End-effector position

End-effector position captures the translation of the relative frame transformation:

$$\Phi_\text{EffPos}(\boldsymbol{x}) = \boldsymbol{P}_A^B,$$

where $\boldsymbol{P}_A^B$ is translational part of $\boldsymbol{M}_A^B$. The Jacobian of this task consists of the rows of the geometric Jacobian corresponding to the translation of the frame.