An asymmetric five-axis cutter path smoothing method based on path weighted synthesis

Abstract

This invention relates to the field of multi-axis CNC machining and industrial robot machining technology, specifically disclosing an asymmetric five-axis toolpath smoothing method based on path weighted synthesis. The method includes: constructing a universal corner smoothing model based on path weighting; constructing an analytical expression for a high-order continuous weighted function; Cartesian space smoothing of the tool tip position path; unit spherical space smoothing of the tool axis direction path; synchronous adjustment of C3 continuous parameters for position and direction paths; interference verification and asymmetric adjustment of adjacent corner transition intervals; continuous speed planning and real-time interpolation; and motion control of the machining equipment. This invention overcomes the shortcomings of existing five-axis path transition smoothing technologies, such as poor geometric versatility, incoordination between tool tip and tool axis movements, easy interference in short path segments, and inconsistent bidirectional machining trajectories. It improves geometric versatility and processing efficiency, achieves high-order continuity and consistent machining surfaces, and can be ported across platforms and extended to higher orders.

Description

Technical Field

[0001] This invention relates to the fields of multi-axis CNC machining and industrial robot machining technology, and in particular to an asymmetric five-axis tool path smoothing method based on path weighted synthesis. Background Technology

[0002] In the fields of five-axis CNC machining and robotic machining, the original toolpaths generated by computer-aided manufacturing systems are typically composed of a series of straight line segments, circular arc segments, and spline curve segments (such as B-splines or NURBS). These heterogeneous path segments usually only satisfy positional continuity at their junctions, resulting in significant abrupt changes in tangential direction, curvature, and rate of curvature change at these junctions. This geometric discontinuity can induce severe vibrations and impacts in machining equipment during high-speed machining, severely limiting the increase in feed rate and directly deteriorating the surface finish and contour accuracy of complex curved parts. To improve the dynamic characteristics of toolpaths, researchers have proposed various path smoothing techniques; among them, local transition smoothing methods have become the mainstream research direction due to their low computational cost and ease of achieving strict geometric error control.

[0003] However, existing transition smoothing techniques still have the following significant limitations in practical engineering applications: (1) Limited geometric versatility: Most methods are designed for specific path combinations (such as straight-straight or straight-arc), lacking a unified analytical expression framework for mixed connection scenarios of straight lines, arcs and various spline curves; (2) Difficulty in synchronizing five-axis motion: The tool tip position path and the tool axis vector orientation path are often treated as independent geometric entities and smoothed separately, making it difficult for them to synchronize accurately in the parameter domain, which in turn leads to problems such as excessive machining errors; (3) Interference and overlap of short path segments: When processing dense short path segments, in order to meet the requirements of high-order continuity, the length of the transition curve is often limited to the length of adjacent segments. When the transition length exceeds half of the path segment, curve overlap is likely to occur, leading to algorithm failure or forced limitation of feed speed; (4) Lack of bidirectional machining consistency: In typical reciprocating parallel path machining such as aerospace grille milling, the transition trajectory geometry generated by traditional symmetrical smoothing methods or some asymmetrical methods in the forward and reverse strokes does not have rotation / mirror invariance, resulting in inconsistent surface texture. Therefore, there is an urgent need for a high-order parameter continuous smoothing method that can handle arbitrary primitive combinations, support five-axis asymmetric transitions, and is computationally efficient. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of existing five-axis path transition smoothing technology, such as poor geometric versatility, lack of coordination between tool tip and tool axis movement, easy interference in short path segments, and inconsistent bidirectional machining trajectories, and to provide an asymmetric five-axis tool path smoothing method based on path weighted synthesis.

