Image Recognition-Based Method for Compensating for Printing Press Registration Deviation

By using image recognition technology to calculate the registration deviation of the printing press, dynamically updating the center point parameters and motor speed integral, and generating a smooth compensation trajectory, the mechanical vibration problem caused by registration deviation in multi-color printing presses is solved, and stable high-speed operation of the printing press is achieved.

CN122492815APending Publication Date: 2026-07-31SHENZHEN HUAN CHENG XIN PRECISION MFG CO LTD
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Patent Information

Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
SHENZHEN HUAN CHENG XIN PRECISION MFG CO LTD
Filing Date
2026-05-06
Publication Date
2026-07-31

AI Technical Summary

Technical Problem

In the existing multicolor printing process, mechanical vibration and material tension fluctuations cause registration deviations, resulting in frequent sudden starts and stops of the printing press. This makes it impossible to achieve stable registration at high speeds, increasing material loss and scrap rate.

Method used

The pixel intensity along the normal direction of the color mark edge is calculated using image recognition technology, a one-dimensional grayscale sequence is extracted, the center point parameters are dynamically updated, the physical geometric distance is obtained by combining standard reference coordinates, the motor speed and acceleration integral are calculated, a smooth compensation trajectory is generated, the control point parameters are solved by solving a system of simultaneous equations, a polynomial compensation trajectory is constructed, and recognition errors and delay misalignment are eliminated.

Benefits of technology

It enables long-term stable operation of the printing press in complex vibration environments, reduces rigid mechanical impact caused by speed changes in the actuator, and ensures the stability and precision of multi-color overprinting processes.

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Abstract

This invention relates to the field of visual inspection technology, specifically to a method for compensating registration deviation in printing presses based on image recognition. The method includes the following steps: calculating the pixel intensity in the normal direction of the color mark and outputting a grayscale sequence; calculating the sum of squared residuals and partial derivatives to update the center parameters and obtain the optimal vector; extracting the vector and the reference coordinates to calculate the geometric distance and outputting the registration deviation value; converting the remaining integral area into an equivalent compensation angular displacement based on the rotational speed record; solving equations with the angular displacement as a constraint to generate a smooth compensation trajectory and outputting the overall rotational speed sequence. In this invention, the registration deviation is determined by analyzing the pixel intensity in the normal direction of the image and updating the optimal vector with the residual partial derivatives; the remaining integral area of ​​the motor is converted into an equivalent compensation angular displacement; a polynomial smooth compensation trajectory is constructed by solving simultaneous equations; the recognition error and hysteresis of the photoelectric sensor under vibration conditions are eliminated; and the smooth rotational speed sequence reduces the rigid impact caused by motor speed changes, thus optimizing the stability of the printing press operation.
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Description

Technical Field

[0001] This invention relates to the field of visual inspection technology, and in particular to a method for compensating for registration deviation in printing presses based on image recognition. Background Technology

[0002] The field of visual inspection technology encompasses the hardware combination of photoelectric conversion equipment, lenses, light sources and sensors, as well as feature extraction logic. It acquires the appearance contour, position coordinates and surface texture attributes of target objects through non-contact methods. Then, the captured object light and shadow information is converted into electrical signals and input into the processing unit for feature analysis and measurement. This technology is widely used in industrial manufacturing industries such as semiconductor manufacturing, automotive parts assembly, pharmaceutical packaging and automated production lines.

[0003] The traditional printing press registration deviation compensation method refers to the physical spatial position correction control operation for misalignment of ink images caused by mechanical vibration, substrate deformation, or fluctuations in feed tension during multi-color printing. This operation typically involves installing single-point photoelectric color mark sensors between each printing unit to capture changes in the light reflection intensity of the color mark at the edge of the substrate to generate a trigger electrical signal. This trigger electrical signal is then logically compared with the phase of the reference pulse output by the rotary encoder of the main drive shaft to calculate the feed phase difference. Finally, the logic controller outputs control pulses of the corresponding frequency to the motor drive module based on this phase difference, thereby driving the paper feed compensation roller or printing plate cylinder to slide axially and rotate circumferentially.

[0004] Existing technologies for misalignment compensation in multi-color printing rely on single-point photoelectric color mark sensors to capture changes in light intensity, generate trigger electrical signals, and compare them with encoder reference pulses to calculate phase differences, thereby driving the motor to perform actions. When faced with complex working conditions, these technologies are susceptible to multiple interferences from mechanical vibrations. Simple phase difference comparisons have response lag defects, leading to frequent sudden starts and stops of the actuator and generating huge mechanical impacts. Smooth motion trajectory planning cannot be achieved, making it difficult to maintain stable registration accuracy under high-speed operation, increasing material loss and scrap rates during the processing stage. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of the existing technology and propose a printing press registration deviation compensation method based on image recognition.

[0006] To achieve the above objectives, the present invention adopts the following technical solution: a printing press registration deviation compensation method based on image recognition, comprising the following steps: S1: Calculate the pixel intensity in the direction of the normal of the aligned color mark edge in the original image, filter the effective pixel points and adjust the spatial arrangement order, and combine the intensity values ​​to output a one-dimensional grayscale sequence of the color mark. S2: Based on the one-dimensional grayscale sequence of the color mark, extract the background noise variance to calculate the position optimization convergence threshold, calculate the residual sum of squares between the one-dimensional grayscale sequence of the color mark and the approximation curve, and the partial derivative of the residual sum of squares with respect to the center point position parameter. Update the center point position parameter according to the partial derivative until the residual is within the convergence range, and output the optimal position parameter vector. S3: Extract the center point coordinates of the optimal position parameter vector, calculate the relative geometric distance between the center point coordinates and the standard reference coordinates, determine the position offset component, adjust the position offset component, filter the magnitude data in the correction interval, and output the spatial registration deviation value. S4: Extract the instantaneous speed and instantaneous acceleration from the motor speed execution record, convert the unexecuted remaining integral area into an equivalent compensation angular displacement, and superimpose it with the theoretical deviation phase associated with the spatial alignment deviation value to output the total target compensation angular displacement. S5: Obtain boundary control points based on instantaneous rotational speed and instantaneous acceleration, solve the intermediate control point parameters by solving a system of equations with the total target compensation angular displacement as the constraint, calculate the sum of the products of polynomial basis functions and control point coordinates to generate a single-segment smooth compensation trajectory, combine the endpoint timestamps to merge coordinate data, and output the overall compensation rotational speed sequence.

