A method for one-time penetration of reinforcement through the through hole of cross steel column based on constraint programming

Abstract

The present application relates to steel structure construction and assembly planning, and proposes a method for once-through of steel bar crossing through the through hole of cross steel column based on constraint programming; in order to solve the scratch, deadlock and rollback caused by the constraint of hole structure and fireproof coating, the method is: a scene model is established with the center of the through hole as the reference, the hole, coating, steel bar and reachable parameters are obtained; the contact normal is determined through geometric reasoning, the minimum bending radius is converted into the upper limit of the cumulative turning angle of the path, and the coating contact limit area is calibrated according to the friction and allowable indentation, and the incident angle range and allowed turning angle are given; the tool angle resolution is discretized and a safety margin is set, and the interlocking relationship table is formed in combination with mutual interference; the constraint satisfaction integer programming is carried out with the steel bar penetration sequence, the incident side, the incident angle and the guide as variables, and when it is not feasible, a detachable trumpet guide is installed at the high-risk hole edge for recalculation. The method ensures that the steel bar is once-through, avoids coating scratches and assembly deadlocks, and improves the construction feasibility.

Description

Technical Field

[0001] This invention relates to the field of steel structure construction and assembly planning, and in particular to a method for one-time penetration of reinforcing bars through the through-hole of a cross-shaped steel column based on constraint planning. Background Technology

[0002] The through-holes through which reinforcing bars pass through cross-shaped steel columns are a crucial step in the construction of steel structure and composite structure joints. The openings are often covered with fire-retardant coatings and chamfered, and are surrounded by obstacles such as flanges, floor slabs, and formwork, limiting the working window. Construction requires passing multiple reinforcing bars through and connecting them within a limited incident angle, while avoiding scratching the coating, enlarging the opening, or requiring repeated backtracking. Tool angle step size, repeatability accuracy, and the minimum bending radius of the reinforcing bars all constrain the operation.

[0003] Current practices largely rely on worker experience combined with simple clamps or fixed guide rings: On-site rough measurements of the opening and obstacles are taken first, and the sequence is arranged according to rules such as "easy first, then difficult; detailed first, then rough; starting from the open side"; the incident angle is visually adjusted using an angle gauge or positioning plate, and temporary anti-wear tape or plastic bushings are applied if necessary; integral flared end guards or permanent sleeves are used locally to reduce friction; some units utilize BIM / point cloud to generate visual guidance or recommended angles. Interference is also mitigated by enlarging the opening, local grinding, or segmented insertion-retraction-reinsertion. These solutions typically only consider geometric passage and empirical safety clearances, lacking a mechanism to unify coating friction and permissible indentation, tool angle resolution, minimum bending radius, and interference from multiple reinforcing bars into a single decision-making framework.

[0004] Therefore, traditional solutions struggle to guarantee that "each rebar is continuously penetrated without touching the coating" under real-world constraints. The key problems are: failure to model coating risks in conjunction with contact normals, cumulative rotation angles, and reachable postures; failure to explicitly eliminate interlocking deadlocks between multiple rebars; and a lack of means to adjust the hole edge contact boundary locally and detachably to align with the plan when infeasibility is not feasible, leading to a disconnect between planning and execution. Summary of the Invention

[0005] One objective of this invention is to propose a method for one-time penetration of reinforcing bars through cross-shaped steel column through holes based on constraint programming. In the case of cross-shaped steel column through holes with fire-retardant coatings, chamfers, and surrounding obstacles, a unified decision-making and execution framework consistent with the capabilities of on-site tools is constructed. This allows multiple reinforcing bars to be penetrated in one go without enlarging the hole or retreating, achieving a penetration consistent with the actual reachable range. Furthermore, the method uniquely and clearly determines the insertion sequence, incident side, and incident angle of each reinforcing bar. When the natural feasible domain is insufficient, it also allows for minimizing adjustments to the contact normal and friction conditions at the hole edge using partially detachable flared guide components to restore feasibility. Simultaneously, it maintains consistency with on-site markings, no-touch zones, and the timing of assembly and disassembly, preventing scratches to the fire-retardant coating from the outset.

[0006] A method for one-time penetration of reinforcing bars through a cross-shaped steel column via a constraint programming-based approach according to an embodiment of the present invention is characterized by comprising:

[0007] S1. Obtain the through-hole size, hole opening protection structure, fireproof coating thickness and surrounding obstacles. Combine the rebar diameter, end shape and minimum bending radius to define the construction reachable range and generate a scene model and rebar parameter set.

[0008] S2. Based on the scene model of S1, perform geometric reasoning, determine the contact normal according to the curvature of the orifice and the chamfer, convert the minimum bending radius into the upper limit of the cumulative turning angle of the path, and define the coating risk area with coating friction and permissible indentation, and output the incident angle range and permissible turning angle.

[0009] S3. Based on the incident angle range of S2, discretize according to the tool angle resolution and add a safety margin, evaluate the mutual interference with the relative pose of the rebar end shape and the hole boundary, form an interlocking relationship table, and obtain the angle candidate set.

[0010] S4. On the angle candidate set of S3, constrained integer programming is adopted. With the rib-piercing sequence, incident side, angle and guide component usage as variables, the incident angle range, allowable rotation angle, coating risk threshold and one-time penetration constraint are applied. Conflicts are disabled according to the interlocking relationship table, and the penetration plan is output.

[0011] S5. When S4 is not feasible or exceeds the coating risk threshold, install detachable guides at the edge of high-risk holes according to the coating risk area, adjust the contact boundary and friction parameters, update the scene model, and constrain the rib-piercing sequence, incident side, angle and guide usage to satisfy integer programming and resolve to obtain the penetration plan using guides.

[0012] S6. Based on the breakthrough plan, generate on-site instructions, clarify the incident side, angle and advance depth, mark the no-collision zone and angle baseline, specify the timing of guide component installation and removal, and implement the one-time breakthrough constraint;

[0013] S7. After the connection is completed, check the integrity and thickness of the fireproof coating, verify whether the connection position with the adjacent beam reinforcement is within the planned range, and confirm that each steel bar is connected in one go without scratching the fireproof coating.

[0014] Optionally, S1 is as follows:

[0015] The scene model is a three-dimensional geometric model with the center of the through hole as a reference, recording the through hole size, fireproof coating thickness, hole opening protection structure, surrounding obstacles, and construction access range;

[0016] The set of rebar parameters includes rebar diameter, end shape, minimum bending radius, and length allowance. The end shape can be a straight end, a hooked end, or a sleeve connection end.

[0017] The reachable range of the construction is a set of incident postures determined by the operator's posture and tool geometry in the coordinate system of the through hole center. The polar angle and azimuth angle reachable areas are determined based on the tool length, beam end elevation and working opening width. The reachable posture area and the upper limit of the advancement distance are formed by superimposing the safety gap with the shape of the surrounding obstacles.

[0018] Optionally, S2 is as follows:

[0019] The geometric reasoning is a process of calculating the surface normal and curvature based on the scene model, which is used to determine the incident attitude and contact relationship;

[0020] The cumulative rotation limit is the total allowed rotation limit of the reinforcement along the through path;

[0021] The permissible indentation threshold is the limit of the allowable indentation depth or contact pressure of the fire-retardant coating.

[0022] The incident angle range is the interval between the polar angle and the azimuth angle relative to the hole axis;

[0023] The allowed turning angle is the set of maximum turning angles for each segment of advancement, provided that the cumulative turning angle limit is not exceeded.

[0024] The method of determining the contact normal based on the curvature and chamfer of the hole is as follows: In the scene model, the surface normal and chamfer direction are collected along the hole edge. Based on the hole edge contact control zone, the angle between the steel bar axis and the surface normal is calculated for each candidate incident posture. Incident postures that will form sliding contact are selected, and incident postures that will produce blade contact are eliminated. Based on this, the upper and lower limits of the incident angle range are limited so that the steel bar is guided to enter along the chamfer and avoids touching the fireproof coating.

