A robotic sampling method for open area multi-radiation source positioning

Abstract

The application discloses a kind of robot sampling methods for open area multi radiation source positioning, comprising the following steps: step S1, robot carries out environment exploration according to spiral path;Step S2, the radiation field counting data of search area is as the parameter of multi radiation source positioning path planning, and path planning is carried out;Step S3, the parameter estimation of radiation source is carried out;Step S4, the above process is repeated, so that particle converges constantly, when the maximum in particle space transverse length and longitudinal length is less than or equal to threshold value, end loop process, obtain the particle set that is no longer updated, the radiation source parameter vector at this time is final estimated value.Through the method in the application, the exploration efficiency and positioning efficiency of multi-region suspicious radiation area are effectively improved.Compared with the single modal information perception in the prior art, the exploration method is improved, the position of effective radiation source is quickly identified and calculated, and high-precision and high-efficiency positioning of the radiation source is realized.

Description

Technical Field

[0001] This invention belongs to the field of radiation protection and radioactive source detection technology, specifically a robotic sampling method for locating multiple radioactive sources in open areas. Background Technology

[0002] Research in the field of nuclear radiation environment sensing under mobile conditions in China started relatively late, and the technology is still immature, mostly in the theoretical research stage. In 2015, Ni Shixiang et al. from Harbin Institute of Technology proposed a unified framework for radiation field construction and exploration based on the Gaussian process regression algorithm. The behavioral planning algorithm incorporates factors such as radiation field strength, obstacle information, and repeatedly explored areas into the optimization function to achieve a multi-objective balanced planning path. In 2016, Zhang Min et al. from Nanhua University proposed a method to reconstruct the radiation field by constructing a locally concave function, and used quadratic and cubic fitting scanning algorithms to search for the gradient direction of the radiation field. Compared with partial differential methods for finding gradient descent, this method has a computational complexity of only O(n), significantly accelerating the online search speed.

[0003] In general, research on mobile robot environmental perception technology has focused primarily on the perception of single-modal information. For example, using laser and vision sensors to correct and model geometric obstacles, and utilizing Geiger counters for obstacle-free searching in radiation environments. However, in real-world complex nuclear environments, the two physical fields inevitably interact and influence each other, such as the impact of radiation data collected in obstacle environments on state prediction algorithms. Therefore, this invention needs to comprehensively consider several issues, including suspicious radiation area detection, decoupling of multiple radiation fields, and estimation of optimal solutions in multiple regions. These are also the main problems and challenges that robot perception technology in nuclear environments needs to address. Summary of the Invention

[0004] The purpose of this invention is to provide a robot sampling method for locating multiple radiation sources in open areas, in order to solve the problem that the research results of mobile robot environmental perception technology in the background art are mostly focused on the perception of single-modal information, and lack the combined consideration of suspicious radiation area exploration, multi-radiation field decoupling and multi-region optimal solution estimation.

[0005] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows:

[0006] A robotic sampling method for locating multiple radiation sources in open areas includes the following steps:

[0007] Step S1: The robot uses the coupled information of SLAM mapping and radiation physics field to divide the environment map into grids and evaluate it. The robot explores the environment according to the spiral path. It uses the lidar and IMU sensor of the ROS robot to obtain the position information of obstacles, boundaries and the robot itself. It uses CeBr3 with multi-channel pulse analysis equipment to obtain the radiation source information.

[0008] Step S2: Use the radiation field count data of the search area as parameters for multi-radiation source localization path planning, and perform path planning; use the SR-PF optimization system sampling particle filter algorithm to estimate the localization information of potential multi-radiation sources in the environment.

[0009] Step S3: Estimate the parameters of the radioactive source. The weighted particle set after the SR-PF optimization system sampling particle filtering algorithm is as follows:

[0010]

[0011] In the above formula, This represents a group of particles at different locations. Clusters representing the weights of particles;

[0012] Based on the above expression, the parameter vector estimate of the radioactive source is denoted as:

[0013]

[0014] In the above formula, A parameter vector representing the position of the particle cluster;

[0015] After completing the above estimation, input a new particle and perform the next iteration and parameter estimation;

[0016] Step S4: Repeat the above process to make the particles converge continuously. The estimated value of the radioactive source will gradually converge to the actual value. When the maximum value of the horizontal and vertical lengths of the particle space representing the 2D coordinates x, y of the radioactive source and the activity information A is less than or equal to the threshold, the loop process ends and a set of particles that is no longer updated is obtained. At this time, the radioactive source parameter vector is the final estimated value, that is, the position and activity of the radioactive source are obtained.

