A Supportless Path Planning Method for Multi-Axis Additive Manufacturing Based on Orientation Field Constraints

Abstract

This invention provides a supportless path planning method for multi-axis additive manufacturing based on orientation field constraints, belonging to the field of additive manufacturing technology, specifically involving multi-axis 3D printing, non-planar slicing, nozzle attitude planning, orientation field optimization control, and multi-axis mechanism inverse kinematics verification. This invention constructs an initial orientation field; it integrates overhang angle exceeding limits, orientation field smoothing, surface fitting, and mechanism accessibility into a unified energy function of multiple constraints. An optimized orientation field satisfying printability and path continuity is obtained through iterative updating of the orientation field. During the orientation field iteration process, the multi-axis mechanism inverse kinematics verification results are fed back to the orientation field update process, and the mechanism accessibility constraint weights are adjusted according to unreachable points. This addresses the problems of high support dependence in overhang areas, difficulty in guaranteeing surface fitting quality, discontinuous nozzle attitude changes, and repetitive planning caused by post-hoc verification of mechanism accessibility in multi-axis additive manufacturing of complex curved parts and large overhang structures.

Description

Technical Field

[0001] This invention belongs to the field of additive manufacturing technology, and in particular relates to a supportless path planning method for multi-axis additive manufacturing based on orientation field constraints. Background Technology

[0002] Additive manufacturing typically generates sliced ​​layers, path points, and equipment control commands based on a 3D model. Traditional triaxial additive manufacturing methods, such as fused deposition modeling (FDM) and material extrusion, generally employ a fixed build-up direction, stacking material layer by layer, with the nozzle posture remaining constant or only undergoing in-plane movement during printing. While these methods are simple to control and have mature processes, when the part has large overhangs, concave structures, free-form surfaces, or areas with significant local curvature changes, fixed-direction layer-by-layer stacking can easily result in material deposition sections without effective support underneath, thus usually requiring additional support structures. Support structures increase material consumption, printing time, and post-processing workload, and may cause surface scratches, residues, or dimensional errors during support removal.

[0003] To reduce the need for supporting structures, existing technologies include multi-axis additive manufacturing, non-planar slicing, and vector field slicing. Multi-axis additive manufacturing equipment typically uses a rotating stage, serial robotic arms, parallel mechanisms, or other multi-degree-of-freedom motion platforms to change the relative posture between the nozzle and the workpiece, allowing the material deposition direction to be locally adjusted according to the part's geometry. Non-planar slicing methods are no longer limited to horizontal planes but attempt to generate curved layers or variable-height paths that better match the surface contour, reducing the staircase effect and improving the surface quality of freeform surfaces. Vector field or direction field-guided path planning methods typically establish direction vectors within the model or on the surface to guide the slice layer normal, material deposition direction, or path orientation.

[0004] The closest existing solutions to this invention mainly include: overhang detection and support generation schemes in traditional triaxial slicing software, ordinary multiaxial normal-following printing schemes, non-planar slicing or vector field slicing schemes, and a posteriori mechanism accessibility verification schemes. These solutions can solve local problems individually, but for multiaxial additive manufacturing path planning of complex curved surface parts, the actual problem is not simply geometric fit or overhang detection, but rather the interrelationship between overhang control, directional continuity, surface fit, and mechanism accessibility. The disadvantages of the above-mentioned prior art are as follows: 1. Overhang handling methods are biased towards posterior time. Traditional three-axis slicing or partially multi-axis path planning methods typically generate the path first, and then detect overhang areas or add supports. This is because the planning variables are mainly the layer height and path profile, the printing direction is usually fixed in advance or directly given by the local normal, and the overhang angle is not used as an active penalty term in the iterative optimization of the orientation field.

[0005] 2. The initial direction of the overhanging region lacks support logic. Common multi-axis normal-following methods often use the local curved surface normal as the nozzle direction, but overhang formation essentially requires consideration of whether there is an effective support reference surface below the current deposition point. If the initial direction only originates from the local normal without establishing a connection with the support point, it may result in a deposition direction that formally conforms to the curved surface but is actually unsupportable.

[0006] 3. Insufficient attitude continuity. Complex surfaces exhibit drastic local normal changes. If nozzle attitude is generated point-by-point, attitude angles between adjacent path points may abruptly change. This is because existing methods typically lack global smoothing constraints on differences in adjacent direction vectors, angular velocities, angular accelerations, or interpolation continuity.

[0007] 4. Lack of unified coordination between surface fitting, unsupported constraints, and mechanism accessibility. Existing solutions often handle one type of constraint separately, such as performing surface fitting first and then accessibility verification, or performing suspension judgment first and then manually adjusting the attitude, lacking a unified directional field energy function and weight feedback mechanism.

[0008] 5. Mechanism accessibility is often handled post-processing. Multi-axis equipment has physical limitations such as joint angle range, drive rod stroke, nozzle tilt angle, platform attitude, and collision space. Post-hoc verification only discovers unreachable points after path generation is complete because the path planning algorithm and the mechanism's inverse kinematics model are independent, and mechanism constraints are not fed back to the orientation field update stage. Summary of the Invention

[0009] To address the aforementioned shortcomings in existing technologies, this invention provides a supportless path planning method for multi-axis additive manufacturing based on directional field constraints. This method solves the problems of high support dependence in the overhang region, difficulty in ensuring the quality of surface fitting, discontinuous nozzle attitude changes, and repetitive planning caused by post-validation of mechanism accessibility in the multi-axis additive manufacturing process of complex curved parts and large overhang structures.

[0010] To achieve the above objectives, the technical solution adopted by this invention is: a supportless path planning method for multi-axis additive manufacturing based on orientation field constraints, comprising the following steps: S1. Input the 3D model to be printed, process the 3D model to be printed, and construct the initial orientation field associated with the supporting reference surface, the surface normal and the construction direction according to the regional classification mechanism of overhang risk area, surface quality sensitive area and ordinary area. S2. Using the direction field vector as the local material deposition direction or nozzle axis direction in the multi-axis additive manufacturing process, the overhang angle exceeding the limit, direction field smoothing, surface fitting, and mechanism accessibility are uniformly introduced into the multi-constraint energy function. Based on the multi-constraint energy function, the direction field is iteratively updated to obtain an optimized direction field that reduces or eliminates support dependence and satisfies path continuity. After each direction field update, the current direction field is converted into a temporary nozzle attitude sequence and input into the mechanism inverse kinematics model of the multi-axis additive manufacturing equipment for accessibility verification and attitude continuity verification. If there are unreachable path points or abrupt attitude change path segments, the corresponding weights in the multi-constraint energy function are adjusted according to the verification results, and the direction field is iteratively updated. S3. When the optimized orientation field satisfies the attitude continuity condition, reachability condition, and convergence condition, a non-planar unsupported path is generated based on the optimized orientation field. The nozzle attitude sequence and extrusion compensation parameters corresponding to the non-planar unsupported path are determined. An enhanced multi-axis printing command containing spatial coordinates, nozzle attitude angle, and extrusion amount is output to complete the planning of the multi-axis additive manufacturing unsupported path.

