A method, equipment, and medium for optimizing the turning motion trajectory of a microlens array

Abstract

This invention provides a method, device, and medium for optimizing the motion trajectory of microlens array turning, relating to the field of microlens array turning motion trajectory optimization technology. The method includes: constructing a continuous trajectory curve P(u) based on discrete tool path points corresponding to the microlens array turning process; discretizing P(u) into multiple trajectory points in the parameter domain to obtain a trajectory point list G; determining the forward maximum feasible parameter velocity for each trajectory point sequentially, starting from the first forward trajectory point; determining the reverse maximum feasible parameter velocity for each trajectory point sequentially, starting from the first reverse trajectory point; determining the target maximum feasible parameter velocity for the corresponding trajectory point; and generating the optimal trajectory corresponding to P(u) that satisfies kinematic constraints based on the target maximum feasible parameter velocity for each trajectory point in G. This invention simplifies the parameter velocity optimization process, reduces the number of trial and error iterations, lowers computational complexity, and significantly improves the computational efficiency of trajectory optimization.

Description

Technical Field

[0001] This invention relates to the field of microlens array turning motion trajectory optimization technology, and in particular to a method, equipment and medium for optimizing microlens array turning motion trajectory. Background Technology

[0002] Microlens arrays (MLAs), as periodic or quasi-periodic components composed of microlenses, are widely used in beam shaping, imaging, optical sensing, augmented reality (AR), and virtual reality (VR) due to their compact size, excellent optical performance, and microscale optical manipulation capabilities. They place extremely high demands on manufacturing precision and efficiency. However, manufacturing high-quality MLAs requires planning high-quality motion trajectories. Existing methods for motion trajectory planning mainly fall into two categories: acceleration / deceleration (ACC / DEC) methods (such as S-curve planning): while having low computational complexity and good real-time performance, they fail to fully utilize the dynamic capabilities of each axis, making it difficult to achieve efficient processing under speed and acceleration constraints; and time-optimal methods (such as bidirectional scanning algorithms): while capable of generating minimum or near-minimum time trajectories, their computational cost is extremely high.

[0003] In servo control, the feedforward mechanism of traditional PID controllers relies on numerical differentiation to obtain speed and acceleration, which easily introduces phase lag and differential error, resulting in a decrease in tracking accuracy and making it difficult to meet the stringent requirements of MLA manufacturing for high-frequency motion. Therefore, there is an urgent need for a microlens array turning motion trajectory optimization method to reduce optimization execution time and solve the problems of high computational cost and excessive iterations of existing time-optimal methods. Summary of the Invention

[0004] To address the aforementioned technical problems, the technical solution adopted by this invention is as follows:

[0005] According to a first aspect of this application, a method for optimizing the turning motion trajectory of a microlens array is provided, the method comprising the following steps:

[0006] S100, construct a continuous trajectory curve P(u) based on the discrete tool path points corresponding to the microlens array turning process, where u is a one-dimensional parameter that maps the microlens array turning continuous trajectory curve from three-dimensional space to the interval [0,1], 0≤u≤1;

[0007] S200, Discretize P(u) into multiple trajectory points in the parameter domain to obtain a list of trajectory points G = (P(u1), P(u2), ..., P(u... i ), ..., P(u) n )), i=1, 2,...,n; P(u i Let be the i-th trajectory point corresponding to P(u), and n be the number of trajectory points corresponding to P(u); u iLet P(u) be the curve parameter of the i-th trajectory point;

[0008] S300 aims to minimize the trajectory running time. Under the preset kinematic constraints, it sequentially determines the positive maximum feasible parameter velocity of each trajectory point starting from P(u1).

[0009] S400, based on the positive maximum feasible parameter velocity at each trajectory point, from P(u n Starting from this point, determine the maximum feasible reverse velocity parameter for each trajectory point in sequence;

[0010] S500, the minimum feasible parameter velocity between the forward maximum feasible parameter velocity and the reverse maximum feasible parameter velocity of each trajectory point is determined as the target maximum feasible parameter velocity of the corresponding trajectory point;

[0011] S600, based on the target maximum feasible parameter velocity of each trajectory point in G, generate the optimal trajectory P(u(t)) that satisfies the kinematic constraints corresponding to P(u); u(t) is the curve parameter at time point t.

[0012] According to another aspect of this application, a non-transitory computer-readable storage medium is also provided, wherein at least one instruction or at least one program is stored in the storage medium, and the at least one instruction or at least one program is loaded and executed by a processor to implement the above-described microlens array turning motion trajectory optimization method.

[0013] According to another aspect of this application, an electronic device is also provided, including a processor and the aforementioned non-transitory computer-readable storage medium.

[0014] The present invention has at least the following beneficial effects:

[0015] The microlens array turning motion trajectory optimization method of the present invention aims to minimize the trajectory running time. Under preset kinematic constraints, it determines the maximum feasible parameter speed of each trajectory point through forward and backward iterations. This fully utilizes the dynamic performance of each axis, making the trajectory running time closer to the theoretical minimum, thus improving the machining efficiency of microlens array turning. By determining the maximum feasible parameter speed in both forward and backward directions and taking the minimum value as the target maximum feasible parameter speed, the optimization process of parameter speed is simplified, the number of trial and error iterations is reduced, the computational complexity is lowered, and the computational efficiency of trajectory optimization is significantly improved. This method is more suitable for practical industrial applications of microlens array ultra-precision turning. Attached Figure Description

[0016] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0017] Figure 1 A flowchart of a microlens array turning motion trajectory optimization method provided in an embodiment of the present invention. Detailed Implementation

[0018] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0019] It should be noted that, based on this disclosure, those skilled in the art will understand that one aspect described herein can be implemented independently of any other aspect, and two or more of these aspects can be combined in various ways. For example, any number of aspects set forth herein can be used to implement the device and / or practice the method. Furthermore, this device and / or practice the method can be implemented using other structures and / or functionalities besides one or more of the aspects set forth herein.

[0020] Example 1:

[0021] The following will refer to Figure 1 The flowchart shown illustrates a method for optimizing the turning motion trajectory of a microlens array, which introduces such a method.

[0022] The method for optimizing the turning motion trajectory of the microlens array may include the following steps:

[0023] S100, construct a continuous trajectory curve P(u) based on the discrete tool path points corresponding to the microlens array turning process, where u is a one-dimensional parameter that maps the continuous trajectory curve of the microlens array turning from three-dimensional space to the interval [0,1], 0≤u≤1.

[0024] In this embodiment, discrete toolpath points (generated by the CAM system and containing surface geometry and tool radius compensation information) of microlens array turning are used as control points, and C... 2 Continuous interpolation is used to construct a cubic B-spline curve P(u)=([x(u),y(u),z(u)]), where 0≤u≤1, to ensure the continuity of the trajectory in terms of position, velocity and acceleration.