[0005] To achieve the above objectives, this invention provides an asymmetric five-axis toolpath smoothing method based on path weighted synthesis, comprising the following steps: S1. Construct a general model for corner smoothing based on path weighting: Construct a weighted generation model for corner smoothing curves from the perspective of path synthesis, and establish a mapping relationship between the order of path geometric continuity and the boundary conditions of the weighting function; Through the weighted generation model, two adjacent heterogeneous original paths are smoothly transitioned, providing theoretical support for achieving smooth transitions with high-order geometric continuity. S2. Construct the analytical expression of the higher-order continuous weighting function: Construct the analytical expression of the weighting function that satisfies the preset higher-order continuity requirement, and establish the analytical relationship between the weighting function and the path transition length; The weighting function is independent of the geometric representation of the original path and is determined only by the arc length parameter of the transition segment, thereby realizing the unified processing of various path primitives; S3. Cartesian Space Smoothing of Tool Tip Position Path: Under the continuous geometric constraints of G3, the tool tip position path in Cartesian space is smoothed; the analytical expression between position smoothing deviation and transition length and path angle is derived; the transition length is constrained according to the preset position error threshold to achieve precise control of position path geometric deviation. S4. Smoothing of the unit spherical space of the tool axis direction path: Under the continuous geometric constraint of G3, the tool axis vector path on the unit spherical surface is smoothed; the analytical expression of the direction smoothing deviation is derived, and the optimal transition length is calculated in reverse according to the preset direction error threshold to achieve strict control of the direction smoothing deviation. S5. C3 continuous parameter synchronization adjustment of position and direction path: Obtain the length ratio of the original direction path segment and the position path segment, and dynamically adjust the length of the transition segment of position and direction accordingly. By establishing the parameterized correspondence between position and direction path, the C3 continuous synchronization of five-axis motion in the parameter domain is realized, and the stability of tool axis motion is improved. S6. Interference verification and asymmetric adjustment of adjacent corner transition intervals: Based on the quantitative relationship between the sum of the transition lengths of two adjacent corners and the total arc length of the original path segment, determine whether there is an overlapping area; if there is an overlap, reduce the transition length of the position and direction path proportionally to avoid the overlap of adjacent corner transition curves and ensure the continuity of the global path. S7. Speed ​​Planning and Real-Time Interpolation with Continuous Jump: Based on the planned C3 continuous machining path, the jump curve in the S acceleration and deceleration motion law is corrected to generate a tool tip feed speed curve with continuous jump; combined with the prediction-correction algorithm, parameter interpolation is performed to generate an interpolation point sequence that satisfies kinematic constraints. S8. Motion control of processing equipment: Based on the inverse kinematics model of the processing equipment, the interpolation point sequence is converted into variable commands for each drive joint to control the processing equipment to perform processing tasks.

[0006] Furthermore, step S1 specifically includes: S11. Construction of the composite curve: For two adjacent original path segments and , For path points, For the knife point index value, construct a composite curve within its transition region. ;set up and These are the start and end points of the transition curve, respectively. and Representing path segments and arc length, and Path segment and The parameter expression, If the position path arc length parameter is used, then the composite curve is defined as: ; In the formula, and Path segment and The weighting function, Let be the curve parameters, and satisfy the following boundary conditions. , , and ; S12. Construction of geometric continuity boundary constraints: make and These represent the original paths. and Let the geometric continuity order be . When the weighted function and its derivatives satisfy the following boundary conditions at the junction: ; Synthetic transition curve At the connection point and Satisfying Geometric continuity of order 1.

[0007] Furthermore, step S2 specifically involves: Let the weight function be ; weighting function with respect to parameters of The first derivative is denoted as ,Will Defined as a five-segment linear distribution: ; In the formula, , , , , Representing functions respectively Relative parameter values ​​at each stage; and Representing functions respectively exist and The value at; For functions By performing continuous integration and combining it with the boundary conditions described in step S12, the weighting function is obtained. The parsing expression.

[0008] Furthermore, step S3 specifically includes: S31. Establish a weighted mathematical model for the transition curve: set up , and The adjacent number in the path of the blade tip position , and Each knife point, and These represent the unit direction vectors of two adjacent path segments formed by the aforementioned points. Let be the angle between the two path segments. Original path segment Length, To reserve the remaining path segment Length; Introducing asymmetric characteristic parameters and , For the first Exit length of segment path, For the first The cut-in length of the segment path; let... The transition curve at the corner has the following analytical expression: ; In the formula, and Let these represent the weighted functions before and after the inflection point, respectively, satisfying the following boundary conditions. , , and ; S32. Establish analytical mapping and smoothing deviation control for position smoothing deviation: set up Indicates the transition curve Upper distance point The nearest point, under the simplified condition of symmetry and smoothness, is the characteristic parameter. The positional smoothness deviation was derived. Analytical expression: ; Preset position error threshold The upper limit of the feature parameters can be obtained by reverse calculation through the above mapping relationship. : ; S33. Determination of transition length under multiple constraints: set up and To meet the required transition length on both sides of the inflection point for synchronized movement of the tool tip and tool axis, let... and This represents the maximum allowable transition length on both sides of the inflection point to avoid overlap between two adjacent corner transition curves. The final transition length is the intersection of all constraint values, expressed as: ; Furthermore, step S4 specifically includes: By combining the principle of spherical linear interpolation, the path weighted synthesis framework is extended to rotation space; S41. Construct a spherical transition curve model: Let the center of the unit sphere be... W , , and The first , and The endpoint of a unit vector along the tool axis. , and All lie on a unit sphere; let and These represent the start and end points of the transition curve, respectively, and the circular arc segment. and The corresponding central angles are respectively and Introducing asymmetric characteristic parameters and , For the first The exit angle of the arc segment. For the first The angle of entry for the segment path is used to construct the initial transition curve. as follows: ; ; In the formula, and Representing arcs and The parameter expression, and Let represent the path weighting functions before and after the inflection point, respectively, satisfying the following boundary conditions: ; S42. Implement normalized projection correction: The composite vector is renormalized onto the unit sphere using the projection operator, expressed as follows: ; Constructed direction transition curve The G3 continuity constraint is still satisfied; S43. Establish an analytical mapping model for directional smoothness deviation: Define directional smoothness deviation as the deviation between the directional transition curve and the original path point. The maximum angular deviation between them; under symmetrical and smooth conditions, i.e. According to the geometric properties of the weighting function, the maximum directional deviation occurs at the midpoint of the parameters of the smooth curve. At this point, the expression is: ; set up Representing a plane and plane The included angle: ; Express the directional smoothness deviation in terms of the transition angle. and included angle Analytical functions: ; ; S44. Solving for the adapter length based on accuracy requirements: Preset directional smoothness deviation threshold Using the analytical mapping relationship described in step S43, the solution satisfying the Newton-Raphson iteration method is obtained. The feature parameters are set to initial values ​​for iteration. The final value of the feature parameter was determined to be: .

