Re: [Paparazzi-devel] Paparazzi Convention for Euler Angles

[Thomas Würfl]

Unsubscribe

Avinash Rao <address@hidden> schrieb:

>Hi Christophe,
>
>Thanks for taking the time to go through all that - much appreciated. Since
>you've confirmed the convention for the order of rotations as being ZYX /
>psi-theta-phi , it would seem that the documentation in the
>doc/pprz_algebra/headfile.pdf may be incorrect (or I may still be!). Given
>the order you mentioned, I would have thought that the rotation matrix
>would be obtained as follows:
>
>R_EarthToBody = R(phi)*R(theta)*R(psi)    i.e. the the constituent rotation
>matrices are in reverse order to the actual order of rotations so that the
>vector to be rotated is rotated in the correct order.
>
>This would mean that to go from body to earth, the rotation matrix would be
>obtained:
>
>R_BodyToEarth = R(-psi)*R(-theta)*R(-phi)
>
>This would seem to agree with the formulae in the code for calculating
>Euler angles from accelerometers and magnetometer.
>
>However, in the document headfile.pdf, it states that the order is:
>
>R_EarthToBody = R(psi)*R(theta)*R(phi)
>
>which would correspond to the order  convention XYZ/phi-theta-psi, or  the
>reverse of the stated convention.
>
>Does this make sense or have I missed something?
>
>Thanks again for your help.
>
>Regards,
>
>Avinash.
>
>On Wed, Feb 15, 2012 at 9:53 PM, Christophe De Wagter <address@hidden>wrote:
>
>> Euler angles are slightly more complex than they appear to many
>> people. The rotation from Earth to Body is done by:
>>
>> First rotate the Earth North-East-Down coordinates with PSI (positive =
>> right hand along the z-axis pointing down = positive to the east). e.g.
>> PSI=90deg -> new set of axes become East-South-Down
>> Then, starting from your newly PSI-rotated coordinate system, rotate an
>> angle THETA along the new y-Axis. e.g.: theta=45deg = nose up. You now
>> already have the final body-X axis.
>> From this PSI-THETA-rotated new set of axes finally apply the PHI or Roll
>> by turning (with right-hand rule) around the already found body-x-axis
>> (which in our sample is then pointing east and 45 degrees up)
>>
>> To go back from Body to Earth, it's the complete opposite: sign as well as
>> order.
>>
>> First un-roll around the body X using  -PHI  (minus PHI).
>> From this un-rolled set of axes un=pitch with MINUS THETA arround the
>> unroll-ed Y-axis.
>> And finally un-PSI your un-rolled and un-pitched set of axes around the z
>> and you should be North-East-Down in Inertial, Local-Tangent-Plane or Earth
>> coordinates (3 names that are not exactly the same but are often simplified
>> as being the same)
>>
>> Because of this funny definition, euler angles are only intuitive at small
>> pitch angles, but once the pitch angle becomes large very non-intuitive
>> things happen. For instance: phi,theta,psi = 0,90,0 is the same attitude as
>> 90,90,90 and there are only 2 degrees of difference between A) 0,89,0 and
>> b) -180,89,180 and c) -90,89,-90 and d) 90,89,90 even if both phi and psi
>> have differences of 180 degrees. This is the case with the nose pointing
>> almost 90 degree vertical with the wings aligned east-west but the nose
>> respectively rotated 1 degree a) north b) south c) west d) east. No need to
>> explain how difficult it is to integrate gyro's in this case: e.g. from a)
>> to b) the Y-gyro will feel 2 degrees and X and Z gyro zero degrees, while
>> the euler angles change 180 in the axes where the gyro feels zero and does
>> not change in theta, the only axis where the gyro was feeling something...
>>
>> Hope this helps in getting some feeling for euler angles. (and switch to
>> quaternions or rotation matrix a.s.a.p. ;-)   )
>>
>> -Christophe
>>
>>
>>
>>
>> On Wed, Feb 15, 2012 at 3:26 AM, Avinash Rao <address@hidden>wrote:
>>
>>> Hi Poine,
>>>
>>> Thanks for your reply. I had been reading through that document already
>>> but I wasn't sure exactly what was meant by the change of reference
>>> co-ordinates.
>>>
>>> For examle,does phi in the code denote the angle from body to earth, or
>>> is phi in the code from earth to body (so we need to take the negative of
>>> it to go from body back to earth)?
>>>
>>> Avinash.
>>>
>>>
>>> On Wed, Feb 15, 2012 at 1:53 PM, antoine drouin <address@hidden> wrote:
>>>
>>>> look in doc/pprz_algebra/headfile.pdf
>>>>
>>>> On Wed, Feb 15, 2012 at 1:48 AM, Avinash Rao <address@hidden>
>>>> wrote:
>>>> > Hi all,
>>>> >
>>>> > I'm trying to understand the convention used for calculating Euler
>>>> angles in
>>>> > paparazzi and how they relate to the drift correction in the AHRS.
>>>> >
>>>> > From looking through the code for determining Euler angles from
>>>> gravity and
>>>> > magnetometer, it would seem that the conventions is such that:
>>>> >
>>>> > x_earth = R(psi)*R(theta)*R(phi)*x_body
>>>> >
>>>> > i.e. the rotation R(psi)*R(theta)*R(phi) will transform a vector x
>>>> measured
>>>> > in the body frame (e.g the gravity vector) back into the earth frame.
>>>> >
>>>> > Is this correct or have I made a mistake somewhere?
>>>> >
>>>> > Thanks very much for your help in advance.
>>>> >
>>>> > Avinash.
>>>> >
>>>> > --
>>>> > Avinash Rao
>>>> >
>>>> >
>>>>
>>>
>
>_______________________________________________
>Paparazzi-devel mailing list
>address@hidden
>https://lists.nongnu.org/mailman/listinfo/paparazzi-devel