# Compensating Uncertainties in Force Sensing for Robotic-Assisted Palpation
## 2 Robotic palpation with Force Based Approach
### Robotic Palpation with Force Compensation  
The uncertainties of force measurement exist widely in a robotic system, and thus may cause unexpected performance. In the robotic palpation, we use YM to quantitatively analyze the mechanical property of the soft tissue and to detect the tumor area based on YM values. But the uncertainties of the sensor measurement may mislead the determination of the tumor inside the soft tissue. Most force sensors are capable of providing a good initialization step before recording force data, which can remove the influence of the probe gravity (\(f_{g}\) as shown in the previous section). However, the inertial force (\(f_{i}\) as presented in the previous section) cannot be solved simply by initialization as it may change during the dynamic robotic manipulation. To achieve an accurate interaction, the inertial force cannot be ignored, and the proper method is desired to cancel the influence of the inertial force.  
A force compensation framework of the robotic palpation is developed as shown in Figure 3. The _yellow_ block shows the normal robotic palpation approach as used in previous studies, in which the measured force from the sensor is directly used for the analysis of the mechanical property of soft tissue (as shown in Equation (3)). It is possible to obtain the close stiffness of the soft tissue once the whole procedure is arranged as static measurement (in which the robot is controlled to palpate the soft tissue with a defined indentation depth and the force data is collected when the robot keeps still at the indentation depth until the force data is stable. The static force data in this paper is defined as an average value from the sensor measurement for 10 s.). However, this static measurement usually slows down the procedure and also requires the operator to focus on the data collection.  
It is desired and necessary to get an accurate determination during the dynamic surgical procedure. Thus a force compensation solution is developed to remove the effect of inertial force during palpation, as shown in the blue block. The inertial force can be modeled online as \(\tilde{f}_{i}\), and then canceled from the force measurement \(f_{m}\). By this method, the compensated contact force \(f_{c}\) during the robotic palpation can be derived as:  
\[f_{c}=f_{m}-\tilde{f}_{i}-f_{g}. \tag{5}\]  
Before the procedure, the gravity influence can be removed by the sensor initialization, thus \(f_{g}\) can be considered as 0. The modeled inertial force \(\tilde{f}_{i}\) can also be canceled by using Equation (5). With this compensated approach, an accurate interaction force during the palpation task can be obtained, and thus can be used to calculate the perceived stiffness of the soft tissue. To model the inertial force, a neural-network-based method will be introduced in the next section.  
Figure 3: Force compensation framework of robotic palpation. The yellow block contains the original information measured directly from the sensor and robot. By using this information, the YM can be calculated but with potential measurement uncertainties such as inertial force. In the blue block, a force compensation framework is designed to remove the influence of inertial force from the sensor measurement. Thus the YMs can be obtained by the compensated force.