[0025] This step transforms discrete toolpath points into smooth, continuous curves, avoiding abrupt trajectory changes caused by directly connecting discrete points. This provides a smooth foundation for subsequent trajectory discretization and optimization, reducing machining vibrations and surface quality defects caused by trajectory discontinuities.

[0026] S200, Discretize P(u) into multiple trajectory points in the parameter domain to obtain a list of trajectory points G = (P(u1), P(u2), ..., P(u... i ), ..., P(u) n )), i=1, 2,...,n; P(u i Let be the i-th trajectory point corresponding to P(u), and n be the number of trajectory points corresponding to P(u); u i Let P(u) be the curve parameter of the i-th trajectory point.

[0027] Within the parameter domain 0 ≤ u ≤ 1, the cubic B-spline curve P(u) is uniformly discretized into n trajectory points, resulting in a list G, where 0 ≤ u1 < u2 < … < u n ≤1, discretization resolution Δu (e.g., Δu=10) -4 It is necessary to balance and optimize accuracy and computational efficiency.

[0028] This step transforms the continuous curve into discrete points that can be numerically calculated, facilitating subsequent iterative calculations for forward / backward optimization. By appropriately selecting Δu, we can ensure that trajectory details are fully captured while avoiding a surge in computational load caused by too many discrete points, thus balancing optimization accuracy and efficiency.

[0029] S300 aims to minimize the trajectory running time. Under preset kinematic constraints, it sequentially determines the positive maximum feasible parameter velocity of each trajectory point, starting from P(u1).

[0030] With the goal of minimizing the trajectory running time, starting from the starting point P(u1), the maximum feasible parameter velocity of each trajectory point is calculated sequentially, while satisfying kinematic constraints during the calculation.

[0031] Maximize the parametric velocity within the kinematic constraints to initially explore the dynamic performance of each axis, laying the foundation for shortening the trajectory running time; ensure that the velocity at each step meets the constraints through point-by-point iteration to avoid machining errors caused by excessively high local velocities.

[0032] Furthermore, step S300 may include the following steps:

[0033] S310, Obtain the maximum operating speed v of the machine tool actuator. max and maximum acceleration a max .

[0034] v max and amax The preset kinematic constraints for the machine tool are determined based on the dynamic performance of the ultra-precision lathe (such as the LD-CL100 V2). Specifically, these include the maximum speed and acceleration limits for each axis, such as the X, Z, and C axes (as defined in the "Slow," "Medium," and "Fast" constraint sets in Table 1). These parameters need to be set in conjunction with the physical properties of the machine tool drive system (such as linear motors and piezoelectric actuators) and the processing requirements (such as the surface quality requirements of the microlens array) to ensure that they do not exceed the machine tool's mechanical load-bearing capacity and dynamic response range.

[0035] This step clarifies the motion boundary conditions of the machine tool, providing a strict constraint benchmark for subsequent parameter speed optimization. It avoids machine tool vibration, drive overload, or decreased machining accuracy caused by exceeding speed or acceleration limits, thus ensuring the safety and feasibility of trajectory optimization from the ground up.

[0036] S320, according to v max a max and P(u) i The corresponding positive maximum feasible parameter velocity. Determine P(u) i+1 The corresponding positive maximum feasible parameter velocity. ;in, Take the maximum value if the following relationship is satisfied:

[0037] ;

[0038] in, =du i / dt, where t is the time point; Δu is u i+1 and u i The difference between them, Δu=u i+1 -u i ; For P(u) in u i+1 The first derivative at that point; For P(u) in u i+1 The second derivative at point; For P(u) in u i+1 The positive curve parameter acceleration at that location.

[0039] Based on the previous trajectory point P(u) i The positive maximum feasible parameter velocity of ) Maximize P(u) under the following constraints. i+1 The corresponding positive maximum feasible parameter velocity. :

[0040] Speed ​​constraints: , For a cubic B-spline curve in u i+1 The first derivative at that point describes the direction of the tangent to the curve at that point, ensuring that the actual operating speed of each axis does not exceed v. max .

[0041] Acceleration constraints: , The second derivative of the curve describes the change in curvature. For the discrete approximation of parametric acceleration, ensure that the actual acceleration of each axis does not exceed a. max During iterative calculations, the above system of inequalities is solved numerically, and the largest solution is selected from the set of solutions that satisfy all constraints. .

[0042] Under the premise of strictly following the kinematic constraints of the machine tool, the parametric velocity of each trajectory point is maximized to fully explore the dynamic capabilities of the machine tool and shorten the processing time. By coupling the calculation of the first and second derivatives with the parametric velocity / acceleration, the geometric characteristics of the curve (such as curvature) and kinematic performance are accurately correlated to avoid velocity / acceleration exceeding the limit due to sudden changes in local curvature. This provides a reasonable positive velocity benchmark for subsequent back-optimization and reduces the number of iterations of the overall optimization.

[0043] S400, based on the positive maximum feasible parameter velocity at each trajectory point, from P(u n Starting from this point, determine the maximum feasible reverse velocity parameter for each trajectory point in sequence.

[0044] Based on the positive optimization results, from the endpoint P(u) n (P(u) n Starting from 0), the maximum feasible parameter velocity for each trajectory point is calculated in reverse iteration. Similarly, the velocity and acceleration constraints must be met to ensure that the trajectory can decelerate smoothly to the end point and come to a standstill.

[0045] This step corrects the "local greed" defect of forward optimization (forward optimization may cause subsequent high curvature segments to fail to meet constraints due to excessive pursuit of local speed). Reverse verification ensures that the trajectory meets constraints throughout the entire segment, especially ensuring that the endpoint can stop smoothly, avoiding a decrease in machining accuracy due to the endpoint speed not meeting the constraints.

[0046] Furthermore, step S400 may include the following steps:

[0047] S410, according to v max a max and P(u) i The corresponding reverse maximum feasible parameter speed Determine P(u) i-1 The corresponding reverse maximum feasible parameter speed ;in, Take the maximum value if the following relationship is satisfied:

[0048] ;

[0049] in, =du i-1 / dt; For P(u) in u i-1 The first derivative at that point; For P(u) in u i-1 The second derivative at point; For P(u) in u i-1 The acceleration parameter of the reverse curve at that point.

[0050] In this embodiment, reverse optimization starts from the trajectory endpoint P(u) n Starting from the current trajectory point P(u) i The reverse maximum feasible parameter velocity, under the premise of satisfying the following constraints, maximizes the parameter velocity of the previous trajectory point:

[0051] Speed ​​constraints: Ensure that the actual speed of each axis does not exceed the machine tool's maximum speed v. max .

[0052] Acceleration constraints: Ensure that the actual acceleration of each axis does not exceed a. max .

[0053] During iterative calculations, the above system of inequalities is solved numerically, and the largest solution is selected from the set of solutions that satisfy all constraints. The reverse velocity planning is then carried out sequentially from i=n to i=2, and finally the reverse velocity planning of all trajectory points is completed.

