A method for searching for a radioactive source based on an unknown environment

Abstract

The application provides a radioactive source searching method based on an unknown environment, and belongs to the field of nuclear and radiation safety. The method comprises the following steps: constructing a multi-dimensional state grid map; controlling a robot to execute a global exploration mode based on a cognitive potential field; when a signal-to-noise ratio triggers a preset threshold, switching to a local accurate positioning mode based on particle filtering and multi-entropy fusion; starting an anisotropic adaptive particle filtering algorithm, recursively estimating a posterior probability distribution of a radioactive source, and constructing a five-dimensional comprehensive evaluation system; generating a dynamic weight vector based on a real-time environment situation of dynamic perception; weighting and fusing the dynamic weight vector and each entropy value in the five-dimensional comprehensive evaluation system to form a comprehensive evaluation manifold; under the non-complete kinematic constraint and physical safety hard constraint of the robot, solving an optimal control instruction for maximizing the comprehensive evaluation manifold to drive the robot platform to approach the radioactive source. In this way, the success rate and positioning accuracy of the radioactive source searching are significantly improved.

Description

Technical Field

[0001] This invention belongs to the field of nuclear and radiation safety, and specifically relates to a method for searching for radioactive sources in unknown environments. Background Technology

[0002] The widespread application of nuclear energy and technology has made the safe management of radioactive sources increasingly important, especially in scenarios such as nuclear accident emergencies, urban rubble searches, and the decommissioning of abandoned nuclear facilities. Lost radioactive sources may be hidden in complex, confined spaces with numerous obstacles. In such environments, heavy obstacles not only hinder the movement of mobile robots but also severely shield and attenuate the gamma rays emitted by the radioactive source, causing strong random fluctuations in the radiation signal received by the detector and creating a deep radiation blind zone behind the obstacles. How to guide robots to autonomously, efficiently, and accurately locate radioactive sources in complex environments with complete unknowns and strong physical shielding has become a core technological bottleneck that urgently needs to be overcome in the field of nuclear safety robotics.

[0003] In practical applications of radiation environment monitoring, obstacles such as complex buildings, vegetation, and terrain can significantly obstruct and attenuate the radiation signals from radioactive sources, directly interfering with the accuracy of monitoring data. Current technologies for radioactive source state estimation largely rely on methods such as static mesh interpolation, gradient ascent, or simple geometric overlay. These methods construct observation models based solely on the assumption of ideal, unobstructed radiation propagation, and their common drawback is the lack of physical modeling capabilities for environmental obstruction, failing to accurately reproduce the attenuation patterns of radiation signals in real-world scenarios. When obstacles exist between the robot and the radioactive source, the actual attenuation of rays along the path cannot be reflected, leading to significant biases in the posterior probability inference of the radioactive source's location based on observation data. In scenarios where the radiation signal is already weak and severely attenuated by obstacles, this bias is further amplified, making the estimation results highly unstable or even divergent, severely restricting the reliability of subsequent decisions. Summary of the Invention

[0004] To address the problem that existing methods often fail to accurately estimate the state of radioactive sources in complex, occluded, and unknown environments, leading to path deadlock and oscillation issues for robots approaching these sources, this invention provides a radioactive source search method based on unknown environments.

[0005] To achieve the above objectives, the present invention provides the following technical solution: A method for searching radioactive sources in an unknown environment, the method comprising: Construct a multidimensional raster map to characterize environmental and radiation field information; The robot is controlled to perform a global search and then switches to a local precise positioning mode after detecting a radiation signal. In the local precise localization mode, multiple particles are initialized to characterize the posterior probability distribution of the radioactive source location, and each particle contains a hypothetical spatial location attribute of the radioactive source and a corresponding weight attribute. For each particle, a virtual ray is emitted from the robot's current position to the hypothetical location of the radiation source corresponding to that particle. All obstacle grids traversed by the virtual ray are identified based on the grid map. The total attenuation length is calculated by summing the path lengths of the robot as it traverses each obstacle grid. This total attenuation length is then incorporated into the observation likelihood function to correct for the influence of environmental occlusion on the radiation signal. The weight of the particle is calculated based on this weight distribution, thereby estimating the location of the radiation source. Based on control instructions that satisfy robot motion constraints and obstacle avoidance constraints, the robot searches for the estimated radiation source as a target.

[0006] Optionally, controlling the robot to search for the estimated radiation source as a target based on control commands that satisfy robot motion constraints and obstacle avoidance constraints includes: Construct target orientation entropy and obstacle avoidance safety entropy, wherein the target orientation entropy is negatively correlated with the estimated distance from the candidate position to the radiation source position, and the obstacle avoidance safety entropy is positively correlated with the distance from the candidate position to the nearest obstacle; Generate a candidate action set consisting of a combination of linear velocity and angular velocity; for each candidate action in the candidate action set, simulate and predict the robot's pose at the next moment, and calculate the target guidance entropy and obstacle avoidance safety entropy at the predicted pose; Under the premise of satisfying robot motion constraints and obstacle avoidance constraints, the candidate action that maximizes the weighted sum of the target orientation entropy and obstacle avoidance safety entropy is selected as the optimal control command for the current moment and searched.

[0007] Optionally, estimating the location of the radioactive source based on the weight distribution of each particle includes: The weights of each particle are normalized, and the hypothetical spatial positions of the radioactive sources corresponding to each particle are weighted and averaged using the normalized weights to obtain the position estimate of the radioactive source at the current moment. The effective sample size is calculated to assess the degradation of the current particle swarm. When the effective sample size is lower than a preset threshold, low-weight particles are removed and high-weight particles are copied to perform system resampling. An anisotropic adaptive Metropolis-Hastings sampling method is adopted to dynamically adjust the proposal distribution using the covariance matrix of the current particle swarm spatial distribution. Anisotropic mutations are performed on the resampled particles to increase particle diversity.

[0008] Optionally, the construction of the target-oriented entropy and obstacle avoidance safety entropy includes: Using the estimated location of the radiation source as the target point and the obstacle information stored in the grid map as the safety constraint, for any candidate location in space, the Euclidean distance from the candidate location to the estimated location of the radiation source is calculated, and the target guidance entropy is constructed in the form of a negative exponent of the Euclidean distance, so that the closer the candidate location is to the estimated location of the radiation source, the higher the value of the target guidance entropy. Calculate the Euclidean distance from the candidate location to the nearest obstacle in the grid map, substitute the distance as the independent variable into the piecewise continuous mapping function, and use the output value of the mapping function as the obstacle avoidance safety entropy, so that the value of the obstacle avoidance safety entropy decreases exponentially as the candidate location gets closer to the obstacle. After constructing the target-oriented entropy and obstacle-avoidance safety entropy, improved Shannon entropy, exploration entropy, and access entropy are also constructed. The improved Shannon entropy is constructed based on the normalized weights of each particle and its spatial distribution covariance matrix, and is used to quantify the uncertainty of the posterior distribution. The exploration entropy is constructed based on the ratio of the number of unexplored grids to the number of passable grids within the perception range around the candidate location, and is used to measure the unknown in the environment. The access entropy is constructed based on the global access frequency map and is used to impose penalties on candidate locations that have been repeatedly accessed.

[0009] Optionally, the step of simulating and predicting the robot's next pose for each candidate action in the candidate action set, and calculating the target guidance entropy and obstacle avoidance safety entropy at the predicted pose, includes: Obtain the robot's current pose information, which includes two-dimensional spatial coordinates and heading angle; For each candidate action in the candidate action set, based on the kinematic model of the differential drive robot, and according to the current pose and the linear and angular velocities in the candidate action, a forward integral of one control cycle is performed to simulate and predict the robot's pose at the next moment after executing the candidate action. Using the coordinates of the predicted pose in two-dimensional space as the candidate position, the target guidance entropy, the obstacle avoidance safety entropy, the improved Shannon entropy, the exploration entropy, and the access entropy are calculated at the candidate position, respectively.

