A Dynamic Path Planning Method for Electric Robotic Arms Based on Rado-Visual Fusion 3D Reconstruction

Abstract

This invention discloses a dynamic path planning method for electric robotic arms based on radar-visual fusion 3D reconstruction, relating to the field of dynamic path planning. It acquires multimodal discrete sensing data streams from the electric robot's operational scenario, performs physical discretization and multidimensional verification to generate a physical verification multimodal entity point cloud, performs manifold solidification on the physical verification multimodal entity point cloud to output a geometric friction feature mapping set, performs specular reflection artifact and topological fracture detection on the geometric friction feature mapping set to identify discontinuous topological fracture regions caused by dynamic shaking and high-reflectivity material coupling, and performs implicit field repair based on the geometric friction feature mapping set to generate a collision-free dynamic gradient-guided path. This allows the generated dynamic gradient-guided path to avoid geometrically accessible but physically unreliable grasping areas.

Description

Technical Field

[0001] This invention relates to the field of dynamic path planning, specifically a dynamic path planning method for electric robotic arms based on radar-visual fusion 3D reconstruction. Background Technology

[0002] In 10kV power distribution network live-line work, to meet stringent insulation protection requirements, power robots typically employ a working configuration combining a long-span insulated boom with a highly integrated insulated end effector. They utilize eye-to-hand multimodal sensors (LiDAR, depth camera, and vision camera) to perform real-time 3D reconstruction of the target object. However, limited by the low structural stiffness of the insulating composite material and the mechanical properties of the long cantilever, the robotic arm inevitably experiences low-frequency structural modal vibrations and high-frequency end effector micro-flickers when performing high-altitude precision operations. This complex dynamic condition is viciously coupled with the high-gloss surface characteristics of the work object (such as ceramic insulator strings and polished metal clamps): when the end effector's posture deflects by milliseconds due to micro-flickers, the LiDAR's incident angle instantaneously exceeds the critical angle for specular reflection, causing the echo signal to escape from the receiving aperture. This results in the data from the solid surface, which should be continuous, appearing as intermittent signal blind spots or high-frequency flickering discrete noise points in the sensor's original field of view.

[0003] Existing multi-source data fusion algorithms have significant shortcomings when processing highly reflective data under dynamic, non-rigid transformations. Due to the spatiotemporal synchronization differences of heterogeneous sensors (radar and camera) under high-frequency flutter, traditional probabilistic raster maps or ICP registration algorithms struggle to correct data gaps caused by specular reflection loss in real-time data streams. Instead, they often force visual textures onto incorrect depth planes due to flawed fusion strategies, leading to a consistent collapse in the microscopic topology of the reconstructed 3D point cloud model: the originally continuous and smooth insulator manifold surface is incorrectly resolved as discontinuous, torn fragments or step faults with false topological connections. This geometric topological fragmentation directly misleads downstream path planning systems, causing them to misjudge data-deficient areas on the insulator surface as passable free space. This can lead robotic arms to perform erroneous actions that penetrate the solid during live-line work, causing serious short circuits or mechanical collisions.

[0004] To address the aforementioned shortcomings, a technical solution is provided. Summary of the Invention

[0005] To address the technical problems mentioned in the background, this invention is proposed. This invention provides a dynamic path planning method for electric robotic arms based on radar-visual fusion 3D reconstruction.

[0006] This invention is achieved through the following technical solution: a dynamic path planning method for electric robotic arms based on radar-visual fusion 3D reconstruction, the method comprising the following steps:

[0007] Acquire multimodal discrete sensing data streams in the operation scenario of electric robots, perform physical discretization and multidimensional verification to generate physical verification multimodal entity point clouds, and perform manifold solidification on the physical verification multimodal entity point clouds to output a geometric friction feature mapping set;

[0008] Specular reflection artifacts and topological fractures are detected on the geometric friction feature mapping set to identify discontinuous topological fracture regions caused by dynamic shaking and coupling of highly reflective materials.

[0009] Based on the geometric friction feature mapping set, physically-aware implicit field repair is performed on the discontinuous topological fracture region to generate a collision-free dynamic gradient-guided path.

[0010] Furthermore, the steps for outputting the geometric friction feature map set are as follows:

[0011] Physical discretization slicing, multidimensional geometry and texture verification, high-inflection blind zone compensation, and physical attribute fusion are performed on the multimodal discrete sensing data stream to generate a physically verified multimodal entity point cloud;

[0012] By introducing a time dimension variable, the physical verification multimodal entity point cloud is discretized and mapped to spatiotemporal index voxel units;

[0013] The physical states of voxel units are divided into rigid occupied states and potential slip states, which are assigned geometric damping weights and low friction coefficient physical weights, respectively, and the physical property mapping spacetime voxel field is output.

[0014] Furthermore, the step of outputting the geometric friction feature map set also includes:

[0015] Based on the physical property mapping spatiotemporal voxel field, the entity filling rate in each voxel unit is calculated, and discrete free voxels are removed based on a preset physical entity threshold.

[0016] The remaining rigid occupied voxels and potential slip voxels are aggregated based on spatial neighborhood relationships, and a voxel manifold solidification operation is performed to output a geometric friction feature mapping set, which includes physical attribute categories, quantitative physical weight values, and connected cluster identifiers.

[0017] Furthermore, the steps for generating the physical verification multimodal entity point cloud are as follows:

[0018] By utilizing the mechanical stability threshold at the end of the robotic arm, the continuous sensing flow is physically discretized into inertial spatiotemporal slices;

[0019] Virtual rigid anchor points are inserted at the geometric centroid of each inertial spacetime slice. The data within the slice is inversely projected onto the static coordinate system of the virtual rigid anchor points. Non-operational domain backgrounds are clipped through solid geometry Boolean operations to output rigidly isolated slices.

[0020] Furthermore, the step of generating the physical verification multimodal entity point cloud also includes:

[0021] The rigid isolation slice is subjected to interlayer ghosting based on physical scan line number and texture consistency verification based on RGB image projection to screen out surviving object surface points;

[0022] Connect the radar launch center, the surface points of the surviving object, and the optical center of the camera to construct a closed optical path triangle. Eliminate false floating points that violate the axiom of visibility due to geometric closure residuals, and output a geometric verification slice.

[0023] Furthermore, the step of generating the physical verification multimodal entity point cloud also includes:

[0024] For the high-reflectivity insulator region within the geometric verification slice, a conjugate mirror virtual source is constructed with the object surface as the axis of symmetry using the principle of geometric optics, generating an equivalent straight-line reflection path connecting the conjugate mirror virtual source and the radar receiver;

[0025] If the deduction shows that the equivalent straight reflection path causes the receiver aperture to escape, it is determined to be a deterministic blind zone and a sensor active yielding strategy is implemented to block the radar flow and take over the coaxial depth camera data, outputting a physical verification observation set.

[0026] Furthermore, the step of generating the physical verification multimodal entity point cloud also includes: aggregating the physical verification observation set into a solidified manifold unit, fusing the material texture semantic information in the RGB image, marking the high-friction diffuse reflection and low-friction specular properties on the solidified manifold unit, and generating the physical verification multimodal entity point cloud.

[0027] Furthermore, the steps for detecting specular reflection artifacts and topological breaks are as follows:

[0028] Traverse the set of geometric friction feature maps, extract voxel clusters that are marked as potential slip states and whose depth gradients undergo abrupt changes, and mark them as potential specular reflection missing regions;

[0029] A time-domain stroboscopic analysis is performed on the potential specular reflection missing area. If the voxel presence state of the area undergoes a high-frequency flip in adjacent time steps, it is determined to be a dynamic stroboscopic blind area.

[0030] Search for the geometrically connected components around the dynamic flicker blind zone, calculate the consistency of the normal vectors of each connected component, merge regions with consistent normal vectors and spatial proximity, and lock them as the discontinuous topological fragmentation region.

[0031] Furthermore, the steps for generating a collision-free dynamic gradient-guided path are as follows:

[0032] The edge point set of the discontinuous topologically broken region is extracted and mapped to the geometric friction feature mapping set to determine the corresponding physical property category, and an anisotropic local geometric guidance field is constructed. If the physical property category is a potential slip state, a C2 continuous guidance field is constructed using a Gaussian kernel; if the physical property category is a rigid occupied state, a C0 continuous guidance field is constructed using a compact support kernel.

[0033] Using the anisotropic local geometric guiding field as the gradient flow direction constraint, and extracting quantitative physical weight values ​​as adaptive stiffness regularization terms, a Poisson equation energy functional with physical stiffness regularization is constructed.

[0034] Furthermore, the step of generating a collision-free dynamic gradient-guided path also includes:

[0035] The minimum value of the energy functional of the Poisson equation with physical stiffness regularization is obtained by solving the problem within the discontinuous topological fracture region, and the implicit indicator scalar field is calculated.

[0036] Calculate the negative gradient vector field of the implicit indicator scalar field, perform gradient descent search from the current pose to the target pose in the negative gradient vector field, extract the spatial curve of the zero isosurface extending along the potential energy descent direction and avoiding the implicit indicator scalar field, and generate the collision-free dynamic gradient guidance path.

[0037] Compared with the prior art, the beneficial effects of the present invention are:

[0038] Existing technologies often rely on probabilistic filtering to process point cloud noise, failing to distinguish between blind zones caused by excessive distance and specular reflection. This invention establishes a deterministic physical criterion for lidar signal loss by constructing a physical optical model of conjugate mirror virtual sources and receiver aperture escape, accurately identifying stealth blind zones caused by coupling between insulator surface smoothness and high-frequency micro-vibration at the robotic arm end. Combined with a sensor active yielding strategy, the radar data stream is forcibly blocked and coaxial depth camera data is seamlessly taken over under blind zone conditions. Utilizing the physical imaging complementarity of heterogeneous sensors (complementarity of time-of-flight ranging and structured light imaging), this fundamentally solves the visual penetration risk caused by data source loss when traditional algorithms face extreme high-reflectivity conditions such as insulator strings and metal clamps, providing a blind-zone-free physical verification observation set for live-line work. Simultaneously, the use of inertial spatiotemporal slicing and virtual rigid anchor points effectively eliminates point cloud ghosting caused by the flexible swaying of the insulated arm, ensuring the quality of rigid reconstruction during dynamic scanning.

[0039] To address the common topological fragmentation problem in real-time reconstruction, a physically stiffness-regularized Poisson equation energy functional is proposed. A Bayesian voting mechanism maps the latent slip states (high inflection / easy slip) of the target object to extremely high adaptive stiffness regularization coefficients. During the implicit field solution process, strong geometric constraints are imposed on the high inflection blind zone, forcing the generated implicit indicator scalar field to bulge and close at data voids, forming potential energy bridges and thus avoiding erroneous smoothing. This mechanism not only repairs false cracks caused by data loss in the mathematical topology but also transforms the physical risk of mirror slippage into a high-potential-energy repulsive force perceptible to the path planning algorithm. This allows the generated dynamic gradient-guided path to avoid geometrically accessible but physically unreliable (easy slip) grasping areas, significantly improving the operational safety of electric robots in complex unstructured environments. Attached Figure Description

[0040] 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. The following drawings are not drawn to scale according to the actual size, but are intended to illustrate the main idea of ​​the present invention.