[0054] By reverse-checking and adjusting the velocity parameters from the endpoint, the infeasibility of subsequent trajectory segments caused by the "local greedy" strategy in forward optimization (such as acceleration exceeding the limit in high curvature segments) is corrected, ensuring that the trajectory can smoothly decelerate to a stationary state at the endpoint. At the same time, strict velocity and acceleration constraint checks further ensure the safety of reverse velocity planning, complementing forward optimization and providing a reliable basis for determining the maximum feasible parameter velocity of the target by taking the minimum value. This reduces the number of trial and error iterations in the overall optimization and improves the efficiency and feasibility of trajectory planning.

[0055] In this embodiment, the overall effects of forward and reverse optimization are as follows:

[0056] On the one hand, forward optimization starts from the trajectory starting point and maximizes the parametric velocity of each trajectory point under kinematic constraints, initially exploring the machine tool's dynamic capabilities to shorten machining time. On the other hand, reverse optimization starts from the trajectory ending point (where the constraint parameter velocity is 0) and adjusts the parametric velocity of each trajectory point in reverse, correcting the problem of excessively high local velocities that may occur in forward optimization, making subsequent segments infeasible, and ensuring that the trajectory satisfies the constraints throughout. Combining the two methods, the minimum value of the maximum feasible parametric velocity in both the forward and reverse directions is taken as the target maximum feasible parametric velocity. This fully utilizes the machine tool's dynamic performance to improve efficiency and ensures the global feasibility of the trajectory through bidirectional verification, significantly reducing the number of trial and error iterations required by traditional unidirectional optimization. While reducing the optimization execution time, it generates a time-optimal trajectory that satisfies kinematic constraints, providing accurate speed and acceleration benchmarks for subsequent servo control, ultimately improving the accuracy and efficiency of microlens array machining.

[0057] In this embodiment, the parameter speed The core physical meaning is "the rate of change of the curve parameter u with time", which reflects the "speed of progress" of the machine tool moving along the trajectory curve P(u); The larger the value, the farther the distance traveled along the parameter domain [0,1] per unit time, and the higher the processing efficiency.

[0058] (Forward): Starting from the trajectory start point P(u1), calculate the maximum feasible parameter speed du / dt point by point. The constraint condition is that "the speed at the current point does not exceed the speed / acceleration limit of each axis of the machine tool, and can smoothly transition to the next point".

[0059] (Reverse): From the endpoint P(u) of the trajectory n Starting from this point, the maximum feasible parameter, speed du / dt, is calculated point by point in reverse. The constraint is that "the speed at the current point does not exceed the upper limit of the speed / acceleration of each axis of the machine tool, and can smoothly transition to the previous point".

[0060] Both are mathematically defined as du / dt, differing only in their calculation direction and reference constraint point. Essentially, they are both "the rate of change of parameter u over time," which aligns with the core logic of trajectory optimization: "corresponding geometric trajectory and time through parameter velocity."

[0061] S500 determines the minimum feasible parameter velocity between the forward maximum feasible parameter velocity and the reverse maximum feasible parameter velocity of each trajectory point as the target maximum feasible parameter velocity of the corresponding trajectory point.

[0062] Furthermore, step S500 includes the following steps:

[0063] S510, according to and Determine P(u) iThe target maximum feasible parameter is velocity mv. max，i =MIN( ); where MIN() is the preset minimum value function.

[0064] This step ensures that the parameter velocity of each trajectory point satisfies both positive and negative constraints, completely eliminating infeasible solutions that may occur in single-direction optimization and guaranteeing the global feasibility of the trajectory. By adopting the "smallest" strategy, the velocity and safety are balanced within the constraints, providing a reliable parameter velocity basis for the generation of the final optimal trajectory.

[0065] S600, based on the target maximum feasible parameter velocity of each trajectory point in P, generate the optimal trajectory P(u(t)) corresponding to P(u) that satisfies the kinematic constraints; u(t) is the curve parameter at time point t.

[0066] Based on the target maximum feasible parameter velocity of all trajectory points, a continuous parameter velocity profile is constructed in the time domain by cubic interpolation; the trajectory u(t) of parameter change with time is obtained by surface integration of this profile; u(t) is substituted into the cubic B-spline curve P(u) to obtain the mapping relationship between spatial position and time P(u(t)), which is the optimal trajectory.

[0067] This step transforms the discrete target maximum feasible parameter velocity into a continuous and smooth time-domain trajectory, avoiding servo vibration caused by sudden velocity changes. The generated trajectory simultaneously satisfies time optimality and kinematic constraints, providing precise position, velocity, and acceleration commands for subsequent direct feedforward control, ultimately improving the efficiency (shortening time) and accuracy (reducing shape errors) of microlens array fabrication.

[0068] In this embodiment, the continuous trajectory curve P(u) constructed in S100 is the fundamental trajectory function of the entire method (generated by interpolation of discrete toolpath points in microlens array turning, such as a cubic B-spline curve). The P appearing in subsequent steps (such as S200 and S600) all refer to this function, not different functions. The same notation is used because the spatial geometric characteristics of the trajectory (such as the positional relationship between the X, Z, and C axes) are determined from the beginning by the initially constructed P(u). Subsequent optimizations only change the mapping relationship between parameter u and time t, rather than the geometry of the trajectory itself. This unified notation conforms to mathematical expression conventions, meaning the function itself remains unchanged, only the physical meaning of the parameters extends with the scenario (from purely geometric parameters to time-related parameters).

[0069] Differences in the representation of parameter u:

[0070] The distinction between discrete and continuous u i These are discretized curve parameters: u in S200 iIt is the specific numerical value obtained by discretizing the continuous parameter domain [0,1], corresponding to the discrete point P(u) on the trajectory. i ), used for numerical computation and iterative optimization (such as forward / backward velocity planning).

[0071] u(t) is a continuous parametric-time function: In S600, u(t) represents the continuous change of parameter u with time t (e.g., u(t) = 0.05t). 2 This is used to describe "the parameter value of the trajectory curve is u(t) at time t", which is essentially a discrete u i It is extended to a continuous time-domain function through interpolation and integration. Both are curve parameters, but the different expressions are to distinguish the "parameter values ​​at discrete points" (u). i "(u(t))" and "continuous evolution of parameters over time" are different representations of the same parameter in discrete analysis and continuous modeling scenarios, and are not two different parameters.

[0072] Furthermore, after step S320, the method may further include the following steps:

[0073] S330, obtain P(u) i The corresponding parameter speed limit value 、P(u i-1 The corresponding parameter speed limit value and P(u) i+1 The corresponding parameter speed limit value ;in, The following relationship must be satisfied:

[0074] .