[0010] Optionally, the step of selecting the candidate action that maximizes the weighted sum of the target guidance entropy and the obstacle avoidance safety entropy as the optimal control command at the current moment, under the premise of satisfying robot motion constraints and obstacle avoidance constraints, includes: For each candidate action, the trajectory segment from the current pose to the predicted pose is checked to see if the trajectory segment intersects with the obstacle safety boundary in the grid map. The obstacle safety boundary is the extended boundary formed by extending the original obstacle boundary outward to the robot's safety radius. Candidate actions corresponding to intersecting trajectory segments are determined to be non-compliant with the obstacle avoidance constraints and are eliminated. For each candidate action that passes the verification, the robot's nonholonomic constraints are used as the motion constraints for selecting the candidate action. Within the set of candidate actions that satisfy the motion constraints and obstacle avoidance constraints, the target guidance entropy and obstacle avoidance safety entropy are weighted and summed. The candidate action that maximizes the weighted sum is selected as the optimal control command at the current moment.

[0011] Optionally, the weighted summation of the target guidance entropy and obstacle avoidance safety entropy includes: The weights of the improved Shannon entropy, exploration entropy, access entropy, obstacle avoidance safety entropy, and target orientation entropy are adaptively adjusted based on the real-time perceived local environmental situation of the robot, and the weighted sum of the adjusted entropy values ​​is then performed. The local environmental situation is characterized by an environmental feature vector that includes the limit avoidance distance, local obstacle density, particle spatial divergence and target approach distance. The weight adjustment is dynamically implemented by a piecewise mapping function with the environmental feature vector as the independent variable. The piecewise mapping function outputs different weight allocation schemes under different physical critical states.

[0012] Optionally, generating a candidate action set consisting of a combination of linear velocity and angular velocity includes: The feasible ranges of linear velocity and angular velocity of the robot are obtained, and the feasible ranges of linear velocity and angular velocity are discretized into a finite set of linear velocity and a finite set of angular velocity according to a preset discrete interval. Traverse all combinations of the finite linear velocity set and the finite angular velocity set, and use each combination of linear velocity and angular velocity as a candidate action to form the candidate action set.

[0013] Optionally, the construction of the multidimensional raster map for characterizing environmental and radiation field information includes: The environment space is discretized into multiple grid cells, each grid cell is configured to store its physical state label, which includes at least unexplored, explored and obstacle; Record the frequency of the robot's historical trajectory accessing each grid cell; The signal variation calculated based on radiation field observation data and the posterior probability distribution entropy value are then associated with the corresponding grid cells to form a multidimensional grid map containing geometric and radiation field information.

[0014] Optionally, the control robot performs a global search and switches to a local precise positioning mode after detecting a radiation signal, including: The robot is driven by a cognitive potential field to preferentially move towards unexplored areas. The cognitive potential field uses the information entropy value of the unvisited grid as the source of gravity, and the grid with higher information entropy has a greater attraction to the robot. When the robot encounters an obstacle that causes the resultant force of the cognitive potential field to fall into a local minimum, sliding mode control is introduced. The robot is controlled to circle around the obstacle boundary according to the tangent direction of the obstacle safety boundary in order to escape the local minimum trap. During the global search process, the radiation detection signal is continuously sampled. When the signal-to-noise ratio accumulated based on the sliding time window exceeds a preset threshold, it is determined that a valid radiation signal has been detected. Then, the robot switches from the global search mode to the local precise positioning mode through the Markov state machine. In the local precise positioning mode, when the signal-to-noise ratio accumulated in the sliding time window is lower than the preset cut-out threshold and continues to exceed the tolerance number of steps, the robot is controlled to return to the global search mode.

[0015] The radioactive source search method based on unknown environments provided by this invention has the following beneficial effects: The proposed radioactive source search method incorporates obstacle information from a grid map into the observation likelihood function of a particle filter. This allows the particle weights to accurately reflect the actual attenuation of rays as they travel through obstacles from each hypothetical source location to the detector. Thus, even under conditions of strong occlusion in physical space, it maintains an unbiased estimate of the posterior probability distribution of the radioactive source location, overcoming the target prior distortion problem caused by the lack of environmental occlusion modeling in traditional observation models. In complex scenarios with weak radiation signals and severe obstacle shielding, this method provides a reliable target prior for subsequent path planning, effectively eliminating path oscillations and deadlocks caused by state estimation biases, and significantly improving the success rate and accuracy of radioactive source localization. Attached Figure Description

[0016] To more clearly illustrate the embodiments and design schemes of the present invention, the accompanying drawings required for this embodiment will be briefly described below. The drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0017] Figure 1 This is a flowchart illustrating a radioactive source search method based on an unknown environment according to an exemplary embodiment of the present invention.

[0018] Figure 2 This is a schematic diagram of a CDRSSF system framework provided by the present invention according to an exemplary embodiment.

[0019] Figure 3 This is a schematic diagram of a grid map label provided by the present invention according to an exemplary embodiment.

[0020] Figure 4 This is a schematic diagram of a CPF provided according to an exemplary embodiment of the present invention. Detailed Implementation

[0021] To enable those skilled in the art to better understand and implement the technical solutions of the present invention, the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments. The following embodiments are only used to more clearly illustrate the technical solutions of the present invention and should not be construed as limiting the scope of protection of the present invention.

[0022] The technical solutions provided by the various embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0023] First, this invention provides a method for searching for radioactive sources in an unknown environment, specifically as follows: Figure 1 As shown, it includes the following steps: S101. Construct a multidimensional raster map to characterize environmental and radiation field information.

[0024] The grid cells in this map are configured to store multi-dimensional environmental information, including exploration status, access frequency, radiation gradient, and information entropy.

[0025] In the construction of the multidimensional state grid map in this step, the physical state of the grid cell is discretized into multiple semantic labels, including unexplored, explored, obstacle, candidate work area and obstacle edge; and the access frequency is updated according to the number of times the grid is covered by the robot's historical trajectory, the radiation gradient is calculated based on the change of radiation signal between continuous effective observation points, and the information entropy is calculated based on the posterior probability distribution entropy value of the grid based on historical observation data.

[0026] For example, the environmental space is discretized into multiple grid cells, each grid cell is configured to store its physical state label, which includes at least unexplored, explored, and obstacle; the frequency of the robot's historical trajectory accessing each grid cell is recorded; and the signal change calculated based on radiation field observation data and the posterior probability distribution entropy value are associated with the corresponding grid cell to form a multidimensional grid map containing geometric and radiation field information.

[0027] S102. Control the robot to perform a global search, and switch to local precise positioning mode after detecting a radiation signal.

[0028] In the global exploration mode based on cognitive potential field, unvisited grids within the perception range are used as attraction sources, and the covering gravity is calculated by combining the information entropy value of each grid in a distance-weighted manner. When the robot encounters a non-convex obstacle that causes the resultant force to fall into a local minimum, sliding mode control is introduced. By calculating the tangent direction of the obstacle's extended safety boundary and designing a sliding surface, the robot is controlled to smoothly circumnavigate along the obstacle boundary.

[0029] When performing mode switching via a Markov state machine, an effective state accumulator is defined to evaluate the number of effective observation steps exceeding the signal-to-noise ratio threshold within a preset sliding time window. Only when the integral value of the accumulator is greater than or equal to a preset mode entry threshold is a switch from the global exploration mode to the local precise positioning mode triggered. In the local precise positioning mode, when the integral value of the accumulator is less than or equal to a preset mode exit threshold and the number of consecutive low signal-to-noise ratio observation steps exceeds the tolerance limit, a fault-tolerant degradation is triggered, and the system reverts to the global exploration mode.

