Microlens array turning servo control method and device and medium

Abstract

The invention provides a micro-lens array turning servo control method and device and a medium, and relates to the technical field of micro-lens array turning servo control, and the method comprises the steps: dispersing a continuous track curve corresponding to a micro-lens array turning process into a plurality of track points in a parameter domain; applying cubic interpolation in a time domain to construct a continuous parameter velocity profile; integrating the parameter velocity profile to obtain a parameter trajectory u (t); generating an optimal trajectory P (u (t)) which corresponds to the continuous trajectory curve and meets kinematics constraints; deriving the P (u (t)) to obtain expected speeds and expected accelerations of an X axis, a Z axis and a C axis of a machine tool execution mechanism; taking the expected speed and the expected acceleration as feed-forward input, substituting the feed-forward input into an output calculation formula of a servo controller, and obtaining servo output to drive X-axis, Z-axis and C-axis movement; the problem that precision and efficiency are difficult to consider in the prior art can be effectively solved.

Description

Technical Field

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

[0002] In the ultra-precision turning of microlens arrays, existing technologies have many limitations: on the one hand, trajectory planning often faces the contradiction between computational efficiency and accuracy, and traditional time-optimal trajectory planning methods require a large number of trial-and-error iterations (e.g., a discretization step size of 10 -4 The number of iterations often exceeds 10,000), resulting in excessively long optimization execution times, making it difficult to meet industrial real-time requirements. Furthermore, the feedforward mechanism of traditional PID controllers in servo control relies on numerical differentiation to obtain velocity and acceleration, which can easily introduce phase lag and differential errors, leading to decreased tracking accuracy. Especially in high-frequency motion scenarios, tracking errors on key axes such as the Z axis are significant, making it difficult to ensure the shape accuracy and surface quality of the microlens array. Furthermore, the lack of coordination between trajectory planning and servo control prevents efficient utilization of the optimized trajectory, making it difficult to simultaneously improve processing efficiency and accuracy. Summary of the Invention

[0003] 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 microlens array turning servo control method is provided, the method comprising the following steps: Q100, discretizes the continuous trajectory curve corresponding to the microlens array turning process into multiple trajectory points in the parameter domain; Q200, based on the target maximum feasible parametric velocity corresponding to each trajectory point, a continuous parametric velocity profile is constructed by applying cubic interpolation in the time domain; Q300, integrating the parameter velocity profile to obtain a parameter trajectory u(t); wherein t is a time point; 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; Q500, derive P(u(t)) to obtain the desired speed and acceleration of the X-axis, Z-axis, and C-axis of the machine tool actuator; Q600 uses the desired velocity and desired acceleration as feedforward inputs and substitutes them into the output calculation formula of the servo controller to obtain the servo output to drive the X-axis, Z-axis and C-axis motion.

[0004] Furthermore, step Q500 includes 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 actuatorx , the expected speed v of the Z axis z and the desired speed v of the C axis c ;in, ; ; ; 、 and The first derivatives of the position functions of the X-axis, Z-axis, and C-axis with respect to the parameter u are respectively; Q520, take the derivative of P(u(t)) and combine it with the acceleration parameter =d 2 u / dt 2 , get the expected acceleration a of the X axis of the machine tool actuator x , the expected acceleration of the Z axis a z and the desired acceleration a of the C axis c ;in, ; ; ; 、 and These are the second-order derivatives of the position function of the X-axis, Z-axis, and C-axis with respect to the parameter u.

[0005] Furthermore, the output calculation formula of the servo controller is: ; Among them, u ctrl K is the output of the servo controller, which is used to drive the actuators of the X-axis, Z-axis and C-axis of the machine tool; P is the proportionality coefficient, K v is the speed feedforward coefficient, K a is the acceleration feedforward coefficient; v(t) is the expected velocity at t, a(t) is the expected acceleration at t, and e(t) is the tracking error between the actual position and the expected position at t.

[0006] Furthermore, the target maximum feasible parameter speed corresponding to each trajectory point is obtained by the following steps: Q210, obtain the trajectory point list P = (P (u1), P (u2), ..., P (u) corresponding to the continuous trajectory curve P (u) i ),…,P(u n ) ), i = 1, 2, ..., n; 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]; 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); Q220, with the goal of minimizing the trajectory running time, under the preset kinematic constraints, determines the maximum feasible parameter velocity of each trajectory point in turn starting from P(u1); Q230, based on the maximum feasible parameter velocity of each trajectory point, from P (u n ) starts, and determines the reverse maximum feasible parameter velocity of each trajectory point in turn; Q240, 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.

[0007] Furthermore, step Q220 includes the following steps: Q221, obtain the maximum operating speed v of the machine tool actuator max and the maximum acceleration a max ; Q222, 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; 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 .

[0008] Furthermore, step Q230 includes the following steps: Q231, 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 / dt; is P(u) at u i-1 Reverse curve parameter acceleration at P(u i-1 ) is the i-1th trajectory point corresponding to P(u); u i-1 is the curve parameter of the i-1th trajectory point corresponding to P(u).

[0009] Furthermore, the machine tool actuator is between P(u1) and P(u n ) are all at 0.

[0010] 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 servo control method.

[0011] 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.

