Mechanical arm control method for tunnel engineering concrete spraying

Abstract

The invention discloses a mechanical arm control method for tunnel engineering concrete spraying, and belongs to the technical field of mechanical arm control, and the mechanical arm control method specifically comprises the steps that a three-dimensional point cloud model of a construction tunnel is obtained, a mechanical arm movement track is generated based on the three-dimensional point cloud model, and the initial spraying speed and flow are set; the curvature radius of a current spraying point is collected in real time through a curvature sensing unit at the tail end of a mechanical arm, a lining surface unit normal vector of the point is obtained based on a three-dimensional model, and the dot product absolute value of the point normal vector and a gravity vector is calculated to serve as a gravity influence factor; inputting the curvature radius and the gravity influence factor into a preset deviation mapping model to obtain a solidification time prediction deviation and a thickness prediction deviation corresponding to the current spraying point; the initial speed and flow are corrected based on the solidification time and the thickness prediction deviation, and a mechanical arm is controlled to conduct spraying; the thickness consistency and solidification stability of concrete linings in different areas of a tunnel are achieved, and the spraying uniformity is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of robot arm control, and in particular to a robot arm control method for concrete spraying in tunnel engineering. Background Art

[0002] In tunnel engineering, concrete lining is a critical component in ensuring tunnel structural stability and durability. The quality of its spraying directly impacts project safety and service life. However, due to the complexity of tunnel structures, the concrete spraying process often faces challenges related to uneven application due to the unique structural characteristics, becoming a significant bottleneck restricting construction efficiency and quality.

[0003] Currently, tunnel concrete spraying mostly relies on automated operations by robotic arms, and tunnel engineering concrete spraying operations are achieved by connecting multiple sub-processes such as "one spray, two sprays, one scraper, three sprays, two scrapers, and one sweep." However, at the same time, for scenarios where the wall surface is pre-leveled manually and then filled with thickness by a robotic arm, the existing methods lack targeted adaptation to the manually pre-processed reference surface. Existing robotic arm control methods generally use fixed motion parameters and spraying parameters, which are difficult to adapt to the diverse structural scenarios in the tunnel. On the one hand, there are a large number of curved surface structures in the tunnel (such as turning sections, transition areas between arches and side walls, etc.), and the path curvature in different areas varies significantly. When the robotic arm moves along a high-curvature path, local concrete accumulation or insufficient spraying is likely to occur at a fixed speed, resulting in the thickness deviation of the deposition layer exceeding the design allowable range; on the other hand, the influence of gravity on concrete spraying has significant spatial differences - in the arch area, concrete is prone to flow due to gravity, while in the side wall area, the thickness may be too large due to gravity deposition. Traditional control methods do not make adaptive adjustments to the spatial changes in the influence of gravity, further exacerbating the problem of uneven spraying.

[0004] These issues often lead to defects in the concrete lining after construction, such as localized excess or insufficient thickness and inconsistent setting times. This not only requires extensive manual repairs to meet design requirements, increasing construction costs and lead times, but also potentially leaving structural safety hazards due to incomplete repairs. While some existing solutions attempt to improve construction results through simple parameter adjustments, these fail to systematically consider the coupling effects of path curvature and gravity, making it difficult to achieve dynamic and precise parameter control and fundamentally addressing the uneven concrete spraying problem inherent in the tunnel's unique structure. Summary of the Invention

[0005] The purpose of the present invention is to provide a method for controlling a robotic arm for concrete spraying in tunnel engineering, thereby solving the following technical problems: How to adjust the dynamic parameters of the robotic arm based on the influence of path curvature and gravity to solve the problem of uneven concrete spraying under the special structure of the tunnel.

[0006] The purpose of the present invention can be achieved through the following technical solutions: A method for controlling a robotic arm for concrete spraying in tunnel engineering includes the following steps: S1, obtaining a three-dimensional point cloud model of the construction tunnel, and generating a robot arm motion trajectory based on the three-dimensional point cloud model, calibrating the robot arm motion trajectory as a construction path and setting an initial spraying speed and an initial spraying flow rate value; S2, collects the curvature radius of the current spraying point on the motion trajectory in real time through the curvature sensing unit integrated at the end of the robotic arm; S3, obtaining a unit normal vector of the lining surface at the current spraying point based on the three-dimensional digital model, calculating an absolute value of a dot product of the unit normal vector and a gravity vector and using the result as a gravity influencing factor; S4, inputting the curvature radius and gravity influence factor into a preset deviation mapping model to obtain a predicted solidification time deviation and a predicted thickness deviation corresponding to the current spraying point; S5, correcting the initial robot arm movement speed based on the solidification time deviation, and controlling the robot arm to spray along the construction path at the corrected movement speed; S6, correcting the initial spraying flow rate based on the thickness prediction deviation, and controlling the robotic arm to spray along the construction path according to the corrected spraying flow rate.

[0007] As a further solution of the present invention: In S1, the specific process of generating the motion trajectory of the robotic arm is: Extracting discrete feature points on the inner surface of the lining from the three-dimensional point cloud model and performing surface fitting to generate a continuous surface model; Generate multiple reference path lines parallel to the axis at a preset distance above the continuous curved surface model along the tunnel axis; discretize the reference path lines to obtain trajectory control points, and calculate the coordinates of each trajectory control point in the manipulator base coordinate system; Based on the limit parameters of the robot arm joint angles, the feasibility of the trajectory control points is verified and the points beyond the workspace are eliminated. The verified trajectory control points are then curve fitted to generate a continuous robot arm motion trajectory.

[0008] As a further solution of the present invention: in S3, the specific construction process of the preset deviation mapping model is: S11, intercepting a preset length segment containing full curvature features from the three-dimensional digital model of the construction tunnel as an experimental surface, dividing the experimental surface into a plurality of experimental sub-areas, and controlling the robotic arm to perform a spraying operation on each experimental sub-area at an initial spraying speed and an initial flow rate value; S12, collecting spatiotemporal evolution data of the concrete surface temperature through an infrared thermal imaging array, determining the actual solidification time based on the temperature rise rate inflection point, and calculating the difference between the actual solidification time and the preset standard solidification time as the solidification time deviation value; A laser profile scanner is used to simultaneously obtain a surface point cloud during the initial setting phase, and the design surface corresponding to the experimental surface is extracted from the 3D digital model. The directed distance from the point cloud to the design surface is calculated along the normal direction of the design surface as the actual construction thickness. The median value of the difference between the actual construction thickness and the design thickness is statistically calculated as the thickness deviation value. S13, obtaining the curvature radius and gravity influence factor of each experimental sub-area, using the curvature radius value as the first-dimensional index and the gravity influence factor value as the second-dimensional index, storing the corresponding solidification time deviation value and thickness deviation value at the intersection of the two-dimensional index to obtain a deviation mapping model.