[0030] For example, the robot is driven by a cognitive potential field to preferentially move towards unexplored areas. This cognitive potential field uses the information entropy value of unvisited grids as a source of attraction, and the higher the information entropy of a grid, the greater the attraction to the robot. When the robot encounters an obstacle that causes the resultant force of the cognitive potential field to fall into a local minimum, sliding mode control is introduced. The robot is controlled to circle around the obstacle boundary according to the tangent direction of the obstacle's safety boundary to escape the local minimum trap. During the global search, radiation detection signals are continuously sampled. When the signal-to-noise ratio accumulated based on the sliding time window exceeds a preset threshold, it is determined that a valid radiation signal has been detected. Then, a mode switch is executed through a Markov state machine, causing the robot to switch from the global search mode to the local precise localization mode. In the local precise localization mode, when the signal-to-noise ratio accumulated in the sliding time window is lower than a preset cut-out threshold and continues to exceed the tolerance step count, the robot is controlled to return to the global search mode.

[0031] S103. In this local precise positioning mode, multiple particles are initialized to characterize the posterior probability distribution of the radioactive source location. Each particle contains the assumed spatial location attribute of the radioactive source and the corresponding weight attribute.

[0032] S104. For each particle, a virtual ray is emitted starting from the robot's current position and ending at the hypothetical radiation source position corresponding to the particle. Based on the grid map, all obstacle grids passed through by the virtual ray are identified, and the path length of the robot when passing through each obstacle grid is accumulated as the total attenuation length. The total attenuation length is incorporated into the observation likelihood function to correct the influence of environmental occlusion on the radiation signal. The weight of the particle is calculated in this way, and the position of the radiation source is estimated based on the weight distribution of each particle.

[0033] Specifically, when correcting particle weights, a ray casting algorithm is used to calculate the total attenuation length of photons passing through obstacles. This total attenuation length is then incorporated into the observation likelihood function to correct the weights and mitigate the impact of environmental occlusion on the observation likelihood function. The effective sample size is calculated, and adaptive system resampling is performed when this effective sample size falls below a preset threshold. An anisotropic adaptive Metropolis-Hastings sampling method is employed, using a dynamically updated covariance matrix to mutate the resampled particles, overcoming particle degradation and sample depletion. Based on the mutated particle swarm and its normalized weights, a weighted estimate of the radioactive source location and activity is calculated to recursively update the posterior probability distribution.

[0034] In addition, in this local precise positioning mode, the standard deviation of the spatial distribution of particles and the peak value of the local radiation count rate are obtained for the estimated location of the radiation source. When the standard deviation of the spatial distribution of particles is less than the preset maximum allowable standard deviation and the local radiation count rate reaches the peak value, the system determines that the positioning is successful and terminates the search.

[0035] For example, multiple particles are randomly scattered near the robot's current position. Each particle contains a hypothetical spatial location attribute of the radiation source and a corresponding weight attribute. For each particle, a virtual ray is emitted from the robot's current position to the hypothetical location of the radiation source corresponding to the particle. All obstacle grids that the virtual ray passes through are identified according to the grid map. The path length of the robot when passing through each obstacle grid is accumulated as the total attenuation length. This total attenuation length is incorporated into the observation likelihood function to correct the influence of environmental occlusion on the radiation signal, thereby calculating the weight of the particle. The weights of each particle are normalized, and the hypothetical radioactive source spatial locations corresponding to each particle are weighted and averaged to obtain the current position estimate of the radioactive source. The effective sample size is calculated to assess the degradation degree of the current particle swarm. When the effective sample size is lower than a preset threshold, low-weight particles are removed and high-weight particles are copied to perform system resampling. An anisotropic adaptive Metropolis-Hastings sampling method is adopted, which dynamically adjusts the proposal distribution using the covariance matrix of the current particle swarm spatial distribution, and anisotropically mutates the resampled particles to increase particle diversity.

[0036] S105. Based on control instructions that satisfy robot motion constraints and obstacle avoidance constraints, control the robot to search for the estimated radiation source as a target.

[0037] In this step, firstly, target orientation entropy and obstacle avoidance safety entropy are constructed. The target orientation entropy is negatively correlated with the estimated distance from the candidate position to the radiation source position, and the obstacle avoidance safety entropy is positively correlated with the distance from the candidate position to the nearest obstacle. Secondly, a set of candidate actions composed of linear velocity and angular velocity is generated. Then, for each candidate action in the set of candidate actions, the robot's pose at the next moment is simulated and predicted, and the target orientation entropy and obstacle avoidance safety entropy are calculated at the predicted pose. Finally, under the premise of satisfying robot motion constraints and obstacle avoidance constraints, the candidate action that maximizes the weighted sum of the target orientation entropy and obstacle avoidance safety entropy is selected as the optimal control command for the current moment for searching.

[0038] Specifically, the target-oriented entropy is negatively correlated with the estimated distance from the candidate location to the radiation source location, providing a driving force for approaching the estimated source. The obstacle avoidance safety entropy is positively correlated with the distance from the candidate location to the nearest obstacle, used to assess the platform's physical safety. Additionally, this step constructs improved Shannon entropy, exploration entropy, and access entropy. The improved Shannon entropy is constructed based on the normalized weights of each particle and their spatial distribution covariance matrix, used to quantify the uncertainty of the posterior distribution. The exploration entropy is constructed based on the ratio of the number of unexplored grids to the number of passable grids within the sensing range of the candidate location, used to measure environmental unknowns. The access entropy is constructed based on a global access frequency map, used to penalize candidate locations that have been repeatedly visited.

[0039] For example, using the estimated location of the radiation source as the target point and the obstacle information stored in the grid map as the safety constraint, for any candidate location in space, the Euclidean distance from the candidate location to the estimated location of the radiation source is calculated, and the target guidance entropy is constructed in the form of a negative exponent of the Euclidean distance, so that the value of the target guidance entropy is higher the closer the candidate location is to the estimated location of the radiation source; the Euclidean distance from the candidate location to the nearest obstacle in the grid map is calculated, and this distance is substituted as an independent variable into a piecewise continuous mapping function, and the output value of the mapping function is used as the obstacle avoidance safety entropy, so that the value of the obstacle avoidance safety entropy decreases exponentially the closer the candidate location is to the obstacle.

[0040] In one embodiment, the improved Shannon entropy is defined as a weighted fusion of particle weight entropy and particle spatial distribution covariance entropy. The particle weight entropy is calculated based on the logarithmic entropy of the normalized weights of each particle, and the particle spatial distribution covariance entropy is calculated based on the logarithm of the determinant of the covariance matrix of the current particle swarm spatial distribution. The exploration entropy is measured by calculating the ratio of the number of unexplored grids to the number of passable grids within the perception radius surrounding a candidate location. The access entropy is calculated based on a global access frequency map and is used to impose a historical cost penalty on spaces that have been repeatedly sampled. The obstacle avoidance safety entropy is constructed as follows: a piecewise continuous distance penalty function is defined, which outputs different penalty values ​​based on the safe interval of the Euclidean distance between the robot and the nearest obstacle; this distance penalty is weighted and fused with a target direction consistency term, which measures the angle between the target vector pointing to the estimated source and the normal vector pointing to the nearest obstacle, driving the robot to prioritize safe tangential directions that do not deviate from the radiation source while moving away from obstacles.

[0041] In addition, for adjusting the weights of each entropy value, firstly, a multi-dimensional environmental feature vector is defined, including the limit avoidance distance, local obstacle density, particle spatial divergence, and target approach distance; secondly, a diagonal gain matrix is ​​constructed with the environmental feature vector as the independent variable. The diagonal elements of the gain matrix are taken according to the preset piecewise boundary conditions. The piecewise boundary conditions respond to at least three physical critical states: collision trigger threshold, warning envelope entry, and strong constraint narrow channel deadlock escape; finally, the diagonal gain matrix is ​​multiplied by the preset basic weight vector, and the product result is subjected to norm projection to obtain the dynamic weight vector.

