Mechanical arm control method for tunnel engineering concrete spraying

Abstract

The application discloses a mechanical arm control method for tunnel engineering concrete spraying, and belongs to the technical field of mechanical arm control, and specifically comprises the following steps: acquiring a three-dimensional point cloud model of a construction tunnel, and generating a mechanical arm motion trajectory based on the three-dimensional point cloud model and setting an initial spraying speed and flow; acquiring a current spraying point curvature radius in real time through a mechanical arm end curvature sensing unit and obtaining a point lining surface unit normal vector based on the three-dimensional model, calculating the absolute value of the dot product of the point lining surface unit normal vector and a gravity vector 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; correcting the initial speed and flow based on the solidification time and thickness prediction deviations and controlling the mechanical arm to spray; and the application realizes the thickness consistency and solidification stability of concrete lining in different regions of a tunnel and improves spraying uniformity.

Description

Technical Field

[0001] This invention relates to the field of robotic arm control technology, and more specifically to a robotic arm control method for concrete spraying in tunnel engineering. Background Technology

[0002] In tunnel engineering, concrete lining is a crucial component ensuring the stability and durability of the tunnel structure, and the quality of its spraying directly affects the safety and service life of the project. However, due to the complexity of tunnel structures, the concrete spraying process often faces the problem of insufficient uniformity caused by special structural features, becoming a significant bottleneck restricting construction efficiency and quality.

[0003] Currently, tunnel concrete spraying relies heavily on automated robotic arm operations. The concrete spraying operation in tunnel engineering is achieved through the connection of multiple sub-processes such as "one spray, two sprays, one scraper, three sprays, two scrapers, and one sweeping". However, for scenarios where the wall surface is pre-leveled manually and then filled with thickness by robotic arms, the existing methods lack specific adaptation to the reference surface of manual pre-treatment. The existing robotic arm control methods generally use fixed motion parameters and spraying parameters, which are difficult to adapt to the diverse structural scenarios in tunnels. On the one hand, tunnels have a large number of curved structures (such as turning sections, transition areas between the arch and sidewalls, etc.), and the curvature of 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 a deviation in the thickness of the deposited layer exceeding the design allowable range. On the other hand, the effect of gravity on concrete spraying has significant spatial variability—in the arch area, concrete is prone to flow due to gravity, while in the sidewall area, gravity deposition may lead to excessive thickness. Traditional control methods have not made adaptive adjustments to this spatial variation of gravity influence, further exacerbating the problem of uneven spraying.

[0004] The aforementioned problems often result in defects in the concrete lining after construction, such as localized areas exceeding or falling short of the required thickness, and inconsistent setting times. This not only necessitates extensive manual repairs to meet design requirements, increasing construction costs and time, but also risks leaving structural safety hazards due to incomplete repairs. While some existing technologies attempt to improve construction results through simple parameter adjustments, none systematically consider the coupling effect of path curvature and gravity, making dynamic and precise parameter control difficult and failing to fundamentally solve the problem of uneven concrete spraying under the special structure of tunnels. Summary of the Invention

[0005] The purpose of this invention is to provide a robotic arm control method for concrete spraying in tunnel engineering, and to solve the following technical problems:

[0006] How to adjust the dynamic parameters of the robotic arm to address the effects of path curvature and gravity, and solve the problem of uneven concrete spraying under the special structure of the tunnel.

[0007] The objective of this invention can be achieved through the following technical solutions:

[0008] A robotic arm control method for concrete spraying in tunnel engineering includes the following steps:

[0009] S1. Obtain a three-dimensional point cloud model of the construction tunnel, and generate a robotic arm motion trajectory based on the three-dimensional point cloud model. Mark the robotic arm motion trajectory as the construction path and set the initial spraying speed and initial spraying flow rate.

[0010] S2, through the curvature sensing unit integrated at the end of the robotic arm, collects the curvature radius of the current spraying point on the motion trajectory in real time;

[0011] S3. Based on the three-dimensional digital model, obtain the unit normal vector of the lining surface at the current spraying point, calculate the absolute value of the dot product of the unit normal vector and the gravity vector, and use it as the gravity influence factor.

[0012] S4. Input the radius of curvature and gravity influence factor into the preset deviation mapping model to obtain the solidification time prediction deviation and thickness prediction deviation corresponding to the current spraying point.

[0013] S5, Based on the solidification time deviation, the initial robotic arm moving speed is corrected, and the robotic arm is controlled to spray along the construction path at the corrected moving speed;

[0014] S6, based on the thickness prediction deviation, the initial spraying flow rate is corrected, and the robotic arm is controlled to spray along the construction path according to the corrected spraying flow rate.

[0015] As a further aspect of the present invention: the specific process of generating the robotic arm motion trajectory in S1 is as follows:

[0016] Discrete feature points of the inner surface of the lining are extracted from the three-dimensional point cloud model and surface fitting is performed to generate a continuous surface model.

[0017] Multiple reference path lines parallel to the tunnel axis are generated at a preset distance above the continuous curved surface model; the reference path lines are discretized to obtain trajectory control points, and the coordinates of each trajectory control point in the robot arm's base coordinate system are calculated;

[0018] Based on the limit parameters of the robotic arm joint angles, the feasibility of the trajectory control points is verified, and points that exceed the workspace are eliminated; curve fitting is performed on the verified trajectory control points to generate a continuous robotic arm motion trajectory.

[0019] As a further aspect of the present invention: in S3, the specific construction process of the preset deviation mapping model is as follows:

[0020] S11, a preset length segment containing full curvature features is extracted from the three-dimensional digital model of the construction tunnel as an experimental surface, the experimental surface is divided into several experimental sub-regions, and the robotic arm is controlled to perform spraying operations on each experimental sub-region with an initial spraying speed and an initial flow rate.

[0021] S12: The spatiotemporal evolution data of concrete surface 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 the setting time deviation value.

[0022] Simultaneously, surface point clouds during the initial setting stage are acquired using a laser contour scanner, 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 and used as the actual construction thickness. The median value of the difference between the actual construction thickness and the design thickness is statistically analyzed and used as the thickness deviation value.

