Three-dimensional scanning modeling method based on kinematic cooperation and sub-group fuzzy ant colony

Abstract

The application belongs to the technical field of three-dimensional modeling, and particularly relates to a three-dimensional scanning modeling method based on kinematics cooperation and sub-group fuzzy ant colony, which comprises the following steps: based on the kinematics theory of multi-body system, a global coordinate system of a scanning system and a homogeneous transformation matrix of each motion axis are established; a depth-of-field constraint is constructed; for a workpiece to be measured, a dynamic edge profile of the workpiece is acquired through the scanning system, a rough visual shell model of the workpiece is constructed, the normal vector distribution of each point on the surface of the workpiece is calculated, and a probe task set is distributed; the probe task set is split into discrete scanning task strips and solved; according to the optimal scanning task strip sequence obtained by solving, the scanning system is used to collect data of the workpiece; an adaptive sampling strategy based on a dynamic chord height error is used for point cloud gridding processing, a bidirectional curve fitting method is used to generate a NURBS surface, and a three-dimensional model of the workpiece is output. The application can realize full-automatic and high-precision digital reconstruction of a complex surface.

Description

Technical Field

[0001] This invention belongs to the field of 3D modeling technology, specifically relating to a 3D scanning modeling method based on kinematic cooperation and subgroup fuzzy ant colony. Background Technology

[0002] With the deepening advancement of intelligent manufacturing and Industry 4.0, the requirements for manufacturing precision of high-end industrial components are becoming increasingly stringent. In the aerospace field, key components such as engine casings and turbine blades typically possess extremely complex free-form surface features, large curvature edges, and deep cavity structures. Three-dimensional laser scanning technology, with its advantages of non-contact operation, high-density sampling, and high acquisition efficiency, has gradually replaced traditional contact coordinate measuring machines (CMMs) and become a core tool for reverse engineering and quality inspection.

[0003] Existing industrial-grade 3D laser scanning systems are mainly divided into two categories: flexible scanning systems based on multi-joint robotic arms (such as 6-axis robots) and dedicated scanning systems based on orthogonal coordinate architectures (such as gantry or bridge-type systems). While 6-axis robot-based systems offer extremely high flexibility, allowing them to approach the object from any spatial angle, their serial open-chain structure results in relatively weak rigidity. The absolute positioning accuracy of the end effector is easily affected by joint accumulation errors and thermal drift, making it difficult to meet the micron-level precision requirements of aerospace-grade measurements. In contrast, gantry-based scanning systems employ a fully closed-loop Cartesian coordinate kinematic chain, possessing extremely high mechanical rigidity, motion stability, and positioning accuracy, making them the preferred platform for high-precision industrial inspection.

[0004] However, in pursuit of ultimate mechanical stability and measurement repeatability, such high-precision gantry scanning systems often employ strict constraints in their degrees of freedom design. A typical configuration is a gantry combined with a turntable, equipped with two independent laser scanning probes, one on the top and one on the side. In this configuration, the physical motion axes of the probes are usually locked within specific two-dimensional planes (e.g., the top probe moves only in the XY plane, and the side probe moves only in the YZ plane), and the probes often lack physical zoom or mechanical feed capabilities along the optical axis (i.e., the depth of field). While this "restricted degrees of freedom" hardware characteristic ensures mechanical accuracy, it presents significant technical challenges to scanning path planning and data acquisition. Specifically, existing general path planning technologies face the following significant technical bottlenecks when dealing with such systems:

[0005] First, there's the issue of viewpoint accessibility under depth-of-field constraints. Traditional algorithms typically assume the probe has the ability to move forward and backward along the normal direction. However, in constrained systems, the effectiveness of scanning is entirely limited by the inherent depth-of-field range of the laser sensor. If the geometric undulations of the workpiece surface exceed this fixed range, traditional equal-slice or helical scanning strategies cannot automatically adjust the workpiece orientation to fit the effective measurement envelope of the probe, leading to data loss or blind spots.

[0006] Second, there are challenges in path planning and obstacle avoidance under complex constraints. For non-rotating parts (such as long blades or irregularly shaped shells), the workpiece generates a complex dynamic envelope as it rotates with the turntable. If the side probe cannot avoid the obstacle in the distance direction, a collision is highly likely; if the distance is too far, effective data cannot be obtained. Existing path planning algorithms are mostly based on the free space assumption and lack the ability to perform geometrical inclusion analysis and intelligent planning for the specific coupled constraint of a fixed depth of field combined with a rotating workpiece.

[0007] Third, the challenge of high-precision registration in the absence of geometric features. Point cloud data acquired by constrained degree-of-freedom systems are usually presented as discrete narrow bands or patches, lacking global geometric features. Traditional geometric feature matching-based stitching algorithms (such as ICP and its variants) are prone to getting stuck in local optima due to insufficient features when processing such data, leading to stitching misalignment or slippage, which seriously affects the accuracy of the final model.

[0008] Fourth, there is a mismatch between sampling density and surface features. In the reverse modeling stage, existing meshing methods often employ uniform or random sampling. For components such as aircraft blades, the leading and trailing edge radii of curvature are extremely small (high-frequency information), while the blade body is flat (low-frequency information). Uniform sampling leads to the loss of detail in high-curvature areas (undersampling), while data in flat areas is extremely redundant (oversampling), which not only reduces modeling accuracy but also significantly increases the computational load of data processing.