[0009] As a further solution of the present invention: it also includes using a bicubic spline interpolation algorithm to generate a continuous solidification time deviation field and a thickness deviation field at an unmeasured curvature-gravity factor combination position, and burning the interpolated mapping table into the robotic arm control unit as a deviation mapping model.

[0010] As a further solution of the present invention: In S5, the specific process of correcting the initial robot arm movement speed is: In the experimental tunnel section, spraying was performed at a step-by-step speed, keeping the spray flow rate constant. The actual setting time deviation of the concrete at different spraying speeds was recorded, and the response relationship between the setting time deviation and the speed correction was fitted using the least squares method to generate a piecewise linear speed compensation function: The predicted solidification time deviation output by the deviation mapping model is input into the speed compensation function to obtain a speed correction value, and a final speed correction instruction is output to the robot arm driver.

[0011] As a further solution of the present invention: in S6, the specific process of correcting the initial spray flow rate is: In the experimental tunnel section, spraying was performed with step-wise varying spray flow rates, while maintaining a constant robotic arm movement speed. The concrete thickness deviations at different flow rates were recorded, and the response relationship between the thickness deviation and the flow correction coefficient was fitted using the least squares method to generate a piecewise linear flow compensation function: The thickness prediction deviation output by the deviation mapping model is input into the flow compensation function, the basic flow correction coefficient is calculated, and the final spray flow correction instruction is output to the robot arm driver.

[0012] As a further solution of the present invention: in the S3, the gravity vector is also included in the negative direction of the Z axis of the earth coordinate system, and the coordinate transformation is corrected in real time by an inclination sensor installed on the base of the robotic arm.

[0013] As a further scheme of the present application: the S6 further comprises establishing a set of mobile speed parameter gradients and a set of spraying flow parameter gradients in the experimental sub-region, to form an orthogonal experiment matrix; For any combination of mobile speed and spraying flow in the orthogonal experiment matrix, the mechanical arm is controlled to execute spraying with the speed parameter and flow parameter of the combination as constant values; The solidification time deviation and the thickness deviation of each experimental sub-region are calculated, and a mapping relationship between the solidification time deviation and the reciprocal of curvature, the gravity influence factor, and the product of speed and flow is established; A mapping relationship between the thickness deviation and the reciprocal of curvature, the gravity influence factor, and the product of speed and flow is established; The coefficient of the product of speed and flow in the mapping relationship is solved by the weighted least squares method, and the ratio of the coefficient to the initial spraying parameter is extracted to generate a standardized interaction influence coefficient; The change amount of the mobile speed of the mechanical arm before and after correction is obtained, and based on the change amount of the mobile speed and the standardized interaction influence coefficient, an interaction effect compensation amount is calculated; The interaction effect compensation amount is superimposed on the basic flow correction coefficient to generate a final flow correction coefficient, and the mechanical arm is controlled to adjust the spraying flow according to the final flow correction coefficient.

[0014] The present application has the following advantages: 1) The present application obtains the curvature radius and the gravity influence factor of the current spraying point in real time, combines the preset deviation mapping model to obtain the prediction deviation of the solidification time and the thickness, and then corrects the initial spraying speed and flow accordingly. It can be understood that the curvature radius reflects the bending degree of the tunnel area, and the more obvious the bending is, the greater the difference in the accumulation or distribution state of the concrete is. The gravity influence factor quantifies the action strength of gravity on the concrete, and the difference in the action of gravity at different positions such as the vault and the side wall will cause different concrete flow or deposition. Based on the dynamic adjustment of these characteristic parameters, the mechanical arm can flexibly adapt to the parameters in different structural regions of the tunnel, such as the turning section, the vault, and the side wall, so that the mechanical arm can flexibly adapt to the parameters according to the curvature characteristics and the difference in the action of gravity in different regions of the tunnel, avoiding the local accumulation or insufficient spraying under fixed parameters, and ensuring the thickness consistency and solidification stability of the concrete lining in complex structural regions.

[0015] 2) The present invention extracts a section containing full curvature features from the three-dimensional digital model as an experimental surface and divides it into zones. After controlling the robotic arm to spray with initial parameters, the infrared thermal imaging array is used to obtain the concrete surface temperature data to determine the actual setting time deviation. The laser profile scanner is simultaneously used to obtain the surface point cloud in the initial setting stage to calculate the thickness deviation. The corresponding deviation values ​​are then stored using the curvature radius and the gravity influence factor as a two-dimensional index, and the unmeasured areas are supplemented through bicubic spline interpolation. At the same time, the least squares method is used to fit a piecewise linear velocity and flow compensation function based on the experimental data, and the predicted deviation is converted into a specific correction amount. This effectively reduces problems such as inconsistent setting time and excessive thickness, reduces the need for later manual repairs, and improves the quality stability of automated spraying.

[0016] 3) It can be understood that the moving spraying speed will indirectly affect the actual spraying flow rate value. Under the same flow rate, a slower speed will increase the amount of concrete per unit area. The present invention establishes an orthogonal experimental matrix of moving speed and spraying flow rate, tests the spraying effects of different parameter combinations in the experimental sub-area, calculates the setting time and thickness deviation, constructs a mapping relationship including the inverse of curvature, gravity influence factor and speed-flow product term, obtains the interaction influence coefficient through weighted solution, and finally superimposes the interaction effect compensation amount in the flow correction. The interaction compensation amount is used to correct the indirect influence of the spraying speed change on the spraying flow rate, solves the superposition error problem when the speed and flow rate are independently corrected, makes the parameter adjustment more accurate, further improves the uniformity of tunnel concrete spraying, and ensures the stability and durability of the lining structure. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] The present invention will be further described below with reference to the accompanying drawings.

[0018] Figure 1 It is a flow chart of a method for controlling a robotic arm for concrete spraying in tunnel engineering according to the present invention. DETAILED DESCRIPTION

[0019] 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 ordinary technicians in this field without making any creative efforts shall fall within the scope of protection of the present invention.

