Microlens array turning motion trail optimization method and device and medium

Abstract

The invention provides a microlens array turning motion trail optimization method and device and a medium, and relates to the technical field of microlens array turning motion trail optimizing.The method comprises the steps that a continuous trail curve P (u) is constructed based on discrete tool path points corresponding to the microlens array turning process; dispersing the P (u) into a plurality of track points in a parameter domain to obtain a track point list G; sequentially determining the forward maximum feasible parameter speed of each track point from the forward first track point; starting from the first reverse track point, determining the reverse maximum feasible parameter speed of each track point in sequence; determining the target maximum feasible parameter speed of the corresponding track point; according to the target maximum feasible parameter speed of each track point in the G, generating an optimal track which corresponds to the P (u) and meets kinematics constraints; according to the method, the optimization process of the parameter speed can be simplified, the number of trial and error iterations is reduced, the calculation complexity is reduced, and the calculation efficiency of trajectory optimization is remarkably improved.

Description

Technical Field

[0001] The present invention relates to the technical field of microlens array turning motion trajectory optimization, and in particular to a microlens array turning motion trajectory optimization method, equipment and medium. Background Art

[0002] Microlens arrays (MLAs), periodic or quasi-periodic components composed of microlenses, are widely used in beam shaping, imaging, optical sensing, augmented reality (AR), virtual reality (VR), and other fields due to their compact size, excellent optical performance, and microscale light manipulation capabilities. These applications place extremely high demands on manufacturing precision and efficiency. However, the manufacture of high-quality MLAs requires the planning of high-quality motion trajectories. Existing methods for motion trajectory planning fall into two main categories: acceleration / deceleration (ACC / DEC) methods (such as S-curve planning): While these methods offer low computational complexity and good real-time performance, they fail to fully utilize the dynamic capabilities of each axis and struggle to achieve efficient processing under speed and acceleration constraints; and time-optimal methods (such as bidirectional scanning algorithms): While these methods can generate minimum or near-minimum time trajectories, they are computationally expensive.

[0003] In terms of servo control, the feedforward mechanism of the traditional PID controller relies on numerical differentiation to obtain velocity 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, a microlens array turning motion trajectory optimization method is urgently needed to reduce the optimization execution time and solve the problems of high computational cost and excessive number of iterations of the existing time optimization method. Summary of the Invention

[0004] In view of the above technical problems, the technical solution adopted by the present invention is: According to a first aspect of the present application, a method for optimizing the turning motion trajectory of a microlens array is provided, the method comprising the following steps: S100, constructing a continuous trajectory curve P(u) based on 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, and obtain a trajectory point list G=(P(u1), P(u2),…, P(u i ),…,P(u n )), i=1, 2,...,n; P(u i ) is the i-th trajectory point corresponding to P(u), n is the number of trajectory points corresponding to P(u); u i is the curve parameter of the i-th trajectory point corresponding to P(u); S300, with the goal of minimizing the trajectory running time, under the preset kinematic constraints, the forward maximum feasible parameter velocity of each trajectory point is determined in sequence starting from P(u1); S400, based on the maximum feasible parameter speed of each trajectory point, from P (u n ) starts, and determines the reverse maximum feasible parameter velocity of each trajectory point in turn; S500, determining the minimum feasible parameter speed between the forward maximum feasible parameter speed and the reverse maximum feasible parameter speed of each trajectory point as the target maximum feasible parameter speed of the corresponding trajectory point; S600 , based on the target maximum feasible parameter velocity of each trajectory point in G, generate an optimal trajectory P(u(t)) corresponding to P(u) that satisfies kinematic constraints; u(t) is a curve parameter at time point t.

[0005] According to another aspect of the present application, a non-transitory computer-readable storage medium is provided, in which at least one instruction or at least one program is stored. The at least one instruction or at least one program is loaded and executed by a processor to implement the above-mentioned microlens array turning motion trajectory optimization method.

[0006] According to another aspect of the present application, an electronic device is provided, including a processor and the above-mentioned non-transitory computer-readable storage medium.

[0007] The present invention has at least the following beneficial effects: The present invention provides a method for optimizing the motion trajectory of microlens array turning, with the goal of minimizing trajectory run time. Under preset kinematic constraints, the maximum feasible parameter speed of each trajectory point is determined through forward and reverse iterations. This method fully exploits the dynamic performance of each axis, bringing the trajectory run time closer to the theoretical minimum, and improving the processing efficiency of microlens array turning. By determining the maximum feasible parameter speed in both forward and reverse directions and taking the minimum value as the target maximum feasible parameter speed, the parameter speed optimization process 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. The method is therefore more suitable for practical industrial applications in ultra-precision turning of microlens arrays. BRIEF DESCRIPTION OF THE DRAWINGS

[0008] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following briefly introduces the drawings required for use in the description of the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0009] Figure 1 This is a flow chart of a method for optimizing the turning motion trajectory of a microlens array provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0010] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by a person of ordinary skill in the art without creative effort belong to the protection scope of the present application.

[0011] It should be noted that, based on the present disclosure, a person of ordinary skill in the art should appreciate 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, an apparatus can be implemented and / or a method can be practiced using any number of the aspects set forth herein. In addition, such an apparatus can be implemented and / or such a method can be practiced using other structure and / or functionality in addition to or other than one or more of the aspects set forth herein.

[0012] Embodiment one: The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by a person of ordinary skill in the art without creative effort belong to the protection scope of the present application. Figure 1 A micro-lens array turning motion trajectory optimization method will be introduced below with reference to the flow chart of the micro-lens array turning motion trajectory optimization method shown in FIG. 1.

[0013] The micro-lens array turning motion trajectory optimization method can include the following steps: S100, constructing a continuous trajectory curve P(u) based on the discrete tool path points corresponding to the micro-lens array turning process, wherein u is a one-dimensional parameter for mapping the micro-lens array turning continuous trajectory curve from a three-dimensional space to an interval [0, 1], 0≤u≤1.

[0014] In this embodiment, the discrete tool path points (generated by a CAM system, containing surface geometry and tool radius compensation information) of the micro-lens array turning are taken as control points, and a C 2 A cubic B-spline curve P(u)=([x(u),y(u),z(u)]) is constructed through continuous interpolation, wherein 0≤u≤1, to ensure the continuity of the trajectory in the position, velocity and acceleration levels.

[0015] Through this step, the discrete tool path points are converted into a smooth continuous curve, avoiding the trajectory mutation caused by directly connecting the discrete points, providing a smooth basis for subsequent trajectory discretization and optimization, and reducing the machining vibration and surface quality defects caused by the discontinuous trajectory.

