# Development of an Adaptive Force Control Strategy for Soft Robotic Gripping
## 3 Results and Discussion
### Visual Force Sensor
#### 3.1.2 Force Sensing  
The generalization of the visual force sensor was tested by training a random forest regression on two separate round shapes, with radii of 10 mm and 50 mm. The regression \begin{table}
\begin{tabular}{c c} \hline
**Parameter** & **Value** \\ \hline Training Time & \(\sim\)9 min \\ \hline Training Error & 0.165 pixels \\ \hline Test Time & \(\sim\)0.5 min \\ \hline Test Error & 0.172 pixels \\ \hline \end{tabular}
\end{table} 
Table 4: Autoencoder training results. Figure 10: Fin ray with occlusions reconstructed using fin ray. Figure 9: Binary cross-entropy loss of autoencoder training process. model took an input of the encoded image, with an output of the predicted force applied by the gripper. Table 5 summarizes the random forest regression model. This model was then tested on a third shape between the two, a 25 mm circle. To ensure that the model was trained on a dataset of high-resolution force data, the data were collected by pushing the finger into the object at steps of one millimeter. The finger was pushed over a range of 32 mm. This indentation depth was chosen as the gripper stalls at 80 N, and 32 mm is the depth that can be reached without stalling for all shapes tested. The training objects and results are shown in Figures 11 and 12, and the results of the novel test object are shown in Figure 13. The results below compare the true value recorded by a load cell next to the force measured by the trained camera sensor as the gripper performs a slow gripping motion across the gripper's trained range of motion. The labeled components describing the gripping process are summarized in Table 6.  
As can be seen in the table, the sensor performs well on the training and test shapes. The novel shape performs the worst while still achieving a mean squared error of 1.029 \(N^{2}\), which is acceptable. Due to the process of perspective warping the input image to view the gripper from a normalized angle, the camera sensor is fairly robust to changes in camera angle if it is calibrated correctly after the change in angle. This, however, is a limitation of this design, as the calibration needs to be performed every time the camera is moved. A comparison of the methods developed in this paper to other work can be seen in Table 8. The force estimation was compared to four methods, each using different strategies. [PERSON] et al. 's work is the most similar to the methods presented, where a U-Net neural network was used to predict the stress in the fin ray structure, and a dense neural network was used to estimate the gripping force, using FEA to generate data [18]. In another work using a more analytical approach, [PERSON] et al. developed a solution using a chained-beam-constraint model, a method used to model flexible cantilever beams [20], and converting the deflections into a force. Other works used more hardware-driven approaches. Using a series of deformation sensors along the back of the finger, [PERSON] et al. measured the deflection and mapped the measurements to the estimated force [19]. The final method, developed by [PERSON] et al., compared to this work used visual markers placed at nodes on the finger to measure the deflections and converted these measurements into forces, once again using FEA tools [22]. \begin{table}
\begin{tabular}{c c} \hline \hline
1 & Estimated Gripping Force \\ \hline
2 & Measured Load Cell Reaction Force \\ \hline
3 & Indentation Depth \\ \hline
4 & Load Cell \\ \hline
5 & Fin Ray Length (135 mm) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Gripping process components. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Radius (mm)** & **50.8 (Training)** & **10 (Training)** & **25.4 (Testing)** \\ \hline MSE (\(N\)) & 0.67 & 0.84 & 1.01 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Sensor results for three shapes. Figure 13: Force profile for novel 25 mm object. (**a**) Novel 25 mm object data capture setup; (**b**) force comparison between load cell sensor and visual sensor for a novel 25 mm object.