[0011] The beneficial effects of this invention are as follows: This invention establishes a regional classification mechanism for overhang risk areas, surface quality sensitive areas, and ordinary areas, and constructs initial orientation fields associated with the support reference surface, surface normal, and construction direction, respectively. Overhang angle exceeding limits, orientation field smoothing, surface fitting, and mechanism accessibility are uniformly introduced into the multi-constraint energy function. An optimized orientation field satisfying printability and path continuity is obtained through iterative updating of the orientation field. During the orientation field iteration process, this invention does not perform a separate mechanism accessibility screening after path generation. Instead, it feeds back the multi-axis mechanism inverse kinematics verification results to the orientation field update process and adjusts the mechanism accessibility constraint weights according to unreachable points. This reduces support dependence and improves surface forming quality while minimizing unreachable attitude points and redundant planning processes, ultimately generating non-planar paths, nozzle attitude sequences, extrusion compensation commands, and enhanced multi-axis printing commands. This invention has at least the following effects: 1) Using the direction field As the core variable for multi-axis additive manufacturing path planning, it unifies region classification, orientation field iteration, nozzle attitude generation, mechanism inverse motion verification, and non-planar path output into the same process, thereby achieving collaborative planning of printing direction and equipment execution capability.

[0012] 2) Initial orientation fields are constructed for the overhang risk region, the surface quality sensitive region, and the ordinary region, respectively; among them, the overhang risk region is constructed by searching for support points on the support reference surface. and according to Generate an initial orientation to avoid unsupportable deposition caused by simply using local surface normals.

[0013] 3) Introduce the overhang angle constraint, direction field smoothing constraint, mechanism reachability constraint, and surface fitting constraint into the comprehensive multi-constraint energy function. It coordinates suspension control, attitude continuity, surface fitting, and mechanism accessibility through iterative updates of the orientation field.

[0014] 4) After each orientation field update, the orientation field is converted into nozzle attitude angles and input into the multi-axis mechanism inverse kinematics model to calculate the driving variables; if there are unreachable path points, the accessibility constraint weights of the mechanism are adjusted and the orientation field is returned for iterative update to form a closed-loop feedback mechanism.

[0015] 5) Dynamically adjust the weights of each constraint based on the overhang ratio, attitude change ratio, and unreachable point ratio, and perform normalization processing so that the optimization priority of different constraints can adapt to the planning results.

[0016] 6) Insert intermediate path points into path segments where the attitude continuity does not meet the requirements, and smooth the nozzle attitude sequence to reduce attitude abrupt changes between adjacent path points.

[0017] 7) Based on the optimized direction field Output non-planar paths, nozzle attitude sequences, extrusion volume compensation parameters, and enhanced multi-axis printing commands. This allows the path results to be directly used for execution in multi-axis additive manufacturing equipment. Attached Figure Description

[0018] Figure 1 This is a flowchart of the method of the present invention.

[0019] Figure 2 A flowchart for constructing the region classification and initial orientation field is provided.

[0020] Figure 3 Flowchart for iterative update of multi-constraint direction fields.

[0021] Figure 4 A flowchart for the verification and feedback process of the institution's reverse motion school. Detailed Implementation

[0022] The specific embodiments of the present invention are described below to enable those skilled in the art to understand the present invention. However, it should be understood that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, various changes are obvious as long as they are within the spirit and scope of the present invention as defined and determined by the appended claims. All inventions utilizing the concept of the present invention are protected.

[0023] Example For complex curved parts, large overhang structures, and areas with drastic changes in normal direction, traditional triaxial layer-by-layer printing and ordinary multiaxial normal-following path planning methods struggle to simultaneously meet the requirements of reducing support requirements, maintaining surface fit quality, ensuring nozzle attitude continuity, and satisfying the physical executability of multiaxial mechanisms. This results in high support material consumption, complex post-processing, abrupt changes in path attitude, local path unreachability, or the need for repeated replanning. To address this, this invention proposes a supportless path planning method for multiaxial additive manufacturing based on orientation field constraints. Through region classification, an initial orientation field associated with a supporting reference surface, multi-constraint energy functions, weighted adaptive feedback, and inverse motion verification closed loops, it generates non-planar paths and enhanced printing instructions executable by multiaxial additive manufacturing equipment.

[0024] This invention takes a 3D model as input and combines 3D model preprocessing, region classification, initial orientation field construction, multi-constraint orientation field iteration, inverse kinematics feedback, non-planar path generation, and enhanced command output into a complete technical process. Orientation field It is a set of unit vectors defined on sampling points, path points, voxel mesh points, or other discrete units on the model surface, used to characterize the local printing direction or nozzle axis direction. The overall process includes: inputting a 3D model; calculating normals, curvature, and adjacency relationships; classifying regions based on overhang angles, curvature, and normal change rates; constructing initial direction fields for ordinary regions, surface quality-sensitive regions, and overhang risk regions respectively; establishing a multi-constraint energy function and iteratively updating the direction field; after each update, converting the direction field into a temporary nozzle attitude sequence and performing inverse kinematics verification; if there are unreachable points, adjusting the corresponding weights in the multi-constraint energy function and returning to the direction field update; if the reachability and convergence conditions are met, generating non-planar paths, nozzle attitudes, extrusion compensation, and enhanced multi-axis printing instructions.

