An FLMSS trajectory planning and machining verification method

Abstract

A kind of FLMSS trajectory planning and processing verification method, comprising the following steps;Step one: obtaining the desired five-degree-of-freedom pose trajectory of FLMSS end beam;Step two: obtain optical non-uniform mapping features and sensitive area distribution;Step three: construct five-axis smooth trajectory satisfying continuity requirement;Step four: establish dynamic limiting model related to trajectory position and pose state, calculate dynamic derating coefficient, obtain path parameter speed upper limit satisfying system dynamic execution capability requirement;Step five: speed planning is carried out to path parameter, and path parameter speed curve satisfying speed, acceleration and jerk constraint is obtained;Realize end beam five-degree-of-freedom pose trajectory planning;Step six: implement processing verification, compare processing result with theoretical trajectory or target structure, and evaluate the execution stability and processing consistency of trajectory planning in complex microstructure processing process.The present application can improve the execution stability and processing consistency of trajectory in complex microstructure processing process.

Description

Technical Field

[0001] This invention relates to the field of laser micromachining and numerical control system technology, specifically to a FLMSS (Five-axis Laser Micromachining Scanning System) trajectory planning and processing verification method. Background Technology

[0002] FLMSS, due to its multi-degree-of-freedom linkage capability, is a key piece of equipment in the field of high-end micro-manufacturing. This type of system achieves precise pose control of the end beam in three-dimensional space through the coordinated control of a two-dimensional scanning module, a dynamic focusing module, and an offset module. However, existing FLMSS trajectory planning methods still have certain limitations. For example, Qiao et al. (QIAO Y, YANGH, DING Y, et al. Large scanning field laser concurrent drilling system with a five-axis independent control for special-shaped holes [J]. Optics Express, 2022, 31(1): 572-84.) proposed a large scanning field five-axis independent control laser processing system, which establishes a five-axis coordinate system (… x , y , z , α , β The mapping relationship between the beam orientation and the motion variables of the drive shaft enables independent control of the beam incident angle (AOI) within a large scanning field. Software compensation is used to correct AOI deviations and spot position errors, thereby improving the machining accuracy of irregular holes. However, this method primarily focuses on beam pose control and error compensation, neglecting research on dynamic planning of five-degree-of-freedom pose trajectories, failing to consider the spatial non-uniformity of dynamic execution capability caused by optical lever effects, and lacking a unified planning model oriented towards velocity, acceleration, and jerk constraints. Furthermore, its control data is mainly generated point-by-point based on the target pose, lacking research on the collaborative propulsion mechanism under a unified time base for position and attitude dimensions. This makes it difficult to meet the high-precision trajectory planning requirements under conditions of high-speed scanning, multi-channel dynamic characteristic differences, and frequent reversals during the machining of complex microstructures. Therefore, the existing technology mainly suffers from the following problems: First, the optical leverage effect leads to significant spatial non-uniformity in the system's dynamic execution capability. Due to the geometrical magnification effect of the reflecting mirrors, the imaging relationship of multiple lens groups, and the coupling effect of the attitude adjustment channel, the displacement response of the end beam exhibits a significant optical leverage effect relative to the driving variable. In the edge region of the field of view, the spot displacement increment corresponding to the same driving angle increment is significantly larger than that in the central region, causing the end beam scanning speed to vary with spatial position. Existing trajectory planning methods typically employ uniform driving constraints across the entire field of view, ignoring this spatial non-uniformity. This can easily lead to differences in laser energy application time and machining trajectory accuracy at different spatial locations, affecting the consistency of machining quality.

[0003] Second, in the case of short, dense micropaths, traditional velocity planning methods are prone to generating high-order excitation spikes (i.e., dynamic response excitation caused by drastic changes in jerk). Microstructure trajectories at the discrete level typically exhibit characteristics such as dense short segments, rapid changes in local curvature, and frequent reversals. Traditional methods employ segmented, independent velocity planning, which repeatedly resets the boundary velocities of each segment. This not only creates excitation spikes in the discrete difference but also passively lengthens the local dwell time of the light spot, thereby amplifying the high-frequency oscillations of the galvanometer and causing edge quality fluctuations.

[0004] Third, it is difficult to achieve coordinated advancement of the position and attitude components of a five-DOF pose trajectory under a unified time reference. Existing methods often perform velocity planning for the position and attitude axes separately before timing stitching, which can easily cause local mismatch between position and attitude in regions of rapid attitude change, resulting in inconsistent end-effector pose evolution and affecting the machining accuracy of the three-dimensional structure.

[0005] Fourth, traditional velocity planning methods mainly focus on velocity and acceleration constraints, with insufficient suppression of jerk. Galvanometer-driven systems are more sensitive to changes in jerk, especially in short segment splicing and reversal regions, where jerk spikes are a significant source of high-frequency response fluctuations and end-beam perturbations. Existing methods lack effective constraints on jerk.

