Comments (4)
Add also random method for each joint
from pinocchio.
For the differentiate
method of SO3 joints, a convention must be chosen. This convention relates to what is being modelled: the rotation group or the unit quaternions group. Each rotation is mapped to 2 quaternions.
Thus, the "difference" between two quaternions a
and b
can be:
- either the angle axis between
a
andb
(the quaternion representation) - or the angle axis that has the shortest angle, between
a
andb
or betweena
and-b
(the rotation representation)
In HPP, we use the rotation representation. This has several implications. The one I can think of now are:
- Equality check:
a
and-a
must be considered as the same rotation for the whole software => two configurationsq1
andq2
can be equal even ifq1.isApprox (q2)
is false. - Difference and distance: use the angle axis that has the shortest angle
See https://github.com/jmirabel/hpp-model/blob/devel/src/joint-configuration.cc#L243
from pinocchio.
The second proposition is the rational one. Because, we are working on base orientation, which can be handled by many representations:
- rotation matrix (unique representation)
- quaternion, with a non-infectivity (a and -a leads to the same orientation)
- Euler angles (with a lot of drawbacks - singularities)
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Solved with #141
from pinocchio.
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