[0020] See also Figure 1 As shown, the present invention is a method for controlling a robotic arm for concrete spraying in tunnel engineering, comprising the following steps: S1, obtaining a three-dimensional point cloud model of the construction tunnel, and generating a robot arm motion trajectory based on the three-dimensional point cloud model, calibrating the robot arm motion trajectory as a construction path and setting an initial spraying speed and an initial spraying flow rate value; S2, collects the curvature radius of the current spraying point on the motion trajectory in real time through the curvature sensing unit integrated at the end of the robotic arm; S3, obtaining a unit normal vector of the lining surface at the current spraying point based on the three-dimensional digital model, calculating an absolute value of a dot product of the unit normal vector and a gravity vector and using the result as a gravity influencing factor; S4, inputting the curvature radius and gravity influence factor into a preset deviation mapping model to obtain a predicted solidification time deviation and a predicted thickness deviation corresponding to the current spraying point; S5, correcting the initial robot arm movement speed based on the solidification time deviation, and controlling the robot arm to spray along the construction path at the corrected movement speed; S6, correcting the initial spraying flow rate based on the thickness prediction deviation, and controlling the robotic arm to spray along the construction path according to the corrected spraying flow rate.

[0021] 1) The present invention obtains the curvature radius and gravity influence factor of the current spraying point in real time, combines it with a preset deviation mapping model to obtain the predicted deviation of the solidification time and thickness, and then corrects the initial spraying speed and flow rate in a targeted manner. It can be understood that the curvature radius reflects the degree of curvature of the tunnel area. The more obvious the curvature, the greater the difference in the concrete accumulation or distribution state; the gravity influence factor quantifies the intensity of gravity on the concrete. The difference in gravity at different locations such as the arch and side walls will cause different concrete flow or deposition. Based on the dynamic adjustment of these characteristic parameters, the robot arm can flexibly adapt parameters in different structural areas such as the turning sections, arches, and side walls of the tunnel, so that the robot arm can flexibly adapt parameters according to the curvature characteristics and gravity differences in different areas of the tunnel, avoiding local accumulation or insufficient spraying that is prone to occur under fixed parameters, and ensuring the thickness consistency and solidification stability of the concrete lining in complex structural areas.

[0022] 2) The present invention extracts a section containing full curvature features from the three-dimensional digital model as an experimental surface and divides it into zones. After controlling the robotic arm to spray with initial parameters, the infrared thermal imaging array is used to obtain the concrete surface temperature data to determine the actual setting time deviation. The laser profile scanner is simultaneously used to obtain the surface point cloud in the initial setting stage to calculate the thickness deviation. The corresponding deviation values ​​are then stored using the curvature radius and the gravity influence factor as a two-dimensional index, and the unmeasured areas are supplemented through bicubic spline interpolation. At the same time, the least squares method is used to fit a piecewise linear velocity and flow compensation function based on the experimental data, and the predicted deviation is converted into a specific correction amount. This effectively reduces problems such as inconsistent setting time and excessive thickness, reduces the need for later manual repairs, and improves the quality stability of automated spraying.

[0023] 3) It can be understood that the moving spraying speed will indirectly affect the actual spraying flow rate value. Under the same flow rate, a slower speed will increase the amount of concrete per unit area. The present invention establishes an orthogonal experimental matrix of moving speed and spraying flow rate, tests the spraying effects of different parameter combinations in the experimental sub-area, calculates the setting time and thickness deviation, constructs a mapping relationship including the inverse of curvature, gravity influence factor and speed-flow product term, obtains the interaction influence coefficient through weighted solution, and finally superimposes the interaction effect compensation amount in the flow correction. The interaction compensation amount is used to correct the indirect influence of the spraying speed change on the spraying flow rate, solves the superposition error problem when the speed and flow rate are independently corrected, makes the parameter adjustment more accurate, further improves the uniformity of tunnel concrete spraying, and ensures the stability and durability of the lining structure.

[0024] In a preferred embodiment of the present invention, the specific process of generating the motion trajectory of the robotic arm in S1 is as follows: Extracting discrete feature points on the inner surface of the lining from the three-dimensional point cloud model and performing surface fitting to generate a continuous surface model; Generate multiple reference path lines parallel to the axis at a preset distance above the continuous curved surface model along the tunnel axis; discretize the reference path lines to obtain trajectory control points, and calculate the coordinates of each trajectory control point in the manipulator base coordinate system; Based on the limit parameters of the robot arm joint angles, the feasibility of the trajectory control points is verified and the points beyond the workspace are eliminated. The verified trajectory control points are then curve fitted to generate a continuous robot arm motion trajectory.

[0025] A 3D point cloud model is a collection of massive spatial points within the tunnel, acquired through methods such as laser scanning. These points contain information about the shape of the inner lining surface. By identifying points in the point cloud that are relevant to the inner lining surface (for example, based on whether the point's spatial position is within the preset range of the tunnel structure and whether the point's normal vector points into the tunnel interior), points that reflect the key morphology of the inner surface are selected as discrete feature points. These points, such as turning points at tunnel bends, the apex of the vault, and the connection points between the side wall and the vault, can outline the basic contours of the inner surface. Surface fitting is performed on these discrete feature points to generate a continuous surface model. This is because discrete points are scattered and cannot be directly used for trajectory planning. Surface fitting connects these points into a smooth, continuous surface according to their spatial distribution patterns, much like connecting discrete points with a curve to form a smooth curve. This fully presents the 3D shape of the inner lining surface and provides a basic shape reference for subsequent trajectory generation.

[0026] Multiple reference path lines parallel to the tunnel axis are generated at a preset distance above the continuous curved surface model. The "preset distance" is determined based on the effective operating range of the spraying device at the end of the robot arm, for example, ensuring that the spray gun maintains an appropriate distance from the lining surface to ensure effective spraying. The tunnel axis represents the direction of tunnel extension. Generating reference path lines parallel to the axis ensures that the path covers the entire length of the tunnel. Setting multiple path lines, such as one at a specific location in the center of the vault and on each side wall, ensures that the entire inner surface of the lining is sprayed, avoiding areas of missed spraying. The reference path lines are discretized to generate trajectory control points because a continuous path line cannot be directly executed by the robot arm. Instead, it needs to be decomposed into a series of specific spatial points. For example, a 10-meter-long reference line is divided into points at 0.5-meter intervals. These points are the trajectory control points, and the robot arm completes the entire path movement by sequentially reaching these points. Calculate the coordinates of each trajectory control point in the robot arm base coordinate system. The robot arm base coordinate system is a three-dimensional coordinate system established with the robot arm mounting base as the origin (for example, the center of the base is the origin, the X-axis is along the tunnel axis, the Y-axis is horizontal and perpendicular to the tunnel axis, and the Z-axis is vertically upward). By converting the coordinates of the trajectory control points in the surface model coordinate system (usually based on the global coordinate system during scanning) to the robot arm base coordinate system, the robot arm can accurately identify the position of each control point and thus plan its own movement.

