A method for adversarial attacks on robotic arm grasping planning based on spatial obstacle removal

Abstract

This invention belongs to the field of robot safety and discloses a method for adversarial attacks on robotic arm grasping planning based on obstacle solution space. The method includes: S1, performing multiple grasping simulations on the robot and recording the path sequence of the end effector during each execution; S2, generating a three-dimensional heatmap representing the robot's path preferences based on the path sequence; S3, discretizing the three-dimensional heatmap into a three-dimensional mesh; S4, calculating the reachability score from each mesh point to the target mesh point based on the three-dimensional mesh; S5, constructing a multi-objective optimization model based on the reachability scores, optimizing the multi-objective optimization model, and obtaining the optimal obstacle set. This invention fundamentally solves the problems of inefficiency and low success rate caused by the blindness of existing technologies. This invention can find a strategy to achieve the attack objective using the smallest, least, and most concealed combination of obstacles, thus essentially solving the drawbacks of high cost and high risk of existing technologies.

Description

Technical Field

[0001] This invention relates to the field of robot safety, and in particular to a method for countering attacks on robotic arm grasping planning based on obstacle removal in spatial design. Background Technology

[0002] With the deepening development of Industry 4.0 and artificial intelligence technologies, automated systems, represented by industrial robots and collaborative robots, have been widely penetrated into key fields such as manufacturing, logistics and warehousing, medical services, and even military and special environment exploration. The stable, safe, and efficient operation of these robot systems has become an important cornerstone for ensuring production efficiency, improving the quality of social services, and even safeguarding national security.

[0003] The resulting security threats to robotic systems are becoming increasingly severe. Currently, security research and protective measures for robotic systems mainly focus on network information security, such as preventing hackers from exploiting network vulnerabilities to intrude into control systems, tamper with motion commands, and inject malicious code. For example, Cerrudo et al. detailed the types of vulnerabilities discovered and the specific threats that robots may pose after being compromised. Their ultimate goal is to drive the entire industry to improve robot security and prevent these vulnerabilities from being maliciously exploited, thereby causing significant damage to businesses, consumers, and their surrounding environment. Dieber et al., in their research, conducted an in-depth discussion on the security of ROS communication. They not only analyzed the most common vulnerabilities in ROS and their corresponding attack paths, but more importantly, they designed and implemented a security solution directly integrated into the ROS core. This solution can provide security protection for the communication channels between all ROS nodes without modifying the operating system kernel, thereby resisting threats such as man-in-the-middle attacks and data tampering. This work is a typical example of research that enhances robot network security by hardening the communication layer. Değirmenci et al. found that DoS attacks can significantly increase the latency of communication between ROS nodes and cause a large number of data packets to be lost. In robotic systems, this directly translates to delays or loss of motion commands, outdated or missing sensor data, ultimately leading to sluggish robot responses, abnormal behavior, or even complete cessation of service.

[0004] However, physical-level security threats, particularly "physical adversarial attacks" that deliberately and subtly alter the robot's working environment to disrupt or damage it, are an emerging field that is increasingly prominent but still under-researched. Compared to the network communication layer, the feasible solution space of the motion planning layer exposes a new attack surface: attackers do not need to crack the control commands; they can induce the planner to fail simply by applying minor perturbations at critical bottlenecks. Existing passive safety measures (safety fences, light curtains, etc.) are designed to prevent accidents, not adversarial attacks, and are therefore ill-suited to defend against such "solution space-level" attacks.

[0005] The aforementioned existing technical solutions have significant drawbacks when dealing with deliberate, intelligent physical interference. The fundamental reason for this is the failure to understand and utilize the robot's own behavioral patterns and decision-making logic.

[0006] Blindness and Inefficiency: Traditional physical grasping adversarial attack methods are "blind." Attackers do not understand the intrinsic optimization criteria of robot path planning (such as shortest path, lowest energy consumption), and simply place obstacles based on surface observation. This intuitive approach has a low success rate because the robot planner can always find avoidance paths that the attacker has not anticipated. The root cause is the lack of predictive models for robot behavior.

