A singularity point-induced-based robotic arm planning adversarial attack method

Abstract

The present application belongs to the field of mechanical arm control safety, and discloses a kind of mechanical arm planning confrontation attack method based on singular point induction, method includes: S1, the joint angle vector and end pose of mechanical arm are acquired, and heat map is generated based on joint angle vector;S2, singular region is acquired based on heat map, and obstacle position is acquired based on singular region;S3, whether the position of obstacle center is located in accessible area is judged, if yes, then entity obstacle is moved to the position of obstacle center;S4, control mechanical arm to execute servo cycle according to original production trajectory, and record the curve of minimum singular value and end deviation.The present application superimposes singular probability modeling in the area that must be passed through in grabbing path, and arranges small obstacle by genetic algorithm, and is specially weakened to take and place cycle kinematics margin;Only external environment is reconstructed to trigger degradation, without modifying gripper control logic or visual identification model, avoid compatibility risk to production line software.

Description

Technical Field

[0001] This invention relates to the field of robotic arm control safety, and in particular to a method for combating robotic arm planning attacks based on singularity-induced methods. Background Technology

[0002] The Industry 4.0 wave is driving the manufacturing industry towards greater flexibility, intelligence, and high reliability. Six-degree-of-freedom (DOF) or higher serial robotic arms, with their high precision, high load capacity, and programmability, are widely used in automotive welding, 3C assembly, collaborative logistics, and additive manufacturing. In these tasks, the robotic arms need to execute continuous, smooth, and highly rigid trajectories within confined spaces. However, due to the geometric constraints and nonlinear coupling characteristics of the linkage structure, the robotic arm may exhibit a singular state where the Jacobian matrix determinant approaches zero under certain joint combinations. At this point, the end-effector velocity mapping becomes highly sensitive to joint rates, leading to a loss of degrees of freedom or theoretically infinite joint velocities. If the controller continues to output with conventional gain, it will cause severe jitter, out-of-tolerance errors, or even sudden stops, directly threatening production line cycle time and equipment safety.

[0003] For the identification and mitigation of singular risks, the academic community first proposed quantifiable indicators. Yoshikawa proposed an operational measure in 1985. This value is positively correlated with the Jacobian singularity and is simplified in industrial controllers as the "minimum singularity" threshold for online singularity warning. Subsequently, safety standards such as ISO 10218 also recommended reducing speed or replanning when operability falls below the threshold. With improved computing power, controllers can calculate the Jacobian singularity in milliseconds and look ahead to trajectory segments longer than 20ms in real time, achieving "soft emergency stop" instead of hardware power failure, thus improving shutdown reliability.

[0004] In terms of commercial implementation, the FANUC controller integrates a "singularity deceleration / attitude switching" algorithm: it monitors the minimum singular value in real time in the trajectory interpolation look-ahead module, and when a singularity risk is detected, it switches through a redundant attitude library or dynamically reduces the end effector speed. The relevant principles and implementation are protected by US6845295 B2. Siemens SINUMERIK's CN113305881 B for five-axis machine tools moves the offline analysis of singular regions to the CAM stage. It first samples the G-code trajectory and calculates the angular feature values ​​formed by the joint axis pairs, using color-coding to warn programmers. If workpiece clamping deviates on the production floor, an online compensation function can be enabled on the controller, providing double protection against singularities.

[0005] For those with redundant degrees of freedom ( In 1997, Chiaverini proposed the Singular Robust Task Prioritization (SR-TP) strategy for collaborative robots: while maintaining task accuracy, the manipulability gradient is projected onto the Jacobian null space to guide redundant joints to move along the direction of "maximizing manipulability". Boeing further reconstructed the Jacobian structure through the concept of "virtual joints", enabling the controller to automatically introduce damping or replace failed degrees of freedom near singularities, thereby ensuring end-effector continuity and joint rate constraints.