[0025] The method of converting the minimum bending radius into the upper limit of the cumulative turning angle is as follows: based on the minimum bending radius in the set of steel reinforcement parameters, the through path is segmented within the reachable attitude zone, the directional change of adjacent segments is calculated and accumulated into the total turning angle, and a limit value of the total turning angle calculated from the minimum bending radius is set. The incident attitude exceeding the limit value is included in the attitude prohibition zone, and only the advancement mode that meets the limit value is retained in the allowed turning angle to avoid jamming or retreat due to excessive bending.

[0026] The method of defining the coating contact restriction zone based on the friction coefficient and the permissible indentation threshold is as follows: In the scene model, the thickness of the fireproof coating and the friction coefficient are called, and combined with the permissible indentation threshold, the contact pressure and tangential friction level are evaluated according to the hole edge position and incident posture. The circumferential section of the hole edge that is prone to scratch is calibrated to form the coating contact restriction zone. This restriction zone is then linked with the incident angle range, and the incident angle range is narrowed to ensure that the steel bar and the coating maintain the minimum safe gap when penetrating.

[0027] Optionally, S3 specifically refers to:

[0028] The tool's angular resolution is the minimum adjustable angular step and repeatability of the field angle ruler or positioning fixture;

[0029] The safety margin is the angular allowance reserved within the incident angle range to avoid touching the coating contact restriction area;

[0030] The evaluation of mutual interference is to determine the contact and occlusion relationship between the insertion path and the aperture boundary and surrounding obstacles under relative pose.

[0031] The interlocking relationship table records the relationships between different combinations of reinforcing bars and different incident angles that lead to assembly deadlock.

[0032] The angle candidate set is the set of available incident angles retained after discretization for each rebar.

[0033] The discretization based on tool angle resolution with added safety margin is as follows: Based on the incident angle range and allowable rotation angle in step S2, combined with the construction reachable range and scene model in step S1, the incident angle range is discretized into an angle step sequence according to tool angle resolution; a safety margin is calculated around each discrete angle so that the discrete angle is still within the safe range after considering the repeatability accuracy of the tool and the minimum gap of the coating contact limit area; discrete angles that cannot meet the safety margin are discarded and combined with the allowable rotation angle, and only discrete angles that meet the allowable rotation angle are retained for subsequent assignment.

[0034] Optionally, calculating the safety margin around each discrete angle specifically involves:

[0035]

[0036] in, The safety margin for discrete angles; For the incident side The edge contact control strip; For the reason A defined unit vector of incident direction; To control the position of the belt The contact normal; For the repeatability accuracy of the tool angle; For tool angle resolution; For steel reinforcement The set of allowed turns along the through path, The maximum angular quantity representing the initial direction change; the judgment rule is as follows: If the discrete angle is retained, it is discarded otherwise, thus reserving the minimum angular gap for the coating contact restriction area within the angular domain, while absorbing the adverse effects of tool error and the initial turning angle of the path.

[0037] Optionally, S4 specifically refers to:

[0038] The constraints satisfy integer programming, which is a planning model composed of discrete decision variables and hard constraints, used to generate a through plan under the constraints of angle candidate set and interlocking relation table.

[0039] The coating risk threshold is the upper limit of the contact pressure and tangential friction determined based on the coating contact restriction zone;

[0040] The constrained integer programming is as follows: Based on the angle candidate set and interlocking relationship table obtained in step S3, a planning model is established with the rebar threading sequence, incident side, incident angle, and use of the detachable flared guide as decision variables; the value range of each decision variable is limited, where the incident angle is taken from the angle candidate set, the incident side is taken from both sides of the through hole, the use of the guide is taken from the installation state, and the rebar threading sequence forms a strict sequential relationship among all rebars; the model is used to uniformly determine the execution order and path under the hard requirements of satisfying fireproof coating protection and one-time penetration.

[0041] The variables for the rebar insertion sequence, incident side, incident angle, and use of the detachable bell-shaped guide are as follows: the incident angle variable is limited to a discrete angle in the angle candidate set, the incident side variable is limited to the left or right side, and the use of the detachable bell-shaped guide variable is limited to not installed or installed; the rebar insertion sequence variable is arranged as a non-repeating sequential index, and corresponds one-to-one with the corresponding incident side and incident angle to ensure that each rebar is assigned only once and is consistent with the reachable range on site;

[0042] The applied incident angle range, allowable turning angle, coating risk threshold, and one-time penetration constraint are as follows: For each assigned incident angle and advancement path, check whether it falls within the incident angle range of step S2 and whether the turning angle of each segment does not exceed the allowable turning angle; for the posture related to coating contact, determine whether it exceeds the limit based on the coating risk threshold and coating contact restriction area, and if it exceeds the limit, it is judged as infeasible; apply one-time penetration constraint to the rebar insertion sequence, prohibit any rebar from requesting retraction or disassembly after insertion, and prohibit the assignment of subsequent rebars from reducing the incident angle range of the inserted rebar to below the safety margin, thereby eliminating assembly deadlock from the source;

[0043] The method of disabling conflicts according to the interlocking relationship table is as follows: the interlocking relationship table formed in step S3 is used as an exclusive condition to set mutual exclusion constraints on the steel reinforcement combination, incident side combination and incident angle combination that cause assembly deadlock; when a combination is marked as interlocked, the planning model prohibits the simultaneous selection of the combination, thereby avoiding the generation of assignments that require backtracking or will touch the coating contact restriction area during the solution stage; after the solution is completed, the penetration plan is output.

[0044] Optionally, the constraints satisfy integer programming, and their feasibility is limited as a hard constraint by the following compliance determination formula, wherein the selected assignment is deemed compliant if and only if the formula evaluates to zero:

[0045]

[0046] in, Choose a binary variable; For steel reinforcement On the incident side Candidate set of angles above; For assignment Predicted contact pressure values; This refers to the upper limit of contact pressure in the coating risk threshold. For assignment The tangential friction level; This represents the upper limit of tangential friction in the coating risk threshold. For the set of allowed corners; This is the maximum cumulative turning angle. The non-negative part of the function represents the positive part of the excess. The non-compliance indication quantity for a single pass indicates whether the assignment requires a reversal or change in the state of the inserted steel bars during the advancement process; a value of zero indicates compliance. This is a disabled matrix entry in the interlock relationship table. A value of 1 indicates combined interlocking, and a value of 0 indicates coexistence. When the total expression is equal to zero, it means that the selected assignment does not trigger any coating risk, corner overrun, or interlock conflict, and satisfies the one-time penetration constraint.

[0047] Optional, S5 specifically includes:

[0048] The installation of detachable flared guides at high-risk hole edges according to the coating contact restriction zone is as follows: In the scene model, the coating contact restriction zone and coating risk threshold calibrated in step S2 are called, and high-risk hole edges at the hole boundary that cause at least one angle candidate to fall into or be close to exceeding the limit are located; the incident side is selected in this hole edge section, and the coverage arc length is determined so that the coverage area can cover the relevant angle candidates obtained in step S3; a detachable flared guide is configured for this coverage area, the inner surface of the flared guide is consistent with the updated contact normal, the minimum radius of curvature of the flared guide is not less than the minimum bending radius of the reinforcing bar, and the friction parameters of the inner surface material are lower than the friction parameters of the reinforcing bar and the fireproof coating; the guide is fixed relative to the hole boundary by means of clips, screws, or magnetic attraction, and the position of the inner edge of the guide and the hole axis is calibrated to ensure that the reinforcing bar slides along the inner surface of the flared guide without contacting the fireproof coating during subsequent insertion;

[0049] The process of resolving the constraints on the rebar insertion sequence, incident side, angle, and guide component usage to satisfy integer programming is as follows: Using the updated scenario model as input, the constraint-satisfying integer programming model from step S4 is used. The variable for the use of the detachable bell-shaped guide component is set to "installed" on the corresponding incident side. The friction parameters and contact boundaries affected by the guide component are replaced. The incident angle range and related constraints are corrected with the updated contact normal and feasibility judgment. The constraints of the allowable rotation angle, one-time penetration constraint, and interlocking relationship table remain effective. The process is resolved under this parameter set, and the penetration plan using the guide component is output. The penetration plan specifies the rebar insertion sequence, incident side, incident angle, and installation status of the detachable bell-shaped guide component for each rebar.

