# Path Planning for Localization of Radiation Sources Based on Principal Component Analysis
## 3 Experiments
### Simulations
#### 3.1.5 Discussion  
Herein, a strategy to approach and circumnavigate radiation sources was proposed. To evaluate its validity, the performance on two paths was compared: (a) the robot did not approach the source and followed a certain path, as in a uniform search; (b) the robot approached the source and measured gamma rays while following a path that surrounds the sources.  
\begin{table}
\begin{tabular}{l c c c} \hline \hline  & **Information-Driven [8]** & **Uniform Deterministic [8]** & **Proposed** \\ \hline Number of measurement points & 24 & 20 & 14 \\ Localization error in X [m] & 0.75 & 3.55 & 0.10 \\ Localization error in Y [m] & 0.72 & 2.18 & 0.69 \\ Total measurement time [s] & 89.9 & 90.1 & 242 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Performance comparison.  
Figure 16: Simulation results in large area: the red dot is the radiation source, and the black line depicts the determined path. It is confirmed that the robot accurately estimated the direction of existing the source despite of the large area. The robot approached to the source and measured gamma rays while circumnavigating the source.  
Figure 17 presents the results. The red dot is a radiation source, and the black line denotes the movement trajectory of the robot. The paths were manually determined. The 5.7 MBq source was placed, and the robot continued the measurement until the number of incident events exceeded 30 counts. The robot's movement speed was assumed to be 1 m/s.  
Table 2 lists the comparison results. It was confirmed that path (b) led to better accuracy in a shorter time than path (a) did. This result demonstrates that approaching the source and having multiple perspectives near the source are effective for radiation source inspection. The number of incident events is approximated to be the squared inverse proportional to the distance between the radiation source and the detector. Therefore, the path approaching the radiation source can reduce the measurement time until sufficient incident events are obtained. The measurement time at P1 along path (b) was 32 s while those at P2, P3, and P4 were 1 s.  
Furthermore, the robot requires multiple perspectives to obtain the depth information because images acquired using a Compton camera are devoid of source-camera distance information. Having multiple perspectives near the radiation source improves the localization accuracy. Figure 18a presents a series of simulation results in Section 3.1.2. It was confirmed that measurement from one side was not sufficient to localize the sources accurately. However, a circumnavigational path is not absolutely necessary for radiation source localization, especially when a single source is placed in the environment. Figure 18b presents a series of simulation results in Section 3.1.1. It was confirmed that the source location was almost specified from one side. This aspect will be part of our future work defining the termination condition for the inspection.  
\begin{table}
\begin{tabular}{l c c} \hline \hline  & **Path (a)** & **Path (b)** \\ \hline Localization error in X [m] & 3.10 & 0.33 \\ Localization error in Y [m] & 0.27 & 0.09 \\ Total measurement time [s] & 80 & 35 \\ Total moving distance [m] & 80 & 83.4 \\ Total search time [s] & 160 & 118.4 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Performance comparison of two paths.  
Figure 17: Comparison of two paths: (a) the robot did not approach the source and followed a certain path. (b) the robot approached the source and followed a path that surrounds the source. The red dot is a radiation source, and the black line depicts the moving trajectory of the robot. The paths were determined manually. The source with 5.7 MBq was placed, and the robot continued the measurement until the number of incident events exceeded 30 counts.