End-effector positionΒΆ
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.