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jcarpent avatar jcarpent commented on June 27, 2024

Add also random method for each joint

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jmirabel avatar jmirabel commented on June 27, 2024

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 and b (the quaternion representation)
  • or the angle axis that has the shortest angle, between a and b or between a 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 configurations q1 and q2 can be equal even if q1.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

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jcarpent avatar jcarpent commented on June 27, 2024

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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fvalenza avatar fvalenza commented on June 27, 2024

Solved with #141

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