# Compensating Uncertainties in Force Sensing for Robotic-Assisted Palpation
## 4 Experiment Studies and Result Analysis
### Neural-Network-Based Force Compensation of Robotic Palpation
The main reason is because the distance depends on the coordinates we choose while velocity and acceleration do not (the constant terms due to coordinate shift will disappear in the differentials of the distance according to time), which means the trained model can be used in different coordinates. In the neural network modeling, the number of input layer nodes is chosen as 2 since only the velocity and acceleration are used, the number of output layer nodes is chosen as 1, and the number of hidden  
Figure 10: Top sub figure: The average of the same free movements (black curves) of the force sensor. Bottom sub figure: The velocity (red curves) and acceleration (blue curves) calculated by the movements and time. Figure 9: Average of force data output from 10 same free motion experiments. Figure 14: Force correction of the ’hard inclusion 8 mm beneath the surface’ case. The blue curve is the original measured force from the sensor, and the black curve shows the corrected force by using the force compensation approach. Peak forces are highlighted with red circles. Figure 12: Force correction of the ’no hard inclusion’ case. The blue curve is the original measured force from the sensor, and the black curve shows the corrected force by using the force compensation approach. Peak forces are highlighted with red circles. Figure 13: Force correction of the ’hard inclusion 5 mm beneath the surface’ case. The blue curve is the original measured force from the sensor, and the black curve shows the corrected force by using the force compensation approach. Peak forces are highlighted with red circles. In addition, to further verify the effect of force correction in palpation, the YM analysis at those peak points are conducted since YM is an important aspect to be considered during robotic palpation [22]. For the purpose of comparison, the static experiments have been conducted under the same depth of hard inclusion. The YM from the static experiments is used as the reference value to reflect the stiffness of soft tissue in the palpation. The original and corrected YM at the peak points can be viewed in Figures 16-19. The average original, corrected and static YM is also presented in Table 2. From Table 2, it can be found that the YM calculated by the corrected force data is more close to the static experiments, which verifies again the effectiveness of the proposed method. Figure 16: Young’s modulus (YM) for the ’no hard inclusion’ case. The blue curve denotes the YM by original force measured by sensor, and the black curve indicates the YM by compensated force. Figure 10.0 Force correction of the ’hard inclusion 10 mm beneath the surface’ case. The blue curve is the original measured force from the sensor, and the black curve shows the corrected force by using the force compensation approach. Peak forces are highlighted with red circles. Figure 10.1 YM for the ’hard inclusion 5 mm beneath the surface.’ The blue curve denotes the YM by original force measured by sensor, and the black curve indicates the YM by compensated force. Figure 10.2 YM for the ’hard inclusion 10 mm beneath the surface’ case. The blue curve denotes the YM by original force measured by sensor, and the black curve indicates the YM by compensated force. Figure 10.3 YM for the ’hard inclusion 5 mm beneath the surface.’ The blue curve denotes the YM by original force measured by sensor, and the black curve indicates the YM by compensated force. In order to further demonstrate the improvement of force compensation approach in terms of YM in the previous experiments, a YM bias term (YMBT) is designed to present the difference of the original/corrected and static YMs as shown:  
Figure 10.4  
Figure 10.5  
in which \(YMBT_{os}\) shows the difference between the original YM and static YM, meanwhile, \(YMBT_{cs}\) indicates the difference between corrected YM and static YM. Since the static YM is used to indicate the real YM of the soft tissue in this paper, a smaller YMBT value means that the obtained YM is much closer to the real YM.