# A Rectangular Toroidal Current-Based Approach for Lung Biopsy Needle Tracking
## 3 Results
### System Test and Response  
A robotic arm was used to test the system's stability and performance. The experiment included position variation tests and angle variation tests, aimed at evaluating the system's positioning accuracy under changes in both position and angle. The robotic arm was employed for control, with the arm's pose used as the true value of the simulated biopsy needle's pose. The deviation between the true value and the system's calculated value was then computed to assess the positioning accuracy of the inertial-assisted electromagnetic positioning system. Figure 10: Moving accuracy for different pitch angles: (**a**) Real and theoretical displacement along the \(x\)-axis at 30\({}^{\circ}\). (**b**) Real and theoretical displacement along the \(x\)-axis at 45\({}^{\circ}\). (**c**) Real and theoretical displacement along the \(x\)-axis at 45\({}^{\circ}\). \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Orientation**} & \multirow{2}{*}{**Shift**} & \multirow{2}{*}{**Right**} & \multirow{2}{*}{**Upward**} & \multirow{2}{*}{**Move**} & **Left** & \multirow{2}{*}{**Right**} & \multirow{2}{*}{**Down**} & **30** & **60** & **45** \\  & & & & & & & **Move** & & & **Degrees** & **Degrees** & **Degrees** \\ \hline \(x\) (mm) & 1.61 & 1.42 & 0.57 & 1.17 & 2.12 & 1.05 & / & / & 1.01 & 0.89 & 0.77 \\ \(y\) (mm) & 1.52 & 1.25 & 1.29 & 1.34 & 1.46 & 1.34 & / & / & 0.36 & 0.53 & 0.69 \\ \(z\) (mm) & 2.22 & 1.89 & 1.41 & 1.78 & 2.58 & 1.71 & 2.46 & 1.26 & 1.07 & 1.04 & 1.02 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: RMSE values for different movement directions and positions. In the experiment, the robotic arm controlled the movement of the simulated biopsy needle. The robotic arm used was the FR-3 model, shown in Figure 11, and it was fixed on a metal frame to ensure the base of the arm remained stationary. The key parameters of the robotic arm are listed in Table 6.  
As shown in the Table 7, the robotic arm's effective payload is capable of bearing the weight of the simulated biopsy needle. Its working radius covers the operational area of the electromagnetic positioning system, and its repeatable positioning accuracy significantly outperforms that of electromagnetic positioning products available on the market. Therefore, this robotic arm can be used to test the positioning accuracy of the inertial-assisted electromagnetic positioning system. The initial position of the simulated biopsy needle was determined, and the specific location of the starting point was obtained using the robotic arm's position information. Induced voltage and angle signals were collected, and the position of the simulated biopsy needle was calculated. The electromagnetic positioning system was used for the positioning of the simulated biopsy needle, and the position error was calculated. The position of the simulated biopsy needle was changed, and the experiment was repeated 2000 times to obtain the computed data and the actual true positions. The robotic arm was used to control the simulated biopsy needle's movement within the working area, with the arm's position information serving as the true position value of the simulated biopsy needle. After \begin{table}
\begin{tabular}{c c} \hline \hline
**Parm Name** & **Value** \\ \hline Effective payload & 3 kg \\ Work radius & 622 mm \\ Repeatability accuracy & \(\pm\)0.02 mm \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Parameters of the robotic arm. Figure 11: System test platform (FR-3 Robotic Arm). The FR-3 Robotic Arm serves as the primary platform for evaluating the performance of the biopsy needle tracking system. The robotic arm is equipped with precise motion control capabilities, enabling the accurate simulation of real-world scenarios for needle positioning and movement.