[0025] like Figure 1 As shown, this invention provides a supportless path planning method for multi-axis additive manufacturing based on direction field constraints, the implementation of which is as follows: S1. Input the 3D model to be printed, perform meshing or sampling processing on the 3D model to be printed, obtain triangular mesh, patch normals, curvature, adjacency relations, and discrete sampling units used to characterize the model's solid domain or surface; and construct initial orientation fields associated with the supporting reference surface, surface normals, and construction direction respectively, based on the region classification mechanism of overhang risk area, surface quality sensitive area, and ordinary area. S101. Input the 3D model to be printed, and perform meshing processing on the 3D model to be printed so that the 3D model to be printed is represented as a triangular mesh M=(V,E,F), where V represents the set of vertices, E represents the set of edges, and F represents the set of triangular faces. S102, Construct a unit vector with reverse direction and for the firstf Each patch or sampling unit defines the overhang angle. :

[0026] in, Indicates the outward normal direction; S103, when the hanging angle Greater than the critical overhang angle At that time, the first f Each area or sampling unit is identified as a hanging risk area. ; S104, Definition of the f Average curvature of a patch or sampling unit :

[0027] in, and Indicates the first f The local principal curvature of each surface patch; S105, when Exceeding the curvature threshold , or the f The variance of the normal angle between a facet and its neighboring faces Exceeding the preset threshold At that time, the first f Each patch or sampling unit, along with its adjacent patches, forms a local region defined as a surface quality-sensitive region. ; S106 will not be considered a hanging risk area. It also does not belong to the surface quality sensitive area. The area, sampling unit, or local region is divided into ordinary regions. Among them, when a certain patch or sampling unit simultaneously meets the requirements of the overhang risk area and surface quality sensitive areas When conditions are met, areas should be prioritized for designation as hanging risk zones. ; S107, For ordinary areas Unit vector in the reverse direction of construction Constructing the initial direction field :

[0028] S108. For areas sensitive to surface quality Construct the initial direction field according to the surface normal. Among them, when the nozzle tilt angle corresponding to the surface normal exceeds the maximum allowable tilt angle of the mechanism. At that time, the direction is truncated to the maximum operable tilt angle. Indicates the direction truncation function; S109. For areas with hanging risks The support point is obtained by searching the substrate, the previously determined reference surface of the previous layer, or the support reference surface in reverse along the construction direction. And based on the support point Construct the initial direction field ,in, Indicates the first i One path point or sampling point to be printed. This represents a vector normalization function that converts the vector within the parentheses into a unit direction vector.

[0029] S2. Using the orientation field vector as the local material deposition direction or nozzle axis direction in the multi-axis additive manufacturing process, the overhang angle exceeding the limit, orientation field smoothing, surface fitting, and mechanism accessibility are uniformly introduced into the multi-constraint energy function. The orientation field is iteratively updated based on the multi-constraint energy function to obtain an optimized orientation field that reduces or eliminates support dependence and satisfies path continuity. After each orientation field update, the current orientation field is converted into a temporary nozzle attitude sequence and input into the mechanism inverse kinematics model of the multi-axis additive manufacturing equipment for accessibility verification and attitude continuity verification. If there are unreachable path points, abrupt attitude change path segments, or collision interference risks, the corresponding weights in the multi-constraint energy function are adjusted according to the verification results, and the orientation field is returned for iterative update.

[0030] In this embodiment, after each round of orientation field iteration update, the weighting coefficients are adjusted according to the overhang exceeding limit, attitude change, and mechanism inaccessibility, including: Overhang ratio attitude change ratio and unreachable point ratio Define; When the overhang exceeds the limit ratio Greater than the first preset threshold When this is done, increase the weight of the overhang angle constraint term. When the attitude change ratio Greater than the second preset threshold At that time, increase the weight of the direction field smoothing constraint term. When the proportion of unreachable points When the value is greater than 0, increase the weight of the mechanism's reachability constraint term. And reduce the weight of the surface fitting constraint term. The updated and normalized weights are obtained. .

[0031] In this embodiment, the current orientation field is converted into a temporary nozzle attitude sequence and input into the inverse kinematics model of the multi-axis additive manufacturing equipment for reachability verification and attitude continuity verification, including: A1. Let the optimized direction field vector be... In a fixed global coordinate system, the direction field vector Converted into temporary nozzle attitude angles around the X and Y axes and ; A2, the first Spatial coordinates of the path points to be printed and nozzle attitude angle Input the inverse kinematics model of the multi-axis mechanism of the multi-axis additive manufacturing equipment, and calculate the multi-axis mechanism drive element variables at the corresponding path points; wherein, the inverse kinematics model of the multi-axis mechanism is expressed as:

[0032] in, Indicates the first The set of multi-axis mechanism drive unit variables at each path point to be printed. Indicates the first The driving variables of the k-th multi-axis mechanism drive unit at each of the path points to be printed. Indicates the total number of drive units in a multi-axis mechanism. Represents the inverse kinematics mapping function of a multi-axis mechanism. This represents the set of structural parameters for a multi-axis mechanism. A3. Determine whether the variables of the multi-axis mechanism drive unit meet the physical range of the mechanism; if they do, proceed to A4; if they do not, mark the corresponding path point to be printed as an unreachable path point, count the proportion of unreachable path points, and feed the proportion of unreachable path points as the mechanism reachability verification result back to the direction field iteration update step S2; the physical range of the mechanism includes the upper and lower limits of the stroke or joint angle of each drive unit of the multi-axis mechanism, the allowable tilt angle range of the nozzle, the workspace boundary, and the preset collision or interference safety distance; A4. Determine whether the attitude continuity of the current temporary nozzle attitude sequence meets the requirements. If it does, output the mechanism reachability verification result and attitude continuity verification result of the current temporary nozzle attitude sequence, and feed the verification result back to the orientation field iterative update step S2 to determine whether the current orientation field meets the reachability condition, attitude continuity condition and convergence condition. If it does not meet the requirements, proceed to A5. A5. Nozzle attitude angle based on adjacent print path points and Calculate the attitude change between adjacent path points to be printed; A6. Calculate adjacent path points to be printed. and The maximum allowable single-step attitude change between calculations and ; A7, when or When printing, insert intermediate path points between adjacent path points to be printed; A8. For the inserted intermediate path points, use interpolation to generate intermediate attitude sequences, smooth the intermediate attitude sequences, and return to A4 to re-evaluate attitude continuity.