[0050] Optionally, the removable flared guide installed at the edge of the high-risk hole according to the coating contact restriction area is selected based on the following criterion for determining the guide coverage area on the incident s: minimizing the following objective, which is determined when the objective reaches its minimum value:

[0051]

[0052] in, For the incident side The coverage area to be covered by the proposed detachable horn-shaped guide component; For the incident side The boundary of the orifice, Indicates arc length; The reinforcing bars obtained in step S3 On the incident side Angle candidate set; As weights, those exceeding the limit in step S4 prediction are marked. The first item is set to 1, and the rest are set to 0. and In coverage respectively Furthermore, the predicted values ​​of contact pressure and tangential friction when using a detachable flared guide component; and From coating ; It is a function with a non-negative part; This is a dimensionless tradeoff coefficient used to penalize the proportion of the coverage arc length in the total arc length; the formula uses threshold normalization to ensure dimensional consistency, and minimizing the target value corresponds to eliminating the bias caused by the shortest possible coverage arc length. and The resulting over-limit items.

[0053] Optional, S6 specifically includes:

[0054] The marking of the no-collision zone and angle baseline is as follows: The coating contact restriction zone, hole edge contact control zone, and incident angle in the penetration plan from the scene model are used to calibrate the hole boundary related to the penetration plan on-site; the hole boundary is located at three points using the through-hole center coordinate system, and the projection of the hole axis onto the hole boundary plane is determined as the zero angle; angle baselines are drawn on the hole boundary plane according to the incident angle of each target in the penetration plan; the safety gap between the coating contact restriction zone and surrounding obstacles is projected onto the hole boundary and its adjacent accessible surface to form a continuous no-collision zone boundary, which is clearly marked on-site with weather-resistant markings or removable patches, ensuring that the operator maintains a spatial gap with the no-collision zone when executing the specified incident angle and penetration depth, preventing contact with the fireproof coating and surrounding obstacles;

[0055] The specified timing for installing and removing the guide is as follows: Based on the penetration plan and the coverage arc length of the high-risk hole edge, determine the incident side and its coverage area where the detachable bell-shaped guide needs to be installed; complete the installation of the guide before inserting the first rebar using the coverage area on the incident side, and only begin advancing after the inner edge of the guide and the hole axis are aligned; the guide can only be removed after all rebars that need to pass through the coverage area have passed and their advancement depth exceeds the end point of the guide's coverage; it is prohibited to install or remove the guide during the advancement of any rebar, and it is prohibited to remove it prematurely while the guide's coverage area is still referenced by subsequent entries in the penetration plan, in order to avoid changes in the contact boundary and friction parameters, which could lead to inconsistencies between the on-site execution and the penetration plan.

[0056] The beneficial effects of this invention are:

[0057] 1. This proposal suggests an improved constraint planning-geometric reasoning fusion method, which parametrically models and imposes executability constraints around the key physical boundaries of a single-pass rebar connection. Technically, the contact normal is determined by the hole edge curvature and chamfer direction, eliminating incident postures that would result in edge-to-edge contact; the minimum bending radius is equivalent to the upper limit of the cumulative path angle, and segmented allowable angles are output; the coating contact restriction zone is calibrated based on the coating's friction coefficient and allowable indentation threshold, and combined with the incident angle range to shrink the usable interval; tool angle resolution and repeatability accuracy are introduced into the angle discretization, supplemented by a safety margin to filter discrete angles. Unlike existing algorithms that determine feasibility solely based on channel size or empirical gaps, this method incorporates curvature-normal constraints, cumulative angles, and coating mechanical boundaries into hard constraints simultaneously, and absorbs tool errors at the discretization level, ensuring the planning solution aligns with on-site capabilities, thereby reducing the probability of jamming and backtracking, and suppressing the risk of coating scratches.

[0058] 2. This proposal introduces a novel collaborative mechanism involving an interlocking relationship table, a one-time penetration constraint, and a detachable flared guide, addressing the prior suppression of deadlocks in multi-reinforcement assembly and the parameter decoupling of infeasibility scenarios. Technically, it assesses mutual interference based on the relative pose of the rebar end shape and the hole boundary, pre-generating an interlocking relationship table and encoding it with exclusive constraints. In integer programming, the rebar insertion sequence, incident side, incident angle, and guide usage are used as decision variables, applying incident angle range, allowable rotation angle, coating risk threshold, and one-time penetration constraints. Any assignment that compresses the safety margin of already inserted rebars or requires retraction is prohibited. When infeasibility occurs or exceeds the coating risk threshold, high-risk hole edges are located, and a detachable flared guide is configured on the minimum necessary coverage arc length. The contact normal and friction parameters are updated and recalculated. Unlike conventional strategies that rely on heuristic sequences or post-hoc concessions, this mechanism eliminates assembly deadlocks at the model level and restores the feasible region through local boundary reconstruction without altering the one-time penetration principle, reducing on-site trial and error and cumulative disturbances to the coating.

[0059] 3. This proposal puts forward an integrated approach to scenario modeling, planning, execution, and acceptance for on-site implementation, ensuring that the algorithm output can be consistently executed and measurably accepted. Technically, a through-hole center coordinate system is used to record the orifice, coating, obstacles, and accessible space, generating on-site instructions including the incident side, target angle, and advancement depth. Angle zero points and baselines are calibrated on the orifice plane, and the coating restriction area and surrounding obstacles are projected as no-collision zones. Guide component assembly and disassembly windows are defined, and assembly / disassembly consistency judgments are given. After breakthrough, coating thickness and integrity are checked, as well as the docking coordinates with adjacent beam reinforcement are verified. Unlike schemes that only output paths in the simulation domain while ignoring tool resolution, on-site benchmarks, and acceptance loops, this method maps planning boundary conditions into operable calibration and quantifiable testing items, improving planning-execution consistency and achieving controllable and traceable risks and processes under the constraint of a single breakthrough. Attached Figure Description

[0060] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used in conjunction with embodiments of the invention to explain the invention and do not constitute a limitation thereof. In the drawings:

[0061] Figure 1 The flowchart is a method for one-time breakthrough of reinforcing bars through the through hole of a cross-shaped steel column based on constraint programming, as proposed in this invention.

[0062] Figure 2 This is a schematic diagram illustrating the one-time breakthrough execution of a method for passing through a cross-shaped steel column through a reinforcing bar based on constraint programming, as proposed in this invention. The method involves a detachable flared guide. Detailed Implementation

[0063] The present invention will now be described in further detail with reference to the accompanying drawings. These drawings are simplified schematic diagrams, illustrating only the basic structure of the invention, and therefore only show the components relevant to the invention.

[0064] refer to Figures 1 to 2 A method for one-time penetration of reinforcing bars through a cross-shaped steel column via a constraint programming-based method, characterized by comprising:

[0065] S1. Obtain the through-hole size, hole opening protection structure, fireproof coating thickness and surrounding obstacles. Combine the rebar diameter, end shape and minimum bending radius to define the construction reachable range and generate a scene model and rebar parameter set.

[0066] S2. Based on the scene model of S1, perform geometric reasoning, determine the contact normal according to the curvature of the orifice and the chamfer, convert the minimum bending radius into the upper limit of the cumulative turning angle of the path, and define the coating risk area with coating friction and permissible indentation, and output the incident angle range and permissible turning angle.

