Jacobian transpose: How to calculate orientation error?

I’m confused about how to compute the error in orientation. All the documents I’ve read don’t explain how to do it.

The error in position is simply the difference between the points.

Let’s assume we have the orientation along the effector axis, and we represent the rotation with quaternions. I have two questions:

• Is describing the orientation with quaternions a good approach?
• How can we compute the error in orientation with the quaternions to use this in jacobian transpose?