[0006] In addition to online control, production safety monitoring systems are beginning to utilize "visualized heatmaps" to present risks. The Battelle Energy Alliance proposed using mobile robots equipped with multimodal sensors to collect real-time hazardous chemical concentrations and generate "discrete grid-hazard intensity" heatmaps in a GUI, allowing operators to intuitively view spatial risk gradients. This concept paves the way for visualizing "singularity": assigning risk weights to each pose within a discrete workspace, enabling maintenance personnel to perceive singular risk distributions without needing to analyze complex mathematics.

[0007] Meanwhile, research on robot path planning delves deeper into dynamic environmental disturbances. GM Global Technology employs 3D vision to estimate the state of moving obstacles in real time, combined with a harmonic planner to output a safe velocity vector, enabling avoidance of fast-moving human bodies or forklifts. The academic community has verified the adversarial characteristic of "slight obstacle disturbances can significantly degrade the path" using a sampling-optimization planner, but related solutions still focus on "collision avoidance and ensuring reachability," lacking a systematic approach that utilizes the external environment to actively guide the robotic arm towards kinematically vulnerable areas.

[0008] In summary, current implementation solutions can be categorized into three types: First, online detection-dynamic avoidance technology based on minimum singular values ​​or conditional numbers—ensuring singularity safety through deceleration, attitude switching, or damping suppression; second, trajectory sampling-singular region labeling methods for CAM / offline programming—identifying and alerting potential singular risks during the planning phase; and third, risk heatmap visualization and dynamic obstacle avoidance schemes relying on multimodal perception and GUI—improving operators' awareness of spatial risks and obstacles. These technologies address specific issues such as singularity detection, offline assessment, or environmental visualization, but they have not yet integrated "singularity metric discretization + targeted placement of external obstacles" to proactively guide the robotic arm trajectory into a singular state, forming a highly concealed path planning attack on production cycle time and equipment health. The "Singularity Heatmap-Induced Path Planning" framework proposed in this invention addresses this technological gap, aiming to provide a novel attack model and experimental benchmark for industrial control security assessment and defense research.

[0009] Existing singularity avoidance solutions generally focus on "post-detection avoidance," ensuring safety only after Jacobian degradation is detected through deceleration, attitude switching, or replanning. This passive nature means that if the look-ahead window is insufficient or external disturbances are sudden, the system may still fall into the singularity zone within a very short time. While offline sampling and labeling methods can provide early warnings, they rely on fixed operating conditions. If on-site changes to clamping or cycle time are required, recalculation is necessary, making it difficult to meet the needs of flexible production. Redundancy avoidance algorithms are limited by model accuracy and real-time computing power; in complex operating conditions, damping or least-squares approximations are needed, which can easily reduce motion efficiency. Heatmap visualization and dynamic obstacle avoidance primarily improve operator perception but lack quantitative strategies linked to singularity measurement, making it difficult to automatically reconstruct risks in unattended scenarios. These limitations stem from current technologies treating singularities as local risks to be avoided, rather than incorporating them into global task parameters that can be controlled by the external environment. This results in a lack of system initiative and precision when dealing with new adversarial scenarios. Summary of the Invention

[0010] The purpose of this invention is to disclose a method for adversarial attacks on robotic arm planning based on singularity-induced methods, thereby solving the technical problems mentioned in the background art.

[0011] To achieve the above objectives, the present invention provides the following technical solution:

[0012] This invention provides a method for adversarial attacks on robotic arm planning based on singularity-induced methods, comprising:

[0013] S1, obtain the joint angle vectors and end-effector pose of the robotic arm, and generate a heat map based on the joint angle vectors;

[0014] S2: Obtain singular regions based on heatmaps, perform multi-objective optimization based on singular regions, and obtain obstacle locations;

[0015] S3, determine whether the center of the obstacle is within the reachable area; if so, move the physical obstacle to the center of the obstacle.

[0016] S4 controls the robotic arm to perform servo loop execution according to the original production trajectory, and records the curve of the minimum singular value and the end deviation.

