# Path Planning for Localization of Radiation Sources Based on Principal Component Analysis
## 2 Proposed Method  
### Overview  
To realize a mobile robot equipped with a gamma-ray detector that sequentially repeats gamma-ray measurements and localize radiation sources, the proposed method determines the position of the next measurement point based on the results of previous measurements. The radiation source distribution is estimated by considering large environments such as urban areas, public facilities, or shopping malls. Moreover, we assume a situation where strong radiation sources are located in the target environment because it would not be necessary to use an inspection robot if the radiation source intensity is low and human workers can be deployed. Our strategy is as follows. First, human workers investigate the areas with low intensity and limit the scope of the inspection. After the target area is determined, the robot is placed near the target area with high intensity. The robot conducts inspection and identifies the exact radiation source locations. Although the region with high count rates is avoided by human inspectors, rapid detection and elimination of radiation sources are still required in cases such as dirty bombs comprising explosives and radiation sources. In addition, it is undesirable to limit the area for long periods even if there is no threat to the human body. Therefore, an investigation that sequentially scans the entire environment is ineffective when the target environment is large. Based on these requirements, the proposed method was designed, as illustrated in Figure 2.  
The proposed system adopts a Compton camera, which uses Compton scattering kinematics to localize a radiation source, as the gamma-ray detector. Compared with other types of gamma cameras, such as pinhole or coded-aperture cameras, the Compton camera has a wide FOV [12; 13]. Particularly, our all-around-view Compton camera, which employs a 3D pixel array CdTe detector, enables measurement in all directions [14]. In [15], it was concluded that a gamma camera with a wide FOV would be preferable for wide-area exploration. The details of the all-around view Compton camera are described in Section 2.2. After the gamma-ray measurement, the reconstruction of the radiation source distribution to a 3D space is conducted based on the measurement results. The proposed system applies a simple back-projection method, which is a general reconstruction method. Details on the reconstruction of the radiation source distribution are provided in Section 2.3. Generally, the lower the distance to the source, the shorter the time required to obtain the same radiation counts measured by the detector. Therefore, if the number of gamma-ray measurement events is insufficient at the current position, a mobile robot is required to approach the radiation sources until the number of events reaches a sufficient value. Moreover, to accurately localize the radiation sources, it is necessary to follow a path that surrounds them. Hence, the proposed method is designed to generate a path that surrounds the radiation source after approaching a distance where a sufficient number  
Figure 1: Conceptual image of measurement path: the proposed method is designed to approach the radiation sources to a distance where a sufficient number of gamma-ray events can be obtained, then, it generates a path to surround the radiation sources. of measurement events can be obtained. The proposed method applies PCA to generate this path based on the reconstruction results of the radiation source distribution, which is constructed by simple back-projection. Comprehensive details on path planning are presented in Section 2.4. The above process is repeated until the measurement path is closed. Then, the localization of the radiation sources is conducted. The final reconstruction of the radiation source distribution is performed by solely adopting the data obtained from where the number of incident events is significant, and then the location of radiation sources is finally estimated as the weighted average of the values added to pixels in the projection space.