While most of the roboticist consider position task-space control, one should also consider orientation of the end-effector. \[ \mathbf{M(q)\ddot{q}+C(q,\dot{q})\dot{q}+g(q)}=\boldsymbol{\tau}_\text{in} \tag{1} \]
The task-space impedance controller for orientation is defined by: \[ \boldsymbol{\tau}_\text{in} = \mathbf{K_p(p_0-p) + B_q(\dot{p}_0-\dot{p})} + \mathbf{g(q)} \tag{2} \] In this equation, \(\mathbf{K_q},\mathbf{B_q} \in \mathbb{R}^{n\times n}\) are constant symmetric positive-definite matrices; \(\mathbf{q_0}(t)\) is a reference joint trajectory.
The example of this controller can be checked .