[0033] In this embodiment, as Figure 2 As shown, the input 3D model to be printed can be STL, OBJ, STEP, or other data formats that can be converted to triangular meshes. First, the 3D model to be printed undergoes mesh repair, hole filling, normalization, redundant facet removal, and necessary scale normalization. The 3D model to be printed is represented as a triangular mesh M=(V,E,F), where V represents the vertex set, E represents the edge set, and F represents the triangular facet set. For each facet and sampling unit... f Calculate spatial location External normal direction curvature and adjacency .

[0034] Let the unit vector in the opposite direction of the construction direction be... Direction opposite unit vector It can be aligned with the direction of gravity, or it can be a user-specified main printing direction. For the... f Each patch or sampling unit defines the overhang angle. for:

[0035] When the overhang angle Greater than the critical overhang angle At that time, the area or sampling unit is identified as a hanging risk area. Critical overhang angle The angle can be set according to the material flowability, curing speed, nozzle diameter and layer height, and the common range is 35° to 60°.

[0036] For regions sensitive to surface quality, the mean curvature is defined. for: ; when Exceeding the curvature threshold or variance of the included angle between the normals of adjacent facets Exceeding the preset threshold At that time, the first fEach patch or sampling unit, along with its adjacent patches, forms a local region defined as a surface quality-sensitive region. Variance of the included angle between the normals of adjacent facets It can be represented as:

[0037]

[0038] in, j Indicates the adjacent face index. Indicates the first f The unit outward normal of a surface patch Indicates the first j The outward normal of an adjacent face Indicates the first f The average value of the normal angle between a facet and its adjacent faces. Indicates the first f The set of adjacent faces of a face, where |N(f)| represents the number of adjacent faces.

[0039] It does not belong to the hanging risk area It also does not belong to the surface quality sensitive area. The area is divided into ordinary areas. When a surface simultaneously meets the conditions for both a sag risk region and a surface quality sensitive region, it is preferentially designated as a sag risk region. This ensures that printability constraints take precedence over surface fit constraints.

[0040] For ordinary areas The initial direction field vector can be taken as the unit vector in the opposite direction of the construction direction. ,Right now:

[0041] Sensitive areas for surface quality The initial direction field vector can be associated with the surface normal. When the nozzle tilt angle corresponding to the normal exceeds the maximum allowable tilt angle of the mechanism... In this case, the direction can be truncated to the maximum executable tilt angle to avoid generating a significantly unreachable attitude during the initialization phase:

[0042] in, This indicates the direction truncation function.

[0043] For hanging risk areas The initial orientation field does not directly use the local surface normal, but is associated with the support point on the support reference surface. Specifically, for the path point or sampling point to be printed... Ray projection is performed in the reverse direction of the construction to search for the set of intersection points with the bottom support surface of the model, the preset substrate plane, the previously generated reference surface of the previous layer, or the previous layer isosurface obtained by the field reconstruction method. If multiple intersection points exist, prioritize those that meet the path time sequence requirements and are closest to the path point to be printed or the sampling point. The nearest point where the initial direction and the local normal deviation are minimized is used as the support point. :

[0044] in, Indicates the first i One path point or sampling point to be printed. Indicates the point to be printed. The corresponding set of candidate support points , and All represent non-negative weight parameters. Represents any candidate support point in the set of candidate support points. The distance normalization scale can be represented by nozzle diameter, layer height, local neighborhood scale, or the maximum distance between candidate points. This represents a time-order penalty term used to avoid using geometry that has not yet been printed or is located after the current layer as a supporting reference. As one possible implementation, the weight parameters can be a=1, b=0.5, and c=0.2.

[0045] Time sequence penalty item The settings can be configured as follows: For candidate points on the substrate, bottom support surface, or the previously generated reference surface, set T(P) = 0; for candidate points on reference layers that conflict with the current layer's time sequence, have not yet been generated, or are located after the current layer, set a larger value, such as T(P) = 10, or directly select from the candidate set. The above values ​​are preferred embodiments and can be adjusted according to model complexity, layer thickness, nozzle diameter, and process requirements.

[0046]

[0047] in, Indicates the first i One path point or sampling point to be printed. This represents the vector normalization function.

[0048] If no valid support reference intersection point is found, the initial direction of the sampling point is set to a conservative direction towards the interior of the model entity or towards the construction direction, and corrected in subsequent direction field iterations by increasing the weight of the overhang angle constraint term. If a reachable path still cannot be generated after reaching the maximum number of iterations, an auxiliary support addition prompt or a model attitude adjustment prompt is output. This process avoids misrepresenting structures that have not yet been printed as already formed geometry and ensures that the path planning process conforms to the interlayer support logic of actual additive manufacturing.

[0049] In this embodiment, as Figure 3 As shown, the present invention establishes an energy function that includes at least a sag angle constraint, a smoothness constraint, and a mechanism reachability constraint. In a preferred embodiment, a surface fitting constraint is further included. The combined multi-constraint energy function... for:

[0050] in, , , and All represent non-negative weight coefficients, and satisfy the following conditions: D represents the set of direction field vectors.

[0051] As a feasible initial setting, the initial weights of the synthesis energy function can be chosen as follows: =0.4、 =0.3、 =0.2、 =0.1, and satisfy .in, Corresponding to the overhang angle constraint Corresponding to smoothing constraints, Corresponding surface fitting constraints. Accessibility constraints of the corresponding institution. When the printing material has poor flowability or the risk of overhanging is high, it can be improved. When the multi-axis mechanism has a narrow motion range, limited drive stroke, or strict requirements for attitude reachability, it can improve... The above initial values ​​are preferred embodiments and can be adjusted according to material properties, equipment performance, and part geometric complexity.

[0052] The overhang angle constraint term is used to penalize cases where the equivalent overhang angle caused by the direction field exceeds the critical angle, and can be defined as:

[0053] The smoothing constraint term is used to reduce abrupt changes in direction between adjacent path points or adjacent sampling points, and can be defined as:

[0054] in, This represents the adjacency weight, which can be set based on the distance between points, topological adjacency relationships, or curvature differences. As a preferred method, , where σ represents the neighborhood scale parameter.

[0055] The surface fitting constraint term is used to improve the path fitting performance in complex surface regions and can be defined as follows:

[0056] in, η can be set according to the curvature range and surface quality requirements. This item has a higher weight in areas sensitive to surface quality, ensuring that the nozzle direction remains as related to the surface normal as possible while meeting overhang and mechanism constraints.