[0016] S200, discretizing P(u) in the parameter domain into a plurality of trajectory points to obtain a trajectory point list G=(P(u1), P(u2), …, P(u i ), …, P(u n), i = 1, 2, …, n; P(u i ) is the i-th trajectory point corresponding to P(u), and n is the number of trajectory points corresponding to P(u). i is the curve parameter of the i-th trajectory point corresponding to P(u).

[0017] In the parameter domain 0≤u≤1, the cubic B-spline curve P(u) is uniformly discretized into n trajectory points to obtain a list G, where 0≤u1<u2<…<u n ≤1, and the discretization resolution Δu (such as Δu=10 -4 ) needs to balance the optimization accuracy and computational efficiency.

[0018] Through this step, the continuous curve is converted into discrete points that can be calculated numerically, facilitating subsequent forward / backward optimization iteration calculation; by reasonably selecting Δu, the trajectory details can be fully captured while avoiding excessive discrete points leading to a sharp increase in computational load, balancing optimization accuracy and efficiency.

[0019] S300, with the goal of minimizing the trajectory running time, determines the forward maximum feasible parameter speed of each trajectory point under the preset kinematic constraints, starting from P(u1).

[0020] With the goal of minimizing the trajectory running time, the maximum feasible parameter speed of each trajectory point is calculated starting from the starting point P(u1), and the kinematic constraints need to be satisfied during calculation.

[0021] Maximizing the parameter speed within the kinematic constraint range, preliminary tapping of dynamic performance of each axis lays the foundation for shortening the trajectory running time; through point-by-point iteration, it is ensured that each step speed satisfies the constraint, avoiding processing errors caused by excessively high local speed.

[0022] Further, step S300 can include the following steps: S310, obtaining the maximum running speed v max and the maximum acceleration a max of the machine tool actuator.

[0023] v max and a max are preset kinematic constraint parameters of the machine tool, determined based on the dynamic performance of the ultra-precision lathe (such as LD-CL100 V2), specifically including the maximum speed and acceleration limits of each axis (such as the parameters defined in the “Slow”, “Medium”, “Fast” constraint set in Table 1). These parameters need to be set in combination with the physical performance of the machine tool driving system (such as linear motor, piezoelectric actuator) and the processing process requirements (such as the surface quality requirements of the microlens array), to ensure that they do not exceed the mechanical carrying capacity and dynamic response range of the machine tool.

[0024] Through this step, the motion boundary conditions of the machine tool are determined, providing strict constraint benchmarks for subsequent optimization of the parameter speed, avoiding machine tool vibration, drive overload or processing precision decline caused by speed or acceleration exceeding the limit, and ensuring the safety and feasibility of trajectory optimization from the bottom.

[0025] S320, according to v max , a max and P(u i ) corresponding forward maximum feasible parameter speed , determine P(u i+1 ) corresponding forward maximum feasible parameter speed ; wherein, Take the maximum value under the following relationship: ; Wherein, =du i / dt, t is the time point; Δu is the difference between u i+1 and u i , Δu=u i+1 -u i ; is the first derivative of P(u) at u i+1 ; is the second derivative of P(u) at u i+1 ; is the positive curve parameter acceleration of P(u) at u i+1 .

[0026] Based on the forward maximum feasible parameter speed of the previous trajectory point P(u i ), maximize the forward maximum feasible parameter speed of P(u i+1 ) under the following constraints: Speed constraint: , is the first derivative of the cubic B-spline curve at u i+1 , describing the tangent direction of the curve at this point, ensuring that the actual running speed of each axis does not exceed v max .

[0027] Acceleration constraint: , is the second derivative of the curve, describing the curvature change, is the discrete approximation of the parameter acceleration, ensuring that the actual acceleration of each axis does not exceed a max . When iteratively calculating, the above inequality system is solved by numerical method, and the maximum is selected from the solution set that satisfies all constraints.

[0028] Under the premise of strictly following the kinematic constraints of the machine tool, the parameter speed of each trajectory point is maximized to fully exploit the dynamic capability of the machine tool to shorten the machining time; through the coupling calculation of the first and second derivatives and the parameter speed / acceleration, the geometric characteristics (such as curvature) of the curve and the kinematic performance are accurately associated to avoid the speed / acceleration overrun caused by the sudden change of local curvature, provide a reasonable forward speed benchmark for subsequent reverse optimization, and reduce the number of iterations of overall optimization.

[0029] S400, based on the forward maximum feasible parameter speed of each trajectory point, the reverse maximum feasible parameter speed of each trajectory point is determined in sequence from P(u n ) starting.

[0030] Based on the forward optimization result, the maximum feasible parameter speed of each trajectory point is iteratively calculated from the end point P(u n ) (P(u n )=0) in reverse, also needs to meet the speed and acceleration constraints to ensure that the trajectory can smoothly decelerate to the end static state.

[0031] Through this step, the "local greed" defect of forward optimization (forward optimization may cause subsequent high curvature section to fail to meet the constraints due to excessive pursuit of local speed) is corrected, and the trajectory is ensured to meet the constraints throughout the whole section through reverse checking, especially to ensure that the end point can be smoothly stopped to avoid the decline of machining precision caused by the end point speed failing to meet the constraints.

[0032] Further, step S400 can include the following steps: S410, according to the reverse maximum feasible parameter speed corresponding to v max , a max and P(u i ), the reverse maximum feasible parameter speed corresponding to P(u i-1 ) is determined; wherein, the maximum value is taken under the condition that the following relationship is met: ; wherein, =du i-1 / dt; is the first derivative of P(u) at u i-1 ; is the second derivative of P(u) at u i-1 ; is the reverse curve parameter acceleration of P(u) at u i-1 .

[0033] In this embodiment, the reverse optimization starts from the trajectory end point P(u nStart, based on the reverse maximum feasible parameter velocity of the current trajectory point P(u i , maximize the parameter velocity of the previous trajectory point under the premise of meeting the following constraints: Velocity constraints: , ensure that the actual velocity of each axis does not exceed the maximum speed v max of the machine tool.

[0034] Acceleration constraints: , ensure that the actual acceleration of each axis does not exceed a max .

[0035] In iterative calculation, the above inequality system is solved by numerical method, and the maximum is selected from the solution set that meets all constraints, and then it is pushed back from i=n to i=2, and finally the reverse velocity planning of all trajectory points is completed.