[0007] High cost and high exposure risk: To compensate for the lack of cover, attackers often need to use large or numerous obstacles to block off as much space as possible. This not only increases deployment costs, but more importantly, conspicuous obstacles are easily spotted and removed by human operators or monitoring systems, resulting in attacks that lack stealth and persistence. The root cause is inefficiency, making it impossible to achieve precise strikes with minimal resources.

[0008] Lack of strategy and quantifiability: Existing methods cannot quantify the effects of interference, nor can they balance the "interference effect," "deployment cost," and "risk of detection." The entire process is a "one-off deal," lacking strategic optimization and adjustment. The root cause is that it treats physical interference as a simple physical problem, rather than an intelligent game problem involving predicting robot behavior. Summary of the Invention

[0009] The purpose of this invention is to disclose a method for counter-attacks on robotic arm grasping planning based on spatial obstacle removal, thereby solving the technical problems mentioned in the background art.

[0010] To achieve the above objectives, the present invention provides the following technical solution:

[0011] This invention provides a method for adversarial attacks on robotic arm grasping planning based on spatial obstacle removal, including:

[0012] S1, perform multiple grasping simulations on the robot and record the path sequence of the end effector during each execution;

[0013] S2, Generate a 3D heatmap that can characterize the robot's path preferences based on the path sequence;

[0014] S3 discretizes the three-dimensional heatmap into a three-dimensional mesh;

[0015] S4, calculate the reachability score from each grid point to the target grid point based on the three-dimensional grid;

[0016] S5: Construct a multi-objective optimization model based on the reachability score, optimize the multi-objective optimization model, and obtain the optimal obstacle set.

[0017] Preferably, S1 includes:

[0018] S10 utilizes a robot operating system and a physical simulation engine to build a high-fidelity robot working environment model;

[0019] S11, In the robot working environment model, set the robot's grasping task;

[0020] S12, randomly introduce background obstacles into the workspace;

[0021] S13, run N independent grasping simulations based on the grasping task, and record the end effector path sequence that is successfully planned and executed each time, where N is a preset integer.

[0022] Preferably, the robot operating system includes ROS, and the physics simulation engine includes Gazebo.

[0023] Preferably, the grasping task includes moving the end effector from the starting point to the target area.

[0024] Preferably, S2 includes:

[0025] By employing data analysis and advanced visualization techniques, all collected path sequences are aggregated to generate a three-dimensional heatmap that can characterize the robot's path preferences.

[0026] Preferably, S4 includes:

[0027] use This represents the coordinates of the grid point corresponding to the starting point. It enumerates all paths from the starting point to the target grid point, where x, y, and z are the coordinates of the X-axis, Y-axis, and Z-axis in three-dimensional coordinates, respectively.

[0028] The reachable score of the grid point corresponding to the starting point is determined using the following formula:

[0029]

[0030] This represents the reachable score of the grid point corresponding to the starting point. Represents the k-th path The coordinates in are The thermal values ​​of the grid points, where K represents the total number of paths.

[0031] Preferably, constructing a multi-objective optimization model based on reachable scores includes:

[0032] The multi-objective optimization model is as follows:

[0033]

[0034] This is a multi-objective optimization model, where O represents the position of the obstacle. This represents the interference effect of obstacle O on the grasping path. This represents the economic cost of deploying obstacle O. This indicates the risk value at which obstacle O is detected.

[0035] Preferably, The calculation process is as follows:

[0036] Before setting obstacle O, obtain the reachable score Scr1 of the grid point corresponding to the starting point;

[0037] After setting obstacle O, obtain the reachable score Scr2 of the grid point corresponding to the starting point;

[0038] Subtracting Scr2 from Scr1 yields the interference effect value.

[0039] Beneficial effects:

[0040] Existing technologies rely on human intuition to guess robot paths, which is blind. This invention takes the opposite approach, collecting vast amounts of robot path data through large-scale simulation experiments and using statistical methods to construct, for the first time, a quantitative three-dimensional heatmap that reflects the robot's inherent path-choice preferences. This shift from "subjective guessing" to "data-driven prediction" allows obstacles to be precisely placed in the "hotspot" areas where the robot is most likely to traverse, thus efficiently blocking tasks with minimal effort and fundamentally solving the inefficiency and low success rate problems caused by the blindness of existing technologies.

