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<DIV><SPAN class=625344518-17072009><FONT face=Arial color=#0000ff size=2>Hi
Florian,</FONT></SPAN></DIV>
<DIV><SPAN class=625344518-17072009><FONT face=Arial color=#0000ff
size=2></FONT></SPAN> </DIV>
<DIV><SPAN class=625344518-17072009><FONT face=Arial color=#0000ff size=2>I had
a look on your file and modified it to get it working. While doing that, I
noticed several important points:</FONT></SPAN></DIV>
<DIV><SPAN class=625344518-17072009><FONT face=Arial color=#0000ff size=2>-
better use dictionary access by bone name instead of index number, it is more
portable</FONT></SPAN></DIV>
<DIV><SPAN class=625344518-17072009><FONT face=Arial color=#0000ff size=2>- you
cannot avoid using the bone rest pose because Blender introduces 180 roll all
the time, which ruins the angle calculation based only on the pose
matrix</FONT></SPAN></DIV>
<DIV><SPAN class=625344518-17072009><FONT face=Arial color=#0000ff size=2>- I
discovered a major flaw in the MathUtil library: it treats the matrix as row
major for matrix operations like multiplication but Blender returns column major
matrices. I wonder how nobody noticed that. I had implement my own matrix
multiplication function to work around that. Maybe it is my ignorance of the
Blender Python API.</FONT></SPAN></DIV>
<DIV><SPAN class=625344518-17072009><FONT face=Arial color=#0000ff
size=2></FONT></SPAN> </DIV>
<DIV><SPAN class=625344518-17072009><FONT face=Arial color=#0000ff
size=2>Attached you will find the script that gives exact joint angles. The
logic is quite simple and systematic: the joint angle is computed from the
difference between 1) the pose of a bone when combining the pose of its
parent and its own rest pose 2) its actual pose. The difference is only due to
the angle and as you only use 1DoF joints, it is quite simple to extract the
angle.</FONT></SPAN></DIV>
<DIV><SPAN class=625344518-17072009><FONT face=Arial color=#0000ff
size=2></FONT></SPAN> </DIV>
<DIV><SPAN class=625344518-17072009><FONT face=Arial color=#0000ff
size=2>Regards,</FONT></SPAN></DIV>
<DIV><SPAN class=625344518-17072009><FONT face=Arial color=#0000ff
size=2>Benoit</FONT></SPAN></DIV>
<DIV><SPAN class=625344518-17072009><FONT face=Arial color=#0000ff
size=2></FONT></SPAN> </DIV>
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<DIV></DIV>
<DIV class=OutlookMessageHeader lang=en-us dir=ltr align=left><FONT
face=Tahoma size=2>-----Original Message-----<BR><B>From:</B>
robotics-bounces@blender.org [mailto:robotics-bounces@blender.org] <B>On
Behalf Of </B>Florian Lier<BR><B>Sent:</B> jeudi 16 juillet 2009
20:51<BR><B>To:</B> Blender and Robotics; Blender Foundation Python
list<BR><B>Subject:</B> [Robotics] Computing IK Joint Angles
Pt.3<BR><BR></FONT></DIV>
<DIV class=moz-text-html lang=x-western><FONT
face="Helvetica, Arial, sans-serif" size=-1>Hey all and especially
Benoit,<BR><BR>i've implemented Benoits approach for computing joint angles
(in degrees)<BR><BR>To recapitulate the problem:<BR><BR>I've modelled a robot
arm with 5 joints (all joints are revolute joints). The arm is<BR>driven by an
"empty" target to an IK solver on top of the bone chain. I need to<BR>get the
joint angles in degrees or rad. Those joint angles are in range of the
X,Y,Z<BR>limits of the bones which form the chain.<BR><BR>The approach:
<BR></FONT><PRE wrap=""><B><FONT face="Helvetica, Arial, sans-serif">relativePose[n] =<SPAN class=moz-txt-citetags> </SPAN>inverse(poseMatrixTail[n-1])*poseMatrix[n]
<SPAN class=moz-txt-citetags>
"</SPAN>where n is the bone for which you compute the joint values and
<SPAN class=moz-txt-citetags></SPAN>poseMatrixTail is simply poseMatrix where the 4th column is replaced by
<SPAN class=moz-txt-citetags></SPAN>tail.<SPAN class=moz-txt-citetags> </SPAN>For the root bone, poseMatrixTail is the identity matrix."
</FONT></B><FONT face="Helvetica, Arial, sans-serif">As far as I've tested the setup all angles are computed correctly. The only problem is, that
I need to convert the angles from poseMatrix -> toEuler(). That's the last pitfall. Euler angles
are a bit tricky because the represent [yaw, pitch, bank]. By rotating some (or one) of the
parent bone/s the YAW, PITCH, BANK locally changes for the "target bone" [n] (for which I want to
compute the joint angle) so the resulting angle is either positive or negative - what's not THAT bad.
The biggest problem is - an euler angle is represented like [x (yaw),z (pitch),y (bank)].
Let's assume a bone rotates about the x axis (its' DoF). If all bones are in rest position the output when
rotation the bone is like: [100, x, x] after rotation one of it's parents the result is maybe: [x,x,100].
To me there's so predictable coherence whether the result can be found in x y or z.
<B>How can someone solve this problem?</B>
I've digged deep in the blender source code especially in armature.c and the IK_Solver sources.
The angle I need is represented as a float value in there :/.
[blender source from svn]
blender/intern/iksolver/intern/IK_QSegment.cpp [line 602]
BUT wrapping this code to Python, making the code invokable and finally extending the Python API
seems a little to exaggerated to me ...
So having the feature to extract several angles from an IK chain would be great in case of using blender
for robotics.
It would be great if someone can help me out - or if we can solve this problem in a more general manner
like really extending the python API ? I'll attach the appropriate blend file so everybody can play around
or visualize the problem. Most of the code is documented.
You can find the blend file here: <B><A class=moz-txt-link-freetext href="http://www.icram.de/BpyJointAngles.blend">http://www.icram.de/BpyJointAngles.blend</A></B>
Cheers, Florian
P.S. Sorry for crossposting this, but this is / maybe / not only a robotics issue...
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