UAV Technology for Source Recovery and Emergency Response

In radiological and nuclear (RN) emergencies, radiation mapping is a process adopted to locate and identify the radioactive source(s) in specific areas and to evaluate their activity. So far, this task has been largely accomplished mobilizing manned aircrafts equipped with bulky and high-weight radiation detectors [1]. This solution, if from one hand guarantees the coverage of large areas during the survey, on the other generates data with low spatial resolution that in some cases not always up to solve positively the mission tasks.  This is due to the altitude at which the manned aircraft operates and to the radiation detectors field of view (FOV). For instance, for a flight altitude of 150 m and a detector FOV of 56° (typical of scintillators) the resolution is around 239 m.

Nowadays, thanks to the rapid and growing advancements in capabilities, unmanned aircraft systems (UAS/drones), once equipped with radiation detectors, can largely improve spatial resolution on the ground by using low altitude fly-over and by doing an appropriate trade-off between ground resolution and total scanned surfaces. It turns out that the use of UAS in RN emergencies is a subject of growing interest for supporting First Responders (FR) when they are called to perform complex tasks under harsh operating conditions. Drones can provide reliable support in their work and the operational concept is that, when a radiation emergency occurs, FRs deploy the UAV to determine the location of radiation sources, to survey the area and to generate a map of radiation levels and finalized at planning and implementation of the appropriate response plan.

Nevertheless, there are many difficulties to solve to make radiation detection by UAS/drones a performing practice in RN emergencies. Among them the main difficulties, as indicated in the paper, are related to constraints imposed by the current UAV technologies for civil purposes ((a) in the following) and by a further self-imposed constraint ((b) in the following):

(a) The small payload allowed for a UAV complies the use of light radiation counter which inhomogeneous sensibilities as a function of the radiation energy;

(b) The limit of being able to make a detection in the time span of a single mission.

The development of low weight radiation detectors and of appropriate flight plans are common to all possible intervention scenarios. In particular, radiological survey mission scenarios can include the following issues: (i) source seeking and localization; (ii) survey of radionuclides deposited on the ground; (iii) radioactive plume tracking; (iv) onsite survey in case of a nuclear/radiological incident; (v) internal survey of a reactor building; (vi) source search after an information alert and (vii) accident involving a vehicle carrying radioactive material on city road/highway.

These scenarios can be implemented through manual or autonomous operations. In the first case, a pilot or an observer in contact with the pilot, should keep the UAS within visual line of sight (VLOS) during flight. The latter include semi-autonomous or fully-autonomous operations where the Unmanned Aerial Vehicles (UAV) adaptively defines its route without the pilot and/or beyond the visual line of site (BVLOS) on the bases of some specific input provided by on-board devices (e.g., sensors). The resulting radiological survey can be represented by a gamma-dos rate map that shows detected radiation hot spots, possibly along with isotopic data.

Typical parameters that should be considered when planning the mentioned scenarios are listed in the following:

• operating environment and identification of natural and anthropic obstacles (e.g., electrical cables);
• environmental conditions (e.g., electromagnetic interference, meteorological);
• operator distance from the monitoring area, affecting VLOS operations and safety;
• flight plan including the flight altitude/height;
• battery duration which could be influenced by the intensive use of sensors (e.g., a Geiger Muller (GM) detector) and by the complexity of onboard algorithms for customized autonomous operations;
• characteristics of the sensor for environmental monitoring (e.g., sensitivity, measurement collection time);
• intensity of the source(s) to be identified, which will influence the flight height and could be detected as background radiation for low intensity;
• distribution of radiation in the environment (isotropic or anisotropic).

In this paper, we investigate how a proper set of the mentioned parameters could be combined and applied in autonomous operations dealing with source seeking and localization, in order to reduce the total time of the operation. However, the weight of these parameter strictly depends on the specific operation plan and cannot be specified in general. Some parameters are also dependent on each other and can lead to conflicting situations: for example, in the case of a high source, too low a flight height will cause sensor saturation while too high a height will cause only background radiation to be detected.