[0042] In another embodiment, this step also requires generating a candidate action set consisting of a combination of linear velocity and angular velocity; for each candidate action in the candidate action set, the robot's pose at the next moment is simulated and predicted, and the target guidance entropy and obstacle avoidance safety entropy are calculated at the predicted pose.

[0043] For example, firstly, the feasible range of linear velocity and the feasible range of angular velocity of the robot are obtained. The feasible range of linear velocity and the feasible range of angular velocity are discretized into a finite set of linear velocity and a finite set of angular velocity according to a preset discrete interval. All combinations in the finite set of linear velocity and the finite set of angular velocity are traversed, and each combination of linear velocity and angular velocity is used as a candidate action to form the candidate action set.

[0044] Secondly, the robot's current pose information is obtained, which includes two-dimensional spatial coordinates and heading angle. For each candidate action in the candidate action set, based on the kinematic model of the differential drive robot, the robot's pose is simulated and predicted by integrating forward for one control cycle according to the current pose and the linear and angular velocities in the candidate action. The predicted pose coordinates in two-dimensional space are used as the candidate position, and the target guidance entropy, obstacle avoidance safety entropy, improved Shannon entropy, exploration entropy, and access entropy are calculated at the candidate position.

[0045] Finally, under the premise of satisfying the robot motion constraints and obstacle avoidance constraints, the candidate action that maximizes the weighted sum of the target orientation entropy and obstacle avoidance safety entropy is selected as the optimal control command for the current moment and searched.

[0046] In this step, the continuous control space is discretized into a set of actionable actions consisting of a finite combination of linear and angular velocities. For each candidate action in this set, the robot's pose at the next moment is predicted by forward simulation based on a differential drive kinematic model. A path safety hard constraint indicator function is defined to verify whether the trajectory segment from the current position to the predicted pose intersects with the boundary of extended obstacles in the map. Only for the predicted pose that satisfies the safety hard constraint, each entropy value is extracted and multiplied by the dynamic weight vector to calculate the action utility value. The candidate action with the maximum action utility value is selected as the optimal control command for the current cycle to control the robot to search.

[0047] For example, for each candidate action, the trajectory segment from the current pose to the predicted pose is checked to see if it intersects with the obstacle safety boundary in the grid map. The obstacle safety boundary is the extended boundary formed by extending the robot's safety radius outward from the original obstacle boundary. Candidate actions corresponding to trajectory segments that intersect are determined to not satisfy the obstacle avoidance constraint and are eliminated. For each candidate action that passes the check, the robot's nonholonomic constraint is used as the motion constraint for selecting the candidate action. Within the set of candidate actions that satisfy the motion constraint and obstacle avoidance constraint, the target guidance entropy and obstacle avoidance safety entropy are weighted and summed. The candidate action that maximizes the weighted sum is selected as the optimal control command at the current moment.

[0048] In addition, the target orientation entropy, obstacle avoidance safety entropy, improved Shannon entropy, exploration entropy, and access entropy can be weighted and summed simultaneously. The weights of the improved Shannon entropy, exploration entropy, access entropy, obstacle avoidance safety entropy, and target orientation entropy can be adaptively adjusted according to the real-time perceived local environmental situation of the robot, and the weighted sum of the adjusted entropy values ​​can be performed. The local environmental situation is characterized by an environmental feature vector that includes the limit avoidance distance, local obstacle density, particle spatial divergence, and target approach distance. The weight adjustment is dynamically achieved through a piecewise mapping function with the environmental feature vector as the independent variable. The piecewise mapping function outputs different weight allocation schemes under different physical critical states.

[0049] Using the above method, this invention constructs a cognitively driven progressive control system. First, it utilizes a Markov state machine triggered by signal-to-noise ratio accumulation to achieve a smooth and robust transition from global cognitive potential field exploration to local multi-entropy fusion localization. In the local localization stage, an anisotropic adaptive particle filter algorithm is introduced to effectively overcome particle degradation and sample depletion under strong Poisson noise and physical occlusion, ensuring stable convergence of the posterior probability distribution. By constructing a five-dimensional comprehensive evaluation system including improved Shannon entropy, exploration entropy, access entropy, obstacle avoidance safety entropy, and target orientation entropy, and dynamically and adaptively adjusting the weights of each entropy value based on the real-time environmental situation, this method simultaneously quantifies state uncertainty, environmental unknowns, historical path costs, platform physical safety, and target chemotaxis driving force within a single optimization framework. Solving for optimal control commands under nonholonomic kinematics and physical safety obstacle avoidance constraints enables the robot to autonomously generate deadlock-free and oscillation-free optimal approximation paths while ensuring its own safety. This method demonstrates excellent robustness and generalization ability in various extreme topological scenarios, significantly improving the success rate and positioning accuracy of radioactive source search, and completely eliminating the path detours and deadlocks common in traditional algorithms. It provides reliable technical support for autonomous search in highly dynamic and strongly shielded nuclear radiation environments.

[0050] Based on the above method steps, the present invention also provides the following embodiments for illustration.

[0051] The proposed Cognitive Two-Layer Robotic Radiation Source Search and Localization Framework (CDRSSF) employs a progressive control architecture. This architecture decouples the complex radiation source search task into two macroscopic stages: global exploration based on a cognitive potential field, and local precise localization based on particle filtering and multi-entropy fusion planning. To achieve the switching between exploration and localization control, a Markov state machine is used to achieve smooth transition and fault-tolerant switching based on real-time situational awareness. This step will first describe the overall closed-loop data flow of the system, and then construct a rigorous multidimensional physical and geometric environment state model.

[0052] To ensure the system's autonomous decision-making capability in complex and unknown environments, the CDRSSF architecture consists of a closed loop of four core modules: environmental representation update, global and local navigation planners, a multimodal state machine, and a low-level kinematic actuator. Airborne lidar and radiation detectors acquire physical point clouds and radiation counts in real time. This multi-source, heterogeneous environmental data is then mapped to a multi-dimensional state grid map for online updates of spatial information entropy and access frequency. The Markov state machine dynamically evaluates the current physical situation based on the radiation signal-to-noise ratio and time window, and outputs mode-switching commands. The global cognitive potential field or local multi-entropy fusion planner controls the entire system's operating mode accordingly, solving for optimal motion control in the discrete action space. The complete system architecture and data flow are as follows: Figure 2 As shown.

[0053] First, we perform multidimensional state vector modeling in the environmental geometric space.

[0054] Radioactive decay and radiation detection processes are inherently stochastic, necessitating the use of appropriate probability density functions (PDFs) to accurately simulate their underlying physical mechanisms. Standard textbooks articulate a fundamental principle: during radioactive decay events, the counts detected by radiation sensors follow a Poisson distribution. Specifically, the number of counts recorded within a fixed time interval follows Poisson's law:

[0055] Here, The mean of the Poisson distribution is represented. The radiation sensor deployed on the robotic platform is a modified sodium iodide (NaI(Tl)) scintillation detector. Radiation dose is quantified in count rate (counts per second, CPS), which refers to the number of counts recorded by the detector per second. This count rate (CPS) is calculated in a vacuum using a reference single-point source A with a known activity (Bq). When the detector measures radiation at observation point P, the count rate can be expressed as:

[0056] In this formula, Indicates the effective detection area of ​​the detector ( ), This represents the intrinsic detection efficiency, determined by the detector design. This refers to the linear attenuation coefficient of photons within a material. ), This represents the path length of a photon through an attenuating material. ). The parameter represents the measurement time. ), It is the Euclidean distance between the radiation source and the detector. In addition to the radiation source events that trigger the detector count, the environmental contribution is also included in the total count. This additional contribution is called the background count rate, denoted as . ( ).

