E-Journal of Advanced Maintenance Vol.9-2 (2017) 97-103
Japan Society of Maintenology

Effect of Detector Pose Uncertainty in Localization of Radiation SourcesDoyeon KIM1,*, Hanwool WOO1, Yonghoon JI1, Yusuke TAMURA1,Atsushi YAMASHITA1, and Hajime ASAMA1
1

The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, JapanABSTRACT
For safety and certain removal of the melted down nuclear fuel debris, the localization of radiation sources
should be required. In this paper, we propose an approach to estimate the accurate localization of radiation
sources by utilizing a gamma-ray CT method with a detector mounted on a mobile robot that has a pose
uncertainty. Gamma-ray CT method aggregates measurement data obtained from the detector to localize
radiation sources. For applying gamma-ray CT method, detector’s position that the measurement data obtained
is important. In a simulation experiment, we confirmed the detector’s position errors and correlated them withthe accuracy of the localization of radiation sources.
KEYWORDS

ARTICLE INFORMATION

Localization, radiation source, mobile robot, gamma-ray CT example4,example5, example6, example7, example8, example9, example10

Article history:
Received 7 November 2016
Accepted 27 April 2017

1.

Introduction

Fukushima Daiichi nuclear power plant, which was damaged by an earthquake and tsunami in2011, is being decommissioned. To ensure safety during decommissioning, risk management focuseson the removal of radioactive material while preventing exterior leakage [1]. Among the removal
tasks, removing the melted-down nuclear fuel debris is the most difficult. Safety and effective
removal of the nuclear fuel debris require thorough preparation. The most important step is to localize
the fuel debris inside the reactor.
An estimation method by actual unit investigation to localize the fuel debris has been studied.
Previous research used a mobile robot in order to investigate inside the primary containment
vessel [2]. In reference [3], using imaging technology for the Fukushima Daiichi reactors withcosmic-ray muons to estimate the location of the fuel debris was proposed. Muons have highpenetration ability even through thick concrete walls and a reactor pressure vessel. The result of avisualization of the inside of the reactor chamber vessel indicates where most of the fuel debris islocated. Nevertheless, the specific location of the fuel debris inside the primary containment chamber,and its properties, are still unknown.
Many studies have been developed for radiation source localization using colocated ordistributed detectors. For example, a distributed sensor network deploying many detectors mounted
on motor vehicles has performed well in low-level radiation [4–6]. These studies requiremeasurements from at least three detectors connected to each other to observe radiation at a specifictime. As the inside area of a nuclear power plant has a complicated and narrow shape, deploying morethan two detectors that communicate wirelessly is not realistic.
To estimate the locations of the fuel debris, which is a radiological source, we propose a novel
localization scheme based on the gamma-ray CT method [7]. In this research, because of the presenceof radiation, a mobile robot equipped with a detector performs an investigation instead of a human.
The gamma-ray CT method for localization employs measurement data from several positions
surrounding a target object. The gamma-ray CT method in the medical field uses detectors installedwith invariable poses to compute a precise estimation of the position information of radiation sources.
*Corresponding author, E-mail: kim@robot.t.u-tokyo.ac.jp

ISSN-1883-9894/10 © 2010 – JSM and the authors. All rights reserved.

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On the other hand, the pose of the detector utilized in this research has uncertainty because
localization of the mobile robot cannot be conducted accurately in general. In this paper, we discuss
the effects of the localization method that resulted from uncertainties in the detector pose.

2.

Localization of radiation sources

2.1. Detection of gamma ray
Emitted radiation from sources is measured by a detector consisting of scintillators that absorb
radiation. As shown in Fig. 1, collimators [8] are placed on scintillators to constrain the angle ofincident radiation in a specific direction. Output data containing coordinates of the scintillator that
detects gamma rays and the number of incident gamma rays (i.e., count rate) are obtained from themeasurement. Observable incidence angle of the gamma ray is controlled by the collimator as shownin Fig. 1. max is the maximum incident angle of the emitted gamma ray that is able to reach thescintillator unobstructed by the collimators. In this paper, as the size of the scintillator is small (0.01 m× 0.01 m), we consider that the range of the incident angle of the gamma ray to the scintillator (0 ≤≤ max) equals the possible angle of the gamma ray (0 ≤  ≤ max).

