Fig. 3.

Block diagram for the closed-loop control system. It shows the high-level controller, the mid-level optimizer and the low-level joint velocity controller. The signals definitions include $F_h^b$: user force, ${\dot{X}}_{\mathit{\text{desired}}}^b$: end-effector desired body velocity, ${\dot{X}}_{\mathit{\text{desired}}}^s$: end-effector desired spatial velocity, ${\dot{X}}_{\mathit{\text{real}}}^s$: end-effector real spatial velocity, ${\dot{q}}_{\mathit{\text{desired}}}$: desired joint velocities, ${\dot{q}}_{\mathit{\text{real}}}$: real joint velocities, F_sx and F_sy: real slcera force components in frame {B}, f_dx and f_dy: desired slcera force components in frame {B}.