[0009] Furthermore, step S5 specifically includes: S51. Establish the position-direction displacement mapping relationship on the remaining path segment: Assume the tool reaches the junction of the position path and the direction path at the same moment; when the tool is in the remaining path segment... When moving upwards, define the arc length of the directional path. and position path arc length Displacement mapping relationship between them: ; S52. Establish continuous synchronization conditions for C3 at the connection point: Assume that the position transition path and the direction transition path share the same curve parameters; retain the remaining direction path segment. Regarding the arc length of the direction path The expression is: ; In the formula, Represents an arc At point The unit tangent vector; To eliminate motion shock, the synchronization constraint at the connection point is expressed as: ; By adjusting the location path feature parameters and With direction path feature parameters and This forces the transition regions of the two to align in the parameter domain, thereby simplifying the complex kinematic synchronization into a proportional constraint of geometric parameters. S53. Construct a shared parameter position-direction transition curve synchronization model: Combining the boundary conditions of the path weighting function on both sides of the inflection point, the continuity condition of C3 can be expressed as: .

[0010] Furthermore, an adjustment strategy based on position priority and direction coordination is adopted: Regardless of the motion properties of the current path segment, the geometric and synchronization constraints of the position path are uniformly used as the benchmark to analyze the characteristic parameters of the induced direction path, ensuring global parameter synchronization; the position path characteristic parameters are initially adjusted. and as follows: ; The direction path feature parameter adjustment process is performed after the adjacent transition overlap elimination in step S6 is completed.

[0011] Furthermore, step S6 specifically includes: S61. Determination of overlap between adjacent transition sections: Determine the constraints Is it true? If not, then it is determined that the adjacent transition curves have local overlap. S62. Proportional asymmetric adjustment of location path characteristic parameters: If overlap is determined, a proportional reduction strategy is used to correct the feature parameters of the location path; the corrected feature parameters are constructed as follows: ; S63. Directional path linkage adjustment based on synchronization constraints: Based on the completed adjustment of the position path feature parameters, in order to maintain the C3 synchronization characteristic described in step S5, the feature parameters of the direction path are updated synchronously; according to the parameter synchronization mapping criterion, the updated direction feature parameters are calculated as follows: ; S64, Reconstruction and Integration of Global C3 Continuous Processing Paths: Based on the updated tool tip position transition length and tool axis direction transition angle, the weighted composite model of steps S3 and S4 is re-substituted to recalculate the transition curves at each corner. Finally, the tool tip position path containing linear segments and transition segments after smoothing, together with the tool axis vector path containing arc segments and transition segments, constitutes the global C3 continuous machining path of the machining equipment.

[0012] The present invention employs the above-mentioned asymmetric five-axis toolpath smoothing method based on path weighted synthesis, and its beneficial effects are as follows: (1) Extremely high algorithm versatility and computational efficiency: The method of this invention is not only applicable to traditional paths composed of straight lines and arcs, but also to complex spline curve paths; since the boundary conditions of the path weighting function constructed by this invention are determined only by the geometric continuity order of the transition points, and do not depend on the specific geometric form of adjacent path segments, a unified smoothing process for any combination of heterogeneous path segments is achieved; in addition, the method is based on analytical closed-form solutions, and does not require complex B-spline control point iterative solutions, which greatly reduces the amount of computation and can meet the real-time calculation requirements of CNC systems; (2) Precise geometric error control and coordinated motion of tool tip and tool axis: By establishing an analytical mapping relationship between smoothness error and asymmetric transition length, this invention can automatically calculate the optimal transition interval under the premise of a given smoothness deviation threshold; by introducing a motion synchronization strategy based on transition length adjustment, this invention solves the problem of incoordination between tool tip position and tool axis pointing motion in five-axis machining; on the basis of ensuring the consistency of curve parameters, it effectively avoids the overlap of smoothness intervals under short path segments, and ensures the global C3 continuity of complex multi-axis linkage motion; (3) Asymmetric transition brings consistent machining surface: In the process of adjusting the feature parameters, the present invention introduces an asymmetric transition mechanism and uses the relative ratio of the feature parameters to the length of the original path segment as the basis for adjustment; when the machining path is a reciprocating parallel (Zig-zag) trajectory, this mechanism can ensure that the smooth trajectory generated at each corner has a completely consistent geometric shape when the tool feed direction changes alternately, effectively avoiding the unevenness of the machining surface texture caused by the difference in path geometry, and significantly improving the surface quality of finishing; (4) Cross-platform portability and high-order scalability: The method proposed in this invention is not only applicable to hybrid robot milling systems, but also to general five-axis CNC machine tools; the algorithm can be integrated as an independent functional module into the preprocessing front end of the CNC system; at the same time, if the path weighting function is further integrated and the same construction framework is adopted, G4 or even higher-order continuous transition paths can be directly obtained without changing the core logic of the algorithm, which has a strong technical foresight. Attached Figure Description