Fig. 1. Gamma ray detector consisting of collimators and scintillators.

2.2. Measurement using detector mounted on mobile robot
We use a gamma ray detector mounted on a mobile robot to investigate the inside high-radiation
environments. Thus, the pose information of the detector is correlated with the pose of the mobilerobot, which includes uncertainty. In general, the uncertainty of the robot pose can be represented by aGaussian distribution [9,10]. The location estimation of radiation sources using measurement data isexpected to contain errors.
2.3. Localization of source using image reconstructionThis subsection presents a back-projection method to localize sources by combining themeasurement data from the detector in a simulation environment. As shown in Fig. 2 (a),measurement data is obtained from a radiation source. If we know the pose of the detector, we cancalculate a line that is perpendicular to the detector, as shown in Fig. 2 (b). The lines from themeasurement data intersect in the image plane (Fig. 2 (c)). Figure 2 (d) shows the results of areconstruction based on the back-projection method. The location of the radiation source is estimatedat the point of intersection. A detailed explanation of the back-projection method appears in
subsection 3.2.

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Fig. 2. Concept of back-projection method: (a) data contains incident radiation emitted source,(b) back-projecting one piece of data obtained from detector to image reconstruction plane, (c)reiterating back-projection with other data, and (d) source localized at overlapped
back-projected data.

3.

Simulation experiment

3.1.

Environment setup

In order to demonstrate the effect of the pose uncertainty on source localization results, asimulation experiment was conducted. In this experiment, we considered that radiation sources arelocated at the same height as the detector. Thus, we assumed a two-dimensional environment toinvestigate the validity of performance in the simplest environment given that the proposed
methodology for neither 2D nor 3D environment does not widely change. Figure 3 (a) shows
the top view of the simulation environment, which includes an 18 m diameter circular carbon steel
wall with a thickness of 15 mm. The detector that is mounted on the mobile robot moves in a 6 m × 6m square path inside the carbon steel wall.
Radiation sources are placed in the middle of an inner circle that has a 4.8 m diameter made ofconcrete wall as shown in the Fig. 3. (b). In addition, we assume that most of the gamma rays are notscattered by the wall. The experimental environment was built as a simulation using the Geant4
library [11,12], which is a toolkit that simulates radiation, as shown in Fig. 3 (b). The coordinate
system of the simulation has its origin at the center of the space. Radiation sources are located at S1 (1m, 1 m), S2 (1 m, -1 m), S3 (-1 m, -1 m), and S4 (-1 m, 1 m).
The detector is composed of eight scintillators in a row array, and the size of each scintillator is
0.01 m × 0.01 m. We limited the maximum incident angle to max = 1.403°. To compute theefficiency, we placed 15 detectors in a row instead of taking several measurements for each movementof the detector. Here, a Gaussian distribution is used to represent the error in the detector’s location(i.e., the pose uncertainty of the mobile robot). The variance of the Gaussian distribution is set as 1.0.

Fig. 3. Top view of simulation environment: (a) environmental conditions and (b) results of
installed environment using Geant4.

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Fig. 4. Back-projection image processing considering the incident angle.

3.2.