[0012] The present invention has at least the following beneficial effects: The microlens array turning servo control method of the present invention discretizes the continuous trajectory and combines it with cubic interpolation to construct a parametric velocity profile, thereby significantly reducing the number of trajectory optimization iterations and improving computational efficiency. The parametric trajectory is obtained by integrating the parametric velocity profile and substituting it into a cubic B-spline curve, thereby ensuring the continuity of the optimal trajectory and satisfying kinematic constraints. The optimal trajectory is directly differentiated to obtain the desired velocity and acceleration, thereby avoiding the lag and error caused by traditional numerical differentiation and improving the tracking accuracy of the servo control. The desired velocity and acceleration are used as feedforward inputs to drive the axis movement, thereby achieving efficient coordination between trajectory planning and servo control. Ultimately, the shape accuracy of the microlens array is ensured (e.g., shape error is reduced) while improving machining efficiency, effectively solving the problem of balancing precision and efficiency in the prior art. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] 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.

[0014] Figure 1 This is a flow chart of a microlens array turning servo control method provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0015] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without making any creative efforts shall fall within the scope of protection of the present invention.

[0016] It should be noted that, based on this disclosure, those skilled in the art will appreciate that an aspect described herein can be implemented independently of any other aspect, and that two or more of these aspects can be combined in various ways. For example, any number of the aspects described herein can be used to implement an apparatus and / or practice a method. In addition, other structures and / or functionalities other than one or more of the aspects described herein can be used to implement such an apparatus and / or practice such a method.

[0017] Example 1: First, the parameter speed of the trajectory point in the microlens array turning process is optimized, which can include 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.

[0018] In this embodiment, the discrete tool path points of micro lens array turning (generated by CAM system, including surface geometry and tool radius compensation information) are used as control points. 2 Continuous interpolation is used to construct the 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.

[0019] Through this step, the discrete tool path points are converted into smooth and continuous curves, avoiding the trajectory mutation caused by directly connecting discrete points, providing a smooth basis for subsequent trajectory discretization and optimization, and reducing machining vibration and surface quality defects caused by trajectory discontinuity.

[0020] 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).

[0021] In the parameter domain 0≤u≤1, the cubic B-spline curve P(u) is uniformly discretized into n trajectory points, and a list G is obtained, where 0≤u1<u2<…<u n ≤1, discretization resolution Δu (e.g. Δu=10 -4 ) It is necessary to balance optimization accuracy and computational efficiency.

[0022] This step converts the continuous curve into discrete points that can be numerically calculated, facilitating the iterative calculations of the subsequent forward / reverse optimization. By properly selecting Δu, we can ensure that the trajectory details are fully captured while avoiding the surge in computational complexity caused by too many discrete points, thus balancing optimization accuracy and efficiency.

[0023] S300, with the goal of minimizing the trajectory running time, under the preset kinematic constraints, the forward maximum feasible parameter speed of each trajectory point is determined in sequence starting from P(u1).

[0024] With the goal of minimizing the trajectory running time, starting from the starting point P(u1), the maximum feasible parameter speed of each trajectory point is calculated in turn, and the kinematic constraints must be met during the calculation.

[0025] Maximize the parameter speed within the kinematic constraints, preliminarily explore the dynamic performance of each axis, and lay the foundation for shortening the trajectory running time; through point-by-point iteration, ensure that the speed of each step meets the constraints, and avoid processing errors caused by excessive local speed.

[0026] Furthermore, step S300 may include the following steps: S310, obtain the maximum operating speed v of the machine tool actuator max and the maximum acceleration a max .

[0027] v max and a max These are preset machine tool kinematic constraint parameters, determined based on the dynamic performance of an ultra-precision lathe (such as the LD-CL100 V2). Specifically, they include the maximum speed and acceleration limits for each axis, including the X-axis, Z-axis, and C-axis (e.g., the parameters defined by the "Slow," "Medium," and "Fast" constraint sets in Table 1). These parameters must be set in conjunction with the physical properties of the machine tool's drive system (e.g., linear motors and piezoelectric actuators) and the machining process requirements (e.g., the surface quality requirements for the microlens array) to ensure they do not exceed the machine tool's mechanical load capacity and dynamic response range.

[0028] This step clarifies the motion boundary conditions of the machine tool, providing a strict constraint benchmark for subsequent parameter speed optimization. This avoids machine tool vibration, drive overload, or reduced machining accuracy caused by speed or acceleration exceeding the limit, thereby ensuring the safety and feasibility of trajectory optimization from the bottom up.

[0029] 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 .

[0030] Based on the previous trajectory point P (u i ) of the forward maximum feasible parameter speed , maximize P(u i+1 ) corresponds to the maximum feasible parameter speed in the positive direction : Speed ​​Constraint: , is a cubic B-spline curve at u i+1 The first-order derivative at the point describes the tangent direction of the curve at that point, ensuring that the actual running speed of each axis does not exceed v max .

[0031] Acceleration constraints: , is the second-order derivative of the curve, describing the change in curvature, It is a discrete approximation of the parameter acceleration, ensuring that the actual acceleration of each axis does not exceed a max During the iterative calculation, the above inequalities are solved by numerical methods, and the largest solution is selected from the solution set that satisfies all constraints. .