[0017] According to the above technical solution, in step S2, the SR-PF optimization system sampling particle filter algorithm is specifically as follows:

[0018] Step A1: Particle initialization. Establish an initial set of weighted particles, where each parameter is uniformly distributed and each particle has the same weight.

[0019] Step A2, particle weight iteration;

[0020] Step A3: Particle state initialization and prediction weight model correction;

[0021] Step A4, resampling; resampling uses self-optimizing resampling.

[0022] Based on the above technical solution, the specific implementation steps of self-optimizing resampling are as follows:

[0023] Step A401: Determine whether the number of valid samples is less than the threshold based on the particle weights; if the condition is met, use the system resampling method to filter and replicate the particles; otherwise, keep the original particle set unchanged.

[0024] Step A402: Optimize the high-weight particles that need to be replicated;

[0025] Step A403: Initialize the particles, i.e., k = 0;

[0026] Step A404, establish the weighted particle set {X} of the initial state. n ω n}, where ω n The weight vector X represents the particle. n It satisfies a uniform distribution; it is assumed that the initial radiation source may exist anywhere in the search area, and that the probability is the same in each search grid.

[0027] Step A405: Update particle weights based on observations; whenever a new observation value z is obtained, update the particle weights using a Bayesian method, as shown in the following equation:

[0028] ω k =ω k-1 ·p(z|X k )=ω k-1 ·p(z, λ) k (X k ))

[0029] In the above formula, ω k For the weight of the latest particle, ω k-1 X is the weight of the previous particle. k This refers to information related to particles;

[0030] Step A406, particle weight normalization;

[0031]

[0032] In the above formula, ω k The weight of the latest particle;

[0033] Step A406: The positions and weights of all the particles obtained are used to obtain the number and weights of all particles belonging to a certain cluster using the K-means++ clustering algorithm, which is the result of particle weight normalization.

[0034] Step A407, optimize system resampling; take the inverse of the sum of squared weights obtained in step A405, and use the inverse as the number of valid samples. If the number of valid samples is less than half the number of particles in that category, then resampling is performed; if the number of valid samples is greater than half the number of particles in that category, then resampling is not performed.

[0035] According to the above technical solution, in step A406, the K-means++ clustering algorithm is specifically as follows:

[0036] Step C1: First, use the K-means++ algorithm to randomly select a center point in the particle set. For the remaining particles, calculate the distance to the center point.

[0037] Step C2: Select a point that is far away as a new center, and repeat step C1 until K centers are selected, where K represents the number of radioactive sources in the environment;

[0038] Step C3: Starting from the first center, calculate the distance of all samples to the center point. If a sample is close to the center, it belongs to a point group. Group all sample points according to the distance and calculate the mean of each group to obtain the centers of multiple clusters, that is, estimate the location information of K radioactive sources.

[0039] Based on the above technical solution, considering the potential problem of poor sample diversity, the following optimizations are needed for high-weight particles:

[0040]

[0041] In the above formula, This represents the updated set of weighted particles. This represents the weights for normalization. This indicates that the x value is uniformly sampled from N particles.

[0042] Compared with the prior art, the present invention has the following beneficial effects:

[0043] The method in this invention combines the processing methods of suspicious radiation area exploration, multi-radiation field decoupling, and multi-region optimal solution estimation, enabling mobile robots to simultaneously explore multiple regions of suspicious radiation areas and decouple multiple radiation fields when probing the nuclear environment, effectively improving the exploration efficiency and positioning efficiency of multiple suspicious radiation areas.

[0044] Compared to the single-modal information perception in existing technologies, this method improves the detection method and quickly identifies and calculates the location of effective radioactive sources, achieving high-precision and high-efficiency positioning of radioactive sources. Attached Figure Description

[0045] Figure 1 This is a flowchart of the sampling process of the present invention;

[0046] Figure 2 This is a sampling diagram of the present invention. Detailed Implementation

[0047] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0048] Example 1

[0049] like Figure 1 As shown, a robotic sampling method for locating multiple radiation sources in open areas includes the following steps:

[0050] Step S1: The robot uses the coupled information of SLAM mapping and radiation physics field to divide the environment map into grids and evaluate it. The robot explores the environment according to the spiral path. It uses the lidar and IMU sensor of the ROS robot to obtain the position information of obstacles, boundaries and the robot itself. It uses CeBr3 with multi-channel pulse analysis equipment to obtain the radiation source information.