[0009] To address the aforementioned technical challenges, there is an urgent need for a systematic solution that can fully leverage the high rigidity of constrained degree-of-freedom systems while simultaneously compensating for degree-of-freedom constraints through deep collaboration at the algorithmic level. Summary of the Invention

[0010] In view of the shortcomings of the prior art, the purpose of this invention is to provide a three-dimensional scanning modeling method based on kinematic cooperation and subgroup fuzzy ant colony, which can realize fully automatic and high-precision digital reconstruction of complex curved surfaces.

[0011] To achieve the above objectives, this invention provides a three-dimensional scanning modeling method based on kinematic cooperation and subgroup fuzzy ant colony, comprising the following steps:

[0012] S1. Based on the kinematics theory of multibody systems, establish the global coordinate system of the scanning system and the homogeneous transformation matrix of each motion axis. The scanning system includes a top probe and a side probe.

[0013] S2. Construct depth constraints and define the visible cone as a set of scanning spatial positions that satisfy the field of view angle, depth range, laser incident angle, and no occlusion conditions.

[0014] S3. For the workpiece to be tested, the dynamic edge contour of the workpiece is obtained through the scanning system. Using the voxel engraving algorithm, a rough visual shell model of the workpiece is constructed through the Boolean intersection operation of the multi-view contours. The normal vector distribution of each point on the workpiece surface is calculated, and the probe task set is allocated according to the normal vector.

[0015] S4. The probe task set is split into discretized scanning task strips, a nominal distance matrix is ​​constructed, and the sorting problem of the scanning task strips is modeled as a generalized traveling salesman problem, which is solved by the subgroup fuzzy ant colony optimization algorithm.

[0016] S5. Based on the optimal scanning task strip order obtained by the solution, the scanning system is used to collect data on the workpiece. During data collection, the real-time axis position is used as strong prior information. The world coordinates of the point cloud are calculated through the forward kinematics solution. Kinematic closed-loop constraints are introduced to distribute the closed-loop constraint error evenly to the full-circumference scanning sequence.

[0017] S6. After the scanning is completed, an adaptive sampling strategy based on dynamic chord height error is used to perform point cloud meshing. A two-way curve fitting method is used to generate NURBS surfaces and output the three-dimensional model of the workpiece.

[0018] As a preferred embodiment of the present invention, in S1, the scanning system is an industrial-grade three-dimensional laser scanning device, comprising:

[0019] The gantry frame is a fully closed-loop regular hexahedron structure with a base installed at the bottom inside.

[0020] The turntable, located at the center of the base, is used to hold the workpiece to be measured and provides a Z-axis rotation. W Infinite rotational degrees of freedom of the axis;

[0021] The top scanning unit H1 is mounted on the top crossbeam of the gantry frame and is driven by a linear motor along the X-axis. W axis or Y W The top scanning unit, which travels along the optical axis, includes a top probe whose optical axis is vertically downward.

[0022] The side scanning unit H2 is mounted on a column on one side of the gantry frame and is driven by a servo motor along the Z-axis. W Axial direction or X W It travels along the axial direction and includes a side probe, with the optical axis of the side probe pointing horizontally towards the center of the turntable.

[0023] An optical grating ruler is used to measure the displacement of a linear motion axis.

[0024] An encoder is used to measure the angle of a rotating shaft, i.e., the rotation angle of the turntable. ;

[0025] The global coordinate system is the world coordinate system, with the origin O.W Defined at the intersection of the turntable's rotation axis and the turntable's bearing plane, Z W The axis is vertically upward, X W The axis points in front of the gantry frame, Y W The axis points to the right side of the gantry frame.

[0026] In a preferred embodiment of the present invention, in S1, the turntable coordinate system is fixed to the turntable surface, with its origin at O. T The turntable coordinate system initially coincides with the world coordinate system. When the turntable rotates by an angle... At that time, the transformation matrix of the turntable coordinate system relative to the global coordinate system For rotation matrix:

[0027] ;

[0028] The top probe coordinate system is fixed to the top probe optical center, and its position is subject to the gantry axis coordinate system. Control, the Z-axis direction is fixed as a constant Transformation matrix of the top probe coordinate system relative to the world coordinate system for:

[0029] ;

[0030] in, The rotation matrix for the mounting attitude of the top probe itself; For the top probe in X W Y W Position on the axis;

[0031] The side probe coordinate system is fixed to the optical center of the side probe, and its position is subject to the gantry axis coordinate system. Control, in X W The axial direction is fixed as a constant Transformation matrix of the side probe coordinate system relative to the world coordinate system for:

[0032] ;

[0033] in, The rotation matrix for the installation posture of the side probe itself; For the side probe in Y W Z W Position on the axis;

[0034] The homogeneous transformation matrix is , and .

[0035] As a preferred embodiment of the present invention, the process of constructing the depth constraint in S2 is as follows:

[0036] The effective working range of the scanning system is a finite frustum, or frustum. Let the effective measurement depth range of the scanning system be... , , These represent the minimum and maximum effective depth of field, respectively.

[0037] For a side-mounted probe, in order to effectively acquire point P on the workpiece surface, the geometric containment condition, i.e., the depth constraint, must be met:

[0038] ;

[0039] In the formula, This is the origin of the side probe coordinate system; These are the local coordinates of a point on the workpiece surface. Indicates taking the vector in X W Length of the module in the axial direction.

[0040] As a preferred embodiment of the present invention, in S3, obtaining the dynamic edge contour of the workpiece through the scanning system specifically involves controlling the top probe and the side probe to move to the safe limit position, driving the turntable to rotate 360°, and obtaining the binary contour image of the workpiece, i.e., the dynamic edge contour.