[0006] Fifth, existing trajectory planning methods do not incorporate the spatial distribution characteristics of the system's dynamic execution capabilities into the constraint model. In actual processing, constraints such as field of view boundaries, incident angles, image quality, and effective working range change with pose states. Using only fixed dynamic constraints is insufficient to adapt to the actual motion requirements under different positions and postures.

[0007] Therefore, there is an urgent need to propose a method for FLMSS trajectory planning and processing verification that can fully consider the characteristics of non-uniform optical mapping and achieve high-precision smooth planning of five-degree-of-freedom pose trajectories. Summary of the Invention

[0008] To overcome the shortcomings of the existing technologies, this invention proposes a FLMSS trajectory planning and processing verification method to solve the technical problems in the existing technologies, such as non-uniformity of system dynamic execution capability due to optical leverage effect, significant high-order excitation peaks under short line segment micropaths, difficulty in coordinating the position axis and attitude axis, and insufficient jerk constraints. This method achieves high-precision and high-smoothness planning and multi-axis collaborative execution of the end beam's five-degree-of-freedom pose trajectory, as well as consistency verification of processing results.

[0009] To achieve the above objectives, the technical solution adopted by the present invention is as follows: A method for FLMSS trajectory planning and processing verification includes the following steps; Step 1: Establish an inverse kinematic analytical mapping from the task space to the driving space; Obtain the desired five-DOF pose trajectory of the FLMSS end beam, perform inverse kinematic analytical mapping based on the system's composite optical path propagation model, generate the corresponding drive space command sequence, and obtain the drive space trajectory. q ( s The driving space instruction sequence is then used as input for subsequent non-uniform mapping feature analysis. Step 2: Analysis and characterization of optical non-uniform mapping features; Based on the driving space instruction sequence obtained in step one, the system Jacobian matrix and its condition number are calculated, the local mapping characteristics between the driving space and the end beam pose are analyzed, the optical non-uniform mapping characteristics and the distribution of sensitive regions are obtained, and the non-uniform mapping characteristics are used for subsequent trajectory synchronization construction and dynamic constraint modeling. Step 3: Multi-axis synchronization and smoothing construction of five-DOF pose trajectory based on non-uniform mapping features; Based on the non-uniform mapping characteristics obtained in step two, the driving space trajectory obtained in step one is analyzed under a unified time reference. q ( s Time parameterization is performed, and the speed, acceleration, and jerk of each drive axis are calculated using the discrete difference method. Speed, acceleration, and jerk constraints are applied separately to construct a smooth five-axis execution trajectory that satisfies the speed, acceleration, and jerk constraints. q ( t )= q ( s ( t )); Step 4: Dynamic amplitude limiting strategy based on non-uniform mapping features; Based on the non-uniform mapping features obtained in step two and the five-axis smooth trajectory constructed in step three, a dynamic limiting model related to the trajectory position and pose state is established, the dynamic derating coefficient is calculated, and the upper limit of the path parameter speed that meets the requirements of the system's dynamic execution capability is obtained. Step 5: Adaptive planning of path parameters and speed for micropaths; Based on the path parameter speed limit obtained in step four, speed planning is performed on the path parameters to obtain a path parameter speed curve that satisfies speed, acceleration, and jerk constraints; based on the speed curve, a five-axis synchronous execution command is generated to realize the five-degree-of-freedom pose trajectory planning of the end beam and generate a five-axis synchronous control command for machining execution. Step Six: Verify the effectiveness of trajectory planning based on processing results; Based on the five-axis synchronous control command generated in step five, laser processing is performed on target microstructures such as planar complex contours, three-dimensional layered microgrooves, and irregular conical holes to obtain the contour dimensions, morphological errors, and consistency indicators after processing, and the trajectory planning effect is verified accordingly.

[0010] The FLMSS in step one includes a two-dimensional scanning module (two-dimensional galvanometer), a dynamic focusing module, and a shifting module (parallel plate), wherein the two-dimensional scanning module is used to control the end beam in... x direction and y The dynamic focusing module is used to control the positional movement of the end beam in the direction of the movement. z The positional movement of the beam in the direction of the offset module is used to control the end beam's position. α direction and β The orientational motion enables the end-beam to achieve a five-degree-of-freedom pose. Coordinated regulation, among which x , y , z These represent the spatial coordinates of the focal point. α , β These represent the two degrees of freedom of the beam relative to the workpiece surface, namely the tilt angle.