[0007] As a further aspect of the present invention, the process of obtaining the one-dimensional grayscale sequence of the color mark is specifically as follows: S101: Collect the original image of the printing material captured by the industrial area array camera during the multi-color overprinting process of the printing press. Extract the edge normal direction for the alignment color mark inside the original image. Perform point-by-point grayscale extraction operation along the edge normal direction. Calculate the pixel intensity data of each coordinate node in the edge normal direction. Merge the pixel intensity data corresponding to multiple coordinate nodes in the edge normal direction to establish a normal intensity distribution sequence. S102: Obtain the preset sampling interval in the set parameter record, perform a step span value comparison operation on the pixel coordinates contained in the normal intensity distribution sequence and the preset sampling interval, remove discrete coordinate points that do not meet the span value, retain data items that meet the sampling interval conditions, and generate a set of valid pixel points. S103: Extract the spatial position coordinates contained within the effective pixel point set, perform a uniaxial position projection operation on the spatial position coordinates to adjust the spatial arrangement order, generate rearranged position coordinates, and stitch together the previously acquired pixel intensity data one by one according to the order corresponding to the rearranged position coordinates to obtain a one-dimensional grayscale sequence of color marks.

[0008] As a further aspect of the present invention, the process of obtaining the optimal position parameter vector is specifically as follows: S201: Extract the grayscale contrast and background noise variance contained in the one-dimensional grayscale sequence of the color mark, read the number of effective pixels in the parameter configuration, perform a numerical multiplication operation on the background noise variance and the number of effective pixels to obtain the product value, set the calculation boundary based on the product value, and generate the position optimization convergence threshold. S202: Obtain the approximation curve from the internal data record, perform curve fitting operation on the one-dimensional grayscale sequence of the color mark and the approximation curve, calculate the residual sum of squares between the one-dimensional grayscale sequence of the color mark and the approximation curve, perform differential operation on the residual sum of squares relative to the center point position parameter to extract the partial derivative, adjust the center point position parameter of the approximation curve based on the value of the partial derivative, and obtain the updated center point position parameter. S203: Call the residual sum of squares associated with the updated center point position parameters, perform a numerical difference comparison operation between the residual sum of squares and the position optimization convergence threshold, and when it is determined that the residual sum of squares after parameter adjustment is within the convergence value range, extract and merge multiple updated center point position parameters of the current update state to construct a data vector structure and generate the optimal position parameter vector.

[0009] As a further aspect of the present invention, the process of performing a numerical multiplication operation on the background noise variance and the number of effective pixels to obtain a product value, and setting a calculation boundary based on the product value, specifically involves: A numerical multiplication operation is performed on the background noise variance and the number of effective pixels to obtain the product value. The base noise data recorded during the historical no-load operation phase is retrieved. A safety tolerance coefficient is calculated based on the fluctuation extreme value range corresponding to the base noise data. An algebraic multiplication operation is performed on the product value and the safety tolerance coefficient to obtain a reference value. The reference value is set as the calculation boundary.

[0010] 5. The printing press registration deviation compensation method based on image recognition according to claim 3, characterized in that the process of numerically adjusting the center point position parameter of the approximation curve based on partial derivatives specifically comprises: Extract the negative gradient direction corresponding to the partial derivative, obtain the initial learning rate and the current optimization iteration cycle under the current operating environment, perform a decreasing decay operation on the initial learning rate based on the current optimization iteration cycle to generate an iteration step size value, perform vector multiplication operation on the negative gradient direction and the iteration step size value to calculate the position offset component, extract the current center point position parameter of the approximation curve, perform coordinate accumulation operation on the current center point position parameter and the position offset component to generate updated center point position parameters.

[0011] As a further aspect of the present invention, the process of obtaining the spatial alignment deviation value is specifically as follows: S301: Decompose the numerical structure contained in the optimal position parameter vector into vector dimensions, extract the pixel center point coordinates corresponding to the numerical structure in the two-dimensional space dimension, read the reference comparison information in the plate registration calibration record, extract the standard reference coordinates corresponding to the pixel center point coordinates, and simultaneously read the interval configuration parameters in the hardware limit record to obtain the position correction interval data. S302: Call the pixel center point coordinates and the standard reference coordinates, perform subtraction difference operation on the coordinate distribution characteristics of the pixel center point coordinates and the standard reference coordinates on the corresponding dimension axis, calculate the spatial displacement vector between the two, output the relative geometric distance and perform vector coordinate system projection decomposition, determine the direction difference attribute of the relative geometric distance on the physical coordinate axis, extract the distance parameters corresponding to the multi-dimensional coordinate axis, and establish the position offset component. S303: Perform a scaling conversion operation on the direction identifier and data magnitude attached to the position offset component to generate reconstructed offset magnitude data. Perform a numerical comparison operation between the value of the reconstructed offset magnitude data and the boundary range defined by the position correction interval data. Remove out-of-bounds deviation records that exceed the limit constraints, and filter the magnitude data within the position correction interval to obtain the spatial registration deviation value.

[0012] As a further aspect of the present invention, the process of performing a scaling conversion operation on the direction identifier and data magnitude of the position offset component to generate reconstructed offset magnitude data specifically involves: The physical field of view size parameters and resolution parameters are extracted by calling the optical imaging calibration record. The physical field of view size parameters and resolution parameters are converted by numerical division to calculate the physical length reference value. The physical length reference value is set as the pixel equivalent conversion coefficient. Extract the data magnitude associated with the position offset component, and perform algebraic multiplication numerical operation on the data magnitude and the pixel equivalent conversion coefficient to obtain the absolute displacement value; Extract the direction identifier attached to the position offset component, identify the positive and negative polarity features corresponding to the direction identifier in the two-dimensional rectangular coordinate system, and assign positive and negative signs to the absolute displacement value in combination with the positive and negative polarity features to generate the reconstructed offset magnitude data.

[0013] As a further aspect of the present invention, the process of obtaining the total target compensation angular displacement is specifically as follows: S401: Obtain the circumferential speed execution record of the printing plate cylinder servo motor, match the time nodes contained in the circumferential speed execution record, extract the instantaneous speed and instantaneous acceleration of the circumferential speed execution record at the set time node, perform the integral operation of the speed over time for the unexecuted time segment in the circumferential speed execution record, calculate the area data accumulated by the speed value in the remaining time dimension, and generate the remaining integrated area. S402: Based on the mapping relationship corresponding to the spatial registration deviation values, extract the theoretical deviation phase associated with the spatial registration deviation values, convert the remaining integral area into the equivalent compensation angular displacement of the angular displacement dimension, combine the extracted theoretical deviation phase and the equivalent compensation angular displacement, and establish a compensation angle calculation set. S403: Extract the compensation angle calculation set, establish a unified angle coordinate system, perform numerical superposition calculation on the equivalent compensation angular displacement and theoretical deviation phase within the unified angle coordinate system, calculate the sum of the superimposed angular displacement values ​​within a set time period to obtain the total compensation angular displacement, merge the integral constraint features within the set time period to construct the corresponding data items, and generate the total target compensation angular displacement.