[0041] Existing technologies, to ensure success, often require the use of large or numerous obstacles, which are costly and easily exposed. This invention first identifies "choke points" affecting global path accessibility from path preferences through reachability score calculation, thus refining the target of attack. Next, this invention constructs the obstacle-setting problem as a multi-objective optimization problem. This model can intelligently balance "maximizing interference effect," "minimizing obstacle volume / number (cost)," and "minimizing the risk of detection." This technical approach, moving from "extensive blocking" to "optimal solution," allows this invention to find a strategy that achieves the attack objective using the smallest, least, and most concealed combination of obstacles, thereby fundamentally solving the high-cost and high-risk drawbacks of existing technologies. Attached Figure Description

[0042] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, 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.

[0043] Figure 1 This is a schematic diagram of a robotic arm grasping planning counter-attack method based on spatial obstacle removal according to the present invention. Detailed Implementation

[0044] 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.

[0045] To overcome the shortcomings of existing technologies, such as the blindness, high cost, and low efficiency of physical interference, the present invention aims to provide a systematic, data-driven, and intelligent method and system for robot grasping obstacles. Specifically, the present invention aims to achieve the following objectives:

[0046] From "passive response" to "active prediction": By modeling and analyzing the robot's historical behavior data, we can accurately predict the path clusters that it is most likely to choose when performing a specific task, that is, identify the "high-probability paths" or "traffic routes" in its workspace.

[0047] From "extensive blocking" to "precision strikes": Based on predicted path preferences, quantitatively assess the importance of each location in the workspace to completing the task, and identify key "bottleneck" nodes that can "hold the pass against all others".

[0048] From "single objective" to "multidimensional optimization": Establish a multi-objective optimization model that comprehensively considers maximizing interference effect, minimizing deployment cost, and minimizing exposure risk, and solve for the optimal obstacle placement strategy (location, size, quantity).

[0049] This invention enables the most effective interference with specific grasping tasks of robots with minimal physical cost and the lowest risk of detection, transforming physical attacks from a "manual labor" into a "technical labor".

[0050] This invention aims to address the technical problems of blindness, inefficiency, and high exposure risk in existing methods of physically interfering with robots. Specifically, current methods of hindering robots from performing tasks by placing obstacles in the environment often rely on the operator's intuition and experience, lacking scientific prediction of robot behavior. This leads to the need for excessively large or numerous obstacles, which are not only costly but also easily detected and removed, making it difficult to achieve effective, reliable, and covert interference. Therefore, how to accurately predict the most likely path a robot will take to complete a specific task, and on this basis, achieve the most effective obstruction with minimal cost and risk, is a pressing technical challenge that needs to be solved.

[0051] like Figure 1 As shown, this invention provides a method for adversarial attacks on robotic arm grasping planning based on de-obstacle design, including:

[0052] S1 performs multiple grasping simulations on the robot and records the path sequence of the end effector during each execution.

[0053] Preferably, S1 includes:

[0054] S10 utilizes a robot operating system and a physics simulation engine to build a high-fidelity robot working environment model.

[0055] S11, In the robot working environment model, set the robot's grasping task;

[0056] S12, randomly introduce background obstacles into the workspace; the workspace here refers to the three-dimensional space that the robotic arm can reach in the simulation environment.

[0057] S13, run N independent grasping simulations based on the grasping task, and record the end effector path sequence of each successfully planned and executed task. N is a preset integer, where N>1000.

[0058] For the i-th capture simulation, , and These represent the X-axis, Y-axis, and Z-axis coordinates of points in the path sequence, respectively.

[0059] Preferably, the grasping task includes moving the end effector from the starting point to the target area.

[0060] Preferably, the robot operating system includes ROS, and the physics simulation engine includes Gazebo.

[0061] S2 generates a 3D heatmap that characterizes the robot's path preferences based on the path sequence.

[0062] Preferably, S2 includes:

[0063] By employing data analysis and advanced visualization techniques, all collected path sequences are aggregated to generate a three-dimensional heatmap that can characterize the robot's path preferences.

[0064] This three-dimensional heatmap is essentially a path density field H(p) in three-dimensional space, where any point in space... The heat value quantifies the cumulative frequency or dwell time of all successful paths in the vicinity of that point. This can be calculated using statistical methods such as kernel density estimation (KDE).

