# Path Planning for Localization of Radiation Sources Based on Principal Component Analysis
## 3 Experiments
### Simulations
#### 3.1.3 Condition (c) Multiple Radiation Sources Dispersed  
A simulation experiment was conducted in an environment in which multiple radiation sources were dispersed. In this case, the location of each radiation source should be specified. Figure 13 presents the simulation conditions. Two radiation sources were placed in two locations: (\(-0.5\) m, \(-2\) m) and (0.5 m, 2 m). Two 1 MBq cesium-137 radiation sources were used. Then, the robot was positioned 7 m from the origin of the coordinates. Under this condition, two cases were evaluated according to the threshold required to switch the principal component vector. Figure 14a,b present the results obtained when the threshold was set to 5000 and 2500, respectively. When the threshold was set to 5000, a path was generated that moved in the direction of the first principal component up to the third measurement point, and in the direction of the second principal component, except for the 5 th and 12 th measurement points. In this case, a path was generated to solely surround radiation source 1. However, no enclosing path was generated for radiation source 2, and a path similar to the single radiation source condition was obtained. Figure 13: Simulation condition in which multiple radiation sources were dispersed: two radiation sources were positioned in two locations: (\(-0.5\) m, \(-2\) m) and (0.5 m, 2 m). Cesium-137 (1 MBq) was adopted as the radiation source. The robot was positioned 7m from the origin of the coordinates. However, the path to surround both radiation sources was generated when the threshold was set to 2500. The robot moved in the direction of the first principal component from the SP to the third measurement point. Then, it moved in the direction of the second principal component. Subsequently, at the 11 th, 17 th, and 22 nd, the movement was performed in the direction of the first principal component to acquire a sufficient number of incident events. At the other measurement points, movement was performed in the direction of the second principal component. It was confirmed that an appropriate path was generated as intended. In both cases, to reconstruct the radiation source distribution, the simple back-projection method was adopted using only the data obtained when the number of incident events exceeded the threshold. Consequently, when the threshold was set as 5000, a distribution was obtained only for a radiation source 1. The location of radiation source 1 was estimated as (\(-\)0.45 m, \(-\)1.8 m), which is compared to that of the ground truth, (\(-\)0.5 m, \(-\)2 m). Hence, the estimation error was approximately 0.21 m. The location of radiation source 2 was not estimated. In contrast, when 2500 was set as the threshold, a distribution was successfully obtained around the ground truth. After the k-means algorithm was performed to separate the reconstructed distribution into two areas, the location of radiation source 1 was estimated as (\(-\)0.48 m, \(-\)1.5 m), which is compared to that of the ground truth, (\(-\)0.5 m, \(-\)2 m). Hence, the estimation error was approximately 0.50 m. In addition, the location of radiation source 2 was estimated as (0.63 m, 2.3 m), which is compared to that of the ground truth, (0.5 m, 2 m) with an estimation error of approximately 0.33 m.  
Gamma rays emitted from radiation source 1 significantly influence the reconstruction result more than the gamma rays emitted from the radiation source 2. This is a limitation of simple back-projection. By setting a large value as the threshold, the robot approached very closely to the radiation source 1. Consequently, gamma rays from radiation source 2 were ignored when the distribution reconstruction was performed via simple back-projection. For the first time, both radiation sources were measured at the 10 th measurement point. However, the number of incident events exceeded the threshold at the 10 th measurement point, and the second principal component was selected as the direction of the next measurement point.