[0014] As a further aspect of the present invention, the process of obtaining the overall compensated speed sequence is specifically as follows: S501: Based on the total target compensation angular displacement, call and identify the endpoint boundary control points corresponding to the instantaneous rotational speed and instantaneous acceleration, obtain the polynomial basis function, set the total target compensation angular displacement as the displacement constraint condition, combine the endpoint boundary control points and the displacement constraint condition to construct the overall constraint equation system, perform numerical solution calculation on the overall constraint equation system, and obtain the coordinate parameters of the intermediate control point. S502: Call the intermediate control point coordinate parameters, merge the endpoint boundary control points to construct all control point coordinates, perform algebraic multiplication operation on the polynomial basis function and all control point coordinates, calculate the sum of the products after numerical multiplication and map the coordinate nodes under the corresponding time nodes, construct the time speed coordinate sequence that matches the compensation constraint conditions, merge the data of each node in the time speed coordinate sequence to perform curve construction operation, and generate a single-segment smooth compensation trajectory. S503: Extract the start and end time data of the trajectory within the single-segment smooth compensation trajectory, obtain the operation record of the motor equipment, perform a comparison and matching operation on the trajectory start and end time data and the operation record, extract the endpoint timestamps corresponding to the overlapping areas, define the data processing interval based on the endpoint timestamps, extract and merge the coordinate data contained within the endpoint timestamp area, and splice the merged coordinate data in chronological order to generate the overall compensation speed sequence.

[0015] As a further aspect of the present invention, the process of obtaining the polynomial basis functions, setting the total target compensation angular displacement as the displacement constraint condition, and simultaneously establishing the overall constraint equation system by combining the endpoint boundary control points and the displacement constraint condition is as follows: The number of kinematic boundary conditions recorded inside the endpoint boundary control points is counted. The displacement boundary conditions represented by the total target compensation angular displacement are combined to extract the overall constraint dimension value. The highest power order corresponding to the interpolation algorithm is determined based on the overall constraint dimension value. A time algebraic polynomial with a corresponding number of undetermined coefficients is constructed based on the highest power order. The time algebraic polynomial is established as the polynomial basis function. Perform differentiation operations on the polynomial basis functions to generate first-order and second-order derivative expressions; The endpoint boundary control points are analyzed to extract the start time parameters and end time parameters. The start time parameters and end time parameters are substituted into the first derivative expression and the second derivative expression to obtain the derivative calculation results. The derivative calculation results are then used to establish algebraic identities with the instantaneous rotational speed and the instantaneous acceleration to generate the endpoint boundary constraint equations. Substitute the start time parameter and the end time parameter into the polynomial basis function respectively, and subtract the calculation result corresponding to the start time from the calculation result corresponding to the end time to generate the target angular displacement expression. Establish an algebraic identity relationship between the target angular displacement expression and the total target compensation angular displacement to construct the displacement constraint equation. Combine the endpoint boundary constraint equation and the displacement constraint equation to generate the overall constraint equation system.

[0016] Compared with the prior art, the advantages and positive effects of the present invention are as follows: In this invention, a one-dimensional grayscale sequence is output by analyzing the normal pixel intensity of the image aligned with the color mark edge. The sum of squares and partial derivatives of the residuals are calculated and the center point parameters are dynamically updated to obtain the optimal vector. The physical geometric distance is extracted by combining the standard reference coordinates to determine the spatial registration deviation value. The instantaneous running characteristics of the motor are extracted, the remaining integral area is converted into an equivalent compensation angular displacement and the theoretical phase is superimposed. Based on the angular displacement constraint conditions, the simultaneous equations are solved to construct the control point and a polynomial smooth compensation trajectory. This eliminates the recognition error and delay misalignment of the single photoelectric capture mode in complex vibration environments. Furthermore, the smooth speed sequence generated by interpolation effectively reduces the rigid mechanical impact caused by the speed change of the actuator, ensuring the long-term stable operation of the multi-color overprinting process. Attached Figure Description

[0017] Figure 1 This is a schematic diagram of the main steps of the present invention. Detailed Implementation

[0018] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0019] Please see Figure 1 This invention provides a technical solution for a printing press registration deviation compensation method based on image recognition, comprising the following steps: S1: Calculate the pixel intensity in the direction of the normal of the aligned color mark edge in the original image, filter the effective pixel points and adjust the spatial arrangement order, and combine the intensity values ​​to output a one-dimensional grayscale sequence of the color mark. S2: Based on the one-dimensional grayscale sequence of the color mark, extract the background noise variance to calculate the position optimization convergence threshold, calculate the residual sum of squares between the one-dimensional grayscale sequence of the color mark and the approximation curve, and the partial derivative of the residual sum of squares with respect to the center point position parameter. Update the center point position parameter according to the partial derivative until the residual is within the convergence range, and output the optimal position parameter vector. S3: Extract the center point coordinates of the optimal position parameter vector, calculate the relative geometric distance between the center point coordinates and the standard reference coordinates, determine the position offset component, adjust the position offset component, filter the magnitude data in the correction interval, and output the spatial registration deviation value. S4: Extract the instantaneous speed and instantaneous acceleration from the motor speed execution record, convert the unexecuted remaining integral area into an equivalent compensation angular displacement, and superimpose it with the theoretical deviation phase associated with the spatial alignment deviation value to output the total target compensation angular displacement. S5: Obtain boundary control points based on instantaneous rotational speed and instantaneous acceleration, solve the intermediate control point parameters by solving a system of equations with the total target compensation angular displacement as the constraint, calculate the sum of the products of polynomial basis functions and control point coordinates to generate a single-segment smooth compensation trajectory, combine the endpoint timestamps to merge coordinate data, and output the overall compensation rotational speed sequence.