[0057] To accurately calculate the discrete occupancy grid map used for robot navigation Photon path length in a discrete occupancy grid map. This study implements a ray-casting algorithm based on voxel traversal. For any assumed radiation source location... and robot position A virtual ray is projected between the two points, and the algorithm identifies all mesh cells (voxels) that intersect this ray and are marked as obstacles. Total attenuation length. The calculation is the sum of the Euclidean segments within these occupied voxels:

[0058] in This represents the set of occupied units along the ray. This geometric calculation allows the theoretical model in the aforementioned count rate formula to be dynamically updated according to the robot's constantly changing environment. As will be explained in detail later in the experimental section, obstacles are modeled as concrete walls with a linear decay coefficient of... .

[0059] The initial environment was discretized into a structured raster map M. To accurately describe the environmental and radiation field characteristics, for any rasterized environment cell... Establish a complete multidimensional state tuple Wherein, the physical state of the grid at a certain time t. : These correspond to unexplored, explored, obstacles, candidate action areas, and obstacle edges, respectively. Figure 3 As shown, for the first in the environment One obstacle Construct an extended safety boundary set that integrates the robot's safe width radius and obstacle avoidance tolerance. Access frequency Record the number of times the robot's historical trajectory covers the grid at a certain time t, which is used for subsequent access entropy calculation. Whenever the robot's position... When the corresponding raster is covered, update according to the following indicator function:

[0060] Radiative gradient vector The changes in radiation signals among consecutive effective observation points at a certain time t are recorded to represent the spatial distribution of the radiation field. Let... and Let be the radiation observations at the current and previous moments, respectively. The update formula is:

[0061] Information entropy value This represents the unknown radiation field of the region at a certain time t, and the posterior probability distribution entropy value of the grid is calculated based on historical observation data.

[0062] Secondly, cognitive-driven navigation and precise positioning are implemented.

[0063] After completing the environmental geometric representation and multi-dimensional physical state modeling, the system has the ability to quantify the static information of unknown radiation fields. However, how to drive the robot to achieve dynamic evolution from large-scale blind search to high-precision locking in an environment with extremely low signal-to-noise ratio and high Poisson noise is the core challenge of autonomous radiation source localization. To this end, this step proposes a cognitive-driven progressive navigation and localization architecture. This architecture takes "the transformation of spatial information entropy into physical motion commands" as the main line: first, the cognitive potential field (CPF) is used to transform the information entropy of unexplored areas into gravity to achieve efficient coverage of the global space; in this process, a Markov state machine based on a sliding window continuously evaluates the physical situation and triggers a seamless switch of cognitive mode when the signal-to-noise ratio crosses a critical threshold; then the system enters the local mining stage, activating adaptive anisotropic particle filtering (AAMH-PF) and multi-entropy fusion programming (MEFPP) to approximate the true posterior distribution. Finally, all multi-scale spatial and information value assessments are rigorously mapped to the robot's nonholonomic kinematics and safety hard constraint model to form optimal control commands.

[0064] In this step, we first explore the global cognitive potential field and sliding mode control, then perform stage switching and state machine design, then particle filtering and multi-entropy fusion path planning, and finally construct a state transition model under nonholonomic kinematic constraints to realize a complete cognitive-driven search process.

[0065] For example, in the initial stage of radioactive source search, the core objective of the robot is to rapidly increase the coverage of unknown areas in the environment and find areas with sufficient radiation signals. Based on the above problem, the search area is first divided into small regions, and on this basis, a cognitive potential field (CPF) is proposed, such as... Figure 4As shown, the grid information entropy of the unexplored region is added to the traditional APF algorithm, using the unexplored region as an attraction source for the robot's current position to achieve rapid environmental exploration. Simultaneously, leveraging the obstacle avoidance capabilities of APF, the robot's safety is ensured during this rapid exploration. The robot is at its current position... The resultant force on the point Defined as:

[0066] in, Attracting gravity to a target; Repulsive force from obstacles. To guide the robot to prioritize exploring areas of high uncertainty, gravity is covered. Defined as the distance-weighted information attraction of unvisited grids within the perception range to the robot:

[0067] in, The set of unvisited grid cells within the sensing range. This represents the coverage gain coefficient. Considering that the traditional APF algorithm may get trapped in a local minimum when encountering non-convex obstacles, sliding mode control (SMC) is introduced to achieve obstacle avoidance along the obstacle boundary. The tangent direction of the obstacle's extended boundary is calculated. Define the sliding surface:

[0068] in To determine the robot's current heading, the control law is designed as follows: Proof of Lyapunov stability: Choosing Lyapunov functions Taking its time derivative yields:

[0069] in For Lyapunov functions, Let be the sliding surface. Substituting the control law into the above equation, we get:

[0070] According to Lyapunov's stability theorem, since Negative semidefinite and with a strict approach term The system can converge to the sliding surface within a finite time. This ensures that the robot moves smoothly and without jitter along the tangent of the obstacle boundary.

[0071] In summary, the cognitive potential field based on SMC endows the system with the ability to efficiently explore complex environments. However, CPF, as a deterministic control strategy, struggles to cope with the significantly increased Poisson statistical noise as it approaches a radiation source. Therefore, the system requires a statistical confidence mechanism to take over behavioral pattern motion control when a valid radiation anomaly is detected.

[0072] The coordinated operation of global exploration and precise local localization relies on the framework's robust switching between two behavioral modes. Since the real nuclear decay process follows a Poisson distribution, instantaneous observation noise can easily lead to false mode triggering. Therefore, a Markov state machine based on a sliding time window is constructed to achieve dynamic mode switching with hysteresis loops and fault-tolerant reset capabilities.

[0073] The system maintains background radiation With signal-to-noise ratio threshold This forms the basis for the switching process. Define the effective state accumulator. Used in time windows Internally, an integral evaluation of the signal-to-noise ratio condition is performed:

[0074] in For the first Radiation count rate per observation step, This is an indicator function. State transitions strictly follow hysteresis loop logic: when the system is running in global exploration mode, state transitions only occur when... When triggered, it enters local mining mode (Exploitation); conversely, in local mining mode, it only enters local mining mode when... And continuous low detection steps Exceeding the tolerance limit At this time, fault tolerance degradation is triggered and global exploration is resumed. The window capacity has been experimentally calibrated to be [value missing]. This ensures that the switching decision has statistical confidence.

[0075] To prevent infinite loops caused by particle filter positioning failures, the system records the number of positioning failure attempts. .when At this time, the system forcibly clears the particle swarm and resets to exploration mode, achieving adaptive fault tolerance to statistical anomalies and environmental mutations.

[0076] Successful termination of the algorithm requires both spatial and physical verification. Let... For the estimation of the location of the radioactive source, The maximum allowable standard deviation of the particle spatial distribution. This represents the peak value of the local radiation count rate. The termination condition is defined as:

[0077] The system determines successful localization, terminates mode switching, and completes radiation source locking only if both equations are true simultaneously. The aforementioned state machine mechanism establishes a reliable switching and fault-tolerant bridge between the global exploration strategy and precise local localization. When the system detects that the radiation signal meets the signal-to-noise ratio threshold condition, the control logic immediately switches from the deterministic global CPF search to a probabilistic reasoning-based local mining mode, thus formally activating the fusion AAMH-PF and multi-entropy fusion planning mechanism proposed in the next section.

[0078] As the state machine switches to local precise localization mode, the core task of the system changes from spatial coverage to posterior distribution approximation. At this point, the system first utilizes AAMH-PF with weights... With state The particles continuously estimate the true location of the radiation source. This guides the robot to efficiently approximate the estimated location. A multi-entropy fusion path planning (MEFPP) strategy based on multi-dimensional feature mapping was designed. Within the local space, the system constructs a comprehensive evaluation system comprising five physical and informational dimensions, specifically defined as follows:

[0079] Improved Shannon entropy The comprehensive uncertainty, to more accurately reflect the posterior uncertainty of physical space, is defined as a weighted fusion of particle weight entropy and spatial distribution covariance entropy. Its defining formula is:

[0080] After normalizing the weighted entropy and spatial entropy respectively, the weighted sum is calculated as follows: in, For the first Normalized weights of individual particles; The total number of particles; Let be the covariance matrix of the current particle swarm spatial distribution; This is a minimum regularization term to prevent singularity in the matrix. The lower the value, the more concentrated the particles are in space and the more convergent the weights are.