In particular, the addressed problem is to allow the UAV to detect the presence of a radiation source hidden in the ground by using a GM detector and without any form of visual inspection provided by cameras. Visual inspection of photos produced by cameras will require a complete detailed photography of the suspected area, but does not always guarantee simplicity to have a source being detected successfully. Moreover, that process must be finally verified through an open-eye inspection, involving investigations with time complexity up to large degrees. Highlighting the fact that visual inspection includes direct physical exposure of a human operator to radiation for a long period of time can be hazardous to the operator’s life.

The proposed approach has been validated by using a Monte Carlo simulation [2] which allows to emulate the path followed by the UAV and to measure the total time required for the UAV to find a radiation source, the resulting accuracy (in terms of the distance between the predicted and the real source location and the difference between the predicted and the real source activity) in an open field. In particular, a background radiation and the position of the source are stochastically determined at each simulation (what does it mean ???). In this context, a generic simulated flight plan consists of a sequence of points at a fixed altitude where a radiation measurement is simulated at each point to emulate the acquisition of a GM detector. In addition, a search strategy was implemented with the aim of avoiding an exhaustive scan of the considered area so as to reduce the total operation time. Indeed, the sequence of measurement points is produced by an optimized procedure based on the Gradient Descent (GD) algorithm [3], which allows to minimize a specific function of the radiation intensity by iteratively moving in the direction of steepest descent as defined by the negative of the gradient. The approach models the physical laws of gamma radiation propagation so that the radiation intensity decreases by the square of the distance from the source, according the inverse square law for radiation. In general, the model integrates: (i) radiologic assumptions (type of source, intensity, background radiation, duration of one GM detector measurement); (ii) geometric assumptions of the search area (extent, UAV altitude, cell size) and (iii) algorithmic assumptions (GD activation properties, maximum moves allowed).

This work follows a practical experience of deployment of a system integrating a commercial UAS (DJI Inspire 2) equipped with a GM detector capable of recording radioactive decay energies and integrated into a Raspberry device to control and transmits data to a ground station [4]. This system was applied to a source seeking and localization mission to implement an optimized strategy with the aim of avoiding an exhaustive scan of the predetermined area so as to reduce the total operation time. In the present paper, details of such procedure are described and validated through simulation.

The described system is part of the actions of the EU INCLUDING project whose main objective is to enhance practical knowledge to boost a European sustainable training and development framework for practitioners in the RN Security sector [4]. The results presented in this work want to validate the search procedure and drive next investments in RN emergencies where the deployment of UAV could contribute to more efficient mission objectives.

This paper is structured as follows. Section 2 describes related work in the area. Section 3 presents radiologic preliminaries. Section 4 focuses on the model implementation properties and discusses model results. Finally, in Section 5, some conclusions and ideas for future works are drawn.

3.1 Search area assumptions

In this Section, geometric properties of the search area will be described. The search area is defined as the region of a space where the UAV is supposed to flight to implement the search and localization operation.

Let Ω be a cartesian space with Ω=ℝ³. A search area β is defined as a rectangle of dimensions L×W that lies on plan α as depicted in Figures 1 and 2. The search area β consists of several adjacent square-shaped cells c_iof size R s.t.: L=X^max ·R, W=Y^max·R with X^max, Y^max, R∈ℝ, 1≤c_i≤X^max+Y^max.

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Figure 1. 3D-view of the UAV search area

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Figure 2. Top view of the search area

Let S∈Ω be a source located in the ground s.t. S=(x_s,y_s,0) and S̅=(x_s, y_s, h) the projection on β. A generic route performed by the UAV consists of an ordered sequence $\bar{\Gamma}_i^K$ of K points at a fixed altitude h that lie on A:

$\Gamma_i^K$={P(x_j, y_j, h)}      (1)

with, j∈{1 ,.., K}, $\left|\Gamma_i^K\right|$=K. Thus, the radial distances d and D of a generic point P(x_j, y_j, h) from S and S̅  are respectively:

d=d(P,S)=|P–S|     (2)

D=d(P,S̅)=|P−S̅|     (3)

Knowing d and H, we could obtain D (from Pythagoras’ theorem):

$D=\sqrt{d^2+h^2}$     (4)

Table 1 summarizes the parameters used to model the search area.