[0065] S3 discretizes the 3D heatmap into a 3D mesh.

[0066] The generated 3D heatmap is discretized into a 3D mesh. Where X1, Y1, and Z1 are the resolutions of the grid. Since obstacles were randomly introduced during the calculation of the heatmap, the original thermal values ​​of each grid point are... It can effectively reflect the robotic arm's preference and probability of performing a grasping action at a specific location when obstacles are present.

[0067] S4 calculates the reachable score from each grid point to the target grid point based on the three-dimensional grid.

[0068] Based on the discretized 3D mesh, the reachability score of each mesh point to the target is further calculated. This score will be calculated based on the original thermal values ​​of the mesh points and through a greedy algorithm.

[0069] Preferably, S4 includes:

[0070] use This represents the coordinates of the grid point corresponding to the starting point. It enumerates all paths from the starting point to the target grid point, where x, y, and z are the coordinates of the X-axis, Y-axis, and Z-axis in three-dimensional coordinates, respectively.

[0071] The reachable score of the grid point corresponding to the starting point is determined using the following formula:

[0072]

[0073] This represents the reachable score of the grid point corresponding to the starting point. Represents the k-th path The coordinates in are The thermal values ​​of the grid points, where K represents the total number of paths.

[0074] The value of this score directly reflects the difficulty of reaching the target point from that point, providing a reference for determining the optimal placement of obstacles.

[0075] S5: Construct a multi-objective optimization model based on the reachability score, optimize the multi-objective optimization model, and obtain the optimal obstacle set.

[0076] The goal of this approach is to determine an optimal set of obstacles within a 3D mesh. Each obstacle From the center point and radius of influence By definition, grid nodes within its affected area will be considered impassable. Deploying barriers aims to cover critical nodes, i.e., those with high reachability scores. Exceeding a specific threshold The core issue is to ensure effective coverage of high-accessibility-score areas while minimizing the number of obstacles m and their influence radius r, thereby efficiently hindering the robot's grasping planning.

[0077] Preferably, constructing a multi-objective optimization model based on reachable scores includes:

[0078] The multi-objective optimization model is as follows:

[0079]

[0080] This is a multi-objective optimization model, where O represents the position of the obstacle. This represents the interference effect of obstacle O on the grasping path. This represents the economic cost of deploying obstacle O, which is related to the number and size of the obstacles, and aims to maximize economic benefits. This represents the risk value of an obstacle O being perceived, used to quantify the risk of an obstacle being perceived due to its size and number.

[0081] Preferably, The calculation process is as follows:

[0082] Before setting obstacle O, obtain the reachable score Scr1 of the grid point corresponding to the starting point;

[0083] After setting obstacle O, obtain the reachable score Scr2 of the grid point corresponding to the starting point;

[0084] Subtracting Scr2 from Scr1 yields the interference effect value.

[0085] Further embodiments are as follows:

[0086] Step 1: Modeling and Generating Path Preferences for Robot Reachable Areas

[0087] 1. Simulation data acquisition

[0088] 1.1 Simulation Environment Setup:

[0089] We used the robot operating system ROS (version: Noetic) and the physics simulation engine Gazebo (version: 11) for simulation. In Gazebo, we constructed a three-dimensional workspace with dimensions of 1.0m x 1.0m x 0.8m.

[0090] 1.2 Robot and Task Setting:

[0091] The Universal Robots UR5e six-axis collaborative robot model was used. The robot's "home" pose was set as the starting state, with its end effector located in the left area of ​​the workspace. A 10cm x 10cm planar area on the right side of the workspace was set as the target area, and the robot needed to move its end effector to any point within this area.

[0092] 1.3 Simulation Execution:

[0093] To simulate the complexity and uncertainty of the real-world environment, 3-5 spherical background obstacles with radii of 1-3 cm were randomly generated in the workspace before each simulation, avoiding the starting and target areas. We used the MoveIt! motion planning framework from ROS and employed the RRT* (Optimal Fast Expanding Random Tree) algorithm for path planning. We performed N=5000 independent grasping simulations. For each successful planning (i.e., finding a collision-free path), we recorded the complete path point sequence of its end effector in Cartesian space. .