[0017] Preferably, S1 includes:

[0018] S10, the host computer uses the robot operating system to perform kinematic analysis on the robotic arm and outputs the joint angle vector q of the robotic arm in real time;

[0019] S11, calls KDL::JacobianSolver to calculate the Jacobian matrix at a preset frequency. Six singular values ​​were obtained. and with the smallest singular value Normalized Singularity Index ;

[0020] S12 uses an octree to divide the Cartesian space into voxels of a preset length. The center position of the voxel is obtained by inverse kinematics to obtain all feasible joint solutions, and the maximum singularity index is marked as the singular value of the voxel.

[0021] S13 uses the Open3D graphics interface to display the voxels in color, and the vision sensor scans the pose of the robotic arm's end effector in real time and highlights the current position in the heat map.

[0022] Preferably, the preset frequency includes 1 kHz.

[0023] Preferably, the preset length includes 30mm.

[0024] Preferably, with the smallest singular value Normalized Singularity Index ,include:

[0025]

[0026] in This is the maximum singular value obtained from the global search before the experiment.

[0027] Preferably, the method of obtaining singular regions based on heatmaps includes:

[0028] The engineering experience threshold T=0.8. When S(q)≥T, the corresponding voxel is marked as a singular voxel; all singular voxels constitute a singular region.

[0029] Preferably, multi-objective optimization based on singular regions is performed to obtain obstacle locations, including:

[0030] Each obstacle is considered a radius. The spherical influence domain, on the volume element have:

[0031]

[0032] In the formula The original achievable target score, For body element The center point coordinate vector, For the first The center point coordinate vector of each obstacle express and The Euclidean distance between them;

[0033] To influence the weight;

[0034] n represents the total number of obstacles in this round of optimization; Let be the radius of influence of the i-th obstacle;

[0035] Represents volume element The reachability score after taking obstacles into account;

[0036] The process of guiding the robotic arm to the singular region is modeled as a multi-objective optimization, maximizing the end-path integral. At the same time, minimize the number of obstacles;

[0037] This represents the joint angle vector measured at sampling time t;

[0038] The fitness function is constructed by encoding the center and radius of obstacles using GA.

[0039] Preferably, the physical obstacle includes a cylindrical stop.

[0040] Preferably, moving the physical obstacle to the center of the obstacle includes:

[0041] By moving the chassis, the physical obstacle is moved to the center of the obstacle, thus modifying the operating environment of the robotic arm.

[0042] Preferably, controlling the robotic arm to perform servo loop execution according to the original production trajectory includes:

[0043] The host computer sends the original production trajectory to the controller through the API provided by the robot manufacturer; the controller does not make any software modifications and simply executes the routine servo cycle.

[0044] Beneficial effects:

[0045] Compared to existing solutions that passively avoid obstacles after anomaly detection and cannot systematically evaluate the gripper's robustness, this invention proposes an active guidance mechanism of "anomaly heatmap + fine obstacle placement" for gripping scenarios, which has the following advantages:

[0046] ① Targeted approach: Singular probability modeling is superimposed on the necessary areas of the grasping path, and small obstacles are placed through a genetic algorithm to specifically reduce the kinematic margin of the grasping and placing cycle;

[0047] ②Non-intrusive: Degradation can be triggered by modifying only the external environment, without modifying the gripper control logic or visual recognition model, thus avoiding compatibility risks with production line software;

[0048] ③ Quantitative Evaluation: The heatmap provides volumetric singular values ​​that are linked to indicators such as capture success rate and loop time, which can quantify the strength of counterattacks;

[0049] ④ Easy Reproduction: Obstacle parameters and placement coordinates can be scripted for reproduction, ensuring consistent degradation test results across different shifts and machines. These advantages stem from the fact that this invention is the first to treat singularity as an adjustable target, achieving a systematic and standardized verification method for combating grabbing attacks through an optimization-obstacle deployment-monitoring closed loop. Attached Figure Description

[0050] 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.