Table 1. Geometric properties of the search area

3.2 Radiologic properties

Based on the above geometric assumptions and the radiologic quantities presented in Appendix A, in this Section, the radiologic properties we considered for the model are presented and related to the position of the UAV in the search area β (Figure 3).

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Figure 3. Horizontal view of the search area

In particular, the model allows to simulate the search operation of different gamma sources with specific activity A (in MBq). Indeed, considering a specific source with activity A, and a quality factor q (see Appendix A.5), the effective dose E, that is calculated by the model and specified in Eq. (4), is dependent on the distance d only, as specified in the following:

$E=E(d) \propto \frac{1}{d^2}$     (5)

Let us assume:

• P(x,h,h) a generic point P∈$\overline{\Gamma_i}$ representing the position of the UAV at altitude h;
• each cell c_iof the search area β has a background radiation associated B_i, B_i∈R, b_i>0;
• B is a stochastic value representing the background radiation of the field in each point of the search area;
• S the source with activity A;
• $\overline{\Gamma_i}$ a generic sequence of points on the search area.

Definition 1. (Radial Radius of influence). The radius of influence d̅ is the maximum radial distance |P–S| between the UAV position P and S s.t.:

E(d̅)=E̅≥B     (6)

Definition 2. (Planar Radius of influence). The planar radius of influence D̅ is the maximum distance |P−S̅| between the UAV position P and S̅ when d=d̅.

In other words, the variable D̅ defines the maximum radius of a circle, called coverage area, where the GM detector can reveal a source. The higher D̅, the more extensive is the area where the GM detector can reveal sources.

Table 2 shows the expected effective doses E for different values of d for ⁶⁰Co isotope. For example, let us consider a background radiation value B=0.17 and a GM detector at an altitude h=10 and apply the above definitions. Indeed, the last row of Table 2 show the value of the radial d̅ and planar D̅ radius of influence respectively. Thus, the value of D̅ is an indicator of the density of measurements that are required by the GM detector to reveal sources in the area of interest.

Table 2. Expected effective dose values evaluated at different radial distances d for Isotope=⁶⁰Co at altitude h=10

3.3 Algorithmic assumptions

Definition 3. (Sample distance). The sample distance F_k+1 is defined as the distance among two points P_k+1 and P_k, s.t.:

F_k+1=|P_k+1−P_k|     (7)

Definition 4. (Total duration of the operation). The total duration of the operation T^op is defined as the duration (in seconds) required to one simulated procedure to find the source, s.t.:

T^op=K·∆T^coll       (8)

with, K≥1 is the number of points visited by the UAV and ∆T^collis the time required by the GM detector for one measurement point. [In practical applications, this parameter may include also the time required to transmit the value to a ground station device where the proposing algorithm executes and the UAV position is calculated and sent to the UAV.] It is worth noting that each point is generated at a time by the proposed automated procedure and a measurement is acquired after the UAV reaches the new position. Thus, in detection time depends on (a) quality of the instruments used; (b) data processing time; (c) activity of the source and (d) detector type.

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Figure 4. Possible configuration of sample distance F

Figure 4 shows three significant values of F that influence the total coverage area performed by the UAV in a search operation. In particular, assuming F=F₂≈2·D̅, a high coverage area will be monitored; however, this will increase the average time T of the operation because the UAV will visit a higher number of points. By choosing F=F₁<<2·D̅ and F=F₃>>2·D̅, no (a complete) overlapping of the influence areas will be implemented. This will decrease the average time T of the operation; however, the success rate of finding the source within the considered interval will be lower. However, the scope of this study is not to find an optimal F-value but to show the dependency of the parameters introduced and how a proper set of them will lead to the source localization.

Table 3. Algorithmic assumptions

3.4 UAV autonomous procedure

The proposed procedure for autonomous search and localization of a source is based on two consecutive phases with different paths: (i) Phase 1: Snail-like path and (ii) Phase 2: Optimized path.