[0067] S3. Based on the incident angle range of S2, discretize according to the tool angle resolution and add a safety margin, evaluate the mutual interference with the relative pose of the rebar end shape and the hole boundary, form an interlocking relationship table, and obtain the angle candidate set.

[0068] S4. On the angle candidate set of S3, constrained integer programming is adopted. With the rib-piercing sequence, incident side, angle and guide component usage as variables, the incident angle range, allowable rotation angle, coating risk threshold and one-time penetration constraint are applied. Conflicts are disabled according to the interlocking relationship table, and the penetration plan is output.

[0069] S5. When S4 is not feasible or exceeds the coating risk threshold, install detachable guides at the edge of high-risk holes according to the coating risk area, adjust the contact boundary and friction parameters, update the scene model, and constrain the rib-piercing sequence, incident side, angle and guide usage to satisfy integer programming and resolve to obtain the penetration plan using guides.

[0070] S6. Based on the breakthrough plan, generate on-site instructions, clarify the incident side, angle and advance depth, mark the no-collision zone and angle baseline, specify the timing of guide component installation and removal, and implement the one-time breakthrough constraint;

[0071] S7. After the connection is completed, check the integrity and thickness of the fireproof coating, verify whether the connection position with the adjacent beam reinforcement is within the planned range, and confirm that each steel bar is connected in one go without scratching the fireproof coating.

[0072] In this specific embodiment, S1 specifically refers to:

[0073] Establish a scenario model to accommodate all inputs for subsequent geometric reasoning, incident angle selection, and connection planning.

[0074] Using the through hole as a reference, the hole boundary is determined on-site using a three-point positioning method, and a coordinate system for the hole center is established, denoted as the hole center coordinate system. .

[0075] In the hole The hole axis is represented by a unit vector, denoted as . The boundary of the orifice is represented by a set of curves, denoted as the orifice. The chamfers of the bore's edge in its neighborhood are recorded as a set of geometric features, including the chamfer direction and chamfer radius. Then, at the bore's opening... The neighborhood is defined as the contact control zone at the hole edge, denoted as the hole edge. This control band is used to subsequently define the contact range between the reinforcing bar and the hole edge, and at any point on the control band, the hole edge is defined. The fields for preset curvature and normal are denoted as follows: and ,in The dimension of curvature of the hole edge surface at that location. This represents the contact normal vector.

[0076] Regarding the parameters related to the fire-retardant coating, the coating thickness distribution is recorded using a surface domain function, denoted as coating thickness. Its domain covers the orifice And its adjacent accessible surfaces. The friction parameters between the coating and the reinforcing steel are divided into static friction coefficient and dynamic friction coefficient, denoted as [formulas to be inserted here]. and And it forms part of the coating parameter set.

[0077] The permissible indentation threshold is given in the form of indentation depth or contact pressure, with the indentation depth threshold denoted as . The upper limit of contact pressure is denoted as .

[0078] For unified use in subsequent planning, the coating risk threshold is represented as an upper limit set, denoted as coating. ,in This represents the upper limit of tangential friction allowed under coating contact limitation conditions. The above set of coating parameters is denoted as coating_parameter_set_. .

[0079] The reinforcement parameter set is indexed by the reinforcement set, denoted as .

[0080] For each steel bar , registered diameter Minimum bending radius End shape With total length End shape Used to describe the occupied shape and end face shape of the insertion end, so as to evaluate mutual interference with the relative pose of the orifice boundary. Minimum bending radius. The minimum curvature constraint allowed for construction is used as the source of parameters for subsequently calculating the upper limit of the cumulative turning angle of the path.

[0081] To ensure consistency between on-site operations and planning, the accessible range for construction is described using lateral set, with the incident set denoted as the incident set. This corresponds to both sides of the through-hole. For each incident side... The accessible range for construction is recorded by volume domain, denoted as It is used to restrict the accessible space for field tools and reinforcing bars on this side.

[0082] The core parameters for tools are tool angular resolution and repeatability. Tool angular resolution is denoted as... This indicates the minimum adjustable angle step that the on-site angle gauge or positioning fixture can achieve; repeatability accuracy is denoted by the allowable deviation in the angular dimension. This is used for subsequent definition of safety margins. If a detachable flared guide component exists on site, its installation state set and friction parameter standby values ​​are recorded as an alternative state, and the friction parameter corresponding to the inner surface of its flared opening is recorded as the guide parameter. The corresponding contact boundary and friction parameters are replaced when the guide is used in step S5.

[0083] In summary, the aforementioned geometry and parameters are uniformly encapsulated into a scene model, denoted as . The model includes a coordinate system aperture. Hole axis Orifice boundary Hole edge contact control strip Curvature field Contact normal field Coating parameter set Coating risk threshold Steel reinforcement assembly Its parameter items Incident side assembly Construction reach area Tool angle resolution With repeatability accuracy .

[0084] During implementation, the orifice boundary orifice Record the measured edge line and chamfered end face combination, and control the hole edge contact with the hole edge. The calibration is performed using a strip-shaped region along the edge of the aperture, and the coordinates are stored within the strip as local coordinates. and Coating parameter set Based on actual on-site thickness With respect to the material specifications Register and set the permissible indentation threshold. and upper limit of contact pressure As a coating risk threshold Components of .

[0085] Reinforcement parameter set for each Minimum bending radius Registered using design allowable values, end shape Registration is performed using a geometric description volume for subsequent evaluation of the relative pose and mutual interference with the orifice boundary. Construction reachability. Recording is performed within a volume domain defined by on-site obstacles and the boundaries of the operating space. Zhongyu Correlation is used to ensure that subsequent assignments on the incident side are consistent with those available on site. Tool angular resolution. With repeatability accuracy The calibration values ​​of the field tools are recorded and used for angle discretization and safety margin calculation in step S3.

[0086] In this specific embodiment, S2 specifically refers to:

[0087] Based on scenario model , with the hole axis Orifice boundary Contact control strip with hole edge Use the curvature field as the geometric reference. With contact normal field And combined with coating parameter set and coating risk threshold For steel reinforcement assembly Perform geometric reasoning for each rebar, outputting the incident angle range and allowable rotation angle for each rebar. To facilitate subsequent angle discretization and constraint planning, this step involves... The incident angle is characterized by the polar angle and azimuth angle relative to the aperture axis, and the polar angle is denoted as . The azimuth is denoted as And organized according to the rebar index Meanwhile, the corner constraints for path segmentation are organized into sets. .

[0088] First, determine the contact normal based on the orifice curvature and chamfer. For Sampling points within Read and Identify the spatial distribution of chamfer direction and radius of curvature, and... This serves as the contact reference normal at that location. For the reinforcing bars. Generate a set of candidate incident poses, in each candidate Below, align the direction of the reinforcing bar axis with... Angle discrimination is performed: if a sliding contact occurs along the chamfered guide without forming an edge contact, the candidate incident attitude is retained; if edge contact occurs within the guide section or a sharp transition requiring crossing the chamfer is required, the candidate is eliminated. After the above screening, for... The upper and lower limits are constrained to ensure that the reinforcing bars enter... When entering the neighborhood, follow the chamfer guide and maintain contact with the surrounding area throughout the initial insertion segment. Consistent contact relationships prevent contact with the sensitive boundaries of the fire-retardant coating from the outset.

[0089] Convert the minimum bending radius to the maximum cumulative rotation angle. For reinforcing bars... Read minimum bending radius In the case of the hole axis To advance the reference path, segments are constructed based on the incident attitude and directional changes accessible in local space. The directional changes of adjacent segments are recorded as corner segments, organized into a set of segmented corners of the path, and accumulated as the upper limit of the cumulative corners, denoted as . .