[0094] 2. Generation of 3D Heatmap

[0095] 2.1 Data Aggregation:

[0096] The data set of all successful paths collected (4500 successful paths) Perform aggregation.

[0097] 2.2 Heatmap Calculation:

[0098] We discretized the entire 1.0m x 1.0m x 0.8m workspace into a 3D voxel mesh with a resolution of 1cm and dimensions of 100x100x80. We used kernel density estimation to generate heatmaps. Specifically, a Gaussian kernel function was applied centered on each path point. The Gaussian distributions generated for all path points were superimposed on the mesh to obtain the heat value H(p) for each voxel p=(x,y,z). The heat value H(p) intuitively represents the frequency or total dwell time of all successful paths passing through the area near that point. Areas with high heat values ​​indicate that the area is a "must-pass" or frequently used area for the robot to successfully complete the task.

[0099] Step 2: Target reachability prediction based on discretized heatmaps

[0100] 3D mesh diagram

[0101] The generated 100x100x80 heatmap is itself a three-dimensional mesh map. Each grid point The heat value calculated in the previous step is stored.

[0102] 2. Accessibility Score Calculation

[0103] Based on this heat map Calculate the reachability score from each grid point to the target region τ. This score is designed to measure progress from a given point. Starting from the target region, how confident are we of successfully reaching it? We employ a backpropagation algorithm similar to Dijkstra's. First, we initialize the reachability scores of all grid points within the target region τ to their maximum values. Then, we iteratively calculate the reachability scores of all other grid points outwards from the target region. For any given grid point... Its accessibility score As determined by formula (1), among all possible paths from this point to the target area, one path is selected that maximizes the minimum heat value along that path. In simpler terms, This reflects the "bottleneck width" of the "widest path" from that point to the target area. A high A high heat value means that there exists at least one path on which all points have a high heat value, thus making it robust and easy to reach the target from that point.

[0104] Step 3: Solving for the optimal obstacle position

[0105] Problem Definition and Objectives

[0106] Objective: To improve the accessibility score Above a certain threshold Among the candidate nodes, select the one to place.

[0107] m = 3 spherical obstacles, whose radii r can be selected from {2cm, 3cm, 5cm}.

[0108] Constraints and trade-offs: The goal is to maximize the hindering effect while minimizing the cost (number and volume) of deploying obstacles and the risk of them being detected (size and number).

[0109] 2. Multi-objective optimization model

[0110] Weight settings:

[0111] Based on task priority, we set the weight as follows: , , This indicates that what we are most concerned about is the hindering effect.

[0112] The objective function is specifically quantified as follows:

[0113] (Interference effect): Defined as placing obstacles Then, the decrease in the maximum reachability score from the starting point set S to the target area.

[0114] (Economic cost): Defined as a linear function related to the number and volume of obstacles. As follows:

[0115] .in, , and It is a cost coefficient.

[0116] (Perceived Risk): Defined as a function of the number of obstacles and their surface area, since larger surface areas are more easily perceived visually. .in, and It is the risk factor.

[0117] Solution:

[0118] This is a complex combinatorial optimization problem. We use a Genetic Algorithm (GA) to solve it. Encoding: Each "individual" (chromosome) represents an obstacle deployment scheme, encoding the center coordinates of three obstacles. And radius r. Fitness function: directly use our defined objective function. Evolutionary operations: Through selection, crossover, and mutation, new deployment schemes (offspring) are iteratively generated, while retaining schemes with high fitness. Termination condition: The algorithm terminates after 200 generations or after the fitness value no longer significantly improves for 50 consecutive generations.

[0119] The key points of this invention are as follows:

[0120] Key Point 1: Robot path preference modeling method based on historical data and simulation.

[0121] Compared to existing technologies: Existing technologies rely on human observation, while this invention collects data through large-scale simulation and generates a quantified three-dimensional path preference heatmap. Differences in technical methods: The core difference lies in the shift from qualitative observation to quantitative modeling. This invention is the first to propose a systematic method for making robot implicit path selection preferences explicit and data-driven. This heatmap is the foundation for all subsequent intelligent decision-making and is one of the key technologies to be protected.

[0122] Key Point Two: A method for quantifying accessibility scores based on the concept of "bottleneck".