[0027] When feasibility checking trajectory control points based on the robot arm's joint angle limits, each joint has a maximum and minimum rotation angle (for example, a rotary joint can rotate up to 170 degrees and down to -90 degrees), which is determined by the robot's structural design. For each trajectory control point, kinematic calculations determine the required rotation angles for each joint. If a joint's angle exceeds its limit, it indicates that the robot cannot maintain stable operation at that point or mechanical interference may occur. Such a point needs to be eliminated. For example, in a narrow corner of a tunnel, where the robot arm joint cannot rotate to the required angle, this point needs to be removed to prevent damage to the robot arm. Curve fitting is performed on the verified trajectory control points to generate a continuous robot arm motion trajectory. This is because the verified control points are still discrete. If the robot arm jumps directly from one point to the next, the motion will be jerky, affecting spraying uniformity. Curve fitting connects these points into a smooth, continuous curve, just like connecting multiple points with a smooth curve. This allows the robot arm to move smoothly along this curve, ensuring the continuity of the spraying process.

[0028] The mechanical arm plans a spraying path which conforms to the shape of the inner surface of the tunnel lining and adapts to the movement ability of the mechanical arm. Feature points are extracted from the point cloud and a curved surface is fitted, so that the trajectory is based on the real tunnel structure, and deviation of the trajectory from the actual surface due to model distortion is avoided; a plurality of reference path lines parallel to the axis are generated, so that the spraying range covers the entire lining inner surface and prevents missed spraying; the path is discretized into control points and the coordinates are converted, so that the mechanical arm can accurately identify each work position; unreachable points are checked and removed, so that the mechanical arm can avoid situations such as jamming, damage or work failure during movement; curve fitting is performed on the control points, so that the movement of the mechanical arm is smooth, and uneven spraying thickness caused by sudden movement is avoided. A reliable trajectory basis is provided for the subsequent mechanical arm to accurately and stably perform the spraying work according to the planned path, and finally the uniformity and efficiency of tunnel concrete spraying are achieved.

[0029] In another preferred embodiment of the present application, the specific construction process of the preset deviation mapping model in S3 is: S11, a preset length section containing full curvature characteristics is intercepted from the three-dimensional digital model of the construction tunnel as an experimental surface, the experimental surface is divided into a plurality of experimental sub-regions, and the mechanical arm is controlled to perform spraying work on each experimental sub-region at an initial spraying speed and an initial flow value; S12, the space-time evolution data of the concrete surface layer temperature is collected by an infrared thermal imaging array, the actual setting time is determined based on the inflection point of the temperature rise rate, and the difference between the actual setting time and the preset standard setting time is calculated as a setting time deviation value; The surface point cloud in the initial setting stage is obtained by a laser profile scanner, and the design surface corresponding to the experimental surface is extracted from the three-dimensional digital model; the directed distance of the point cloud to the design surface is calculated along the normal direction of the design surface as the actual construction thickness; and the median value of the difference between the actual construction thickness and the design thickness is taken as the thickness deviation value; S13, the curvature radius and the gravity influence factor of each experimental sub-region are obtained, the curvature radius value is taken as the first-dimensional index, the gravity influence factor value is taken as the second-dimensional index, the corresponding setting time deviation value and thickness deviation value are stored at the intersection of the two-dimensional indexes, and the deviation mapping model is obtained.

[0030] A segment of a preset length containing full curvature characteristics is extracted from the 3D digital model of the construction tunnel to serve as the experimental surface. Full curvature characteristics here refer to the segment covering all possible degrees of curvature in the tunnel, such as both low-curvature segments close to a straight line (e.g., straight tunnel sections with a large curvature radius) and high-curvature segments at turns (e.g., curved tunnel sections with a small curvature radius). This segment represents the curvature of different tunnel structures, paving the way for subsequent models to cover all operating conditions. The experimental surface is divided into several experimental sub-areas, such as multiple 1-meter-by-1-meter square sub-areas. Each sub-area serves as an independent test unit, facilitating separate data recording and analysis. The robotic arm is controlled to spray each experimental sub-area at an initial spraying speed and flow rate. The initial parameters are pre-set baseline values, such as an initial speed of 0.5 m / s and an initial flow rate of 10 liters / minute. This allows observation of deviations in different sub-areas due to their own characteristics (curvature, gravity effects), under uniform initial conditions. The spatial and temporal evolution data of the concrete surface temperature are collected using an infrared thermal imaging array. During the solidification process, concrete undergoes a hydration reaction, releasing heat, and the surface temperature changes over time. The infrared thermal imaging array can capture the spatial distribution and time series of this temperature change in real time. The actual solidification time is determined based on the inflection point of the temperature rise rate. Because during the concrete solidification process, the hydration reaction is fast in the early stage and the temperature rises quickly (the temperature rise rate is large). When it approaches solidification, the reaction slows down and the temperature rise rate will have a clear turning point (inflection point). The time corresponding to this inflection point is the actual solidification time. The difference between this and the preset standard solidification time is calculated as the solidification time deviation value. The preset standard solidification time is the solidification time of this type of concrete under ideal conditions, for example, 2 hours. If the actual measured solidification time of a sub-area is 2.2 hours, the deviation value is 0.2 hours.