[0032] Under the premise of strictly adhering to the kinematic constraints of the machine tool, the parametric speed of each trajectory point is maximized, and the dynamic capabilities of the machine tool are fully exploited to shorten the processing time. Through the coupled calculation of first-order and second-order derivatives and parametric speed / acceleration, the geometric characteristics of the curve (such as curvature) and kinematic performance are accurately associated to avoid speed / acceleration exceeding the limit due to local curvature mutations, provide a reasonable forward speed benchmark for subsequent reverse optimization, and reduce the number of iterations of the overall optimization.

[0033] S400, based on the maximum feasible parameter speed of each trajectory point, from P (u n ) and determine the reverse maximum feasible parameter velocity of each trajectory point in turn.

[0034] Based on the forward optimization results, from the end point P (u n )(P(u n ) = 0), the maximum feasible parameter velocity of each trajectory point is calculated by reverse iteration, which also needs to meet the velocity and acceleration constraints to ensure that the trajectory can decelerate smoothly to the terminal stationary state.

[0035] This step corrects the "local greed" defect of forward optimization (forward optimization may excessively pursue local speed, resulting in subsequent high-curvature segments failing to meet constraints). Reverse verification ensures that the trajectory meets constraints throughout the entire segment, especially ensuring that the end point can stop smoothly, avoiding a decrease in machining accuracy due to the end point speed not meeting the constraints.

[0036] Furthermore, step S400 may include 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 .

[0037] In this embodiment, the reverse optimization starts from the trajectory end point P (u n ) starts, based on the current trajectory point P (ui ), maximizes the parameter velocity of the previous trajectory point under the premise of satisfying the following constraints: Speed ​​Constraint: , ensure that the actual speed of each axis does not exceed the maximum speed of the machine tool v max .

[0038] Acceleration constraints: , ensure that the actual acceleration of each axis does not exceed a max .

[0039] During iterative calculation, the above inequalities are solved by numerical methods, and the largest solution is selected from the solution set that satisfies all constraints. , and reversely advance from i=n to i=2 in sequence, and finally complete the reverse velocity planning of all trajectory points.

[0040] By reverse-checking and adjusting the parameter speed from the endpoint, the infeasibility problem of subsequent trajectory segments caused by the "local greedy" strategy in forward optimization (such as excessive acceleration 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 speed and acceleration constraint checks further ensure the safety of reverse speed planning, complementing forward optimization and providing a reliable basis for subsequently taking the minimum value to determine the target maximum feasible parameter speed, reducing the number of trial-and-error iterations of the overall optimization, and improving the efficiency and feasibility of trajectory planning.

[0041] In this embodiment, the overall effect of forward and reverse optimization is as follows: On the one hand, forward optimization begins at the trajectory's starting point, maximizing the parameter velocity at each trajectory point under kinematic constraints. This initially exploits the machine tool's dynamic capabilities to shorten processing time. On the other hand, reverse optimization begins at the trajectory's endpoint (where the parameter velocity is constrained to 0) and adjusts the parameter velocity at each trajectory point in reverse. This corrects any potential issues with excessively high local velocities during forward optimization, rendering subsequent segments infeasible, and ensures that the trajectory satisfies constraints throughout. Combining these two approaches, the minimum of the maximum feasible parameter velocity in both the forward and reverse directions is taken as the target maximum feasible parameter velocity. This fully utilizes the machine tool's dynamic performance to improve efficiency, while ensuring the trajectory's global feasibility through bidirectional verification. This significantly reduces the number of trial-and-error iterations required for traditional one-way optimization. While reducing optimization execution time, it also generates a time-optimal trajectory that satisfies kinematic constraints. This provides a precise velocity and acceleration benchmark for subsequent servo control, ultimately improving the accuracy and efficiency of microlens array processing.

[0042] In this embodiment, the parameter speed The core physical meaning of is the "rate of change of curve parameter u over time", which reflects the "progress speed" of the machine tool moving along the trajectory curve P(u); The larger it is, the farther the distance advanced along the parameter domain [0,1] per unit time is, and the higher the processing efficiency is.

[0043] (Forward): Starting from the trajectory starting point P(u1), the maximum feasible parameter speed du / dt is calculated point by point. The constraint condition is that "the speed at the current point does not exceed the speed / acceleration upper limit of each axis of the machine tool and can smoothly transition to the next point."

[0044] (Reverse): From the end point of the trajectory P(u n ) starts from the beginning and reversely calculates the maximum feasible parameter speed du / dt point by point. The constraint condition is that "the speed of the current point does not exceed the speed / acceleration upper limit of each axis of the machine tool and can smoothly transition to the previous point."

[0045] The mathematical definition of both is du / dt, and they only differ in the calculation direction and reference constraint point. In essence, they are both the "time rate of change of parameter u", which conforms to the core logic of "associating geometric trajectory and time through parameter speed" in trajectory optimization.

[0046] S500 : Determine 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.

[0047] Furthermore, step S500 includes the following steps: S510, according to and , determine P(u i ) target maximum feasible parameter speed mv max，i =MIN( ); where MIN() is the preset minimum value function.

