# Compensating Uncertainties in Force Sensing for Robotic-Assisted Palpation
## 4 Experiment Studies and Result Analysis
### Neural-Network-Based Force Compensation of Robotic Palpation  
Besides determining the structure of the neural network model, the training process is also important to build a proper model and the training data should be selected carefully. In addition, the training process should be designed in a simplified way to provide for the concerns of the real application. In the proposed approach, the training data is generated by the free movement of the force sensor without any touch on the tip. However, non-negligible noise is found during the movement, which makes the data hard to analyze. To address the random noise, the same free movement experiments are conducted 10 times and then we use the average of those data to train the neural network model. The data of the 10 experiments can be viewed in Figure 8 and the average of the data can be viewed in Figure 9. It can be found that after averaging all of the 10 experiments, the force response in Figure 9 is much smoother than those in Figure 8. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Time** & **No Hard Inclusion** & **Hard Inclusion 5 mm** & **Hard Inclusion 8 mm** & **Hard Inclusion 10 mm** \\ \hline
1 & 7.8037 \(\times\) 104 (1.62 N and 3 mm) & 1.4403 \(\times\) 105 (2.99 N and 3 mm) & 1.0212 \(\times\) 105 (2.12 N and 3 mm) & 1.3777 \(\times\) 105 (2.86 N and 3 mm) \\ \hline
2 & 8.1764 \(\times\) 104 (2.61 N and 4 mm) & 1.3627 \(\times\) 105 (4.35 N and 4 mm) & 1.0526 \(\times\) 105 (3.36 N and 4 mm) & 1.3251 \(\times\) 105 (4.23 N and 4 mm) \\ \hline
3 & 7.0185 \(\times\) 104 (3.11 N and 5 mm) & 1.3643 \(\times\) 105 (6.10 N and 5 mm) & 1.005 \(\times\) 105 (4.48 N and 5 mm) & 1.3643 \(\times\) 105 (6.10 N and 5 mm) \\ \hline
4 & 6.7953 \(\times\) 104 (3.98 N and 6 mm) & 1.3487 \(\times\) 105 (7.84 N and 6 mm) & 1.2959 \(\times\) 105 (7.34 N and 6 mm) & 1.2959 \(\times\) 105 (7.59 N and 6 mm) \\ \hline
5 & 6.721 \(\times\) 104 (4.98 N and 7 mm) & 1.4133 \(\times\) 105 (10.45 N and 7 mm) & 1.2985 \(\times\) 105 (9.88 N and 7 mm) & 1.3971 \(\times\) 105 (10.33 N and 7 mm) \\ \hline
6 & 7.1527 \(\times\) 104 (6.47 N and 8 mm) & 1.477 \(\times\) 105 (13.31 N and 8 mm) & 1.3394 \(\times\) 105 (12.07 N and 8 mm) & 1.362 \(\times\) 105 (12.32 N and 8 mm) \\ \hline
7 & 6.8273 \(\times\) 104 (7.34 N and 9 mm) & 1.5738 \(\times\) 105 (16.92 N and 9 mm) & 1.4328 \(\times\) 105 (15.43 N and 9 mm) & 1.3498 \(\times\) 105 (14.56 N and 9 mm) \\ \hline
8 & 6.8231 \(\times\) 104 (8.59 N and 10 mm) & 1.6283 \(\times\) 105 (20.53 N and 10 mm) & 1.4822 \(\times\) 105 (18.66 N and 10 mm) & 1.3324 \(\times\) 105 (16.80 N and 10 mm) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: YM with static palpation experiments (Unit: Pa). From the movements of the force sensor, the velocity and acceleration of the movements can be calculated by the differential of the distance according to time, which are very important information of the movements. The values of the distance, velocity, and acceleration can be viewed in Figure 10. It should be pointed out that a moving average process is conducted on those values (the distance, velocity, and acceleration) to make them more smooth, which will further make the obtained model more robust. To train the neural network model, the state variables such as the distance, velocity, and acceleration of the force sensor can be used as the training input while the force output of the force sensor will be used as the training target output. The purpose of the modeling is to establish the mapping from the states of the force sensor by the input and output data, as illustrated in Figure 11.  
In the training process, 500 uniformly sampled data from the state variables and the force output are used as the training input and output. To make the modeling method easier to implement, we adopt only the velocity and acceleration of the force sensor as the training input instead of including the distance.