[0057] The mechanism reachability constraint term penalizes situations where the driving variables obtained from nozzle attitude transformation exceed physical upper and lower limits. Taking a multi-axis mechanism with K driving units as an example, it can be defined as:

[0058] in, Represents the multi-constraint energy function. , , and Each represents a non-negative weight coefficient for each constraint term, and satisfies... D represents the set of direction field vectors. This indicates that the overhang angle exceeds the constraint. This indicates a direction field smoothing constraint. This indicates a surface fitting constraint. This indicates institutional accessibility constraints. f Indicates the first f A piece of dough, Indicates the area of ​​hanging risk. Indicates the area sensitive to surface quality. Indicates the first f The direction field vector at each surface patch Indicates a unit vector in the opposite direction. and This represents the index of an adjacent face or adjacent sampled cell, where A represents the set of adjacent pairs. Indicates the adjacency weight. and These represent the nth adjacency pair (u,v) in the adjacency pair. The direction field vectors at the vth and vth facets Indicates the curvature-related weights. Indicates the curvature weighting coefficient. Indicates outward normal direction. Indicates the mean curvature. iIndicates the index of the path point to be printed. This indicates the total number of path points to be printed, k represents the multi-axis mechanism drive unit index, and K represents the total number of multi-axis mechanism drive units. Indicates the first i The driving variables of the k-th multi-axis mechanism drive unit at each of the path points to be printed. and Let these represent the upper and lower physical limits of the k-th multi-axis mechanism drive unit, respectively. This represents the reachability penalty weight of the k-th multi-axis mechanism drive unit.

[0059] The initial value of the direction field vector is taken as follows: Iterative updates can employ gradient descent, Gauss-Newton method, quasi-Newton method, or other conventional numerical optimization algorithms. As one possible implementation, updates can be performed using the following formula:

[0060] in, t Indicates the number of iterations. Indicates the step size. This indicates that the field vector in each direction is normalized. When the change in the energy function between two consecutive iterations is less than a threshold... or reaching the maximum number of iterations. Stop iterating when the time is right.

[0061] In this embodiment, the weighted adaptive feedback mechanism is as follows: To address the conflict between overhang control, surface fitting, attitude continuity, and mechanism accessibility, this invention introduces a weighted adaptive feedback mechanism. After each round of orientation field iteration update, the weight coefficients are adjusted based on overhang exceeding limits, attitude changes, and mechanism inaccessibility.

[0062] Define the overhang ratio attitude change ratio and unreachable point ratio They are respectively:

[0063] in, This indicates the number of sampling points in the overhang risk area where the equivalent overhang angle exceeds the critical overhang angle or the sum of the critical overhang angle and the preset margin. This represents the total number of sampling points involved in the assessment within the overhang risk area. This indicates the number of point pairs where the attitude change between adjacent printed path points or adjacent sampling points exceeds a preset attitude change threshold. This represents the total number of adjacent point pairs involved in the attitude continuity determination. This indicates the number of path points that are determined to be unreachable after the inverse motion test of the multi-axis mechanism. This represents the total number of path points participating in the accessibility verification of the participating institutions; When the overhang exceeds the limit ratio Greater than the first preset threshold When this is done, increase the weight of the overhang angle constraint term. When the attitude change ratio Greater than the second preset threshold At that time, increase the weight of the direction field smoothing constraint term. When the proportion of unreachable points When the value is greater than 0, increase the weight of the mechanism's reachability constraint term. This can correspondingly reduce the weight of the surface fitting constraint term. After the weights are updated, normalization is performed:

[0064] in, This indicates the adjusted weights of each constraint term, which, after normalization, satisfy the following: , Indicates the constraint weight index. This represents the constraint weight index in the normalization summation process, j=1,2,3,4.

[0065] This normalization process is used to prevent a single weight from increasing indefinitely or to avoid imbalance in the optimization process. First preset threshold. Second preset threshold Both the sag angle margin and the attitude change margin can be set according to the material, equipment, and quality requirements.

[0066] Furthermore, each weight adjustment can be performed using a proportional update method. When the overhang exceeds the limit... Exceeding the first preset threshold season When the attitude change ratio Exceeding the second preset threshold season When the proportion of unreachable points When it is greater than 0, let .in , , It can be between 0.10 and 0.20, for example, 0.15.

[0067] If the proportion of inaccessible points is high and the surface fitting constraints conflict with the mechanism's accessibility constraints, then... ,in A value between 0.05 and 0.15 is acceptable. If multiple weights are being adjusted simultaneously, update their respective proportions first, then execute the algorithm. The normalization process is applied to maintain the sum of all weights at 1 and ensure the stability of the optimization process. The above adjustment range is the preferred implementation parameter and can be set according to the device's response capability and path complexity.

[0068] In this embodiment, as Figure 4 As shown, let the optimized direction field vector be... In a fixed global coordinate system, this can be converted into temporary nozzle attitude angles around the X and Y axes. , :

[0069]

[0070] Here, ε represents a very small positive number, used to avoid numerical instability when the denominator is close to zero. When the attitude angle exceeds the allowable range of the mechanism, the path point to be printed is marked as unreachable, and the inverse kinematics feedback step is initiated.

[0071] For adjacent path points to be printed i -1 and i Define attitude change , ,in, Indicates attitude angle Adjacent attitude angles, Indicates attitude angle Adjacent attitude angles.

[0072] Let the maximum angular velocities of the multi-axis mechanism in the corresponding attitude directions be respectively and The estimated motion time between adjacent path points to be printed is Then the maximum allowable single-step attitude change can be set as: ,

[0073] when or When interpolating between adjacent path points, an intermediate point is inserted. The number of points to insert can be determined using the following formula:

[0074] in, This indicates rounding up. For inserted intermediate path points, linear interpolation, spherical linear interpolation, or fifth-order polynomial interpolation can be used to generate intermediate attitude sequences. When it is necessary to ensure the continuity of spatial position simultaneously, spatial coordinates and nozzle attitude can be interpolated synchronously. This processing is used to limit single-step attitude changes and reduce mechanical shock, speed fluctuations, and path tracking errors during the execution of multi-axis mechanisms.

