### DCM Tutorial – An Introduction to Orientation Kinematics

While following William Premerlani and Paul Bizard work (DCM Draft 2) I put together some notes  that I eventually cleaned up and turned into a small tutorial on DCM matrix , orientation kinematics, angular velocity and a IMU algorithm (slighly different from Williams and Paul's) , for anyone interested check it out:

http://www.starlino.com/dcm_tutorial.html

• Flavio, you don't need DCM always in fact I describe another method of calculating device inclination in this article http://www.starlino.com/imu_kalman_arduino.html for theory see http://www.starlino.com/imu_guide.html

And you can get away with simple gyro and acc filters to stabilize for example a quad as long as you don't have extreme "acrobatic" movements.

However DCM or quaternions (which can be deducted from one another) are more accurate in tracking orientation on the entire sphere.

Just see what your project needs and choose the simplest solution. Start simple and only complicate if necessary...

Arduino code for IMU Guide algorithm. Using a 5DOF IMU (accelerometer and gyroscope combo)
Arduino code for IMU Guide algorithm. Using a 5DOF IMU (accelerometer and gyroscope combo) - This article introduces an  implementation of a simplifi…
• dydx I replied to your other comment on my site see http://www.starlino.com/dcm_tutorial.html#comments
DCM Tutorial – An Introduction to Orientation Kinematics
• The thing that I keep struggling with is why I don't see a Euler equation like this anywhere.

When you say:

Please note that we’re stressing out that these are small rotations, since in general when you combine large rotations the order in which rotations are performed become important and you cannot simply sum them up.

I just can't work out why small rotations would make any difference. Could this hold true for a gyro only solution? Can you help me understand this?

• I still dont understand why is a DCM so important if I can just integrate gyro and low pass accelerometers. Could somebody explain me? Thanks in advance.
• Developer
Very nice polish to DCM, I wish someone would add flash animations to your document, it would aid in expanation and understanding of relative frame motions. Thanks again!
• :-) I thought you said you simplified it...