[0051] Figure 1 This is a schematic diagram of a robotic arm planning adversarial attack method based on singularity-induced attack according to the present invention. Detailed Implementation

[0052] 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.

[0053] like Figure 1 As shown, this invention provides a method for adversarial attacks on robotic arm planning based on singularity-induced attacks, including:

[0054] S1, obtain the joint angle vectors and end-effector pose of the robotic arm, and generate a heat map based on the joint angle vectors;

[0055] S2: Obtain singular regions based on heatmaps, perform multi-objective optimization based on singular regions, and obtain obstacle locations;

[0056] S3, determine whether the center of the obstacle is within the reachable area; if so, move the physical obstacle to the center of the obstacle.

[0057] S4 controls the robotic arm to perform servo loop execution according to the original production trajectory, and records the curve of the minimum singular value and the end deviation.

[0058] Furthermore, the reachable area refers to the spatial area that the end effector of the robotic arm can move into.

[0059] Furthermore, the end-point deviation refers to the error between the actual end-point pose T_real(t) measured in real time when executing the original production trajectory and the trajectory planning reference pose T_ref(t).

[0060] Preferably, S1 includes:

[0061] S10, the host computer uses the robot operating system to perform kinematic analysis on the robotic arm and outputs the joint angle vector q of the robotic arm in real time;

[0062] The host computer uses the KDL library built into ROS2 (Robot Operating System 2) to perform forward and inverse kinematic analysis on the robotic arm and outputs the joint angle vector q in real time.

[0063] S11, calls KDL::JacobianSolver to calculate the Jacobian matrix at a preset frequency. Six singular values ​​were obtained. and with the smallest singular value Normalized Singularity Index ;

[0064] S12 uses an octree to divide the Cartesian space into voxels of a preset length. The center position of the voxel is obtained by inverse kinematics to obtain all feasible joint solutions, and the maximum singularity index is marked as the singular value of the voxel.

[0065] S13 uses the Open3D graphics interface to display voxels in shaded form, with red representing... (High exotic risk), blue represents (Low risk) The vision sensor scans the pose of the robotic arm's end effector in real time and highlights the current position on the heat map.

[0066] Preferably, the preset frequency includes 1 kHz.

[0067] Preferably, the preset length includes 30mm.

[0068] Preferably, with the smallest singular value Normalized Singularity Index ,include:

[0069]

[0070] in This is the maximum singular value obtained from the global search before the experiment.

[0071] Preferably, the method of obtaining singular regions based on heatmaps includes:

[0072] Set the engineering experience threshold T = 0.8 (configurable to 0.70–0.9). When S(q) ≥ T, mark the corresponding voxel as a singular voxel; all singular voxels constitute a singular region; at the rendering level, the heatmap uses a linear gradient (colormap=Jet).

[0073] Preferably, multi-objective optimization based on singular regions is performed to obtain obstacle locations, including:

[0074] Each obstacle is considered a radius. The spherical influence domain, on the volume element have:

[0075]

[0076] In the formula The original achievable target score, For body element The center point coordinate vector, For the first The center point coordinate vector of each obstacle express and The Euclidean distance between them, where n represents the total number of obstacles in this round of optimization;

[0077] To influence the weight;

[0078] Let be the radius of influence of the i-th obstacle. , This is a weighting factor, with a default value of 0.5.

[0079] Represents volume element The reachability-objective score after considering obstacles (PyReachability-Objective Score after penalty). This is the "path integral" unit that the genetic algorithm (GA) aims to maximize, used to measure the effectiveness of pulling the final trajectory towards the singular region. The original reachability score is the reachability score when there are no obstacles. It tells the optimizer how much "exotic benefit" the attack can bring if the voxel is reached.