[0075] In this embodiment, R is the value of P(u) in u. i The radius of curvature at that point; For P(u) in u i The first derivative at the point; the parameter velocity limit is based on the curvature of the trajectory curve and the system's maximum acceleration a. max Calculation. Formula In this context, R represents P(u) in u. i The radius of curvature at point (R=1 / k, k is the curvature), For P(u) in u i The first derivative at the point (describing the direction of the tangent).

[0076] Combining the existing curvature calculation formula k= It can be deduced that The centripetal force constraint (determined by acceleration limits) must be satisfied. This means calculating the maximum allowable parametric velocity at that point using the first and second derivatives of the curve and the system's maximum acceleration. Similarly, the velocity at adjacent points u can be calculated.i-1 u i+1 The parameter speed limit value.

[0077] By linking curvature and acceleration constraints, the parametric velocity of high curvature segments is precisely limited to avoid centripetal force exceeding limits due to trajectory curvature, thus ensuring motion safety from a geometric perspective. At the same time, the constraint values ​​of adjacent points are considered to lay the foundation for subsequent conservative verification.

[0078] S340, according to , and Determine P(u) i The corresponding final parameter speed limit value .

[0079] The minimum value of the parameter velocity limit for the current trajectory point and its preceding and succeeding points is taken as P(u i The final limit for the corresponding final parameter velocity. Discretization error needs to be handled conservatively by incorporating the constraints of adjacent points to avoid omission of local constraints due to parameter domain discretization.

[0080] A conservative strategy is adopted to handle discretization errors, ensuring that kinematic constraints are met even at the intersection of trajectory segments. This reduces the infeasibility of optimization solutions due to insufficient discretization accuracy and improves the global reliability of the trajectory.

[0081] S350, if > Then Updated to Otherwise, keep constant.

[0082] To correct the problem of excessively high speed that may be caused by considering only a single point constraint in forward optimization (such as the more stringent constraints on adjacent points in high curvature segments), we incorporate adjacent point constraints to ensure that the speed satisfies the kinematic constraints globally, thus avoiding a large number of adjustments during subsequent backward optimization.

[0083] By preemptively trunculating the speed exceeding the upper limit using a limit value, the process of repeated iterations and corrections due to the forward speed exceeding the limit, as required in traditional bidirectional scanning algorithms (such as reducing the number of iterations from over 10,000 to 0), is avoided, significantly improving optimization efficiency.

[0084] The corrected speed simultaneously satisfies the constraints of the current point and adjacent points, avoiding machining vibrations caused by sudden speed changes at the intersection of trajectory segments. This lays the foundation for generating a continuous and smooth parametric velocity profile, indirectly improving the surface machining quality of the microlens array. Furthermore, the maximum acceleration of the machine tool actuator includes the maximum acceleration along the X-axis, Z-axis, and C-axis, and the final parametric velocity limit value... This is the minimum value among the maximum accelerations of each axis.

[0085] This step calculates the speed limit parameters by splitting the axis and taking the minimum value, then combines the constraints of adjacent points to determine the final speed limit parameters, as detailed below:

[0086] Speed ​​limit for split-axis calculation parameters: for trajectory point P(u) i The maximum acceleration a based on the X-axis, Z-axis, and C-axis. Xmax a Zmax and a Cmax Calculate the speed limit values ​​for each axis.

[0087] For example, the calculation for the X-axis is as follows:

[0088] ;

[0089] in, The X-axis at the trajectory point u i The velocity limit value at the point is used to constrain the kinematic acceleration along the X-axis and is a core parameter for generating the optimal trajectory. For the trajectory curve in u i The first derivative of the parameter u with respect to the X-axis describes the rate of change of the X-axis direction with respect to the parameter u, reflecting the "tangent slope" of the trajectory on the X-axis (in a cubic B-spline curve, it is calculated from the first derivative of the basis function and the coordinates of the control point). For the trajectory curve in u i The first derivative of the Y-axis with respect to parameter u describes the rate of change of the Y-axis direction with respect to parameter u (since the formula focuses on the X-axis constraint, the Y-axis derivative is used to calculate the trajectory curvature related terms). For the trajectory curve in u i The second derivative of the parameter u with respect to the X-axis reflects the "curvature trend" of the X-axis direction, and is combined with the first derivative to calculate the trajectory curvature; For the trajectory curve in u i The second derivative with respect to parameter u along the Y-axis is used to calculate the curvature-related terms, similarly combined with the first derivative with the Y-axis. The maximum permissible acceleration of the X-axis of a machine tool, and the physical constraints of the machine tool's actuators, directly determine the maximum dynamic load that the X-axis can withstand.

[0090] The calculation methods for the Z-axis and C-axis are the same as those for the X-axis, and will not be repeated here.

[0091] The minimum value of the calculated parameter speed limit for each axis is taken to obtain the preliminary parameter speed limit for that point.

[0092] To handle discretization errors, the neighboring points P(u) are calculated simultaneously. i-1 ), P(u i+1 The speed limit of the parameters is determined by taking the minimum value of the three as P(u). iThe final parameter is the speed limit.

[0093] This step has at least the following beneficial effects:

[0094] Ensure multi-axis collaborative safety: By calculating and taking the minimum value for each axis, ensure that the actual acceleration of the X-axis, Y-axis and C-axis does not exceed their respective maximum limits, and avoid vibration, drive overload or decrease in machining accuracy caused by a single axis exceeding the acceleration limit.

[0095] To handle discretization errors, the constraints of adjacent points are incorporated, and a conservative strategy is adopted to avoid the omission of local constraints caused by parameter domain discretization, ensuring that all kinematic constraints are still satisfied at the intersection of trajectory segments.

[0096] Improve optimization efficiency: By predetermining strict upper limits for parameter speed, speed values ​​that may exceed the limits during forward / backward optimization can be directly truncated, eliminating a large number of trial-and-error iterations in traditional algorithms (such as reducing from over 10,000 times to 0 times), and significantly reducing optimization execution time.

[0097] In this embodiment, with the goal of minimizing the trajectory running time, the maximum feasible parameter speed of each trajectory point is determined through forward and backward iterations under preset kinematic constraints. This fully leverages the dynamic performance of each axis, making the trajectory running time closer to the theoretical minimum and improving the machining efficiency of microlens array turning. By determining the maximum feasible parameter speed in both forward and backward directions and taking the minimum value as the target maximum feasible parameter speed, the optimization process of parameter speed is simplified, the number of trial and error iterations is reduced, the computational complexity is lowered, and the computational efficiency of trajectory optimization is significantly improved. This approach is more suitable for practical industrial applications of microlens array ultra-precision turning.

[0098] Example 2:

[0099] Based on the velocity and acceleration parameters of each trajectory point obtained in Embodiment 1 above, servo control of the machine tool is performed through the following steps:

[0100] Q100 discretizes the continuous trajectory curve corresponding to the microlens array turning process into multiple trajectory points in the parameter domain.