[0090] When a candidate The corresponding advancement path exceeds during the accumulation process. At that time, the candidate was judged as exceeding the limit and was removed from the list. Remove from the middle; in Only retain no more than The segmented turning points allow subsequent advancements to complete the breakthrough without causing jamming or reversal. This transition is based on... As the only source parameter, with The spatial boundaries are linked to ensure that the directional changes of the path segments satisfy both the construction curvature constraints of the reinforcing bars and are within the allowable direction set of the reachable space.

[0091] In the step of defining the coating contact restriction zone based on the coefficient of friction and the permissible indentation threshold, the following is called... In and ,right The circumferential sections of the adjacent accessible surface that may be scratched are identified and a coating contact restriction zone is formed, denoted as... For each candidate The insertion path is evaluated under contact prediction. Relative relationship: If the contact pressure generated along the path exceeds [a certain value] in any segment, [the following applies]. Or the tangential friction level exceeds If so, the candidate is judged as exceeding the limit and is excluded from the list. Remove from the middle; if the path is locally close If there is a boundary but still a spatial gap, then in China to the corresponding Narrowing the upper and lower limits makes the usable range of the incident angle consistent with... Maintain a minimum safe clearance. The above criteria and... The linkage ensures that the sliding contact guided by the chamfer does not transform into a contact on the coated surface.

[0092] Finally, the range of incident angles and allowable rotation angles are output for subsequent angle discretization and constraint programming. For each reinforcing bar... ,by Record relative hole axis The polar angle and azimuth angle intervals, with interval boundaries derived from contact normal selection and cumulative rotation angle upper limit. Contact Restricted Area with Coating Joint constraints. Record the set of allowed turning angles for each segment along the through path, and this set is compared with... The input for step S3 is used to determine the tool angle resolution. Discretize and achieve repeatable accuracy in the field. Add a safety margin under the premise of scenario model. In a consistent data context, the geometric reasoning in step S2 clarifies the contact normal, the upper limit of the cumulative rotation angle, the coating contact restriction area, and the range of incident angles and allowable rotation angles.

[0093] In this specific embodiment, S3 specifically refers to:

[0094] The range of incident angles output in step S2 With the set of allowed corners Based on the scene model With coordinate system hole Below, for each steel bar and each incident side Angle discretization and safety margin assessment are performed to form a candidate set of angles, and the angles are determined based on the shape of the rebar ends. and the boundary of the orifice Mutual interference is determined based on the relative poses, and an interlocking relationship table is generated. In the discrete process, along... polar angle With azimuth Using tool angle resolution Sampling is performed to generate discrete angle indexes. corresponding In conjunction with on-site repeatability accuracy A safety margin determination is configured for each discrete angle to ensure that the discrete angle maintains a safe clearance for the coating contact restriction area even under field operation errors and changes in the direction of the initial segment of the path.

[0095] In the calculation of the safety margin of discrete angles, the following formula is used for each reinforcing bar. Incident side and discrete angle index The determination is made, and the result is used to filter available discrete angles:

[0096]

[0097] in, The safety margin for discrete angles; For the incident side The edge contact control strip; For the reason A defined unit vector of incident direction; To control the position of the belt The contact normal; For the repeatability accuracy of the tool angle; For tool angle resolution; For steel reinforcement The set of allowed turns along the through path, The maximum angular quantity representing the initial change in direction. The determination rule is as follows: If the discrete angle is retained, it is discarded otherwise, thus reserving the minimum angular gap for the coating contact restriction area within the angular domain, while absorbing the adverse effects of tool error and the initial turning angle of the path.

[0098] In the mutual interference assessment stage, the retained discrete angles Rigid body pose transformation Shape of the end of the reinforcing bar Mapped to and along the hole axis The direction of advancement is being checked and examined step by step. and The relationship between them. If hard contact, obstruction, or insertion occurs... And cause another steel bar range of incident angles Compressed to ensure a safety margin for any discrete angle Then the combination and Records indicating interlocks are marked as disabled combinations in the interlock relationship table. The interlock relationship table covers rebar-rebar, incident side-incident side, and incident angle-incident angle conflict types, used to prevent assembly deadlocks or coating risk thresholds from being triggered during subsequent assignment phases. Exceeding the limit.

[0099] Based on comprehensive safety margin screening and mutual interference determination, for each steel bar On each incident side Generate an angle candidate set, which contains only those angles that satisfy... , No triggering at the orifice Discrete angles with hard contact that are not disabled by the interlocking relation table The candidate angle set and the interlocking relation table are used together as input to step S4, ensuring that the constraints satisfy the integer programming rules that simultaneously adhere to the coating contact restriction zone in both the angle and sequence domains. Allowable corner set Tool angle resolution With field repeatability accuracy A unified boundary is established, thereby setting comprehensive pre-constraints for the variable assignment and disabling combinations of the through plan.

[0100] In this specific embodiment, S4 specifically refers to:

[0101] In scene model Next, based on the angle candidate set and interlocking relationship table obtained in step S3, establish a constraint-satisfying integer programming problem, with each rebar... The threading sequence, incident side, incident angle, and detachable flared guide are used as decision variables. The threading sequence is indexed sequentially. Indicates the incident-side variable. The incident angle variable is taken from the candidate set. Discrete angles in Detachable flared guide component uses variable These represent "not installed" and "installed," respectively.

[0102] To facilitate linear assignment, a binary selection variable is defined. If and only if the steel reinforcement Assigned to the side of incidence Selecting Discrete Angle Index The guide component is in the following state: The value is 1 if it is true, and 0 otherwise.

[0103] The unique assignment of each rebar is achieved through incident radiation. It is guaranteed in the model that, Constrain the sequence with a strict, non-repeating order to avoid skipping execution.

[0104] For the constraint, the incident angle value must fall within the incident angle range output in step S2. And the segmented turning angles along the path do not exceed the set of allowed turning angles. The cumulative turning angle does not exceed .

[0105] Coating risk threshold As a rigid boundary, the contact pressure and tangential friction are checked in the contact prediction for each assigned insertion path, and must not exceed [a certain limit]. and The single-pass constraint is implemented on-site, prohibiting the retraction or removal of inserted rebars during any rebar advancement process, and prohibiting the compression of the candidate angle set of inserted rebars to a negative safety margin due to subsequent assignments. The interlock relationship table is encoded in the form of a disable matrix. In the model, mutual exclusion constraints are set for any combination marked as interlocked to avoid assembly deadlock or touching the coating contact restriction area.

[0106] This step uses the combined constraint of disabling conflict and coating risk threshold as the core calculation formula to make a one-time determination of the compliance of the selected assignment:

[0107]

[0108] in, Choose a binary variable; For steel reinforcement On the incident side Candidate set of angles above; For assignment Predicted contact pressure values; This refers to the upper limit of contact pressure in the coating risk threshold. For assignment The tangential friction level; This represents the upper limit of tangential friction in the coating risk threshold. For the set of allowed corners; This is the maximum cumulative turning angle. The non-negative part of the function represents the positive part of the excess. The non-compliance indication quantity for a single pass indicates whether the assignment requires a reversal or change in the state of the inserted steel bars during the advancement process; a value of zero indicates compliance. This is the disabled matrix entry in the interlock relationship table. A value of 1 indicates combined interlocking, and a value of 0 indicates coexistence. When the total expression equals zero, it means that the selected assignment does not trigger any coating risk, corner overrun, or interlock conflict, and satisfies the one-through constraint.

[0109] In the model solution, the incident angle variable is only allowed from the angle candidate set. Take the value to ensure the tool's angle resolution. With field repeatability accuracy The safety margin has already been absorbed in the safety margin determination in step S3; the guide uses variables. On the applicable incident side, the coverage area is set to installed or not installed according to step S5, and this is distinguished in the call to the contact boundary and friction parameters. and Reinforcing bar sequence Compared with the incident side Under the condition that the constraints are satisfied, the prohibition matrix of the interlocking relation table is uniformly determined and mutually exclusive within the assignment space. After the solution is completed, the through-line plan is output, which specifies the order of threading each rebar. Incident side Angle of incidence And the use of detachable flared mouth guide components .