[0023] S13. Obtain the radius of curvature and gravity influence factor of each experimental sub-region. Use the radius of curvature as the first dimension index and the gravity influence factor as the second dimension index. Store the corresponding solidification time deviation value and thickness deviation value at the intersection of the two-dimensional indexes to obtain the deviation mapping model.

[0024] As a further aspect of the present invention, it also includes generating a continuous solidification time deviation field and a thickness deviation field at the unmeasured curvature-gravity factor combination location using a bicubic spline interpolation algorithm, and burning the interpolated mapping table into the robotic arm control unit as a deviation mapping model.

[0025] As a further aspect of the present invention: the specific process of correcting the initial robotic arm moving speed in step S5 is as follows:

[0026] Spraying was performed at a stepped speed in the experimental tunnel section while maintaining a constant spraying flow rate. The actual setting time deviation of the concrete was recorded at different spraying speeds. 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.

[0027] The solidification 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 command is output to the robot arm driver.

[0028] As a further aspect of the present invention: the specific process of correcting the initial spraying flow rate in step S6 is as follows:

[0029] Spraying was performed in the experimental tunnel section with stepped spray flow rates while maintaining a constant robotic arm movement speed. The concrete forming thickness deviation under different flow rates was recorded. The response relationship between the thickness deviation and the flow rate correction coefficient was fitted using the least squares method to generate a piecewise linear flow rate compensation function.

[0030] The thickness prediction deviation output by the deviation mapping model is input into the flow compensation function to calculate the basic flow correction coefficient, and the final spraying flow correction command is output to the robotic arm driver.

[0031] As a further aspect of the present invention: S3 further includes the gravity vector being in the negative direction of the Z-axis of the geodetic coordinate system, and the coordinate transformation is corrected in real time by an inclination sensor installed on the base of the robotic arm.

[0032] As a further aspect of the present invention: S6 further includes establishing a set of gradients for moving speed parameters and a set of gradients for spraying flow rate parameters within the experimental sub-region, forming an orthogonal experimental matrix;

[0033] For any combination of moving speed and spraying flow rate in the orthogonal experimental matrix, the robotic arm is controlled to perform spraying with the speed and flow rate parameters as constant values.

[0034] Calculate the solidification time deviation and thickness deviation for each experimental sub-region; establish the mapping relationship between the solidification time deviation and the inverse of curvature term, gravity influence factor term, and velocity-flow product term;

[0035] Establish the mapping relationship between thickness deviation and the inverse of curvature, gravity influence factor, and velocity-flow product;

[0036] The coefficients of the velocity-flow product term in the mapping relationship are solved by weighted least squares method; the ratio of the product term coefficients to the initial spraying parameters is extracted to generate standardized interaction influence coefficients.

[0037] Obtain the change in the movement speed of the robotic arm before and after correction, and calculate the interaction effect compensation based on the change in movement speed and the standardized interaction effect coefficient.

[0038] The interaction effect compensation is added to the basic flow correction coefficient to generate the final flow correction coefficient, and the robotic arm is controlled to adjust the spraying flow according to the final flow correction coefficient.

[0039] The beneficial effects of this invention are:

[0040] 1) This invention obtains the radius of curvature and gravity influence factor of the current spraying point in real time, and combines this with a preset deviation mapping model to obtain the predicted deviation of solidification time and thickness. This allows for targeted correction of the initial spraying speed and flow rate. The radius of curvature reflects the degree of curvature in the tunnel area; the more pronounced the curvature, the greater the difference in concrete accumulation or distribution. The gravity influence factor quantifies the intensity of gravity's effect on concrete; differences in gravity at different locations, such as the arch and sidewalls, lead to different concrete flow or deposition patterns. Based on the dynamic adjustment of these characteristic parameters, the robotic arm can flexibly adapt parameters in different structural areas of the tunnel, such as curves, arches, and sidewalls. This allows the robotic arm to flexibly adapt parameters according to the curvature characteristics and gravity differences in different areas of the tunnel, avoiding localized accumulation or insufficient spraying that easily occurs with fixed parameters, and ensuring the thickness consistency and solidification stability of the concrete lining in complex structural areas.

[0041] 2) This invention extracts a segment containing full curvature features from a three-dimensional digital model as an experimental surface and divides it into sections. After controlling the robotic arm to spray with initial parameters, the surface temperature data of the concrete is obtained through an infrared thermal imaging array to determine the actual setting time deviation. Simultaneously, a laser contour scanner is 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 radius of curvature and gravity influence factor as a two-dimensional index. The unmeasured areas are completed by bicubic spline interpolation. At the same time, based on the experimental data, a piecewise linear velocity and flow compensation function is fitted using the least squares method to convert the predicted deviation into a specific correction amount. This effectively reduces problems such as inconsistent setting time and excessive thickness, reduces the need for manual repairs in the later stage, and improves the quality stability of automated spraying.

[0042] 3) It can be understood that the moving spraying speed indirectly affects the actual spraying flow rate. Under the same flow rate, a slower speed will increase the amount of concrete per unit area. This invention establishes an orthogonal experimental matrix of moving speed and spraying flow rate, tests the spraying effect of different parameter combinations in the experimental sub-region, calculates the setting time and thickness deviation, constructs a mapping relationship including the inverse of curvature, gravity influence factor and speed-flow rate product, obtains the interaction influence coefficient through weighted solution, and finally superimposes the interaction effect compensation amount in the flow rate 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 corrected independently, makes the parameter adjustment more accurate, further improves the uniformity of tunnel concrete spraying, and ensures the stability and durability of the lining structure. Attached Figure Description

[0043] The invention will now be further described with reference to the accompanying drawings.

[0044] Figure 1 This is a schematic diagram of the robotic arm control method for concrete spraying in tunnel engineering according to the present invention. Detailed Implementation

[0045] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0046] Please see Figure 1 As shown, the present invention is a robotic arm control method for concrete spraying in tunnel engineering, comprising the following steps:

[0047] S1. Obtain a three-dimensional point cloud model of the construction tunnel, and generate a robotic arm motion trajectory based on the three-dimensional point cloud model. Mark the robotic arm motion trajectory as the construction path and set the initial spraying speed and initial spraying flow rate.