[0013] Figure 1 This is a flowchart of an asymmetric five-axis toolpath smoothing method based on path weighted synthesis according to an embodiment of the present invention; Figure 2 This is a schematic diagram of a general corner smoothing model based on path weighting, which is an embodiment of the present invention for an asymmetric five-axis toolpath smoothing method based on path weighting synthesis. Figure 3 This is the geometry of the S-shaped path weighting function analytically constructed according to an embodiment of the present invention, which is an asymmetric five-axis tool path smoothing method based on path weighting synthesis. Figure 4 This is a schematic diagram of linear position path transition smoothing in an embodiment of the present invention, which is an asymmetric five-axis tool path smoothing method based on path weighted synthesis. Figure 5 This is a schematic diagram of tool axis vector path smoothing on a unit sphere in an embodiment of the present invention, which is an asymmetric five-axis tool path smoothing method based on path weighted synthesis. Figure 6 This is a schematic diagram illustrating the synchronization of position-direction path parameters and interference avoidance of an asymmetric five-axis toolpath smoothing method based on path weighted synthesis according to an embodiment of the present invention. Figure 7 This is the result of continuous transition smoothing of the pentagonal path C3 and speed planning of an asymmetric five-axis toolpath smoothing method based on path weighted synthesis according to an embodiment of the present invention. Figure 8 This is a configuration sequence of a hybrid robot milling process at different times based on a path weighted synthesis asymmetric five-axis tool path smoothing method according to an embodiment of the present invention; Detailed Implementation

[0014] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to specific embodiments and the accompanying drawings. It should be understood that these descriptions are merely exemplary and not intended to limit the scope of the invention. Furthermore, descriptions of well-known structures and techniques are omitted in the following description to avoid unnecessarily obscuring the concept of the invention.

[0015] For ease of understanding, the technical terms used in this embodiment are defined as follows: Tool tip position path: refers to the movement trajectory of the center point of the tool tip in three-dimensional space; Tool axis direction path: refers to the trajectory of the unit vector of the tool axis on a unit sphere; G3 continuity: Third-order geometric continuity, meaning that the tangent, curvature, and rate of change of curvature of a path are all continuous at the junction points; C3 continuity: Third-order parametric continuity, meaning that position, velocity, acceleration, and jerk are all continuous with respect to time or parameters; Asymmetric feature parameters: refer to the fact that the transition length or transition angle on both sides of a corner can be unequal, which is used to adapt to path segments of different lengths.

[0016] like Figure 1 As shown, an embodiment of the present invention provides an asymmetric five-axis toolpath smoothing method based on path weighted synthesis, comprising the following steps: S1. Read the five-axis linkage machining toolpath file: The system first reads the standard toolpath file to obtain a series of raw discrete machining data; among which, the tool tip position sequence is represented as... The sequence of endpoints of the cutter axis unit vector is represented as .

[0017] S2. Construct a general model for smoothing continuous corners in G3: like Figure 2 As shown, in two adjacent segments of the original path and , For path points, For the knife point index value, this embodiment does not use traditional spline fitting, but constructs a transition curve based on the path weighted synthesis principle. ;set up and These are the start and end points of the transition curve, respectively. and Representing path segments and arc length, and Path segment and The parameter expression, Here is the arc length parameter for the location path; the model merges the two path segments using two analytical weighting functions: ; In the formula, and Path segment and The weighting function, The parameters are curve parameters, and they satisfy preset boundary conditions: ; The resulting transition curve At the connection point and It satisfies third-order geometric continuity.

[0018] S3. Construct a five-segment analytical path weighting function: like Figure 3 As shown, to support real-time calculation in CNC systems, this invention proposes an analytical weighting function based on the integral of a five-segment third-order derivative curve. The weight function with respect to the parameters The third derivative is denoted as And it is defined as a five-segment linear distribution: ; In the formula, , , , , Representing functions respectively Relative parameter values ​​at each stage; and Representing functions respectively exist and The value at; By analyzing the function By performing continuous integration and combining it with the boundary conditions described in step S2, the weighting function is obtained. The analytical expression; where the second derivative It exhibits a piecewise parabolic shape: ; First derivative It presents an "S-shaped" curve, ensuring a smooth transition during the path synthesis process: ; The final original function For analytic polynomial form: ; In the third derivative In this context, the following geometric constraints exist: ; In the weighting function In this context, what geometric constraints exist? ; In the formula, Representation function In parameters The value at that location.