[0041] Figure 1 The flowchart shows the dynamic path planning method for electric robotic arms based on radar-visual fusion 3D reconstruction.

[0042] Figure 2 This is a schematic diagram of the optical path closed triangle verification principle;

[0043] Figure 3 This is a schematic diagram of virtual source geometry derivation and receiver aperture escape determination;

[0044] Figure 4 This is a detailed implementation data flow diagram of the dynamic path planning method for electric robotic arms based on radar-visual fusion 3D reconstruction. Detailed Implementation

[0045] The technical solutions in 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 also within the scope of protection of the present invention.

[0046] like Figure 1 , Figure 4 As shown, the dynamic path planning method for electric robotic arms based on radar-visual fusion 3D reconstruction includes:

[0047] Step S100: Obtain the multimodal discrete sensing data stream in the electric robot's operation scenario, perform physical discretization and multidimensional verification on it to generate a physical verification multimodal entity point cloud, and perform manifold solidification on the physical verification multimodal entity point cloud to output a geometric friction feature mapping set.

[0048] Step S101: Perform physical discretization slicing, multidimensional geometry and texture verification, high-inflection blind zone compensation and physical attribute fusion on the multimodal discrete sensing data stream to generate a physical verification multimodal entity point cloud;

[0049] Step S1011: Using the mechanical stability threshold at the end of the robotic arm, the continuous sensing flow is physically discretized into inertial spatiotemporal slices;

[0050] Virtual rigid anchor points are inserted at the geometric centroid of each inertial spacetime slice. The data within the slice is inversely projected onto the static coordinate system of the virtual rigid anchor points. Non-operational domain backgrounds are clipped through solid geometry Boolean operations to output rigidly isolated slices.

[0051] The physical discretization of the continuous sensing stream employs a dynamic state monitoring algorithm based on a sliding time window. The continuous sensing stream refers to the original multimodal data sequence with high-frequency temporal characteristics, synchronously acquired by the LiDAR, depth camera, and vision camera under a unified clock reference during the operation of the electric robot. This sequence completely preserves all temporal fluctuation characteristics during the robot's motion. The specific implementation process of discretization is as follows: The angular velocity vector and linear acceleration vector output by the robot's end-effector inertial measurement unit are read in real time. The statistical variance norm of the motion data within the current sliding time window is calculated. This variance norm is calculated using a dimensionless weighted Euclidean distance algorithm: Z-Score standardization is performed on the angular velocity and acceleration sequences within the window, transforming observations with different physical units into dimensionless statistical distribution values ​​to eliminate the interference of dimensional differences on the calculation results; the squared differences between the standardized values ​​at each sampling time and the mean of the window are calculated and weighted summed. The weighting coefficients in the weighted summation are determined based on the sensor imaging's sensitivity to motion patterns. Since lidar and cameras are far more sensitive to rotational jitter than translational jitter, the angular velocity component is assigned a weight greater than that of the linear acceleration component. The final calculated weighted variance norm is compared with a preset mechanical stability threshold. This mechanical stability threshold is a physical parameter calibrated based on the inherent damping characteristics and self-locking capability of the robotic arm's servo system, characterizing the limit motion boundary of the robotic arm in a "quasi-static" operating mode. When the variance norm within the window is less than the mechanical stability threshold, the robotic arm is determined to be in a physically stable state for the current time period. All laser point clouds, depth maps, and RGB frames acquired within this time period are extracted into an independent inertial spatiotemporal slice. The physical meaning of the inertial spatiotemporal slice is a data packet that is continuous in time but can be considered a "rigid body" in dynamics. It removes and physically discards nonlinear noise data generated by large-amplitude maneuvers or high-frequency flutter of the robotic arm at the source.

[0052] The inverse projection correction within the inertial spacetime slice employs a spacetime freeze transformation method: the midpoint between the start and end times of the inertial spacetime slice is extracted as the temporal geometric centroid, and the six-DOF pose of the robotic arm's end effector corresponding to this midpoint is obtained. This pose is defined as a virtual rigid anchor point. The basis for defining this midpoint pose as a virtual rigid anchor point lies in its topological centrality. Choosing the midpoint in the time domain as the projection reference minimizes the cumulative deviation distance between the start and end data within the slice relative to the reference coordinate system, thus mathematically ensuring that the global deformation error of the data during the projection process is minimized. The static coordinate system of the virtual rigid anchor point refers to a fixed spatial reference system based on the robotic arm's end effector coordinate system at this midpoint. The specific operation of inverse projection is as follows: Iterate through the sensing data points collected at any time within the slice to obtain the instantaneous pose of the data point at the time of collection; using the principle of inverse homogeneous transformation, calculate the product of the inverse matrix of the virtual rigid anchor point pose and the instantaneous pose matrix to obtain the relative pose transformation matrix; use this relative pose transformation matrix to forcibly map and transform the sensing data points from their instantaneous coordinate system at the time of collection to the static coordinate system of the virtual rigid anchor point. This process eliminates the slight pose drift caused by the passage of time within the slice, forcibly "pinning" the data points that were originally "flowing" on the time axis to the same static spatial reference frame, thus achieving instantaneous rigid reconstruction of the work scene.

[0053] Background interference clipping employs entity geometric Boolean intersection operations: a priori geometric envelope of the work scene is constructed. This priori geometric envelope is a virtual three-dimensional spatial region formed by extending a preset safety buffer radius outward from the theoretical axis position of the target object. The safety buffer radius is obtained by taking the maximum physical diameter of the target object (such as an insulator string), superimposing the maximum allowable positioning error value of the robotic arm's end effector servo control system, and reserving a preset proportion of redundant space margin; the sum of these three is the safety buffer radius. The resulting virtual three-dimensional spatial region constitutes an effective observation channel that theoretically necessarily contains the work object and minimizes environmental noise. In this embodiment, the shape of the priori geometric envelope can be set to an infinitely long cylinder or cuboid according to the shape of the work object; this invention does not specifically limit this. The entity geometric Boolean operation process is as follows: determining whether the data points after inverse projection correction are located within the internal space of the priori geometric envelope; retaining data points whose spatial coordinates are located inside the envelope, and discarding data points located outside the envelope. The rigid isolation slice output by this step is pure observation data that contains only the entity of the work object and has removed background interference from the ground, tower, and sky.

[0054] The three-level processing logic established in this step—physical discretization, inverse projection, and entity Boolean clipping—is a prerequisite for achieving high-precision dynamic reconstruction. Physical discretization solves the observation blurring problem caused by dynamic shaking; without slicing, the cumulative error of the robotic arm over a long period will cause ghosting in the reconstructed model. Virtual rigid anchor points and inverse projection solve the temporal non-RGB alignment problem of multi-source sensors, eliminating relative motion through mathematical means and achieving sub-millimeter-level rigid coupling of data from different sensors in space. Entity geometric Boolean operations greatly reduce the computational dimension of subsequent processing through physical boundary constraints, ensuring the embedded system's real-time processing capability for effective data.

[0055] Step S1012: Perform interlayer ghosting based on physical scan line number and texture consistency verification based on RGB image projection on the rigid isolation slice to screen out surviving object surface points;

[0056] Connect the radar launch center, the surface points of the surviving object, and the optical center of the camera to construct a closed optical path triangle. Eliminate false floating points that violate the visibility axiom due to geometric closure residuals, and output a geometric verification slice.

[0057] like Figure 2 The diagram shown is a schematic diagram of the optical path closed triangle verification principle.

[0058] Reference Figure 2 The diagram illustrates the following: Node A is the radar transmission center, Node B is a surviving object surface point, and Node C is the camera optical center. Scenario 1 on the left shows the closed optical path of a real entity; the solid black arrows represent radar measurement rays, and the dashed blue arrows represent camera line-of-sight rays. Scenario 2 on the right shows the unclosed optical path of a spurious floating point; the double red arrows represent geometrically closed residuals that violate the line-of-sight axiom. Scenario 1: [Example 1 would be inserted here] Figure 2 As shown on the left, if node B is a real physical reflection point, such as the surface of an insulator, according to the axiom of geometrical visibility, the camera's line-of-sight ray (blue dashed line) originating from the camera's optical center (node ​​C) and passing through the corresponding pixel of point B in the image plane must precisely pass through or be extremely close to node B in three-dimensional space. At this time, the perpendicular Euclidean distance (geometric closure residual) between the camera's line-of-sight ray and the laser measurement point B approaches zero or is less than a preset threshold (e.g., 3-5 mm, set based on the statistical distribution of reprojection error). The system determines that the optical path closure triangle is valid and retains the point. Case Two: (e.g.) Figure 2As shown on the right, if the point detected by the radar is dust or strong light noise in the air, it is marked as a spurious floating point. Although it exists on the radar measurement ray (solid black line), it is not located on the path of the camera's line-of-sight ray (dashed blue line). In this case, the geometric closure residual between the two (indicated by the red arrow) will be significantly greater than the tolerance threshold, indicating that the radar and the camera are not observing the same physical entity, resulting in a broken triangle. The system determines this point as a spurious floating point and discards it.