[0036] By checking and adjusting the parameter velocity from the end point in reverse, the problem of subsequent trajectory segment infeasibility caused by the "local greedy" strategy in forward optimization (such as high curvature segment acceleration exceeding limit) is corrected, ensuring that the trajectory can smoothly decelerate to the end static state; At the same time, strict speed and acceleration constraint check further ensures the safety of reverse velocity planning, which is complementary to forward optimization, providing reliable basis for subsequent minimum value determination of target maximum feasible parameter velocity, reducing the trial and error iteration times of overall optimization, and improving the efficiency and feasibility of trajectory planning.

[0037] In this embodiment, the overall effect of forward and reverse optimization is as follows: On the one hand, through forward optimization, the parameter velocity of each trajectory point is maximized under kinematic constraints from the trajectory starting point, preliminarily tapping the dynamic capability of the machine tool to shorten the processing time; On the other hand, the reverse optimization starts from the trajectory end point (constraint parameter velocity is 0), and adjusts the parameter velocity of each trajectory point in reverse, correcting the problem of subsequent segment infeasibility caused by local high speed in forward optimization, ensuring that the trajectory meets the constraints throughout the process. After the combination of the two, the minimum value of the maximum feasible parameter velocity of each point is taken as the target maximum feasible parameter velocity, which not only fully utilizes the dynamic performance of the machine tool to improve efficiency, but also guarantees the global feasibility of the trajectory through bidirectional checking, significantly reducing the trial and error iteration times required by traditional single-direction optimization, reducing the optimization execution time, generating time-optimal trajectory that meets kinematic constraints, providing accurate speed and acceleration reference for subsequent servo control, and finally improving the precision and efficiency of microlens array processing.

[0038] In this embodiment, the core physical meaning of the parameter velocity is "the rate of change of curve parameter u with time", which reflects the "speed of progress" of the machine tool along the trajectory curve P(u) The larger the distance is pushed along the parameter domain [0, 1] in a unit of time, the higher the processing efficiency is.

[0039] (Forward): Starting from the starting point P(u1) of the trajectory, the maximum feasible parameter velocity du / dt is calculated point by point, with the constraint condition being "the current point velocity does not exceed the upper limit of the velocity / acceleration of each axis of the machine tool, and can smoothly transit to the next point".

[0040] (Reverse): Starting from the ending point P(u n ) of the trajectory, the maximum feasible parameter velocity du / dt is calculated point by point in reverse, with the constraint condition being "the current point velocity does not exceed the upper limit of the velocity / acceleration of each axis of the machine tool, and can smoothly transit to the previous point".

[0041] Both the mathematical definitions are du / dt, only the calculation direction and the reference constraint point are different, and the essence is "the time change rate of the parameter u", which conforms to the core logic of "relating the geometric trajectory and the time through the parameter velocity" in the trajectory optimization.

[0042] S500, the minimum feasible parameter velocity of 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.

[0043] Further, step S500 includes the following steps: S510, according to and , the target maximum feasible parameter velocity mv max，i of P(u i ) is determined as mv max，i =MIN( ); wherein MIN() is a preset minimum value function.

[0044] Through this step, it is ensured that the parameter velocity of each trajectory point satisfies the forward and reverse constraints at the same time, completely eliminates the infeasible solution that may appear in single direction optimization, and guarantees the global feasibility of the trajectory; through the "smaller" strategy, the velocity and safety are balanced within the constraint range, and a reliable parameter velocity basis is provided for the generation of the final optimal trajectory.

[0045] S600, according to the target maximum feasible parameter velocity of each trajectory point in P, the optimal trajectory P(u(t)) satisfying the kinematics constraint corresponding to P(u) is generated; u(t) is the curve parameter at time point t.

[0046] 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 integral of the profile is obtained to obtain the parameter change trajectory u(t) with time; u(t) is substituted into the cubic B-spline curve P(u) to obtain the mapping relationship between space position and time P(u(t)), that is, the optimal trajectory.

[0047] Through this step, the discrete target maximum feasible parameter velocity is converted into a continuous smooth time domain trajectory, avoiding servo vibration caused by sudden changes in velocity; the generated trajectory simultaneously satisfies time optimality and kinematic constraints, providing accurate position, velocity and acceleration instructions for subsequent direct feedforward control, ultimately improving the efficiency (shortening the time) and precision (reducing shape error) of microlens array processing.

[0048] In this embodiment, the continuous trajectory curve P(u) constructed in S100 is the basic trajectory function of the entire method (interpolated from discrete tool path points based on micro-lens array turning, such as cubic B-spline curve), and P in subsequent steps (such as S200, S600) refers to this function, not a different function. The same notation is used because the spatial geometric characteristics of the trajectory (such as the position relationship of the X-axis, Z-axis, and C-axis) are determined by the initially constructed P(u) throughout, and subsequent optimization only changes the mapping relationship between the parameter u and the time t, not the geometry of the trajectory itself. This unified notation conforms to the mathematical expression habit, that is, the function itself does not change, only the physical meaning of the parameter extends with the scene (from a pure geometric parameter to a parameter associated with time).

[0049] Differences in the representation of parameter u: Discrete and continuous distinction u i is the discrete curve parameter: u in S200 i is the specific numerical value obtained after discretizing the continuous parameter domain [0, 1], corresponding to the discrete point P(u i ) on the trajectory, used for numerical calculation and iterative optimization (such as forward / backward velocity planning).

[0050] u(t) is a continuous parameter-time function: u(t) in S600 is the continuous change relationship of parameter u with time t (such as u(t)=0.05t 2 ), used to describe "at time t, the parameter value of the trajectory curve is u(t)", which essentially extends the discrete u i to a continuous time domain function through interpolation and integration. Both are curve parameters, and the difference in expression is to distinguish between "discrete point parameter value" (u i ) and "continuous evolution of parameter with time" (u(t)), which are different representations of the same parameter in discrete analysis and continuous modeling scenarios, not two different parameters.

[0051] Furthermore, after step S320, the method may further include the following steps: S330, obtain P (u i ) corresponding parameter speed limit value 、P(u i-1 ) corresponding parameter speed limit value and P(u i+1 ) corresponding parameter speed limit value ;in, Satisfies the following relationship: .

[0052] In this embodiment, R is the value of P(u) at u i The radius of curvature at is P(u) at u i The first derivative at ; the parameter speed limit value is based on the curvature of the trajectory curve and the maximum acceleration a of the system max Calculation. Formula In the equation, R is the value of P(u) at u. i The radius of curvature at (R=1 / k, k is the curvature), is P(u) at u i The first derivative at (describing the tangent direction).