[0019] Therefore, it is only necessary to determine the first derivative. By defining the boundary conditions, the shape of the weighted function before and after the inflection point can be completely determined. This analytical construction method avoids complex iterative solutions and greatly improves the real-time performance of the smoothing process. Specifically, for the weighted function before the corner... Set its boundary conditions to , , and ; Backside weighting function The corresponding setting is , , and .

[0020] S4. Asymmetric smoothing construction and deviation control of position path: like Figure 4 As shown, in Cartesian space, let... , and The adjacent number in the path of the blade tip position , and Each knife point, and These represent the unit direction vectors of two adjacent path segments formed by the aforementioned points. Let be the angle between the two path segments. Original path segment Length, To reserve the remaining path segment Length; Introducing asymmetric characteristic parameters and , For the first Exit length of segment path, For the first The cut-in length of the segment path; then the position transition curve can be represented as: ; In the formula, and Let these represent the weighted functions before and after the inflection point, respectively, satisfying the following boundary conditions. , , and The analytical expression can be obtained by using the weighted function construction method in step S3.

[0021] To ensure machining accuracy, the geometric deviations caused by the transition must be strictly limited. Let... Indicates the transition curve Upper distance point The nearest point, under the simplified condition of symmetry and smoothness, is the characteristic parameter. The positional smoothness deviation was derived. Analytical expression: ; Given a preset position error threshold The upper limit of the feature parameters can be obtained by reverse calculation through the above mapping relationship. : ; This upper limit ensures that, when considering only geometric tolerance constraints, the positional smoothness deviation will not exceed the allowable range.

[0022] In actual machining, the transition length must also meet the requirements of high-order continuity of the tool axis motion trajectory and non-overlapping corner curves. Let... and To meet the required transition length on both sides of the inflection point for synchronized movement of the tool tip and tool axis, let... and This represents the maximum allowable transition length on both sides of the inflection point to avoid overlap between two adjacent corner transition curves. The final transition length is the minimum value of all constraint values, expressed as: ; Through this multi-constraint mechanism, the present invention can ensure the continuous high dynamic performance of G3 while taking into account both machining accuracy and global path coordination.

[0023] S5. Spherical weighted smoothing and projection correction of the direction path: like Figure 5 As shown, the original tool axis vector path on the unit sphere is composed of concentric circular arc segments on the unit sphere. Let the center of the unit sphere be... W , , and The first , and The endpoint of a unit vector along the tool axis. , and All lie on a unit sphere; let and These represent the start and end points of the transition curve, respectively, and the circular arc segment. and The corresponding central angles are respectively and Introducing asymmetric characteristic parameters and , For the first The exit angle of the arc segment. For the first The angle of entry for the segment path is used to construct the initial transition curve. as follows: ; ; In the formula, and Representing arcs and The parameter expression, and Let represent the path weighting functions before and after the inflection point, respectively, and satisfy the following boundary conditions: ; The analytical directional path weighting function can be obtained by using the weighting function construction method in step S3, thereby ensuring that the synthesized initial directional transition curve satisfies the G3 continuity constraint at the connection point.

[0024] Since linear weighted composition can cause scaling of the tool axis vector magnitude, this embodiment introduces a projection operator to reproject the composed vector onto a unit sphere, ensuring that the tool axis magnitude is always 1 and that G3 remains continuous. The expression is as follows: ; To meet machining accuracy requirements, the directional smoothness deviation is defined as the deviation between the directional transition curve and the original path point. The maximum angular deviation between them; under symmetrical and smooth conditions, i.e. Based on the geometric properties of the weighting function, it is easy to see that the maximum directional deviation occurs at the midpoint of the parameters of the smooth curve. At this point, the expression is: ; set up Representing a plane and plane The included angle: ; Therefore, the directional smoothness deviation can be expressed as a function of the transition angle. and included angle Analytical functions: ; ; Analysis of the overall trend shows that the smoothness deviation along the tool axis direction varies with the smoothness angle. It exhibits a monotonically increasing characteristic; preset directional smoothness deviation threshold. Based on the above analytical mapping relationship, Newton's iterative method is used to solve for the condition that satisfies... The feature parameters are set to initial values ​​for iteration. The final value of the feature parameter was determined to be: .

[0025] S6. The parameters of the tool tip position path and the tool axis direction path are synchronized: like Figure 6 As shown, it is assumed that the tool reaches the junction of the position path and the direction path at the same time; when the tool is in the remaining path segment (linear or circular arc segment)... During the upward motion, to ensure that the tool tip and tool axis are synchronized, the arc length of the directional path is defined. and position path arc length Displacement mapping relationship between them: ; Remaining directional path segment Regarding the arc length of the direction path The expression is: ; In the formula, Represents an arc At point The unit tangent vector; Assuming the position transition path and the direction transition path share the same curve parameters, to eliminate motion shock, the synchronization constraint at the connection point is expressed as follows: ; By adjusting the location path feature parameters and With direction path feature parameters and This forces the transition regions of the two to align in the parameter domain, thereby simplifying the complex kinematic synchronization into a proportional constraint of geometric parameters. Combining the boundary conditions of the path weighting function on both sides of the inflection point, the continuity condition of C3 can be expressed as: .