Let us generalize the sequence of points Γ=Γ^K of a generic mission as defined in (1) to include the two above mentions UAV paths:

$\Gamma=\bar{\Gamma} \cup \widehat{\Gamma} \cup \dot{\Gamma}$     (9)

where,

• |Γ|=K, |$\bar{\Gamma}$|=σ, |$\dot{\Gamma}$|=µ, |$\widehat{\Gamma}$|=2µ with K=σ+3µ being the total number of visited points.
• $\bar{\Gamma}=\left\{\bar{p}_1, \ldots, \bar{p}_\sigma\right\}$ is the set of points visited in Phase 1;

• $\hat{\Gamma}=\left\{\hat{p}_{\sigma+2}^{\sigma+1}, \hat{p}_{\sigma+3}^{\sigma+1}, \hat{p}_{\sigma+1}^{\sigma+2}, \hat{p}_{\sigma+1}^{\sigma+2}, . ., \hat{p}^\mu, \hat{p}^\mu\right\}$ is the set of points, called control points, that are visited in Phase 2 in order to calculate the direction of the path towards the source;
• $\dot{F}=\left\{\dot{p}_{\sigma+1}, \dot{p}_{\sigma+4}, \ldots, \dot{p}_{2 \mu+1}\right\}$ is the set of points visited in Phase 2 based on the measurements provided by the control points.

Considering that the position of the source is not known at the beginning of any search, Phase 1 performs a snail-like path until a radiation measurement is higher than the expected radiation background B, an optimized procedure will start to continue the search in a smaller area. However, in case the search area in the snail-like path has a high value of F, all the search area will be visited in Phase 1; in this case, the Phase 2 will not execute.

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Figure 5. An example of snail-like path

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Figure 6. An example of an optimized path

3.4.1 Snail-like path

This phase is performed at the beginning of the procedure and consists of a set of points at a fixed altitude h defined by $\bar{\Gamma}$. The length F of each step constant in Phase 1 and is defined s:F=N·R with N∈Z being a constant value with N≥1, s.t.:

|P_j+1−P_j|=F     (10)

with, 0≤j≤σ, P_j+1,P_j∈$\bar{\Gamma}$. Figure 5 represents an example of the points that are generated in this Phase according to a snail-like path.

3.4.2 Optimized path

In order to increase the fitting in a specific area, Phase 2 employs "Gradient-Descent (GD hereafter) technique (also often called steepest-descent) that is an iterative first-order optimization algorithm used to find a local minimum/maximum of a given function. This method is commonly used in machine learning (ML) to minimize a cost/loss function (e.g., in a linear regression).

In order to find the minimum of a continuously differentiable function f(x), the general form of the Gradient-Descent algorithm is given as:

$\begin{gathered}x_1=x_0-\eta \cdot \nabla f\left(x_0\right) \\ x_2=x_1-\eta \cdot \nabla f\left(x_1\right) \\ \cdots \\ x_{n+1}=x_n-\eta \cdot \nabla f\left(x_n\right)\end{gathered}$     (11)

where, η is the learning-rate, t that determines the step size at each iteration. In our case, the objective is to maximize the function E(x, y, z) representing the radiation intensities on the Cartesian space P(x, y, z).

Figure 6 shows an example of the application of GD algorithm that follows a snail-like path depicted in Figure 5. In particular, at step 10 of the procedure, we have:

• $\bar{\Gamma}=\left\{\bar{P}_1, \bar{P}_2, \bar{P}_3, \bar{P}_4, \bar{P}_5, \bar{P}_6\right\}$ is the set of points visited during the snail-like path;
• $\hat{\Gamma}=\left\{\hat{P}_8^7, \hat{P}_9^7\right\}$ is the set of control points that are used to calculate $\dot{P}_{10}$;
• $\dot{\Gamma}=\left\{\dot{P}_7 \dot{P}_{10}\right\}$ is the set of points visited and calculated by the GD algorithm;

It can be noticed by the code, that the sample distance F it remains constant in Phase 1 whereas it varies in Phase 2 according to the learning rate η. The value set for η is purely empirical, which we have decided according to multiple simulation results. Any value higher than the one considered (η=1) will increase the number of samplings before reaching the maximum; on the other hand for lower values, may lead to simulations missing the maximum. In other words, in Phase 2, the algorithm adaptively tries to increase the density of the number of measurements to find a maximum of the function E.