[0059] The specific implementation of inter-layer ghosting removal based on physical scan line numbers and texture consistency verification based on RGB image projection is as follows: Inter-layer ghosting removal focuses on identifying and removing anomalous points that are spatially adjacent but exhibit discontinuous jumps in physical scan line levels. Specifically, for each laser point in a rigid isolation slice, its physical scan line number is obtained; a KD-Tree spatial index is established to accelerate neighborhood search; for any query point, all neighboring points within a preset small spatial radius are searched (e.g., 2mm); the absolute value of the difference between the query point and each neighboring point in terms of physical scan line numbers is calculated. If the three-dimensional Euclidean distance between the query point and a neighboring point is less than the spatial radius threshold, but the difference in their physical scan line numbers is greater than a preset jump threshold (e.g., crossing more than three scan lines), then a discontinuous level jump, i.e., inter-layer ghosting, is determined between the point pair and it is removed. This processing method is based on the principle of surface continuity, meaning that on a continuous object surface, spatially adjacent points should also exhibit continuous or gradually changing characteristics in terms of scan line numbering. Texture consistency verification is performed, a process that aims to further filter valid points using visual semantic information. A 3D-2D perspective projection model is constructed using the extrinsic parameter matrix provided by the radar-camera joint calibration and the camera's intrinsic parameter matrix. The remaining point cloud data after interlayer ghosting removal is projected one by one onto the RGB image pixel coordinate system synchronized with the timestamp, obtaining 2D geometric projection points. Centered on these geometric projection points, a pixel neighborhood of a preset size (e.g., 5×5 pixels) is extracted from the RGB image, and the pixel gradient magnitude and texture complexity within this neighborhood are calculated. The pixel gradient magnitude is calculated by convolving the gray values ​​of neighboring pixels using the Sobel operator, taking the square root of the sum of the squares of the horizontal and vertical gradients. This metric represents the sharpness of edges in local image regions. Texture complexity is calculated using the statistical variance of the gray values ​​of neighboring pixels, representing the richness of detail in local image regions. Based on these calculations, a consistency check is performed: the calculated pixel gradient magnitude and texture complexity are compared with preset edge thresholds and variance thresholds, respectively. Simultaneously, the HSV color saturation of neighboring pixels is compared with a preset effective color threshold. If the projection point falls within the RGB image... If the geometric projection point is within a region with significant texture features or an effective color region, it is determined that the geometric projection point is consistent with the RGB texture features. This point is a valid surviving object surface point with visual semantic support. If the projection point falls outside the image boundary or falls in an area marked as visually occluded, the consistency verification is deemed to have failed and the point is removed. The region with significant texture features refers to the image region where the pixel gradient magnitude is greater than the edge threshold or the texture complexity is greater than the variance threshold, corresponding to the object outline and texture surface in the physical world. The effective color region refers to the image region where the color saturation is greater than the effective color threshold, used to exclude high-brightness overexposed areas (pure white) or low-light shadow areas (pure black).The physical basis for determining the consistency between geometric projection points and RGB texture features lies in the fact that effective LiDAR echoes are typically generated on solid objects with a certain physical volume and surface roughness. These solid objects will inevitably exhibit edge gradients (contours) or grayscale changes (textures) in optical images. Conversely, if the area projected onto the image by a radar point has neither gradient nor texture, such as a smooth solid-color background, sky, or even lens smudges, it is highly likely to be noise generated by the radar or drift points caused by calibration errors. Therefore, removing points that fail consistency verification can prevent visually meaningless radar noise from being introduced into the subsequent texture mapping process, avoiding the generation of incorrect color point clouds.

[0060] Construct a closed optical path triangle by connecting the radar transmission center, the surface point of the surviving object, and the optical center of the camera: (Refer to...) Figure 2 This step utilizes the geometric position constraints of multimodal sensors to verify the physical authenticity of surviving object surface points. For each surviving object surface point, a geometric structure is constructed consisting of the radar transmission center (node ​​A), the surviving object surface point (node ​​B), and the camera optical center (node ​​C). According to the geometrical line-of-sight axiom, if point B is a real physical reflection point, then a ray originating from the camera optical center (node ​​C) and passing through the corresponding pixel of point B in the image plane must precisely pass through point B in three-dimensional space. The algorithm calculates the perpendicular Euclidean distance between the camera's line-of-sight ray and the laser measurement point B, defining this distance as the geometrical closure residual. The line-of-sight tolerance threshold is set based on the statistical distribution value of the reprojection error generated during the joint calibration of the radar and camera, typically taking three times this reprojection error value as the limit tolerance threshold, for example, 3-5 mm. If the geometrical closure residual is less than this threshold, the optical path closure triangle is determined to be geometrically valid, and the point is retained. Figure 2 As shown in the scenario on the left, if the geometric closure residual exceeds the threshold, it indicates that the depth point measured by the radar is not located on the camera's line of sight, and the two are not observing the same physical entity. This often occurs due to dust reflection or strong light noise in the air, and is judged as a false floating point and discarded. Figure 2 The second scenario on the right shows a failed verification. The final output dataset is a geometrically verified slice that has passed the triple verification of inter-layer topology, texture semantics, and geometric visibility.

[0061] The multi-level physical cleaning logic established in step S1012—scanline topology denoising, RGB texture verification, and optical path closure verification—is indispensable. Scanline topology denoising, starting from the rationality of the internal data structure of a single sensor, solves the problem of removing high-density clustered ghosting through traditional distance filtering. RGB texture verification and optical path closure verification, starting from the spatial consistency of multimodal data, utilize the camera's texture semantics and projection geometry constraints to verify the radar point cloud. Among them, RGB texture verification ensures the visual interpretability of the point cloud, preventing the radar noise from being incorrectly mapped onto the image background; optical path closure verification uses hard triangular geometry constraints to accurately remove floating noise points that, although projected into the image, have incorrect depth information. These three progressive steps purify the originally discrete and noisy point cloud into solid surface data with a clear geometric topology structure and strict alignment with visual texture.

[0062] Step S1013: For the high-reflectivity insulator region within the geometric verification slice, construct a conjugate mirror virtual source with the object surface as the axis of symmetry using the principle of geometric optics, and generate an equivalent straight-line reflection path connecting the conjugate mirror virtual source and the radar receiver.

[0063] If the deduction shows that the equivalent straight reflection path causes the receiver aperture to escape, it is determined to be a deterministic blind zone and a sensor active yielding strategy is implemented to block the radar flow and take over the coaxial depth camera data, and output a physical verification observation set.

[0064] like Figure 3 The diagram shown is a schematic diagram of virtual source geometry derivation and receiver aperture escape determination.

[0065] Reference Figure 3 In the diagram, the solid source point marked at the top is the physical emission center of the lidar; the finite aperture disk next to it is the radar receiver; the curved surface in the middle is the surface of the high-reflectivity insulator region; the red dots on the curved surface are the target observation points; the dashed circle at the bottom is the derived conjugate mirror virtual source; the blue dashed line and the red solid line connecting the virtual source and the physical space together form the equivalent straight-line reflection path. Figure 3 As indicated by the arrow, the surface normal direction at the target observation point is obtained by performing least-squares plane fitting on the local point cloud. This process utilizes eigenvalue decomposition to select the minimum eigenvector, ensuring that the normal vector accurately represents the local orientation of the insulator surface at the current point. Figure 3 As shown, the plane passing through the target observation point and perpendicular to the normal vector of the infinitesimal surface is taken as the tangent plane. Based on the geometric optics specular reflection law, the real source point of the radar is spatially symmetrically transformed about this tangent plane to obtain... Figure 3The conjugate mirror virtual source is marked below. Based on the principle of virtual sources, the originally complex emission-reflection-reception zigzag optical path can be equivalently represented as a path emanating from the conjugate mirror virtual source, passing through the target observation point, and along the reflection direction (…). Figure 3 The straight line extending from the solid red line (in the center) is an equivalent straight reflection path. This path utilizes the geometric visibility of a straight line to visually represent the propagation trajectory of laser energy after reflection. For example... Figure 3 As indicated by the red arrow, if the calculated intersection point is located outside the effective receiving radius of the finite aperture disk, meaning that the energy of the main lobe of the reflected light completely avoids the radar receiving field of view, then it is determined that receiving aperture escape has occurred.

[0066] The construction of the conjugate mirror virtual source employs the local differential surface symmetric mapping method: (Refer to...) Figure 3 For the high-reflectivity insulator region within the geometric verification slice, the target observation points within the slice are traversed, and least-squares plane fitting is performed on the local point cloud around the target observation point to obtain the micro-element surface normal vector at that location. The high-reflectivity insulator region refers to the prior geometric envelope constructed in step S1011, i.e., the theoretical space occupied by the insulator string. The set of points within the geometric verification slice falling within this envelope is defined as the high-reflectivity insulator region. The micro-element surface normal vector is obtained by: searching for the k nearest neighbors of the target observation point within a preset neighborhood radius (e.g., 3 cm), constructing the local point cloud covariance matrix; performing eigenvalue decomposition on this covariance matrix, and selecting the eigenvector corresponding to the smallest eigenvalue as the surface normal direction at that location. Figure 3 The normal vector of the infinitesimal surface shown in the figure is mathematically ensured to accurately characterize the orientation of the local tangent plane of the insulator surface at the current observation point. Based on the specular reflection law in geometric optics, the physical emission center of the lidar is taken as the real source point, such as... Figure 3 As shown, taking the tangent plane passing through the target observation point and perpendicular to the normal vector of the infinitesimal surface as the symmetry reference plane, the spatial symmetry point of the real source point with respect to this tangent plane is calculated, and this symmetry point is defined as... Figure 3 The conjugate mirror virtual source is marked in the image. Based on this conjugate mirror virtual source, a ray connecting the virtual source and the target observation point and extending along the reflection direction is generated, which is defined as the equivalent straight reflection path. The physical meaning of the equivalent straight reflection path is that the originally complex emission-reflection-reception polygonal optical path is transformed into a straight optical path emanating from the virtual source through virtual source transformation, thereby using the geometric visibility of the straight line to characterize the propagation trajectory of light energy.

[0067] When the equivalent straight reflection path is found to have receiver aperture escape, the area is identified as a deterministic blind zone and a sensor active yielding strategy is implemented. The process for determining receiver aperture escape is as follows: A three-dimensional geometric model of the lidar receiver is established. This model is based on the "Optomechanical Structure Parameter Specification" or factory calibration document provided by the lidar hardware manufacturer. The rigid transformation parameters of the optical center of the lidar receiving lens relative to the transmitting center, as well as the effective light transmission aperture of the receiving lens, are directly read from this document. Based on the above parameters, the receiver is abstractly modeled as a finite aperture disk in three-dimensional space, and its center coordinates and effective receiving radius in the current coordinate system are determined. This model is... Figure 3 The diagram shows a finite aperture disk (receiver). The spatial intersection of the equivalent straight reflection path and the infinite plane containing the receiver aperture is calculated. If the calculated intersection point is outside the effective receiving radius of the receiver (i.e., the Euclidean distance between the intersection point and the center of the disk is greater than the effective receiving radius), then aperture escape is determined to have occurred. Figure 3 The path is shown by the red arrow in the middle. At this point, although the laser beam successfully illuminates the surface of the object, due to the mirror properties of the highly reflective surface, the main lobe energy of the reflected light completely avoids the radar's receiving field of view, causing the radar to be unable to receive the echo signal due to the limitations of physical laws.

[0068] The sensor proactive failover strategy is implemented as follows: A dynamic weighted control law based on blind zone determination is deployed at the input port of the data fusion layer. When an area is marked as a deterministic blind zone, the data flow channel of the lidar is immediately blocked, and its confidence weight is forcibly set to zero to prevent the radar's "zero measurement" from being misread as free space. Simultaneously, data from the depth camera coaxially mounted with the radar is seamlessly taken over, and the depth camera's observation weight is elevated to the highest priority. The characteristics of the depth camera based on diffuse reflection or active structured light imaging are used to fill the radar blind zone. The retained effective radar data (non-high-reflection areas) and the taken-over depth camera data (high-reflection blind zones) are spatially joined and assembled to output a physical verification observation set.

[0069] The strategy of combining virtual source geometric deduction with sensor-based active yielding is the fundamental means to solve the stealth effect of highly reflective materials. The conjugate mirror virtual source and aperture escape determination, starting from the underlying logic of physical optics, provide a deterministic criterion for signal loss. Unlike traditional probabilistic filtering algorithms, it can accurately identify which areas are truly invisible rather than simply too far away. The sensor-based active yielding strategy utilizes the physical complementarity of heterogeneous sensors. Through hard switching under specific working conditions, it ensures that the power robot can still obtain continuous and complete environmental perception data when facing extreme highly reflective conditions such as insulator strings and metal clamps, providing an absolutely safe geometric foundation for the subsequent generation of collision-free paths.