[0011] Step one specifically involves: Based on the beam propagation path of FLMSS, a positive kinematic model is established between the end beam pose and the variables of each driving axis. Under paraxial conditions, the end-beam pose is established based on the small-angle approximation and the equivalent imaging approximation. With drive shaft motion variables Simplified analytical relation And introduce a static geometric error compensation model. The mapping is corrected, where, For the rotation angle of the two galvanometers of the two-dimensional scanning module, The distance the lens of the dynamic focusing module moves. The two parallel plates of the offset module rotate at an angle to control the five-degree-of-freedom pose of the end beam. AThis is the matrix relating pose and drive axis variables. For a given desired pose, the corrected target pose is first obtained based on the compensation function, and then substituted into the ideal inverse kinematics formula to obtain the corresponding drive space command, thus realizing the analytical generation from the task space trajectory to the drive space command sequence.

[0012] Step two specifically involves: Analysis of drive shaft motion variables With end beam pose The optical lever mapping relationship between them is used to establish the system. Jacobian matrix To describe the local mapping relationship from the driving space velocity to the end-effector pose change rate. ; Introducing feature length , Construct the normalized Jacobian matrix Define planar velocity sensitivity index and condition number index to quantitatively characterize the velocity mapping amplification effect and directional imbalance characteristics within the processing field of view.

[0013] Furthermore, the planar velocity sensitivity index is defined as the value in the normalized Jacobian matrix. XY planar subarray Maximum Singularity This is used to characterize the maximum magnification of the driving speed fluctuation on the working plane; The condition number index is defined as the ratio of the maximum singular value to the minimum singular value of the Jacobian matrix. It is used to evaluate the dynamic consistency and numerical stability of the system in different motion directions; By performing spatial sampling calculations on the normalized Jacobian matrix, the kinematic non-uniform spatial distribution characteristics of the system within the micro-machining region are obtained, and sensitive areas of non-uniform mapping are identified. By spatially discretizing the normalized Jacobian matrix within the micromachining region, the planar velocity sensitivity index and condition number index corresponding to each sampling point are calculated, and their spatial distribution within the machining region is obtained. Among them, the planar velocity sensitivity index is used to characterize the amplification degree of the driving velocity disturbance on the working plane, and the condition number index is used to characterize the consistency of the mapping capability in different motion directions. The spatial distribution of the two indices is used to identify the optical non-uniform mapping sensitive area, providing a basis for subsequent dynamic limiting strategies.

[0014] Step three specifically involves: Under a unified time reference, the function defining the change of the drive shaft motion variable with time is as follows: The driving spatial trajectory is described by separating path and time. Define dimensionless path parameters Represents trajectory progress, driving axis motion variables Write the function as a path parameter, and then parameterize it using time. Establish actual execution trajectory ; The speed of each drive shaft is approximated using a consistent difference form within the discrete domain. acceleration With jerk Discrete velocity, acceleration, and jerk constraints are applied to each drive shaft. , This forms a smooth five-axis execution trajectory that satisfies the joint constraints of velocity, acceleration, and jerk. Based on the physical upper bound of each axis and the components of the derivative of each axis with respect to the path parameters, the upper bound function for the path parameter velocity is derived: : To avoid the introduction of extremely small positive numbers due to zero denominators, the executable speed range of a given geometric path under a unified time base is determined; The drive space instruction sequence is the drive space trajectory. q ( s It consists of five drive axis position commands corresponding to each sampling point, namely: As input for subsequent trajectory parameterization, dynamic constraint modeling, and velocity planning; after path parameterization reconstruction, the path parameters are obtained. s The described five-axis drive path And establish time parameterization relationships. This provides a unified path description for subsequent velocity planning; and a smooth five-axis trajectory that satisfies continuous constraints on velocity, acceleration, and jerk. .

[0015] Step four specifically involves: Based on unified time parameterization and discrete smoothing constraints, a dynamic limiting model related to trajectory position and pose state is further established. Since the mapping relationship between the end-beam pose and each driving channel has significant positional and tilt angle correlations, the same pose increment may correspond to different amplitude driving responses at different scanning positions, focal positions, and tilt angles, resulting in significant differences in the tolerance of each path segment to velocity, acceleration, and jerk. A dynamic limiting function related to local mapping sensitivity is constructed to obtain better execution stability and local dynamic consistency across the entire path range. The mapping relationship between the end-beam pose and the driving space is as follows: , , , ; in End beam pose p Motion variables of the drive shaft q The mapping relationship, s For path parameters, For the local mapping Jacobian matrix, These represent the first, second, and third derivatives of the pose trajectory with respect to the path parameters. To comprehensively reflect the strength of the non-uniform mapping, a nominal reference path velocity is introduced. Define the normalized non-uniform mapping index: In the formula: , and For the first Speed, acceleration, and jerk limit of each drive channel; , and Let be the weight coefficient, and satisfy... ; To prevent the introduction of extremely small positive numbers with a denominator of zero, a pose-related depreciation coefficient is defined based on this: In the formula: The minimum reduction factor; The derating sensitivity coefficient is used. In the high sensitivity region, the derating coefficient decreases monotonically as the sensitivity index increases. A continuously differentiable logistic function is used to achieve a smooth transition of the derating coefficient. The path parameter speed limit obtained in step four With reduction coefficient Multiplying these together yields the upper limit of the path parameter speed that satisfies the system's dynamic execution capability requirements. The path parameter speed upper limit serves as a constraint condition for the path parameter speed adaptive planning in step five, ensuring that the trajectory meets the local dynamic execution capability requirements of FLMSS in different positions and pose states.

