Disagreement between TransformStamped comment and sendTransformMessage?

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The problem that you're seeing is that the value of the transform depends on what the object is that you are applying the transform, the data in frame A or the frame itself.

The sendTransform documentation is ambiguous and references the data transform, whereas the message is not and fully references the frame. The sentTransform documentation could be made more explicit to do this differentiation.

There's a duplicate question and answer here: https://answers.ros.org/question/1940...

People most often encounter this in lookup vs echo: https://github.com/ros/geometry/issue...

I think that both comments are correct, assuming you distinguish a subtle difference between the words "transform" and "transformation".

The pose in the TransformStamped message describes the pose of the child frame within the parent frame. For example, using standard xy axes and identity quaternion, the msg value transform.translation.x = 1 places the child_frame origin to the right of the parent_frame origin. The TF Tree clearly describes a parent to child relationship.

The terminology gets less clear if your goal is to convert a child pose into the equivalent parent frame pose. You can reformat the TF msg as an equivalent homogeneous 4x4 matrix M and use this linear algebra equation:

pose_in_parent = M * pose_in_child

If you expect to use this equation, then M can be interpreted as providing a "transformation" operation from child_frame to parent_frame, which is what that second comment is describing.