[0101] Based on the design of surface profiles and toolpaths using microlens arrays, a continuous trajectory curve P(u)=[x(u),z(u),c(u)] is first constructed using cubic B-spline interpolation, where u is the curve parameter, 0≤u≤1; then, within the parameter domain u, the curve is designed according to a preset resolution (e.g., Δu=10). -4 Uniformly discretize the data to obtain a list of trajectory points P(u1), P(u2), ..., P(u... n ), satisfying 0≤u1<u2<…<u n ≤1. For example, if the curve parameter range is 0 to 1, then Δu=10 -4Discretization yields 10,001 trajectory points, covering the entire curve.

[0102] Transforming continuous curves into discrete points that can be numerically calculated provides a foundation for subsequent parameter and speed optimization. By reasonably selecting the discrete resolution, we can ensure that trajectory details are fully captured while avoiding a surge in computation caused by too many discrete points, thus balancing optimization accuracy and efficiency.

[0103] Q200 constructs a continuous parametric velocity profile in the time domain by applying cubic interpolation based on the target maximum feasible parameter velocity corresponding to each trajectory point.

[0104] Furthermore, the target maximum feasible parameter velocity corresponding to each trajectory point can be obtained through the following steps:

[0105] Q210, Obtain the list of trajectory points corresponding to the continuous trajectory curve P(u), P = (P(u1), P(u2), ..., P(u...). i ), ..., P(u) n ), i=1,2,…,n; u is the curve parameter; P(u i Let be the i-th trajectory point corresponding to P(u), and n be the number of trajectory points corresponding to P(u); u i Let P(u) be the curve parameter of the i-th trajectory point.

[0106] In this embodiment, step Q210 is the same as step S200 in embodiment one, and will not be described again here.

[0107] Q220 aims to minimize the trajectory running time. Under the preset kinematic constraints, the positive maximum feasible parameter velocity of each trajectory point is determined sequentially starting from P(u1).

[0108] Furthermore, step Q220 includes the following steps:

[0109] Q221, Obtain the maximum operating speed v of the machine tool actuator. max Maximum acceleration a max .

[0110] Q222, according to v max a max and P(u) i The corresponding positive maximum feasible parameter velocity. Determine P(u) i+1 The corresponding positive maximum feasible parameter velocity. ;in, Take the maximum value if the following relationship is satisfied:

[0111] ;

[0112] in, =du i / dt;Δu is u i+1 and u i The difference between them, Δu=u i+1 -u i ; For P(u) in u i+1 The first derivative at that point; For P(u) in u i+1 The second derivative at point; For P(u) in u i+1 The positive curve parameter acceleration at that location.

[0113] In this embodiment, steps Q221-Q222 are the same as steps S310-S320 in Embodiment 1, and will not be described again here.

[0114] Q230, based on the positive maximum feasible parameter velocity at each trajectory point, from P(u n Starting from this point, determine the maximum feasible reverse velocity parameter for each trajectory point in sequence.

[0115] Furthermore, step Q230 includes the following steps:

[0116] Q231, according to v max a max and P(u) i The corresponding reverse maximum feasible parameter speed Determine P(u) i-1 The corresponding reverse maximum feasible parameter speed ;in, Take the maximum value if the following relationship is satisfied:

[0117] ;

[0118] in, =du i / dt; For P(u) in u i-1 The acceleration parameter of the reverse curve at that point.

[0119] In this embodiment, step Q231 is the same as step S410 in embodiment one, and will not be described again here.

[0120] Q240, the minimum feasible parameter velocity between the forward maximum feasible parameter velocity and the reverse maximum feasible parameter velocity of each trajectory point is determined as the initial maximum feasible parameter velocity of the corresponding trajectory point.

[0121] In this embodiment, the target maximum feasible parameter speed obtained through Q240 may not be feasible for the machine tool. Therefore, the target maximum feasible parameter speed obtained in Q240 is used as the initial maximum feasible parameter speed, and the following method is provided to obtain the target maximum feasible parameter speed:

[0122] Q250, obtain P(u) i The corresponding parameter speed limit value 、P(u i-1 The corresponding parameter speed limit value and P(u) i+1 The corresponding parameter speed limit value ;in, The following relationship must be satisfied:

[0123] .

[0124] In this embodiment, the velocity limit value is based on the curvature of the trajectory curve and the system's maximum acceleration a. max Calculation. Formula In the equation, R represents the trajectory in u. i The radius of curvature at point (R=1 / k, k is the curvature), For the curve in u i The first derivative at the point (describing the direction of the tangent).

[0125] Combining the existing curvature calculation formula k= It can be deduced that The centripetal force constraint (determined by acceleration limits) must be satisfied. This means calculating the maximum allowable parametric velocity at that point using the first and second derivatives of the curve and the system's maximum acceleration. Similarly, the velocity at adjacent points u can be calculated. i-1 u i+1 The parameter speed limit value.

[0126] By linking curvature and acceleration constraints, the parametric velocity of high curvature segments is precisely limited to avoid centripetal force exceeding limits due to trajectory curvature, thus ensuring motion safety from a geometric perspective. At the same time, the constraint values ​​of adjacent points are considered to lay the foundation for subsequent conservative verification.

[0127] Q260, according to , and Determine P(u) i The corresponding final parameter speed limit value .

[0128] The minimum value of the parameter velocity limit for the current trajectory point and its preceding and succeeding points is taken as P(u iThe final limit for the corresponding final parameter velocity. Discretization error needs to be handled conservatively by incorporating the constraints of adjacent points to avoid omission of local constraints due to parameter domain discretization.

[0129] A conservative strategy is adopted to handle discretization errors, ensuring that kinematic constraints are met even at the intersection of trajectory segments. This reduces the infeasibility of optimization solutions due to insufficient discretization accuracy and improves the global reliability of the trajectory.

[0130] Q270, if mv max，i > Then Determined as P(u) i The corresponding target maximum feasible parameter velocity; otherwise, mv max，i Determined as P(u) i The corresponding target maximum feasible parameter is velocity.

[0131] By pre-limiting the parameter speed, infeasible solutions are avoided in both forward and backward optimization. By truncating the target speed beyond the upper limit by the limit value, trial and error adjustments in subsequent iterations are completely eliminated, significantly reducing the number of iterations in the traditional bidirectional scanning algorithm (e.g., from over 10,000 to 0), and greatly improving optimization efficiency; at the same time, it ensures that the target speed strictly satisfies all constraints.

[0132] Furthermore, the maximum acceleration of the machine tool actuator includes the maximum acceleration along the X-axis, the maximum acceleration along the Y-axis, and the maximum acceleration along the C-axis, and the final parameter speed limit value... This is the minimum value among the maximum accelerations of each axis.

[0133] This step calculates the speed limit parameters by splitting the axis and taking the minimum value, then combines the constraints of adjacent points to determine the final speed limit parameters, as detailed below:

[0134] Speed ​​limit for split-axis calculation parameters: for trajectory point P(u) i The maximum acceleration a based on the X-axis, Z-axis, and C-axis. Xmax a Zmax and a Cmax Calculate the speed limit values ​​for each axis.