[0051] Specifically, in step S1, the evaluation mainly assesses the count rate of the radiation field within a certain grid. Grids that exceed the count rate threshold will participate in the particle swarm algorithm process, while grids that do not exceed the threshold will be discarded and will not participate in the particle swarm calculation.

[0052] The SLAM mapping method mainly uses the Fast-SLAM method, which associates the mobile robot's pose with the environmental map. This algorithm combines the robot's pose at various times, point cloud map and other observations, and uses conditional independence to form many small grids. The algorithm marks the small grids as free grids (white grids, no obstructions), gray grids (undetected grids), and black grids (obstacles). During mapping, the robot stores information such as the height, width and resolution of the map, radiation count rate and energy characteristics locally, performs odometry prediction, laser observation, grid map construction and resampling to build a coupled field map with radiation field information.

[0053] Step S2: Use the radiation field count data of the search area as parameters for multi-radiation source localization path planning, and perform path planning; use the SR-PF optimization system sampling particle filter algorithm to estimate the localization information of potential multi-radiation sources in the environment.

[0054] Step S3: Estimate the parameters of the radioactive source. The weighted particle set after the SR-PF optimization system sampling particle filtering algorithm is as follows:

[0055]

[0056] In the above formula, the meanings of each letter are as follows: This represents a group of particles at different locations. Clusters representing the weights of particles;

[0057] Based on the above expression, the parameter vector estimate of the radioactive source is denoted as:

[0058]

[0059] In the above formula, the meanings of each letter are as follows: A parameter vector representing the position of the particle cluster;

[0060] After completing the above estimation, input a new particle and perform the next iteration and parameter estimation;

[0061] Step S4: Repeat the above process to allow the particles to converge continuously. The estimated value of the radioactive source will gradually converge towards the actual value. When the maximum value of the horizontal and vertical lengths of the particle space representing the 2D coordinates x and y of the radioactive source and the activity information A is less than or equal to the threshold (for example, after iteration, if the standard deviation of x and y in the last 5 iterations is less than the threshold of 10 cm, it indicates that the data has converged, and the iteration stops), the loop process ends, and a set of particles that is no longer updated is obtained. At this point, the radioactive source parameter vector is the final estimated value, that is, the position and activity of the radioactive source are obtained.

[0062] The method in this invention combines the processing methods of suspicious radiation area exploration, multi-radiation field decoupling, and multi-region optimal solution estimation, enabling mobile robots to simultaneously explore multiple regions of suspicious radiation areas and decouple multiple radiation fields when probing the nuclear environment, effectively improving the exploration efficiency and positioning efficiency of multiple suspicious radiation areas.

[0063] Compared to the single-modal information perception in existing technologies, this method improves the detection method and quickly identifies and calculates the location of effective radioactive sources, achieving high-precision and high-efficiency positioning of radioactive sources.

[0064] Example 2

[0065] This embodiment is a further refinement of Embodiment 1.

[0066] In step S2, the SR-PF optimization system sampling particle filter algorithm is specifically as follows:

[0067] Step A1: Particle initialization. Establish an initial set of weighted particles, where each parameter is uniformly distributed and each particle has the same weight.

[0068] Step A2, particle weight iteration;

[0069] Step A3: Particle state initialization and prediction weight model correction;

[0070] Step A4, resampling; resampling uses self-optimizing resampling.

[0071] The specific steps for implementing self-optimizing resampling are as follows:

[0072] Step A401: Determine whether the number of valid samples is less than the threshold based on the particle weights; if the condition is met, use the system resampling method to filter and replicate the particles; otherwise, keep the original particle set unchanged.

[0073] Assuming a total number of particles of 100, a valid sample after weight normalization refers to a sample with a weight greater than 0.01, and a sample with a weight less than 0.01 is an invalid sample. When the number of valid samples is less than 60% of the total number of particles, i.e., less than 60 valid particles, resampling is required.