[0026] Considering that the actual machining path may contain a mixture of pure three-axis path segments (with the tool axis vector remaining unchanged) and five-axis path segments, this embodiment adopts an adjustment strategy based on position priority and direction coordination: regardless of the motion attributes of the current path segment, the geometric and synchronization constraints of the position path are uniformly used as the benchmark to analyze the characteristic parameters of the induced direction path, ensuring global parameter synchronization; the position path characteristic parameters are initially adjusted. and as follows: ; The adjustment process of the directional path characteristic parameters is performed after the elimination of adjacent transition overlap in step S7, so as to ensure that the adjusted length can meet the motion synchronization requirements and will not cause geometric interference at adjacent corners.

[0027] S7. Interference verification and asymmetric adjustment of adjacent corner transition intervals: For any path segment The starting point of the remaining path segment is affected by the first The exit length at the first corner is affected by the endpoint being influenced by the first... The cut-in length at each corner has an impact. Determine the constraint conditions. Is it true? If not, then it is determined that the adjacent transition curves have local overlap. If overlap is determined, this embodiment uses a proportional reduction strategy to correct the feature parameters of the location path; and the corrected feature parameters are constructed as follows: ; This method ensures that the smoothing curves do not overlap while preserving the original smoothing characteristics to the maximum extent through proportional adjustment.

[0028] After adjusting the position path feature parameters, in order to maintain the C3 synchronization characteristic described in step S6, the directional path feature parameters (transition angle) need to be updated synchronously. According to the parameter synchronization mapping criterion, the updated directional feature parameters are calculated as follows: ; Based on this, according to the updated tool tip position transition length and tool axis direction transition angle, the weighted synthesis model of steps S4 and S5 is re-substituted to recalculate the transition curves at each corner; finally, the tool tip position path containing linear segments and transition segments after smoothing and the tool axis vector path containing arc segments and transition segments together constitute the global C3 continuous machining path of the machining equipment.

[0029] S8. Continuous velocity planning and real-time interpolation: In this embodiment, a continuously increasing feed rate curve is planned along the tool tip position path. Specifically, the tool adopts an S-shaped acceleration / deceleration trajectory in the remaining path segment and a constant feed rate in the transition path. This embodiment uses the prediction-correction method to generate an interpolation point sequence with the CNC interpolation cycle as the time interval.

[0030] S9. Motion control and accuracy verification of machining equipment: In this embodiment, according to a preset interpolation cycle, the Cartesian space pose is converted into position commands for each drive joint using the inverse kinematics model of a five-axis hybrid robot, thereby driving the machining equipment to perform the machining task. The smoothed pentagonal path and velocity curve in this embodiment are shown below. Figure 7 As shown. Figure 8 The invention's method is demonstrated in a real-world scenario applied to a robot on the machining side of a mirror milling system. Results show that the machined surface exhibits highly consistent texture, and the robot operates smoothly with minimal vibration.

[0031] Therefore, this invention adopts the above-mentioned asymmetric five-axis tool path smoothing method based on path weighted synthesis, which has the following advantages: 1) Extremely high algorithm versatility and computational efficiency: The method of this invention is not only applicable to traditional paths composed of straight lines and arcs, but also to complex spline curve paths; since the boundary conditions of the path weighting function constructed by this invention are determined only by the geometric continuity order of the transition point, and do not depend on the specific geometric form of adjacent path segments, unified smoothing processing of any heterogeneous path segment combination is achieved; in addition, this method is based on analytical closed-form solutions, eliminating the need for complex B-spline control point iteration, greatly reducing the computational load and meeting the real-time calculation requirements of CNC systems; 2) Precise geometric error control and coordinated movement of tool tip and tool axis: By establishing an analytical mapping relationship between smoothing error and asymmetric transition length, this invention can automatically calculate the optimal transition interval under the premise of a given smoothing deviation threshold; by introducing a motion synchronization strategy based on transition length adjustment, this invention solves the problem of incoordination between tool tip position and tool axis pointing motion in five-axis machining; while ensuring the consistency of curve parameters, it has Effectively avoids overlapping smooth intervals in short path segments, ensuring global C3 continuity of complex multi-axis linkage motion; 3) Asymmetric transition brings consistent machining surface: In the process of feature parameter adjustment, this invention introduces an asymmetric transition mechanism and uses the relative ratio of feature parameters to the original path segment length as the adjustment basis; when the machining path is a reciprocating parallel (Zig-zag) trajectory, this mechanism can ensure that the smooth trajectory generated at each corner has a completely consistent geometric shape when the tool feed direction changes alternately, effectively avoiding the unevenness of machining surface texture caused by path geometric differences, and significantly improving the surface quality of finishing; 4) Cross-platform portability and high-order scalability: The method proposed in this invention is not only applicable to hybrid robot milling systems, but also to general five-axis CNC machine tools; the algorithm can be integrated as an independent functional module into the preprocessing front end of the CNC system; at the same time, if the path weighting function is further integrated and the same construction framework is used, G4 or even higher-order continuous transition paths can be directly obtained without changing the core logic of the algorithm, which has a strong technical foresight.