[0075] This invention is applicable to various multi-axis additive manufacturing equipment, including but not limited to 3-RPS parallel mechanisms, serial robotic arms, and rotary table-type five-axis printing platforms. The following uses a 3-RPS parallel mechanism as an example to illustrate the inverse motion verification method. Let the hinge point of the stationary platform be... The hinge point of the moving platform in the local coordinate system is The central position of the moving platform is The attitude rotation matrix is A rotation matrix in XY order around a fixed axis can be used. :

[0076] in, Indicates rotation about the X-axis of a fixed global coordinate system The rotation matrix of the angle. Indicates rotation about the Y-axis of a fixed global coordinate system The rotation matrix of the angle.

[0077] No. i The first path point to be printed k Position of the hinge point of the individual platform in the global coordinate system for:

[0078] Drive rod length for:

[0079] If the length of any drive rod Not belonging to If an unreachable path point is found, it is determined to be unreachable. If an unreachable path point exists, the weight coefficients corresponding to the mechanism reachability constraint terms in the multi-constraint energy function are increased, and all weight coefficients are normalized before returning to the orientation field iteration update step. If an unreachable path point still exists after N consecutive iterations, an auxiliary support addition prompt or a model attitude adjustment prompt is output, where N is a preset positive integer, preferably 3 to 5.

[0080] S3. When the optimized orientation field satisfies the attitude continuity condition, reachability condition, and convergence condition, a non-planar unsupported path is generated based on the optimized orientation field. The nozzle attitude sequence and extrusion amount compensation parameters corresponding to the non-planar unsupported path are determined, and an enhanced multi-axis printing command containing spatial coordinates, nozzle attitude angle, and extrusion amount is output to complete the planning of the multi-axis additive manufacturing unsupported path. The implementation method is as follows: B1. Interpolate the optimized orientation field that satisfies the attitude continuity condition, accessibility condition and convergence condition to the entity domain of the 3D model to be printed or the surface sampling point of the 3D model to be printed, and generate a non-planar unsupported path by the path projection method or the field reconstruction method. B2. Generate the final nozzle attitude sequence corresponding to the non-planar unsupported path based on the path point coordinates and optimized direction field on the non-planar unsupported path; B3. Perform a pre-output check on the final nozzle attitude sequence. The pre-output check includes mechanism accessibility verification, attitude continuity verification, and collision or interference verification. If the final nozzle attitude sequence meets the pre-output check requirements, proceed to B4. If there are unreachable path points, abrupt attitude change path segments, or collision or interference risks, the corresponding path points or path segments to be printed are fed back to S2 for orientation field weight adjustment, or returned to B1 for resampling, smoothing, or local adjustment of non-planar unsupported paths. B4. Calculate the extrusion compensation parameters based on the nozzle tip composite velocity, reference velocity, and nozzle attitude angle. :

[0081] in, Indicates the baseline extrusion amount. Indicates the synthesis velocity at the nozzle tip. Indicates the baseline printing speed. and These represent the tilt compensation coefficients for the attitude angles around the X and Y axes, respectively. and All indicate the first i The nozzle attitude angle at each point on the path to be printed; B5. Based on extrusion rate compensation parameters Output enhanced multi-axis printing commands ,in, , and Indicates the first i The spatial coordinates of the path points to be printed.

[0082] In this embodiment, the present invention can generate non-planar unsupported paths using either path projection or field reconstruction methods. The path projection method includes: first, performing conventional horizontal slicing to obtain initial contour points; then, projecting the contour points along the opposite direction of the optimized orientation field onto the previous layer reference surface, substrate plane, or supporting reference surface; next, adjusting the height of the path points to be printed based on the projection results, and resampling, smoothing, and sorting the paths to be printed to generate non-planar unsupported paths. This method is simple to implement and suitable for path modification guided by orientation field based on existing slicing results.

[0083] The field reconstruction method includes: interpolating the optimized orientation field to a voxel grid, calculating the divergence on the voxel grid using a finite difference scheme, and solving the Poisson equation associated with the orientation field to obtain the scalar field. :

[0084] The isosurface S = k·Δh is extracted as the k-th non-planar layer, where Δh represents the average layer height. After extracting the boundary contour of the isosurface, an equidistant offset fill or zigzag continuous connection method can be used to generate the fill path, resulting in a non-planar unsupported path. For non-planar layers with large curvature, local resampling and collision detection can be performed to avoid path self-intersection or exceeding the model boundary.

[0085] In this embodiment, before the final nozzle attitude sequence is output, the nozzle, moving platform, printed part, frame, and wire feeding pipeline can be checked for accessibility, attitude continuity, and collision or interference. The wire feeding pipeline can be simplified into several straight segments, arc segments, or cylindrical segments. At each point on the printing path, the minimum distance between the simplified segment and the workpiece triangular mesh, frame bounding box, or motion chain is calculated based on the nozzle attitude angle and the fixed point position of the wire feeding pipeline. If this distance is less than a preset safety distance, interference is determined to exist, and direction field or path adjustment is triggered.

[0086] Because the nozzle attitude and nozzle tip combining speed change during multi-axis printing, the extrusion amount can be compensated based on the nozzle tip combining speed, reference speed, and attitude angle. As an optional implementation, the extrusion amount... It can be calculated using the following formula:

[0087] in, and It can be set according to the material rheological properties and nozzle structure.

[0088] Once all pathpoints to be printed satisfy reachability, attitude continuity, and collision constraints, an enhanced multi-axis printing command is output. Each pathpoint to be printed may include... ,in, , and Indicates the first The spatial coordinates of the path points to be printed. and Indicates the first The nozzle attitude angle at each point on the path to be printed. Indicates the first The extrusion amount compensation parameters at each point on the printing path. This instruction can be parsed by the controller and converted into motor motion instructions, extruder instructions, and multi-axis synchronous interpolation instructions.

[0089] In summary, this invention proactively reduces the risk of overhang exceeding limits during the path generation stage by setting overhang angle constraints and introducing support point search in overhang risk areas, thus reducing reliance on additional support structures. By setting surface fitting constraints and curvature-related weights, it maintains the correlation between the orientation field and the surface normal while satisfying overhang control and mechanism accessibility, improving path fitting quality in complex curved surface regions. Through orientation field smoothing constraints and attitude interpolation correction mechanisms, it reduces abrupt changes in orientation and attitude angle between adjacent path points, minimizing mechanical shock, speed fluctuations, and path tracking errors during multi-axis mechanism execution. Furthermore, by inverting the multi-axis mechanism... The kinematics calibration results are fed back to the orientation field iteration stage to identify and correct unreachable attitude points before path output, reducing repetitive planning and manual adjustments after path generation. Through weighted adaptive feedback and normalization mechanisms, the relationship between suspension control, surface fitting, attitude continuity, and mechanism accessibility is coordinated, improving the stability of orientation field optimization under multiple constraints. By outputting enhanced multi-axis printing commands that include spatial coordinates, nozzle attitude angles, and extrusion amounts, the convenience of synchronous interpolation and actual printing execution by the multi-axis controller is improved. By setting the inverse kinematics calibration module as a replaceable mechanism model, this invention can be applied to various multi-axis additive manufacturing equipment such as 3-RPS parallel mechanisms, serial robotic arms, and rotary table-type five-axis printing platforms.