[0041] Constructing a coarse visual shell model specifically involves initializing a three-dimensional voxel mesh surrounding the workpiece, for each voxel V... k The voxel is projected onto the contour image at various angles. If the projection point is outside the contour image, the voxel is removed. After multi-view cropping, the remaining voxels form a rough visual shell model of the workpiece.

[0042] Mesh the surface of the rough visual shell model and compute the values ​​for each facet. normal vector Define the visibility function:

[0043] ;

[0044] ;

[0045] In the formula, , These represent the visibility functions for the top probe and the side probe, respectively. Using the world coordinate system Z W Axial unit vector; World coordinate system X W -Y W The set of horizontally outward-pointing unit vectors in a plane;

[0046] All satisfied and The set of facets constitutes the top probe task set T top ;

[0047] All satisfied and The set of facets constitutes the side probe task set T side ;

[0048] All satisfied and The set of facets forms the overlapping task set T overlap T overlap This refers to the overlapping area that requires scanning by both probes.

[0049] As a preferred embodiment of the present invention, in S4, the nominal distance matrix is ​​constructed as follows: a state node is defined as a system state unit corresponding to a discretized scan task strip, and each state node carries the state parameters of the scan system, including... The probe's position coordinates and task assignment are defined, and the status node S is defined. i and S j The nominal distance C between them ij For time cost:

[0050] ;

[0051] In the formula, Axial switching penalty term; This represents the maximum angular velocity of the turntable. , , X W Y W Z W Maximum linear velocity of the shaft; The difference in turntable angle represents the difference from state node S. i To S j At that time, the turntable rotates around Z W The change in the rotation angle of the shaft; , , X W Y W Z W The difference in axis translation distance represents the distance from state node S. i To S j At that time, the probe was in X W Y W Z W The change in position of the axis.

[0052] As a preferred embodiment of the present invention, in S4, the subgroup fuzzy ant colony optimization algorithm is based on the ant colony algorithm and incorporates the following improvements:

[0053] Improvement 1: Multi-subgroup cooperation mechanism, dividing the artificial ant colony M into three subgroups:

[0054] The radical group, comprising 20% ​​of the total, has a pheromone evaporation coefficient heuristic factor Guided by pheromones, they are responsible for wide-area exploration;

[0055] The conservative group, comprising 60% of the total, has a pheromone volatility coefficient. heuristic factor Following the best historical path, they are responsible for local development;

[0056] The balanced group, comprising 20% ​​of the total, has a pheromone volatility coefficient between [missing information]. and Between, the heuristic factor lies between and Between them, they are responsible for relaying information between the radical and conservative groups;

[0057] Improvement 2: Fuzzy logic controller to adjust the global pheromone evaporation coefficient in real time. ;

[0058] The input variable of the fuzzy logic controller is population diversity. , Defined as the ratio of the standard deviation to the mean of all ant path lengths in the current iteration;

[0059] Define a fuzzy set:

[0060] The membership is divided into {low, medium, high}, and the membership function is a Gaussian function.

[0061] Volatility coefficient adjustment amount Divide into {negative decrease, remain the same, positive increase}:

[0062] The fuzzy rule base is:

[0063] Rule 1, if If it is low, then It is increasing positively;

[0064] Rule 2, if If it is high, then It decreases negatively;

[0065] Rule 3, if If it is in the middle, then To maintain;

[0066] Improvement 3: Dynamic neighborhood 3-opt local search. After each generation of ant colonies has constructed its path, the globally optimal path L is searched. best Perform 3-opt optimization: randomly select three edges on the path. Disconnect, try all 7 possible reconnection methods, and if the new path length after reconnection is... If the path is updated, then a, b, c, d, e, and f are the six state nodes corresponding to the three edges to be disconnected randomly selected from the current scan path during the 3-opt optimization process.

[0067] As a preferred embodiment of the present invention, in S5, the real-time shaft position feedback from the grating ruler and encoder is utilized. As strong prior information, the world coordinates of the point cloud are calculated using forward kinematics solutions; where... The coordinates of the probe's real-time translational position in the world coordinate system;

[0068] The kinematic closed-loop constraints are:

[0069] The kinematic chain of the scanning system is a closed loop: the turntable rotates from 0° to 360° and then physically resets; therefore, the point cloud P in the 0° frame... start With the point cloud P in the 360° frame end Precisely coincident in the world coordinate system;

[0070] Construct a pose graph where nodes represent the poses of each scan frame, edges represent the relative motion measurements of adjacent frames, and add closed-loop constraint edges, i.e., kinematic closed-loop constraints:

[0071] ;

[0072] In the formula, This refers to the closed-loop constraint error. The pose matrix for the 0° frame; This is the pose matrix for a 360° frame. Denotes the Frobenius norm; I is the identity matrix;

[0073] The Levenberg-Marquardt algorithm is used to solve the nonlinear least squares problem of kinematic closed-loop constraints, and the closed-loop constraint error is evenly distributed across the full-circuit scan sequence.

[0074] As a preferred embodiment of the present invention, in S6, the adaptive sampling strategy based on dynamic chord height error specifically defines the chord height error as the maximum distance from the line connecting the sampling points to the actual curved surface, and sets the maximum allowable chord height error as... ;

[0075] For each point in the point cloud Calculate its local radius of curvature. , for Local curvature;

[0076] Sampling step size and The relationship is as follows:

[0077] .