[0070] Step S1014: Aggregate the physical verification observation set into a solidified manifold unit, fuse the material texture semantic information in the RGB image, mark the high-friction diffuse reflection and low-friction specular properties on the solidified manifold unit, and generate a physical verification multimodal solid point cloud;

[0071] The physical verification observation set is aggregated into solidified manifold units, and a region growing clustering algorithm based on Euclidean distance using normal vector consistency is adopted: Each discrete data point in the physical verification observation set output in step S1013 is traversed, and a spatial KD-Tree index is established; taking any point as the seed point, all neighboring points within a preset neighborhood radius are searched, with the preset neighborhood radius being 5 mm; the cosine value of the angle between the neighboring point and the seed point in the normal vector direction is calculated. If the spatial distance is less than a threshold and the angle between the normal vectors is less than a preset angle threshold, such as 15 degrees, then the neighboring point and the seed point are determined to belong to the same local continuous surface, and it is added to the current growing cluster. The above growing process is repeated until no new points can be added. Each finally generated independent and connected point cloud cluster is defined as a solidified manifold unit. The physical meaning of a solidified manifold unit is: it represents the smallest physical surface element with topological continuity and geometric smoothness on the surface of the work object.

[0072] By fusing material texture semantic information from RGB images, high-friction diffuse reflection and low-friction specular properties are marked on solidified manifold units. A dual-verification marking mechanism based on sensor source and visual texture is established: For the marking of high-friction diffuse reflection properties: solidified manifold units whose data source is marked as LiDAR are selected, i.e., areas where aperture escape did not occur in S1013; these units are projected onto the RGB image, the corresponding texture regions are extracted, and the HSV color space component distribution of these regions is calculated; if the variance of the luminance component of this region is lower than a preset uniformity threshold, and no white spots with a sudden drop in saturation are detected, then this region is determined to be a rough diffuse reflection material. For example, rubber sheaths and contaminated surfaces are marked as having high-friction diffuse reflection properties. A pre-set physical parameter library of power equipment materials is retrieved. Based on the identified diffuse reflection material type (e.g., rubber / contamination), the corresponding empirical value range of the static friction coefficient is directly retrieved, for example, empirical values ​​∈ [0.6, 0.8]. The average value of this range is taken as the estimated friction coefficient of the manifold unit. The method for determining white spots with a sudden drop in saturation is as follows: traverse the pixels within the texture area and identify pixels that simultaneously satisfy a brightness value greater than a highlight threshold (e.g., 200) and a saturation value less than a desaturation threshold (e.g., 0.1). If such pixels cluster into connected components and their area exceeds a preset noise threshold, then a white spot with a sudden drop in saturation is determined to exist. The physical basis of this criterion is that highlight spots on the insulator surface are usually formed by specular reflection of the light source. The light intensity at this location is extremely high, and the reflected light is mainly the color of the light source rather than the object color, i.e., low saturation / desaturation. This is completely different from the characteristic of diffuse reflection surfaces retaining the original color of the object. For the labeling of low-friction mirror properties: filter out those materialized manifold units whose data sources are labeled as being taken over by the depth camera, i.e., the areas in S1013 that are blinded by the camera due to aperture escape. Similarly, the unit is projected onto an RGB image, and a threshold segmentation algorithm is used to detect whether there are pixel connected regions within the texture area whose brightness values ​​exceed a preset highlight threshold, such as 220 / 255. If such a highlight pixel connected region exists, the region is directly identified as a smooth mirror material, such as a clean ceramic glaze or polished metal, and a friction coefficient inversion estimation based on visual gloss is performed: the average brightness value of the region in the RGB image and the highlight area ratio are extracted, and the friction coefficient estimate of the region is calculated using a preset gloss-friction coefficient inverse correlation mapping function. The calculation logic of this inverse correlation mapping function is as follows: a linear regression fitting model is used to construct a negative correlation between the friction coefficient and the highlight area ratio, that is, the larger the highlight area ratio, the smaller the calculated friction coefficient value; and the calculation result is constrained to below a preset low friction limit threshold (e.g., 0.2) by a preset fitting coefficient. The physical meaning of this estimate is that the brighter the region visually and the larger the highlight ratio, the smoother its microscopic surface, and the lower the corresponding physical friction coefficient.This is because, under natural lighting conditions, only objects with sufficiently smooth and flat surface microstructures can form high-intensity specular reflection spots in a localized area. This visual feature corroborates the physical phenomenon of radar signal receiving aperture escape in step S1013, thus confirming that the region has a low coefficient of friction.

[0073] The specific implementation method for generating the physical verification multimodal entity point cloud is as follows: Perform an attribute-geometry recombination and encapsulation operation. Traverse all entityized manifold units with completed attribute labeling, extract the three-dimensional geometric coordinates of each discrete point within the unit, and inherit the physical attribute label (high friction / low friction) and the corresponding friction coefficient estimate of the unit. Encapsulate the geometric coordinates, RGB color information, physical attribute label, and friction coefficient into a high-dimensional feature vector, and format it as the physical verification multimodal entity point cloud. This point cloud data is no longer a simple set of geometric points in terms of data structure, but rather an enhanced data stream carrying tractable physical semantics, serving as the sole data source for the subsequent voxelization mapping in step S102.

[0074] The physical verification multimodal entity point cloud generated in step S1014 forms a deep progression in the geometric-physical dimensions with the output data of step S1013: step S1013 only solves the problem of whether the data exists, while step S1014 further solves the problem of whether the surface is slippery. This explicit labeling mechanism of multimodal attributes is indispensable: in traditional pure geometric reconstruction, the ceramic glaze and rubber sheath of the insulator may be completely identical in geometry. If physical attributes are not distinguished, the path planning algorithm may incorrectly guide the robotic arm to grasp the glaze area, thus causing a slippage accident. This step, by fusing RGB texture semantics and sensor source information, directly implants physical tribology priors into the underlying data structure of the point cloud, providing a decisive physical decision basis for the subsequent construction of the voxel field containing friction risk in S102 and the generation of collision-free dynamic gradient-guided paths in S300.

[0075] Step S102: Introduce a time dimension variable to discretize and map the physical verification multimodal entity point cloud to a spatiotemporal index voxel unit;

[0076] The physical states of voxel units are divided into rigid occupied states and potential slip states, which are assigned geometric damping weights and low friction coefficient physical weights, respectively, and the physical property mapping spacetime voxel field is output.

[0077] The physical verification multimodal entity point cloud is discretized and mapped to spatiotemporal index voxel units, using a four-dimensional hash mapping algorithm based on a rolling circular buffer: the voxelization resolution is set to... (e.g., 10mm), construct a global hash table; traverse each discrete point in the physical verification multimodal entity point cloud output by step S1014. Calculate its corresponding hash index The calculation formula is: ,in, These represent the continuous geometric coordinates and timestamp values ​​of a discrete point in four-dimensional spacetime, respectively. The round-up operator is used to quantize consecutive floating-point coordinates into integer grid coordinates, thereby achieving discretization of the physical space into a grid. Represents a pre-defined large prime coefficient, for example This method, etc., is used to scatter bit features across various dimensions through multiplication operations, leveraging the irreducibility of prime numbers to reduce the probability of hash collisions. : Represents the XOR logical operation, used to mix feature information from four dimensions. Compared to addition, it preserves the independence of each dimension better. : Represents the modulo operation. The preset capacity of the hash table is used to map the calculated huge values ​​to the limited address space of computer memory. It should be noted that using hash functions for dimensionality reduction mapping and indexing of multidimensional discrete spatial data is a common technique in computer graphics and sparse spatial data management; its underlying mathematical principles will not be elaborated upon here. Hash Index The physical meaning is: it is the unique address of a spacetime cube (voxel) at a specific location in four-dimensional physical space in computer memory. When multiple different discrete points are calculated using the above formula, they yield the same hash index. This indicates that these points fall into the same resolution in physical space. Within the spatiotemporal grid, the system performs an aggregation operation: a spatiotemporal index voxel cell is generated or updated in memory using this index as the key, and the geometric centroid of all points falling within this grid is calculated using the incremental averaging method.

[0078] The physical states of voxel units are divided into rigid occupied states and potential slip states. A Bayesian voting mechanism based on physical label statistics is adopted: for each non-empty spatiotemporal indexed voxel unit, the number of points carrying high-friction diffuse reflection attribute labels in the aggregated point cloud data within it is counted. Points with the "low-friction mirror finish" label Calculate the slip risk ratio .like Greater than the preset risk threshold, for example If the physical state of the voxel unit is determined to be a potential glide state, then the physical state of the voxel unit is determined to be a potential glide state; otherwise, if If the value is less than or equal to the risk threshold, it is determined to be in a rigid occupied state. The specific implementation of assigning geometric damping weights and low friction coefficient physical weights is as follows: For voxel elements determined to be in a rigid occupied state, a geometric damping weight is assigned. ,For example In the subsequently constructed potential field, this manifests as a hard constraint, generating an extremely strong normal repulsive force to prevent collisions, but allowing low-speed approach or contact operations along the tangential direction, simulating a highly damped viscous effect. For voxel elements identified as potential slip states, low-friction coefficient physical weights are assigned. The value of this weight is set based on the reciprocal form of Coulomb's law of friction, for example... ,in The friction coefficient estimated in step S1014 represents risk expansion in the potential field, forcing the path planning algorithm to move away from the area during the planning phase. The output physical property mapping spatiotemporal voxel field is a four-dimensional enhanced mesh map that includes not only geometric location information but also physical interaction attribute information (where to grab, where to slide).

[0079] Although step S1014 identifies materials and assigns labels at the point cloud level, the point cloud data is unstructured and massive in volume, making it unsuitable for direct real-time path search. Through voxel mapping in S102, the computational dimensionality is reduced in the data structure, achieving engineering dimensionality reduction, and hash indexes are used to solve the problem of fast dynamic data retrieval. More importantly, a Bayesian voting mechanism addresses potential label noise in the point cloud, ensuring that a few misjudged points do not affect the properties of the entire voxel. Assigning different physical weights essentially mathematically transforms the physical risk of mirror slippage into a high-stiffness regularization constraint, providing crucial prior constraints for constructing the physically-aware Poisson energy functional in subsequent step S302. This processing results in steep potential energy barriers forming slippery regions in the implicit field calculated in S303, generating strong repulsive forces in the gradient descent path search in S304. This forces the robotic arm to automatically avoid geometrically accessible but physically unreliable (slippery) regions, something traditional planning methods based solely on geometric obstacle avoidance cannot achieve.

[0080] Step S103: Based on the physical property mapping spatiotemporal voxel field, calculate the entity filling rate in each voxel unit, and remove discrete free voxels based on the preset physical entity threshold;

[0081] The remaining rigid occupied voxels and potential slip voxels are aggregated based on spatial neighborhood relationships, and a voxel manifold solidification operation is performed to output a geometric friction feature mapping set, which includes physical property categories, quantitative physical weight values, and connected cluster identifiers.