[0048] This step ensures that the parameter velocity of each trajectory point satisfies both the forward and reverse constraints, completely eliminating infeasible solutions that may arise from single-direction optimization and ensuring the global feasibility of the trajectory. By balancing speed and safety within the constraints through a "minimum" strategy, a reliable parameter velocity foundation is provided for the generation of the final optimal trajectory.

[0049] S600 , based on the target maximum feasible parameter speed 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.

[0050] Based on the target maximum feasible parametric velocity of all trajectory points, a continuous parametric velocity profile is constructed in the time domain through cubic interpolation. The profile is integrated to obtain the trajectory u(t) of the parameter changes over time. Substituting u(t) into the cubic B-spline curve P(u), the mapping relationship between spatial position and time P(u(t)) is obtained, which is the optimal trajectory.

[0051] Through this step, the discrete target maximum feasible parameter velocity is converted 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 instructions for subsequent direct feedforward control, ultimately improving the efficiency (shortening time) and accuracy (reducing shape errors) of microlens array processing.

[0052] 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 tool path points based on microlens array turning, such as a cubic B-spline curve). P appearing in subsequent steps (such as S200 and S600) all refer to this function and are not different functions. The same notation is used because the spatial geometric characteristics of the trajectory (such as the positional relationship between the X-axis, Z-axis, and C-axis) are determined from beginning to end by the initially constructed P(u). Subsequent optimization changes only the mapping relationship between the parameter u and time t, not the geometry of the trajectory itself. This unified notation conforms to mathematical conventions, meaning that the function itself remains unchanged, and only the physical meaning of the parameters evolves with the scenario (from purely geometric parameters to parameters associated with time).

[0053] Differences in the representation of parameter u: The distinction between discrete and continuous i is the discretized curve parameter: u in S200 i It is the specific value obtained by discretizing the continuous parameter domain [0,1], corresponding to the discrete point P(u i ), used for numerical calculations and iterative optimization (such as forward / reverse velocity planning).

[0054] u(t) is a continuous parameter-time function: In S600, u(t) is the continuous change relationship of parameter u with time t (e.g. u(t)=0.05t 2 ), used to describe "at time t, the parameter value of the trajectory curve is u(t)", which is essentially the discrete u i Through interpolation and integration, it is expanded into a continuous time domain function. Both are curve parameters. The different expressions are to distinguish the "parameter value of discrete points" (u i ) and “the continuous evolution of the parameter over time” (u(t)) are different representations of the same parameter in discrete analysis and continuous modeling scenarios, not two different parameters.

[0055] 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, The following relationship is satisfied: .

[0056] 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).

[0057] 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.

[0058] 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 considered to lay the foundation for subsequent conservative verification.

[0059] S340, according to 、 and , determine P(u i ) corresponds to the final parameter speed limit value .

[0060] 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.

[0061] 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.

[0062] S350, if > , then Updated to Otherwise, keep constant.

[0063] 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.

[0064] 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.

[0065] 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.

[0066] 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.

[0067] For example, the calculation for the X-axis is as follows: ; in, is the X-axis at trajectory point u i The parameter speed limit value at is used to constrain the X-axis kinematic acceleration and is the core parameter for subsequent generation of the optimal trajectory; is the trajectory curve at u i The first-order derivative of the X-axis with respect to the parameter u describes the rate of change of the X-axis direction with the parameter u, reflecting the "tangent slope" of the trajectory on the X-axis (in the cubic B-spline curve, it is calculated by the first-order derivative of the basis function and the coordinates of the control point); is the trajectory curve at u iThe first-order derivative of the Y axis with respect to the parameter u describes the rate of change of the Y axis direction with the parameter u (because the formula focuses on the X axis constraint, the Y axis derivative is used to calculate the trajectory curvature related terms); is the trajectory curve at u i The second-order derivative of the parameter u with respect to the X-axis reflects the "curvature trend" of the change in the X-axis direction, and is combined with the first-order derivative to calculate the trajectory curvature; is the trajectory curve at u i The second derivative of the Y axis with respect to the parameter u is calculated. Similarly, the curvature related terms are calculated in combination with the first derivative of the Y axis. The maximum allowable acceleration of the machine tool's X-axis. The physical constraints of the machine tool's actuators directly determine the maximum dynamic load that the X-axis can withstand.

[0068] The calculation method for the Z-axis and C-axis is the same as that for the X-axis and is not described here in detail.

[0069] Take the minimum value of the calculated parameter speed limit values ​​corresponding to each axis to obtain the preliminary parameter speed limit of the point.

[0070] To deal with the discretization error, the adjacent points P(u i-1 )、P(u i+1 ) parameter speed limit, take the minimum value of the three as P(u i )’s final parameter speed limit.

[0071] This step has at least the following beneficial effects: Ensure multi-axis collaboration safety: By calculating the minimum value for each axis, the actual acceleration of the X-axis, Y-axis, and C-axis does not exceed their respective maximum limits, avoiding vibration, drive overload, or reduced machining accuracy caused by excessive acceleration of a single axis.

[0072] Dealing with discretization errors: Incorporating constraints from adjacent points and adopting a conservative strategy to avoid missing local constraints due to the discretization of the parameter domain, ensuring that all kinematic constraints are still satisfied at the intersection of trajectory segments.