[0048] S2, through the curvature sensing unit integrated at the end of the robotic arm, collects the curvature radius of the current spraying point on the motion trajectory in real time;

[0049] S3. Based on the three-dimensional digital model, obtain the unit normal vector of the lining surface at the current spraying point, calculate the absolute value of the dot product of the unit normal vector and the gravity vector, and use it as the gravity influence factor.

[0050] S4. Input the radius of curvature and gravity influence factor into the preset deviation mapping model to obtain the solidification time prediction deviation and thickness prediction deviation corresponding to the current spraying point.

[0051] S5, Based on the solidification time deviation, the initial robotic arm moving speed is corrected, and the robotic arm is controlled to spray along the construction path at the corrected moving speed;

[0052] S6, based on the thickness prediction deviation, the initial spraying flow rate is corrected, and the robotic arm is controlled to spray along the construction path according to the corrected spraying flow rate.

[0053] 1) This invention obtains the radius of curvature and gravity influence factor of the current spraying point in real time, and combines this with a preset deviation mapping model to obtain the predicted deviation of solidification time and thickness. This allows for targeted correction of the initial spraying speed and flow rate. The radius of curvature reflects the degree of curvature in the tunnel area; the more pronounced the curvature, the greater the difference in concrete accumulation or distribution. The gravity influence factor quantifies the intensity of gravity's effect on concrete; differences in gravity at different locations, such as the arch and sidewalls, lead to different concrete flow or deposition patterns. Based on the dynamic adjustment of these characteristic parameters, the robotic arm can flexibly adapt parameters in different structural areas of the tunnel, such as curves, arches, and sidewalls. This allows the robotic arm to flexibly adapt parameters according to the curvature characteristics and gravity differences in different areas of the tunnel, avoiding localized accumulation or insufficient spraying that easily occurs with fixed parameters, and ensuring the thickness consistency and solidification stability of the concrete lining in complex structural areas.

[0054] 2) This invention extracts a segment containing full curvature features from a three-dimensional digital model as an experimental surface and divides it into sections. After controlling the robotic arm to spray with initial parameters, the surface temperature data of the concrete is obtained through an infrared thermal imaging array to determine the actual setting time deviation. Simultaneously, a laser contour scanner is 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 radius of curvature and gravity influence factor as a two-dimensional index. The unmeasured areas are completed by bicubic spline interpolation. At the same time, based on the experimental data, a piecewise linear velocity and flow compensation function is fitted using the least squares method to convert the predicted deviation into a specific correction amount. This effectively reduces problems such as inconsistent setting time and excessive thickness, reduces the need for manual repairs in the later stage, and improves the quality stability of automated spraying.

[0055] 3) It can be understood that the moving spraying speed indirectly affects the actual spraying flow rate. Under the same flow rate, a slower speed will increase the amount of concrete per unit area. This invention establishes an orthogonal experimental matrix of moving speed and spraying flow rate, tests the spraying effect of different parameter combinations in the experimental sub-region, calculates the setting time and thickness deviation, constructs a mapping relationship including the inverse of curvature, gravity influence factor and speed-flow rate product, obtains the interaction influence coefficient through weighted solution, and finally superimposes the interaction effect compensation amount in the flow rate 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 corrected independently, makes the parameter adjustment more accurate, further improves the uniformity of tunnel concrete spraying, and ensures the stability and durability of the lining structure.

[0056] In a preferred embodiment of the present invention, the specific process of generating the robotic arm motion trajectory in step S1 is as follows:

[0057] Discrete feature points of the inner surface of the lining are extracted from the three-dimensional point cloud model and surface fitting is performed to generate a continuous surface model.

[0058] Multiple reference path lines parallel to the tunnel axis are generated at a preset distance above the continuous curved surface model; the reference path lines are discretized to obtain trajectory control points, and the coordinates of each trajectory control point in the robot arm's base coordinate system are calculated;

[0059] Based on the limit parameters of the robotic arm joint angles, the feasibility of the trajectory control points is verified, and points that exceed the workspace are eliminated; curve fitting is performed on the verified trajectory control points to generate a continuous robotic arm motion trajectory.

[0060] A 3D point cloud model is a collection of massive spatial points inside a tunnel obtained through methods such as laser scanning. These points contain shape information of the inner surface of the tunnel lining. By identifying points in the point cloud that are related to the inner surface of the lining (e.g., based on whether the point's spatial location is within the preset range of the tunnel structure, or whether the point's normal vector points into the tunnel), points that can reflect the key morphology of the inner surface are selected as discrete feature points, such as inflection points at tunnel bends, the apex of the arch, and the connection points between the sidewalls and the arch. These points can outline the basic contour of the inner surface. Surface fitting is performed on these discrete feature points to generate a continuous surface model because discrete points are scattered and cannot be directly used for trajectory planning. Surface fitting can connect these points according to their spatial distribution to form a smooth and continuous surface, just like connecting discrete points with a curve to form a smooth curve. This can completely present the 3D morphology of the inner surface of the lining, providing a basic shape reference for subsequent trajectory generation.

[0061] 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 working range of the spraying device at the end of the robotic arm, ensuring a suitable distance between the spray gun and the lining surface for optimal spraying results. The tunnel axis represents the direction of tunnel extension; generating reference path lines parallel to the axis ensures the path covers the entire length of the tunnel. Setting multiple path lines, such as one at the center of the arch and one at each of the two side walls, ensures the entire inner surface of the lining is sprayed, avoiding missed areas. The reference path lines are discretized to obtain trajectory control points because continuous path lines cannot be directly executed by the robotic arm; they need to be decomposed into a series of specific spatial points. For example, points are taken at 0.5-meter intervals along a 10-meter reference line; these points are the trajectory control points. The robotic arm completes the movement of the entire path by sequentially reaching these points. The coordinates of each trajectory control point in the robot arm's base coordinate system are calculated. The robot arm's base coordinate system is a three-dimensional coordinate system established with the robot arm's mounting base as the origin (for example, with the center of the base as the origin, the X-axis along the tunnel axis, the Y-axis horizontally perpendicular to the tunnel axis, and the Z-axis vertically upward). By transforming 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's base coordinate system, the robot arm can accurately identify the position of each control point and thus plan its own motion.