[0082] Calculate the entity fill rate within each voxel unit, and remove discrete free voxels with insufficient fill rates based on a preset physical entity threshold: traverse each non-empty voxel unit in the spatiotemporal voxel field of the physical attribute mapping output in step S102, and obtain the number of aggregated discrete point clouds within that voxel. and the Euclidean distance from the geometric center of the voxel to the radar transmission center. Calculate the solid fill rate. The calculation is based on the ratio of the actual number of points within a voxel to the theoretical saturation number of points. The calculation formula can be expressed as follows: Among them, the theoretical saturation point number density function used to calculate the denominator. It is a range inverse function based on the angular resolution characteristics of lidar, and is usually expressed as a function of distance. The attenuation relationship is inversely proportional to the square of the sum. The specific formula form of this invention is not limited. The physical meaning of this function is: because the scanning beam of the lidar diverges radially, the attenuation increases with the detection distance. As the density increases, the spatial spacing between adjacent beams increases linearly, causing a sharp, non-linear decrease in the theoretically maximum number of laser points that can be hit per unit volume. Density normalization compensation for voxels at both long and short distances must be performed using this function to prevent distant effective entities from being misclassified as noise due to the natural sparseness of the number of points. The calculated entity fill rate... It is compared with a preset physical entity threshold, such as... If the entity fill rate If the value is less than this threshold, the voxel is determined to be a discrete free voxel and is discarded. Discrete free voxels typically correspond to mixed pixel noise such as flying insects, dust, rain and fog noise, or object edges. If the entity fill rate... If the value is greater than or equal to the threshold, the voxel is retained. This process achieves denoising of the three-dimensional morphological opening operation of the voxel field while preserving the main structure.

[0083] The remaining rigidly occupied voxels and potential glide voxels are aggregated based on spatial neighborhood relationships, and a voxel manifold solidification operation is performed. A 3D connected component labeling algorithm based on 26-neighborhood connectivity is used: traversing the hash table after the elimination operation, using any unlabeled voxel as a seed, it checks whether there are non-empty voxels in its 26 adjacent directions (face adjacency, edge adjacency, and vertex adjacency) in 3D space; if so, it is added to the current connected cluster, and this search process is recursively executed until the cluster cannot expand outwards. This process is repeated until all voxels are classified. Each independent connected voxel cluster generated in this way represents an independent physical object. The implementation method of the voxel manifold solidification operation is as follows: extracting the outer surface boundary voxel set of the above connected voxel clusters. For any voxel within a cluster, if at least one empty voxel exists in its 26-neighborhood, it is determined to be a surface voxel, and its physical weight attributes (geometric damping weight or low friction coefficient physical weight) are preserved and solidified. If all of its 26-neighborhoods are non-empty voxels, it is determined to be an internal voxel, and only geometric occupancy information is retained while physical weight calculation is omitted. The physical significance of voxel manifold solidification is that it transforms the originally Lego-like data composed of discrete lattices into a solid shell structure with clear internal and external boundaries, so that the discrete voxel set possesses the properties of a manifold in its topology.

[0084] The specific implementation of the output geometric friction feature map set is as follows: each surface voxel after manifold solidification is encapsulated into a feature node data packet containing multidimensional attribute information. The data structure of this feature node data packet is denoted as follows. ,in This represents the unique index number of the voxel unit in the global hash table, used for fast data addressing and retrieval; The three-dimensional coordinates of the geometric centroid of the voxel unit in the world coordinate system accurately characterize the spatial position of the physical element. The physical property category representing the voxel unit is either Rigid (rigid) or Slip (potentially slipping), which determines whether the region is suitable for gripping or poses a risk of slippage. This represents the quantitative physical weight value corresponding to the above physical attribute category, where Weight represents the quantitative physical weight attribute field, and W represents the specific quantitative physical weight value, that is, the geometric damping weight value or the inverse value of the low friction coefficient assigned in the previous step. This represents the connected cluster identifier to which the voxel belongs, used to distinguish whether the voxel belongs to an insulator string, the robotic arm body, or other hardware. All feature nodes are packaged, resulting in a set of geometric friction feature maps.

[0085] Although step S102 generates voxels with attributes, these voxels still contain a large number of isolated noise points caused by environmental dust or sensor noise, and there is a lack of topological correlation between voxels. If the topological break detection in subsequent S200 is performed directly based on the output of S102, these isolated noise points will be misjudged as broken fragments, causing the algorithm to fail. Through entity fill rate filtering in S103, non-entity noise is eliminated at the physical density level; through spatial neighborhood aggregation and manifold solidification, discrete voxels are bonded into continuous entities with topological structure. This process is essentially a morphological reconstruction of the environmental model, ensuring that the discontinuous regions identified in subsequent step S200 are indeed structural defects caused by high reflection or shaking, rather than discrete noise itself, thus ensuring the topological correctness of the path planning base map.

[0086] Step S200: Perform specular reflection artifact and topological fracture detection on the geometric friction feature mapping set to identify discontinuous topological fracture regions caused by dynamic shaking and high reflectivity material coupling;

[0087] Step S201: Traverse the geometric friction feature mapping set, extract voxel clusters marked as potential slip states and with a step change in depth gradient, and mark them as potential specular reflection missing regions;

[0088] Iterate through each feature node in the geometric friction feature map set output by step S103, and perform pre-filtering based on physical attribute category: extract only the physical attribute category. Voxel nodes in potential slip states are entered into the detection queue, while voxel nodes marked as rigidly occupied states, along with their weights and cluster information, are temporarily retained and passed through to subsequent steps. The physical basis for this screening is that only smooth surfaces with low friction coefficients (such as ceramic glazes and glass) possess the optical conditions for specular reflection, while the geometric depth abrupt changes caused by diffuse reflection on rigid, rough surfaces usually represent true physical edges. Therefore, pre-screening using attribute classification can prevent physical gaps from being misjudged as optical holes from the outset. For each voxel in a potential slip state selected... Based on its three-dimensional coordinates Search for it in three-dimensional space -Nearest neighbor voxels set to obtain the central voxel With each neighboring voxel in the set Radial depth value to the sensor origin and And calculate the local depth gradient operator. The calculation formula is: ,in, This represents the range size of the neighborhood search, for example, taking... or , corresponding to Moore's neighborhood or cube full neighborhood; Represented by voxels The set of indices of spatially adjacent voxels centered on the center; The index of the target center voxel currently undergoing gradient calculation; Representative set The index of any adjacent voxel in the dataset; This represents the maximum value operation, which is to traverse the set. All the neighbors Find the central voxel The value with the largest absolute value of the depth difference is used as the basis for gradient calculation; The spatial step size between voxels. The calculated local depth gradient... It is compared with a preset topological continuity threshold; this preset topological continuity threshold is a critical value calculated based on the maximum theoretical surface curvature of the standard digital model of the target object (such as an insulator), superimposed with the statistical variance of the sensor ranging noise (e.g., three standard deviations). If If the value is less than this threshold, it indicates that the region is geometrically continuous; if If the depth gradient exceeds this threshold, a step change has occurred, and the voxel is determined to be at an abnormal fracture edge. The physical meaning of a depth gradient step change is: a sudden change in depth occurs on a smooth surface that should be continuous, violating the axiom of geometric continuity. This is highly likely due to a ranging hole edge caused by the loss of laser signal due to specular reflection. Clustering and labeling of anomalous voxel clusters are performed: all voxel nodes that simultaneously satisfy the conditions of potential slip state and depth gradient step change are extracted, and an anomalous index list is established; spatially adjacent anomalous voxels are aggregated into independent clusters using the Euclidean distance clustering method, and these clusters are formally labeled as potential specular reflection missing regions in the data structure.

[0089] Although a sensor proactive yielding strategy was implemented in the preceding step S1013, i.e., blocking the radar flow and taking over the depth camera data, this only solved the physical blind spot problem at the signal acquisition level, i.e., ensuring data in high-reflectivity areas. However, due to the high-frequency dynamic shaking during robotic arm operation and the small spatial registration error during heterogeneous sensor fusion, the supplemented data often presents discontinuous, torn, or step-like patterns in the microscopic geometric topology, rather than a perfectly smooth surface. Step S201 aims to perform a secondary diagnosis on these areas that have been initially supplemented in S1013 but are not yet of perfect quality at the data topology level. Through the dual constraints of physical properties and geometric gradients, it accurately distinguishes between false topological cracks left by high reflection and shaking and real mechanical structural gaps, thereby locking in the precise spatial domain to be repaired for the implicit field repair performed by physical perception in subsequent S300, avoiding erroneous smoothing of the real physical boundaries.

[0090] Step S202: Perform time-domain stroboscopic analysis on the potential specular reflection missing area. If the voxel presence state of the area changes frequently in adjacent time steps, it is determined to be a dynamic stroboscopic blind area.

[0091] For each voxel unit marked as a potential specular reflection missing region, its 3D spatial coordinate index remains unchanged, and a backtracking search is performed along the time dimension. The voxel existence state sequence corresponding to that spatial location within a preset time window prior to the current moment is extracted; the preset time window is, for example, the past ten frames. The voxel existence state is defined as a binary logical value: if a non-empty voxel can be found at that moment and location in the hash table, the state is marked as occupied; if the query result is empty or the point cloud density is lower than the entity threshold, the state is marked as empty. The state sequence within this time window is traversed, and the cumulative number of "from none to one" or "from one to none" transitions in voxel existence state is counted, defined as the cumulative state flip count. The flip frequency is calculated as the ratio of the cumulative state flip count to the total number of frames within the time window. The calculated flip frequency is compared with a preset flicker threshold. The preset flicker threshold is based on the statistical distribution differences between real physical entities and highly reflective artifacts in a large amount of experimental test data. Real physical entities exhibit low-frequency or zero-flipping behavior, while highly reflective artifacts exhibit high-frequency, violent flipping behavior. The critical probability boundary value is determined using a binary classification statistical method. If the calculated flipping frequency is greater than the preset flicker threshold, it indicates that the spatial location is repeatedly and violently oscillating between "something is there" and "nothing is there" within a very short time, and the voxel cluster is determined to be a dynamic flicker blind zone. The physical basis for this determination is that the specular reflection phenomenon on the surface of highly reflective insulators is extremely sensitive to the incident angle, while the robotic arm of a power robot inevitably experiences high-frequency micro-vibrations during operation. These tiny angular jitters cause the laser beam to repeatedly switch between the critical state of receiver aperture escape (blind zone) and diffuse reflection echo (visible); or during multimodal fusion, the blind spot data from the depth camera and the radar data generate high-frequency spatial mutual repulsion due to slight changes in dynamic extrinsic parameters. In contrast, real physical voids are stable and continuously vacant in the time domain, like fracture gaps or real physical entities that are stable and continuously occupied in the time domain. Therefore, only spurious topological faults caused by the coupling of high-reflectivity characteristics with system vibrations will exhibit significant high-frequency scintillation features.