[0020] The specific process for obtaining the one-dimensional grayscale sequence of the color mark is as follows: S101: Collect the original image of the printing material captured by the industrial area array camera during the multi-color overprinting process of the printing press. Extract the edge normal direction for the alignment color mark inside the original image. Perform point-by-point grayscale extraction operation along the edge normal direction. Calculate the pixel intensity data of each coordinate node in the edge normal direction. Merge the pixel intensity data corresponding to multiple coordinate nodes in the edge normal direction to establish a normal intensity distribution sequence. When the printing press performs multi-color overprinting, an industrial area scan camera fixed at the corresponding acquisition position captures images of the substrate surface according to the current acquisition cycle, and writes the obtained raw images into the image processing buffer. Next, the aligned color mark region in the raw image is read, and the edge positions of the color marks are extracted within this region. An edge normal direction perpendicular to the edge tangential direction is established according to the local edge direction. Then, starting from the intersection of the normal and the color mark edge, the grayscale values ​​of each coordinate node in the raw image are read point by point along the edge normal direction. The grayscale value corresponding to each coordinate node is used as the pixel intensity data for that coordinate node. If the same aligned color mark region corresponds to multiple edge normals, the same grayscale reading operation is performed on each edge normal, and the pixel intensity data corresponding to each edge normal are arranged according to the order of the coordinate nodes in the normal direction. Finally, the edge normals are merged according to their spatial correspondence on the color mark edge to form a normal intensity distribution sequence.

[0021] S102: Obtain the preset sampling interval in the set parameter record, perform a step span value comparison operation on the pixel coordinates contained in the normal intensity distribution sequence and the preset sampling interval, remove discrete coordinate points that do not meet the span value, retain data items that meet the sampling interval conditions, and generate a set of valid pixel points. The system reads the preset sampling interval from the set parameter record and extracts the pixel coordinates corresponding to each pixel intensity data from the normal intensity distribution sequence. Then, it performs a difference operation on the projection positions of any two adjacent candidate coordinate points along the edge normal direction to obtain the current coordinate span value. This current coordinate span value is then compared item by item with the preset sampling interval. When the current coordinate span value meets the set step size requirement, the coordinate point and its corresponding pixel intensity data are retained; when the current coordinate span value does not meet the set step size requirement, it is not retained. Finally, all pixel coordinates that meet the sampling interval conditions and their corresponding pixel intensity data are retained to form a set of valid pixel locations.

[0022] S103: Extract the spatial position coordinates contained in the effective pixel point set, perform a single-axis position projection operation on the spatial position coordinates to adjust the spatial arrangement order, generate rearranged position coordinates, and stitch together the previously acquired pixel intensity data one by one according to the order corresponding to the rearranged position coordinates to obtain a one-dimensional grayscale sequence of color marks. The spatial coordinates of each data item within the set of valid pixels are extracted, and a single projection axis is established based on the edge normal direction. Each spatial coordinate is then projected onto this projection axis to obtain the projected position value of each valid pixel along the single axis. Subsequently, all valid pixels are rearranged based on their projected position values. If two valid pixels have different projected position values, they are arranged in ascending order; if two valid pixels have the same projected position value, their original order in the acquisition sequence is maintained. Next, the pixel intensity data previously obtained for each valid pixel is extracted one by one according to the rearranged coordinate order, and these are continuously stitched together in this order to obtain a one-dimensional grayscale sequence of color stops arranged along the single axis.

[0023] The process of obtaining the optimal position parameter vector is as follows: S201: Extract the grayscale contrast and background noise variance contained in the one-dimensional grayscale sequence of the color mark, read the number of effective pixels in the parameter configuration, perform a numerical multiplication operation on the background noise variance and the number of effective pixels to obtain the product value, set the calculation boundary based on the product value, and generate the position optimization convergence threshold. Read the gray values ​​corresponding to each position in the one-dimensional grayscale sequence of color markers, and identify the grayscale variation regions of the color markers and the background grayscale variation regions within the sequence. Then, subtract the minimum grayscale value from the maximum grayscale value in the color marker region to obtain the grayscale contrast. Finally, divide the sum of squared differences between each grayscale value in the background region and the mean grayscale value of the background region by the number of data points in the background region to obtain the background noise variance. Next, the number of effective pixels in the parameter configuration is read, and the background noise variance is multiplied by the number of effective pixels to obtain the product value: Product value = Background noise variance × Number of effective pixels. Then, the base noise data recorded in the historical idle operation phase is read, the maximum and minimum fluctuation values ​​are extracted, the fluctuation extreme value range is calculated, and the safety tolerance coefficient is determined based on the correspondence between the fluctuation extreme value range and the base noise mean. The product value is then multiplied by the safety tolerance coefficient to obtain a reference value: Reference value = Product value × Safety tolerance coefficient. This reference value is then set as the position optimization convergence threshold.

[0024] S202: Obtain the approximation curve from the internal data record, perform curve fitting operation on the one-dimensional grayscale sequence of the color mark and the approximation curve, calculate the residual sum of squares between the one-dimensional grayscale sequence of the color mark and the approximation curve, perform differential operation on the residual sum of squares relative to the center point position parameter to extract the partial derivative, adjust the center point position parameter of the approximation curve based on the value of the partial derivative, and obtain the updated center point position parameter. The approximation curve is read from the internal data record. Each position in the one-dimensional grayscale sequence of the color scale is used as the independent variable, and the grayscale value at the corresponding position is used as the target value. This is then compared sequentially with the output value of the approximation curve under the current center point position parameter to obtain the residual value at each position. The residual value is calculated as: current position grayscale value - approximation curve output value at that position. Finally, the sum of squares is performed on all residual values ​​to obtain the residual sum of squares. Next, the partial derivatives are extracted by taking the derivative of the sum of squared residuals with respect to the position parameter of the relative center point. Then, the negative gradient direction corresponding to the partial derivatives is extracted. The initial learning rate and the current optimization iteration cycle are read from the current operating environment, and the initial learning rate is decreased according to the current optimization iteration cycle to obtain the iteration step size. Then, the negative gradient direction is multiplied by the iteration step size to obtain the position offset component, which is calculated as iteration step size × negative gradient direction. The current position parameter and the position offset component are then summed to obtain the updated center point position parameter, which is calculated as current center point position parameter + position offset component. The updated center point position parameter is then used to re-determine the approximation curve position and recalculate the corresponding residual sum of squares.

