# Path Planning for Localization of Radiation Sources Based on Principal Component Analysis
## 3 Experiments
### Simulations
#### 3.1.1 Condition (a) Single Radiation Source  
A simulation experiment was conducted by arranging a single radiation source, which can be regarded as a point source, as illustrated in Figure 10. We positioned 1 MBq of cesium-137 15 m from the all-around view Compton camera. The threshold for switching the principal component vector was set to 400. Triplets and higher multiplicities of Compton events were not considered; only Compton event pairs were considered. The moving distance of the mobile robot at each time step between the measurement points was set to 5 m. The measurement at each point was performed for 60 s, and the robot stopped during the measurement. The background radiation was not considered. Figure 8: All-around view Compton camera implemented in Geant4: the camera consists of a 12 \(\times\) 4 \(\times\) 30 array of CdTe detectors. The red, green, and blue arrows represent the \(X\)-, \(Y\)-, and \(Z\)- axes, respectively. Figure 9: Process of simulation experiments: the measurement data of gamma rays were produced using Geant4. Then, the radiation source distribution was reconstructed via simple back-projection. Finally, the next measurement point was determined using the PCA based on previous measurements. Figure 11a illustrates the simulation result. SP represents the first measurement point where the robot started to move, while EP is the position at which the gamma-ray measurements were completed. The color bar on the right represents the value added to each pixel. The black and red arrows represent the directions of the first and second principal components, respectively. The ground truth of the position of the radiation source is represented as a red dot. The detector was fixed on the mobile robot; therefore, the detector orientation at position \(\mathbf{x}_{i}\) was determined along the robot's movement direction, i.e., \(\mathbf{\overline{x}}_{i-1}\mathbf{\overline{x}}_{i}\). Figure 11b shows the detector orientation during the inspection. The detector orientation was zero when the X axis was facing upward, and clockwise rotation was defined as positive. Because the number of incident events was insufficient at the first and second measurement points, the robot moved toward the first principal component, thus approaching the radiation source. Subsequently, the robot altered the moving direction toward the second principal component as a sufficient number of incident events was later obtained. Accordingly, a path was generated to surround the radiation source. Because the number of incident events fell below the threshold at the 7 th and 11 th measurement points, the robot moved toward the first principal component. After that, the measurement was completed at the 14 th measurement point. The final reconstruction of the radiation source distribution was performed by solely adopting the data obtained from the cases in which the number of incident events exceeded  
Figure 11: Simulation result of the condition that single radiation source exists: (**a**) SP represents the first measurement point at which the robot started to move, while EP is the position at which gamma-ray measurements were completed. The color bar on the right represents the value added to each pixel via the proposed method. The blue and red arrows represent the directions of the first and second principal components, respectively. The ground truth of the position of the radiation source is represented by a red dot. It was confirmed that the distribution of the radiation source was estimated around the ground truth. In addition, the measurement path was successfully generated as intended. (**b**) The orientation of the detector was zero when X axis was facing up, and clockwise rotation was defined as positive. Figure 10: Simulation condition in which one radiation source exists: a single radiation source was positioned 15 m from the mobile robot. Cesium-137 (1 MBq) was adopted as the radiation source. the threshold.