[0135] For example, the calculation for the X-axis is as follows:

[0136] ;

[0137] in, The X-axis at the trajectory point u i The velocity limit value at the point is used to constrain the kinematic acceleration along the X-axis and is a core parameter for generating the optimal trajectory. For the trajectory curve in u iThe first derivative of the parameter u with respect to the X-axis describes the rate of change of the X-axis direction with respect to the parameter u, reflecting the "tangent slope" of the trajectory on the X-axis (in a cubic B-spline curve, it is calculated from the first derivative of the basis function and the coordinates of the control point). For the trajectory curve in u i The first derivative of the Y-axis with respect to parameter u describes the rate of change of the Y-axis direction with respect to parameter u (since the formula focuses on the X-axis constraint, the Y-axis derivative is used to calculate the trajectory curvature related terms). For the trajectory curve in u i The second derivative of the parameter u with respect to the X-axis reflects the "curvature trend" of the X-axis direction, and is combined with the first derivative to calculate the trajectory curvature; For the trajectory curve in u i The second derivative with respect to parameter u along the Y-axis is used to calculate the curvature-related terms, similarly combined with the first derivative with the Y-axis. The maximum permissible acceleration of the X-axis of a machine tool, and the physical constraints of the machine tool's actuators, directly determine the maximum dynamic load that the X-axis can withstand.

[0138] By quantifying the influence of trajectory geometry on X-axis acceleration, the "trace curvature" is directly linked to the "machine tool dynamic constraints," ensuring that: high curvature segments (such as the inflection points of the curved surfaces of microlens arrays) automatically limit parameter speeds to avoid X-axis acceleration exceeding limits.

[0139] This formula serves as a bridge between "trajectory geometry, actuator constraints, and parameter velocity," allowing parameterized trajectory optimization to meet the surface accuracy requirements of the microlens array without exceeding the physical limits of the machine tool.

[0140] The calculation method for the C-axis of the Z-axis is the same as that for the X-axis, and will not be repeated here.

[0141] The minimum value of the calculated parameter speed limit for each axis is taken to obtain the preliminary parameter speed limit for that point.

[0142] To handle discretization errors, the neighboring points P(u) are calculated simultaneously. i-1 ), P(u i+1 The speed limit of the parameters is determined by taking the minimum value of the three as P(u). i The final parameter is the speed limit.

[0143] This step has at least the following beneficial effects:

[0144] Ensure multi-axis collaborative safety: By calculating and taking the minimum value for each axis, ensure that the actual acceleration of the X-axis, Y-axis and C-axis does not exceed their respective maximum limits, and avoid vibration, drive overload or decrease in machining accuracy caused by a single axis exceeding the acceleration limit.

[0145] To handle discretization errors, the constraints of adjacent points are incorporated, and a conservative strategy is adopted to avoid the omission of local constraints caused by parameter domain discretization, ensuring that all kinematic constraints are still satisfied at the intersection of trajectory segments.

[0146] Improve optimization efficiency: By predetermining strict upper limits for parameter speed, speed values ​​that may exceed the limits during forward / backward optimization can be directly truncated, eliminating a large number of trial-and-error iterations in traditional algorithms (such as reducing from over 10,000 times to 0 times), and significantly reducing optimization execution time.

[0147] In this embodiment, with the goal of minimizing the trajectory running time, the maximum feasible parameter speed of each trajectory point is determined through forward and backward iterations under preset kinematic constraints. This fully leverages the dynamic performance of each axis, making the trajectory running time closer to the theoretical minimum and improving the machining efficiency of microlens array turning. By determining the maximum feasible parameter speed in both forward and backward directions and taking the minimum value as the target maximum feasible parameter speed, the optimization process of parameter speed is simplified, the number of trial and error iterations is reduced, the computational complexity is lowered, and the computational efficiency of trajectory optimization is significantly improved. This approach is more suitable for practical industrial applications of microlens array ultra-precision turning.

[0148] Q300, integrate the parameter velocity profile to obtain the parameter trajectory u(t); where t is the time point.

[0149] In this embodiment, the continuous parametric velocity profile constructed by Q200 is integrated over time to obtain the trajectory of parameter u changing with time t.

[0150] By establishing a direct relationship between parameter u and time t through integration, the temporal evolution law of velocity information is transformed into position information, providing a core basis for the subsequent generation of the temporal characteristics of spatial trajectories.

[0151] Q400, substitute u(t) into the cubic B-spline curve to generate the optimal trajectory P(u(t)) that satisfies the kinematic constraints corresponding to the continuous trajectory curve.

[0152] Substituting the parameter trajectory u(t) obtained from Q300 into the cubic B-spline curve P(u), we obtain the spatial position-time mapping relationship P(u(t))=[x(u(t)),z(u(t)),c(u(t))], where x(u(t)), z(u(t)), and c(u(t)) are functions of the position along the X-axis, Z-axis, and C-axis, respectively, over time. For example, if x(u)=0.5u and u(t)=0.05t in the cubic B-spline curve... 2 Then x(u(t)) = 0.025t 2 That is, the X-axis position increases with the square of time.

[0153] This step generates an optimal trajectory that simultaneously satisfies time minimization and kinematic constraints (velocity and acceleration limits). It fully utilizes the dynamic performance of the machine tool to shorten machining time while ensuring trajectory smoothness to reduce machining vibration, providing a reliable path for high-precision turning.

[0154] Q500, by differentiating P(u(t)), we can obtain the desired speed and desired acceleration of the X-axis, Z-axis and C-axis of the machine tool actuator.

[0155] Based on the chain rule, differentiate P(u(t)):

[0156] Expected speed: That is, the velocity along each axis is the product of the first derivative of the curve with respect to the parameter u and the velocity of the parameter. For example, the desired velocity along the X-axis. ,in, Let be the derivative of the X-axis position function with respect to u.

[0157] Expected acceleration: That is, the acceleration along each axis is the product of the second derivative of the curve with respect to u and the square of the parameter velocity, plus the product of the first derivative and the parameter acceleration. For example, the desired acceleration along the Z-axis... .

[0158] This step allows for the direct acquisition of the desired velocity and acceleration through analytical differentiation, avoiding the phase lag and errors introduced by numerical differentiation in traditional PID controllers (such as noise caused by first-order differential), and significantly improving the tracking accuracy of servo control.

[0159] Furthermore, step Q500 may include the following steps:

[0160] Q510, differentiate P(u(t)) and combine it with the parameter velocity. =du / dt, thus obtaining the desired speed v of the machine tool actuator along the X-axis. x The desired velocity v along the Z-axis z and the desired velocity v along the C-axis c ;in, ; ; ; , and These are the first derivatives of the position functions of the X-axis, Z-axis, and C-axis with respect to the parameter u, respectively.