[0081] Exploring Entropy Indicates environmental unknowns, designed to evaluate candidate locations. Surrounding sensing radius The proportion of unvisited space within the robot drives the robot to explore unknown areas: in, For The local detection domain centered on the center For grid state, This is an indicator function.

[0082] Access Entropy Indicates path redundancy based on a global access frequency map. The calculation is used to apply historical cost penalties to the repeatedly sampled space to prevent the robot from getting stuck in path deadlock and oscillation: Obstacle avoidance safety entropy This indicates the platform's physical safety level, which is crucial for ensuring the platform's ability to navigate complex environments. It incorporates the Euclidean distance to the nearest obstacle. Consistency with the target direction. Define the distance penalty function. For piecewise continuous mapping:

[0083] Combining goal-oriented consistency, obstacle avoidance safety entropy is strictly defined as: in, Let be the normal vector pointing to the nearest obstacle. Let the vector point to the estimation source be... , As a fusion coefficient, this design ensures that the robot prioritizes a safe tangential direction that does not deviate from the radiation source while moving away from obstacles.

[0084] Goal-oriented entropy This represents the chemotactic driving force, providing a continuous driving force towards the estimated source location while ensuring safety. It is constructed using an exponentially decaying function. in, This is the distance scaling constant. The closer the candidate location is to the estimated source, the closer this entropy value is to 1.

[0085] The aforementioned five-dimensional entropy field orthogonally quantifies the system's statistical confidence, spatial exploration degree, historical cost, physical security, and target chemotaxis. If static weights are used for linear combination, the system is highly susceptible to local deadlock or collision hazards in complex kernel environments. Therefore, the physical importance of each entropy value must possess nonlinear time-varying characteristics. To this end, this step constructs a multi-dimensional environmental feature space to dynamically perceive the current physical situation. Definition The environmental state feature vector at time t is The mathematical definitions of its components are as follows:

[0086] Extreme avoidance distance The shortest Euclidean distance from the robot's center to the safety boundary of all obstacles in the environment. Local obstacle density Define the early warning detection radius Using indicator functions Calculate local congestion: Particle spatial divergence The physical uncertainty of the posterior estimate is quantified using the determinant of the particle space covariance matrix. Target approach distance The distance from the robot to the currently estimated source location. .

[0087] For a nonlinear weight mapping matrix driven by a dynamic environment, let the prior basic weight vector be... To achieve adaptive adjustment of weights, a system based on environmental feature vectors is constructed. The diagonal gain matrix of the independent variable , The mapping rules follow strict piecewise boundary conditions in response to specific physical critical states: To ensure the dimensionality consistency of the subsequent cost function scoring and to satisfy the convex combination property, the modulated weight vector is subjected to... Norm projection yields Dynamic weight vector at time step : .

[0088] Through multidimensional entropy field and dynamic weight mapping, the system has obtained the theoretical value gradient of the current local space. However, in real-world environments, differential-driven robots equipped with radiation detectors are constrained by nonholonomic kinematics and cannot perform instantaneous displacement along arbitrary gradient directions. To realize the control logic from information decision-making to physical execution, this section transforms local navigation into an optimal control solution with safety hard constraints.

[0089] Define the system in continuous time The state manifold is The control input vector is To meet the response characteristics of the physical actuator, the continuous control space is discretized into a finite set of actions. Set the linear velocity set. Angular velocity set For any control input Based on the differential drive kinematic model, the system in the integral time step Predicted state after The state transition equation is expressed as:

[0090] Extracting the two-dimensional Euclidean coordinate components from the state manifold and defining them as the predicted pose. Traversal It can generate a set of predicted endpoints that are physically reachable by the robot. Define the path safety hard constraint indicator function. If and only if the robot's predicted trajectory line segment Not bounded by any extended obstacle When there is an intersection, .

[0091] At each predicted pose Extracting the five-dimensional entropy field column vector Define the action utility function based on dynamic weights as follows: .

[0092] Optimal control law in the local mining stage It can be rigorously formalized as a discrete-space optimization problem with nonholonomic kinematics and hard safety constraints: Within a single control cycle, the system solves the aforementioned optimization equations through forward simulation and matrix computation, and then assigns the optimal command. This is mapped to the underlying motor drive. At the mathematical level, this equation achieves a precise conversion of multi-entropy field potential energy into the robot's actual physical motion, completely closing the loop of the system's autonomous decision-making flow.

[0093] Based on the above five-dimensional entropy field and dynamic weight mapping, the complete planning cycle of MEFPP can be formalized as shown in Table 1.

[0094] Table 1. Main Loop Algorithm of Path Planning Based on Multi-Entropy Fusion (MEFPP) The data flow and multi-dimensional environmental vector modeling of the system architecture together constitute the underlying physical foundation. Integrating the aforementioned spatial perception, global situational field driving, local multi-entropy mining, and dynamic state machine switching mechanisms, the complete decision-making chain can be condensed into a discrete-time optimization process. The system updates the grid state and particle distribution online using real-time radiation source sensor data in each control cycle. After switching modes using an adaptive signal-to-noise ratio threshold, the algorithm outputs the optimal control command for the current moment while ensuring the robot's motion safety. In summary, the cognitive-driven architecture constructed above realizes the mapping from spatial entropy field to physical motion. Table 2 summarizes the core execution flow of the above mechanism: In the global phase (rows 14-15), the system rapidly eliminates environmental unknowns using the cognitive potential field defined by equation (X)-(Y); once the signal-to-noise ratio accumulator exceeds the threshold to trigger state transition, the system seamlessly enters local mining. In this phase, adaptive particle filtering (rows 5-9) continuously compresses the posterior distribution, while the multi-entropy fusion planner (rows 11-13) solves the optimal control law subject to nonholonomic constraints based on the dynamic situation. This algorithm achieves a smooth transition between two heterogeneous behavior modes, exploration and mining, within a unified entropy space with minimal computational overhead. The complete flowchart for the cognitively driven robot's radioactive source search is shown in Table 2.

[0095] Table 2. Cognitive-Driven Radioactive Source Search Framework (CDRSSF) Based on AAMH-PF and Multientropy Navigation In addition, to further verify the above method, the present invention also conducted experimental verification.

[0096] To comprehensively evaluate the search performance and robustness of the proposed CDRSSF architecture in complex and constrained environments, this step involves building a two-dimensional nuclear radiation search simulation environment based on the MATLAB platform (the computing platform is configured with an AMD Ryzen 7 5800H CPU 3.2GHz and 16GB RAM).

[0097] 1) Physical Environment and Sensor Modeling The simulation defined a non-convex region of interest (ROI) measuring 60 m × 30 m. Within this region, the radioactive source was modeled as an isotropic ideal point source, randomly deployed at unknown locations. The radioactivity of the point source was set to 80 MBq, and the characteristic gamma-ray energy was 1.33 MeV (to simulate a typical cobalt-60 radioactive source). The airborne sensing module carried a NaI(Tl) scintillator detector, with a sampling time window... The time interval is set to 10 s. Assume the detector's calibration count rate at a distance of 1 m from the source under unobstructed conditions is [value missing]. =14000 CPS, environmental uniform background count rate set to =10 CPS. Considering the shielding effect of complex environments on radiation, solid obstacles in the environment are treated as homogeneous attenuation media, and their linear attenuation coefficient is set to... .