[0062] When verifying the feasibility of trajectory control points based on the joint angle limit parameters of the robotic arm, each joint of the robotic arm has its maximum and minimum rotation angle (for example, a certain rotary joint can rotate a maximum of 170 degrees and a minimum of -90 degrees), which is determined by the structural design of the robotic arm. For each trajectory control point, the required rotation angle of each joint of the robotic arm can be obtained through kinematic calculations. If the angle of a certain joint exceeds its limit range, it means that the robotic arm cannot maintain stable operation at that point or mechanical interference will occur. Such points need to be eliminated. For example, in a very narrow corner of a tunnel, the joint of the robotic arm cannot rotate to the corresponding angle, so this point needs to be removed to avoid damage to the robotic arm. Curve fitting is performed on the verified trajectory control points to generate a continuous robotic arm motion trajectory because the verified control points are still discrete. If the robotic arm jumps directly from one point to the next, it will lead to unstable movement and affect the uniformity of spraying. Curve fitting can connect these points into a smooth continuous curve, just like connecting multiple points with a smooth curve, so that the robotic arm can move smoothly along this curve and ensure the continuity of the spraying process.

[0063] The robotic arm plans a spraying path that conforms to the shape of the tunnel lining's inner surface and is adapted to its own movement capabilities. Extracting feature points from the point cloud and fitting a curved surface ensures the trajectory is based on the actual tunnel structure, preventing deviations from the actual surface due to model distortion. Generating multiple reference path lines parallel to the axis ensures the spraying area covers the entire inner surface of the lining, preventing missed areas. Discretizing the path into control points and transforming their coordinates allows the robotic arm to accurately identify each work position. Verifying and eliminating unreachable points prevents the robotic arm from getting stuck, damaged, or failing during movement. Curve fitting of the control points ensures smooth robotic arm movement, avoiding uneven spray thickness caused by sudden changes in movement. This provides a reliable trajectory foundation for the robotic arm to accurately and stably execute spraying operations along the planned path, ultimately contributing to the uniformity and efficiency of tunnel concrete spraying.

[0064] In another preferred embodiment of the present invention, the specific construction process of the preset deviation mapping model in step S3 is as follows:

[0065] S11, a preset length segment containing full curvature features is extracted from the three-dimensional digital model of the construction tunnel as an experimental surface, the experimental surface is divided into several experimental sub-regions, and the robotic arm is controlled to perform spraying operations on each experimental sub-region with an initial spraying speed and an initial flow rate.

[0066] S12: The spatiotemporal evolution data of concrete surface 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 the setting time deviation value.

[0067] Simultaneously, surface point clouds during the initial setting stage are acquired using a laser contour scanner, 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 and used as the actual construction thickness. The median value of the difference between the actual construction thickness and the design thickness is statistically analyzed and used as the thickness deviation value.

[0068] S13. Obtain the radius of curvature and gravity influence factor of each experimental sub-region. Use the radius of curvature as the first dimension index and the gravity influence factor as the second dimension index. Store the corresponding solidification time deviation value and thickness deviation value at the intersection of the two-dimensional indexes to obtain the deviation mapping model.

[0069] A pre-defined length segment containing full curvature characteristics is extracted from the 3D digital model of the tunnel under construction as the experimental surface. Here, full curvature characteristics refer to the segment encompassing various degrees of curvature that the tunnel may exhibit. This includes both low-curvature segments that are nearly straight (such as straight tunnel sections with a large radius of curvature) and high-curvature segments at bends (such as curved tunnel sections with a smaller radius of curvature). This extracted segment represents the curvature of different tunnel structures, preparing for subsequent model coverage of all working conditions. The experimental surface is divided into several experimental sub-regions, for example, multiple square sub-regions of 1m x 1m size. Each sub-region serves as an independent test unit, facilitating individual data recording and analysis. A robotic arm is controlled to perform spraying operations on each experimental sub-region at an initial spraying speed and flow rate. The initial parameters are pre-set base values, such as an initial speed of 0.5 m / s and an initial flow rate of 10 liters / minute. This allows for observation of deviations in different sub-regions due to their own characteristics (curvature, gravity effects) under uniform initial conditions. The spatiotemporal evolution data of concrete surface temperature is collected by an infrared thermal imaging array. During the solidification process, concrete undergoes a hydration reaction that releases heat, and the surface temperature changes over time. The infrared thermal imaging array can capture the spatial distribution and temporal sequence of this temperature change in real time. The actual solidification time is determined based on the inflection point of the temperature rise rate. This is because during the concrete solidification process, the hydration reaction is rapid in the early stage, and the temperature rises quickly (high temperature rise rate). As solidification approaches, the reaction slows down, and the temperature rise rate shows a clear 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, such as 2 hours. If the actual measured solidification time of a certain sub-region is 2.2 hours, the deviation value is 0.2 hours.