[0016] Step five specifically involves: Under the dynamic amplitude constraint in step four, this step solves the problems of dense short line segments, sudden changes in local curvature, and five-axis synchronous propulsion in the micropath.

[0017] A symmetric shaping method combining forward and backward recursion is used to construct a reference velocity sequence: Calculations are performed along the trajectory in the forward direction to ensure the current velocity does not exceed the upper limit due to excessive acceleration, resulting in an intermediate velocity sequence. ; Backtrack correction ensures the system has sufficient deceleration distance before entering corners or the endpoint to obtain the final reference speed. By using bidirectional shaping, low-speed constraints can propagate in both directions, creating a smooth transition zone before entering complex and dense regions; The discrete progress increment is calculated using the shaped reference velocity combined with the local arc length density. This leads to the recursive relationship of path progress. Unified generation of discrete instructions for five drive channels This enables the position and attitude components to advance in tandem under the same time reference. A velocity shaping process combining forward and backward recursion is used to generate a path parameter velocity curve that satisfies velocity, acceleration, and jerk constraints. As a trajectory integral and five-axis synchronization command The basis for its generation.

[0018] Step six specifically involves: The machining verification is carried out based on the five-axis synchronous control command generated in step five. The contour dimensions, morphological errors and consistency indicators are obtained for planar complex contours, three-dimensional layered microgrooves and irregular conical holes respectively. By comparing the machining results with the theoretical trajectory or target structure, the execution stability and machining consistency of trajectory planning in the machining process of complex microstructures are evaluated.

[0019] The beneficial effects of this invention are: This invention first establishes an inverse kinematic mapping relationship between the five-DOF pose of the FLMSS end beam and the driving space variables in step one, realizing the analytical transformation from machining trajectory to driving space trajectory. Then, in step two, it calculates the system's Jacobian matrix and condition number, analyzes the optical non-uniform mapping characteristics under different positions and poses, and identifies sensitive areas for dynamic response. In step three, it synchronously constructs trajectories for each driving axis based on a unified time reference, and simultaneously applies velocity, acceleration, and jerk constraints, thereby avoiding velocity abrupt changes and high-order excitation spikes caused by short segment splicing, frequent reversals, and local curvature abrupt changes, reducing multi-channel dynamic response fluctuations. In step four, it establishes a dynamic limiting model based on the non-uniform mapping characteristics, implements adaptive derating control for sensitive areas, matches the trajectory execution speed with the system's local dynamic execution capability, and reduces local contour deviations caused by optical leverage effects. Finally, in step five, it performs adaptive path parameter velocity planning and five-axis coordinated execution, enabling each driving channel to advance synchronously under a unified time reference, thereby improving the continuity, smoothness, and multi-axis coordination consistency of the end beam's five-DOF pose trajectory. By verifying the machining contour dimensions, morphological errors, and consistency indicators in step six, we can further evaluate the execution stability and machining consistency of the planning instructions in actual microstructure machining.

[0020] In the machining of complex planar contours, this invention identifies local high-sensitivity areas in step two and uses a dynamic limiting strategy in step four to adaptively adjust the speed of sensitive sections, thereby reducing local contour errors and edge overshoot. In the machining of three-dimensional layered microgrooves, a five-axis synchronous smooth trajectory is constructed under a unified time reference in step three, and continuous advancement of the trajectory of each layer is achieved in step five, thereby improving the consistency of the contour between layers and the surface smoothness. In the machining of irregular conical holes, synchronous and coordinated movement of position and attitude dimensions is achieved in steps three and five, and dynamic constraint adjustment is performed on areas with rapidly changing tilt angles in step four, thereby improving the hole wall contour retention capability and spatial forming accuracy.

[0021] In summary, this invention systematically solves the problem of spatial differences in dynamic execution capability caused by non-uniform optical mapping in FLMSS, and effectively improves the executability of end beam pose trajectory and the consistency of processing results under complex microstructure tasks. Attached Figure Description

[0022] Figure 1 This is a schematic diagram of the FLMSS structure.

[0023] Figure 2 This is a schematic diagram of the kinematic mapping relationship of FLMSS.

[0024] Figure 3 The flowchart shows the FLMSS trajectory planning and processing verification method.