Localization method by back-projection

In this subsection, we describe source localization by a back-projection method using themeasurement data obtained in the simulation experiment. The data has a range of incident angle asshown in Fig. 4. At the coordiantes of the detector position (xDn, yDn ), measurement data f(xDn,yDn ) is
obtained by observing the radiation sources. Here, n denotes the number of observations.
To apply the back-projection method using the observation data, we consider a two-dimensional
image reconstruction plane. Each pixel has a size of Δx = 0.01 m and Δy = 0.01 m. We assume thatthe detector mounted on the mobile robot moves on its designated path on which there are noobstacles and obtains M measurement data. Here, the incident angle between the observation
direction and vertical direction to the scintillator is defined, as follows:  arccos ( y nD  y Pj )( xiP  x nD ) 2  ( y Pj  y nD ) 2(1)

Equation (1) converts detector’s position (xDn, yDn ) and image plane pixel information (xPi, yPj) which
denotes center coordinates of pixel (i, j) to the incident angle  Finally, each pixel is assigned
aggregated measurement data, which is considered the maximum incident angle(≤max) as follows:b( xiP , y Pj ) M f ( xnD , ynD )

(2)

n 1

where function b(·) means the aggreated measurement data which are accumulated count rates at thecoordinates of (xiP, yjP) in the reconstruction image plane.
3.3.

Experimental results

Figure 5 (a) shows a result for the localization of radiation sources without the pose uncertaintyof the detector. By contrast, the result shown in Fig. 5 (b) is considered the uncertainty. Images
reconstructed by the back-projection method are shown in the upper images in Figs. 5 (a) and (b).
Here, (x, y) indicates a coordinate in the reconstrution image plane and z is the aggregatedmeasurement data (i.e., count rate). In the image plane, the area where values of z converge indicatesthe localized radiation sources. Moreover, the below of the Figs. 5 (a) and (b) respectively show theresults for localized radiation sources over 400 count rates and 200 count rates.
As shown at the upper of Fig. 5 (a) and (b), four areas of radiation sources were estimated. For
the result without the uncertainty of the pose detector, localized results indicate all positions ofradiation sources, including ±0.02 m of errors. Likewise, the result that includes the uncertainty of the100

D. Kim, et al./Effect of Detector Pose Uncertainty in Localization of Radiation Sources

detector pose indicates all positions of sources within ±0.07 m. As a consequence, the result without
the uncertainty of the pose of the detector has a more accurate localization result than that with theuncertainty.
In addition, the converged value of z from S1 to S4 is larger compared with the value of z fromS1to S4. This indicates that the estimated location of the radiation source in Fig. 5 (b) is less reliable
than the estimated location of the radiation source in Fig. 5 (a). Because the detector is closer to thelocation of the radiation source, higher count rates are obtained. Thus, the point with the largest valueof z denotes the location of the radiation source with high possibility. Moreover, in the Fig. 5 (b), zconverges to the single point with noises generated around radiation source position. In conclusion,
we confirmed that an uncertainty in the detector pose affects the accuracy of the localization ofradiation sources.
The reason for the errors in the result without the uncertainty was the incident angle of thedetector, as shown in Figs. 6 (a) and (b). The detector does not consider the maximum incident angle(max = 0). Comparisons were conducted under the same conditions: without considering themaximum incident angle (max = 0) as shown in Fig. 6 (a) and considering the maximum incident
angle as shown in Fig. 6 (b). The former case shows the localization results in a single pixel (i.e., a redsquare in Fig. 6 (a)) at the reconstruction image plane (x and y); however, the latter localizes theposition of the source for widespread pixels (x and y).

Fig. 5. Results of localization of radiation sources: (a) results without uncertainty in detectorand (b) results with uncertainty in detector.

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Fig. 6. Zoomed images of convergence in reconstruction image: (a) converged pixels without
considering incident angle range and (b) converged pixels considering incident angle range.

