# Compensating Uncertainties in Force Sensing for Robotic-Assisted Palpation
## 5 Discussion  
This paper firstly investigates the sensor measurement uncertainties in the surgical application of force based robotic palpation, and mainly focuses on the inertial force caused by the surgical tools and/or probe on the robotic system. The inertial force issue has been noticed and researched in the industrial robotic application, in which a tool with a certain payload is normally utilized. From the surgical application point of view, safety and accuracy are important, thus making inertial force analysis and avoidance critical. Although the sensory technique is developing quite fast, with high sensitivity and resolution, the uncertainties and the inertial force caused by the tools attached to the sensor cannot be ignored. Force is a principal factor for some surgical procedures such as robotic palpation, in which the force is used for the stiffness analysis of the soft tissue. However, such analysis would be affected by force uncertainties. We have performed several free motion robotic palpation experiments, and the significant force feedback indicates that inertial force is inevitable, which will affect the stiffness analysis of soft tissue, further possibly leading to the inaccurate detection of a tumor in robotic palpation. This free motion force information is used to model the inertial force, and a force  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Palpation Cases** & **Original** & **Corrected** & **Static** \\ \hline No hard inclusion & \(1.0158\times 10^{5}\) & \(0.94711\times 10^{5}\) & \(0.71647\times 10^{5}\) \\ \hline Hard inclusion at 5 mm & \(1.7233\times 10^{5}\) & \(1.6567\times 10^{5}\) & \(1.45105\times 10^{5}\) \\ \hline Hard inclusion at 8 mm & \(1.2957\times 10^{5}\) & \(1.2283\times 10^{5}\) & \(1.2364\times 10^{5}\) \\ \hline Hard inclusion at 10 mm & \(1.5441\times 10^{5}\) & \(1.4772\times 10^{5}\) & \(1.3505\times 10^{5}\) \\ \hline \hline \end{tabular}
\end{table}
Table 2: The average YM during palpation (Unit: Pa).  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Palpation Cases** & \(YMBT_{os}\) & \(YMBT_{cs}\) \\ \hline No hard inclusion & 41.78\% & 32.19\% \\ \hline Hard inclusion at 5 mm & 18.76\% & 14.17\% \\ \hline Hard inclusion at 8 mm & 4.80\% & 0.65\% \\ \hline Hard inclusion at 10 mm & 14.34\% & 9.38\% \\ \hline \hline \end{tabular}
\end{table}
Table 3: YM bias term (YMBT) during the robotic palpation experiments.  
compensation framework is proposed to cancel the inertial force during the robotic palpation task. In this paper, a neural-network-based approach is used to model the inertial force by considering the velocity and acceleration of the robot end effector.  
From the experimental studies, it is seen that the inertial force affects the accurate analysis of the soft tissue stiffness. Since it is the first study of the inertial force in surgical robots, the approach developed in this paper can also be extended to other surgical applications, such as bilateral teleoperation for RAS. In bilateral teleoperation, the whole operation is a dynamic procedure, and the inertial force is caused once the robot is teleoperated either with a small or long distance. Using the force compensation framework developed in this paper, the operator can obtain enhanced force feedback from the operative site, thus guaranteeing safe and accurate surgical operations.  
It is also worth mentioning that the proposed approach is simple to implement in real applications when compared with other approaches like a Kalman filter. To train the inertial force compensation model, one only needs to obtain data from the free motion experiments. The collected data will be used to train the neural network. Then, the trained neural network is utilized to compensate for the inertial force during the robotic palpation in an online manner.