[0032] It is worth noting that all contents not described in detail in this invention are existing technologies and are well known to those skilled in the art.

[0033] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. An asymmetric five-axis toolpath smoothing method based on path weighted synthesis, characterized in that, Includes the following steps: S1. Construct a general corner smoothing model based on path weighting: Construct a weighted generation model of corner smoothing curves from the perspective of path synthesis, and establish the mapping relationship between the order of path geometric continuity and the boundary conditions of the weighting function; S2. Construct the analytical expression of the higher-order continuous weighting function: Construct the analytical expression of the weighting function that satisfies the preset higher-order continuity requirement, and establish the analytical relationship between the weighting function and the path transition length; S3. Cartesian Space Smoothing of Tool Tip Position Path: Under the continuous geometric constraints of G3, the tool tip position path in Cartesian space is smoothed; the analytical expression between position smoothing deviation and transition length and path angle is derived, and the transition length is constrained according to the preset position error threshold. S4. Smoothing of the cutter axis direction path on a unit spherical surface: Under the continuous geometric constraint of G3, the cutter axis vector path on the unit sphere surface is smoothed. The analytical expression for the directional smoothness deviation is derived, and the optimal transition length is calculated in reverse based on the preset directional error threshold. S5. Synchronous adjustment of C3 continuous parameters of position and direction path: Obtain the length ratio of the original direction path segment and the position path segment, and dynamically adjust the length of the transition segment of position and direction accordingly. S6. Interference verification and asymmetric adjustment of adjacent corner transition sections: Based on the quantitative relationship between the sum of the transition lengths of two adjacent corners and the total arc length of the original path segment, determine whether there is an overlapping area; if there is an overlap, the transition length of the position and direction path is reduced proportionally. S7. Speed ​​Planning and Real-Time Interpolation with Continuous Jump: Based on the planned C3 continuous machining path, the jump curve in the S acceleration and deceleration motion law is corrected to generate a tool tip feed speed curve with continuous jump; combined with the prediction-correction algorithm, parameter interpolation is performed to generate an interpolation point sequence that satisfies kinematic constraints. S8. Motion control of processing equipment: Based on the inverse kinematics model of the processing equipment, the interpolation point sequence is converted into variable commands for each drive joint to control the processing equipment to perform processing tasks.

2. The asymmetric five-axis toolpath smoothing method based on path weighted synthesis according to claim 1, characterized in that, Step S1 specifically includes: S11. Construction of the composite curve: For two adjacent original path segments and , For path points, For the knife point index value, construct a composite curve within its transition region. ;set up and These are the start and end points of the transition curve, respectively. and Representing path segments and arc length, and Path segment and The parameter expression, If the position path arc length parameter is used, then the composite curve is defined as: ； In the formula, and Path segment and The weighting function, Let be the curve parameters, and satisfy the following boundary conditions. , , and ; S12. Construction of geometric continuity boundary constraints: make and These represent the original paths. and Let the geometric continuity order be . When the weighted function and its derivatives satisfy the following boundary conditions at the junction: ； Synthetic transition curve At the connection point and Satisfying Geometric continuity of order 1.

3. The asymmetric five-axis toolpath smoothing method based on path weighted synthesis according to claim 2, characterized in that, Step S2 is as follows: Let the weight function be ; weighting function with respect to parameters of The first derivative is denoted as ,Will Defined as a five-segment linear distribution: ； In the formula, , , , , Representing functions respectively Relative parameter values ​​at each stage; and Representing functions respectively exist and The value at; For functions By performing continuous integration and combining it with the boundary conditions described in step S12, the weighting function is obtained. The parsing expression.