[0053] Combined with the existing curvature calculation formula k= , it can be deduced that The centripetal force constraint (determined by the acceleration limit) must be satisfied, that is, the maximum parameter velocity limit allowed at this point is calculated through the first-order derivative, second-order derivative and maximum acceleration of the curve. Similarly, the adjacent point u is calculated. i-1 、u i+1 Parameter speed limit value.

[0054] By associating curvature with acceleration constraints, the parameter speed of high-curvature sections can be precisely limited to avoid exceeding the centripetal force limit caused by trajectory bending, thereby ensuring motion safety from a geometric perspective. At the same time, the limit values ​​of adjacent points are taken into account, laying the foundation for subsequent conservative verification.

[0055] S340, according to 、 and , determine P(u i ) corresponds to the final parameter speed limit value .

[0056] The minimum value of the parameter speed limit value of the current trajectory point and its preceding and succeeding points is taken as P(u i) corresponds to the final constraint on the final parameter velocity. Discretization errors need to be treated conservatively by incorporating constraints from neighboring points to avoid missing local constraints due to discretization of the parameter domain.

[0057] A conservative strategy is adopted to handle discretization errors, ensuring that kinematic constraints are met even at the intersection of trajectory segments, reducing the problem of infeasible optimization solutions caused by insufficient discretization accuracy, and improving the global reliability of the trajectory.

[0058] S350, if > , then Updated to Otherwise, keep constant.

[0059] Corrected the problem of excessively high velocities caused by only considering single-point constraints in forward optimization (for example, the constraints on adjacent points in high curvature sections are tighter). By incorporating adjacent point constraints, the velocities are ensured to meet the kinematic constraints globally, avoiding a large number of adjustments during subsequent reverse optimization.

[0060] By cutting off the speed exceeding the upper limit in advance through the limit value, the traditional two-way scanning algorithm avoids the repeated iterative correction process due to the forward speed exceeding the limit (such as reducing the number of iterations from more than 10,000 to 0), which greatly improves the optimization efficiency.

[0061] The corrected speed satisfies the constraints of the current point and adjacent points at the same time, avoiding machining vibration caused by sudden speed changes at the intersection of trajectory segments, laying the foundation for the subsequent generation of continuous and smooth parameter velocity profiles, and indirectly improving the surface machining quality of the microlens array. Furthermore, 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 It is the minimum value among the maximum accelerations of each axis.

[0062] This step calculates the parameter speed limit by splitting the axes and taking the minimum value. It then combines the constraints of adjacent points to determine the final parameter speed limit. The details are as follows: Split-axis calculation parameter speed limit: for trajectory point P(u i ), based on the maximum acceleration a of the X, Z, and C axes Xmax 、a Zmax and a Cmax , calculate the parameter speed limit value corresponding to each axis respectively.

[0063] For example, the calculation for the X-axis is as follows: ; in, is the X-axis at trajectory point u iThe parameter velocity limit value of the point is used to constrain the X-axis kinematic acceleration, which is a core parameter for subsequent generation of an optimal trajectory. The X-axis first-order derivative of the trajectory curve at u i , describes the rate of change of the X-axis direction with respect to the parameter u, and reflects the "tangent slope" of the trajectory in the X-axis (in a cubic B-spline curve, it is calculated from the first-order derivative of the basis function and the control point coordinates); The Y-axis first-order derivative of the trajectory curve at u i , describes the rate of change of the Y-axis direction with respect to the parameter u (as the formula focuses on X-axis constraints, the Y-axis derivative is used to calculate trajectory curvature-related terms); The X-axis second-order derivative of the trajectory curve at u i , reflects the "curvature trend" of the X-axis direction change, and is combined with the first-order derivative to calculate the trajectory curvature; The Y-axis second-order derivative of the trajectory curve at u i , and for the same reason, it is combined with the Y-axis first-order derivative to calculate the curvature-related terms; The maximum allowed acceleration of the machine tool X-axis, the physical constraint of the machine tool actuator, directly determines the maximum dynamic load that the X-axis can withstand.

[0064] The calculation method of Z-axis and C-axis is the same as that of X-axis, which is not described here.

[0065] The minimum value of the calculated parameter velocity limit values of each axis is taken to obtain the preliminary parameter velocity limit of the point.

[0066] To handle discretization errors, the parameter velocity limits of adjacent points P(u i-1 ), P(u i+1 ) are calculated, and the minimum value of the three is taken as the final parameter velocity limit of P(u i ).

[0067] This step has at least the following beneficial effects: Ensure multi-axis coordination safety: By calculating and taking the minimum value of each axis, it is ensured that the actual acceleration of the X-axis, Y-axis, and C-axis does not exceed their respective maximum limit, avoiding vibration, drive overload, or decline in machining precision caused by acceleration exceeding the limit of a single axis.

[0068] Handle discretization errors: Incorporate the limit values of adjacent points and use a conservative strategy to avoid missing local constraints due to parameter domain discretization, ensuring that the trajectory segment junction still meets all kinematic constraints.

[0069] Improve optimization efficiency: Strict parameter velocity upper limit is determined in advance, which can directly truncate the velocity values that may exceed the limit in forward / reverse optimization, eliminating a large number of trial and error iterations (such as reducing from over 10,000 times to 0 times) in traditional algorithms, significantly reducing optimization execution time.

[0070] In this embodiment, the maximum feasible parameter speed of each trajectory point is determined by forward and reverse iteration under the preset kinematic constraint, aiming to minimize the trajectory running time, which can fully exploit the dynamic performance of each axis, make the trajectory running time closer to the theoretical minimum value, and improve the machining efficiency of micro-lens array turning; the maximum feasible parameter speed is determined by forward and reverse respectively and the minimum value is taken as the target maximum feasible parameter speed, which simplifies the optimization process of parameter speed, reduces the number of trial and error iterations, reduces the calculation complexity, significantly improves the calculation efficiency of trajectory optimization, and is more suitable for the practical industrial application scene of micro-lens array ultra-precision turning.

[0071] Embodiment two: Based on the parameter speed and acceleration of each trajectory point obtained in the above embodiment one, the machine tool is servo-controlled, and the following steps are implemented: Q100, discretizing the continuous trajectory curve corresponding to the micro-lens array turning process into a plurality of trajectory points in the parameter domain.

[0072] Based on the design surface profile and tool path of the micro-lens array, a continuous trajectory curve P(u)=[x(u),z(u),c(u)] is first constructed by cubic B-spline interpolation, u is the curve parameter, and 0≤u≤1; then it is uniformly discretized in the parameter domain u according to a preset resolution (such as Δu=10 -4 ) to obtain a trajectory point list P(u1), P(u2), …, P(u n ), which satisfies 0≤u1<u2<…<u n ≤1. For example, if the curve parameter range is 0 to 1, discretization according to Δu=10 -4 can obtain 10001 trajectory points covering the entire curve.

