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I want to calculate the Jacobian of a robot system while I want to restrict the rotational change of the pose to only the unit vector of the relative rotation, which essentially says that I don't care the rotation amount around that unit vector. This would be useful for example when the end-effector is a needle and has rotational symmetry.
I want to leverage the existing KDL implementation of Jac calculation. Any suggestions on how to do that?

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I have figured this out. And it seems to be fairly simple:

  1. find out the direction of symmetric axis w.r.t the final effector frame. For example in my case it's x direction.
  2. Select a Euler angle format in which the last axis is along that direction.
  3. Calculate the relation of time derivative of the Euler angles with the angular velocity. This is straight forward since each of these rotations is a along one of the intermediate axis of rotations for euler angles. The result is a matrix multiplication.
  4. By inverting this relationship matrix from the Jacobian matrix from KDL and dropping the 6-th row we get the Jacobian from the 5 cartesian dof relative to the joint variables of the system.
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