[0078] As a preferred embodiment of the present invention, in step S6, generating the NURBS surface using a two-way curve fitting method includes:

[0079] U-axis fitting: Fitting a B-spline curve along each laser scanning line;

[0080] V-axis fitting: In the direction perpendicular to the laser scanning line, the corresponding points of each strip are connected to fit a B-spline curve;

[0081] Mesh fusion: Constructing a tensor product NURBS surface, control points Determined by the weighted average of the control points of the U-direction and V-direction curves. A control point is a two-dimensional grid jointly determined by the u-th U-direction control point and the v-th V-direction control point, and is the basic unit for constructing the NURBS surface.

[0082] The beneficial effects of this invention are:

[0083] This invention does not rely on changes in hardware structure. Instead, it transforms the physical constraints of the hardware into mathematical boundary conditions for path planning by establishing an accurate system kinematic model and the "visibility field" theory. It uses an improved fuzzy ant colony algorithm to solve the path optimization problem in a multidimensional coupled space. Furthermore, it combines kinematic prior information with an adaptive sampling strategy to achieve high-precision point cloud registration and surface reconstruction.

[0084] This invention significantly improves the full-surface scanning efficiency of complex workpieces through a collaborative task planning mechanism using top and side dual probes. A coarse visual shell model constructed based on a voxel engraving algorithm can automatically divide the task sets for both probes into dedicated sets and overlapping sets based on the surface normal vector distribution. This avoids redundant paths encountered during single-probe scanning and ensures the measurement reliability of key feature areas through cross-validation in overlapping regions. The scanning path sorting is modeled as a generalized traveling salesman problem and solved using a subgroup fuzzy ant colony optimization algorithm. Utilizing a multi-subgroup collaborative strategy involving aggressive, conservative, and balanced groups, combined with dynamic neighborhood 3-opt local search, it effectively solves the premature convergence problem in path optimization within a high-dimensional coupled space, exhibiting stronger global exploration capabilities and higher local development accuracy compared to traditional single-group ant colony algorithms.

[0085] At the data processing level, this invention constructs a pose graph optimization model based on the kinematic closed-loop constraints of the 360° physical reset of the turntable. The Levenberg-Marquardt algorithm is used to evenly distribute the closed-loop error to the full-circuit scan sequence, which suppresses the propagation of accumulated error from a mechanistic perspective. Combined with an adaptive sampling strategy based on dynamic chord height error, the sampling step size is automatically adjusted according to the local curvature to reduce data redundancy in flat areas of the surface and retain geometric details in areas with complex features. Finally, a smooth NURBS surface is generated through bidirectional curve fitting.

[0086] This invention realizes intelligent processing of the entire process, from automatic allocation of scanning tasks, optimal path planning, real-time pose correction to adaptive fine reconstruction. It can adapt to the scanning needs of workpieces with different geometric features without manual teaching, and significantly shortens the three-dimensional digitization cycle of complex freeform workpieces while ensuring sub-millimeter-level measurement accuracy. Attached Figure Description

[0087] Figure 1 This is a flowchart illustrating the principle of this invention;

[0088] Figure 2 This is a schematic diagram of the scanning system of the present invention. Detailed Implementation

[0089] The embodiments of the present invention will be further described below with reference to the accompanying drawings:

[0090] like Figure 1 As shown, the 3D scanning modeling method based on kinematic cooperation and subgroup fuzzy ant colony includes the following steps:

[0091] S1. Based on the kinematics theory of multibody systems, establish the global coordinate system of the scanning system and the homogeneous transformation matrix of each motion axis. The scanning system includes a top probe and a side probe.

[0092] S2. Construct depth constraints and define the visible cone as a set of scanning spatial positions that satisfy the field of view angle, depth range, laser incident angle, and no occlusion conditions.

[0093] S3. For the workpiece to be tested, the dynamic edge contour of the workpiece is obtained through the scanning system (only the workpiece surface area falling within the frustum can be effectively acquired by the probe, and the area outside this range will be judged as an invalid scanning area). Using the voxel engraving algorithm, a rough visual shell model of the workpiece is constructed through the Boolean intersection operation of the multi-view contours. The normal vector distribution of each point on the workpiece surface is calculated, and the probe task set is allocated according to the normal vector.

[0094] S4. The probe task set is split into discretized scanning task strips, a nominal distance matrix is ​​constructed, and the sorting problem of the scanning task strips is modeled as a generalized traveling salesman problem, which is solved by the subgroup fuzzy ant colony optimization algorithm.

[0095] S5. Based on the optimal scanning task strip order obtained by the solution, the scanning system is used to collect data on the workpiece. During data collection, the real-time axis position is used as strong prior information. The world coordinates of the point cloud are calculated through the forward kinematics solution. Kinematic closed-loop constraints are introduced to distribute the closed-loop constraint error evenly to the full-circumference scanning sequence.

[0096] S6. After the scanning is completed, the point cloud is meshed using an adaptive sampling strategy based on dynamic chord height error. A two-way curve fitting method is used to generate a NURBS (non-uniform rational B-spline) surface, and the three-dimensional model of the workpiece is output.

[0097] In S1, the scanning system is an industrial-grade 3D laser scanning device, such as... Figure 2 As shown, taking scanning a turbine blade workpiece as an example, the scanning system includes:

[0098] The gantry frame is a fully closed-loop regular hexahedral structure (high rigidity), with a base installed at the inner bottom;

[0099] The turntable (precision turntable), located at the center of the base, is used to hold the workpiece to be measured and provides Z-axis rotation. W Infinite rotational degrees of freedom of the axis;

[0100] The top scanning unit H1 is mounted on the top crossbeam of the gantry frame and is driven by a linear motor along the X-axis. W axis or Y W The top scanning unit, which travels along the optical axis, includes a top probe whose optical axis is vertically downward.