[0073] Converting the continuous curve into discrete points for numerical calculation provides a basis for subsequent parameter speed optimization; by reasonably selecting the discrete resolution, the optimization accuracy and efficiency can be balanced while ensuring that the trajectory details are fully captured and the calculation amount caused by excessive discrete points is avoided.

[0074] Q200, according to the target maximum feasible parameter speed corresponding to each trajectory point, a continuous parameter speed profile is constructed in the time domain by applying cubic interpolation.

[0075] Further, the target maximum feasible parameter speed corresponding to each trajectory point can be obtained by the following steps: Q210, obtaining the trajectory point list P=(P(u1), P(u2), …, P(u i ), …, P(u n ), i=1, 2, …, n; u is the curve parameter; P(ui ) is the i-th trajectory point corresponding to P(u), and n is the number of trajectory points corresponding to P(u); u i is the curve parameter of the i-th trajectory point corresponding to P(u).

[0076] In this embodiment, step Q210 is the same as step S200 in Embodiment One, and will not be repeated here.

[0077] Q220, starting from P(u1), determines the forward maximum feasible parameter speed of each trajectory point in turn under the preset kinematic constraints, aiming to minimize the trajectory running time.

[0078] Further, step Q220 includes the following steps: Q221, obtaining the maximum running speed v max of the machine tool actuator max .

[0079] Q222, according to v max , a max and the forward maximum feasible parameter speed i corresponding to P(u i+1 ), determine the forward maximum feasible parameter speed corresponding to P(u i ); wherein, the maximum value is taken when the following relationship is satisfied: ; wherein, =du i+1 / dt; Δu is the difference between u i and u i+1 ; Δu = u i -u i+1 ; is the first derivative of P(u) at u i+1 ; is the second derivative of P(u) at u i+1 ; is the forward curve parameter acceleration of P(u) at u n .

[0080] In this embodiment, steps Q221-Q222 are the same as steps S310-S320 in Embodiment One, and will not be repeated here.

[0081] Q230, based on the forward maximum feasible parameter speed of each trajectory point, determines the reverse maximum feasible parameter speed of each trajectory point in turn, starting from P(u max ).

[0082] Further, step Q230 includes the following steps: Q231, according to v max , a max and P(u i ) corresponding reverse maximum feasible parameter speed , determine P(u i-1 ) corresponding reverse maximum feasible parameter speed ; wherein, The maximum value is taken when the following relationship is satisfied: ; Wherein, = du i / dt; P(u) is the reverse curve parameter acceleration at u i-1 .

[0083] In this embodiment, step Q231 is the same as step S410 in embodiment one, which will not be repeated here.

[0084] Q240, the minimum feasible parameter speed of the forward maximum feasible parameter speed and the reverse maximum feasible parameter speed of each trajectory point is determined as the initial maximum feasible parameter speed of the corresponding trajectory point.

[0085] In this embodiment, the target maximum feasible parameter speed obtained by Q240 may not be executable by the machine tool. Therefore, the target maximum feasible parameter speed obtained by Q240 is taken as the initial maximum feasible parameter speed, and the following method is provided to obtain the target maximum feasible parameter speed: Q250, obtaining the parameter speed limit value i corresponding to P(u i-1 ), the parameter speed limit value i+1 corresponding to P(u max ), and the parameter speed limit value i corresponding to P(u i ); wherein, The following relationship is satisfied: .

[0086] In this embodiment, the parameter speed limit value is calculated based on the curvature of the trajectory curve and the system maximum acceleration a i-1 . In the formula , R is the curvature radius of the trajectory at u i+1 (R=1 / k, k is the curvature), is the first derivative of the curve at u i (describing the tangent direction).

[0087] Combined with the existing curvature calculation formula k= , it can be deduced that The centripetal force constraint (determined by the acceleration limit) needs to be met, that is, the maximum parameter speed limit of the point is calculated through the first derivative, the second derivative of the curve and the maximum acceleration of the system. The parameter speed limit values of adjacent points u i-1 、 i+1 are calculated in the same way.

[0088] By associating the curvature with the acceleration constraint, the parameter speed of the high-curvature segment is accurately limited to avoid centripetal force over-limiting due to trajectory bending, and the motion safety is guaranteed from the geometric characteristic point of view; at the same time, the limit values of adjacent points are considered to lay a foundation for subsequent conservative checking.

[0089] Q260, according to 、 and , determine the final parameter speed limit value of P(u i ).

[0090] The minimum value of the parameter speed limit values of the current trajectory point and its previous and subsequent points is taken as the final limit of the final parameter speed of P(u i ). The discretization error needs to be handled conservatively, and by including the limit of the adjacent points, the local constraint omission caused by parameter domain discretization is avoided.

[0091] The discretization error is handled by a conservative strategy to ensure that the kinematic constraints are met even at the junction of the trajectory segments, reduce the problem of infeasible optimization solution caused by insufficient discretization accuracy, and improve the global reliability of the trajectory.

[0092] Q270, if mv max，i > , determine as the target maximum feasible parameter speed of P(u i ); otherwise, determine mv max，i as the target maximum feasible parameter speed of P(u i ).

[0093] By limiting the parameter speed in advance, infeasible solutions in forward / backward optimization are avoided. By limiting the value to truncate the target speed that exceeds the upper limit, trial and error adjustment in subsequent iterations is completely eliminated, the number of iterations of the traditional bidirectional scanning algorithm is significantly reduced (such as from more than 10,000 times to 0 times), and the optimization execution efficiency is greatly improved; at the same time, it is guaranteed that the target speed strictly meets all constraints.

[0094] Further, the maximum acceleration of the machine tool execution mechanism includes the maximum acceleration of the X-axis, the maximum acceleration of the Y-axis and the maximum acceleration of the C-axis, and the final parameter speed limit value is the minimum value of the maximum accelerations of the axes.

[0095] This step determines the final parameter speed limit by calculating the parameter speed limit of each axis and taking the minimum value, combined with adjacent point constraints, as follows: Calculate the parameter speed limit of each axis: For the trajectory point P(u i ), based on the maximum accelerations a Xmax , a Zmax and a Cmax of the X-axis, Z-axis and C-axis, respectively, calculate the corresponding parameter speed limit value of each axis.