[0110] In this specific embodiment, S5 specifically includes:

[0111] When the constraints of step S4 satisfy the infeasibility of integer programming, or in the assignment Contact prediction has or At this time, initiate this step to install a detachable flared guide at the edge of the high-risk hole, adjust the contact boundary and friction parameters, and update the scene model. Firstly, based on the coating contact restriction area Coating risk threshold Shot from the incident side High-risk hole edge positioning, forming This set covers the orifice boundary sections that caused the aforementioned exceedance. Parameterization along arc length, in Several candidate coverage segments are generated internally to evaluate the coverage arc length of the guide and its effect on risk reduction.

[0112] To determine the minimum necessary coverage area and make subsequent recalculation of S4 feasible, the following formula is used for the incident side. Previous section of guide component coverage Make a selection:

[0113]

[0114] in, For the incident side The coverage area to be covered by the proposed detachable horn-shaped guide component; For the incident side The boundary of the orifice, Indicates arc length; The reinforcing bars obtained in step S3 On the incident side Angle candidate set; As weights, those exceeding the limit in step S4 prediction are marked. The first item is set to 1, and the rest are set to 0. and In coverage respectively Furthermore, the predicted values ​​of contact pressure and tangential friction when using a detachable flared guide component; and From coating ; It is a function with a non-negative part; This is a dimensionless tradeoff coefficient used to penalize the proportion of the coverage arc length in the total arc length. The formula uses threshold normalization to ensure dimensional consistency, and minimizing the objective value corresponds to eliminating the bias caused by the shortest possible coverage arc length. and The resulting over-limit items.

[0115] Get coverage Then, configure the geometric and material parameters of the detachable flared guide. The inner surface of the flared opening... A new contact boundary is formed, the minimum radius of curvature of which is not less than the reinforcement group participating in the covered section. The upper bound of the minimum bending radius, that is, satisfying The friction parameters of the inner surface material of the guide component are registered in the scene model as follows: and satisfy The installation method uses clips, screws, or magnetic attachment to fix the guide component in place. Stable coverage .

[0116] Subsequently, the contact boundary and friction parameters were updated for consistency. Lieutenant General The inner edge of the contact control zone at the hole edge is replaced by the inner edge of the hole chamfer or guard with the inner edge of the flared opening, and the contact normal field in the coverage area is replaced with... This normal direction coincides with the generation normal of the inner surface of the bell mouth; at the level of friction parameters, the friction parameters of the steel bar-surface pair in the covered area are changed from... Replace with ; Coating in the restricted contact area Perform partial downgrading or removal to make No longer involved in coating risk assessment. The above update generates a new scene model. However, the angle candidate set remains unchanged. The set of discrete points is refreshed only for its feasibility marking and risk assessment results.

[0117] At the on-site implementation level, on the incident side Press up Complete the installation and positioning of the detachable flared guide component. Positioning is determined by the holes. For reference, align the inner edge of the flared opening with the axis of the hole. The relative positions satisfy the incident direction requirements of the penetration plan, and in Colonel's verification The angle between the steel bar and the target incident direction in the initial stage ensures that the steel bar slides along the inner surface of the flared end in the initial stage of propulsion without touching the coating surface.

[0118] S4 is recalculated accordingly. As input, following the constraints of step S4 to satisfy the integer programming structure, the process involves... The assignment item is switched to guide status. Call the updated contact boundary and Perform contact prediction while maintaining the allowable corner set. Cumulative turning angle limit The single-pass constraint and interlocking relationship table remain in effect. If the solution is feasible, output the pass plan using guides, specifying the threading sequence of each rebar. Incident side Angle of incidence And the use of detachable flared mouth guide components If there are still cases of exceeding limits or infeasibility, then in Internal Extend the above objective formula or on the opposite side. Assess coverage until satisfaction is achieved. Furthermore, a feasible through-connection plan consistent with the interlocking relationship table is established. Through the above process, step S5 uses the high-risk hole edge as the positioning object and the detachable flared guide as the constraint adjustment means to achieve parameterized updating of the contact boundary and friction parameters, and restores the feasibility of step S4 with the minimum necessary coverage arc length.

[0119] In this specific embodiment, S6 specifically refers to:

[0120] According to the reinforcement sequence in the through plan Incident side Angle of incidence And the use of detachable flared mouth guide components Generate field instruction set Each field instruction entry Determine the incident side Unit vector of the target incident direction , advance in depth and the status of the guide components To advance in depth Along the hole axis Orifice boundary from the incident side Starting point, ensure reinforcement Complete the insertion without backtracking. On-site instructions are in... The no-touch zones are marked, and these zones are derived from the coating contact restriction areas. Within the reach of construction The projection is used to clearly mark the boundaries of the opening and adjacent accessible surfaces with weather-resistant markings.

[0121] In the angle calibration process, the coordinate system of the through hole center is used as the coordinate system on the plane where the hole boundary is located. Perform three-point positioning and establish the zero-position reference line as the hole axis. The projection onto that plane. According to the through-connection plan. ,by Draw an angular baseline on the projection of the aperture boundary plane, and then draw the reference lines in the vicinity of the baseline according to the tool angular resolution. Set visual scales to match on-site repeatability accuracy. Provides a visual angle window, allowing the operator to maintain contact with the normal field during the initial stage of advancement. A consistent sliding contact, without touching the fire-retardant coating. No-touch zone markings are in place. exist The projection of the incident direction and its adjacent surface serves as the boundary, ensuring that the execution of the propulsion depth always maintains a safe clearance.

[0122] During the guide assembly and disassembly process, the coverage area determined in step S5 is used as a guide. With the connection plan For each incident side Determine the assembly / disassembly window as Before starting this window, complete the installation and positioning of the detachable flared guide component, ensuring that the inner edge of the flared opening aligns with the axis of the hole. The relative positions satisfy the specified The dismantling must be completed after the window is closed. Dismantling operations are prohibited during any rebar advancement process, and premature dismantling is prohibited while the covered area is still referenced by subsequent entries, to ensure that the contact boundary and friction parameters do not change during execution.

[0123] Regarding the implementation of constraints in a single process, on-site instructions are listed in sequence. Each steel bar is required according to Execution is sequential, proceeding continuously in a single step until... It must not be reversed or pulled out midway. For angle operation, the permissible deviation is limited to [specific parameters]. and Within the synthesis window, and where deviations may lead to coating risk thresholds When approaching the limit, execution is suspended and the process returns to the connection plan for review. Items marked as prohibited combinations in the interlock relationship table are explicitly marked as non-executable in the on-site instructions to avoid triggering assembly deadlock or compressing the angle candidate set of subsequent reinforcement bars.

[0124] To rigorously verify the consistency between the timing of guide component assembly and disassembly and the on-site sequence, the following assembly and disassembly consistency judgment formula is adopted for each incident side. Verification was performed, and the sum was zero when compliance was achieved.

[0125]

[0126] in, This is an indicator function representing the reinforcement bars. Is it on the incident side? ; Variables are used for the detachable flared mouth guide; For the incident side In sequence index The installation status function of the guide component at the location is always 1 within the installation / disassembly window and always 0 outside the window; This is a non-negative function used to measure the excess number of assembly / disassembly state transitions. The first term of this equation guarantees that for all on-side... The entry, in its instruction Compared with the actual situation on site Consistent; the second item limits the number of state transitions to two, allowing assembly and disassembly only at the start and end points of the window, thus excluding the possibility of changing the state of the guide component during the advancement process.

