If this is not document, this is extremly confusing especially in the INERTIAL_FIXED_REPRESENTATION case, as in that case "inertial-fixed representaton" is used a synonime for "right-trivialized representation", that is true for the absolute velocity, but that is misleading for the relative velocity, as in that case the velocity is expressed in the reference frame $R$ instead of the inertial-fixed frame.
Currently, the dcs of getRelativejacobian do not clarify in which frame the velocity obtained multipling the relative jacobian by the internal joint velocity vector is expressed, and it only say "w.r.t. frame expressed depending on the velocity representation", see https://github.com/robotology/idyntree/blob/f9051752ca5a6ca8f3a4f101e4a536fe1eb62c5f/src/high-level/include/iDynTree/KinDynComputations.h#L708 . the actual semantics is documented only in the code itself in https://github.com/robotology/idyntree/blob/f9051752ca5a6ca8f3a4f101e4a536fe1eb62c5f/src/high-level/src/KinDynComputations.cpp#L1690 . In particular, the semantics is (if we call $R$ the referenceFrame and $F$ the frame, and we use the notation from https://research.tue.nl/en/publications/multibody-dynamics-notation-version-2):
getFrameVelocityRepresentation
valuegetRelativeJacobian
semanticsMIXED_REPRESENTATION
(default)INERTIAL_FIXED_REPRESENTATION
BODY_FIXED_REPRESENTATION
If this is not document, this is extremly confusing especially in the
INERTIAL_FIXED_REPRESENTATION
case, as in that case "inertial-fixed representaton" is used a synonime for "right-trivialized representation", that is true for the absolute velocity, but that is misleading for the relative velocity, as in that case the velocity is expressed in the reference frame $R$ instead of the inertial-fixed frame.Related issues: https://github.com/robotology/idyntree/issues/395, https://github.com/robotology/wb-toolbox/issues/225#issuecomment-903143803 .
cc @HosameldinMohamed @Giulero