Claims

1. A supportless path planning method for multi-axis additive manufacturing based on orientation field constraints, characterized in that, Includes the following steps: S1. Input the 3D model to be printed, process the 3D model to be printed, and construct the initial orientation field associated with the supporting reference surface, the surface normal and the construction direction according to the regional classification mechanism of overhang risk area, surface quality sensitive area and ordinary area. S2. Using the direction field vector as the local material deposition direction or nozzle axis direction in the multi-axis additive manufacturing process, the overhang angle exceeding the limit, direction field smoothing, surface fitting, and mechanism accessibility are uniformly introduced into the multi-constraint energy function. Based on the multi-constraint energy function, the direction field is iteratively updated to obtain an optimized direction field that reduces or eliminates support dependence and satisfies path continuity. After each direction field update, the current direction field is converted into a temporary nozzle attitude sequence and input into the mechanism inverse kinematics model of the multi-axis additive manufacturing equipment for accessibility verification and attitude continuity verification. If there are unreachable path points, abrupt attitude change path segments, or collision interference risks, the corresponding weights in the multi-constraint energy function are adjusted according to the verification results, and the direction field is iteratively updated. S3. When the optimized orientation field satisfies the attitude continuity condition, reachability condition, and convergence condition, a non-planar unsupported path is generated based on the optimized orientation field. The nozzle attitude sequence and extrusion compensation parameters corresponding to the non-planar unsupported path are determined. An enhanced multi-axis printing command containing spatial coordinates, nozzle attitude angle, and extrusion amount is output to complete the planning of the multi-axis additive manufacturing unsupported path.

2. The multi-axis additive manufacturing unsupported path planning method based on direction field constraints according to claim 1, characterized in that, S1 includes: S101. Input the 3D model to be printed, and perform meshing processing on the 3D model to be printed so that the 3D model to be printed is represented as a triangular mesh M=(V,E,F), where V represents the set of vertices, E represents the set of edges, and F represents the set of triangular faces. S102, Construct a unit vector with reverse direction and for the first f Each patch or sampling unit defines the overhang angle. : wherein represents the outer normal; S103、when the overhang angle is greater than the critical overhang angle , the first f patch or sampling unit is determined as an overhang risk area ; S104, defining the average curvature of the first f :​ wherein, and denotes the local principal curvatures of the f th patch. S105, when Exceeding the curvature threshold , or the f The variance of the normal angle between a facet and its neighboring faces Exceeding the preset threshold At that time, the first f Each patch or sampling unit, along with its adjacent patches, forms a local region defined as the surface quality-sensitive region. ; S106 will not be considered a hanging risk area. It also does not belong to the surface quality sensitive area. The area, sampling unit, or local region is divided into ordinary regions. Among them, when a certain patch or sampling unit simultaneously meets the requirements of the overhang risk area and surface quality sensitive areas When conditions are met, areas should be prioritized for designation as hanging risk zones. ; S107, For ordinary areas Unit vector in the reverse direction of construction Constructing the initial direction field : S108, for the curved surface quality sensitive area , construct the initial direction field according to the curved surface normal ; wherein, when the curved surface normal corresponding to the nozzle inclination angle exceeds the maximum inclination angle allowed by the mechanism , truncate the direction to the maximum executable inclination angle; , the direction truncation function S109. For areas with hanging risks The support point is obtained by searching the substrate, the previously determined reference surface of the previous layer, or the support reference surface in reverse along the construction direction. And based on the support point Construct the initial direction field ,in, Indicates the first i One path point to be printed. This represents the vector normalization function.

3. The multi-axis additive manufacturing support-free path planning method based on direction field constraints of claim 2, wherein, the normal angle variance The expression of the normal angle variance is as follows: in, j Indicates the adjacent face index. Indicates the first f The unit outward normal of a surface patch Indicates the first j The outward normal of an adjacent face Indicates the first f The average value of the normal angle between a facet and its adjacent faces. Indicates the first f The set of adjacent faces of a face, where |N(f)| represents the number of adjacent faces; The support point The expression is as follows: in, Indicates the first i One path point to be printed. Represents any candidate support point in the set of candidate support points. Indicates the path point to be printed. The corresponding set of candidate support points Indicates the path point to be printed. The outward normal of the corresponding facet. , and All represent non-negative weight parameters. Indicates the distance normalization scale. This represents the time sequence penalty term for the candidate support point P.

4. The method of claim 1, wherein, The expression for the multi-constraint energy function is as follows: in, Represents the multi-constraint energy function. , , and Each represents a non-negative weight coefficient for each constraint term, and satisfies... D represents the set of direction field vectors. This indicates that the overhang angle exceeds the constraint. This indicates a direction field smoothing constraint. This indicates a surface fitting constraint. This indicates institutional accessibility constraints. f Indicates the first f A piece of dough, Indicates the area of ​​hanging risk. Indicates the area sensitive to surface quality. Indicates the first f The direction field vector at each surface patch Indicates a unit vector in the opposite direction. and Let A denote the set of adjacent faces, and let A denote the set of adjacent pairs. Indicates the adjacency weight. and These represent the nth adjacency pair (u,v) in the adjacency pair. The and the first The direction field vector at each surface patch Indicates the curvature-related weights. Indicates the curvature weighting coefficient. Indicates outward normal direction. Indicates the mean curvature. i Indicates the index of the path point to be printed. This indicates the total number of path points to be printed, k represents the multi-axis mechanism drive unit index, and K represents the total number of multi-axis mechanism drive units. Indicates the first i The driving variables of the k-th multi-axis mechanism drive unit at each of the path points to be printed. and Let these represent the upper and lower physical limits of the k-th multi-axis mechanism drive unit, respectively. This represents the reachability penalty weight of the k-th multi-axis mechanism drive unit.