[0031] Synchronization is obtained by laser profile scanner in the initial setting stage surface point cloud, the initial setting stage concrete has been initially formed but not completely hardened, the surface morphology at this time can reflect the actual shape after spraying, the laser profile scanner can generate three-dimensional point cloud data of the surface by emitting laser and receiving reflected signal; the design surface corresponding to the experimental surface is extracted from the three-dimensional digital model, the design surface is the ideal surface shape that the tunnel lining should achieve, and is the target reference of construction; the directed distance of point cloud to design surface is calculated as the actual construction thickness along the normal direction of design surface, the normal direction is perpendicular to the direction of design surface, the point cloud is on the outside of the design surface (sprayed too thick) and the distance is positive, on the inside (sprayed too thin) and the distance is negative, the distance directly reflects the actual spraying thickness; the difference between the actual construction thickness and the design thickness is taken as the thickness deviation value, and the statistical median value is because the deviation of a single point may be affected by accidental factors (such as local spatter), and the median value can more stably represent the overall thickness deviation of the sub-region, for example, the actual thickness of a sub-region has 10 measurement values, and the 5th value is taken as the median value after sorting. The curvature radius and gravity influence factor of each experimental sub-region are obtained, the curvature radius can be calculated by the bending degree of the surface where the sub-region is located, for example, a sub-region is located in a straight section, the curvature radius is 100 meters, and is located in a turning section, the curvature radius may be 20 meters; the gravity influence factor is the dot product absolute value of the unit normal vector of the lining surface of the sub-region and the gravity vector, for example, the normal vector of the vault is upward, and the angle between the downward gravity vector is close to 90 degrees, the dot product absolute value is small (such as 0.2), the normal vector of the side wall is horizontal, and the angle between the gravity vector is close to 0 degrees, the dot product absolute value is large (such as 0.8); the curvature radius value is taken as the first dimension index, and the gravity influence factor value is taken as the second dimension index, like establishing a two-dimensional table, the rows are different curvature radii, and the columns are different gravity influence factors; the corresponding setting time deviation and thickness deviation exist in the intersection position of the two-dimensional index, for example, when the curvature radius is 50 meters and the gravity influence factor is 0.5, the corresponding setting time deviation and thickness deviation exist in the intersection position, so as to form the deviation mapping model.

[0032] A correspondence was established between the initial values ​​of spraying parameters and actual construction deviations (setting time deviation and thickness deviation) under different curvature and gravity conditions. By extracting segments containing full curvature features and dividing them into subregions, the model ensures that all possible tunnel structural scenarios are covered, avoiding the narrowing of the model's applicability due to missed scenarios. Infrared thermal imaging and laser scanning were used to obtain setting time and thickness data, respectively, because these two methods accurately capture key quality indicators after concrete construction, and measurements based on concrete's inherent physical properties (hydration heat release and surface morphology) are more reliable. Statistical median values ​​were used as thickness deviations to reduce the impact of random errors on the data, making the deviations more representative. Deviations were stored using curvature and gravity factors as a two-dimensional index, because these two factors are the primary causes of spraying deviations. This correspondence allows the robot arm to subsequently operate by simply obtaining the curvature and gravity factors at its current position to identify the corresponding deviations in the model, providing a basis for parameter adjustment. This allows the deviation mapping model to accurately reflect the construction deviation patterns under different working conditions, laying the foundation for subsequent dynamic correction of spraying parameters, ultimately helping to achieve uniform and stable quality in tunnel concrete spraying.

[0033] In another preferred embodiment of the present invention, a bicubic spline interpolation algorithm is used to generate a continuous solidification time deviation field and a thickness deviation field at an unmeasured curvature-gravity factor combination position, and the interpolation mapping table is burned into the robotic arm control unit as a deviation mapping model.

[0034] When processing unmeasured curvature-gravity factor combinations, these locations refer to combinations of curvature radius and gravity factor that have not been measured in previous experiments. For example, a curvature radius of 10 meters, a gravity factor of 0.2, and a curvature radius of 30 meters, a gravity factor of 0.6 may have been measured in an experiment, but there is no measured data for a combination like a curvature radius of 20 meters and a gravity factor of 0.4. When using the bicubic spline interpolation algorithm, the algorithm first selects existing measured data points around these unmeasured locations. For example, for a point with a curvature of 20 meters and a gravity factor of 0.4, it finds four nearby measured points, such as (10, 0.2), (30, 0.2), (10, 0.6), and (30, 0.6). Then, based on the solidification time deviation and thickness deviation values ​​of these points, a smooth curve transition relationship is constructed on the two-dimensional plane. Because bicubic spline interpolation can simultaneously account for the changing trends of two dimensions (curvature and gravity factor), the calculated deviation values ​​for unmeasured locations are close to the adjacent measured values ​​while maintaining the continuity and smoothness of the entire data field. For example, the deviation change from (10, 0.2) to (30, 0.6) does not show a sudden jump. In this way, a continuous solidification time deviation field and thickness deviation field can be generated. The deviation field here can be understood as a complete two-dimensional data surface. Regardless of the values ​​of the curvature and gravity factor, the corresponding deviation value can be found on this surface. For example, the corresponding deviation data for previously unmeasured combinations such as a curvature of 15 meters and a gravity factor of 0.3 or a curvature of 25 meters and a gravity factor of 0.5 can be obtained through this continuous field. Afterwards, the interpolated mapping table is burned into the robotic arm control unit. The mapping table is a complete data set containing all curvature-gravity factor combinations and their corresponding deviation values. The burning process is to store this data set in the storage component of the robotic arm control unit. In this way, when the robotic arm is actually working, it only needs to obtain the curvature and gravity influence factors of the current position, and can quickly retrieve the corresponding deviation value directly from the control unit without the need for real-time calculation.

[0035] It is impossible to measure all possible curvature-gravity factor combinations in the experimental stage, because the values of curvature and gravity influence factors are continuously changing, and experiments can only cover a limited number of discrete points. If the unmeasured positions are not processed, the robot arm has no corresponding deviation data as a basis for parameter adjustment when encountering these situations, which may lead to inaccurate adjustment. The use of a bicubic spline interpolation algorithm can fill in the blanks of these unmeasured positions, and the continuous deviation field generated can ensure smooth transition of the data, avoiding sudden changes in parameter adjustment due to data breaks. Burning the mapping table to the control unit allows the robot arm to quickly obtain the required data during operation, ensuring the real-time nature of parameter adjustment and preventing data calculation delays from affecting construction. The deviation mapping model can cover all possible curvature and gravity scenarios encountered during tunnel construction, providing accurate basis for parameter adjustment of the robot arm at any position, ultimately helping to achieve uniformity and stability of tunnel concrete spraying, and ensuring that the construction quality meets the requirements.

[0036] In another preferred embodiment of the present application, the specific process of correcting the initial mechanical arm movement speed in S5 is: Spraying is performed at a stepwise varying speed in the experimental tunnel section, and the spraying flow value is kept constant. The actual setting time deviation of the concrete under different spraying speeds is recorded, and the response relationship between the setting time deviation and the speed correction is fitted by the least squares method to generate a segmented linear speed compensation function: The setting time prediction deviation output by the deviation mapping model is input into the speed compensation function to obtain the speed correction amount, and the final speed correction instruction is output to the mechanical arm driver.