[0101] The side scanning unit H2 is mounted on a column on one side of the gantry frame and is driven by a servo motor along the Z-axis. W Axial direction or X W It travels along the axial direction and includes a side probe, with the optical axis of the side probe pointing horizontally towards the center of the turntable.

[0102] Both the top probe and the side probe use laser line scanning probes;

[0103] High-precision grating rulers are used to measure the displacement of linear motion axes.

[0104] An encoder is used to measure the angle of a rotating shaft, i.e., the rotation angle of the turntable. ;

[0105] The global coordinate system is the world coordinate system, with the origin O. W Defined at the intersection of the turntable's rotation axis and the turntable's bearing plane, Z W The axis is vertically upward, X W The axis points in front of the gantry frame, Y W The axis points to the right side of the gantry frame.

[0106] The rotary table coordinate system is fixed to the rotary table surface, with its origin at O. T The turntable coordinate system initially coincides with the world coordinate system. When the turntable rotates by an angle... At that time, the transformation matrix of the turntable coordinate system relative to the global coordinate system For rotation matrix:

[0107] ;

[0108] The top probe coordinate system is fixed to the top probe optical center, and its position is subject to the gantry axis coordinate system. Control, the Z-axis direction is fixed as a constant Transformation matrix of the top probe coordinate system relative to the world coordinate system for:

[0109] ;

[0110] in, The rotation matrix for the mounting attitude of the top probe itself; For the top probe in X W Y W Position on the axis;

[0111] The side probe coordinate system is fixed to the optical center of the side probe, and its position is subject to the gantry axis coordinate system. Control, in X W The axial direction is fixed as a constant Transformation matrix of the side probe coordinate system relative to the world coordinate system for:

[0112] ;

[0113] in, The rotation matrix for the installation posture of the side probe itself; For the side probe in Y W Z W Position on the axis;

[0114] The homogeneous transformation matrix is , and .

[0115] To address the physical limitation that the probe cannot move in the depth of field, a depth constraint is constructed, and the feasible region of the configuration space is further solved. This involves using the coupled motion of the turntable rotation and the gantry axis translation to ensure that the probe falls into all possible machine states of the aforementioned visible cone. This step transforms the scanning path planning problem from a traditional Cartesian space coverage problem into a geometric containment and connectivity problem in a high-dimensional configuration space.

[0116] In S2, the process of constructing depth constraints is as follows:

[0117] The effective working range of the scanning system is a finite frustum, or frustum. Let the effective measurement depth range of the scanning system be... , , These represent the minimum and maximum effective depth of field, respectively.

[0118] For a side-mounted probe, in order to effectively acquire point P on the workpiece surface, the geometric containment condition, i.e., the depth constraint, must be met:

[0119] ;

[0120] In the formula, This is the origin of the side probe coordinate system; These are the local coordinates of a point on the workpiece surface. Indicates taking the vector in X W Length of the module in the axial direction.

[0121] In S3, the dynamic edge contour of the workpiece is obtained through the scanning system by controlling the top probe and the side probe to move to the safe limit position, driving the turntable to rotate 360°, and obtaining the binary contour image of the workpiece, i.e., the dynamic edge contour.

[0122] Constructing a coarse visual shell model specifically involves initializing a three-dimensional voxel mesh surrounding the workpiece, for each voxel V... k The voxel is projected onto the contour image at various angles. If the projection point is outside the contour image, the voxel is removed. After multi-view cropping, the remaining voxels form a rough visual shell model of the workpiece.

[0123] Mesh the surface of the rough visual shell model and compute the values ​​for each facet. normal vector Define the visibility function:

[0124] ;

[0125] ;

[0126] In the formula, , These represent the visibility functions for the top probe and the side probe, respectively. Using the world coordinate system Z W Axial unit vector; World coordinate system X W -Y W The set of horizontally outward-pointing unit vectors in a plane;

[0127] All satisfied and The set of facets constitutes the top probe task set T top ;

[0128] All satisfied and The set of facets constitutes the side probe task set T side ;

[0129] All satisfied and The set of facets forms the overlapping task set T overlap T overlap This provides a benchmark for subsequent data fusion by identifying overlapping areas that require scanning by both probes.

[0130] The nominal distance matrix is ​​normalized to unify the rotation cost (angular velocity) of the turntable and the translation cost (linear velocity) of the gantry shaft into time dimensions, and an axial switching penalty factor is introduced to suppress mechanical vibration.

[0131] In S4, the nominal distance matrix is ​​constructed as follows: State nodes are the system state units corresponding to the discretized scan task strips. Each state node carries the state parameters of the scan system, including... The probe's position coordinates and task assignment are defined, and the status node S is defined. i and S j The nominal distance C between them ij For time cost:

[0132] ;

[0133] In the formula, Axial switching penalty term; This represents the maximum angular velocity of the turntable. , , X W Y W Z W Maximum linear velocity of the shaft; The difference in turntable angle represents the difference from state node S. i To S j At that time, the turntable rotates around Z W The change in the rotation angle of the shaft; , , X W Y W Z W The difference in axis translation distance represents the distance from state node S. i To S j At that time, the probe was in X W Y W Z W The change in position of the axis.

