, Angular Rate and Gravity) sensor. Add a
compute engine to a MARG, and you get an
AHRS (Attitude and Heading Reference System).
Add a pressure sensor to a MARG or AHRS, and you get a slightly smarter MARG
or AHRS – I haven’t found any standard terms. I simply refer to
them as “10-axis solutions”.
So remember, use “DOF” when describing motion. Use
“axis” or “axes” when describing sensor
configurations. And when in doubt, draw a picture.