[0096] For example, the calculation of the X-axis is as follows: ; Where, is the parameter speed limit value of the X-axis at the trajectory point u i , used to constrain the kinematic acceleration of the X-axis, which is the core parameter for generating the optimal trajectory subsequently; is the first-order derivative of the X-axis of the trajectory curve at u i with respect to the parameter u, describing the rate of change of the X-axis direction with respect to the parameter u, reflecting the "tangent slope" of the trajectory in the X-axis (in a cubic B-spline curve, it is calculated from the first-order derivative of the basis function and the control point coordinates); is the first-order derivative of the Y-axis of the trajectory curve at u i with respect to the parameter u, describing the rate of change of the Y-axis direction with respect to the parameter u (as the formula focuses on the X-axis constraint, the Y-axis derivative is used to calculate the trajectory curvature related term); is the second-order derivative of the X-axis of the trajectory curve at u i with respect to the parameter u, reflecting the "curvature trend" of the change of the X-axis direction, combined with the first-order derivative to calculate the trajectory curvature; is the second-order derivative of the Y-axis of the trajectory curve at u i with respect to the parameter u, and for the same reason, combined with the first-order derivative of the Y-axis to calculate the curvature related term; is the maximum allowed acceleration of the machine tool X-axis, which is the physical constraint of the machine tool actuator, directly determining the maximum dynamic load that the X-axis can withstand.

[0097] By quantifying the influence of the trajectory geometric characteristics on the X-axis acceleration, the "trajectory bending degree" is directly related to the "machine tool dynamic constraint", ensuring that the parameter speed is automatically limited in high curvature sections (such as the inflection points of the curved surface of the microlens array), avoiding X-axis acceleration over-limit.

[0098] This formula is a bridge between "trajectory geometry - actuator constraint - parameter speed", allowing parameterized trajectory optimization to meet the curved surface accuracy of the microlens array while not breaking the physical limit of the machine tool.

[0099] The calculation method of the C-axis of the Z-axis is the same as that of the X-axis, which is not described here.

[0100] The minimum value of the calculated parameter speed limit values corresponding to each axis is taken to obtain the preliminary parameter speed limit of the point.

[0101] To handle the discretization error, the parameter speed limits of the adjacent points P(u i-1 ), P(u i+1 ) are calculated, and the minimum value of the three is taken as the final parameter speed limit of P(u i ).

[0102] This step has at least the following beneficial effects: Ensure multi-axis safety: By calculating and taking the minimum value of each axis, it is ensured that the actual acceleration of the X-axis, Y-axis and C-axis does not exceed the maximum limit value, avoiding vibration, drive overload or decline in machining precision caused by acceleration exceeding the limit of a single axis.

[0103] Handle discretization error: Include the limit values of adjacent points and use a conservative strategy to avoid missing local constraints due to parameter domain discretization, ensuring that the trajectory segment junction still meets all kinematic constraints.

[0104] Improve optimization efficiency: Determine the strict parameter speed limit in advance, which can directly cut off the speed value that may exceed the limit in forward / backward optimization, eliminating a large number of trial and error iterations (such as reducing from more than 10,000 times to 0 times) in traditional algorithms, significantly reducing optimization execution time.

[0105] In this embodiment, the goal is to minimize the trajectory running time, and the maximum feasible parameter speed of each trajectory point is determined through forward and backward iterations under the preset kinematic constraints, which can fully exploit the dynamic performance of each axis, making the trajectory running time closer to the theoretical minimum value and improving the machining efficiency of micro-lens array turning; by determining the maximum feasible parameter speed through forward and backward iterations and taking the minimum value as the target maximum feasible parameter speed, the optimization process of the parameter speed is simplified, the number of trial and error iterations is reduced, the computational complexity is reduced, and the calculation efficiency of trajectory optimization is significantly improved, making it more suitable for practical industrial application scenarios of micro-lens array ultra-precision turning.

[0106] Q300, integrate the parameter speed profile to obtain the parameter trajectory u(t); where t is the time point.

[0107] In this embodiment, the continuous parameter speed profile constructed by Q200 is time-integrated to obtain the trajectory of parameter u with respect to time t.

[0108] By integrating to establish the direct relationship between parameter u and time t, the speed information is converted into the time evolution law of position information, providing a core basis for the time characteristics of the subsequent generated spatial trajectory.

[0109] Q400, substitute u(t) into the cubic B-spline curve to generate the optimal trajectory P(u(t)) corresponding to the continuous trajectory curve that satisfies the kinematic constraints.

[0110] Substituting the parameter trajectory u(t) obtained by Q300 into the cubic B-spline curve P(u), we can get the mapping relationship between spatial position and time P(u(t))=[x(u(t)),z(u(t)),c(u(t))], where x(u(t)), z(u(t)), and c(u(t)) are the functions of the position of the X-axis, Z-axis, and C-axis over time, respectively. 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 grows with the square of time.

[0111] Through this step, the generated optimal trajectory satisfies both time minimization and kinematic constraints (speed and acceleration limits), fully utilizing the dynamic performance of the machine tool to shorten processing time, while ensuring trajectory smoothness to reduce processing vibration, providing a reliable path for high-precision turning.

[0112] Q500, differentiate P(u(t)) to obtain the desired velocity and acceleration of the X-axis, Z-axis, and C-axis of the machine tool actuator.

[0113] Based on the derivative rule of composite function, the derivative of P(u(t)) is: Expected speed: , that is, the speed of each axis is the product of the first derivative of the curve with respect to parameter u and the parameter speed. For example, the expected speed of the X axis is ,in, is the derivative of the X-axis position function with respect to u.

[0114] Expected acceleration: , that is, the acceleration of each axis is the product of the second-order derivative of the curve with respect to u and the square of the parameter velocity, plus the product of the first-order derivative and the parameter acceleration. For example, the expected acceleration of the Z axis is .

[0115] Through this step, the desired velocity and acceleration are directly obtained through analytical derivation, avoiding the phase lag and error (such as noise caused by first-order difference) introduced by numerical differentiation in traditional PID controllers, and significantly improving the tracking accuracy of servo control.

[0116] Furthermore, step Q500 may include the following steps: Q510, derive P(u(t)) and combine it with the speed parameter =du / dt, get the expected speed v of the X axis of the machine tool actuator x , the expected speed v of the Z axis zand the desired velocity v of the C-axis c ; wherein, ; ; ; , and are the first derivatives of the position functions of the X-axis, Z-axis and C-axis with respect to the parameter u, respectively.

[0117] Taking the derivative of the optimal trajectory P(u(t)) = [x(u(t)), z(u(t)), c(u(t))] with respect to the parameter velocity , the desired velocities of the axes are obtained.