[0134] The subgroup fuzzy ant colony optimization algorithm is based on the ant colony algorithm and introduces the following improvements:

[0135] Improvement 1: Multi-subgroup cooperation mechanism, dividing the artificial ant colony M into three subgroups:

[0136] The radical group, comprising 20% ​​of the total, has a pheromone evaporation coefficient heuristic factor Guided by pheromones, they are responsible for wide-area exploration;

[0137] The conservative group, comprising 60% of the total, has a pheromone volatility coefficient. heuristic factor Following the best historical path, they are responsible for local development;

[0138] The balanced group, comprising 20% ​​of the total, has a pheromone volatility coefficient between [missing information]. and Between, the heuristic factor lies between and Between them, they are responsible for relaying information between the radical and conservative groups;

[0139] Improvement 2: Fuzzy logic controller to adjust the global pheromone evaporation coefficient in real time. ;

[0140] The input variable of the fuzzy logic controller is population diversity. , Defined as the ratio of the standard deviation to the mean of all ant path lengths in the current iteration;

[0141] Define a fuzzy set:

[0142] The membership is divided into {low, medium, high}, and the membership function is a Gaussian function.

[0143] Volatility coefficient adjustment amount Divide into {negative decrease, remain the same, positive increase}:

[0144] The fuzzy rule base is:

[0145] Rule 1, if If it is low, then To increase positively, old information is forcibly forgotten, thus escaping local optima;

[0146] Rule 2, if If it is high, then This negatively reduces the current optimal path, thus accelerating convergence.

[0147] Rule 3, if If it is in the middle, then To maintain a balance between exploration and development;

[0148] Improvement 3: Dynamic neighborhood 3-opt local search. After each generation of ant colonies has constructed its path, the globally optimal path L is searched. best Perform 3-opt optimization: randomly select three edges on the path. Disconnect, try all 7 possible reconnection methods, and if the new path length after reconnection is... If the path is updated, then a, b, c, d, e, and f are the six state nodes corresponding to the three edges to be disconnected randomly selected from the current scan path during the 3-opt optimization process.

[0149] The multi-subgroup cooperation mechanism divides ant colonies into aggressive groups (high volatility, heavy exploration), conservative groups (low volatility, heavy utilization), and balanced groups to maintain population diversity.

[0150] The fuzzy logic controller takes population diversity as input and dynamically adjusts the global pheromone evaporation factor in real time to prevent premature convergence or search stagnation.

[0151] Dynamic neighborhood 3-opt local search introduces the 3-opt local search operator to perform microscopic smoothing on the paths generated by the ant colony, eliminating redundant movements.

[0152] In S5, the real-time axis position feedback is obtained using a grating ruler and an encoder. As strong prior information, the world coordinates of the point cloud are calculated using forward kinematics solutions; where... The coordinates of the probe's real-time translational position in the world coordinate system;

[0153] The kinematic closed-loop constraints are:

[0154] The kinematic chain of the scanning system is a closed loop: the turntable rotates from 0° to 360° and then physically resets; therefore, the point cloud P in the 0° frame... start With the point cloud P in the 360° frame end Precisely coincident in the world coordinate system;

[0155] Construct a pose graph where nodes represent the poses of each scan frame, edges represent the relative motion measurements of adjacent frames, and add closed-loop constraint edges, i.e., kinematic closed-loop constraints:

[0156] ;

[0157] In the formula, This refers to the closed-loop constraint error. The pose matrix for the 0° frame; This is the pose matrix for a 360° frame. Denotes the Frobenius norm; I is the identity matrix;

[0158] The Levenberg-Marquardt algorithm is used to solve the nonlinear least squares problem of kinematic closed-loop constraints, and the closed-loop constraint error is evenly distributed across the full-circuit scan sequence.

[0159] To address potential mechanical backlash and cumulative drift in the scanning system, kinematic closed-loop constraints are introduced. Utilizing the physical reset property of the turntable after a 360° rotation, the point cloud data of the 0° frame and the 360° frame are spatially aligned. A nonlinear least-squares optimization graph is constructed to uniformly distribute the closed-loop error across the pose matrix of the full-circle scan data, achieving high-precision hard-constraint registration without relying on workpiece surface texture features.

[0160] In S6, the adaptive sampling strategy based on dynamic chord height error specifically defines the chord height error as the maximum distance from the line connecting the sampling points to the actual curved surface, and sets the maximum allowable chord height error as... ;

[0161] For each point in the point cloud Calculate its local radius of curvature. , for Local curvature;

[0162] Sampling step size and The relationship is as follows:

[0163] .

[0164] The adaptive sampling strategy establishes a nonlinear mapping relationship between the sampling interval and the radius of curvature by calculating the local principal curvature of the point cloud: it automatically densifies the sampling points in high curvature regions (such as the leading and trailing edges of the blade) and sparsely samples in low curvature regions (such as the blade plane).

[0165] Finally, a bidirectional curve fitting method is used to generate NURBS surfaces, that is, B-spline curves are fitted along the scan line direction and perpendicular to the scan line direction respectively and then weighted and fused, which effectively suppresses the data ripples caused by unidirectional scanning and outputs a CAD model with high smoothness and high precision.

[0166] The generation of NURBS surfaces using a two-way curve fitting method includes:

[0167] U-axis fitting: Fitting a B-spline curve along each laser scanning line;

[0168] V-axis fitting: In the direction perpendicular to the laser scanning line, the corresponding points of each strip are connected to fit a B-spline curve;

[0169] Mesh fusion: Constructing a tensor product NURBS surface, control points Determined by the weighted average of the control points of the U-direction and V-direction curves. A control point is a two-dimensional grid jointly determined by the u-th U-direction control point and the v-th V-direction control point, and is the basic unit for constructing the NURBS surface.

[0170] The algorithm calculations involved in this embodiment can be executed by an electronic device, which includes a memory, a processor, and a computer program stored in the memory and capable of running on the processor. The algorithm calculations described above are implemented by executing the software through the processor.