[0073] Improve optimization efficiency: By setting a strict upper limit on parameter speed in advance, you can directly cut off speed values ​​that may exceed the limit during forward / reverse optimization, eliminating the large number of trial-and-error iterations in traditional algorithms (for example, reducing it from over 10,000 times to 0 times), and significantly reducing optimization execution time.

[0074] 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 reverse iterations under preset kinematic constraints. This can fully exploit the dynamic performance of each axis, make the trajectory running time closer to the theoretical minimum value, and improve the processing efficiency of microlens array turning. By determining the maximum feasible parameter speed in the forward and reverse directions respectively 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. This makes it more suitable for actual industrial application scenarios of ultra-precision turning of microlens arrays.

[0075] Example 2: The following will refer to Figure 1 The flowchart of the micro-lens array turning servo control method shown in FIG. 1 introduces a micro-lens array turning servo control method.

[0076] Q100, discretizes the continuous trajectory curve corresponding to the microlens array turning process into multiple trajectory points in the parameter domain.

[0077] Based on the design surface profile and tool path of the microlens array, a continuous trajectory curve P(u)=[x(u),z(u),c(u)] is first constructed by cubic B-spline interpolation, where u is the curve parameter, 0≤u≤1; then the continuous trajectory curve P(u)=[x(u),z(u),c(u)] is constructed by cubic B-spline interpolation, where u is the curve parameter, 0≤u≤1; and ... -4 ) is uniformly discretized, and the trajectory point list 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, press Δu=10 -4 Discretization can obtain 10001 trajectory points, covering the entire curve.

[0078] Converting continuous curves into discrete points that can be numerically calculated provides a basis for subsequent parameter and speed optimization. By properly selecting the discrete resolution, it is possible to ensure that trajectory details are fully captured while avoiding the surge in calculations caused by too many discrete points, thus balancing optimization accuracy and efficiency.

[0079] Q200, based on the target maximum feasible parametric velocity corresponding to each trajectory point, a continuous parametric velocity profile is constructed by applying cubic interpolation in the time domain.

[0080] Furthermore, the target maximum feasible parameter speed corresponding to each trajectory point can be obtained by the following steps: Q210, obtain the trajectory point list P = (P (u1), P (u2), ..., P (u) corresponding to the continuous trajectory curve P (u) i ),…,P(u n)), i=1, 2, ..., n; u is the curve parameter; 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).

[0081] In this embodiment, step Q210 is the same as step S200 in the first embodiment and is not described again here.

[0082] Q220, with the goal of minimizing the trajectory running time, under the preset kinematic constraints, determines the forward maximum feasible parameter velocity of each trajectory point in sequence starting from P(u1).

[0083] Furthermore, step Q220 includes the following steps: Q221, obtain the maximum operating speed v of the machine tool actuator max Maximum acceleration a max .

[0084] Q222, 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; 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 .

[0085] In this embodiment, steps Q221-Q222 are the same as steps S310-S320 in the first embodiment and are not described in detail here.

[0086] Q230, based on the maximum feasible parameter velocity of each trajectory point, from P (u n ) and determine the reverse maximum feasible parameter velocity of each trajectory point in turn.

[0087] Furthermore, step Q230 includes the following steps: Q231, 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 / dt; is P(u) at u i-1 Reverse curve parameter acceleration at P(u i-1 ) is the i-1th trajectory point corresponding to P(u); u i-1 is the curve parameter of the i-1th trajectory point corresponding to P(u).

[0088] In this embodiment, step Q231 is the same as step S410 in the first embodiment and is not described again here.

[0089] Q240, 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.

[0090] In this embodiment, the target maximum feasible parameter speed obtained by Q240 may not be able to be executed by the machine tool. Based on this, the target maximum feasible parameter speed obtained by Q240 is used as the initial maximum feasible parameter speed. The following method is provided to obtain the target maximum feasible parameter speed: Q250, get 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: .

[0091] In this embodiment, the parameter speed limit value is based on the curvature of the trajectory curve and the maximum acceleration of the system a max Calculation. Formula In the example, R is the trajectory at u i The radius of curvature at (R=1 / k, k is the curvature), For the curve at u i The first derivative at (describing the tangent direction).

[0092] 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.

[0093] 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 considered to lay the foundation for subsequent conservative verification.

[0094] Q260, according to 、 and , determine P(u i ) corresponds to the final parameter speed limit value .

[0095] 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.

[0096] 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.

[0097] Q270, if mv max，i > , then Determined as P(u i ) corresponds to the target maximum feasible parameter speed; otherwise, mv max，i Determined as P(u i ) corresponds to the target maximum feasible parameter speed.

[0098] By pre-limiting parameter speeds, infeasible solutions are avoided during forward and reverse optimization. By limiting the target speed that exceeds the upper limit, trial-and-error adjustments in subsequent iterations are completely eliminated, significantly reducing the number of iterations of the traditional bidirectional scanning algorithm (for example, from over 10,000 to 0), greatly improving optimization execution efficiency while ensuring that the target speed strictly meets all constraints.

[0099] Furthermore, the maximum acceleration of the machine tool actuator 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 It is the minimum value among the maximum accelerations of each axis.

[0100] 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.