[0037] In the experimental tunnel section, spraying is performed at a step-by-step speed, keeping the spraying flow rate constant. An experimental section is pre-determined based on the actual construction tunnel structure, and the spraying flow rate is set to a fixed value (for example, 15 liters of concrete are delivered per minute). Then, the robotic arm is allowed to spray in sections at different speeds. The speed step change can start from 0.2 m / s and increase by 0.1 m / s each time, and then complete the spraying of a small area at speeds of 0.2 m / s, 0.3 m / s, 0.4 m / s, etc. This is done to observe the impact of speed changes on the concrete setting time under the condition of a single variable (speed) and eliminate the interference of flow changes. Because if the flow and speed are changed at the same time, it is impossible to distinguish which factor causes the deviation in the setting time. Recording the deviation of the actual setting time of concrete at different spraying speeds means that after each step speed spraying is completed, the actual setting time of the concrete in that area is measured using a previously determined method (such as infrared thermal imaging array monitoring the inflection point of the temperature rise rate), and then compared with the preset standard setting time to obtain the deviation value corresponding to each speed. For example, at 0.2 m / s, the deviation is +0.3 hours (slow setting), and at 0.4 m / s, the deviation is -0.2 hours (fast setting). The least squares method is used to fit the response relationship between solidification time deviation and speed correction. The speed correction here refers to the speed value that needs to be adjusted to eliminate a specific solidification time deviation (for example, to eliminate a deviation of +0.3 hours, the speed may need to be increased by 0.1 m / s from the initial value; this 0.1 m / s is the correction). The role of the least squares method is to find a line that best reflects the corresponding relationship between all measured deviations and correction values ​​by calculation, so that the sum of the distances from each measured point to this line is minimized, thereby more accurately reflecting the inherent relationship between the two. The piecewise linear speed compensation function is generated because the relationship between solidification time deviation and speed correction value may exhibit different linear characteristics within different speed ranges. For example, when the speed is below 0.3 m / s, the rate of change of the deviation with the correction value is larger, while the rate of change is smaller when the speed is above 0.3 m / s. Therefore, the entire speed range is divided into two segments, and linear relationships are fitted to form a segmented compensation function. The predicted solidification time deviation output by the deviation mapping model is input into the speed compensation function. For example, if the model predicts that the solidification time deviation at the current position is +0.2 hours, after entering the function, the function will calculate the need to increase the speed by 0.08 m / s based on the corresponding piecewise linear relationship. This 0.08 m / s is the speed correction amount; the final speed correction instruction is output to the robot arm driver, that is, the calculated speed correction amount is converted into a control signal that the robot arm can recognize, and sent to the component that drives the movement of the robot arm, so that the robot arm moves according to the corrected speed (initial speed plus or minus the correction amount).

[0038] The robot's movement speed directly affects the dwell time of concrete per unit area, which in turn affects setting time. Slower speeds result in denser spraying of concrete, creating a more stable hydration reaction environment and potentially slower setting. Faster speeds result in thinner spraying, faster heat dissipation, and potentially faster setting. Therefore, adjusting the setting time requires speed correction. Maintaining a constant spray flow rate isolates the effect of spray speed on setting time, avoiding interference from other factors and ensuring a more accurate relationship between speed and setting deviation. Least squares fitting allows the resulting response relationship to better align with actual measurement data, reducing the impact of random errors. Generating a piecewise linear function is important because the effect of speed on setting time may vary across different intervals, and piecewise fitting improves compensation accuracy. Inputting the predicted deviation into the compensation function generates a correction value and outputs a command. This allows the robot to adjust its speed in real time based on the predicted setting deviation at its current position, keeping the setting time as close to the standard as possible during actual construction. By dynamically correcting the movement speed of the robotic arm, the problem of inconsistent solidification time at different locations due to factors such as curvature and gravity is solved, ultimately helping to achieve uniform solidification of tunnel concrete spraying and ensure stable lining quality.

[0039] In another preferred embodiment of the present invention, in S6, the specific process of correcting the initial spray flow rate is: In the experimental tunnel section, spraying was performed with step-wise varying spray flow rates, while maintaining a constant robotic arm movement speed. The concrete thickness deviations at different flow rates were recorded, and the response relationship between the thickness deviation and the flow correction coefficient was fitted using the least squares method to generate a piecewise linear flow compensation function: The thickness prediction deviation output by the deviation mapping model is input into the flow compensation function, the basic flow correction coefficient is calculated, and the final spray flow correction instruction is output to the robot arm driver.

[0040] Concrete thickness is primarily determined by the volume of concrete sprayed per unit area. When the robot arm's movement speed is fixed, the spray flow rate is the key factor in determining this volume. Excessive or insufficient flow rates can cause thickness deviations from the designed value, necessitating flow rate correction to adjust the thickness. Maintaining a constant robot arm movement speed eliminates velocity interference with thickness, ensuring that measured thickness deviations are solely due to flow rate variations, thus improving the relationship between flow rate and thickness deviation. Using the least squares method to fit the relationship between thickness deviation and flow rate correction coefficients allows the fitting results to better align with actual measurement data and reduce the impact of random errors. Generating a piecewise linear compensation function is crucial because the effect of flow rate on thickness may vary across different intervals, and piecewise fitting improves the accuracy of flow rate correction. The predicted deviation output by the deviation mapping model is input into the compensation function to generate correction coefficients and output instructions. This allows the robot arm to adjust the spray flow rate in real time based on the thickness deviation prediction at the current location, ensuring that the actual thickness is as close to the designed value as possible. Dynamically correcting the spray flow rate addresses uneven thickness at different locations due to factors such as curvature and gravity, ultimately helping to achieve consistent thickness in tunnel concrete spraying and ensuring the stability and safety of the lining structure.

[0041] In another preferred embodiment of the present invention, said S3 further includes that the gravity vector is in the negative direction of the Z axis of the earth coordinate system, and the coordinate transformation is corrected in real time by an inclination sensor installed on the base of the robotic arm.

[0042] The accuracy of the gravity vector's direction and the correctness of the coordinate transformation directly impact the calculation of the gravity influence factor, which serves as a crucial basis for subsequent deviation mapping models and parameter corrections. The gravity vector is set to the negative Z-axis of the geodetic coordinate system to ensure that the theoretical direction of gravity aligns with the actual physical direction of gravity, thus avoiding subsequent calculation errors caused by incorrectly defined directions. When the manipulator is installed in a tunnel, its base may tilt due to uneven ground or installation errors, causing its coordinate system to be non-parallel to the geodetic coordinate system. Failure to correct the coordinate transformation will lead to an error in the calculated relative angle between the unit normal vector and the gravity vector, resulting in distortion of the gravity influence factor. Real-time correction using a tilt sensor ensures that the coordinate transformation remains accurate regardless of the manipulator base's tilt, ensuring that the calculated gravity influence factor is consistent with the actual situation. This ensures the accuracy of the gravity influence factor, providing a reliable foundation for subsequent deviation prediction and parameter correction based on this factor. Ultimately, this allows the manipulator to precisely adjust spraying parameters at different positions, improving the uniformity of concrete spraying in tunnels.