4. Conclusion
This paper proposed a novel localization scheme for radiation sources based on gamma-ray CT
using a detector mounted on a mobile robot. We considered an uncertainty in a pose of the detector
caused by the mobile robot localization, and demonstrated the results of the localization of radiation
sources in a simulation environment. The results indicated that when there is an uncertainty in adetector pose, the estimated localization of radiation sources contains error propagation. Thus, inorder to eliminate the errors in the localization results, we plan to apply a simultaneous localizationand mapping (SLAM) scheme to estimate the accurate pose of the detector. In addition, a localization
method considering a distribution of radiation sources is required, as the fuel debris spread like lava at
the Fukushima Daiichi nuclear power plant. Moreover, inside the Fukushima Daiichi nuclear power
plant is a complex, narrow area with obstacles, as opposed to the environment that we set up.
Therefore, the investigation route for the mobile robot should be discussed further in the future. Inaddition, even if it is sufficient to conduct the experiment in the two-dimensional
environment for verification of the proposed method, we will investigate the validity in more
complex environment (i.e., three-dimensional environment) which is more similar to the realworld as a future work.
Acknowledgement
Part of this study is the result of “HRD for Fukushima Daiichi Decommissioning Based on
Robotics and Nuclide Analysis” carried out under the Center of World Intelligence Project for
Nuclear S&T and Human Resource Development by the Ministry of Education, Culture, Sports andTechnology of Japan.

References[1] Nuclear Emergency Response Headquaters: “Mid-and-Long-Term Roadmap Towards theDecommissioning of TEPCO’s Fukushima Daiichi Nuclear Power Station Units 1–4”, Ministry ofEconomy, Trade and Industry Press Release Archive (2015)
http://www.meti.go.jp/english/press/2013/pdf/0627_01.pdf (Accessed October 14, 2016).
[2] Tokyo Electric Power Corporation: “Development of a Technology to Investigate Inside the Reactor
Primary Containment Vessel (PCV)”, Tokyo Electric Power Co. Press Release Archive (2012-2015)
http://www.tepco.co.jp/en/nu/fukushima-np/handouts/2015/images/handouts_150430_04-e.pdf(Accessed October 14, 2016)[3] H. Miyadera, K. N. Borozdin, S. J. Greene, Z. Lukic, K. Masuda, E. C. Milner, C. L. Morris, andJ. O. Perry: “Imaging Fukushima Daiichi Reactors with Muons”, AIP Advances, Vol. 3, No. 3, pp. 052133,
2013.
[4] N. S. V. Rao, M. Shankar, J. C. Chin, D. K. Y. Yau, S. Srivathsan, S. S. Iyengar, Y. Yang, and J. C. Hou:“Identification of Low-Level Point Radiation Sources Using a Sensor Network”, Proceedings ofACM/IEEE International Conference on Information Processing in Sensor Networks (IPSN), pp. 493–504,
2008.

102

D. Kim, et al./Effect of Detector Pose Uncertainty in Localization of Radiation Sources[5] R. J. Nemzek, J. S. Dreicer, D. C. Torney, and T. T. Warnock: “Distributed Sensor Networks for Detectionof Mobile Radioactive Sources”, IEEE Transactions on Nuclear Science, Vol. 51, No. 4, pp. 1693–1700,
2004.
[6] J. Chin, D. Yau, N. Rao, Y. Yang, C. Ma, and M. Shankar: “Accurate Localization of Low-level
Radioactive Source Under Noise and Measurement Errors”, Proceedings of the 6th ACM Conference onEmbedded Network Sensor Systems, pp. 183–196, 2008.
[7] H. Turbell: “Cone-Beam Reconstruction Using Filtered Backprojection”, Ph. D. Dissertation, Linkoping
University, Sweden, 2001.
[8] C. J. Thompson: “The Effect of Collimation on Scatter Fraction in Multi-slice PET”, IEEE Transactions on
Nuclear Science, Vol. 35, No. 1, pp. 598-602, 1988.
[9] S. Thrun, W. Burgard, and D. Fox: “Probabilistic Robotics”, MIT Press, 2005.
[10] H. Durrant-Whyte and T. Bailey: “Simultaneous Localization and Mapping: Part I”, IEEE Robotics &Automation Magazine, Vol. 13, No. 2, pp. 99–110, 2006.
[11] S. Agostinelli, et al.: “GEANT4-A Simulation Toolkit”, Nuclear Instruments and Methods in Physics
Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, Vol. 506, No. 3,
pp. 250–303, 2003.
[12] J. Allison, et al.: “Geant4 Developments and Applications”, IEEE Transactions on Nuclear Science, Vol. 53,
No. 1, pp. 270–278, 2006.

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