[0123] Compared to existing technologies: Existing technologies lack this concept. This invention goes beyond identifying "hotspots"; it identifies crucial pathways through defined accessibility scores. Differences in technical methods: The core difference lies in the shift from "point density" analysis to "path accessibility" analysis. Even if an area isn't the hottest, if it's a bottleneck for multiple high-scoring paths, its strategic value is extremely high. This accessibility score and its calculation method are another key technology to be protected.

[0124] Key Point 3: Multi-objective optimization of obstacle-setting strategies that integrate interference, cost, and risk.

[0125] Compared to existing technologies: Existing technologies involve simple physical placement, only considering "whether it can block the path." This invention constructs the obstacle-setting problem as a solvable, constrained multi-objective optimization problem. Differences in technical means: The core difference lies in the elevation from "physical execution" to "strategic decision-making." By treating obstacle setting as an intelligent game process, mathematical optimization is used to solve for the optimal strategy, making the attack itself intelligent, economical, and covert. This multi-objective optimization model and its solution framework are the third key technology to be protected.

[0126] The preferred embodiments of the present invention disclosed above are merely illustrative of the invention. These preferred embodiments do not exhaustively describe all details, nor do they limit the invention to the specific implementations described. Clearly, many modifications and variations can be made based on the content of this specification. This specification selects and specifically describes these embodiments to better explain the principles and practical applications of the invention, thereby enabling those skilled in the art to better understand and utilize the invention. The invention is limited only by the claims and their full scope and equivalents.

Claims

1. A method for adversarial attacks on robotic arm grasping planning based on spatial obstacle removal, characterized in that, include: S1, perform multiple grasping simulations on the robot and record the path sequence of the end effector during each execution; S2, Generate a 3D heatmap that can characterize the robot's path preferences based on the path sequence; S3 discretizes the three-dimensional heatmap into a three-dimensional mesh; S4, calculate the reachability score from each grid point to the target grid point based on the three-dimensional grid; S5. Construct a multi-objective optimization model based on the reachability score, optimize the multi-objective optimization model, and obtain the optimal set of obstacles; S1 includes: S10 utilizes a robot operating system and a physical simulation engine to build a high-fidelity robot working environment model; S11, In the robot working environment model, set the robot's grasping task; S12, randomly introduce background obstacles into the workspace; S13, run N independent grasping simulations based on the grasping task, and record the end effector path sequence that is successfully planned and executed each time, where N is a preset integer; S4 includes: Let (x,y,z) represent the coordinates of the grid point corresponding to the starting point. Enumerate all paths from the starting point to the target grid point, where x, y, and z are the coordinates of the X-axis, Y-axis, and Z-axis in three-dimensional coordinates, respectively. The reachable score of the grid point corresponding to the starting point is determined using the following formula: This represents the reachable score of the grid point corresponding to the starting point. Represents the k-th path The coordinates in are The thermal values ​​of the grid points, where K represents the total number of paths; Constructing multi-objective optimization models based on reachability scores includes: The multi-objective optimization model is as follows: This is a multi-objective optimization model, where O represents the position of the obstacle. This represents the interference effect of obstacle O on the grasping path. This represents the economic cost of deploying obstacle O. This indicates the risk value at which obstacle O is detected.

2. The method for adversarial attacks on robotic arm grasping planning based on spatial obstacle removal as described in claim 1, characterized in that, The robot operating system includes ROS, and the physics simulation engine includes Gazebo.

3. The method for adversarial attacks on robotic arm grasping planning based on spatial obstacle removal as described in claim 1, characterized in that, The grabbing task involves moving the end effector from the starting point to the target area.

4. The method for adversarial attacks on robotic arm grasping planning based on spatial obstacle removal as described in claim 1, characterized in that, S2 include: By employing data analysis and advanced visualization techniques, all collected path sequences are aggregated to generate a three-dimensional heatmap that can characterize the robot's path preferences.

5. The method for adversarial attacks on robotic arm grasping planning based on spatial obstacle removal as described in claim 1, characterized in that, The calculation process is as follows: Before setting obstacle O, obtain the reachable score Scr1 of the grid point corresponding to the starting point; After setting obstacle O, obtain the reachable score Scr2 of the grid point corresponding to the starting point; Subtracting Scr2 from Scr1 yields the interference effect value.

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