[0025] Figure 4 This is a schematic diagram of the three-dimensional layered microgroove processing.

[0026] Figure 5 This is a diagram showing the result of layered projection processing of three-dimensional layered microgrooves. Detailed Implementation

[0027] The present invention will now be described in further detail with reference to the accompanying drawings.

[0028] like Figure 1 As shown, the FLMSS used in this invention includes a scanning module ( x , y ), Dynamic Focusing Module ( z ) and offset module ( α , β The scanning module is a two-dimensional galvanometer, used to control the two-dimensional positional movement of the end beam within the working plane, thereby achieving... x direction and y Directional beam scanning; the dynamic focusing module is used to adjust the focal point position to achieve beam scanning at the end of the beam. z Directional position control; the offset module is used to adjust the incident direction of the beam, so that the end beam is in the correct position.α direction and β Orientation and attitude control. The above modules achieve five-degree-of-freedom pose control of the end-beam through composite optical path coupling. The coordinated regulation of these mechanisms provides a kinematic basis for subsequent trajectory planning.

[0029] like Figure 2 As shown, the kinematic mapping relationship of FLMSS is jointly constituted by the driving space, optical modules, and end-beam pose space. Among them, the beam expander and focuser module corresponds to... z Direction focus control, corresponding to the offset module α direction and β Orientation and attitude control, corresponding to the planar scanning module x direction and y Directional position control is achieved through a dedicated motor driving each drive channel. The driving variables, after being processed by the beam expander / focuser, offset module, planar scanning module, and focusing module, form the end-beam trajectory, realizing the mapping relationship between the driving spatial variables and the five-degree-of-freedom pose of the end-beam. Because the beam propagation process is simultaneously affected by optical effects such as mirror deflection, lens imaging, and beam offset, the mapping relationship varies significantly at different positions and attitudes. Therefore, it is necessary to analyze its non-uniform mapping characteristics and, based on this analysis, perform trajectory synchronization construction, dynamic constraint modeling, and adaptive velocity planning.

[0030] like Figure 3 As shown, the trajectory planning method of this invention first performs inverse kinematic analytical mapping based on the desired five-DOF pose trajectory of the end-beam to generate a drive space command sequence; then, it calculates the system Jacobian matrix and condition number, analyzes the optical non-uniform mapping characteristics between the drive space and the end-beam pose, and identifies the mapping sensitive region; based on this, it applies velocity, acceleration, and jerk constraints to the drive space trajectory under a unified time reference to construct a five-axis synchronous smooth trajectory; further, it establishes a dynamic amplitude limiting model based on the non-uniform mapping characteristics, calculates the dynamic derating coefficient, and obtains the upper limit of the safe path parameter velocity; finally, it performs adaptive velocity planning in the parameter domain, generates a path parameter velocity curve that satisfies the dynamic constraint conditions through a combination of forward and backward recursion, calculates the trajectory progress increment, and uniformly generates five-axis synchronous execution commands to realize the five-DOF pose trajectory planning of the end-beam.

[0031] This embodiment uses a tapered three-dimensional layered microgroove as the test object to verify the actual processing effect of the method of the present invention under three-dimensional layered trajectory conditions.

[0032] 1. Experimental conditions The experiment was conducted on a self-built FLMSS. The laser used was a PX200-2-GF picosecond laser manufactured by EdgeWave, with a maximum laser output power of 100 W. The theoretical tank was discretized into 5 layers, each corresponding to a two-dimensional cross-sectional profile, as shown below. Figure 4 As shown.

[0033] During processing, the tilt angle was maintained at 4° and linked to the plane scanning position. The laser power was 10 W, with 8 concentric rectangles per layer, a layer spacing of 100 μm, 1000 scans per layer, and a scanning speed of 300 mm / s. The processing was carried out on a 0.5 mm thick GH4169 nickel-based superalloy sheet. The processing was repeated 5 times to observe the overall forming consistency and repeatability stability.

[0034] To facilitate the identification of contour errors, the laser repetition frequency was appropriately reduced in the experiment, so that the processing boundary was presented in the form of a separated point array, which facilitated subsequent contour extraction and interlayer comparison. After ultrasonic cleaning, the processed samples were used to acquire two-dimensional microscopic images of the surface using a Keyence optical microscope (VHX-600), and typical local areas were magnified and analyzed using a laser scanning confocal microscope. Under the premise of maintaining the same microscopic imaging conditions, pixel calibration method, and image processing flow, MATLAB was used to extract the contours from the microscopic images of typical local areas. It should be noted that, affected by factors such as microscopic imaging resolution, edge grayscale transition, and image segmentation errors, the extracted contour deviation is not directly equivalent to the actual motion pose error during execution, but is used to evaluate the degree of closeness between the final formed contour and the theoretical trajectory.