[0092] Although step S201 identified suspected problem areas through physical properties and gradient abrupt changes, static geometric features cannot completely distinguish between structurally complex real gaps and unstable optical artifacts. Introducing temporal stroboscopic analysis essentially utilizes the optical sensitivity of highly reflective materials as a distinguishing feature, effectively filtering out real physical boundaries that, while exhibiting large geometric gradients, are temporally stable. This ensures that subsequent repair operations target only those truly high-reflectivity blind zones that are smooth, fragmented, and unstable, significantly improving the system's robustness and repair accuracy in dynamic and complex environments.

[0093] Step S203: Search for the geometrically connected components around the dynamic flicker blind zone, calculate the consistency of the normal vectors of each connected component, merge the regions with consistent normal vectors and spatial proximity, and lock them as the discontinuous topological fragmentation region.

[0094] Searching for geometrically connected components around the dynamic flicker blind zone: Performing a search and definition of a set of voxels of homologous geometrically connected components. This process uses the geometric centroid of the dynamic flicker blind zone determined in step S202 as the search center and sets a preset spatial search radius, such as 5cm. All geometrically connected components falling within this radius are retrieved from the geometric friction feature map set output in step S103. Here, a geometrically connected component refers to an independent cluster of connected voxels that carries a unique connected cluster identifier and is generated by aggregating rigid occupied voxels and potential slip voxels using a three-dimensional connected component labeling algorithm in step S103. The algorithm reads the connected cluster identifiers of voxels within the dynamic flashing blind zone and compares them with the connected cluster identifiers of each geometrically connected component found. Only connected components with the same identifier are retained, and these voxel clusters that have passed authentication are defined as a set of voxels of the same geometrically connected components. In complex high-altitude scenarios, insulator strings may be very close to metal clamps or background towers. If connected cluster identifiers are not introduced for same-origin constraints, the algorithm is very likely to mistakenly identify voxels of the background tower as part of the broken insulator and merge them incorrectly, causing the subsequent repair algorithm to stick two objects that should be separated together. By verifying the connected cluster identifiers, it is ensured that the searched fragments only come from the same physical entity, just like a string of insulators.

[0095] The calculation and consistency verification of the normal vector are performed as follows: The edge region voxel set of the dynamic flicker blind zone and the edge region voxel set of the homologous geometrically connected component voxel set are extracted. The edge region is determined by whether there is an empty state in the 26-neighborhood of the voxel; if so, it is determined to be an edge voxel. Then, principal component analysis is used to perform local surface fitting on the two edge region voxel sets respectively, calculating the local covariance matrix of the blind zone edge and the local covariance matrix of the fragment edge. Eigenvalue decomposition is performed on the matrices respectively, and the eigenvector corresponding to the smallest eigenvalue is selected as the blind zone edge normal vector at that location. With the fragment edge normal vector Based on this, calculate the absolute value of the dot product of the two normal vectors. If the dot product result is greater than a preset consistency threshold, such as 0.85, then the normal vectors of the two are considered to be consistent. The physical meaning of normal vector consistency is to characterize the continuity of the geometric trend between the broken fragments and the main structure. Although the actual insulator skirt is broken, the surface orientation of its residual fragments should maintain a smooth transition with the surface orientation of the main fracture. If the normal vector deviates sharply, it indicates that the area may be a structural abrupt change of the object itself or an obstruction by foreign objects, and does not belong to the missing surface that should be smoothly repaired.

[0096] The specific implementation method for merging regions with consistent normal vectors and spatial proximity to lock them as the discontinuous topological fragmentation region is as follows: The central dynamic flicker blind zone voxel set is indexed and merged with all homologous geometrically connected component voxel sets that simultaneously satisfy spatial proximity and pass the above-mentioned normal vector consistency check. That is, a new data object is created, and the global index numbers of the two types of voxels are stored in it. This merged object is then locked as the discontinuous topological fragmentation region. Spatially proximity means that the homologous geometrically connected component voxel sets fall within a preset spatial search radius centered on the geometric centroid of the dynamic flicker blind zone. The physical meaning of the discontinuous topological fragmentation region is: it is a macroscopic topological subset marked as "to be shaped" in the data structure. This subset spatially contains both "missing voids (blind zones)" and "effective supporting structures around the voids (homogeneous fragments)," and is the smallest geometric unit capable of completely describing the physical fracture morphology at that location.

[0097] The preceding step S202 only identified the location of unstable voids but did not specify the set of reference fragments to repair them. Without the filtering and merging in S203, the subsequent repair algorithm might fail to converge due to a lack of boundary constraints or incorrectly involve background noise in the repair process. Semantic isolation of objects was achieved through connected cluster identifier constraints, and geometric continuity filtering was achieved through normal vector consistency. The finally identified broken regions provided complete and pure geometric boundary conditions for the subsequent S300 steps of physically-aware implicit field repair and the solution of continuous implicit indicator scalar fields.

[0098] Step S300: Perform physically-aware implicit field repair on the discontinuous topological fracture region based on the geometric friction feature mapping set to generate a collision-free dynamic gradient-guided path.

[0099] Step S301: Extract the edge point set of the discontinuous topological fragmentation region, map it to the geometric friction feature mapping set to determine the corresponding physical property category, and construct an anisotropic local geometric guidance field; if the physical property category is a potential slip state, use a Gaussian kernel to construct a C2 continuous guidance field; if the physical property category is a rigid occupied state, use a compact support kernel to construct a C0 continuous guidance field.

[0100] The specific implementation of extracting the edge point set of the discontinuous topologically broken region and mapping it to the geometric friction feature mapping set to determine the corresponding physical attribute category is as follows: Traverse the discontinuous topologically broken region data packet output in step S203. This region consists of a series of discrete voxel indices. For each voxel within the region, check the voxel state in its 26-neighborhood. If there are unoccupied empty voxels in the neighborhood, the voxel is determined to be an edge voxel. Extract the geometric center coordinates of the edge voxel in the world coordinate system and add them to the edge point set. It should be noted that the geometric center coordinate system here refers to the geometric center of the cube corresponding to the voxel unit in physical space. Using the global hash index of the edge voxel as the key, the geometric friction feature mapping set output in step S103 is queried, and the feature node data packet corresponding to that position is read, thereby determining the physical attribute category to which the edge point set belongs.

[0101] An anisotropic local geometric guiding field is constructed using a radial basis function implicit surface interpolation algorithm with polynomial constraints: a scalar function is established. To describe any point in three-dimensional space The potential energy at that location is expressed mathematically as follows:

[0102] ;

[0103] in: Representative edge point set The total number of points in the field, i.e., the number of constraint points participating in the field construction; This represents the index number of a point in the edge point set, with a value range of 1. arrive ; The first edge point in the set The three-dimensional spatial coordinates of each point; Indicates the current spatial query point With the edge points The Euclidean distance between them; This is a kernel function, the specific form of which is dynamically selected based on the physical property category; For the first The weight coefficients of the basis functions represent the th basis function. The intensity of the influence of each edge point on the surrounding spatial field; Collectively referred to as the coefficients of the lower-order polynomial, among which This is the global constant bias term for the field, used to adjust the reference level of the field; They are respectively in the field Linear trend coefficients along the three coordinate axes. The mathematical purpose of introducing these four polynomial coefficients is to ensure that the generated implicit surface possesses affine transformation invariance; that is, when the input point cloud data as a whole undergoes rotation or translation, the shape of the reconstructed surface remains strictly unchanged and will not produce distortion. Weighting coefficients. With polynomial coefficients The solution process is as follows: construct and solve the system of linear equations. in, Let be the vector of unknown parameters to be solved, containing all weights. and polynomial coefficients ,Right now , Let be the objective function value vector. To avoid obtaining trivial solutions that are zero everywhere, we need to consider the edge points. Add off-axis constraint points along the normal direction: at each edge point outer distance Set a positive constraint point at the location and assign it a value. ), at the inner distance Set a negative constraint point at the location and assign it a value. The edge points themselves are assigned values. .vector Based on this series of preset target values ​​of field potential energy ( )composition. The interpolation system matrix is ​​a symmetric block matrix, primarily composed of kernel function matrix blocks and polynomial matrix blocks. The elements in the record contain the kernel function response values ​​between all pairwise constraints. And the coordinate polynomial terms of the constraint points, The first representative constraint point in the set The three-dimensional spatial coordinates of each point; The first representative constraint point in the set The three-dimensional spatial coordinates of each point; Representing the The point and the first The strength of the interaction between Euclidean distances between points under the action of the kernel function. By analyzing the matrix By inverting the equations or solving the system of equations using the LU decomposition method, the unique weighting coefficients and polynomial coefficients can be obtained.

[0104] Kernel function for different physical property categories The specific construction method is as follows: If the physical property category is a potential slip state, construct a C2 continuous guiding field: the system selects a Gaussian kernel function as... Its mathematical expression is ,in Here, is the shape parameter, typically taken as the reciprocal of the average spacing of the edge point set. Since the Gaussian function is infinitely differentiable, the scalar field generated by its linear combination is continuous on the second derivative. r represents the spatial Euclidean distance, equal to... , This represents the modulus length. Its physical meaning is: simulating the natural smoothing effect under the action of fluid surface tension, the smoothing property of the Gaussian kernel can forcibly smooth out the tiny jitters caused by radar noise at the edge points, making the generated zero isosurface exhibit a smooth "melting" characteristic like a droplet, thus restoring a curved surface that conforms to the physical properties of glaze. If the physical property category is a rigid occupied state, a continuous guiding field C0 is constructed: the system selects a compactly supported linear kernel function as... Its mathematical expression is .in The cutoff radius is the radius of the cutoff line. The method for obtaining the value is as follows: read the voxelization resolution set in step S102. ,For example ,set up ,in, For example, take the preset neighborhood multiplier coefficient. This means that the influence of the kernel function is limited to a local sphere centered at the edge point and with a radius of twice the size of a voxel; outside this range, its value remains constant. This function is in Since it is not differentiable at certain points, the generated field only satisfies the requirement of continuous function values. Its physical meaning is: simulating the rigid splicing characteristics of mechanical structures, the locality of the compactly supported kernel function ensures that each edge point only affects the field distribution within its minimal range, without causing smoothing interference to distant points. This macroscopically preserves the broken line characteristics or sharp edges between points, preventing the erroneous repair of square metal parts into circles. Gradient calculation and normalization are performed, transforming the constructed scalar-form guiding field into a vector-form flow field constraint: for the spatial domain of discontinuous topologically broken regions... any point within For the output scalar function Perform spatial differentiation and calculate its gradient vector. Since the direction of the gradient vector represents the direction of the most drastic change in the scalar field potential energy, i.e., the normal direction of the implicit surface, it is normalized and defined as an anisotropic local geometric guiding field. The calculation formula is: , Represents a scalar field The magnitude of the gradient vector. At this point... It has been transformed from a simple numerical value into a directional vector that guides the direction in which the surface should grow.

