# Path Planning for Localization of Radiation Sources Based on Principal Component Analysis
## 3 Experiments
### Experiments  
An actual experiment was conducted to evaluate the proposed method. Figure 19 illustrates the mobile robot and the all-around view Compton camera used in the experiment. Pioneer-3 DX was adopted as the mobile robot [31], and an all-around view Compton camera was mounted above the mobile robot. The Compton camera has an energy resolution of approximately 60 keV; therefore, the margin to consider the energy resolution \(\Delta E\) was set as 30 keV. The energy window to identify the radionuclide type was set as 630-690 keV for the source. The position of the mobile robot was measured using motion capture systems. Reflection markers were installed on top of the all-around view Compton camera. In addition, a reflection marker was installed on the radiation source and used to obtain the ground truth of the radiation source position. Cesium-137 (2 MBq) was adopted as the radiation source. The mobile robot was stationary for 10 min at each measurement point, and measurements were performed using an all-around view Compton camera. After measurement  
Figure 19: Experimental setup: pioneer-3 DX was adopted as the mobile robot, and the all-around view Compton camera was mounted above the mobile robot. A single radiation source is expected in the environment. In the right figure, the red line represents the measurement points determined by the proposed method. Figure 18: Series of simulation results: (**a**) the results in Section 3.1.2. (**b**) the results in Section 3.1.1. The red dot depicts a radiation source, and the black line is the determined path with the proposed method. was completed at each point, the reconstruction of the radiation source distribution was performed via simple back-projection. Then, PCA was performed based on the reconstruction results to determine the next measurement point. When the number of incident events did not exceed the threshold, the next measurement point was determined according to the direction of the first principal component. However, the second principal component was selected to determine the next measurement point when the number of incident events exceeded the threshold. The moving distance of the mobile robot at each time step between the measurement points was set to 0.8 m. Figure 19 illustrates the experimental setup. In the right figure, the black arrow represents the direction that the mobile robot faces, and the red arrow denotes the movement direction to the next measurement point, as determined by the proposed method. Figure 20 presents the results obtained from the environment in which a single radiation source was located. The red dot in the figure indicates the ground truth of the location of the radiation source. The threshold required to switch the principal component vector was set to 4000. The mobile robot moved from SP to the sixth measurement point in the direction approaching the radiation source, and then followed the path surrounding the radiation source. At the 9 th measurement point, the number of incident events fell below the threshold, such that the path approaching the radiation source was selected again. After the 10 th measurement point, a path was generated to surround the radiation source, and the measurement was completed at the 15 th measurement point. The final reconstruction of the radiation source distribution was performed via simple back-projection using only the data obtained from the case where the number of incident events exceeded the threshold. In Figure 20, the radiation source distribution is depicted in yellow. It can be confirmed that the radiation source distribution was successfully estimated around the ground truth. The location of the radiation source was estimated as (0.02 m, 0.07 m), which was compared to that of the ground truth, (0.23 m, 0.21 m). Hence, the estimation error was approximately 0.29 m. Based on this result, it was verified that the proposed method can be implemented to real systems and can successfully generate the measurement path for the localization of radiation sources.