Algorithm 1 Automated Centering Procedure

1: Procedure AutoCenter(${\mathit{q}}_d$)  # ${\mathit{q}}_d$ is the desired joints configuration to measure 2: MAX_EPSILON $\leftarrow$ 0.010   # 0.010 mm = position repeatability 3: Move the robot to ${\mathit{q}}_d$    # from MATLAB to Controller 4: Wait 1 s                # to ensure effective communication 5: Send data request             # from MATLAB to U-WAVE-R 6: $r_x\leftarrow$ Measurement of indicator along the tool X  # from U-WAVE-R to MATLAB 7: $r_y\leftarrow$ Measurement of indicator along the tool Y  # from U-WAVE-R to MATLAB 8: $r_z\leftarrow$ Measurement of indicator along the tool Z  # from U-WAVE-R to MATLAB 9: $\mathit{r}\leftarrow \left[r_x,r_y,r_z\right]$ 10: while(norm($\mathit{r}$)) >= MAX_EPSILON do 11:  Move the robot’s TCP by vector $\mathit{r}$         # from MATLAB to Controller 12:  Wait 1 s                     # to ensure effective communication 13:  Send data request                # from MATLAB to U-WAVE-R 14:  $r_x\leftarrow$ Measurement of indicator along the tool X  # from U-WAVE-R to MATLAB 15:  $r_y\leftarrow$ Measurement of indicator along the tool Y  # from U-WAVE-R to MATLAB 16:  $r_z\leftarrow$ Measurement of indicator along the tool Z  # from U-WAVE-R to MATLAB 17: $\mathit{r}\leftarrow \left[r_x,r_y,r_z\right]$ 18: return ${\mathit{q}}_a\leftarrow$ Actual joints configuration        # from Controller to MATLAB