[0105] The geometric friction feature mapping set constructed in steps S301 and S103 forms a data synergy and constitutes the core foundation of physical perception repair. The geometric friction feature mapping set provides the underlying physical truth, i.e., what material the location is, allowing step S301 to directly retrieve the attribute conclusion determined in S103 via indexing, without needing to guess the material through complex image texture analysis. This synergy is indispensable: without the physical attribute categories provided by S103, S301 would be unable to distinguish between false light spot voids on the insulator and real structural gaps on the metal clamp, resorting to a one-size-fits-all smoothing algorithm. This would lead to two serious consequences: either the insulator is not smooth enough, resulting in subsequent misjudgment of friction, or the metal fittings are made too smooth, leading to the loss of grasping features. Through the construction of the differentiated field in this step, a precise unity of opposites is achieved between smoothness due to high reflectivity and fidelity due to rigidity, providing a gradient constraint that conforms to objective physical laws for solving the Poisson equation in subsequent step S302.

[0106] Step S302: Using the anisotropic local geometric guiding field as the gradient flow direction constraint, and extracting quantitative physical weight values ​​as adaptive stiffness regularization terms, construct the Poisson equation energy functional with physical stiffness regularization.

[0107] Constructing the energy functional of the Poisson equation This functional aims to find an optimal implicit indicator function. This makes the function's own gradient field... Alignment with the aforementioned guiding field to the greatest extent possible It is also constrained by the stiffness of its physical properties. The mathematical expression of the energy functional is:

[0108] ;

[0109] in: For the integration domain Continuous three-dimensional spatial coordinate variables within; The implicit indicator scalar field to be solved is physically defined as the internal field of the object. External The entity feature function, its gradient It represents the normal of the reconstructed actual surface; the first term The first term is the gradient fitting term, used to constrain the geometry of the reconstructed surface to tend towards the ideal smooth direction of the S301 program; the second term... This is a physical stiffness regularization term used to control the spatial position of the surface. The tightness of the area; The adaptive physical stiffness regularization coefficient is a key variable connecting geometric calculations and physical properties.

[0110] Adaptive physical stiffness regularization coefficient The extraction and mapping process is as follows: using the current spatial coordinates Using the voxel index, query the geometric friction feature map set output in step S103, extract the corresponding quantitative physical weight values, denoted as... Establish a positive correlation mapping function from physical weights to mathematical regularization coefficients:

[0111] ;

[0112] in The preset adjustment constant, This represents the sigmoid activation function, mapping any real number to the range 0 to 1. This mapping enables differentiated constraints on regions with different materials: for regions whose physical properties are in a potential slip state: the output of step S103... The value is relatively high; the result obtained at this time is... A large value assigns extremely high mathematical stiffness to the region; physically, this means the system determines that the original data in this region contains significant noise or voids due to specular reflection, making it unreliable; therefore, the regularization weight is forcibly increased, forcing the implicit surface to ignore minute local positional deviations and strictly maintain its tension within the region. The trajectory indicated by the smooth normal generated by the Gaussian kernel acts like a tight "bulletproof vest" for a broken insulator, forcibly closing the void. For regions with rigidly occupied physical properties: the output of step S103... The value is low. The result calculated at this time... A smaller numerical value means that the region is given a lower mathematical stiffness; the physical meaning is that the system determines that the data in this region is a real physical structure and is reliable; therefore, the regularization weight is reduced, allowing the implicit surface to bend freely to fit the original data points, like a soft "underwear", accurately preserving high-frequency mechanical features such as bolts and right angles.

[0113] The physical stiffness regularization established in step S302 provides the mathematical guarantee for achieving high-fidelity and error-proof repair. Traditional Poisson reconstruction algorithms typically use a globally uniform regularization parameter, i.e., a constant regularization parameter across the entire image. This leads to a dilemma: increasing the regularization parameter to repair insulator voids results in rounded edges of metal clamps (underfitting); decreasing the regularization parameter to preserve clamp edges prevents voids on the insulator surface from closing (overfitting). Step S302 utilizes the quantitative physical weights provided in S103 as prior knowledge, introducing spatial variational constraints in the solution of the Poisson equation. This mechanism is essentially a data fusion strategy based on physical trust: trusting the mathematical algorithm (strong smoothing) where physical impossibility (high reflectivity) exists, and trusting the original data (weak smoothing) where physical reliability (diffuse reflectivity) exists. This dialectical mathematical processing ensures that the final implicit scalar field can perfectly heal the large data gaps caused by dynamic shaking, while also fully preserving the key geometric features required for the robotic arm to grasp, providing the most accurate geometric base for S304 to generate collision-free paths.

[0114] Step S303: Solve for the minimum value of the energy functional of the Poisson equation with physical stiffness regularization in the discontinuous topological fragmentation region, and calculate the implicit indicator scalar field.

[0115] The constructed energy functional This can be transformed into its corresponding Euler-Lagrange partial differential equation form, i.e., the Sieve of Poisson equation:

[0116] ;

[0117] in, For the Laplace operator, As a divergence operator, the equation is essentially a diffusion equation with physical reaction terms: the left side... Represents geometrically smooth diffusion. Represents the positional constraint response determined by physical properties; the right side This represents the divergence of the guiding field, i.e., the source term of the geometric flow field.

[0118] The solution process mainly includes three stages: mesh discretization, system matrix assembly and load vector calculation, and multi-mesh iterative solution. The first stage is mesh discretization: an octree mesh structure is constructed in the discontinuous topologically fragmented region, and the depth level of the mesh is determined according to the voxel resolution set in step S102. Adaptive determination; finite element basis functions are defined at each leaf node of the octree, typically trilinear B-spline basis functions, thereby providing continuous infinite-dimensional indicator functions. Discretized into a finite-dimensional grid node coefficient vector The second stage involves system matrix assembly and load vector calculation: constructing a large-scale sparse linear equation system. Among them, the system matrix By the Laplace operator and the physical stiffness regularization term A joint decision; in this process, the result calculated in step S302 will be used. Values ​​are mapped to corresponding mesh nodes: For potential slip states, the values ​​of the diagonal elements of the matrix are significantly increased, enhancing the numerical stability and positional constraints of the equations in that region and preventing surface collapse; for rigidly occupied states, the values ​​of the diagonal elements of the matrix are kept small, allowing the solution vector to vary freely to fit details. Let be the geometrically guided field divergence projection vector, and explain its meaning and solution process: Vector This represents the driving force of the anisotropic local geometric guiding field generated in step S301 on the implicit surface generation. The specific solution process is as follows: calculate the guiding field vector. The cumulative projection of the inner product of the gradient of the finite element basis function at each grid node onto the entire spatial domain; physically, the vector Each element in the vector represents the flux balance of the guiding field at the corresponding grid node: a positive value indicates that the guiding field converges at that node, driving the indicator function to generate solids (bulges); a negative value indicates that the guiding field diverges at that node, driving the indicator function to generate voids (decays). It is precisely through vectors... The geometric trend information of "what shape the surface should take" planned in step S301 is transformed into algebraic source terms driving the solution of the equations. In the third stage, multi-grid iterative solution is used: the V-Cycle multi-grid iterative strategy is employed to solve the above linear equations; first, the low-frequency components of the solution are quickly calculated at the coarse grid level to determine the macroscopic topological structure of the surface; then, the solution is transferred to the fine grid level using interpolation operators, and high-frequency errors are corrected using Gauss-Seidel smoothing operators to restore the detailed texture of the surface. Iteration continues until the residual norm is less than a preset convergence threshold, outputting scalar field data continuously distributed throughout the entire space. By utilizing the interpolation properties of finite element basis functions, discrete scalar field data can be... Mapping back to continuous space, we construct a globally differentiable implicit indicator scalar field. This makes it possible for any coordinate in space Each field value can be uniquely obtained through weighted summation of basis functions, thus providing a continuous mathematical object for gradient calculation in subsequent step S304. The physical meaning of this implicit indicator scalar field is: it defines a potential energy topography describing the probability of a spatial point belonging to the interior of an object; in free space far from the broken region, the field value approaches... Within the deep interior of an object, the field value approaches... The most crucial characteristic lies in the fact that, at the previously existing large data gaps, i.e., the high-response blind zone, the physical stiffness regularization term... Strong constraints and vectors Driven by geometry, the field values ​​do not break like the original data; instead, they are forced to bulge, forming a potential energy bridge connecting the broken edges. The zero isosurface of this scalar field is necessarily closed in mathematical topology, meaning that no matter how severely the original point cloud is fragmented, the solved implicit field... It can always provide a leak-proof, closed interface, thus mathematically and completely repairing the topological void.

[0119] Step S303 employs a reaction-diffusion type Poisson equation solver, which is the core computational engine for achieving physical sensing repair. Ordinary Poisson reconstruction only solves the pure geometric diffusion equation, which often leads to over-smoothing or non-uniqueness of solutions in high-reflectivity regions with severe data loss, and the generated surface may collapse inward. This step introduces a physical stiffness term, transforming the purely geometric reconstruction problem into a physically constrained energy minimization problem. In the high-reflectivity blind region of the insulator, the equation exhibits strong reaction characteristics, forcing the indicator function to decay rapidly and close, preventing surface collapse and generating a full and smooth filling surface. In the metal clamp region, the equation exhibits strong diffusion characteristics, allowing the surface to conform to the guidance of the guiding field and retaining sharp geometric features. Through this solution process, the physical properties of step S103 and the geometric guidance of step S301 are truly fused into a unified mathematical field, providing a physically safe and geometrically continuous navigation potential field for the subsequent step S304 to directly utilize the field gradient to generate a path.

[0120] Step S304: Calculate the negative gradient vector field of the implicit indicator scalar field, perform gradient descent search from the current pose to the target pose in the negative gradient vector field, extract the spatial curve that extends along the potential energy descent direction and avoids the zero isosurface, and generate the collision-free dynamic gradient guidance path.

[0121] Due to the implicit indicator scalar field It is a continuous function constructed from a smooth kernel function, and its position is calculated using numerical differentiation. Spatial gradient vector at The gradient vector The physical direction always points in the direction of the fastest increase in scalar field potential energy, that is, towards the interior of the object, because the interior of the object... External implicit scalar field Define the negative gradient vector field. The calculation formula is: Negative gradient vector field In the iterative formula, this vector acts as an active safety repulsion force, always perpendicular to the isosurface of the implicit surface and pointing in the direction of the fastest decrease in scalar field potential energy—that is, away from obstacles and towards free space. Specifically, it is influenced by the physical stiffness regularization coefficient in step S302. Due to the influence of this force, in the potential slip state, i.e. the high anti-blind zone, the magnitude of the repulsive field will increase significantly, forming a strong mathematical air wall that forces the path to detour over a large area; while in the rigid occupied state region, the repulsive field is more gentle, allowing the path to pass at close range.