[0043] In another preferred embodiment of the present invention, said S6 further comprises establishing a moving speed parameter gradient set and a spray flow parameter gradient set in said experimental sub-area to form an orthogonal experimental matrix; For any combination of moving speed and spraying flow in the orthogonal experimental matrix, control the robotic arm to perform spraying with the speed parameter and flow parameter set as constant values; Calculate the coagulation time deviation and thickness deviation of each experimental sub-area; establish the mapping relationship between the coagulation time deviation and the inverse of curvature, gravity influence factor, and velocity and flow product; Establish the mapping relationship between thickness deviation and the inverse of curvature, gravity influence factor, and velocity and flow product; Solving the coefficient of the product term of velocity and flow in the mapping relationship by weighted least squares method; extracting the ratio of the product term coefficient to the initial spraying parameter to generate a standardized interaction coefficient; Obtaining a change in the movement speed of the robot arm before and after correction, and calculating an interaction effect compensation amount based on the change in the movement speed and a standardized interaction influence coefficient; The interaction effect compensation amount is superimposed on the basic flow correction coefficient to generate a final flow correction coefficient, and the robotic arm is controlled to adjust the spray flow according to the final flow correction coefficient.

[0044] In the experimental sub-area, several different values ​​of the moving speed are first determined to form a gradient set. For example, taking the initial moving speed as the benchmark, several different speed values ​​are taken upward and downward. At the same time, several different values ​​of the spray flow rate are determined to form a gradient set. Similarly, the initial flow rate is used as the benchmark to select up and down. These speed values ​​and flow values ​​are matched with each other to form an orthogonal experimental matrix. This is done to cover different speed and flow combinations, avoid repeated experiments, and fully reflect the situations under different parameter combinations. Afterwards, any set of moving speeds and spraying flow rates are selected from the orthogonal experimental matrix. For example, a set of lower speeds and medium flow rates is selected, and the robotic arm is controlled to continuously spray at this set of speeds and flow rates in the experimental sub-area. These two parameters are kept unchanged during the entire process, which ensures that the experimental results under this set of parameters are stable and not affected by parameter fluctuations. Next, the setting time deviation of each experimental sub-area is calculated. Specifically, the temperature change during the concrete solidification process is observed. When the temperature rise rate slows down significantly, the corresponding time is the actual setting time. The actual setting time is subtracted from the pre-set standard setting time of this type of concrete. The difference is the setting time deviation. At the same time, the thickness deviation is calculated. The distance from each surface point to the designed lining surface is obtained by laser scanning the concrete surface after initial setting. These distances are the actual construction thickness. The actual construction thickness is subtracted from the designed thickness, and the value in the middle of these differences is selected as the thickness deviation, because the value in the middle is less affected by extreme values ​​and can better represent the overall thickness deviation of the area. After that, a mapping relationship between the setting time deviation and multiple factors is established, including the inverse of the curvature, which is the inverse of the curvature radius. The smaller the curvature radius, the larger the inverse, which means the more obvious the curvature of the area. The curvature will affect the accumulation of concrete and thus affect the setting time. The gravity influence factor is the absolute value of the dot product of the unit normal vector of the lining surface and the gravity direction. For example, the normal vector at the arch is upward, and the angle with the downward gravity direction is large, so the absolute value of the dot product is small. The angle at the side wall is small, and the absolute value of the dot product is large. Different gravity effects will lead to different concrete flow or accumulation, which in turn affects the setting time. There is also a product term of speed and flow, because when speed and flow act together, they will affect the amount and residence time of concrete per unit area, which in turn affects the setting time. Similarly, a mapping relationship is established between the thickness deviation and these terms, because these factors will also affect the thickness of the concrete. Then, the coefficient of the product term of velocity and flow in the mapping relationship is solved by the weighted least squares method. The ratio of the product term coefficient to the initial spraying parameters (the product of initial velocity and initial flow) is extracted to generate a standardized interaction coefficient. This can eliminate the influence of different initial parameter sizes and make the interaction coefficients under different regions and different initial parameters comparable. Afterwards, the change in the moving speed of the robotic arm before and after correction is obtained, that is, the difference between the corrected speed and the initial speed. Based on this change and the previously obtained standardized interaction coefficient, the interaction effect compensation is calculated. Because after the speed changes, even if the flow rate remains unchanged, the amount of concrete per unit area will change. This compensation is needed to adjust the flow correction to cope with the impact of the speed change; finally, the basic flow correction coefficient (the flow correction coefficient calculated only based on the thickness deviation) is added to the interaction effect compensation to obtain the final flow correction coefficient, and the robotic arm is controlled to adjust the spraying flow according to this final flow correction coefficient.

[0045] It can be understood that the mutual influence between the moving speed and the spraying flow rate will cause inaccurate individual spraying flow rate correction, for example, when the moving speed slows down, even if the flow rate remains unchanged, the amount of concrete per unit area will increase, at this time, if only the flow rate is individually corrected according to the thickness deviation, it may cause overcorrection, and the orthogonal experiment matrix can comprehensively cover different speed and flow rate combinations, ensure that the combined effect of the two is captured, and the mapping relationship containing multiple factors can clearly show the influence of each factor on the deviation, especially the interaction of speed and flow rate, weighted solution coefficients can make the influence of key areas more important, make the results more in line with actual needs, standardized interaction coefficients can make the interaction under different conditions comparable, facilitate unified calculation, and interaction effect compensation can correct the influence of speed change on flow rate correction. The final flow rate correction coefficient obtained by superimposition can make the flow rate adjustment consider the influence of thickness deviation and speed change, make the thickness of the concrete spraying more uniform, meet the design requirements, thereby improving the quality of tunnel concrete spraying, and ensuring the stability of the lining structure.

[0046] The above describes one embodiment of the present application in detail, but the content described is only the preferred embodiment of the present application, and cannot be considered as limiting the scope of the present application. Any equivalent changes and improvements made within the scope of the present application should still belong to the patent scope of the present application.