[0098] 2) Algorithm parameters and platform constraints The single-step control step size of the mobile robot chassis is set to 1m. Considering the GPS rejection characteristics of complex occlusion environments (such as inside a nuclear power plant or urban ruins), this simulation assumes that a high-precision LiDAR SLAM system is already installed at the bottom layer, capable of providing drift-free global pose priors for the upper-layer algorithms. To meet the computational requirements of the MEFPP planner, the global space is discretized into a 1m*1m state grid. The particle filter pool capacity in the local Bayesian estimation stage is set to N = 3500.

[0099] Considering obstacle occlusion, the experimental parameters are set as follows: Assume a radioactive source with unknown location and activity exists within a 60*30m two-dimensional matrix region (considering a fixed detector height), as shown in the figure. The source activity is set to 80 MBq, and the source energy is set to 1.33 MeV (its size is ignored, treating it as a point source). Black obstacles exist in the environment, with an attenuation coefficient of μ=0.05. The robot's initial position is (1m, 1m), and each step is 1m. Autonomous localization is ensured by a high-precision real-time dynamic global navigation satellite system (RTK-GNSS) receiver. The particle number N is set to 3500, and the grid size is 1m*1m. Considering the limitations of the robot's onboard sensors, a 10*10m area is selected for exploration. When a detected CPS exceeds the preset SNR=900, a data caching mechanism is activated. When more than 10 sets of data are collected, a localization algorithm is used. The robot, equipped with a detector, enters the area to search for radioactive sources. At the same time, the environment in the area is unknown, and the activity of the radioactive sources is unknown. In the initial stage, due to the weak or no significant fluctuations in radiation information, it is necessary to first explore the area. After detecting sufficient radiation information, it switches to positioning mode and finally determines and arrives at the location of the radioactive source.

[0100] To simplify the problem, the radiation source is modeled as a point source. The robot moves within the region of interest, continuously measuring radiation intensity and collecting field information. This step uses the Magic-MC program based on the Monte Carlo method to simulate the radiation field in a real-world scenario. The actual location of the radiation source is set at (45 m, 10 m). The flux reaches its peak at the source location and decreases sharply with distance, conforming to the inverse square law of point source attenuation.

[0101] In the initial search phase, insufficient radiation information prevented accurate localization of the radiation source. Therefore, the robot first implemented a grid-based global exploration strategy. During this phase, a cognitive potential field (CPF) and sliding mode boundary following strategy were employed, using regional information entropy calculation to guide the robot to prioritize exploring grid areas with unknown information content. The robot focused on a 10m x 10m sub-region for concentrated searching, while obstacle avoidance navigation ensured effective obstacle avoidance during the exploration process. When the data collected by the detector consistently exceeded the preset signal-to-noise ratio threshold of 900 and accumulated more than 10 sets of valid data, the system immediately activated the AAMH-PF algorithm and switched to a local precise localization mode. The final search path length was 78.5 meters, the predicted radiation source location was (44.89, 9.90) with an error of 0.21 meters, and the number of iterations was 143.

[0102] To verify the necessity of the five-dimensional entropy field design in this step, an ablation experiment was conducted on the MEFPP module. In the Single Entropy driven model, the robot is only driven by the information gain of the unexplored region. The trajectory results show that the robot exhibits high-frequency oscillations when approaching the radiation source and the edge of the obstacle. This is because the algorithm lacks a smooth transition weight between pursuing information maximization and preventing physical collisions, resulting in frequent switching between the two targets. The final search path length is 125 meters, the predicted position of the radiation source is (44.53, 9.25), the error is 1.28 meters, and the number of iterations is 229. When AAMH-PF is introduced on this basis, the posterior probability distribution of the source position is established, and the robot's macroscopic pointing is significantly enhanced. However, the sawtooth oscillation of the trajectory still exists. This phenomenon illustrates that accurate source location estimation is not equivalent to efficient physical movement. Lacking the constraint of a multidimensional cost function, the robot's motion control still relies too heavily on high-weight particles, neglecting the optimality of obstacle avoidance. The final search path length was 86 meters, the predicted radioactive source location was (44.63, 9.80) with an error of 0.57 meters, and the number of iterations was 168. The classic radiation gradient search method exhibits extreme vulnerability in complex nuclear environments. The fundamental reason is that real nuclear decay follows a Poisson distribution, and strong statistical fluctuations easily create false directional gradients in local space, leading to severe boundary jamming when the robot encounters non-convex obstacles. Although the classic Infotaxis algorithm theoretically balances exploration and mining, its trajectory exhibits severe spiral oscillations. Analysis suggests that Infotaxis does not couple the robot's differential kinematic hard constraints when calculating the expected information gain and lacks penalty memory for historical paths. This caused the system to repeatedly shuttle through the narrow passage, exhibiting severe spiral oscillations. The final search path length was 108 meters, the predicted location of the radioactive source was (44.73, 9.45) with an error of 0.92 meters, and the number of iterations was 194.

[0103] The change in radiation gradient value was detected after 100 explorations, and it was higher than the preset radiation threshold in 10 of them. The MEFFTP algorithm was launched at 110 explorations to enter the local precise localization stage. When crossing obstacles in Iteration Steps∈[120,140], the obstacle avoidance safety entropy weight instantly jumped to the dominant position. In the approaching target stage, the target guidance entropy and the improved Shannon entropy formed a competitive synergy to jointly compress the particle divergence.

[0104] In stark contrast to all the aforementioned degenerate or baseline models, the CDRSSF architecture proposed in this invention exhibits overwhelming trajectory superiority. First, during the global exploration phase, by combining CPF and SMC, the robot perfectly bypasses obstacles with an extremely smooth manifold tangent, completely immune to local minima traps. Second, after the Markov state machine triggers smooth transitions, the trajectory exhibits excellent kinematic continuity. This is attributed to the access entropy introduced during the local phase (…). ) and obstacle avoidance safety entropy ( The former endows the system with spatial memory, completely eliminating spiral backslides similar to Infotaxis; the latter, through exponential distance penalties, forces the robot to plan a tangential direct path that conforms to the safety boundary of the obstacle while ensuring safety. CDRSSF successfully intercepted the radiation source with a path length approaching the theoretical physical lower limit without any high-frequency oscillations or useless backslides, perfectly demonstrating the superiority of the architecture of deep decoupling and re-fusion of multi-dimensional information perception and underlying kinematic control.

[0105] The present invention also provides a computer-readable storage medium storing a computer program that can be used to execute the above-described... Figure 1 The steps of a method for searching for radioactive sources in unknown environments are provided.

[0106] This invention also provides a computer device. At the hardware level, the computer device includes a processor, an internal bus, a network interface, memory, and non-volatile memory, and may also include other hardware required for various operations. The processor reads the corresponding computer program from the non-volatile memory into memory and then executes it to achieve the above-mentioned functions. Figure 1 The steps of a method for searching for radioactive sources in unknown environments are provided.

[0107] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0108] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, as well as combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0109] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0110] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0111] It should be noted that the specific embodiments described above enable those skilled in the art to more fully understand the present invention, but do not limit the present invention in any way. Therefore, although the present invention has been described in detail in this specification, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the present invention; and all technical solutions and improvements that do not depart from the spirit and scope of the present invention are covered within the protection scope of the patent of the present invention. No reference numerals in the claims should be construed as limiting the scope of the claims.

Claims

1. A method for searching radioactive sources in an unknown environment, characterized in that, The method includes: Construct a multidimensional raster map to characterize environmental and radiation field information; The robot is controlled to perform a global search and then switches to a local precise positioning mode after detecting a radiation signal. In the local precise localization mode, multiple particles are initialized to characterize the posterior probability distribution of the radioactive source location, and each particle contains a hypothetical spatial location attribute of the radioactive source and a corresponding weight attribute. For each particle, a virtual ray is emitted from the robot's current position to the hypothetical location of the radiation source corresponding to that particle. All obstacle grids traversed by the virtual ray are identified based on the grid map. The total attenuation length is calculated by summing the path lengths of the robot as it traverses each obstacle grid. This total attenuation length is then incorporated into the observation likelihood function to correct for the influence of environmental occlusion on the radiation signal. The weight of the particle is calculated based on this weight distribution, thereby estimating the location of the radiation source. Based on control instructions that satisfy robot motion constraints and obstacle avoidance constraints, the robot searches for the estimated radiation source as a target.