[0101] For example, the calculation for the X-axis is as follows: ; in, is the X-axis at trajectory point u i The parameter speed limit value at is used to constrain the X-axis kinematic acceleration and is the core parameter for subsequent generation of the optimal trajectory; is the trajectory curve at u i The first-order derivative of the X-axis with respect to the parameter u describes the rate of change of the X-axis direction with the parameter u, reflecting the "tangent slope" of the trajectory on the X-axis (in the cubic B-spline curve, it is calculated by the first-order derivative of the basis function and the coordinates of the control point); is the trajectory curve at u i The first-order derivative of the Y axis with respect to the parameter u describes the rate of change of the Y axis direction with the parameter u (because the formula focuses on the X axis constraint, the Y axis derivative is used to calculate the trajectory curvature related terms); is the trajectory curve at u i The second-order derivative of the parameter u with respect to the X-axis reflects the "curvature trend" of the change in the X-axis direction, and is combined with the first-order derivative to calculate the trajectory curvature; is the trajectory curve at u i The second derivative of the Y axis with respect to the parameter u is calculated. Similarly, the curvature related terms are calculated in combination with the first derivative of the Y axis. The maximum allowable acceleration of the machine tool's X-axis. The physical constraints of the machine tool's actuators directly determine the maximum dynamic load that the X-axis can withstand.

[0102] The calculation method of the Z-axis and the C-axis is the same as that of the X-axis and is not repeated here.

[0103] Take the minimum value of the calculated parameter speed limit values ​​corresponding to each axis to obtain the preliminary parameter speed limit of the point.

[0104] To deal with the discretization error, the adjacent points P(ui-1 )、P(u i+1 ) parameter speed limit, take the minimum value of the three as P(u i )’s final parameter speed limit.

[0105] This step has at least the following beneficial effects: Ensure multi-axis collaboration safety: By calculating the minimum value for each axis, the actual acceleration of the X-axis, Y-axis, and C-axis does not exceed their respective maximum limits, avoiding vibration, drive overload, or reduced machining accuracy caused by excessive acceleration of a single axis.

[0106] Dealing with discretization errors: Incorporating constraints from adjacent points and adopting a conservative strategy to avoid missing local constraints due to the discretization of the parameter domain, ensuring that all kinematic constraints are still satisfied at the intersection of trajectory segments.

[0107] Improve optimization efficiency: By setting a strict upper limit on parameter speed in advance, you can directly cut off speed values ​​that may exceed the limit during forward / reverse optimization, eliminating the large number of trial-and-error iterations in traditional algorithms (for example, reducing it from over 10,000 times to 0 times), and significantly reducing optimization execution time.

[0108] 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 reverse iterations under preset kinematic constraints. This can fully exploit the dynamic performance of each axis, make the trajectory running time closer to the theoretical minimum value, and improve the processing efficiency of microlens array turning. By determining the maximum feasible parameter speed in the forward and reverse directions respectively 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. This makes it more suitable for actual industrial application scenarios of ultra-precision turning of microlens arrays.

[0109] Q300, integrating the parameter velocity profile to obtain a parameter trajectory u(t); wherein t is a time point.

[0110] In this embodiment, the continuous parameter velocity profile constructed by Q200 is time-integrated to obtain the trajectory of the parameter u changing with time t.

[0111] By integrating the parameters u and time t, a direct relationship is established, and the velocity information is converted into the time evolution law of the position information, providing the core basis for the subsequent generation of the time characteristics of the spatial trajectory.

[0112] 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.

[0113] 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.

[0114] 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.

[0115] Q500, differentiate P(u(t)) to obtain the desired velocity and desired acceleration of the X-axis, Z-axis, and C-axis of the machine tool actuator.

[0116] 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.

[0117] 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 .

[0118] 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.

[0119] 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 z and the desired speed v of the C axis c ;in, ; ; ; 、 and These are the first-order derivatives of the position function of the X-axis, Z-axis, and C-axis with respect to the parameter u.

[0120] Derivative the optimal trajectory P(u(t))=[x(u(t)),z(u(t)),c(u(t))], combined with the parameter speed Get the expected speed of each axis.

[0121] For the X-axis, the position function is x(u(t)). According to the derivative rule of composite function, its derivative with respect to time is ,in, is the first-order derivative of the X-axis position function with respect to the parameter u (derived from the cubic B-spline basis function, such as , is the first-order derivative of the 4th-order B-spline basis function); the solutions for the Z-axis and C-axis are the same as those for the X-axis.

[0122] Directly calculating the desired speed through analytical derivation avoids the phase lag and noise introduced by traditional methods that obtain speed through numerical differentiation (such as the difference between adjacent positions divided by the time interval). This improves the accuracy of the speed signal and provides more precise feedforward input for servo control.

[0123] Q520, take the derivative of P(u(t)) and combine it with the acceleration parameter =d 2 u / dt 2 , get the expected acceleration a of the X axis of the machine tool actuator x , the expected acceleration of the Z axis a z and the desired acceleration a of the C axis c ;in, ; ; ; 、 and These are the second-order derivatives of the position function of the X-axis, Z-axis, and C-axis with respect to the parameter u.

[0124] Derivative the desired velocity of each axis again, combined with the parameter acceleration Get the expected acceleration.

