## 3 Experimental Results
### In Vivo Experiment  
This section introduces the result of the reconstruction of a 3D coordinate system of a C-arm and a vascular map of a mini pig's SFA for the operation of an MMR controlled by an MNS using two X-ray images and four corners of the MNS. We also controlled the magnetic field to operate the MMR along the SFA. This animal experiment was conducted with the approval of the Animal Experiment Ethics Committee of Yonsei University Medical Center (Approval Number: CPEC-IACUC-22-1008) and conformed to the Animal Protection Act (Law No. 16544, enacted on 27 August 2019) and the Laboratory Animal Act (Law No. 15944, enacted on 12 March 2019). Figure 6 shows the experimental setup. The experimental space is divided into an operating room where the procedure is conducted and a control room where a medical doctor can control the procedure remotely to avoid the radiation hazard. The operating room is equipped with a feeding robot, an MNS, and a commercial C-arm. The feeding robot consists of a feeding part to insert a delivery catheter with an untethered micro robot and a guidewire into the vessel, and a syringe part to inject contrast agent and drug into the vessel. The MNS used in this experiment was a RAMAN system (RAMAN-01, Intermag Inc., Seoul, Republic of Korea) [7]. To calculate the relative rotation angle between the two views, we utilized four corners of the RAMAN system's upper electromagnets as the corresponding points, as shown in Figure 7. For the two electromagnets connected by \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \(\boldsymbol{\theta_{disp}}\)[\({}^{\circ}\)] & \(\boldsymbol{\varphi_{disp}}\)[\({}^{\circ}\)] & \multicolumn{4}{c}{**2D Errors [mm]**} & \multicolumn{4}{c}{**3D Errors**} \\  & & **Max.** & **Min.** & **Mean** & **Max.** & **Min.** & **Mean** \\ \hline \hline \multirow{5}{*}{\(-15\)} & \(-10\) & 0.266 & 0.003 & 0.101 & 1.883 & 0.022 & 0.669 \\  & \(-5\) & 0.231 & 0.001 & 0.097 & 1.088 & 0.004 & 0.438 \\  & 0 & 0.197 & 0.001 & 0.073 & 0.881 & 0.000 & 0.357 \\  & 0 & 5 & 0.249 & 0.001 & 0.113 & 0.879 & 0.007 & 0.279 \\  & 10 & 0.312 & 0.003 & 0.119 & 1.189 & 0.010 & 0.336 \\ \hline \multirow{5}{*}{\(-10\)} & \(-10\) & 0.305 & 0.001 & 0.089 & 1.552 & 0.012 & 0.521 \\  & \(-5\) & 0.250 & 0.002 & 0.089 & 2.079 & 0.007 & 0.528 \\  & 0 & 0.181 & 0.006 & 0.125 & 2.479 & 0.048 & 0.943 \\  & 5 & 0.240 & 0.003 & 0.093 & 1.516 & 0.004 & 0.336 \\  & 10 & 0.308 & 0.001 & 0.103 & 1.162 & 0.004 & 0.368 \\ \hline \multirow{5}{*}{10} & \(-10\) & 0.401 & 0.003 & 0.099 & 1.533 & 0.007 & 0.447 \\  & \(-5\) & 0.341 & 0.003 & 0.098 & 3.203 & 0.007 & 0.781 \\  & 0 & 0.190 & 0.001 & 0.103 & 2.442 & 0.038 & 0.946 \\  & 5 & 0.456 & 0.005 & 0.101 & 1.589 & 0.007 & 0.409 \\  & 10 & 0.782 & 0.003 & 0.105 & 2.617 & 0.036 & 1.168 \\ \hline \multirow{5}{*}{15} & \(-10\) & 0.318 & 0.001 & 0.103 & 1.821 & 0.016 & 0.670 \\  & \(-5\) & 0.292 & 0.001 & 0.101 & 1.826 & 0.034 & 0.770 \\ \cline{1-1}  & 0 & 0.193 & 0.003 & 0.089 & 1.642 & 0.217 & 0.911 \\ \cline{1-1}  & 5 & 0.263 & 0.005 & 0.111 & 1.707 & 0.015 & 0.574 \\ \cline{1-1}  & 10 & 0.311 & 0.002 & 0.118 & 2.133 & 0.016 & 0.870 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The 2D and 3D errors between the calculated and actual coordinates for the centerline of a jig. the same back yoke, the distance between the inner corners is 55.0 mm and the distance between the outer corners is 69.5 mm, as shown in Figure 7a. In addition, the distance between the two electromagnets located on opposite sides was 200.0 mm, as shown in Figure 7b. We set the four corresponding points from the four inner or four outer corners of the two electromagnets, which are more clearly captured in the X-ray image. The selected corresponding points indicate the position of the electromagnet and, therefore, can be used to determine the 3D coordinate system of the MNS workspace. The commercial C-arm used in the experiment was an INFX-8000V (Canon Medical Systems Corporation, Ottawa, Japan).