[0035] 2. Processing steps The process of generating and executing driving instructions according to the FLMSS trajectory planning method proposed in this invention specifically includes the following steps: First, based on the 3D model of the layered microgroove, the contour trajectory of each layer is obtained. Then, combining the focal positions and beam tilt angle requirements of each layer, a five-DOF pose trajectory of the end-beam is constructed. Using the inverse kinematic analytical model of FLMSS, the end-beam pose trajectory is converted into a driving space trajectory, obtaining the corresponding driving space command sequence.

[0036] Secondly, the Jacobian matrix of the system is calculated based on the driving space trajectory, and the position and attitude dimensions are normalized to obtain the normalized Jacobian matrix. Further calculations of the planar velocity sensitivity index and condition number index are performed to analyze the local mapping amplification effect and directional imbalance characteristics between the driving space and the end-beam pose at different processing positions, thus obtaining the distribution of optical non-uniform mapping characteristics within the processing area.

[0037] Then, path parameters are introduced to parametrically describe the drive space trajectory, and the relationship between path parameters and drive space trajectory is established under a unified time reference. Based on the physical constraints of velocity, acceleration, and jerk of each drive axis, a path parameter velocity constraint model is constructed to obtain the allowable velocity range of path parameters at each sampling point, thereby realizing the synchronous and smooth construction of the five-axis drive trajectory.

[0038] Next, a dynamic derating model is constructed based on the planar velocity sensitivity index and the condition number index, and the allowable speed of the path parameters is dynamically corrected in combination with the non-uniform mapping characteristics within the processing area. For sensitive areas with strong mapping amplification effects or large condition numbers, the allowable speed of the path parameters is reduced; for areas with relatively uniform mapping characteristics, a higher speed level is maintained, thereby obtaining a safe upper limit for the path parameter speed that meets the requirements of the system's local dynamic execution capability.

[0039] Subsequently, with the upper limit of the safe path parameter speed as a constraint, adaptive speed planning is performed in the parameter domain using a combination of forward and backward propagation to obtain the path parameter speed curve that satisfies the constraints of speed, acceleration, and jerk. The path progress increment at each sampling moment is calculated based on the path parameter speed curve, and a five-axis synchronous execution command is generated in combination with the driving space trajectory function to realize the continuous processing of the trajectory of each layer of the three-dimensional layered microgroove.

[0040] Finally, the machining verification of the five-axis synchronous execution command was carried out to obtain the contour size, morphological error and repeatability consistency index of the layered microgroove, and the index was compared with the theoretical layered contour to verify the trajectory planning effect.

[0041] 3. Processing Results and Analysis Figure 5 Optical microscope images of the processing results for layers 1, 3, and 5 are shown. (By...) Figure 5 As can be seen, the method of this invention can achieve stable processing of each layer's contour, with generally regular contour boundaries, smooth local transition areas, and natural interlayer variations. Extracting the groove length and width data for all five layers, the theoretical groove length and width gradually decrease as the layer number increases. The measured values ​​under the method of this invention show a gradual change, closely approximating the theoretical trend. Statistical analysis of the contour errors for each layer shows that the maximum error is controlled within 32 μm, and the root mean square error is controlled within 18 μm. The results of five repeated processing iterations remain consistent, indicating that the method of this invention has good repeatability. In summary, this embodiment verifies the effectiveness of the method of this invention in three-dimensional layered microgroove processing, maintaining the overall shape of the layered contours, reducing interlayer fluctuations, and achieving stable interlayer dimensional evolution.

[0042] Besides three-dimensional layered microgrooves, the method of this invention is also applicable to typical micromachining tasks such as planar irregular petal contours, irregular conical holes, complex flow channel microgrooves, and free-form surface microstructures. For example, in the machining of planar irregular petal contours, traditional planning methods are prone to velocity fluctuations and local overshoots due to the large number of short line segments and continuous curvature variation regions contained in the contour boundary. This invention identifies the optical non-uniform mapping sensitive area in step two and adaptively adjusts the local trajectory velocity using a dynamic limiting strategy in step four, thereby improving the accuracy of boundary contour preservation. In the machining of overlapping elliptical irregular conical holes, as the machining depth increases, the position and attitude of the end beam need to continuously change in tandem, which can easily lead to asynchrony between the position and attitude dimensions. This invention constructs a five-axis synchronous smooth trajectory under a unified time reference in step three and implements adaptive planning of path parameter velocity in step five, enabling each driving channel to advance in tandem, thereby improving the consistency of the hole wall contour and the spatial forming accuracy of the irregular conical hole. Therefore, this invention is particularly suitable for complex microstructure machining scenarios with dense short line segments, frequent reversals, rapid curvature changes, and significant position and attitude coupling motions.