[0070] Simultaneously, a laser contour scanner is used to acquire surface point clouds during the initial setting stage. In this stage, the concrete has initially formed but is not fully hardened; the surface morphology at this point reflects the actual shape after spraying. The laser contour scanner generates three-dimensional point cloud data of the surface by emitting laser light and receiving reflected signals. The design surface corresponding to the experimental surface is extracted from the three-dimensional digital model. The design surface represents the ideal surface shape that the tunnel lining should achieve and serves as the target benchmark for construction. 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 normal direction is perpendicular to the design surface. If the point cloud is outside the design surface (excessive spraying thickness), the distance is positive; if it is inside (excessive spraying thickness), the distance is negative. This distance directly reflects the actual spraying thickness. The median value of the difference between the actual construction thickness and the design thickness is statistically analyzed and used as the thickness deviation value. The median value is used because the deviation of a single point may be affected by accidental factors (such as local splashing), while the median value can more stably represent the overall thickness deviation of the sub-region. For example, if there are 10 measured values ​​for the actual thickness of a sub-region, 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 curvature of the surface where the sub-region is located. For example, if a sub-region is located on a straight section, the curvature radius is 100 meters, while if it is located on a turning section, it may be 20 meters. The gravity influence factor is the absolute value of the dot product of the unit normal vector of the lining surface of the sub-region and the gravity vector. For example, at the arch, the normal vector is upward and the angle with the downward gravity vector is close to 90 degrees, so the absolute value of the dot product is small (e.g., 0.2). At the side wall, the normal vector is horizontal and the angle with the gravity vector is close to 0 degrees, so the absolute value of the dot product is large (e.g., 0.8). The curvature radius value is used as the first dimension index, and the gravity influence factor value is used as the second dimension index, just like creating a two-dimensional table. The rows are different curvature radii, and the columns are different gravity influence factors. The corresponding solidification time deviation value and thickness deviation value are stored at the intersection of the two-dimensional indexes. For example, when the curvature radius is 50 meters and the gravity influence factor is 0.5, the corresponding solidification time deviation and thickness deviation exist at this intersection position, thus forming a deviation mapping model.

[0071] This study establishes a correspondence between the initial values ​​of spraying parameters and actual construction deviations (setting time deviation and thickness deviation) under different curvature and gravity influence conditions. Extracting sections containing full curvature characteristics and dividing them into sub-regions ensures the model covers all possible structural scenarios of the tunnel, avoiding narrow applicability due to omissions. Infrared thermal imaging and laser scanning are used to acquire setting time and thickness data because these two methods accurately capture key quality indicators after concrete construction, and measurements based on the concrete's own physical properties (hydration heat release, surface morphology) are more reliable. The statistical median value is used as the thickness deviation to reduce the interference of random errors and make the deviation more representative. Curvature and gravity influence factors are used as a two-dimensional index to store the deviation because these two factors are the main causes of spraying deviations. Through this correspondence, during subsequent robotic arm operations, only the curvature and gravity influence factors at the current position need to be obtained to find the corresponding deviation 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 and ultimately helping to achieve uniformity and quality stability in tunnel concrete spraying.

[0072] In another preferred embodiment of the present invention, a continuous solidification time deviation field and thickness deviation field are generated at the unmeasured curvature-gravity factor combination location using a bicubic spline interpolation algorithm, and the interpolated mapping table is burned into the robotic arm control unit as a deviation mapping model.

[0073] When processing locations with unmeasured curvature-gravity factor combinations, these locations refer to combinations of curvature radius and gravity influence factor that have not been measured in previous experiments. For example, experiments might have measured combinations of curvature radius of 10 meters and gravity influence factor of 0.2, and curvature radius of 30 meters and gravity influence factor of 0.6, but combinations like curvature radius of 20 meters and gravity influence factor of 0.4 lack measured data. When using the bicubic spline interpolation algorithm, the algorithm first selects existing measured data points around these unmeasured locations. For instance, for the point with curvature of 20 meters and gravity influence 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 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 consider 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) will not have a sudden jump. In this way, continuous solidification time deviation fields and thickness deviation fields can be generated. This deviation field can be understood as a complete two-dimensional data surface. Regardless of the values ​​of curvature and gravity factor, the corresponding deviation value can be found on this surface. For example, previously unmeasured combinations such as curvature of 15 meters and gravity factor of 0.3 or curvature of 25 meters and gravity factor of 0.5 can all yield corresponding deviation data through this continuous field. Next, 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 stores 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 at the current position, and can directly and quickly retrieve the corresponding deviation value from the control unit without real-time calculation.

[0074] It's impossible to measure all possible curvature-gravity factor combinations during the experimental phase because the values ​​of curvature and gravity factors are continuously changing. Experiments can only cover a limited number of discrete points. Without addressing unmeasured locations, the robotic arm lacks corresponding deviation data for parameter adjustments in these situations, potentially leading to inaccurate adjustments. Using a bicubic spline interpolation algorithm fills these gaps in unmeasured locations, and the generated continuous deviation field ensures smooth data transitions, preventing abrupt changes in parameter adjustments due to data breaks. Burning the mapping table to the control unit allows the robotic arm to quickly acquire the necessary data during operation, ensuring real-time parameter adjustments and preventing construction delays from affecting data calculations. This deviation mapping model covers all possible curvature and gravity influence scenarios encountered during tunnel construction, providing an accurate basis for parameter adjustments at any location for the robotic arm. Ultimately, this helps achieve uniformity and stability in tunnel concrete spraying, ensuring construction quality meets requirements.

[0075] In another preferred embodiment of the present invention, the specific process of correcting the initial robotic arm moving speed in step S5 is as follows:

[0076] Spraying was performed at a stepped speed in the experimental tunnel section while maintaining a constant spraying flow rate. The actual setting time deviation of the concrete was recorded at different spraying speeds. 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.

[0077] The solidification 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 command is output to the robot arm driver.