[0080] Indicates the first Local singularity of an obstacle:

[0081]

[0082]

[0083] This means that T(q) = The complete set of inverse kinematics solutions (attitude can be selected as the original process trajectory in) The target pose at the location; if simplification is needed, it can be solved using only "position constraints + default pose").

[0084] if Empty ( If it is unattainable, then let =0, and directly classify the chromosome as invalid (fitness 0) in GA fitness.

[0085] Taking into account both obstacle geometry and local singularity risk, It allows for easy adjustment of attack and defense strength in the configuration file.

[0086] The process of guiding the robotic arm to the singular region is modeled as a multi-objective optimization, maximizing the end-path integral. At the same time, minimize the number of obstacles;

[0087] This represents the joint angle vector measured at sampling time t (discrete time index, unit: ms);

[0088] The fitness function is constructed by encoding the obstacle center and radius using GA. :

[0089]

[0090]

[0091] means GA chromosome [ ,..., ], The maximum number of obstacles is less than or equal to the maximum number of obstacles. , It can be 3.

[0092]

[0093] These are the X-axis, Y-axis, and Z-axis coordinates of the i-th obstacle, respectively, and the unit can be millimeters. ∈W (reachable region)

[0094] For the singular integral of the terminal path,

[0095]

[0096]

[0097]

[0098]

[0099] Tn is the number of discrete trajectory points.

[0100] This is the set of coordinate vectors of the centers of n obstacles in this round of optimization;

[0101] This is the column vector of the corresponding obstacle radii;

[0102] Let k be the center coordinates of the volume element corresponding to the discrete trajectory point k;

[0103] In consideration and The achievable score after that.

[0104] This refers to the number of obstacles during this round of optimization. and These are the first weight and the second weight, respectively, and the values ​​of the first weight and the second weight can be 0.7 and 0.3, respectively.

[0105] and These are the maximum and minimum values ​​of the singular integral of the terminal path recorded during the optimization process, used for normalization. and These represent the minimum and maximum values ​​of the number of obstacles, respectively. It can be 1, The value and same.

[0106] Genetic operators include single-point crossover, mutation, and elite retention. The algorithm converges after 200 generations of iteration.

[0107] Preferably, the physical obstacle includes a cylindrical stop.

[0108] Preferably, moving the physical obstacle to the center of the obstacle includes:

[0109] By moving the chassis, the physical obstacle is moved to the center of the obstacle, thus modifying the operating environment of the robotic arm.

[0110] The mobile chassis moves precisely and places the physical cylindrical blocks according to TCP / IP (Transmission Control Protocol / Internet Protocol) instructions, thus modifying the operating environment of the robotic arm.

[0111] Preferably, controlling the robotic arm to perform servo loop execution according to the original production trajectory includes:

[0112] The host computer sends the original production trajectory to the controller through the API provided by the robot manufacturer; the controller does not make any software modifications and simply executes the routine servo cycle.

[0113] Preferably, after recording the curve with the minimum singular value and the terminal deviation, the method further includes:

[0114] Generate a JSON (JavaScriptObjectNotation) report for any unusual events that exceed a threshold, facilitating subsequent offline evaluation.

[0115] For the minimum singular value Each of the end-point deviation Δp and attitude error Δθ has one threshold: singular value threshold. :when (t), that is, the minimum singular value at time t is lower than Determine if the robotic arm has entered a kinematic singularity risk zone; end-effector deviation threshold. and attitude error threshold When the end position error Δp(t) at time t exceeds Or the attitude error Δθ(t) at time t exceeds The trajectory control was determined to be unstable.

[0116] Recommended default value: =0.20× . =5mm (position).

[0117] =2° (attitude). This parameter can be adjusted in config.yaml. A JSON record is triggered when any of the following conditions are met: ① (t)≤ And duration ≥ (Default 20ms); ②Δp(t)≥ or Δθ(t)≥ ③ Joint velocity Exceeding 90% of the manufacturer's rated limit.