5. The direction field constraint based multi-axis additive manufacturing support- free path planning method of claim 1, wherein, After each round of orientation field iteration update, the weight coefficients are adjusted based on the overhang exceeding limits, attitude changes, and mechanism inaccessibility.

6. The multi-axis additive manufacturing support-free path planning method based on direction field constraints of claim 5, wherein, The non-negative weighting coefficients are adjusted based on factors such as overhang exceeding limits, attitude changes, and inaccessibility of the mechanism, including: Definitions , the proportion of pose mutations , and the proportion of inaccessibility points are respectively: in, This indicates the number of sampling points in the overhang risk area where the equivalent overhang angle exceeds the critical overhang angle. This represents the total number of sampling points involved in the assessment within the overhang risk area. This indicates the number of point pairs whose attitude change between adjacent path points to be printed exceeds a preset attitude change threshold. This represents the total number of adjacent point pairs involved in the attitude continuity determination. This indicates the number of path points that are determined to be unreachable after the inverse motion test of the multi-axis mechanism. This indicates the total number of path points to be printed that participated in the accessibility verification of the participating institutions; When the overhang exceeds the limit ratio Greater than the first preset threshold When this is done, increase the weight of the overhang angle constraint term. When the attitude change ratio Greater than the second preset threshold At that time, increase the weight of the direction field smoothing constraint term. When the proportion of unreachable points When the value is greater than 0, increase the weight of the mechanism's reachability constraint term. And reduce the weight of the surface fitting constraint term. The updated and normalized weights are obtained. : wherein, denotes the adjusted constraint term weight, normalized to satisfy: , denotes the constraint term weight index, denotes the constraint term weight index in the normalization summation process, j = 1, 2, 3, 4.

7. The direction field constraint based multi-axis additive manufacturing support- free path planning method of claim 1, wherein, The process of converting the current orientation field into a temporary nozzle attitude sequence and inputting it into the inverse kinematics model of the multi-axis additive manufacturing equipment for reachability and attitude continuity verification includes: A1. Let the optimized direction field vector be... In a fixed global coordinate system, the direction field vector Converted into temporary nozzle attitude angles around the X and Y axes and : in, Represents a very small positive number; A2, the first Spatial coordinates of the path points to be printed and nozzle attitude angle Input the inverse kinematics model of the multi-axis mechanism of the multi-axis additive manufacturing equipment, and calculate the multi-axis mechanism drive element variables at the corresponding path points; wherein, the inverse kinematics model of the multi-axis mechanism is expressed as: in, Indicates the first The set of multi-axis mechanism drive unit variables at each path point to be printed. Indicates the first The driving variables of the k-th multi-axis mechanism drive unit at each of the path points to be printed. Indicates the total number of drive units in a multi-axis mechanism. Represents the inverse kinematics mapping function of a multi-axis mechanism. This represents the set of structural parameters for a multi-axis mechanism. A3. Determine whether the variables of the multi-axis mechanism drive unit meet the physical range of the mechanism; if they do, proceed to A4; if they do not, mark the corresponding path point to be printed as an unreachable path point, count the proportion of unreachable path points, and feed the proportion of unreachable path points as the mechanism reachability verification result back to the direction field iteration update step S2; the physical range of the mechanism includes the upper and lower limits of the stroke or joint angle of each drive unit of the multi-axis mechanism, the allowable tilt angle range of the nozzle, the workspace boundary, and the preset collision or interference safety distance; A4. Determine whether the attitude continuity of the current temporary nozzle attitude sequence meets the requirements. If it does, output the mechanism reachability verification result and attitude continuity verification result of the current temporary nozzle attitude sequence, and feed the verification result back to the orientation field iterative update step S2 to determine whether the current orientation field meets the reachability condition, attitude continuity condition and convergence condition. If it does not meet the requirements, proceed to A5. A5. Nozzle attitude angle based on adjacent print path points and Calculate the attitude change between adjacent path points to be printed: ， wherein denotes the attitude angle adjacent to the attitude angle denotes the attitude angle adjacent to the attitude angle A6. Calculate adjacent to-be-printed path points and between which a calculated single-step maximum pose change is allowed and : , in, and Both represent the maximum angular velocity of the multi-axis mechanism in the corresponding attitude direction. This represents the estimated motion time between adjacent path points to be printed. A7, when or When printing, insert intermediate path points between adjacent path points to be printed, where the number of inserted intermediate path points is... The expression is as follows: wherein denotes the ceiling function; A8. For the inserted intermediate path points, use interpolation to generate intermediate attitude sequences, smooth the intermediate attitude sequences, and return to A4 to re-evaluate attitude continuity.

8. The direction field constraint based multi-axis additive manufacturing support- free path planning method of claim 1, wherein, S3 includes: B1. Interpolate the optimized orientation field that satisfies the attitude continuity condition, accessibility condition and convergence condition to the entity domain of the 3D model to be printed or the surface sampling point of the 3D model to be printed, and generate a non-planar unsupported path by the path projection method or the field reconstruction method. B2. Based on the coordinates of the path points to be printed on the non-planar unsupported path and the optimized direction field, generate the final nozzle attitude sequence corresponding to the non-planar unsupported path; B3. Perform a pre-output check on the final nozzle attitude sequence. The pre-output check includes mechanism accessibility verification, attitude continuity verification, and collision or interference verification. If the final nozzle attitude sequence meets the pre-output check requirements, proceed to B4. If there are unreachable path points, abrupt attitude change path segments, or collision or interference risks, feed back the corresponding path points or path segments to be printed to S2, adjust the corresponding weights in the multi-constraint energy function, or return to B1 to resample the non-planar unsupported path. B4. Calculate the extrusion amount compensation parameter from the nozzle tip synthetic velocity, the reference velocity, and the nozzle attitude angle : in, Indicates the baseline extrusion amount. Indicates the synthesis velocity at the nozzle tip. Indicates the baseline printing speed. and These represent the tilt angle compensation coefficients for the attitude angles around the X and Y axes, respectively. and All indicate the first i The nozzle attitude angle at each point on the path to be printed; B5. Extrusion amount compensation parameter , outputting enhanced multi-axis printing instructions wherein, , and represent the spatial coordinates of the i th path point to be printed.

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