[0078] Spraying was performed in the experimental tunnel section at a stepped speed while maintaining a constant spraying flow rate. An experimental section was pre-determined from the actual tunnel structure, and the spraying flow rate was set to a fixed value (e.g., 15 liters of concrete per minute). The robotic arm was then allowed to spray in segments at different speeds. The speed step change could start at 0.2 m / s and increase by 0.1 m / s each time, and so on, completing the spraying of a small area at speeds of 0.2 m / s, 0.3 m / s, 0.4 m / s, etc. This was done to observe the effect of speed changes on concrete setting time under the condition of a single variable (speed), eliminating the interference of flow rate changes. If both flow rate and speed are changed at the same time, it would be impossible to distinguish which factor caused the setting time deviation. Recording the actual setting time deviation of concrete at different spraying speeds means that after each step of spraying is completed, the actual setting time of the concrete in that area is measured using a previously determined method (such as monitoring the inflection point of the temperature rise rate with an infrared thermal imaging array), and then compared with the preset standard setting time to obtain the deviation value corresponding to each speed. For example, the deviation is +0.3 hours (slower setting) at 0.2 m / s and -0.2 hours (faster setting) at 0.4 m / s. The response relationship between solidification time deviation and velocity correction is fitted using the least squares method. Here, velocity correction refers to the velocity value that needs to be adjusted to eliminate a certain solidification time deviation (for example, to eliminate a deviation of +0.3 hours, the velocity may need to be increased from the initial value by 0.1 m / s, and this 0.1 m / s is the correction). The purpose of the least squares method is to find a line that best reflects the correspondence between all measured deviations and corrections, minimizing the sum of the distances from each measured point to this line, thus more accurately reflecting the intrinsic relationship between the two. A piecewise linear velocity compensation function is generated because the relationship between solidification time deviation and velocity correction may exhibit different linear characteristics in different velocity ranges. For example, when the velocity is below 0.3 m / s, the rate of change of deviation with the correction is larger, while the rate of change is smaller when the velocity is above 0.3 m / s. Therefore, the entire velocity range is divided into two segments, and linear relationships are fitted to each segment to form a piecewise compensation function. The solidification time prediction deviation output by the deviation mapping model is input into the velocity compensation function. For example, if the model predicts that the solidification time deviation at the current position is +0.2 hours, after inputting into the function, the function will calculate the required velocity increase of 0.08 m / s based on the corresponding piecewise linear relationship. This 0.08 m / s is the velocity correction amount. The final velocity correction command is output to the robotic arm driver, that is, the calculated velocity correction amount is converted into a control signal that the robotic arm can recognize and sent to the component that drives the robotic arm to move, so that the robotic arm moves at the corrected velocity (initial velocity plus or minus the correction amount).

[0079] The moving speed of the robotic arm directly affects the residence time of concrete per unit area, thus affecting the setting time. A slower speed results in denser concrete spraying and a more stable hydration environment, potentially leading to slower setting. Conversely, a faster speed results in a thinner spray layer and faster heat dissipation, potentially leading to faster setting. Therefore, adjusting the speed is necessary to regulate the setting time. Maintaining a constant spray flow rate is crucial for studying the effect of spraying speed on setting time independently, avoiding interference from other factors, and ensuring a more accurate relationship between speed and setting deviation. Least squares fitting allows the obtained response relationship to better match actual measurement data, reducing the impact of random errors. Generating a piecewise linear function is necessary because the effect of speed on setting time may differ across different intervals; piecewise fitting improves the accuracy of compensation. Inputting the predicted deviation into the compensation function to obtain the correction amount and outputting commands allows the robotic arm to adjust its speed in real time based on the predicted setting deviation at the current position during actual construction, making the setting time as close as possible to the standard value. By dynamically adjusting the movement speed of the robotic arm, the problem of inconsistent setting time caused by factors such as curvature and gravity at different locations is solved, ultimately helping to achieve uniform setting of tunnel concrete spraying and ensuring stable lining quality.

[0080] In another preferred embodiment of the present invention, the specific process of correcting the initial spray flow rate in step S6 is as follows:

[0081] Spraying was performed in the experimental tunnel section with stepped spray flow rates while maintaining a constant robotic arm movement speed. The concrete forming thickness deviation under different flow rates was recorded. The response relationship between the thickness deviation and the flow rate correction coefficient was fitted using the least squares method to generate a piecewise linear flow rate compensation function.

[0082] The thickness prediction deviation output by the deviation mapping model is input into the flow compensation function to calculate the basic flow correction coefficient, and the final spraying flow correction command is output to the robotic arm driver.

[0083] The thickness of the concrete layer is primarily determined by the amount of concrete sprayed per unit area. With a fixed robotic arm movement speed, the spraying flow rate is the key factor determining this amount; excessive or insufficient flow rate will cause the thickness to deviate from the design value. Therefore, it is necessary to adjust the thickness by correcting the flow rate. Maintaining a constant robotic arm movement speed eliminates the interference of speed on thickness, ensuring that the measured thickness deviation is caused only by changes in flow rate, making the relationship between flow rate and thickness deviation more accurate. Fitting the relationship between thickness deviation and flow rate correction coefficient using the least squares method allows the fitting results to better match the actual measurement data, reducing the impact of random errors. Generating a piecewise linear compensation function is necessary because the influence of flow rate on thickness may differ in different intervals; piecewise fitting improves the accuracy of flow rate correction. Inputting the predicted deviation output from the deviation mapping model into the compensation function to obtain the correction coefficient and outputting instructions allows the robotic arm to adjust the spraying flow rate in real time based on the predicted thickness deviation at the current location during actual construction, making the actual thickness as close as possible to the design value. By dynamically correcting the spraying flow rate, the problem of uneven thickness caused by factors such as curvature and gravity at different locations is solved, ultimately helping to achieve consistent thickness of tunnel concrete spraying and ensuring the stability and safety of the lining structure.

[0084] In another preferred embodiment of the present invention, step S3 further includes the gravity vector being in the negative direction of the Z-axis of the geodetic coordinate system, and the coordinate transformation being corrected in real time by an inclination sensor installed on the base of the robotic arm.

[0085] The accuracy of the gravity vector's direction and the correctness of the coordinate transformation directly affect the calculation results of the gravity influence factor, which is a crucial basis for subsequent deviation mapping models and parameter corrections. Setting the gravity vector to the negative Z-axis of the geodetic coordinate system ensures that the theoretical direction of gravity aligns with the actual physical direction, preventing calculation deviations due to incorrect direction definition. However, when the robotic arm is installed in the tunnel, uneven ground and installation errors may cause the base to tilt, resulting in its own coordinate system not being parallel to the geodetic coordinate system. Without correcting the coordinate transformation, the relative angle between the unit normal vector and the gravity vector will be calculated incorrectly, leading to a distortion of the gravity influence factor. Real-time correction using tilt sensors ensures accurate coordinate transformation regardless of the robotic arm's base tilt, allowing the gravity influence factor calculation to reflect reality. The aim is to guarantee the accuracy of the gravity influence factor, providing a reliable foundation for subsequent deviation predictions and parameter corrections based on this factor. Ultimately, this helps the robotic arm precisely adjust spraying parameters at different locations, improving the uniformity of tunnel concrete spraying.