[0127] Through the above generation and verification process, the field instruction set... In the hole Under the unified coordinate context, the incident side, angle and propulsion depth are clearly defined, the no-collision zone and angle baseline are marked on site, the timing of guide component installation and removal is specified, and the consistency judgment method of installation and removal and the execution sequence are used to implement the one-time connection constraint to ensure that the on-site execution is consistent with the connection plan.

[0128] In this specific embodiment, S7 specifically refers to:

[0129] After the breakthrough is completed, the coordinate system of the through hole center is used to determine the hole size. The acceptance testing will begin by verifying the integrity and thickness of the fireproof coating: along the boundary of the orifice. and coating contact restricted area Set up inspection points, visually inspect for peeling, damage, and scratches, and use a thickness measuring tool to measure the coating thickness at the corresponding points, comparing it with the coating thickness distribution function registered in step S1. The results were compared with the design requirements to confirm that the thickness was within the allowable range and that the coating surface was continuous and free of defects. The test results were recorded and archived, with any abnormal points marked for subsequent verification.

[0130] Then verify whether the connection position with the adjacent beam reinforcement is within the scope of the continuous reinforcement plan: based on the incident side of each reinforcement in the continuous reinforcement plan. Angle of incidence With depth of advancement In Kong Check the actual connection coordinates and direction of the ends of the reinforcing bars and the adjacent beam reinforcement to confirm that they are within the planned reachable range. Inside, and the incident direction of the designated target Consistent and did not touch any no-touch zones. (Based on the on-site instruction set) With one-time through-restrain constraint, for each reinforcing bar Check execution sequence The process records confirm that each step was a single, continuous advancement. The connection was completed without any backtracking or midway pulling out on site, and no scratches or indentations appeared within the coating contact restriction area. An acceptance confirmation was issued for the above-mentioned qualified items, and non-qualified items were recorded according to their location and cause and transferred to the connection plan review and rectification process.

[0131] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A method for one-time penetration of reinforcing bars through a cross-shaped steel column through a borehole based on constrained programming, characterized in that, include: S1. Obtain the through-hole size, hole opening protection structure, fireproof coating thickness and surrounding obstacles. Combine the rebar diameter, end shape and minimum bending radius to define the construction reachable range and generate a scene model and rebar parameter set. S2. Based on the scene model of S1, perform geometric reasoning, determine the contact normal according to the curvature of the orifice and the chamfer, convert the minimum bending radius into the upper limit of the cumulative turning angle of the path, and define the coating risk area with coating friction and permissible indentation, and output the incident angle range and permissible turning angle. S3. Based on the incident angle range of S2, discretize according to the tool angle resolution and add a safety margin, evaluate the mutual interference with the relative pose of the rebar end shape and the hole boundary, form an interlocking relationship table, and obtain the angle candidate set. S4. On the angle candidate set of S3, constrained integer programming is adopted. With the rib-piercing sequence, incident side, angle and guide component usage as variables, the incident angle range, allowable rotation angle, coating risk threshold and one-time penetration constraint are applied. Conflicts are disabled according to the interlocking relationship table, and the penetration plan is output. S5. When S4 is not feasible or exceeds the coating risk threshold, install detachable guides at the edge of high-risk holes according to the coating risk area, adjust the contact boundary and friction parameters, update the scene model, and constrain the rib-piercing sequence, incident side, angle and guide usage to satisfy integer programming and resolve to obtain the penetration plan using guides. S6. Based on the breakthrough plan, generate on-site instructions, clarify the incident side, angle and advance depth, mark the no-collision zone and angle baseline, specify the timing of guide component installation and removal, and implement the one-time breakthrough constraint; S7. After the connection is completed, check the integrity and thickness of the fireproof coating, verify whether the connection position with the adjacent beam reinforcement is within the planned range, and confirm that each steel bar is connected in one go without scratching the fireproof coating.

2. The method for one-time penetration of reinforcing bars through a cross-shaped steel column via a constraint programming-based method according to claim 1, characterized in that, S1 specifically refers to: The scene model is a three-dimensional geometric model with the center of the through hole as a reference, recording the through hole size, fireproof coating thickness, hole opening protection structure, surrounding obstacles, and construction access range; The set of rebar parameters includes rebar diameter, end shape, minimum bending radius, and length allowance. The end shape can be a straight end, a hooked end, or a sleeve connection end. The reachable range of the construction is a set of incident postures determined by the operator's posture and tool geometry in the coordinate system of the through hole center. The polar angle and azimuth angle reachable areas are determined based on the tool length, beam end elevation and working opening width. The reachable posture area and the upper limit of the advancement distance are formed by superimposing the safety gap with the shape of the surrounding obstacles.

3. The method for one-time penetration of reinforcing bars through a cross-shaped steel column via a constraint programming-based method according to claim 1, characterized in that, S2 specifically refers to: The geometric reasoning is a process of calculating the surface normal and curvature based on the scene model, which is used to determine the incident attitude and contact relationship; The cumulative rotation limit is the total allowed rotation limit of the reinforcement along the through path; The permissible indentation threshold is the limit of the allowable indentation depth or contact pressure of the fire-retardant coating; The incident angle range is the interval between the polar angle and the azimuth angle relative to the hole axis; The allowed turning angle is the set of maximum turning angles for each segment of advancement, provided that the cumulative turning angle limit is not exceeded. The method of determining the contact normal based on the curvature and chamfer of the hole is as follows: In the scene model, the surface normal and chamfer direction are collected along the hole edge. Based on the hole edge contact control zone, the angle between the steel bar axis and the surface normal is calculated for each candidate incident posture. Incident postures that will form sliding contact are selected, and incident postures that will produce blade contact are eliminated. Based on this, the upper and lower limits of the incident angle range are limited so that the steel bar is guided to enter along the chamfer and avoids touching the fireproof coating. The method of converting the minimum bending radius into the upper limit of the cumulative turning angle is as follows: based on the minimum bending radius in the set of steel reinforcement parameters, the through path is segmented within the reachable attitude zone, the directional change of adjacent segments is calculated and accumulated into the total turning angle, and a limit value of the total turning angle calculated from the minimum bending radius is set. The incident attitude exceeding the limit value is included in the attitude prohibition zone, and only the advancement mode that meets the limit value is retained in the allowed turning angle to avoid jamming or retreat due to excessive bending. The coating contact restriction zone is defined by the coefficient of friction and the permissible indentation threshold: the fireproof coating thickness and coefficient of friction are called in the scene model, combined with the permissible indentation threshold, and the contact pressure and tangential friction level are evaluated according to the hole edge position and incident attitude. The circumferential section of the hole edge that is prone to scratch is calibrated to form the coating contact restriction zone. This restriction zone is linked with the incident angle range, and the incident angle range is narrowed to ensure that the steel bar and the coating maintain the minimum safe gap when penetrating.

4. The method for one-time penetration of reinforcing bars through a cross-shaped steel column via a constraint programming-based method according to claim 1, characterized in that, S3 specifically refers to: The tool's angular resolution is the minimum adjustable angular step and repeatability of the field angle ruler or positioning fixture; The safety margin is the angular allowance reserved within the incident angle range to avoid touching the coating contact restriction area; The evaluation of mutual interference is to determine the contact and occlusion relationship between the insertion path and the aperture boundary and surrounding obstacles under relative pose. The interlocking relationship table records the relationships between different combinations of reinforcing bars and different incident angles that lead to assembly deadlock. The angle candidate set is the set of available incident angles retained after discretization for each steel bar; The discretization based on tool angle resolution with added safety margin is as follows: Based on the incident angle range and allowable rotation angle in step S2, combined with the construction reachable range and scene model in step S1, the incident angle range is discretized into an angle step sequence according to tool angle resolution; a safety margin is calculated around each discrete angle so that the discrete angle is still within the safe range after considering the repeatability accuracy of the tool and the minimum gap of the coating contact limit area; discrete angles that cannot meet the safety margin are discarded and combined with the allowable rotation angle, and only discrete angles that meet the allowable rotation angle are retained for subsequent assignment.