[0074] Step A402: Optimize the high-weight particles that need to be replicated;

[0075] Step A403: Initialize the particles, i.e., K = 0;

[0076] Step A404, establish the weighted particle set {X} of the initial state. n ω n}, where ω n The weight vector X represents the particle. n It satisfies a uniform distribution; it is assumed that the initial radiation source may exist anywhere in the search area, and that the probability is the same in each search grid.

[0077] Step A405: Update particle weights based on observations; whenever a new observation value z is obtained, update the particle weights using a Bayesian method, as shown in the following equation:

[0078] ω k =ω k-1 ·p(z|X k )=ω k-1 ·p(z, λ) k (X k ))

[0079] In the above formula, ω k For the weight of the latest particle, ω k-1 X is the weight of the previous particle. k This refers to information related to particles;

[0080] Step A406, particle weight normalization;

[0081]

[0082] In the above formula, ω k The weight of the latest particle;

[0083] Step A406: The positions and weights of all the particles obtained are used to obtain the number and weights of all particles belonging to a certain cluster using the K-means++ clustering algorithm, which is the result of particle weight normalization.

[0084] Step A407, optimize system resampling; take the inverse of the sum of squared weights obtained in step A405, and use the inverse as the number of valid samples. If the number of valid samples is less than half the number of particles in that category, then resampling is performed; if the number of valid samples is greater than half the number of particles in that category, then resampling is not performed.

[0085] In step A406, the K-means++ clustering algorithm is specifically as follows:

[0086] Step C1: First, use the K-means++ algorithm to randomly select a center point in the particle set. For the remaining particles, calculate the distance to the center point.

[0087] Step C2: Select a point that is far away (e.g., a point 1m away) as the new center, and repeat step C1 until K centers are selected, where K represents the number of radioactive sources in the environment;

[0088] Step C3: Starting from the first center, calculate the distance of all samples to the center point. If a sample is close to the center, it belongs to a point group. Group all sample points according to the distance and calculate the mean of each group to obtain the centers of multiple clusters, that is, estimate the location information of K radioactive sources.

[0089] Considering the potential problem of poor sample diversity, the following optimizations are needed for high-weight particles:

[0090]

[0091] In the above formula, This represents the updated set of weighted particles. This represents the weights for normalization. This indicates that the x value is uniformly sampled from N particles.

[0092] Furthermore, the multichannel pulse analysis equipment utilizes existing devices, such as CAEN's DT5770.

[0093] Example 3

[0094] The inventive concept of this invention is as follows:

[0095] A robotic sampling method for locating multiple radiation sources in open areas includes the following steps:

[0096] Step 1: The robot uses the coupled information of SLAM mapping and radiation physics field to divide the environment map into grids and evaluate it. The robot explores the environment according to the spiral path. It uses the lidar and IMU sensor of the ROS robot to obtain the position information of obstacles, boundaries and the robot itself. It uses CeBr3 with multi-channel pulse analysis equipment to obtain the radiation source information.

[0097] By coupling information from robot SLAM mapping with radiation physics, the environmental map is divided into grid-based evaluation. During map construction, the mobile robot carries relevant sensors to navigate around the radiation area to map the unknown environment. Simultaneously, a radiation detector on the robot detects radiation information, recording the radiation and coordinates of each observation location. Once mapping is complete, detection stops. Areas with radiation data greater than the background radiation are considered valid search areas; otherwise, they are considered invalid search areas.

[0098] Step 2: Use the radiation field count data of the search area as parameters for multi-radiation source localization path planning; and use the SR-PF optimization system sampling particle filter algorithm to estimate the localization information of potential multi-radiation sources in the environment.

[0099] Radiation field count data of the search area is used as an important parameter for multi-radiation source localization path planning, discarding invalid search areas and improving localization efficiency. Simultaneously, the SR-PF optimization system sampling particle filter algorithm is used to estimate the localization information of potential multi-radiation sources in the environment.