[0161] Differentiate the optimal trajectory P(u(t))=[x(u(t)),z(u(t)),c(u(t))] and combine it with the velocity parameter. The desired speeds for each axis are obtained.

[0162] For the X-axis, the position function is x(u(t)), and according to the chain rule, its derivative with respect to time is... ,in, It is the first derivative of the X-axis position function with respect to the parameter u (obtained by differentiating the cubic B-spline basis functions, such as...). , (The first derivative of the 4th-order B-spline basis function); the solutions for the Z-axis and C-axis are the same as for the X-axis.

[0163] The desired speed is calculated directly by analytical differentiation, avoiding the phase lag and noise introduced by obtaining speed through numerical difference (such as the difference between adjacent positions divided by the time interval) in traditional methods. This improves the accuracy of the speed signal and provides more precise feedforward input for servo control.

[0164] Q520, differentiate P(u(t)) and combine it with the parameter acceleration. =d 2 u / dt 2 The desired acceleration a along the X-axis of the machine tool actuator is obtained. x The desired acceleration a along the Z-axis z And the desired acceleration a along the C-axis c ;in, ; ; ; , and The first two terms are the second derivatives of the position functions of the X-axis, Z-axis, and C-axis with respect to the parameter u.

[0165] Differentiate the desired velocities along each axis again, and combine with the parameter acceleration. The desired acceleration is obtained.

[0166] The x-axis acceleration is the derivative of velocity with respect to time: ;in, It is the second derivative of the X-axis position function with respect to u (calculated from the second derivative of the cubic B-spline basis functions, such as...). The solutions for the Z-axis and C-axis are the same as those for the X-axis.

[0167] Acceleration is obtained by second-order analytical differentiation, avoiding the problem of noise amplification in numerical second-order differential calculations and ensuring the smoothness of the acceleration signal. At the same time, the curvature characteristics of the curve are directly correlated with the parameter velocity / acceleration, enabling acceleration feedforward to accurately compensate for the dynamic requirements caused by trajectory curvature, further improving servo tracking accuracy.

[0168] Q600 takes the desired velocity and desired acceleration as feedforward inputs, substitutes them into the output calculation formula of the servo controller, and obtains the servo output to drive the X-axis, Z-axis and C-axis motion.

[0169] Furthermore, the output calculation formula of the servo controller is as follows: Among them, K P K is the proportionality coefficient. v K is the velocity feedforward coefficient. a is the acceleration feedforward coefficient; v(t) is the desired velocity at time t, a(t) is the desired acceleration at time t, and e(t) is the tracking error between the actual position and the desired position at time t.

[0170] Substituting the desired velocity v(t) and desired acceleration a(t) obtained from Q500 into the servo controller's output formula as feedforward terms: Among them, K P K is the proportionality coefficient. v K is the velocity feedforward coefficient. a Here, e is the acceleration feedforward coefficient; e(t) is the tracking error between the actual position and the desired position at time t, for example, when the desired velocity v along the X-axis... x =0.1t, acceleration a x When the value is 0.1, the feedforward term will drive the motor to respond earlier, reducing errors caused by system lag.

[0171] Feedforward input enables the controller to "anticipate" changes in the velocity and acceleration of the trajectory, and adjust the output in advance to compensate for the dynamic lag of the system, significantly reducing tracking errors (e.g., a 30% reduction in Z-axis tracking error). At the same time, combined with the high efficiency of optimized trajectory, it achieves a simultaneous improvement in the processing accuracy (reduced shape error) and efficiency (shortened processing time) of the microlens array.

[0172] In this embodiment, by discretizing the continuous trajectory and constructing a parametric velocity profile using cubic interpolation, the number of iterations for trajectory optimization is significantly reduced, improving computational efficiency. By integrating the parametric velocity profile to obtain the parametric trajectory and substituting it into a cubic B-spline curve, the continuity of the optimal trajectory and the satisfaction of kinematic constraints are ensured. Directly differentiating the optimal trajectory to obtain the desired velocity and acceleration avoids the lag and error caused by traditional numerical differentiation, improving the tracking accuracy of servo control. Using the desired velocity and acceleration as feedforward inputs to drive the axis motion achieves efficient coordination between trajectory planning and servo control. Ultimately, while ensuring the shape accuracy of the microlens array (such as reducing shape error), processing efficiency is improved, effectively solving the problem of difficulty in balancing accuracy and efficiency in the prior art.

[0173] Furthermore, although the steps of the method in this disclosure are described in a specific order in the accompanying drawings, this does not require or imply that the steps must be performed in that specific order, or that all the steps shown must be performed to achieve the desired result. Additional or alternative steps may be omitted, multiple steps may be combined into one step, and / or a step may be broken down into multiple steps.

[0174] Embodiments of the present invention also provide a non-transitory computer-readable storage medium that can be disposed in an electronic device to store at least one instruction or at least one program related to implementing a method in the method embodiments, wherein the at least one instruction or the at least one program is loaded and executed by the processor to implement the method provided in the above embodiments.

[0175] The program product may employ any combination of one or more readable media. A readable medium may be a readable signal medium or a readable storage medium. A readable storage medium may be, for example, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination thereof. More specific examples of readable storage media (a non-exhaustive list) include: an electrical connection having one or more wires, a portable disk, a hard disk, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination thereof.

[0176] Computer-readable signal media may include data signals propagated in baseband or as part of a carrier wave, carrying readable program code. Such propagated data signals may take various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination thereof. A readable signal medium may also be any readable medium other than a readable storage medium, capable of sending, propagating, or transmitting programs for use by or in conjunction with an instruction execution system, apparatus, or device.

[0177] The program code contained on the readable medium may be transmitted using any suitable medium, including but not limited to wireless, wired, optical fiber, RF, etc., or any suitable combination thereof.

[0178] Program code for performing the operations of this application can be written in any combination of one or more programming languages, including object-oriented programming languages ​​such as Java and C++, and conventional procedural programming languages ​​such as C or similar languages. The program code can execute entirely on the user's computing device, partially on the user's device, as a standalone software package, partially on the user's computing device and partially on a remote computing device, or entirely on a remote computing device or server. In cases involving remote computing devices, the remote computing device can be connected to the user's computing device via any type of network, including a local area network (LAN) or a wide area network (WAN), or it can be connected to an external computing device (e.g., via the Internet using an Internet service provider).

[0179] Embodiments of the present invention also provide an electronic device, including a processor and the aforementioned non-transitory computer-readable storage medium.

[0180] The electronic device is merely an example and should not impose any limitations on the functionality and scope of use of the embodiments in this application.

[0181] Electronic devices are manifested in the form of general-purpose computing devices. Components of an electronic device may include, but are not limited to: at least one processor, at least one memory, and a bus connecting different system components (including memory and processor).