[0125] The X-axis acceleration is the time derivative of velocity: ;in, is the second-order derivative of the X-axis position function with respect to u (calculated by the second-order derivative of the cubic B-spline basis function, such as ); The solution of Z axis and C axis is the same as that of X axis.

[0126] Acceleration is obtained through second-order analytical derivation, avoiding the problem of numerical second-order differential amplification noise and ensuring the smoothness of the acceleration signal. At the same time, the curvature characteristics of the curve are directly associated with the parameter velocity / acceleration, so that the acceleration feedforward can accurately compensate for the dynamic requirements brought by the trajectory curvature, further improving the servo tracking accuracy.

[0127] Q600 uses the desired velocity and desired acceleration as feedforward inputs and substitutes them into the output calculation formula of the servo controller to obtain the servo output to drive the X-axis, Z-axis and C-axis motion.

[0128] Furthermore, the output calculation formula of the servo controller is: ; Among them, u ctrl K is the output of the servo controller, which is used to drive the actuators of the X-axis, Z-axis and C-axis of the machine tool; P is the proportionality coefficient, K v is the speed feedforward coefficient, K a is the acceleration feedforward coefficient; v(t) is the expected velocity at t, a(t) is the expected acceleration at t, and e(t) is the tracking error between the actual position and the expected position at t.

[0129] The desired velocity v(t) and desired acceleration a(t) obtained by Q500 are used as feedforward terms and substituted into the output formula of the servo controller: ; Among them, u ctrl K is the output of the servo controller, which is used to drive the actuators of the X-axis, Z-axis and C-axis of the machine tool; P is the proportionality coefficient, K v is the speed feedforward coefficient, K a is the acceleration feedforward coefficient; e(t) is the tracking error between the actual position and the expected position at t, for example, when the expected speed of the X axis is v x =0.1t, acceleration a x =0.1, the feedforward term drives the motor response in advance, reducing the error caused by system lag.

[0130] Feedforward input enables the controller to "foresee" changes in trajectory velocity and acceleration, adjust the output in advance to compensate for the system's dynamic lag, and significantly reduce tracking error (for example, Z-axis tracking error is reduced by 30%). At the same time, combined with the high efficiency of the optimized trajectory, it can achieve a simultaneous improvement in the processing accuracy (reduced shape error) and efficiency (shortened processing time) of the microlens array.

[0131] In this embodiment, by discretizing the continuous trajectory and combining it with cubic interpolation to construct a parametric velocity profile, the number of trajectory optimization iterations is greatly reduced, thereby 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. The optimal trajectory is directly differentiated to obtain the desired velocity and acceleration, thereby avoiding the lag and error caused by traditional numerical differentiation and improving the tracking accuracy of the servo control. The desired velocity and acceleration are used as feedforward inputs to drive the axis motion, thereby achieving efficient coordination between trajectory planning and servo control. Ultimately, the processing efficiency is improved while ensuring the shape accuracy of the microlens array (such as reducing the shape error), effectively solving the problem of finding a balance between accuracy and efficiency in the prior art.

[0132] Furthermore, although the steps of the method of 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 steps shown must be performed to achieve the desired results. Additionally or alternatively, some steps may be omitted, multiple steps may be combined into one step, and / or one step may be decomposed into multiple steps.

[0133] An embodiment of the present invention also provides a non-transitory computer-readable storage medium, which can be set in an electronic device to store at least one instruction or at least one program related to implementing a method in a method embodiment. 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 embodiment.

[0134] The program product may utilize any combination of one or more readable media. The readable medium may be a readable signal medium or a readable storage medium. The readable storage medium may be, for example, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, device, or component, or any combination thereof. More specific examples (a 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 thereof.

[0135] A computer-readable signal medium may include a data signal propagated in baseband or as part of a carrier wave, which carries readable program code. Such propagated data signals may take a variety of 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 that can transmit, propagate, or transfer a program for use by or in conjunction with an instruction execution system, apparatus, or device.

[0136] The program code embodied on the readable medium may be transmitted using any appropriate medium, including but not limited to wireless, wireline, optical fiber cable, RF, etc., or any suitable combination of the foregoing.

[0137] The program code for performing the operations of the present application can be written in any combination of one or more programming languages, including object-oriented programming languages ​​such as Java, C++, etc., and conventional procedural programming languages ​​such as "C" or similar programming languages. The program code can be executed entirely on the user computing device, partially on the user device, as a separate software package, partially on the user computing device and partially on a remote computing device, or entirely on a remote computing device or server. In the case of a remote computing device, the remote computing device can be connected to the user computing device through any type of network, including a local area network (LAN) or a wide area network (WAN), or can be connected to an external computing device (e.g., via the Internet using an Internet service provider).

[0138] An embodiment of the present invention further provides an electronic device including a processor and the aforementioned non-transitory computer-readable storage medium.

[0139] The electronic device is merely an example and should not limit the functions and scope of use of the embodiments of the present application.

[0140] The electronic device is implemented as a general-purpose computing device. Components of the electronic device may include, but are not limited to, the aforementioned at least one processor, the aforementioned at least one memory, and a bus connecting different system components (including the memory and the processor).