[0100] Step S3: Estimate the parameters of the radioactive source. The weighted particle set after the SR-PF optimization system sampling particle filtering algorithm is as follows:

[0101]

[0102] In the above formula, This represents a group of particles at different locations. Clusters representing the weights of particles;

[0103] Based on the above expression, the parameter vector estimate of the radioactive source is denoted as:

[0104]

[0105] In the above formula, A parameter vector representing the position of the particle cluster;

[0106] After completing the above estimation, input a new particle and perform the next iteration and parameter estimation;

[0107] Step S4: Repeat the above process to make the particles converge continuously. The estimated value of the radioactive source will gradually converge to the actual value. When the maximum value of the horizontal and vertical lengths of the particle space representing the 2D coordinates x, y of the radioactive source and the activity information A is less than or equal to the threshold, the loop process ends and a set of particles that is no longer updated is obtained. At this time, the radioactive source parameter vector is the final estimated value, that is, the position and activity of the radioactive source are obtained.

[0108] Particle filtering can lead to sample degradation because the variance of particle weights increases with the number of iterations, resulting in a few particles having very large weights. In radiation source localization, this manifests as only identifying the target source with the highest count rate in a multi-source environment. To address the problem of falling into a single extreme value during iteration, a self-optimizing resampling algorithm is used, as follows:

[0109] The effective sample size is determined based on the particle weights. If the condition is met, the particles are filtered and replicated using the SR algorithm; otherwise, the original particle set is maintained.

[0110] Considering the problem of particle extrema, the position coordinates x and y of high-weight particles and the radioactivity A after each observation are replaced by random numbers that satisfy the corresponding normal distribution. Thus, considering that the particle cluster will gradually converge with the increase in the number of iterations, the variance affecting particle fluctuations will decrease with the increase in the number of iterations, thereby improving the accuracy of predicting the location and activity of the radioactive source.

[0111] While the standard particle filter algorithm can roughly locate runaway radioactive sources, its positioning error is relatively large, necessitating improvements. However, system resampling, while addressing sample degradation, introduces a new problem—poor sample diversity. To solve this issue, this embodiment proposes a self-optimizing system resampling method. The specific implementation steps are as follows:

[0112] Step A1: Determine whether the number of valid samples is less than the threshold based on the particle weights. If the condition is met, use the system resampling method to filter and replicate the particles; otherwise, keep the original particle set unchanged.

[0113] Step A2: Considering the potential lack of sample diversity in Step A1, we optimize the high-weight particles that need to be replicated. Since the particle set converges more rapidly with increasing iterations, the particle space shrinks accordingly. Therefore, we need to limit the particle fluctuation range based on the number of iterations (i.e., the number of observations).

[0114] The specific method involves appropriately reducing the variance of particle parameters following a corresponding normal distribution as the number of observations increases. A suitable normal distribution variance can effectively increase particle diversity, thereby improving the accuracy of radioactive source parameter estimation.

[0115] Step B1, Particle Initialization (K=0). N particles are evenly and randomly scattered throughout the search area of ​​the mobile robot. This establishes the initial weighted particle set {X}. n， ω n}, where vector X n It satisfies a uniform distribution. It is assumed that the initial radiation source may exist anywhere in the search area, and that the probability is the same in each search grid.

[0116] Step B2, observe and update particle weights;

[0117] Whenever a new observation z is obtained, the weights of the particles are updated using the Bayesian method, as shown in the following equation.

[0118] ω k =ω k-1 ·p(z|X k )=ω k-1 ·p(z, λ) k (X k ))

[0119] In the above formula, ω k For the weight of the latest particle, ω k-1 X is the weight of the previous particle. k This refers to information related to particles;

[0120] Step B3, particle weight normalization;

[0121] In existing technologies, particle filter normalization uses fixed formulas.

[0122]

[0123] In the above formula, ω k The weight of the latest particle;

[0124] The method that directly calculates the average weights results in a significant bias in the normalized weights, failing to accurately reflect the statistical distribution characteristics of multiple particles. Therefore, this method uses the positions and weights of all particles and applies the K-means++ clustering algorithm to obtain the number and weights of all particles belonging to a specific cluster. This is then used as the result of particle weight normalization. K-means++ clustering can simultaneously satisfy the requirements of multiple normalization results, meeting the needs of scenarios with multiple radioactive source targets in the environment.

[0125] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus.

