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
Comments
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...
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 thought you said you simplified it...
Seriously, thanks for your efforts