[0025] S203: Call the residual sum of squares associated with the updated center point position parameters, perform a numerical difference comparison operation between the residual sum of squares and the position optimization convergence threshold, and when it is determined that the residual sum of squares after parameter adjustment is within the convergence value range, extract and merge multiple updated center point position parameters of the current update state to construct a data vector structure and generate the optimal position parameter vector. The algorithm reads the updated center point location parameters and their corresponding residual sums of squares, and compares the current residual sum of squares with the location optimization convergence threshold. If the current residual sum of squares is less than the location optimization convergence threshold, the current parameter is considered to have entered the convergence interval, and the current updated center point location parameters are retained. If the current residual sum of squares equals the location optimization convergence threshold, the current parameter is considered to be on the convergence boundary, and the current updated center point location parameters are retained. If the current residual sum of squares is greater than the location optimization convergence threshold, the current parameter is considered to have not entered the convergence interval, and the current updated center point location parameters are used as the new current location parameters to continue calculating the residual sum of squares and updating the location parameters. This process continues until the current residual sum of squares is less than or equal to the location optimization convergence threshold. Then, multiple updated center point location parameters in the current update state are extracted and merged into a data vector according to a predetermined dimensional order to obtain the optimal location parameter vector.

[0026] The process of obtaining the spatial alignment deviation value is as follows: S301: Decompose the numerical structure contained in the optimal position parameter vector into vector dimensions, extract the pixel center point coordinates corresponding to the numerical structure in the two-dimensional space dimension, read the reference comparison information in the plate registration calibration record, extract the standard reference coordinates corresponding to the pixel center point coordinates, and simultaneously read the interval configuration parameters in the hardware limit record to obtain the position correction interval data. The optimal position parameter vector is read and decomposed according to the predetermined dimensional correspondence within the vector. The decomposed parameters are then mapped to two-dimensional spatial positions, with the two parameters corresponding to these positions serving as the horizontal and vertical coordinates of the current color mark center point in the image coordinate system. Next, the reference information in the plate registration and calibration record is read, and the standard reference coordinates corresponding to the pixel center point coordinates are extracted. Then, the interval configuration parameters in the hardware limit record are read, and the lower and upper boundaries corresponding to the allowable correction range are extracted to obtain the position correction interval data.

[0027] S302: Call the pixel center point coordinates and the standard reference coordinates, perform subtraction difference operation on the coordinate distribution characteristics of the pixel center point coordinates and the standard reference coordinates on the corresponding dimension axis, calculate the spatial displacement vector between the two, output the relative geometric distance and perform vector coordinate system projection decomposition, determine the direction difference attribute of the relative geometric distance on the physical coordinate axis, extract the distance parameters corresponding to the multi-dimensional coordinate axis, and establish the position offset component. The pixel center point coordinates and the standard reference coordinates are used, and interpolation is performed on the corresponding axes to obtain the horizontal and vertical displacement components. The horizontal displacement component = pixel center point horizontal coordinate - standard reference horizontal coordinate, and the vertical displacement component = pixel center point vertical coordinate - standard reference vertical coordinate. The horizontal and vertical displacement components are then combined into a spatial displacement vector, and then... The relative geometric distance is calculated. Then, coordinate projection decomposition is performed on the spatial displacement vector to obtain the directional difference attributes of the lateral and longitudinal displacement components on the physical coordinate axes. When the lateral displacement component is greater than 0, the lateral direction attribute is recorded as positive; when the lateral displacement component is equal to 0, the lateral direction attribute is recorded as zero offset; when the lateral displacement component is less than 0, the lateral direction attribute is recorded as negative. When the longitudinal displacement component is greater than 0, the longitudinal direction attribute is recorded as positive; when the longitudinal displacement component is equal to 0, the longitudinal direction attribute is recorded as zero offset; when the longitudinal displacement component is less than 0, the longitudinal direction attribute is recorded as negative. Subsequently, the lateral and longitudinal displacement components are used as distance parameters corresponding to each coordinate axis, together with the corresponding directional attributes, to form the position offset component.

[0028] S303: Perform a scaling conversion operation on the direction identifier and data magnitude attached to the position offset component to generate reconstructed offset magnitude data. Perform a numerical comparison operation on the value of the reconstructed offset magnitude data and the boundary range defined by the position correction interval data to remove out-of-bounds deviation records that exceed the limit constraints, and filter the magnitude data within the position correction interval to obtain the spatial registration deviation value. The orientation identifier and data magnitude of the position offset component are read, and the physical field-of-view size and resolution parameters are retrieved from the optical imaging calibration record. The physical field-of-view size parameter is then divided by the resolution parameter to obtain the physical length reference value, which is set as the pixel equivalent conversion factor. The data magnitude of the position offset component is then multiplied by the pixel equivalent conversion factor to obtain the absolute displacement value: Absolute displacement value = Data magnitude × Pixel equivalent conversion factor. Next, the sign of the absolute displacement value is determined based on the direction indicator: a positive direction indicator assigns a positive sign; a zero direction indicator assigns a zero sign; and a negative direction indicator assigns a negative sign, resulting in the reconstructed offset magnitude data. This reconstructed offset magnitude data is then compared with the lower and upper boundaries of the position correction interval data. If the reconstructed offset magnitude data is less than the lower boundary, it is considered an out-of-bounds deviation record and discarded; if it equals the lower boundary, it is retained; if it is greater than the lower boundary but less than the upper boundary, it is retained; if it equals the upper boundary, it is retained; and if it is greater than the upper boundary, it is considered an out-of-bounds deviation record and discarded. The retained data is then used as the spatial registration deviation value.

[0029] The process for obtaining the total target compensation angular displacement is as follows: S401: Obtain the circumferential speed execution record of the printing plate cylinder servo motor, match the time nodes contained in the circumferential speed execution record, extract the instantaneous speed and instantaneous acceleration of the circumferential speed execution record at the set time node, perform the integral operation of the speed over time for the unexecuted time segment in the circumferential speed execution record, calculate the area data accumulated by the speed value in the remaining time dimension, and generate the remaining integrated area. The circumferential speed execution record of the printing plate roller servo motor is read, and time series data is extracted from the record. Then, based on the set time node corresponding to the current compensation calculation, each time node in the circumferential speed execution record is matched, and the record item corresponding to the set time node is read. Subsequently, the instantaneous speed and instantaneous acceleration at that set time node are extracted from the corresponding record item. When the instantaneous acceleration is a directly recorded item, it is read directly; when the instantaneous acceleration is formed by changes in speed between adjacent time points, the instantaneous acceleration of the current record item is determined according to the speed difference and time difference between adjacent time nodes. Next, the unexecuted time segment is determined from the circumferential speed execution record, and the speed values ​​corresponding to each time node within that time segment are read. The speed values ​​corresponding to each time node are first converted into angular velocity values, and then the angular velocity in the unexecuted time segment is integrated over time. The angular velocity values ​​at each time node are accumulated and summed in chronological order to obtain the corresponding cumulative angular displacement.