[0086] In another preferred embodiment of the present invention, step S6 further includes establishing a set of gradients for moving speed parameters and a set of gradients for spraying flow rate parameters within the experimental sub-region, forming an orthogonal experimental matrix;

[0087] For any combination of moving speed and spraying flow rate in the orthogonal experimental matrix, the robotic arm is controlled to perform spraying with the speed and flow rate parameters as constant values.

[0088] Calculate the solidification time deviation and thickness deviation for each experimental sub-region; establish the mapping relationship between the solidification time deviation and the inverse of curvature term, gravity influence factor term, and velocity-flow product term;

[0089] Establish the mapping relationship between thickness deviation and the inverse of curvature, gravity influence factor, and velocity-flow product;

[0090] The coefficients of the velocity-flow product term in the mapping relationship are solved by weighted least squares method; the ratio of the product term coefficients to the initial spraying parameters is extracted to generate standardized interaction influence coefficients.

[0091] Obtain the change in the movement speed of the robotic arm before and after correction, and calculate the interaction effect compensation based on the change in movement speed and the standardized interaction effect coefficient.

[0092] The interaction effect compensation is added to the basic flow correction coefficient to generate the final flow correction coefficient, and the robotic arm is controlled to adjust the spraying flow according to the final flow correction coefficient.

[0093] Within the experimental sub-region, several different values ​​of the moving speed are first determined to form a gradient set. For example, based on the initial moving speed, several different speed values ​​are taken upwards and downwards. At the same time, several different values ​​of the spraying flow rate are determined to form a gradient set. Similarly, based on the initial flow rate, these values ​​are selected upwards and downwards. These speed values ​​and flow rate values ​​are combined to form an orthogonal experimental matrix. This is done so that different combinations of speed and flow rate can be covered, and repeated experiments can be avoided, so as to fully reflect the situation under different parameter combinations.

[0094] Next, any set of moving speed and spraying flow rate is selected from the orthogonal experimental matrix. For example, a set might be a low speed and a medium flow rate. The robotic arm is controlled to continuously spray within the experimental sub-region at this set of speed and flow rate, keeping these two parameters constant throughout the process. This ensures that the experimental results under this set of parameters are stable and unaffected by parameter fluctuations. Then, the setting time deviation of each experimental sub-region is calculated. Specifically, this is done by observing the temperature change during the concrete setting process. When the rate of temperature rise slows down significantly, the corresponding time is the actual setting time. This time is subtracted from the pre-set standard setting time for this type of concrete, and the difference is the setting time deviation. Simultaneously, the thickness deviation is calculated by scanning the surface of the initially set concrete with a laser to obtain the distance from each point on the surface to the designed lining surface. These distances are the actual construction thickness. The actual construction thickness is subtracted from the designed thickness, and the value at the midpoint of these differences is selected as the thickness deviation, because the value at the midpoint is less affected by extreme values ​​and better represents the overall thickness deviation of the region.

[0095] Next, a mapping relationship is established between the setting time deviation and multiple factors, including the inverse of curvature, which is the reciprocal of the radius of curvature. The smaller the radius of curvature, the larger the inverse, indicating a more pronounced degree of curvature in the area. The degree of curvature affects the concrete accumulation and thus 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 direction of gravity. For example, at the arch, the normal vector is upward and the angle between it and the downward gravity direction is large, resulting in a small absolute value of the dot product. At the side walls, the angle is small, resulting in a large absolute value of the dot product. Different gravity influences lead to different concrete flow or accumulation conditions, thus affecting the setting time. There is also the product of velocity and flow rate, because when velocity and flow rate work together, they affect the amount of concrete per unit area and the residence time, thus affecting the setting time. Similarly, a mapping relationship is established between the thickness deviation and these terms, because these factors also affect the thickness of the concrete.

[0096] Then, the coefficient of the velocity-flow product term in the mapping relationship is solved by weighted least squares method. The ratio of the coefficient of this product term to the initial spraying parameters (the product of initial velocity and initial flow rate) is extracted to generate a standardized interaction coefficient. This can eliminate the influence of different initial parameter values ​​and make the interaction coefficients of different regions and different initial parameters comparable.

[0097] Next, the change in the moving speed of the robotic arm before and after correction is obtained, which 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 amount is calculated. Because the amount of concrete per unit area will change after the speed changes, even if the flow rate remains the same, this compensation amount is needed to adjust the flow rate correction to cope with the impact of the speed change. Finally, the basic flow rate correction coefficient (the flow rate correction coefficient calculated only based on the thickness deviation) is added to the interaction effect compensation amount to obtain the final flow rate correction coefficient. The robotic arm is then controlled to adjust the spraying flow rate according to this final flow rate correction coefficient.

[0098] It is understandable that the interaction between moving speed and spraying flow rate can lead to inaccurate correction of spraying flow rate alone. For example, when the moving speed decreases, even if the flow rate remains unchanged, the amount of concrete per unit area will increase. In this case, if the flow rate is corrected only based on the thickness deviation, it may lead to overcorrection. However, an orthogonal experimental matrix can comprehensively cover different combinations of speed and flow rate, ensuring that the combined effect of the two is captured. Establishing a mapping relationship that includes multiple factors can clarify the impact of each factor on the deviation, especially the interaction between speed and flow rate. Weighted solution coefficients can give more attention to the impact of key areas, making the results more in line with actual needs. Standardized interaction influence coefficients can make the interaction influences under different conditions comparable and facilitate unified calculation. The interaction effect compensation amount can correct the impact of speed changes on flow rate correction. Finally, the final flow rate correction coefficient obtained by superposition can make the flow rate adjustment consider the impact of thickness deviation and speed changes simultaneously, making the concrete spraying thickness more uniform and meeting the design requirements, thereby improving the quality of tunnel concrete spraying and ensuring the stability of the lining structure.