[0118] Immediately after triggering, a data entry containing a timestamp is generated. A JSON report with keys such as Δp, Δθ, joint_speed, and severity is provided for offline evaluation. Optional: If both ① and ② occur simultaneously, the severity field in the JSON is set to "HIGH".

[0119] Preferably, after S4, the following is also included:

[0120] After the experiment, the mobile chassis automatically removed the obstacles, and the host computer reloaded and verified the baseline heat map. Restore the equipment to ensure it is not permanently damaged.

[0121] The equipment used in this invention includes:

[0122] Host computer: Intel i7 industrial control computer, Ubuntu 22.04, responsible for algorithm calculation, heat map rendering and optimization.

[0123] Industrial robotic arm: six-axis servo drive, with an open EtherCAT interface for real-time status reading.

[0124] Visual depth sensor: RGB-D camera, 1280×720 resolution, 30Hz refresh rate, used to calibrate the workspace and obstacle positions.

[0125] Mobile chassis and gripping mechanism: Equipped with a SLAM (Simultaneous Localization and Mapping) module, it achieves centimeter-level obstacle placement accuracy.

[0126] Safety monitoring unit: Independent PLC (Programmable Logic Controller), which samples servo information and performs hardware interlocking on the emergency stop relay.

[0127] All modules are interconnected via a gigabit Ethernet switch, and low-latency communication is achieved using ROS2 DDS (Data Distribution Service). To facilitate third-party reproduction, all software parameters are open in the configuration file: the voxel side length can be adjusted to 10–50 mm, and the GA generation, population size, and crossover probability can be modified according to experimental requirements.

[0128] Through the above embodiments, the present invention can stably and repeatedly induce a robotic arm to enter a predetermined singular state without intruding on the controller or tampering with the sensor, providing a highly automated and parameterizable experimental platform for evaluating the robustness and safety protection capabilities of the control strategy.

[0129] In a further embodiment, a standard parts gripping unit is composed of an UR5e six-axis collaborative robotic arm (working radius 850mm), an RG2 gripper, and an Intel RealSense D455 depth camera. M8 bolts are randomly scattered in the material tray. The baseline program uses MoveIt! to plan a "camera recognition-path generation-grip-place" loop, achieving an average success rate of 98% within 100 loops. After enabling the framework of this invention, a 30mm resolution singular value heatmap is first constructed in Cartesian space by the kinematic solver. Then, GA optimizes the positions of three Φ40mm and H50mm cylindrical obstacles with the goal of "maximizing the singular integral of the path and constraining the number of obstacles to ≤3". The moving chassis precisely places the obstacles near the high singular value channel at the front edge of the material tray, forcing the robotic arm to detour and gradually approach the wrist singularity point when picking up the material.

[0130] The key points of this invention are as follows:

[0131] Key Point 1: Singularity Field Modeling of the Grabbing Path. This invention constructs a volume-level two-dimensional heatmap of "singularity - grasping success rate" in the gripper's mandatory workspace, and updates it in real time with the joint angles; existing solutions only monitor the operability of a single point within the controller, failing to quantify the overall risk of the path. This invention externalizes internal indicators into a callable field, facilitating direct application of subsequent algorithms.

[0132] Key Point Two: Precise placement of obstacles for grasping. The invention employs a genetic algorithm that links singularity with grasping posture constraints to perform multi-objective optimization of the obstacle center and radius, thereby simultaneously weakening the optimal posture of the obstacle's end approaching the bolt and increasing the singular integral; while existing obstacle avoidance technologies only guarantee collision avoidance without a mechanism to deliberately compress the gripper's kinematic margin.

[0133] Key Point Three: The Induction-Monitoring-Reset Closed-Loop Device. This invention uses a mobile chassis to automatically deploy / remove cylindrical obstacles, and an independent PLC collects and captures success rates to form a closed loop. This allows for non-intrusive, repeatable, and quantifiable degradation. Traditional attack methods and robustness tests require code modification or manual changes to operating conditions, resulting in poor reproducibility. These three differences are all reflected in the specific methods of "spatial field representation - optimized obstacle deployment - automatic reset," rather than simply in functional comparisons.