[0030] S402: Based on the mapping relationship corresponding to the spatial registration deviation values, extract the theoretical deviation phase associated with the spatial registration deviation values, convert the remaining integral area into the equivalent compensation angular displacement of the angular displacement dimension, combine the extracted theoretical deviation phase and the equivalent compensation angular displacement, and establish a compensation angle calculation set. The spatial registration deviation value is read, and the theoretical deviation phase corresponding to the value is extracted based on the pre-established mapping relationship between deviation and phase. The sign of the spatial registration deviation value corresponds to the direction attribute of the theoretical deviation phase, and the magnitude of the deviation value corresponds to the phase magnitude of the theoretical deviation phase. Then, the accumulated angular displacement is called and written as the equivalent compensated angular displacement into the compensation angle calculation set. The theoretical deviation phase is also written into this set, ensuring that all data items maintain a consistent format for recording angle values ​​and direction attributes.

[0031] S403: Extract the compensation angle calculation set, establish a unified angle coordinate system, perform numerical superposition calculation on the equivalent compensation angular displacement and theoretical deviation phase within the unified angle coordinate system, calculate the sum of the superimposed angular displacement values ​​within a set time period to obtain the total compensation angular displacement, merge the integral constraint features within the set time period to construct the corresponding data items, and generate the total target compensation angular displacement. The theoretical deviation phase and equivalent compensation angular displacement are read from the compensation angle calculation set, and a unified angular coordinate system is established so that the theoretical deviation phase and equivalent compensation angular displacement use the same angular reference direction and the same angular unit. Then, numerical superposition is performed within the unified angular coordinate system: total compensation angular displacement = equivalent compensation angular displacement + theoretical deviation phase; when the two are in the same direction, their values ​​are summed; when they are in opposite directions, their algebraic sum is taken; when one angle value is 0, the superposition result uses the other angle value; when both are 0, the superposition result is 0. Next, the time boundary corresponding to the set time period and the superposition result are merged to form the corresponding data item, obtaining the total target compensation angular displacement.

[0032] The process of obtaining the overall compensated speed sequence is as follows: S501: Based on the total target compensation angular displacement, call and identify the endpoint boundary control points corresponding to the instantaneous rotational speed and instantaneous acceleration, obtain the polynomial basis function, set the total target compensation angular displacement as the displacement constraint condition, combine the endpoint boundary control points and the displacement constraint condition to construct the overall constraint equation system, perform numerical solution calculation on the overall constraint equation system, and obtain the coordinate parameters of the intermediate control point. The total target angular displacement is read, and instantaneous rotational speed and instantaneous acceleration data are retrieved. The endpoint boundary control points corresponding to the start and end points of the compensation time period are identified. These endpoint boundary control points record the start time parameter, end time parameter, start instantaneous rotational speed, end instantaneous rotational speed, start instantaneous acceleration, and end instantaneous acceleration. The number of kinematic boundary conditions recorded at the endpoint boundary control points is then counted, and the overall constraint dimension value is determined in conjunction with the total target angular displacement. Based on the overall constraint dimension value, the highest power order required for interpolation is determined, and a time algebraic polynomial with a corresponding number of undetermined coefficients is established. This time algebraic polynomial is used as the angular displacement trajectory function. The first and second derivatives of the angular displacement trajectory function are then performed to obtain the angular velocity and angular acceleration expressions. The start and end time parameters are then substituted into the angular velocity and angular acceleration expressions, respectively, to obtain the calculation results at the start and end points. An algebraic identity is established between the calculated angular velocity expression and the instantaneous rotational speed, and the calculated angular acceleration expression is established between the calculated instantaneous acceleration, forming the endpoint boundary constraint equations. Then, the start time parameter and the end time parameter are substituted into the angular displacement trajectory function respectively. The target angular displacement expression is obtained by subtracting the angular displacement at the start time from the angular displacement at the end time. The target angular displacement expression is then established with the total target compensation angular displacement to form a displacement constraint equation. The endpoint boundary constraint equation and the displacement constraint equation are then combined to form an overall constraint equation system. Finally, the equation system is numerically solved to obtain the coordinate parameters of the intermediate control point.

[0033] S502: Call the intermediate control point coordinate parameters, merge the endpoint boundary control points to construct all control point coordinates, perform algebraic multiplication operation on the polynomial basis function and all control point coordinates, calculate the sum of the products after numerical multiplication and map the coordinate nodes under the corresponding time nodes, construct the time speed coordinate sequence that matches the compensation constraint conditions, merge the data of each node in the time speed coordinate sequence to perform curve construction operation, and generate a single-segment smooth compensation trajectory. The coordinate parameters of intermediate control points are read and merged with those of the starting and ending boundary control points to form the coordinates of all control points. These coordinates are then arranged chronologically, with the first and last control points corresponding to the starting and ending boundary control points, and the intermediate control points corresponding to the obtained coordinate parameters. Subsequently, at each time point, the products of each term of the angular displacement trajectory function and the corresponding control point coordinates are calculated, and all products are summed to obtain the angular displacement coordinate value for that time point. Next, the angular displacement trajectory function is differentiated once at each time node to obtain the compensation speed value corresponding to each time node, forming a time-speed coordinate sequence in which the time node and the compensation speed value correspond one-to-one. Then, the data of each node in the time-speed coordinate sequence are connected in chronological order to obtain a single-segment smooth compensation trajectory.

[0034] S503: Extract the start and end time data of the trajectory within the single-segment smooth compensation trajectory, obtain the operation record of the motor equipment, perform comparison and matching calculation on the trajectory start and end time data and the operation record, extract the endpoint timestamps corresponding to the overlapping areas, define the data processing interval based on the endpoint timestamps, extract and merge the coordinate data contained within the endpoint timestamp area, and splice the merged coordinate data in chronological order to generate the overall compensation speed sequence. The system reads the start and end times of a single-segment smooth compensation trajectory and retrieves the time series from the motor equipment's operation record. It then compares each time point in the operation record with the trajectory's start and end times to determine the start endpoint timestamp corresponding to the trajectory's start time and the end endpoint timestamp corresponding to the trajectory's end time. Time points in the operation record earlier than the trajectory's start time are not included in the current compensation data processing interval. Time points equal to the trajectory's start time are included as start endpoint timestamps in the current compensation data processing interval. Time points later than the trajectory's start time but earlier than the trajectory's end time are included in the current compensation data processing interval. Time points equal to the trajectory's end time are included as end endpoint timestamps in the current compensation data processing interval. Time points later than the trajectory's end time are not included in the current compensation data processing interval. Subsequently, within the interval defined by the start and end endpoint timestamps, the time coordinates and speed coordinates corresponding to each time point are extracted. These coordinate data within the interval are then merged and concatenated in chronological order to obtain the overall compensated speed sequence.