Claims

1. A 3D scanning modeling method based on kinematic cooperation and subgroup fuzzy ant colony, characterized in that... Includes the following steps: S1. Based on the kinematics theory of multibody systems, establish the global coordinate system of the scanning system and the homogeneous transformation matrix of each motion axis. The scanning system includes a top probe and a side probe. S2. Construct depth constraints and define the visible cone as a set of scanning spatial positions that satisfy the field of view angle, depth range, laser incident angle, and no occlusion conditions. S3. For the workpiece to be tested, the dynamic edge contour of the workpiece is obtained through the scanning system. Using the voxel engraving algorithm, a rough visual shell model of the workpiece is constructed through the Boolean intersection operation of the multi-view contours. The normal vector distribution of each point on the workpiece surface is calculated, and the probe task set is allocated according to the normal vector. S4. The probe task set is split into discretized scanning task strips, a nominal distance matrix is ​​constructed, and the sorting problem of the scanning task strips is modeled as a generalized traveling salesman problem, which is solved by the subgroup fuzzy ant colony optimization algorithm. The subgroup fuzzy ant colony optimization algorithm is based on the ant colony algorithm and introduces the following improvements: Improvement 1: Multi-subgroup cooperation mechanism, dividing the artificial ant colony M into three subgroups: The radical group, comprising 20% ​​of the total, has a pheromone evaporation coefficient heuristic factor Guided by pheromones, they are responsible for wide-area exploration; The conservative group, comprising 60% of the total, has a pheromone volatility coefficient. heuristic factor Following the best historical path, they are responsible for local development; The balanced group, comprising 20% ​​of the total, has a pheromone volatility coefficient between [missing information]. and Between, the heuristic factor lies between and Between them, they are responsible for relaying information between the radical and conservative groups; Improvement 2: Fuzzy logic controller to adjust the global pheromone evaporation coefficient in real time. ; The input variable of the fuzzy logic controller is population diversity. , Defined as the ratio of the standard deviation to the mean of all ant path lengths in the current iteration; Define a fuzzy set: The membership is divided into {low, medium, high}, and the membership function is a Gaussian function. Volatility coefficient adjustment amount Divide into {negative decrease, remain the same, positive increase}: The fuzzy rule base is: Rule 1, if If it is low, then It is increasing positively; Rule 2, if If it is high, then It decreases negatively; Rule 3, if If it is in the middle, then To maintain; Improvement 3: Dynamic neighborhood 3-opt local search. After each generation of ant colonies has constructed its path, the globally optimal path L is searched. best Perform 3-opt optimization: randomly select three edges on the path. Disconnect, try all 7 possible reconnection methods, and if the new path length after reconnection is... If the path is updated, then a, b, c, d, e, and f are six state nodes corresponding to three randomly selected edges to be disconnected from the current scan path during the 3-opt optimization process. The state nodes are the system state units corresponding to the discretized scan task strips. S5. Based on the optimal scanning task strip order obtained by the solution, the scanning system is used to collect data on the workpiece. During data collection, the real-time axis position is used as strong prior information. The world coordinates of the point cloud are calculated through the forward kinematics solution. Kinematic closed-loop constraints are introduced to distribute the closed-loop constraint error evenly to the full-circumference scanning sequence. S6. After the scanning is completed, an adaptive sampling strategy based on dynamic chord height error is used to perform point cloud meshing. A two-way curve fitting method is used to generate NURBS surfaces and output the three-dimensional model of the workpiece.

2. The three-dimensional scanning modeling method based on kinematic cooperation and subgroup fuzzy ant colony as described in claim 1, characterized in that, In S1, the scanning system is an industrial-grade 3D laser scanning device, including: The gantry frame is a fully closed-loop regular hexahedron structure with a base installed at the bottom inside. The turntable, located at the center of the base, is used to hold the workpiece to be measured and provides a Z-axis rotation. W Infinite rotational degrees of freedom of the axis; The top scanning unit H1 is mounted on the top crossbeam of the gantry frame and is driven by a linear motor along the X-axis. W axis or Y W The top scanning unit, which travels along the optical axis, includes a top probe whose optical axis is vertically downward. The side scanning unit H2 is mounted on a column on one side of the gantry frame and is driven by a servo motor along the Z-axis. W Axial direction or X W It travels along the axial direction and includes a side probe, with the optical axis of the side probe pointing horizontally towards the center of the turntable. An optical grating ruler is used to measure the displacement of a linear motion axis. An encoder is used to measure the angle of a rotating shaft, i.e., the rotation angle of the turntable. ; The global coordinate system is the world coordinate system, with the origin O. W Defined at the intersection of the turntable's rotation axis and the turntable's bearing plane, Z W The axis is vertically upward, X W The axis points in front of the gantry frame, Y W The axis points to the right side of the gantry frame.

3. The three-dimensional scanning modeling method based on kinematic cooperation and subgroup fuzzy ant colony as described in claim 2, characterized in that, In S1, the turntable coordinate system is fixed to the turntable surface, with its origin at O. T The turntable coordinate system initially coincides with the world coordinate system. When the turntable rotates by an angle... At that time, the transformation matrix of the turntable coordinate system relative to the global coordinate system For rotation matrix: ； The top probe coordinate system is fixed to the top probe optical center, and its position is subject to the gantry axis coordinate system. Control, the Z-axis direction is fixed as a constant Transformation matrix of the top probe coordinate system relative to the world coordinate system for: ； in, The rotation matrix for the mounting attitude of the top probe itself; For the top probe in X W Y W Position on the axis; The side probe coordinate system is fixed to the optical center of the side probe, and its position is subject to the gantry axis coordinate system. Control, in X W The axial direction is fixed as a constant Transformation matrix of the side probe coordinate system relative to the world coordinate system for: ； in, The rotation matrix for the installation posture of the side probe itself; For the side probe in Y W Z W Position on the axis; The homogeneous transformation matrix is , and .