[0134] 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 planning based on singularity-induced attacks, characterized in that, include: S1, obtain the joint angle vectors and end-effector pose of the robotic arm, and generate a heat map based on the joint angle vectors; S2: Obtain singular regions based on heatmaps, perform multi-objective optimization based on singular regions, and obtain obstacle locations; S3, determine whether the center of the obstacle is within the reachable area; if so, move the physical obstacle to the center of the obstacle. S4 controls the robotic arm to perform servo loop execution according to the original production trajectory, and records the curve of the minimum singular value and the end deviation; Multi-objective optimization based on singular regions is performed to obtain obstacle locations, including: Each obstacle is considered a radius. The spherical influence domain, on the volume element have: In the formula The original achievable target score, For body element The center point coordinate vector, Let be the coordinate vector of the center point of the i-th obstacle. express and The Euclidean distance between them; To influence the weight; n represents the total number of obstacles in this round of optimization; Let be the radius of influence of the i-th obstacle; Represents volume element The reachability score after taking obstacles into account; The process of guiding the robotic arm to the singular region is modeled as a multi-objective optimization, maximizing the end-path integral. At the same time, minimize the number of obstacles; This represents the joint angle vector measured at sampling time t; The fitness function is constructed by encoding the center and radius of obstacles using GA.

2. The method for adversarial attacks on robotic arm planning based on singularity-induced attacks according to claim 1, characterized in that, S1 includes: S10, the host computer uses the robot operating system to perform kinematic analysis on the robotic arm and outputs the joint angle vector q of the robotic arm in real time; S11, at a preset frequency, call KDL::JacobianSolver to calculate the Jacobian matrix. Six singular values ​​were obtained. and with the smallest singular value Normalized Singularity Index ; S12 uses an octree to divide the Cartesian space into voxels of a preset length. The center position of the voxel is obtained by inverse kinematics to obtain all feasible joint solutions, and the maximum singularity index is marked as the singular value of the voxel. S13 uses the Open3D graphics interface to display the voxels in color, and the vision sensor scans the pose of the robotic arm's end effector in real time and highlights the current position in the heat map.

3. The method for adversarial attacks on robotic arm planning based on singularity-induced attack as described in claim 2, characterized in that, The preset frequency includes 1kHz.

4. The method for adversarial attack on robotic arm planning based on singularity-induced attack as described in claim 2, characterized in that, The preset length includes 30mm.

5. The method for adversarial attacks on robotic arm planning based on singularity-induced attack as described in claim 2, characterized in that, With the smallest singular value Normalized Singularity Index ,include: in This is the maximum singular value obtained from the global search before the experiment.

6. The method for adversarial attacks on robotic arm planning based on singularity-induced attack as described in claim 5, characterized in that, Singular regions are identified based on heatmaps, including: The engineering experience threshold T=0.

8. When S(q)≥T, the corresponding voxel is marked as a singular voxel; all singular voxels constitute a singular region.

7. The method for adversarial attacks on robotic arm planning based on singularity-induced attacks according to claim 1, characterized in that, Solid obstacles include cylindrical blocks.

8. The method for adversarial attacks on robotic arm planning based on singularity-induced attack as described in claim 1, characterized in that, Moving a physical obstacle to its center position includes: By moving the chassis, the physical obstacle is moved to the center of the obstacle, thus modifying the operating environment of the robotic arm.

9. The method for adversarial attacks on robotic arm planning based on singularity-induced attacks according to claim 1, characterized in that, The robotic arm is controlled to perform servo loop execution according to the original production trajectory, including: The host computer sends the original production trajectory to the controller through the API provided by the robot manufacturer; the controller does not make any software modifications and simply executes the routine servo cycle.

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