[0118] For the X-axis, the position function is x(u(t)), and according to the derivative rule of composite functions, its derivative with respect to time is , wherein, is the first derivative of the X-axis position function with respect to the parameter u (calculated by the derivative of the cubic B-spline basis function, such as , is the first derivative of the fourth-order B-spline basis function); the Z-axis and C-axis are solved in the same way as the X-axis.

[0119] By directly calculating the desired velocity through analytical derivation, the phase lag and noise introduced when obtaining the velocity through numerical difference (such as the difference between adjacent positions divided by the time interval) in traditional methods are avoided, the accuracy of the velocity signal is improved, and more accurate feedforward input is provided for servo control.

[0120] Q520, taking the derivative of P(u(t)) with respect to the parameter acceleration = d 2 u / dt 2 , the desired accelerations a x of the X-axis, a z of the Z-axis and a c of the C-axis of the machine tool actuator are obtained; wherein, ; ; ; , and are the second derivatives of the position functions of the X-axis, Z-axis and C-axis with respect to the parameter u, respectively.

[0121] Taking the derivative of the desired velocity of each axis again with respect to the parameter acceleration , the desired acceleration is obtained.

[0122] The X-axis acceleration is the derivative of the velocity with respect to time: ; wherein, is the second derivative of the X-axis position function with respect to u (calculated by the second derivative of the cubic B-spline basis function, such as ) ; the solution of Z axis and C axis is the same as X axis.

[0123] The acceleration is obtained by second-order analytical derivation to avoid the problem of amplifying noise by numerical second-order difference and ensure the smoothness of the acceleration signal; at the same time, the curvature characteristics of the curve are directly related to the parameter velocity / acceleration, so that the acceleration feedforward can accurately compensate the dynamic demand caused by the bending of the trajectory, further improving the servo tracking accuracy.

[0124] Q600, the expected speed and expected acceleration are taken as feedforward inputs, substituted into the output calculation formula of the servo controller, and the servo output is obtained to drive the X axis, Z axis and C axis to move.

[0125] Further, the output calculation formula of the servo controller is: ; wherein, K P is a proportional coefficient, K v is a velocity feedforward coefficient, and K a is an acceleration feedforward coefficient; v(t) is the expected speed at t, a(t) is the expected acceleration at t, and e(t) is the tracking error of the actual position and the expected position at t.

[0126] The expected speed v(t) and the expected acceleration a(t) obtained by Q500 are taken as feedforward terms, and substituted into the output formula of the servo controller: ; wherein, K P is a proportional coefficient, K v is a velocity feedforward coefficient, and K a is an acceleration feedforward coefficient; e(t) is the tracking error of the actual position and the expected position at t, for example, when the expected speed v x of the X axis is 0.1t and the acceleration a x is 0.1, the feedforward term will drive the motor in advance to respond, reducing the error caused by system lag.

[0127] The feedforward input enables the controller to "predict" the speed and acceleration changes of the trajectory, and adjusts the output in advance to compensate for the system dynamic lag, significantly reducing the tracking error (such as reducing the tracking error of the Z axis by 30%); at the same time, combined with the efficiency of the optimized trajectory, the machining precision (shape error reduction) and efficiency (machining time reduction) of the microlens array are simultaneously improved.

[0128] In the embodiment, the iteration number of trajectory optimization is greatly reduced and the calculation efficiency is improved by discretizing the continuous trajectory and constructing the parameter velocity profile by combining the cubic interpolation; the continuity of the optimal trajectory and the satisfaction of the kinematic constraint are ensured by integrating the parameter velocity profile to obtain the parameter trajectory and substituting the parameter trajectory into the cubic B-spline curve; the expected velocity and acceleration are directly derived from the optimal trajectory to avoid the lag and error caused by the traditional numerical differentiation, thereby improving the tracking accuracy of the servo control; the expected velocity and acceleration are used as the feedforward input to drive the shaft movement, thereby realizing the efficient cooperation of the trajectory planning and the servo control, finally ensuring the shape accuracy of the microlens array (such as reducing the shape error) while improving the machining efficiency, and effectively solving the problem that the accuracy and efficiency are difficult to be considered in the prior art.

[0129] In addition, although the various steps of the methods in the present disclosure are described in a particular order in the accompanying drawings, this does not require or imply that the steps must be performed in this particular order, or that all of the steps shown must be performed to achieve the desired result. Additionally or alternatively, certain steps can be omitted, multiple steps can be combined into one step, and / or one step can be divided into multiple steps, etc.

[0130] The embodiments of the present application also provide a non-transitory computer-readable storage medium, which can be arranged in an electronic device to save at least one instruction or at least one program related to a method in the method embodiments, and the at least one instruction or the at least one program is loaded and executed by the processor to implement the method provided by the above embodiments.

[0131] The program product can adopt any combination of one or more readable media. The readable medium can be a readable signal medium or a readable storage medium. The readable storage medium may, for example, be but is not limited to an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, device or component, or any combination of the above. More specific examples (non-exhaustive list) of readable storage media include an electrical connection having one or more wires, a portable disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disk read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the above.

[0132] A computer readable signal medium can include a propagated data signal with computer readable program code embodied therein, for example, in baseband or as part of a carrier wave. Such a propagated signal can take any of a variety of forms, including, but not limited to, electro-magnetic, optical, or any suitable combination thereof. A computer readable signal medium can be any computer readable medium that can be involved in

[0133] The program code embodied on the computer readable medium can be transmitted using any appropriate medium, including but not limited to wireless, wire line, optical fiber cable, RF, etc., or any suitable combination of the foregoing.

[0134] Computer program code for carrying out operations of the present application can be written in any combination of one or more programming languages, including an object oriented programming language such as Java, C++, or the like, and conventional procedural programming languages, such as the "C" programming language or similar programming languages. The program code can execute entirely on the user's computing device, partly on the user's computing device, as a stand-alone software package, partly on the user's computing device and partly on a remote computing device or entirely on the remote computing device or server. In the latter scenario, the remote computing device can be connected to the user's computing device through any type of network, including a local area network (LAN) or a wide area network (WAN), or the connection can be made to an external computing device, such as through the Internet using an Internet Service Provider.

[0135] Embodiments of the present application also provide an electronic device including a processor and the aforementioned non-transitory computer readable storage medium.

[0136] The electronic device is merely an example and should not bring any limitation to the function and usage range of the embodiments of the present application.

[0137] The electronic device is in the form of a general purpose computing device. The components of the electronic device can include, but are not limited to, the aforementioned at least one processor, the aforementioned at least one memory, a bus connecting different system components, including the memory and the processor.

[0138] The memory stores program codes which can be executed by the processor, so that the processor performs steps in various embodiments described in the specification.