Claims

1. A method for FLMSS trajectory planning and processing verification, characterized in that, Includes the following steps; Step 1: Obtain the desired five-DOF pose trajectory of the FLMSS end beam, perform inverse kinematic analytical mapping based on the system's composite optical path propagation model, generate the corresponding driving space command sequence, and obtain the driving space trajectory. q ( s ); Step 2: Based on the driving space instruction sequence obtained in Step 1, calculate the system Jacobian matrix and its condition number, analyze the local mapping characteristics between the driving space and the end beam pose, obtain the optical non-uniform mapping characteristics and the distribution of sensitive regions, and use the non-uniform mapping characteristics for subsequent trajectory synchronization construction and dynamic constraint modeling. Step 3: Based on the non-uniform mapping features obtained in Step 2, and under a unified time reference, analyze the driving space trajectory obtained in Step 1. q ( s Time parameterization is performed, and the speed, acceleration, and jerk of each drive axis are calculated using the discrete difference method. Speed, acceleration, and jerk constraints are applied separately to construct a smooth five-axis execution trajectory that satisfies the speed, acceleration, and jerk constraints. q ( t )= q ( s ( t )); Step 4: Based on the non-uniform mapping features obtained in Step 2 and the five-axis smooth trajectory constructed in Step 3, establish a dynamic limiting model related to the trajectory position and pose state, calculate the dynamic derating coefficient, and obtain the upper limit of the path parameter speed that meets the requirements of the system's dynamic execution capability. Step 5: Based on the path parameter speed limit obtained in Step 4, perform speed planning on the path parameters to obtain a path parameter speed curve that satisfies speed, acceleration, and jerk constraints; generate a five-axis synchronous execution command based on the speed curve to realize the five-degree-of-freedom pose trajectory planning of the end beam, and generate a five-axis synchronous control command for machining execution. Step Six: Perform laser processing on the target microstructure according to the five-axis synchronous control command generated in Step Five, obtain the contour size, shape error and consistency index, and verify the trajectory planning effect based on the contour size, shape error and consistency index.

2. The FLMSS trajectory planning and processing verification method according to claim 1, characterized in that, The FLMSS in step one includes a two-dimensional scanning module, a dynamic focusing module, and an offset module, wherein the two-dimensional scanning module is used to control the end beam in x direction and y The dynamic focusing module is used to control the positional movement of the end beam in the direction of the movement. z The positional movement of the beam in the direction of the offset module is used to control the end beam's position. α direction and β The orientational motion enables the end-beam to achieve a five-degree-of-freedom pose. Coordinated regulation, among which x , y , z These represent the spatial coordinates of the focal point. α , β These represent the two degrees of freedom of the beam relative to the workpiece surface at tilt angles; The two-dimensional scanning module is a two-dimensional galvanometer, and the offset module is a parallel plate.

3. The FLMSS trajectory planning and processing verification method according to claim 2, characterized in that, Step one specifically involves: Based on the beam propagation path of FLMSS, a positive kinematic model is established between the end beam pose and the variables of each driving axis. Under paraxial conditions, the end-beam pose is established based on the small-angle approximation and the equivalent imaging approximation. With drive shaft motion variables Simplified analytical relation And introduce a static geometric error compensation model. The mapping is corrected, where, For the rotation angle of the two galvanometers of the two-dimensional scanning module, The distance the lens of the dynamic focusing module moves. The two parallel plates of the offset module rotate at an angle to control the five-degree-of-freedom pose of the end beam. A This is the matrix relating pose and drive axis variables. For a given desired pose, the corrected target pose is first obtained based on the compensation function, and then substituted into the ideal inverse kinematics formula to obtain the corresponding drive space command, thus realizing the analytical generation from the task space trajectory to the drive space command sequence.

4. The FLMSS trajectory planning and processing verification method according to claim 3, characterized in that, Step two specifically involves: Analysis of drive shaft motion variables With end beam pose The optical lever mapping relationship between them is used to establish the system. Jacobian matrix To describe the local mapping relationship from the driving space velocity to the end-effector pose change rate. ; Introducing feature length , Construct the normalized Jacobian matrix Define planar velocity sensitivity index and condition number index to quantitatively characterize the velocity mapping amplification effect and directional imbalance characteristics within the processing field of view.