[0122] The specific implementation method for generating the collision-free dynamic gradient-guided path by performing gradient descent search from the current pose to the target pose in the negative gradient vector field is as follows: Iterative path optimization is performed using a variant algorithm of the artificial potential field method. The gradient descent iterative formula for the comprehensive navigation potential function is constructed as follows:

[0123] ;

[0124] in, Represents the repulsive force gain coefficient. Representing the gravitational gain coefficient, it is used to adjust the weight between obstacle avoidance safety and target attraction. The values ​​of these two coefficients are usually set based on simulation experiments. In power operation scenarios, in order to ensure the absolute safety of obstacles (especially high-voltage live conductors), the repulsive gain coefficient is... The value is usually set to be significantly greater than the gravitational gain coefficient. ,For example This establishes a motion principle of safety first and efficiency second at the algorithm level, ensuring that the robotic arm prioritizes avoidance actions rather than forcibly moving towards the target when encountering a strong repulsive force field. The counter index representing the iteration step, with values ​​ranging from 1 to 2. ; Representing the In each iteration, the end effector of the robotic arm is abstracted as the instantaneous coordinate position of a virtual particle in three-dimensional space; Representing the The next coordinate position after the next iteration update; The step size factor represents the gradient descent step size, which determines the distance a particle moves along the gradient direction in a single iteration. This represents the implicit indicator scalar field at its current position. The gradient vector at that point; The target pose represents the predetermined position that the robotic arm's end effector needs to reach in three-dimensional space. The formula's construction basis and the physical meaning of each term are explained below: This formula is based on the energy minimization principle in Hamiltonian mechanics, assuming the robotic arm's end effector is a point mass moving in a virtual potential energy field, always sliding towards the state of lowest total potential energy (i.e., the target point). The formula is a linear superposition of the following two core physical vectors: the first part is the obstacle repulsive force vector term, i.e. This is based on the implicit indicator scalar field obtained by solving step S303. As a natural obstacle potential function; due to This represents the direction of the normal pointing from the current position into the obstacle; therefore, multiplying by the negative sign and the step factor... Then, this term is transformed into a repulsive displacement pushing outward from the obstacle surface; its physical function is to prevent collisions, and because it includes the physical stiffness information introduced in the previous steps, this repulsive force becomes extremely large in slippery, highly reactive regions, thus dynamically forcing the path away from the risk area. The second part is the target gravity vector term, i.e. The basis for this is: constructing a target point The global quadratic gravitational potential field centered at the target point; according to the differentiation rule, the negative gradient of the quadratic distance function is exactly the linear difference vector from the current point to the target point. Therefore, multiply by the negative sign and the step factor. Subsequently, this term is transformed into a tensile displacement that always points towards the target point. Its physical function is to drive the robotic arm to overcome the resistance of the repulsive force field and ultimately converge to the work target. Algorithm execution process: From the current pose of the robotic arm... Right now Initially, in each iteration, the calculated repulsive displacement and tensile displacement are vector-synthesized to update and obtain the next position. This process is repeated until the position converges to the target point. Within the nearby preset error range, record the position of the last iteration as... . All iteratively generated discrete point sequences Connect them sequentially and perform B-spline smooth interpolation to output a collision-free dynamic gradient-guided path.

[0125] In step S304, traditional path planning typically requires first meshing the reconstructed model, then voxelizing it, and finally running the algorithm. The algorithm search process is not only computationally cumbersome, but also prone to losing the physical stiffness microscopic features established in S302 during discretization. Step S303 solves for the implicit scalar field. It is itself a natural, physically aware navigation potential field. Using the gradient descent formula, we allow the robotic arm to glide automatically towards the target like a "water droplet" along the potential energy "valley." The physical properties of S103 and the geometric repair results of S303 are directly converted into dynamic constraints for path generation. In the high anti-blind zone of the potential slip state, due to the high stiffness provided by S302, The repulsive force generated by the extremely large physical risk gradient is also extremely large, causing the generated path to bypass these dangerous areas with a large radius; while in the rigidly occupied region, the repulsive force is smaller, and the path can pass along the edge. This direct utilization of the physical risk gradient is a key technical means to fundamentally solve the collision accidents caused by electric robots due to their unseen blind spots and instability.

[0126] It should be understood that although the steps in the flowcharts of the various embodiments of the present invention are shown sequentially according to the arrows, these steps are not necessarily executed in the order indicated by the arrows. Unless explicitly stated herein, there is no strict order restriction on the execution of these steps, and they can be executed in other orders. Moreover, at least some steps in the various embodiments may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily completed at the same time, but can be executed at different times. The execution order of these sub-steps or stages is not necessarily sequential, but can be performed alternately or in turn with other steps or at least a portion of the sub-steps or stages of other steps.

[0127] Those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware. The program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments described above. Any references to memory, storage, databases, or other media used in the embodiments provided in this application can include non-volatile and / or volatile memory. Non-volatile memory can include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), or flash memory. Volatile memory can include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in various forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), dual data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), Rambus direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM), etc.

[0128] The foregoing description is illustrative of the invention and should not be construed as limiting it. Although several exemplary embodiments of the invention have been described, those skilled in the art will readily understand that many modifications can be made to the exemplary embodiments without departing from the novel teachings and advantages of the invention. Therefore, all such modifications are intended to be included within the scope of the invention as defined in the claims. It should be understood that the foregoing description is illustrative of the invention and should not be construed as limiting it to the specific embodiments disclosed, and modifications to the disclosed embodiments and other embodiments are intended to be included within the scope of the appended claims. The invention is defined by the claims and their equivalents.

Claims

1. A dynamic path planning method for electric robotic arms based on radar-visual fusion 3D reconstruction, characterized in that, The method includes: Acquire multimodal discrete sensing data streams in the operation scenario of electric robots, perform physical discretization and multidimensional verification to generate physical verification multimodal entity point clouds; Manifold solidification is performed on the physical verification multimodal entity point cloud to output a set of geometric friction feature maps; Specular reflection artifacts and topological fractures are detected on the geometric friction feature mapping set to identify discontinuous topological fracture regions caused by dynamic shaking and coupling of highly reflective materials. Based on the geometric friction feature mapping set, physically-aware implicit field repair is performed on the discontinuous topological fracture region to generate a collision-free dynamic gradient-guided path. The steps for generating the output geometric friction feature map set are as follows: Physical discretization slicing, multidimensional geometry and texture verification, high-inflection blind zone compensation, and physical attribute fusion are performed on the multimodal discrete sensing data stream to generate a physically verified multimodal entity point cloud; By introducing a time dimension variable, the physical verification multimodal entity point cloud is discretized and mapped to spatiotemporal index voxel units; The physical states of voxel units are divided into rigid occupied states and potential slip states, which are assigned geometric damping weights and low friction coefficient physical weights, respectively, and the physical property mapping spacetime voxel field is output. The steps for generating the physical verification multimodal entity point cloud are as follows: By utilizing the mechanical stability threshold at the end of the robotic arm, the continuous sensing flow is physically discretized into inertial spatiotemporal slices; Virtual rigid anchor points are inserted at the geometric centroid of each inertial spacetime slice. The data within the slice is inversely projected onto the static coordinate system of the virtual rigid anchor points. Non-operational domain backgrounds are clipped through solid geometry Boolean operations to output rigidly isolated slices. The rigid isolation slice is subjected to interlayer ghosting based on physical scan line number and texture consistency verification based on RGB image projection to screen out surviving object surface points; Connect the radar launch center, the surface points of the surviving object, and the optical center of the camera to construct a closed optical path triangle. Eliminate false floating points that violate the visibility axiom due to geometric closure residuals, and output a geometric verification slice. For the high-reflectivity insulator region within the geometric verification slice, a conjugate mirror virtual source is constructed with the object surface as the axis of symmetry using the principle of geometric optics, generating an equivalent straight-line reflection path connecting the conjugate mirror virtual source and the radar receiver; If the deduction shows that the equivalent straight reflection path causes the receiver aperture to escape, it is determined to be a deterministic blind zone and a sensor active yielding strategy is implemented to block the radar flow and take over the coaxial depth camera data, and output a physical verification observation set. The physical verification observation set is aggregated into a solidified manifold unit, and the material texture semantic information in the RGB image is fused. The high-friction diffuse reflection and low-friction specular properties are marked on the solidified manifold unit to generate a physical verification multimodal solid point cloud.

2. The dynamic path planning method for electric robotic arms based on radar-visual fusion 3D reconstruction according to claim 1, characterized in that, The step of outputting the geometric friction feature map set further includes: Based on the physical property mapping spatiotemporal voxel field, the entity filling rate in each voxel unit is calculated, and discrete free voxels are removed based on a preset physical entity threshold. The remaining rigid occupied voxels and potential slip voxels are aggregated based on spatial neighborhood relationships, and a voxel manifold solidification operation is performed to output a geometric friction feature mapping set, which includes physical attribute categories, quantitative physical weight values, and connected cluster identifiers.

3. The dynamic path planning method for electric robotic arms based on radar-visual fusion 3D reconstruction according to claim 1, characterized in that, The steps for detecting specular reflection artifacts and topological breaks are as follows: Traverse the set of geometric friction feature maps, extract voxel clusters that are marked as potential slip states and whose depth gradients undergo abrupt changes, and mark them as potential specular reflection missing regions; A time-domain stroboscopic analysis is performed on the potential specular reflection missing area. If the voxel presence state of the area undergoes a high-frequency flip in adjacent time steps, it is determined to be a dynamic stroboscopic blind area. Search for geometrically connected components around the dynamic flicker blind zone, calculate the consistency of the normal vectors of each geometrically connected component, merge regions with consistent normal vectors and spatial proximity, and lock them as the discontinuous topological fragmentation region.

4. The dynamic path planning method for electric robotic arms based on radar-visual fusion 3D reconstruction according to claim 1, characterized in that, The steps for generating a collision-free dynamic gradient-guided path are as follows: The edge point set of the discontinuous topologically broken region is extracted and mapped to the geometric friction feature mapping set to determine the corresponding physical property category, and an anisotropic local geometric guidance field is constructed. If the physical property category is a potential slip state, a C2 continuous guidance field is constructed using a Gaussian kernel; if the physical property category is a rigid occupied state, a C0 continuous guidance field is constructed using a compact support kernel. Using the anisotropic local geometric guiding field as the gradient flow direction constraint, and extracting quantitative physical weight values ​​as adaptive stiffness regularization terms, a Poisson equation energy functional with physical stiffness regularization is constructed.

5. The dynamic path planning method for electric robotic arms based on radar-visual fusion 3D reconstruction according to claim 4, characterized in that, The step of generating a collision-free dynamic gradient-guided path further includes: The minimum value of the energy functional of the Poisson equation with physical stiffness regularization is obtained by solving the problem within the discontinuous topological fracture region, and the implicit indicator scalar field is calculated. Calculate the negative gradient vector field of the implicit indicator scalar field, perform gradient descent search from the current pose to the target pose in the negative gradient vector field, extract the spatial curve of the zero isosurface extending along the potential energy descent direction and avoiding the implicit indicator scalar field, and generate the collision-free dynamic gradient guidance path.

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