4. The asymmetric five-axis toolpath smoothing method based on path weighted synthesis according to claim 3, characterized in that, Step S3 specifically includes: S31. Establish a weighted mathematical model for the transition curve: set up , and The adjacent number in the path of the blade tip position , and Each knife point, and These represent the unit direction vectors of two adjacent path segments formed by the aforementioned points. Let be the angle between the two path segments. Original path segment Length, To reserve the remaining path segment Length; Introducing asymmetric characteristic parameters and , For the first Exit length of segment path, For the first The cut-in length of the segment path; let... The transition curve at the corner has the following analytical expression: ； In the formula, and Let these represent the weighted functions before and after the inflection point, respectively, satisfying the following boundary conditions. , , and ; S32. Establish analytical mapping and smoothing deviation control for position smoothing deviation: set up Indicates the transition curve Upper distance point The nearest point, under the simplified condition of symmetry and smoothness, is the characteristic parameter. The positional smoothness deviation was derived. Analytical expression: ； Preset position error threshold The upper limit of the feature parameters can be obtained by reverse calculation through the above mapping relationship. : ； S33. Determination of transition length under multiple constraints: set up and To meet the required transition length on both sides of the inflection point for synchronized movement of the tool tip and tool axis, let... and This represents the maximum allowable transition length on both sides of the inflection point to avoid overlap between two adjacent corner transition curves. The final transition length is the intersection of all constraint values, expressed as: 。 5. The asymmetric five-axis toolpath smoothing method based on path weighted synthesis according to claim 4, characterized in that, Step S4 specifically includes: By combining the principle of spherical linear interpolation, the path weighted synthesis framework is extended to rotation space; S41. Construct a spherical transition curve model: Let the center of the unit sphere be... W , , and The first , and The endpoint of a unit vector along the tool axis. , and All lie on a unit sphere; let and These represent the start and end points of the transition curve, respectively, and the circular arc segment. and The corresponding central angles are respectively and Introducing asymmetric characteristic parameters and , For the first The exit angle of the arc segment. For the first The angle of entry for the segment path is used to construct the initial transition curve. as follows: ； ； In the formula, and Representing arcs and The parameter expression, and Let represent the path weighting functions before and after the inflection point, respectively, satisfying the following boundary conditions: ； S42. Implement normalized projection correction: The composite vector is renormalized onto the unit sphere using the projection operator, expressed as follows: ； Constructed direction transition curve The G3 continuity constraint is still satisfied; S43. Establish an analytical mapping model for directional smoothness deviation: Define directional smoothness deviation as the deviation between the directional transition curve and the original path point. The maximum angular deviation between them; under symmetrical and smooth conditions, i.e. According to the geometric properties of the weighting function, the maximum directional deviation occurs at the midpoint of the parameters of the smooth curve. At this point, the expression is: ； set up Representing a plane and plane The included angle: ； Express the directional smoothness deviation in terms of the transition angle. and included angle Analytical functions: ； ； S44. Solving for the adapter length based on accuracy requirements: Preset directional smoothness deviation threshold Using the analytical mapping relationship described in step S43, the solution satisfying the Newton-Raphson iteration method is obtained. The feature parameters are set to initial values ​​for iteration. The final value of the feature parameter was determined to be: 。 6. The asymmetric five-axis toolpath smoothing method based on path weighted synthesis according to claim 5, characterized in that, Step S5 specifically includes: S51. Establish the position-direction displacement mapping relationship on the remaining path segment: Assume the tool reaches the junction of the position path and the direction path at the same moment; when the tool is in the remaining path segment... When moving upwards, define the arc length of the directional path. and position path arc length Displacement mapping relationship between them: ； S52. Establish continuous synchronization conditions for C3 at the connection point: Assume that the position transition path and the direction transition path share the same curve parameters; retain the remaining direction path segment. Regarding the arc length of the direction path The expression is: ； In the formula, Represents an arc At point The unit tangent vector; To eliminate motion shock, the synchronization constraint at the connection point is expressed as: ； By adjusting the location path feature parameters and With direction path feature parameters and This forces the transition regions of the two to align in the parameter domain, thereby simplifying the complex kinematic synchronization into a proportional constraint of geometric parameters. S53. Construct a shared parameter position-direction transition curve synchronization model: Combining the boundary conditions of the path weighting function on both sides of the inflection point, the continuity condition of C3 can be expressed as: 。 7. The asymmetric five-axis toolpath smoothing method based on path weighted synthesis according to claim 6, characterized in that, An adjustment strategy based on position priority and direction coordination is adopted: Regardless of the motion properties of the current path segment, the geometric and synchronization constraints of the position path are uniformly used as the benchmark to analyze the characteristic parameters of the induced direction path, ensuring global parameter synchronization; the position path characteristic parameters are initially adjusted. and as follows: ； The direction path feature parameter adjustment process is performed after the adjacent transition overlap elimination in step S6 is completed.

8. The asymmetric five-axis toolpath smoothing method based on path weighted synthesis according to claim 7, characterized in that, Step S6 specifically includes: S61. Determination of overlap between adjacent transition sections: Determine the constraints Is it true? If not, then it is determined that the adjacent transition curves have local overlap. S62. Proportional asymmetric adjustment of location path characteristic parameters: If overlap is determined, a proportional reduction strategy is used to correct the feature parameters of the location path; the corrected feature parameters are constructed as follows: ； S63. Directional path linkage adjustment based on synchronization constraints: Based on the completed adjustment of the position path feature parameters, in order to maintain the C3 synchronization characteristic described in step S5, the feature parameters of the direction path are updated synchronously; according to the parameter synchronization mapping criterion, the updated direction feature parameters are calculated as follows: ； S64, Reconstruction and Integration of Global C3 Continuous Processing Paths: Based on the updated tool tip position transition length and tool axis direction transition angle, the weighted composite model of steps S3 and S4 is re-substituted to recalculate the transition curves at each corner. Finally, the tool tip position path containing linear segments and transition segments after smoothing, together with the tool axis vector path containing arc segments and transition segments, constitutes the global C3 continuous machining path of the machining equipment.

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