[0141] The memory stores program codes, which can be executed by the processor, so that the processor performs the steps of various embodiments described in this specification.

[0142] 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).

[0143] The memory may also include a program / utility having a set (at least one) of program modules, such program modules including but not limited to: an operating system, one or more application programs, other program modules, and program data, each of which or some combination may include an implementation of a network environment.

[0144] The bus may represent one or more of several types of bus structures, including a memory bus or memory controller, a peripheral bus, an accelerated graphics port, a processor, or a local bus using any of a variety of bus architectures.

[0145] The electronic device may also communicate with one or more external devices (e.g., keyboards, pointing devices, Bluetooth devices, etc.), one or more devices that enable a user to interact 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.). Such communication may be performed via an input / output (I / O) interface. Furthermore, the electronic device may also 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 a network adapter. 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 may 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.

[0146] Through the description of the above embodiments, it is easy for those skilled in the art to understand that the example embodiments described herein can be implemented by software or by combining software with necessary hardware. Therefore, the technical solution according to the embodiments of the present disclosure can be embodied in the form of a software product, which can be stored in a non-volatile storage medium (which can be a CD-ROM, a USB flash drive, a mobile hard disk, etc.) or on a network, and includes several instructions to enable a computing device (which can be a personal computer, a server, a terminal device, or a network device, etc.) to execute the method according to the embodiments of the present disclosure.

[0147] An embodiment of the present invention further provides a computer program product comprising program code. When the program product is run on an electronic device, the program code is used to enable the electronic device to execute the steps of the method according to various exemplary embodiments of the present invention described above in this specification.

[0148] Although some specific embodiments of the present invention have been described in detail by way of examples, it should be understood by those skilled in the art that the above examples are for illustration only and are not intended to limit the scope of the present invention. It should also be understood by those skilled in the art that various modifications may be made to the embodiments without departing from the scope and spirit of the present invention.

Claims

1. A microlens array turning servo control method, characterized in that: The method comprises the following steps: Q100, discretizes the continuous trajectory curve corresponding to the microlens array turning process into multiple trajectory points in the parameter domain; Q200, based on the target maximum feasible parametric velocity corresponding to each trajectory point, a continuous parametric velocity profile is constructed by applying cubic interpolation in the time domain; Q300, integrating the parameter velocity profile to obtain a parameter trajectory u(t); wherein t is a time point; 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; Q500, derive P(u(t)) to obtain the desired speed and acceleration of the X-axis, Z-axis, and C-axis of the machine tool actuator; Q600 uses the desired velocity and desired acceleration as feedforward inputs and substitutes them into the output calculation formula of the servo controller to obtain the servo output to drive the X-axis, Z-axis and C-axis motion.

2. The microlens array turning servo control method according to claim 1, characterized in that: Step Q500 includes 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 desired speed v of the Z axis z and the desired speed v of the C axis c ;in, ; ; ; 、 and The first-order derivatives of the position functions of the X-axis, Z-axis, and C-axis with respect to the parameter u; Q520, take the derivative of P(u(t)) and combine it with the acceleration parameter =d 2 u / dt 2 , get the expected acceleration a of the X axis of the machine tool actuator x , the expected acceleration of the Z axis a z and the desired acceleration a of the C axis c ;in, ; ; ; 、 and These are the second-order derivatives of the position function of the X-axis, Z-axis, and C-axis with respect to the parameter u.

3. The microlens array turning servo control method according to claim 1, characterized in that: The output calculation formula of the servo controller is: ; Among them, u ctrl K is the output of the servo controller, which is used to drive the actuators of the X-axis, Z-axis and C-axis of the machine tool; P is the proportionality coefficient, K v is the speed feedforward coefficient, K a is the acceleration feedforward coefficient; v(t) is the expected velocity at t, a(t) is the expected acceleration at t, and e(t) is the tracking error between the actual position and the expected position at t.

4. The microlens array turning servo control method according to claim 1, wherein: The target maximum feasible parameter speed corresponding to each trajectory point is obtained by the following steps: Q210, obtain the trajectory point list P = (P (u1), P (u2), ..., P (u) corresponding to the continuous trajectory curve P (u) i ),…,P(u n ))、i=1,2,…,n; 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]; 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); Q220, with the goal of minimizing the trajectory running time, under the preset kinematic constraints, determines the maximum feasible parameter velocity of each trajectory point in turn starting from P(u1); Q230, based on the maximum feasible parameter velocity of each trajectory point, from P (u n ) starts, and determines the reverse maximum feasible parameter velocity of each trajectory point in turn; Q240, 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.

5. The microlens array turning servo control method according to claim 4, characterized in that: Step Q220 includes the following steps: Q221, obtain the maximum operating speed v of the machine tool actuator max and the maximum acceleration a max ; Q222, 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; 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 .

6. The microlens array turning servo control method according to claim 5, characterized in that: Step Q230 includes the following steps: Q231, 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 / dt; is P(u) at u i-1 Reverse curve parameter acceleration at P(u i-1 ) is the i-1th trajectory point corresponding to P(u); u i-1 is the curve parameter of the i-1th trajectory point corresponding to P(u).

7. The microlens array turning servo control method according to claim 4, characterized in that: 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 servo control 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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