OK, I've been puzzling over this question for a while, but I've not found an answer yet. Perhaps the gurus here can tell me?
So when integrating the three gyros that are obviously rotating simultaneously, when you come to fuse them together to rotate your reference vector/DCM/what-have-you, which order do you choose to do it in and, more importantly, why that order?
I may have it wrong, but the APM/Premerlani/DCM code seems to choose Roll-Pitch-Yaw in that order, but what is the science behind this?
I'm assuming that to execute a turn, a fixed-wing aircraft must first roll, then (perhaps) pitch, followed by a resultant yaw, but I'm not sure if this is a good enough reason alone. (probably not) Of course for a quadcopter, et al, this makes no sense either.
Any clues?
Replies
Andrew,
One more comment, because I realize my comment regarding "symmetry" might be confusing. So, a bit more clarification.
The matrix itself is not necessarily symmetric. What I mean by symmetry in the matrix calculations is that the calculations take the same form for each axis, and that there is no "ordering" in the multiplication of two matrices. The primitive multiplications and addition steps involved in performing the multiplication of two matrices can be done in any order whatsoever, and the result will be the same.
Best regards,
Bill
Andrew,
One more thought on the subject....
The use of the rotation matrix frees you up entirely from Euler roll-pitch-yaw angles, which are not symmetric. The labeling of the gyro signals as "roll-pitch-yaw" is not the same thing as the Euler roll-pitch-yaw angles.
Best regards,
Bill
Hi Andrew,
The rotation of the matrix is computed by multiplying two matrices, so there is no preference given to roll, pitch or yaw. The matrix multiplication operation is perfectly symmetric with respect to roll, pitch, and yaw.
Of course, you have to build up the rotation matrix before you you can do the matrix multiply, but it makes no difference what order you compute the elements of the matrix since the elements are independent.
Best regards,
Bill