[0126] Finally, it should be noted that the above descriptions are merely preferred embodiments of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A robotic sampling method for locating multiple radiation sources in open areas, characterized in that: Includes the following steps: In step S1, the robot uses the coupled information of SLAM mapping and radiation physics field to divide the environment map into grids and evaluate them. The evaluation is to assess the count rate of the radiation field within the grid. Grids with a count rate exceeding the threshold participate in the subsequent particle swarm optimization algorithm; otherwise, they are discarded and do not participate in the particle swarm optimization calculation. The SLAM mapping adopts the Fast-SLAM method. During mapping, grids are marked as free grids, gray unexplored grids, or black grids occupied by obstacles, and map height, width, resolution, radiation count rate, and energy characteristic information are stored. The robot explores the environment according to a spiral path. The robot explores the environment along a spiral path, using the ROS robot's lidar and IMU sensors to acquire position information of obstacles, boundaries, and the robot itself, and using CeBr3 in conjunction with a multichannel pulse analysis device to acquire information on radiation sources. Step S2 involves using the radiation field count data of the search area as parameters for multi-radiation source localization path planning; and using the SR-PF optimization system sampling particle filter algorithm to estimate the localization information of potential multi-radiation sources in the environment; specifically: Step A1: Particle initialization. Establish an initial set of weighted particles, where each parameter is uniformly distributed and each particle has the same weight. Step A2, particle weight iteration; Step A3: Particle state initialization and prediction weight model correction; Step A4, resampling; Resampling uses self-optimizing resampling; Step A401: Determine whether the number of valid samples is less than the threshold based on the particle weights; if the condition is met, use the system resampling method to filter and replicate the particles; otherwise, keep the original particle set unchanged. Step A402: Optimize the high-weight particles that need to be replicated; Step A403: Initialize the particles; Step A404: Establish the weighted particle set of the initial state. ,in, The weight vector representing the particle It satisfies a uniform distribution; it is assumed that the initial radiation source may exist anywhere in the search area, and that the probability is the same in each search grid. Step A405, update particle weights based on observations; whenever there are new observations... Then, the particle weights are updated using the Bayesian method, as shown in the following equation: In the above formula, The weight of the latest particle, The weight of the previous particle. This refers to information related to particles; Step A406, particle weight normalization; In the above formula, The weight of the latest particle; Step A406: The positions and weights of all the particles obtained are used to obtain the number and weights of all particles belonging to a certain cluster using the K-means++ clustering algorithm, which is the result of particle weight normalization. Step A407, optimize system resampling; take the reciprocal of the sum of squared weights obtained in step A405, and use the reciprocal as the number of valid samples. If the number of valid samples is less than half the number of particles in that category, then resampling is performed; if the number of valid samples is greater than half the number of particles in that category, then resampling is not performed. Step S3: Estimate the parameters of the radioactive source. The weighted particle set after the SR-PF optimization system sampling particle filtering algorithm is as follows: In the above formula, This represents a group of particles at different locations. Clusters representing the weights of particles; Based on the above expression, the parameter vector estimate of the radioactive source is denoted as: In the above formula, A parameter vector representing the position of the particle cluster; After completing the above estimation, input a new particle and perform the next iteration and parameter estimation; Step S4: Repeat the above process to make the particles converge continuously. The estimated value of the radioactive source will gradually converge to the actual value. When the maximum value of the horizontal and vertical lengths of the particle space representing the 2D coordinates x and y of the radioactive source is less than or equal to the threshold, the loop process ends and a set of particles that is no longer updated is obtained. At this time, the radioactive source parameter vector is the final estimated value, that is, the position and activity of the radioactive source are obtained.

2. A robotic sampling method for locating multiple radiation sources in open areas according to claim 1, characterized in that: In step A406, the K-means++ clustering algorithm is specifically as follows: Step C1: First, use the K-means++ algorithm to randomly select a center point in the particle set. For the remaining particles, calculate the distance to the center point. Step C2: Select a point that is far away as a new center, and repeat step C1 until K centers are selected, where K represents the number of radioactive sources in the environment; Step C3: Starting from the first center, calculate the distance of all samples to the center point. If a sample is close to the center, it belongs to a point group. Group all sample points according to the distance and calculate the mean of each group to obtain the centers of multiple clusters, that is, estimate the location information of K radioactive sources.

3. A robotic sampling method for locating multiple radiation sources in open areas according to claim 1, characterized in that: For particles with high weights, the following optimizations are performed: In the above formula, the meanings of each letter are as follows: This represents the updated set of weighted particles. Indicates the normalized weights; This indicates that the x value is uniformly sampled from N particles.

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