Claims

1. A method for controlling a robotic arm for concrete spraying in tunnel engineering, characterized in that: The following steps are involved: S1, obtaining a three-dimensional point cloud model of the construction tunnel, and generating a robot arm motion trajectory based on the three-dimensional point cloud model, calibrating the robot arm motion trajectory as a construction path and setting an initial spraying speed and an initial spraying flow rate value; S2, collects the curvature radius of the current spraying point on the motion trajectory in real time through the curvature sensing unit integrated at the end of the robotic arm; S3, obtaining a unit normal vector of the lining surface at the current spraying point based on the three-dimensional digital model, calculating an absolute value of a dot product of the unit normal vector and a gravity vector and using the result as a gravity influencing factor; S4, inputting the curvature radius and gravity influence factor into a preset deviation mapping model to obtain a predicted solidification time deviation and a predicted thickness deviation corresponding to the current spraying point; S5, correcting the initial robot arm movement speed based on the solidification time deviation, and controlling the robot arm to spray along the construction path at the corrected movement speed; S6, correcting the initial spraying flow rate based on the thickness prediction deviation, and controlling the robotic arm to spray along the construction path according to the corrected spraying flow rate.

2. The method for controlling a mechanical arm for concrete spraying in tunnel engineering according to claim 1, characterized in that: In S1, the specific process of generating the motion trajectory of the robotic arm is as follows: Extracting discrete feature points on the inner surface of the lining from the three-dimensional point cloud model and performing surface fitting to generate a continuous surface model; Generate multiple reference path lines parallel to the axis at a preset distance above the continuous surface model along the tunnel axis; Discretize the reference path line to obtain the trajectory control points, and calculate the coordinates of each trajectory control point in the robot arm base coordinate system; Based on the limit parameters of the robot arm joint angle, the feasibility of the trajectory control points is checked and the points beyond the workspace are eliminated; The verified trajectory control points are subjected to curve fitting to generate a continuous robotic arm motion trajectory.

3. The method for controlling a mechanical arm for concrete spraying in tunnel engineering according to claim 1, characterized in that: In S3, the specific construction process of the preset deviation mapping model is as follows: S11, intercepting a preset length segment containing full curvature features from the three-dimensional digital model of the construction tunnel as an experimental surface, dividing the experimental surface into a plurality of experimental sub-areas, and controlling the robotic arm to perform a spraying operation on each experimental sub-area at an initial spraying speed and an initial flow rate value; S12, collecting spatiotemporal evolution data of the concrete surface temperature through an infrared thermal imaging array, determining the actual solidification time based on the temperature rise rate inflection point, and calculating the difference between the actual solidification time and the preset standard solidification time as the solidification time deviation value; A laser profile scanner is used to simultaneously obtain a surface point cloud during the initial setting phase, and the design surface corresponding to the experimental surface is extracted from the 3D digital model. The directed distance from the point cloud to the design surface is calculated along the normal direction of the design surface as the actual construction thickness. The median value of the difference between the actual construction thickness and the design thickness is statistically calculated as the thickness deviation value. S13, obtaining the curvature radius and gravity influence factor of each experimental sub-area, using the curvature radius value as the first-dimensional index and the gravity influence factor value as the second-dimensional index, storing the corresponding solidification time deviation value and thickness deviation value at the intersection of the two-dimensional index to obtain a deviation mapping model.

4. The method for controlling a mechanical arm for concrete spraying in tunnel engineering according to claim 3, characterized in that: It also includes using a bicubic spline interpolation algorithm to generate a continuous solidification time deviation field and a thickness deviation field at an unmeasured curvature-gravity factor combination position, and burning the interpolation-completed mapping table into the robotic arm control unit as a deviation mapping model.

5. The method for controlling a mechanical arm for concrete spraying in tunnel engineering according to claim 1, characterized in that: In S5, the specific process of correcting the initial robot arm movement speed is as follows: In the experimental tunnel section, spraying was performed at a step-by-step speed, keeping the spray flow rate constant. The actual setting time deviation of the concrete at different spraying speeds was recorded, and the response relationship between the setting time deviation and the speed correction was fitted using the least squares method to generate a piecewise linear speed compensation function: The predicted solidification time deviation output by the deviation mapping model is input into the speed compensation function to obtain a speed correction value, and a final speed correction instruction is output to the robot arm driver.

6. The method for controlling a mechanical arm for concrete spraying in tunnel engineering according to claim 1, characterized in that: In S6, the specific process of correcting the initial spray flow rate is as follows: In the experimental tunnel section, spraying was performed with step-wise varying spray flow rates, while maintaining a constant robotic arm movement speed. The concrete thickness deviations at different flow rates were recorded, and the response relationship between the thickness deviation and the flow correction coefficient was fitted using the least squares method to generate a piecewise linear flow compensation function: The thickness prediction deviation output by the deviation mapping model is input into the flow compensation function, the basic flow correction coefficient is calculated, and the final spray flow correction instruction is output to the robot arm driver.

7. The method for controlling a mechanical arm for concrete spraying in tunnel engineering according to claim 1, characterized in that: In the above S3, the gravity vector is in the negative direction of the Z axis of the earth coordinate system, and the coordinate transformation is corrected in real time by an inclination sensor installed on the base of the robotic arm.

8. The method for controlling a mechanical arm for concrete spraying in tunnel engineering according to claim 6, characterized in that: Said S6 further includes establishing a moving speed parameter gradient set and a spray flow parameter gradient set in said experimental sub-area to form an orthogonal experimental matrix; For any combination of moving speed and spraying flow in the orthogonal experimental matrix, control the robotic arm to perform spraying with the speed parameter and flow parameter set as constant values; Calculate the coagulation time deviation and thickness deviation of each experimental sub-area; establish the mapping relationship between the coagulation time deviation and the inverse of curvature, gravity influence factor, and velocity and flow product; Establish the mapping relationship between thickness deviation and the inverse of curvature, gravity influence factor, and velocity and flow product; Solving the coefficient of the product term of velocity and flow in the mapping relationship by weighted least squares method, extracting the ratio of the product term coefficient to the initial spraying parameter, and generating a standardized interaction coefficient; Obtaining a change in the movement speed of the robot arm before and after correction, and calculating an interaction effect compensation amount based on the change in the movement speed and a standardized interaction influence coefficient; The interaction effect compensation amount is superimposed on the basic flow correction coefficient to generate a final flow correction coefficient, and the robotic arm is controlled to adjust the spray flow according to the final flow correction coefficient.

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