4. The three-dimensional scanning modeling method based on kinematic cooperation and subgroup fuzzy ant colony as described in claim 3, characterized in that, In S2, the process of constructing the depth constraint is as follows: The effective working range of the scanning system is a finite frustum, or frustum. Let the effective measurement depth range of the scanning system be... , , These represent the minimum and maximum effective depth of field, respectively. For a side-mounted probe, in order to effectively acquire point P on the workpiece surface, the geometric containment condition, i.e., the depth constraint, must be met: ； In the formula, The origin of the side probe coordinate system; These are the local coordinates of a point on the workpiece surface. Indicates taking the vector in X W Length of the module in the axial direction.

5. The three-dimensional scanning modeling method based on kinematic cooperation and subgroup fuzzy ant colony as described in claim 2, characterized in that, In S3, obtaining the dynamic edge contour of the workpiece through the scanning system specifically involves controlling the top probe and the side probe to move to the safe limit position, driving the turntable to rotate 360°, and obtaining the binary contour image of the workpiece, i.e., the dynamic edge contour. Constructing a coarse visual shell model specifically involves initializing a three-dimensional voxel mesh surrounding the workpiece, for each voxel V... k The voxel is projected onto the contour image at various angles. If the projection point is outside the contour image, the voxel is removed. After multi-view cropping, the remaining voxels form a rough visual shell model of the workpiece. Mesh the surface of the rough visual shell model and compute the values ​​for each facet. normal vector Define the visibility function: ； ； In the formula, , These represent the visibility functions for the top probe and the side probe, respectively. Using the world coordinate system Z W Axial unit vector; World coordinate system X W -Y W The set of horizontally outward-pointing unit vectors in a plane; All satisfied and The set of facets constitutes the top probe task set T top ; All satisfied and The set of facets constitutes the side probe task set T side ; All satisfied and The set of facets forms the overlapping task set T overlap T overlap This refers to the overlapping area that requires scanning by both probes.

6. The three-dimensional scanning modeling method based on kinematic cooperation and subgroup fuzzy ant colony as described in claim 2, characterized in that, In S4, the nominal distance matrix is ​​constructed as follows: State nodes are the system state units corresponding to discretized scan task strips, and each state node carries the state parameters of the scan system, including... The probe's position coordinates and task assignment are defined, and the status node S is defined. i and S j The nominal distance C between them ij For time cost: ； In the formula, Axial switching penalty term; This represents the maximum angular velocity of the turntable. , , X W Y W Z W Maximum linear velocity of the shaft; The difference in turntable angle represents the difference from state node S. i To S j At that time, the turntable rotates around Z W The change in the rotation angle of the shaft; , , X W Y W Z W The difference in axis translation distance represents the distance from state node S. i To S j At that time, the probe was in X W Y W Z W The change in position of the axis.

7. The three-dimensional scanning modeling method based on kinematic cooperation and subgroup fuzzy ant colony as described in claim 2, characterized in that, In S5, the real-time axis position is fed back by the grating ruler and the encoder. As strong prior information, the world coordinates of the point cloud are calculated using forward kinematics solutions; where... The coordinates of the probe's real-time translational position in the world coordinate system; The kinematic closed-loop constraints are: The kinematic chain of the scanning system is a closed loop: the turntable rotates from 0° to 360° and then physically resets; therefore, the point cloud P in the 0° frame... start With the point cloud P in the 360° frame end Precisely coincident in the world coordinate system; Construct a pose graph where nodes represent the poses of each scan frame, edges represent the relative motion measurements of adjacent frames, and add closed-loop constraint edges, i.e., kinematic closed-loop constraints: ； In the formula, This refers to the closed-loop constraint error. The pose matrix for the 0° frame; This is the pose matrix for a 360° frame. Denotes the Frobenius norm; I is the identity matrix; The Levenberg-Marquardt algorithm is used to solve the nonlinear least squares problem of kinematic closed-loop constraints, and the closed-loop constraint error is evenly distributed across the full-circuit scan sequence.

8. The three-dimensional scanning modeling method based on kinematic cooperation and subgroup fuzzy ant colony as described in claim 1, characterized in that, In S6, the adaptive sampling strategy based on dynamic chord height error specifically defines the chord height error as the maximum distance from the line connecting the sampling points to the actual curved surface, and sets the maximum allowable chord height error as... ; For each point in the point cloud Calculate its local radius of curvature. , for Local curvature; Sampling step size and The relationship is as follows: 。 9. The three-dimensional scanning modeling method based on kinematic cooperation and subgroup fuzzy ant colony as described in claim 1, characterized in that, In step S6, generating the NURBS surface using a two-way curve fitting method includes: U-axis fitting: Fitting a B-spline curve along each laser scanning line; V-axis fitting: In the direction perpendicular to the laser scanning line, the corresponding points of each strip are connected to fit a B-spline curve; Mesh fusion: Constructing a tensor product NURBS surface, control points Determined by the weighted average of the control points of the U-direction and V-direction curves. A control point is a two-dimensional grid jointly determined by the u-th U-direction control point and the v-th V-direction control point, and is the basic unit for constructing the NURBS surface.

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