[0182] The memory stores program code that can be executed by the processor, causing the processor to perform the steps in the various embodiments described in this specification.

[0183] The memory may include readable media in the form of volatile memory, such as random access memory (RAM) and / or cache memory, and may further include read-only memory (ROM).

[0184] The memory may also include programs / utilities having a set (at least one) of program modules, including but not limited to: an operating system, one or more application programs, other program modules, and program data, each or some combination of these examples may include an implementation of a network environment.

[0185] A bus can represent one or more of several types of bus structures, including a memory bus or memory controller, a peripheral bus, a graphics acceleration port, a processor, or a local bus that uses any of the various bus structures.

[0186] Electronic devices can also communicate with one or more external devices (e.g., keyboards, pointing devices, Bluetooth devices, etc.), one or more devices that enable user interaction with the electronic device, and / or any device that enables the electronic device to communicate with one or more other computing devices (e.g., routers, modems, etc.). This communication can be achieved through input / output (I / O) interfaces. Furthermore, electronic devices can communicate with one or more networks (e.g., local area networks (LANs), wide area networks (WANs), and / or public networks, such as the Internet) via network adapters. The network adapter communicates with other modules of the electronic device via a bus. It should be understood that other hardware and / or software modules can be used in conjunction with the electronic device, including but not limited to: microcode, device drivers, redundant processors, external disk drive arrays, RAID systems, tape drives, and data backup storage systems.

[0187] From the above description of the embodiments, those skilled in the art will readily understand that the exemplary embodiments described herein can be implemented by software or by combining software with necessary hardware. Therefore, the technical solutions according to the embodiments of this disclosure can be embodied in the form of a software product, which can be stored in a non-volatile storage medium (such as a CD-ROM, USB flash drive, external hard drive, etc.) or on a network, including several instructions to cause a computing device (such as a personal computer, server, terminal device, or network device, etc.) to execute the methods according to the embodiments of this disclosure.

[0188] Embodiments of the present invention also provide a computer program product including program code, which, when the program product is run on an electronic device, causes the electronic device to perform the steps of the methods described above in various exemplary embodiments of the present invention.

[0189] While specific embodiments of the invention have been described in detail by way of examples, those skilled in the art should understand that the examples are for illustrative purposes only and are not intended to limit the scope of the invention. Those skilled in the art should also understand that various modifications can be made to the embodiments without departing from the scope and spirit of the invention.

Claims

1. A method for optimizing the turning motion trajectory of a microlens array, characterized in that, The method includes the following steps: S100, construct a continuous trajectory curve P(u) based on the discrete tool path points corresponding to the microlens array turning process, where u is a one-dimensional parameter that maps the microlens array turning continuous trajectory curve from three-dimensional space to the interval [0,1], 0≤u≤1; S200, Discretize P(u) into multiple trajectory points in the parameter domain to obtain a list of trajectory points G = (P(u1), P(u2), ..., P(u... i ), ..., P(u) n )), i=1, 2,...,n; P(u i Let be the i-th trajectory point corresponding to P(u), and n be the number of trajectory points corresponding to P(u); u i Let P(u) be the curve parameter of the i-th trajectory point; S300 aims to minimize the trajectory running time. Under the preset kinematic constraints, it sequentially determines the positive maximum feasible parameter velocity of each trajectory point starting from P(u1). S400, based on the positive maximum feasible parameter velocity at each trajectory point, from P(u n Starting from this point, determine the maximum feasible reverse velocity parameter for each trajectory point in sequence; S500, the minimum feasible parameter velocity between the forward maximum feasible parameter velocity and the reverse maximum feasible parameter velocity of each trajectory point is determined as the target maximum feasible parameter velocity of the corresponding trajectory point; S600, based on the target maximum feasible parameter velocity of each trajectory point in G, generate the optimal trajectory P(u(t)) that satisfies the kinematic constraints corresponding to P(u); u(t) is the curve parameter at time point t.

2. The method for optimizing the turning motion trajectory of a microlens array according to claim 1, characterized in that, Step S300 includes the following steps: S310, Obtain the maximum operating speed v of the machine tool actuator. max and maximum acceleration a max ; S320, according to v max a max and P(u) i The corresponding positive maximum feasible parameter velocity. Determine P(u) i+1 The corresponding positive maximum feasible parameter velocity. ;in, Take the maximum value if the following relationship is satisfied: ； in, =du i / dt, where t is the time point; Δu is u i+1 and u i The difference between them, Δu=u i+1 -u i ; For P(u) in u i+1 The first derivative at that point; For P(u) in u i+1 The second derivative at point; For P(u) in u i+1 The positive curve parameter acceleration at that location.

3. The method for optimizing the turning motion trajectory of a microlens array according to claim 2, characterized in that, Step S400 includes the following steps: S410, according to v max a max and P(u) i The corresponding reverse maximum feasible parameter speed Determine P(u) i-1 The corresponding reverse maximum feasible parameter speed ;in, Take the maximum value if the following relationship is satisfied: ； in, =du i-1 / dt; For P(u) in u i-1 The first derivative at that point; For P(u) in u i-1 The second derivative at point; For P(u) in u i-1 The acceleration parameter of the reverse curve at that point.

4. The method for optimizing the turning motion trajectory of a microlens array according to claim 3, characterized in that, Step S500 includes the following steps: S510, according to and Determine P(u) i The target maximum feasible parameter is velocity mv. max，i =MIN ; where MIN() is the preset minimum value function.

5. The method for optimizing the turning motion trajectory of a microlens array according to claim 2, characterized in that, Following step S320, the method further includes the following steps: S330, obtain P(u) i The corresponding parameter speed limit value 、P(u i-1 The corresponding parameter speed limit value and P(u) i+1 The corresponding parameter speed limit value ;in, The following relationship must be satisfied: ； R is P(u) in u i The radius of curvature at that point; For P(u) in u i The first derivative at that point; S340, according to , and Determine P(u) i The corresponding final parameter speed limit value ; S350, if > Then Updated to Otherwise, keep constant.

6. The method for optimizing the turning motion trajectory of a microlens array according to claim 5, characterized in that, The maximum acceleration of the machine tool actuator includes the maximum acceleration of the X-axis, the maximum acceleration of the Z-axis, and the maximum acceleration of the C-axis, and the final parameter speed limit value. This is the minimum value among the maximum accelerations of each axis.

7. The method for optimizing the turning motion trajectory of a microlens array according to claim 2, characterized in that, The machine tool actuator is in P(u1) and P(u) n The running speed at each location is 0.

8. A non-transitory computer-readable storage medium, wherein the storage medium stores at least one instruction or at least one program segment, characterized in that, The at least one instruction or the at least one program segment is loaded and executed by the processor to implement the microlens array turning motion trajectory optimization method as described in any one of claims 1-7.

9. An electronic device, characterized in that, Includes a processor and the non-transitory computer-readable storage medium as described in claim 8.

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