[0139] The memory can include a readable medium in the form of a volatile memory, such as a random access memory (RAM) and / or a cache memory, and can further include a read only memory (ROM).

[0140] The storage can also include a number of program modules that are stored in a computer- readable medium such as a memory, a floppy disk, a CD-ROM, a DVD, a Blu-ray Disc, a Flash drive, a memory stick, or a magnetic tape. These program modules include, but are not limited to, an operating system, one or more application programs, other program modules, and program data. Each of these examples, or a subset or

[0141] The 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 bus, a processor or local bus using any of a variety of bus architectures.

[0142] The electronic device can also communicate with one or more external devices such as a keyboard or a pointing device, through an I / O interface. Additionally, the electronic device can communicate with one or more devices that enable a user to interact with the electronic device through an input device or devices 1102. In the embodiment of the electronic device, the input device or devices 1102 can include a microphone, a camera, a button, a switch, a touch-sensitive screen, or any combination thereof. The input device or devices 1102 can also include a network interface device or devices that enable a user to interact with the electronic device through an output device or devices 1104. The output device or devices 1104 can include a speaker, a camera, a button, a switch, a touch-sensitive screen, or any combination thereof. The input device or devices 1102 and the output device or devices 1104 can also include any devices that enable a user to interact with the electronic device through the Internet or World Wide Web. In the embodiment of the electronic device, the input device or devices 1102 and the output device or devices 1104 can include devices that enable the electronic device to communicate with users through a web browser such as Microsoft Internet Explorer® or Google Chrome®. The input device or devices 1102 and the output device or devices 1104 can further include any devices that enable a user to interact with the electronic device through a web browser on a server or on a user's Internet service provider's server. The input device or devices 1102 and the output device or devices 1104 can also include devices that enable the electronic device to communicate with users through a mobile application such as Apple's iOS® or Google's Android®. The input device or devices 1102 and the output device or devices 1104 can further include any devices that enable a user to interact with the electronic device through a mobile application on a server or on a user's Internet service provider's server. The input device or devices 1102 and the output device or devices 1104 can also include devices that enable the electronic device to communicate with users through a virtual reality or augmented reality system. The input device or devices 1102 and the output device or devices 1104 can further include any devices that enable a user to interact with the electronic device through a virtual reality or augmented reality system on a server or on a user's Internet service provider's server. The input device or devices 1102 and the output device or devices 1104 can also include devices that enable the electronic device to communicate with users through a voice-activated system such as Amazon's Alexa®, Apple's Siri®, Google's Assistant®, or Microsoft's Cortana®. The input device or devices 1102 and the output device or devices 1104 can further include any devices that enable a user to interact with the electronic device through a voice-activated system on a server or on a user's Internet service provider's server.

[0143] Those skilled in the art will readily understand that the example embodiments described herein can be implemented by software and / or by software in combination with the necessary hardware. Thus, the technical solutions of the embodiments of the present disclosure can be embodied in the form of a software product. The software product can be stored in a non-volatile storage medium (which can be a CD-ROM, a USB flash disk, a mobile hard disk, or the like) or a network, and includes a number of instructions to enable a computing device (which can be a personal computer, a server, a terminal device, or a network device, etc.) to perform the methods according to the embodiments of the present disclosure.

[0144] The embodiments of the present disclosure also provide a computer program product, which comprises program codes for causing an electronic device to perform the steps of the methods according to the various example embodiments of the present disclosure described above when the program product is run on the electronic device.

[0145] While certain specific embodiments of the application have been described in detail herein for the purposes of exemplification, it will be understood by those skilled in the art that the examples are for illustration only and are not intended to limit the scope of the application. It will be further understood by those skilled in the art that various modifications can be made to the embodiments without departing from the scope and spirit of the application.

Claims

1. A method for optimizing the turning motion trajectory of a microlens array, characterized in that: The method comprises the following steps: S100, constructing a continuous trajectory curve P(u) based on 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, and obtain a trajectory point list G=(P(u1), P(u2),…, P(u i ),…,P(u n )), i=1, 2,...,n; P(u i ) is the i-th trajectory point corresponding to P(u), n is the number of trajectory points corresponding to P(u); u i is the curve parameter of the i-th trajectory point corresponding to P(u); S300, with the goal of minimizing the trajectory running time, under the preset kinematic constraints, the forward maximum feasible parameter velocity of each trajectory point is determined in sequence starting from P(u1); S400, based on the maximum feasible parameter speed of each trajectory point, from P (u n ) starts, and determines the reverse maximum feasible parameter velocity of each trajectory point in turn; S500, determining the minimum feasible parameter speed between the forward maximum feasible parameter speed and the reverse maximum feasible parameter speed of each trajectory point as the target maximum feasible parameter speed of the corresponding trajectory point; S600 , based on the target maximum feasible parameter velocity of each trajectory point in G, generate an optimal trajectory P(u(t)) corresponding to P(u) that satisfies kinematic constraints; u(t) is a curve parameter at time point t.

2. The microlens array turning motion trajectory optimization method 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 the maximum acceleration a max ; S320, according to v max 、a max and P(u i ) corresponds to the maximum feasible parameter speed in the positive direction , determine P(u i+1 ) corresponds to the maximum feasible parameter speed in the positive direction ;in, Take the maximum value when the following relationship is satisfied: ； in, =du i / dt, t is the time point; Δu is u i+1 and u i The difference between them, Δu=u i+1 -u i ; is P(u) at u i+1 The first derivative at ; is P(u) at u i+1 The second derivative at ; is P(u) at u i+1 The positive curve parameter acceleration at .

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

4. The microlens array turning motion trajectory optimization method according to claim 3, characterized in that: Step S500 includes the following steps: S510, according to and , determine P(u i ) target maximum feasible parameter speed mv max，i =MIN ; Among them, MIN() is the preset minimum value function.

5. The microlens array turning motion trajectory optimization method according to claim 2, characterized in that: After step S320, the method further includes the following steps: S330, obtain P (u i ) corresponding parameter speed limit value 、P(u i-1 ) corresponding parameter speed limit value and P(u i+1 ) corresponding parameter speed limit value ;in, The following relationship is satisfied: ； R is P(u) at u i The radius of curvature at is P(u) at u i The first derivative at ; S340, according to 、 and , determine P(u i ) corresponds to the 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, wherein: 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 It 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, wherein: The machine tool actuator is between P(u1) and P(u n ) are all at 0.

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

9. An electronic device, characterized in that: The device comprises a processor and the non-transitory computer-readable storage medium of claim 8.

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