## 3 Experiments and Results
### Inclination Calibration
However, when inclination is present, the inclination and CoM are coupled, making it impossible to reduce the error using only the crosstalk matrix. Furthermore, as seen in Equation (3), when there is no inclination, the sine term becomes 0, eliminating many terms. However, when inclination is present, a sine value appears, increasing the non-linearity. \begin{table}
\begin{tabular}{c c c c c c c c} \hline  & & \(f_{x}^{ext}\) & \(f_{y}^{ext}\) & \(f_{z}^{ext}\) & \(\tau_{x}^{ext}\) & \(\tau_{y}^{ext}\) & \(\tau_{z}^{ext}\) \\ \hline \multirow{4}{*}{MSE} & _No Calib._ & 3.113 & 0.650 & 4.413 & 0.011 & 0.060 & 0.000 \\  & _LSM Calib._ & 2.454 & 0.468 & 2.826 & 0.011 & 0.056 & 0.000 \\  & _Full Calib._ & 0.442 & 0.615 & 1.905 & 0.008 & 0.013 & 0.000 \\  & Improved (\%) & 85.8 & 5.4 & 56.8 & 27.3 & 65.3 & - \\ \hline \end{tabular}
\end{table} 
Table 6: The table of the MSE of force and torque for each axis with respect to 0 when calibration is performed using three methods on an inclined base. Figure 8: The graph comparing the external force and torque when calibration is performed using three methods on an inclined base. (**a**) The graph of the external force and torque when the scenario is performed on an inclined base with _No Calibration_. (**b**) The graph of the external force and torque when the scenario is performed on an inclined base with _LSM Calibration_ applied. (**c**) The graph of the external force and torque when the scenario is performed on an inclined base with _Full Calibration_ applied. Hence, the influence of inclination can be considered the most significant factor. This is notable in the experimental results shown in Figure 8, where the error remains large until the inclination is compensated for. We conduct the same pick-and-place motion with the gripper holding an object with 2 kg of mass. Since the gripper is grasping the object, the FT sensor measures the wrench resulting from both the gripper's weight and the object's weight. Given that the calibration was performed using the previously described method to compensate for the gripper's weight, the external wrench should reflect only the effect of the object's weight. The results of estimating the object's mass under three conditions are shown in Figure 9. To estimate the mass of an object grasped by the gripper, we calculated the l2-norm of external force. However, the actual wrench applied is not ideally separated into force and torque components. In the _No Calibration_ results, during the period between 2 and 8 s, where both force and torque are applied together, there is a significant fluctuation in the magnitude of the external force. This is due to the lack of ideal separation between force and torque, which requires the crosstalk calibration we propose. With _LSM Calibration_, force and torque separation is achieved, resulting in a more stable external force magnitude over the same period. However, due to the inclined base, there remains an offset from the true mass of 2 kg. Finally, in the _Full Calibration_ results, where the base incline is accounted for, the estimated mass converges closer to the actual 2 kg. The analysis of mass estimation data from the three calibration stages in the pick-and-place scenario is shown in Table 7. In the _No Calibration_ results, the error is due to crosstalk from external torque, while in the _LSM Calibration_ results, it is due to an offset from the inclined base. This is evident from the MSE result, which decreased 40% with respect to _No Calibration_. However, the remaining error reflects the failure to accurately separate force and torque due to the inclined base. With _Full Calibration_, compensating for the gravity axis error brought the estimated mass closer to 2 kg, and alignment of the gravity axis further reduced the MSE by an additional 91.7%. The above results were obtained from dynamic data collected during the pick-and-place scenario.