3.4.3 Pseudocode

Pseudocode 1 describes the algorithm of a generic iteration of the Monte Carlo simulation.

After variable setting, the algorithm starts the snail-like path (line number 15) at altitude h. Line number 20 indicates that the GD algorithm will be executed if the effective dose E is greater than the background radiation B. The GD algorithm is described in Pseudocode 2.

Based on Figure 6, in the following we analyze the mail algorithm steps assuming that the GD has been triggered at point $\dot{P}_{7}$:

(1) two radiologic measurements are performed and two control points $\hat{P}_8^7$ and $\hat{P}_9^7$ are produced s.t. (line numbers 2-3 in Pseudocode 2);

(2) a new step size D₈ is calculated through the gradient of function f(·) along x and y axis (line numbers 6-7 in Pseudocode 2) where η gives a doping effect to the reduction of the step size while approaching the function’s maximum.

$\nabla f\left(\dot{P}_7\right)=\left(\left(f\left(\dot{P}_8^7\right)-f\left(\dot{P}_7\right)\right) / G\right) \cdot \eta$     (12)

$\nabla f\left(\dot{P}_8\right)=\left(\left(f\left(\dot{P}_9^7\right)-f\left(\dot{P}_7\right)\right) / G\right) \cdot \eta$      (13)

$F_{10}=F_7-\left|\nabla f\left(\hat{P}_8^7\right)\right|$       (14)

$F_{10}=F_7-\left|\nabla f\left(\hat{P}_9^7\right)\right|$       (15)

(3) a new point P₁₀ (P₁₀∈$\dot{\Gamma}_i$) is calculated and visited (line numbers 9-16 in Pseudocode 2) where +(−) applies when ∇x≥0 (∇y≥0) respectively.

x₁₀=x₇±F₁₀       (16)

y₁₀=y₇±F₁₀     (17)

The GD algorithm terminates when a maximum dose value $\bar{E}$=P_µis reached after 5 consecutive increasing values of E. The termination condition called exit_cond is defined as follows:

exit_cond : E(P˙_µ)≥E(P˙_µ−i)      (18)

where i=1, ..., 5.

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Figure 7. Path tracking of the UAV from a simulation

Figure 7 depicts the result of one simulation consisting of 45 points in a search a L x W field with L=150 and W=150. In this particular execution, the GD algorithm was triggered at point P₂₀.

The physical security of nuclear material and sites around the world is of paramount importance, and the use cases for incorporating new technologies into established and evolving security and operational approaches are growing.

This work proposed a Monte Carlo simulation that is able to simulate the effectiveness of UAV search and localization operations. The model proposed allows to evaluate different technological constraints (e.g., UAV altitude, sample size) and to estimate the total duration of the operation based on a subset of mission parameters. In addition, the procedure can be used to infer the location and the intensity of the source with a certain margin error.

The proposed procedure has been designed for a simple energy landscape which is characterized by a unique source (i.e., with a single maximum). In the case of multiple sources, one may implement a specific strategy aiming to find the more intense sources (i.e., that with the higher dose) or those with at a given frequency. In both cases, the algorithm should be adapted to accordingly. In the first case, the presence of multiple sources will necessarily produce a radiation map which will be constituted by the sum of all radiation sources of all the sources. A possible way to adapt the algorithm could consider the estimate of the difference of the radiation map as if it were induced by a single source. The eventual difference between the measured and estimated values might be used to infer the eventual presence of additional sources as well as their location.

Future developments involve the implementation of the GD procedure on a real UAV to validate simulation results analyzed in this work and apply to real mission scenarios. Other possible developments include the implementation of optimization techniques to find the best set of parameters that will lead to the quickest localization of a source.