5. The FLMSS trajectory planning and processing verification method according to claim 4, characterized in that, The planar velocity sensitivity index is defined as the value in the normalized Jacobian matrix. XY planar subarray Maximum Singularity This is used to characterize the maximum magnification of the driving speed fluctuation on the working plane; The condition number index is defined as the ratio of the maximum singular value to the minimum singular value of the Jacobian matrix. It is used to evaluate the dynamic consistency and numerical stability of the system in different motion directions; By performing spatial sampling calculations on the normalized Jacobian matrix, the kinematic non-uniform spatial distribution characteristics of the system within the micro-machining region are obtained, and sensitive areas of non-uniform mapping are identified. By spatially discretizing the normalized Jacobian matrix within the micromachining region, the planar velocity sensitivity index and condition number index corresponding to each sampling point are calculated, and their spatial distribution within the machining region is obtained. Among them, the planar velocity sensitivity index is used to characterize the amplification degree of the driving velocity disturbance on the working plane, and the condition number index is used to characterize the consistency of the mapping capability in different motion directions. The spatial distribution of the two indices is used to identify the optical non-uniform mapping sensitive area, providing a basis for subsequent dynamic limiting strategies.

6. The FLMSS trajectory planning and processing verification method according to claim 5, characterized in that, Step three specifically involves: Under a unified time reference, the function defining the change of the drive shaft motion variable with time is as follows: The driving spatial trajectory is described by separating path and time. Define dimensionless path parameters Represents trajectory progress, driving axis motion variables Write the function as a path parameter, and then parameterize it using time. Establish actual execution trajectory ; The speed of each drive shaft is approximated using a consistent difference form within the discrete domain. acceleration With jerk Discrete velocity, acceleration, and jerk constraints are applied to each drive shaft. , ; Based on the physical upper bound of each axis and the components of the derivative of each axis with respect to the path parameters, the upper bound function for the path parameter velocity is derived: ： To avoid introducing extremely small positive numbers due to a zero denominator, the executable speed range of a given geometric path under a unified time base is determined; the drive space instruction sequence is the drive space trajectory. q ( s It consists of five drive axis position commands corresponding to each sampling point, namely: As input for subsequent trajectory parameterization, dynamic constraint modeling, and velocity planning; after path parameterization reconstruction, the path parameters are obtained. s The described five-axis drive path And establish time parameterization relationships. This provides a unified path description for subsequent velocity planning; and a smooth five-axis trajectory that satisfies continuous constraints on velocity, acceleration, and jerk. .

7. The FLMSS trajectory planning and processing verification method according to claim 6, characterized in that, Step four specifically involves: Based on unified time parameterization and discrete smoothing constraints, a dynamic limiting model related to trajectory position and pose state is further established; the mapping relationship from end-effector pose to the driving space is as follows: ， ， ， ； in End beam pose p Motion variables of the drive shaft q The mapping relationship, s For path parameters, For the local mapping Jacobian matrix, These represent the first, second, and third derivatives of the pose trajectory with respect to the path parameters. To comprehensively reflect the strength of the non-uniform mapping, a nominal reference path velocity is introduced. Define the normalized non-uniform mapping index: In the formula: , and For the first Speed, acceleration, and jerk limit of each drive channel; , and Let be the weight coefficient, and satisfy... ; To prevent the introduction of extremely small positive numbers with a denominator of zero, a pose-related depreciation coefficient is defined based on this: In the formula: The minimum reduction factor; The derating sensitivity coefficient is used; a continuously differentiable logistic function is employed to achieve a smooth transition of the derating coefficient. The path parameter speed limit obtained in step four With reduction coefficient Multiplying these together yields the upper limit of the path parameter speed that satisfies the system's dynamic execution capability requirements. The path parameter speed upper limit serves as a constraint condition for the path parameter speed adaptive planning in step five, ensuring that the trajectory meets the local dynamic execution capability requirements of FLMSS in different positions and pose states.

8. The FLMSS trajectory planning method according to claim 7, characterized in that, Step five specifically involves: A symmetric shaping method combining forward and backward recursion is used to construct a reference velocity sequence: Calculations are performed along the trajectory in the forward direction to ensure the current velocity does not exceed the upper limit due to excessive acceleration, resulting in an intermediate velocity sequence. ； Backtrack correction ensures the system has sufficient deceleration distance before entering corners or the endpoint to obtain the final reference speed. Bidirectional shaping enables low-speed constraints to propagate bidirectionally, creating a smooth transition zone before entering complex and dense regions. The discrete progress increment is calculated using the shaped reference velocity combined with the local arc length density. This leads to the recursive relationship of path progress. Unified generation of discrete instructions for five drive channels This enables the position and attitude components to advance in tandem under the same time reference. A velocity shaping process combining forward and backward recursion is used to generate a path parameter velocity curve that satisfies velocity, acceleration, and jerk constraints. As a trajectory integral and five-axis synchronization command The basis for its generation.

9. The method for trajectory planning and processing verification of a five-axis laser micromachining scanning system according to claim 8, characterized in that, Step six specifically involves: Based on the five-axis synchronous control commands generated in step five, machine planar complex contours, three-dimensional layered microgrooves, or irregular conical holes, obtain the contour dimensions, morphological errors, and consistency indicators after machining, and evaluate the execution stability and machining consistency of trajectory planning in the machining process of complex microstructures.

Images