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ptc-13682881-Visitor
1-Visitor
April 29, 2010
Question

3D Rotation [Quaternion]

  • April 29, 2010
  • 1 reply
  • 5853 views
This is the quaternion rotation. The note may not apply exactly, it comes from the TrigRot ... which I have removed to avoid confusion. The difference with "this" typical QuatRot and the traditional TrigRot is that the axis system is different. Otherwise, setup your quaternion vector to rotate. Accordingly to the literature, there is economy in the APOS [Arithmetic Operations]. This point is debatable, considering the real or not real need for the about 21 AOPS trig approximation for about 18 decimals or more exactly 16 machine precision decimals ... that in fact no aircraft need such angular accuracy !!!
But Philip insisted and made his point on AOPS reduction based QuatRot.
TrigRot metafile added.

jmG

1 reply

P
PhilipOakley1-Visitor
1-Visitor
May 2, 2010
On 4/29/2010 10:45:39 PM, jmG wrote:

... that in fact no
>aircraft need such angular
>accuracy !!!
>But Philip insisted and made
>his point on AOPS reduction
>based QuatRot.
>
>jmG

Jean,

The reason that the aircraft do rely on
quaternions is because they are computing the
compound action of the roll, pitch and yaw from
the aircraft gryo scopes at a few hundred Hz, in
some cases over a kHz, so round off errors can
build very quickly. Any technique that is simple
to compute and has a wide accuracy range is sought
- hence quaternions are used.

Apollo used quaternions for attitude control for
the same reasons.

Philip Oakley
P
ptc-13682881-VisitorAuthor
1-Visitor
May 2, 2010
On 5/2/2010 8:47:00 PM, philipoakley wrote:
>On 4/29/2010 10:45:39 PM, jmG wrote:
>
>... that in fact no
>>aircraft need such angular
>>accuracy !!!
>>But Philip insisted and made
>>his point on AOPS reduction
>>based QuatRot.
>>
>>jmG
>
>Jean,
>
>The reason that the aircraft do rely on
>quaternions is because they are
>computing the
>compound action of the roll, pitch and
>yaw from
>the aircraft gryo scopes at a few
>hundred Hz, in
>some cases over a kHz, so round off
>errors can
>build very quickly. Any technique that
>is simple
>to compute and has a wide accuracy range
>is sought
>- hence quaternions are used.
>
>Apollo used quaternions for attitude
>control for
>the same reasons.
>
>Philip Oakley
_____________________________________

I understand all that Philip, and take it graciously. In my times, computers were mostly analog, black boxes [Dassault was a big black box by itself]. My first employer had the contract for the automatic pilot of the Concorde, even that one was dark gray. Quaternions are then new to me, but from some of the work sheets, a bit mystic as there are only 3 axes and 4 inputs. I'm haunted by: how is the quaternion vector [4 inputs] collected from a 3 axes system.

Very interesting.

Jean
P
PhilipOakley1-Visitor
1-Visitor
May 3, 2010
On 5/2/2010 10:49:13 PM, jmG wrote:

>Quaternions are then new to me, but from
>some of the work sheets, a bit mystic as
>there are only 3 axes and 4 inputs.

>I'm
>haunted by: how is the quaternion vector
>[4 inputs] collected from a 3 axes
>system.
>
>Very interesting.
>
>Jean

They certainly can be confusing..... which is why I have been pursuing the discussion.

[3->4 componet question]
When they take in the small angle rotations (for a delta t step) the values in radians are placed as the three 'vector' elements, and the scalar part is left as 1 (unity). This is essentially a tan(theta) approximation). Plus the p=qrq* formulation means that they can use theta/2, rather than theta, so the range of near linear angles increase, and they have pushed the 'bad' scalar part (1 ratehr than cos(theta)) into a component that can be ignored (that is, we know the object hasn't expanded, so we can ignore the scale change!).

There are still one or two 'Mathematics to Engineering' steps I'm trying to make sure I fully comprehend, but I feel I'm pretty close.

Philip Oakley
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