2. The method according to claim 1, characterized in that, The method of controlling the robot to search for the estimated radiation source as a target based on control commands that satisfy robot motion constraints and obstacle avoidance constraints includes: Construct target orientation entropy and obstacle avoidance safety entropy, wherein the target orientation entropy is negatively correlated with the estimated distance from the candidate position to the radiation source position, and the obstacle avoidance safety entropy is positively correlated with the distance from the candidate position to the nearest obstacle; Generate a candidate action set consisting of a combination of linear velocity and angular velocity; for each candidate action in the candidate action set, simulate and predict the robot's pose at the next moment, and calculate the target guidance entropy and obstacle avoidance safety entropy at the predicted pose; Under the premise of satisfying robot motion constraints and obstacle avoidance constraints, the candidate action that maximizes the weighted sum of the target orientation entropy and obstacle avoidance safety entropy is selected as the optimal control command for the current moment and searched.

3. The method according to claim 1, characterized in that, The estimation of the location of the radiation source based on the weight distribution of each particle includes: The weights of each particle are normalized, and the hypothetical spatial positions of the radioactive sources corresponding to each particle are weighted and averaged using the normalized weights to obtain the position estimate of the radioactive source at the current moment. Specifically, the effective sample size is calculated to assess the degradation level of the current particle swarm. When the effective sample size is lower than a preset threshold, low-weight particles are removed and high-weight particles are copied to perform system resampling. Anisotropic adaptive Metropolis-Hastings sampling method is adopted to dynamically adjust the proposal distribution using the covariance matrix of the current particle swarm spatial distribution. Anisotropic mutation is performed on the resampled particles to increase particle diversity.

4. The method according to claim 2, characterized in that, The constructed target-oriented entropy and obstacle avoidance safety entropy include: Using the estimated location of the radiation source as the target point and the obstacle information stored in the grid map as the safety constraint, for any candidate location in space, the Euclidean distance from the candidate location to the estimated location of the radiation source is calculated, and the target guidance entropy is constructed in the form of a negative exponent of the Euclidean distance, so that the closer the candidate location is to the estimated location of the radiation source, the higher the value of the target guidance entropy. Calculate the Euclidean distance from the candidate location to the nearest obstacle in the grid map, substitute the distance as the independent variable into the piecewise continuous mapping function, and use the output value of the mapping function as the obstacle avoidance safety entropy, so that the value of the obstacle avoidance safety entropy decreases exponentially as the candidate location gets closer to the obstacle. After constructing the target-oriented entropy and obstacle-avoidance safety entropy, improved Shannon entropy, exploration entropy, and access entropy are also constructed. The improved Shannon entropy is constructed based on the normalized weights of each particle and its spatial distribution covariance matrix, and is used to quantify the uncertainty of the posterior distribution. The exploration entropy is constructed based on the ratio of the number of unexplored grids to the number of passable grids within the perception range around the candidate location, and is used to measure the unknown in the environment. The access entropy is constructed based on the global access frequency map and is used to impose penalties on candidate locations that have been repeatedly accessed.

5. The method according to claim 4, characterized in that, The step of simulating and predicting the robot's pose at the next moment for each candidate action in the candidate action set, and calculating the target guidance entropy and obstacle avoidance safety entropy at the predicted pose, includes: Obtain the robot's current pose information, which includes two-dimensional spatial coordinates and heading angle; For each candidate action in the candidate action set, based on the kinematic model of the differential drive robot, and according to the current pose and the linear and angular velocities in the candidate action, a forward integral of one control cycle is performed to simulate and predict the robot's pose at the next moment after executing the candidate action. Using the coordinates of the predicted pose in two-dimensional space as the candidate position, the target guidance entropy, the obstacle avoidance safety entropy, the improved Shannon entropy, the exploration entropy, and the access entropy are calculated at the candidate position, respectively.

6. The method according to claim 5, characterized in that, The step of selecting the candidate action that maximizes the weighted sum of the target guidance entropy and obstacle avoidance safety entropy as the optimal control command at the current moment, under the premise of satisfying robot motion constraints and obstacle avoidance constraints, includes: For each candidate action, the trajectory segment from the current pose to the predicted pose is checked to see if the trajectory segment intersects with the obstacle safety boundary in the grid map. The obstacle safety boundary is the extended boundary formed by extending the original obstacle boundary outward to the robot's safety radius. Candidate actions corresponding to intersecting trajectory segments are determined to be non-compliant with the obstacle avoidance constraints and are eliminated. For each candidate action that passes the verification, the robot's nonholonomic constraints are used as the motion constraints for selecting the candidate action. Within the set of candidate actions that satisfy the motion constraints and obstacle avoidance constraints, the target guidance entropy and obstacle avoidance safety entropy are weighted and summed. The candidate action that maximizes the weighted sum is selected as the optimal control command at the current moment.

7. The method according to claim 6, characterized in that, The weighted summation of the target guidance entropy and obstacle avoidance safety entropy includes: The weights of the improved Shannon entropy, exploration entropy, access entropy, obstacle avoidance safety entropy, and target orientation entropy are adaptively adjusted based on the real-time perceived local environmental situation of the robot, and the weighted sum of the adjusted entropy values ​​is then performed. The local environmental situation is characterized by an environmental feature vector that includes the limit avoidance distance, local obstacle density, particle spatial divergence and target approach distance. The weight adjustment is dynamically implemented by a piecewise mapping function with the environmental feature vector as the independent variable. The piecewise mapping function outputs different weight allocation schemes under different physical critical states.

8. The method according to claim 2, characterized in that, The generation of the candidate action set consisting of a combination of linear velocity and angular velocity includes: The feasible ranges of linear velocity and angular velocity of the robot are obtained, and the feasible ranges of linear velocity and angular velocity are discretized into a finite set of linear velocity and a finite set of angular velocity according to a preset discrete interval. Traverse all combinations of the finite linear velocity set and the finite angular velocity set, and use each combination of linear velocity and angular velocity as a candidate action to form the candidate action set.

9. The method according to claim 1, characterized in that, The construction of the multidimensional raster map for characterizing environmental and radiation field information includes: The environment space is discretized into multiple grid cells, each grid cell is configured to store its physical state label, which includes at least unexplored, explored and obstacle; Record the frequency of the robot's historical trajectory accessing each grid cell; The signal variation calculated based on radiation field observation data and the posterior probability distribution entropy value are then associated with the corresponding grid cells to form a multidimensional grid map containing geometric and radiation field information.

10. The method according to claim 1, characterized in that, The control robot performs a global search and switches to a local precise positioning mode after detecting a radiation signal, including: The robot is driven by a cognitive potential field to preferentially move towards unexplored areas. The cognitive potential field uses the information entropy value of the unvisited grid as the source of gravity, and the grid with higher information entropy has a greater attraction to the robot. When the robot encounters an obstacle that causes the resultant force of the cognitive potential field to fall into a local minimum, sliding mode control is introduced. The robot is controlled to circle around the obstacle boundary according to the tangent direction of the obstacle safety boundary in order to escape the local minimum trap. During the global search process, the radiation detection signal is continuously sampled. When the signal-to-noise ratio accumulated based on the sliding time window exceeds a preset threshold, it is determined that a valid radiation signal has been detected. Then, the robot switches from the global search mode to the local precise positioning mode through the Markov state machine. In the local precise positioning mode, when the signal-to-noise ratio accumulated in the sliding time window is lower than the preset cut-out threshold and continues to exceed the tolerance number of steps, the robot is controlled to return to the global search mode.

Images