[0099] The foregoing has provided a detailed description of one embodiment of the present invention, but this description is merely a preferred embodiment and should not be construed as limiting the scope of the invention. All equivalent variations and modifications made within the scope of the claims of this invention should still fall within the patent coverage of this invention.

Claims

1. A robotic arm control method for concrete spraying in tunnel engineering, characterized in that, Includes the following steps: S1. Obtain a three-dimensional point cloud model of the construction tunnel, and generate a robotic arm motion trajectory based on the three-dimensional point cloud model. Mark the robotic arm motion trajectory as the construction path and set the initial spraying speed and initial spraying flow rate. S2, through the curvature sensing unit integrated at the end of the robotic arm, collects the curvature radius of the current spraying point on the motion trajectory in real time; S3, obtain the unit normal vector of the lining surface at the current spraying point based on the three-dimensional digital model, calculate the absolute value of the dot product of the unit normal vector and the gravity vector and use it as the gravity influence factor; S4. Input the radius of curvature and gravity influence factor into the preset deviation mapping model to obtain the solidification time prediction deviation and thickness prediction deviation corresponding to the current spraying point. S5, Based on the predicted deviation of the solidification time, the initial moving speed of the robotic arm is corrected, and the robotic arm is controlled to spray along the construction path at the corrected moving speed; S6, Based on the thickness prediction deviation, the initial spraying flow rate value is corrected, and the robotic arm is controlled to spray along the construction path according to the corrected spraying flow rate; In step S4, the specific construction process of the preset deviation mapping model is as follows: S11, a preset length segment containing full curvature features is extracted from the three-dimensional digital model of the construction tunnel as an experimental surface, the experimental surface is divided into several experimental sub-regions, and the robotic arm is controlled to perform spraying operations on each experimental sub-region with an initial spraying speed and an initial flow rate. S12: The spatiotemporal evolution data of concrete surface 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 the setting time deviation value. Simultaneously, surface point clouds during the initial setting stage are acquired using a laser contour scanner, 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 and used as the actual construction thickness. The median value of the difference between the actual construction thickness and the design thickness is statistically analyzed and used as the thickness deviation value. S13. Obtain the radius of curvature and gravity influence factor of each experimental sub-region. Use the radius of curvature as the first dimension index and the gravity influence factor as the second dimension index. Store the corresponding solidification time deviation value and thickness deviation value at the intersection of the two-dimensional indexes to obtain the deviation mapping model.

2. The robotic arm control method for concrete spraying in tunnel engineering according to claim 1, characterized in that, In step S1, the specific process of generating the robotic arm's motion trajectory is as follows: Discrete feature points of the inner surface of the lining are extracted from the three-dimensional point cloud model and surface fitting is performed to generate a continuous surface model. Multiple reference path lines parallel to the tunnel axis are generated at a preset distance above the continuous curved surface model along the tunnel axis direction; Discretize the baseline path to obtain the trajectory control points, and calculate the coordinates of each trajectory control point in the robot arm's base coordinate system. Based on the limit parameters of the robotic arm joint angle, the feasibility of the trajectory control points is verified, and points that exceed the workspace are eliminated. Curve fitting is performed on the verified trajectory control points to generate a continuous robotic arm motion trajectory.

3. The robotic arm control method for concrete spraying in tunnel engineering according to claim 1, characterized in that, It also includes generating continuous solidification time deviation fields and thickness deviation fields at unmeasured curvature-gravity factor combination locations using a bicubic spline interpolation algorithm, and burning the interpolated mapping table into the robotic arm control unit as a deviation mapping model.

4. The robotic arm control method for concrete spraying in tunnel engineering according to claim 1, characterized in that, In step S5, the specific process of correcting the initial robotic arm movement speed is as follows: Spraying was performed at a stepped speed in the experimental tunnel section while maintaining a constant spraying flow rate. The actual setting time deviation of the concrete was recorded at different spraying speeds. 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 solidification 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 command is output to the robot arm driver.

5. The robotic arm control method for concrete spraying in tunnel engineering according to claim 1, characterized in that, In step S6, the specific process of correcting the initial spray flow rate value is as follows: Spraying was performed in the experimental tunnel section with stepped spray flow rates while maintaining a constant robotic arm movement speed. The concrete forming thickness deviation under different flow rates was recorded. The response relationship between the thickness deviation and the flow rate correction coefficient was fitted using the least squares method to generate a piecewise linear flow rate compensation function. The thickness prediction deviation output by the deviation mapping model is input into the flow compensation function to calculate the basic flow correction coefficient, and the final spraying flow correction command is output to the robotic arm driver.

6. The robotic arm control method for concrete spraying in tunnel engineering according to claim 1, characterized in that, S3 further includes the gravity vector being in the negative direction of the Z-axis of the geodetic coordinate system, and the coordinate transformation is corrected in real time by an inclination sensor installed on the base of the robotic arm.

7. The robotic arm control method for concrete spraying in tunnel engineering according to claim 5, characterized in that, S6 further includes establishing a set of gradients for moving speed parameters and a set of gradients for spraying flow rate parameters within the experimental sub-region, forming an orthogonal experimental matrix; For any combination of moving speed and spraying flow rate in the orthogonal experimental matrix, the robotic arm is controlled to perform spraying with the speed and flow rate parameters as constant values. Calculate the solidification time deviation and thickness deviation for each experimental sub-region; establish the mapping relationship between the solidification time deviation and the inverse of curvature term, gravity influence factor term, and velocity-flow product term; Establish the mapping relationship between thickness deviation and the inverse of curvature, gravity influence factor, and velocity-flow product; The coefficients of the velocity-flow product term in the mapping relationship are solved by weighted least squares method, and the ratio of the product term coefficients to the initial spraying parameters is extracted to generate standardized interaction influence coefficients. Obtain the change in the movement speed of the robotic arm before and after correction, and calculate the interaction effect compensation based on the change in movement speed and the standardized interaction effect coefficient. The interaction effect compensation is added to the basic flow correction coefficient to generate the final flow correction coefficient, and the robotic arm is controlled to adjust the spraying flow according to the final flow correction coefficient.

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