[0035] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention in any other way. Any person skilled in the art may make changes or modifications to the above-disclosed technical content to create equivalent embodiments that can be applied to other fields. However, any simple modifications, equivalent changes, and modifications made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the protection scope of the present invention.

Claims

1. A printing press registration deviation compensation method based on image recognition, characterized in that, Includes the following steps: S1: Calculate the pixel intensity in the direction of the normal of the aligned color mark edge in the original image, filter the effective pixel points and adjust the spatial arrangement order, and combine the intensity values ​​to output a one-dimensional grayscale sequence of the color mark. S2: Based on the one-dimensional grayscale sequence of the color mark, extract the background noise variance to calculate the position optimization convergence threshold, calculate the residual sum of squares between the one-dimensional grayscale sequence of the color mark and the approximation curve, and the partial derivative of the residual sum of squares with respect to the center point position parameter. Update the center point position parameter according to the partial derivative until the residual is within the convergence range, and output the optimal position parameter vector. S3: Extract the center point coordinates of the optimal position parameter vector, calculate the relative geometric distance between the center point coordinates and the standard reference coordinates, determine the position offset component, adjust the position offset component, filter the magnitude data in the correction interval, and output the spatial registration deviation value. S4: Extract the instantaneous speed and instantaneous acceleration from the motor speed execution record, convert the unexecuted remaining integral area into an equivalent compensation angular displacement, and superimpose it with the theoretical deviation phase associated with the spatial alignment deviation value to output the total target compensation angular displacement. S5: Obtain boundary control points based on instantaneous rotational speed and instantaneous acceleration, solve the intermediate control point parameters by solving a system of equations with the total target compensation angular displacement as the constraint, calculate the sum of the products of polynomial basis functions and control point coordinates to generate a single-segment smooth compensation trajectory, combine the endpoint timestamps to merge coordinate data, and output the overall compensation rotational speed sequence.

2. The printing press registration deviation compensation method based on image recognition according to claim 1, characterized in that, The specific process for obtaining the one-dimensional grayscale sequence of the color mark is as follows: S101: Collect the original image of the printing material captured by the industrial area array camera during the multi-color overprinting process of the printing press. Extract the edge normal direction for the alignment color mark inside the original image. Perform point-by-point grayscale extraction operation along the edge normal direction. Calculate the pixel intensity data of each coordinate node in the edge normal direction. Merge the pixel intensity data corresponding to multiple coordinate nodes in the edge normal direction to establish a normal intensity distribution sequence. S102: Obtain the preset sampling interval in the set parameter record, perform a step span value comparison operation on the pixel coordinates contained in the normal intensity distribution sequence and the preset sampling interval, remove discrete coordinate points that do not meet the span value, retain data items that meet the sampling interval conditions, and generate a set of valid pixel points. S103: Extract the spatial position coordinates contained within the effective pixel point set, perform a uniaxial position projection operation on the spatial position coordinates to adjust the spatial arrangement order, generate rearranged position coordinates, and stitch together the previously acquired pixel intensity data one by one according to the order corresponding to the rearranged position coordinates to obtain a one-dimensional grayscale sequence of color marks.

3. The printing press registration deviation compensation method based on image recognition according to claim 2, characterized in that, The process of obtaining the optimal position parameter vector is as follows: S201: Extract the grayscale contrast and background noise variance contained in the one-dimensional grayscale sequence of the color mark, read the number of effective pixels in the parameter configuration, perform a numerical multiplication operation on the background noise variance and the number of effective pixels to obtain the product value, set the calculation boundary based on the product value, and generate the position optimization convergence threshold. S202: Obtain the approximation curve from the internal data record, perform curve fitting operation on the one-dimensional grayscale sequence of the color mark and the approximation curve, calculate the residual sum of squares between the one-dimensional grayscale sequence of the color mark and the approximation curve, perform differential operation on the residual sum of squares relative to the center point position parameter to extract the partial derivative, adjust the center point position parameter of the approximation curve based on the value of the partial derivative, and obtain the updated center point position parameter. S203: Call the residual sum of squares associated with the updated center point position parameters, perform a numerical difference comparison operation between the residual sum of squares and the position optimization convergence threshold, and when it is determined that the residual sum of squares after parameter adjustment is within the convergence value range, extract and merge multiple updated center point position parameters of the current update state to construct a data vector structure and generate the optimal position parameter vector.

4. The printing press registration deviation compensation method based on image recognition according to claim 3, characterized in that, The process of performing a numerical multiplication operation on the background noise variance and the number of effective pixels to obtain the product value, and setting the calculation boundary based on the product value, is as follows: A numerical multiplication operation is performed on the background noise variance and the number of effective pixels to obtain the product value. The base noise data recorded during the historical no-load operation phase is retrieved. A safety tolerance coefficient is calculated based on the fluctuation extreme value range corresponding to the base noise data. An algebraic multiplication operation is performed on the product value and the safety tolerance coefficient to obtain a reference value. The reference value is set as the calculation boundary.

5. The printing press registration deviation compensation method based on image recognition according to claim 3, characterized in that, The process of numerically adjusting the center point position parameter of the approximation curve based on partial derivatives is as follows: Extract the negative gradient direction corresponding to the partial derivative, obtain the initial learning rate and the current optimization iteration cycle under the current operating environment, perform a decreasing decay operation on the initial learning rate based on the current optimization iteration cycle to generate an iteration step size value, perform vector multiplication operation on the negative gradient direction and the iteration step size value to calculate the position offset component, extract the current center point position parameter of the approximation curve, perform coordinate accumulation operation on the current center point position parameter and the position offset component to generate updated center point position parameters.

6. The printing press registration deviation compensation method based on image recognition according to claim 3, characterized in that, The process of obtaining the spatial alignment deviation value is as follows: S301: Decompose the numerical structure contained in the optimal position parameter vector into vector dimensions, extract the pixel center point coordinates corresponding to the numerical structure in the two-dimensional space dimension, read the reference comparison information in the plate registration calibration record, extract the standard reference coordinates corresponding to the pixel center point coordinates, and simultaneously read the interval configuration parameters in the hardware limit record to obtain the position correction interval data. S302: Call the pixel center point coordinates and the standard reference coordinates, perform subtraction difference operation on the coordinate distribution characteristics of the pixel center point coordinates and the standard reference coordinates on the corresponding dimension axis, calculate the spatial displacement vector between the two, output the relative geometric distance and perform vector coordinate system projection decomposition, determine the direction difference attribute of the relative geometric distance on the physical coordinate axis, extract the distance parameters corresponding to the multi-dimensional coordinate axis, and establish the position offset component. S303: Perform a scaling conversion operation on the direction identifier and data magnitude attached to the position offset component to generate reconstructed offset magnitude data. Perform a numerical comparison operation between the value of the reconstructed offset magnitude data and the boundary range defined by the position correction interval data. Remove out-of-bounds deviation records that exceed the limit constraints, and filter the magnitude data within the position correction interval to obtain the spatial registration deviation value.

7. The printing press registration deviation compensation method based on image recognition according to claim 6, characterized in that, The process of performing a scaling conversion operation on the direction identifier and data magnitude of the position offset component to generate reconstructed offset magnitude data is as follows: The physical field of view size parameters and resolution parameters are extracted by calling the optical imaging calibration record. The physical field of view size parameters and resolution parameters are converted by numerical division to calculate the physical length reference value. The physical length reference value is set as the pixel equivalent conversion coefficient. Extract the data magnitude associated with the position offset component, and perform algebraic multiplication numerical operation on the data magnitude and the pixel equivalent conversion coefficient to obtain the absolute displacement value; Extract the direction identifier attached to the position offset component, identify the positive and negative polarity features corresponding to the direction identifier in the two-dimensional rectangular coordinate system, and assign positive and negative signs to the absolute displacement value in combination with the positive and negative polarity features to generate the reconstructed offset magnitude data.

8. The printing press registration deviation compensation method based on image recognition according to claim 6, characterized in that, The process for obtaining the total target compensation angular displacement is as follows: S401: Obtain the circumferential speed execution record of the printing plate cylinder servo motor, match the time nodes contained in the circumferential speed execution record, extract the instantaneous speed and instantaneous acceleration of the circumferential speed execution record at the set time node, perform the integral operation of the speed over time for the unexecuted time segment in the circumferential speed execution record, calculate the area data accumulated by the speed value in the remaining time dimension, and generate the remaining integrated area. S402: Based on the mapping relationship corresponding to the spatial registration deviation values, extract the theoretical deviation phase associated with the spatial registration deviation values, convert the remaining integral area into the equivalent compensation angular displacement of the angular displacement dimension, combine the extracted theoretical deviation phase and the equivalent compensation angular displacement, and establish a compensation angle calculation set. S403: Extract the compensation angle calculation set, establish a unified angle coordinate system, perform numerical superposition calculation on the equivalent compensation angular displacement and theoretical deviation phase within the unified angle coordinate system, calculate the sum of the superimposed angular displacement values ​​within a set time period to obtain the total compensation angular displacement, merge the integral constraint features within the set time period to construct the corresponding data items, and generate the total target compensation angular displacement.

9. The printing press registration deviation compensation method based on image recognition according to claim 8, characterized in that, The process of obtaining the overall compensated speed sequence is as follows: S501: Based on the total target compensation angular displacement, call and identify the endpoint boundary control points corresponding to the instantaneous rotational speed and instantaneous acceleration, obtain the polynomial basis function, set the total target compensation angular displacement as the displacement constraint condition, combine the endpoint boundary control points and the displacement constraint condition to construct the overall constraint equation system, perform numerical solution calculation on the overall constraint equation system, and obtain the coordinate parameters of the intermediate control point. S502: Call the intermediate control point coordinate parameters, merge the endpoint boundary control points to construct all control point coordinates, perform algebraic multiplication operation on the polynomial basis function and all control point coordinates, calculate the sum of the products after numerical multiplication and map the coordinate nodes under the corresponding time nodes, construct the time speed coordinate sequence that matches the compensation constraint conditions, merge the data of each node in the time speed coordinate sequence to perform curve construction operation, and generate a single-segment smooth compensation trajectory. S503: Extract the start and end time data of the trajectory within the single-segment smooth compensation trajectory, obtain the operation record of the motor equipment, perform a comparison and matching operation on the trajectory start and end time data and the operation record, extract the endpoint timestamps corresponding to the overlapping areas, define the data processing interval based on the endpoint timestamps, extract and merge the coordinate data contained within the endpoint timestamp area, and splice the merged coordinate data in chronological order to generate the overall compensation speed sequence.

10. The printing press registration deviation compensation method based on image recognition according to claim 9, characterized in that, The process of obtaining the polynomial basis functions, setting the total target compensation angular displacement as the displacement constraint, and constructing the overall constraint equation system by simultaneously establishing the endpoint boundary control points and the displacement constraint is as follows: The number of kinematic boundary conditions recorded inside the endpoint boundary control points is counted. The displacement boundary conditions represented by the total target compensation angular displacement are combined to extract the overall constraint dimension value. The highest power order corresponding to the interpolation algorithm is determined based on the overall constraint dimension value. A time algebraic polynomial with a corresponding number of undetermined coefficients is constructed based on the highest power order. The time algebraic polynomial is established as the polynomial basis function. Perform differentiation operations on the polynomial basis functions to generate first-order and second-order derivative expressions; The endpoint boundary control points are analyzed to extract the start time parameters and end time parameters. The start time parameters and end time parameters are substituted into the first derivative expression and the second derivative expression to obtain the derivative calculation results. The derivative calculation results are then used to establish algebraic identities with the instantaneous rotational speed and the instantaneous acceleration to generate the endpoint boundary constraint equations. Substitute the start time parameter and the end time parameter into the polynomial basis function respectively, and subtract the calculation result corresponding to the start time from the calculation result corresponding to the end time to generate the target angular displacement expression. Establish an algebraic identity relationship between the target angular displacement expression and the total target compensation angular displacement to construct the displacement constraint equation. Combine the endpoint boundary constraint equation and the displacement constraint equation to generate the overall constraint equation system.