5. The method for one-time penetration of reinforcing bars through a cross-shaped steel column through a hole based on constrained programming according to claim 4, characterized in that, The calculation of the safety margin around each discrete angle specifically involves: ； in, The safety margin for discrete angles; For the incident side The edge contact control strip; For the reason A defined unit vector of incident direction; To control the position of the belt The contact normal; For the repeatability accuracy of the tool angle; For tool angle resolution; For steel reinforcement The set of allowed turns along the through path, The maximum angular quantity representing the initial direction change; the judgment rule is as follows: If the discrete angle is retained, it is discarded otherwise, thus reserving the minimum angular gap for the coating contact restriction area within the angular domain, while absorbing the adverse effects of tool error and the initial turning angle of the path.

6. The method for one-time penetration of reinforcing bars through a cross-shaped steel column via a constraint programming-based method according to claim 1, characterized in that, S4 specifically refers to: The constraints satisfy integer programming, which is a planning model composed of discrete decision variables and hard constraints, used to generate a through plan under the constraints of angle candidate set and interlocking relation table. The coating risk threshold is the upper limit of the contact pressure and tangential friction determined based on the coating contact restriction zone; The constrained integer programming is as follows: Based on the angle candidate set and interlocking relationship table obtained in step S3, a planning model is established with the rebar threading sequence, incident side, incident angle, and use of the detachable flared guide as decision variables; the value range of each decision variable is limited, where the incident angle is taken from the angle candidate set, the incident side is taken from both sides of the through hole, the use of the guide is taken from the installation state, and the rebar threading sequence forms a strict sequential relationship among all rebars; the model is used to uniformly determine the execution order and path under the hard requirements of satisfying fireproof coating protection and one-time penetration. The variables are: rebar insertion sequence, incident side, incident angle, and the use of detachable bell-shaped guides. The incident angle variable is limited to a discrete angle in the angle candidate set, the incident side variable is limited to the left or right side, and the use of detachable bell-shaped guides is limited to whether they are installed or not. The rebar insertion sequence variable is arranged into a non-repeating sequential index and corresponds one-to-one with the corresponding incident side and incident angle to ensure that each rebar is assigned only once and is consistent with the reachable range on site. The applied incident angle range, allowable turning angle, coating risk threshold, and one-time penetration constraint are as follows: For each assigned incident angle and advancement path, check whether it falls within the incident angle range of step S2 and whether the turning angle of each segment does not exceed the allowable turning angle; for the posture related to coating contact, determine whether it exceeds the limit based on the coating risk threshold and coating contact restriction area, and if it exceeds the limit, it is judged as infeasible; apply one-time penetration constraint to the rebar insertion sequence, prohibit any rebar from requesting retraction or disassembly after insertion, and prohibit the assignment of subsequent rebars from reducing the incident angle range of the inserted rebar to below the safety margin, thereby eliminating assembly deadlock from the source; The method of disabling conflicts according to the interlocking relationship table is as follows: the interlocking relationship table formed in step S3 is used as an exclusive condition to set mutual exclusion constraints on the steel reinforcement combination, incident side combination and incident angle combination that cause assembly deadlock; when a combination is marked as interlocked, the planning model prohibits the simultaneous selection of the combination, thereby avoiding the generation of assignments that require backtracking or will touch the coating contact restriction area during the solution stage; after the solution is completed, the penetration plan is output.

7. The method for one-time penetration of reinforcing bars through a cross-shaped steel column via a constraint programming-based method according to claim 6, characterized in that, The constraints satisfy integer programming, and their feasibility is limited as a hard constraint by the following compliance determination formula. The selected assignment is deemed compliant if and only if the following formula evaluates to zero: ； in, Choose a binary variable; For steel reinforcement On the incident side Candidate set of angles above; For assignment Predicted contact pressure values; This refers to the upper limit of contact pressure in the coating risk threshold. For assignment The tangential friction level; This represents the upper limit of tangential friction in the coating risk threshold. For the set of allowed corners; This is the maximum cumulative turning angle. The non-negative part of the function represents the positive part of the excess. The non-compliance indication quantity for a single pass indicates whether the assignment requires a reversal or change in the state of the inserted steel bars during the advancement process; a value of zero indicates compliance. This is the disabled matrix entry in the interlock relationship table. A value of 1 indicates combined interlocking, and a value of 0 indicates coexistence. When the above expression equals zero, it means that the selected assignment does not trigger any coating risk, corner overrun, or interlock conflict, and satisfies the one-time penetration constraint.

8. The method for one-time penetration of reinforcing bars through a cross-shaped steel column via a constraint programming-based method according to claim 1, characterized in that, S5 specifically refers to: Installing a detachable flared guide at the edge of a high-risk hole according to the coating contact restriction area is as follows: In the scene model, call the coating contact restriction area and coating risk threshold calibrated in step S2, locate the high-risk hole edge on the hole boundary that causes at least one angle candidate to fall into or be close to exceeding the limit; select the incident side in this hole edge section and determine the coverage arc length so that the coverage range can cover the relevant angle candidate obtained in step S3. A detachable flared guide is configured for this coverage area. The inner surface of the flared guide is aligned with the updated contact normal. The minimum radius of curvature of the flared guide is not less than the minimum bending radius of the reinforcing bar. The friction parameters of the inner surface material are lower than those of the reinforcing bar and the fireproof coating. The guide is fixed relative to the hole boundary by means of clips, screws, or magnetic attraction. The position of the inner edge of the guide and the hole axis is marked to ensure that the reinforcing bar slides in along the inner surface of the flared guide without contacting the fireproof coating during subsequent insertion. The process of resolving the constraints on the rebar insertion sequence, incident side, angle, and guide component usage to satisfy integer programming is as follows: Using the updated scenario model as input, the constraint-satisfying integer programming model from step S4 is used. The variable for the use of the detachable bell-shaped guide component is set to "installed" on the corresponding incident side. The friction parameters and contact boundaries affected by the guide component are replaced. The incident angle range and related constraints are corrected with the updated contact normal and feasibility judgment. The constraints of the allowable rotation angle, one-time penetration constraint, and interlocking relationship table remain effective. The process is resolved under this parameter set, and the penetration plan using the guide component is output. The penetration plan specifies the rebar insertion sequence, incident side, incident angle, and installation status of the detachable bell-shaped guide component for each rebar.

9. The method for one-time penetration of reinforcing bars through a cross-shaped steel column via a constraint programming-based method according to claim 1, characterized in that, A detachable flared guide is installed at the edge of a high-risk orifice according to the coating contact restriction zone. The selection criterion for determining the guide coverage area on the incident beam is determined by minimizing the following objective, which is then determined when the objective reaches its minimum value: ； in, For the incident side The coverage area to be covered by the proposed detachable horn-shaped guide component; For the incident side The boundary of the orifice, Indicates arc length; The reinforcing bars obtained in step S3 On the incident side Angle candidate set; As weights, those exceeding the limit in step S4 prediction are marked. The first item is set to 1, and the rest are set to 0. and In coverage respectively Furthermore, the predicted values ​​of contact pressure and tangential friction when using a detachable flared guide component; and From coating ; It is a function with a non-negative part; The dimensionless tradeoff coefficient is used to penalize the proportion of the coverage arc length in the total arc length. The above formula uses threshold normalization to ensure dimensional consistency, and minimizing the target value corresponds to eliminating the bias caused by the shortest possible coverage arc length. and The resulting over-limit items.

10. A method for one-time penetration of reinforcing bars through a cross-shaped steel column via a constraint programming-based method according to claim 1, characterized in that, S6 specifically refers to: The marking of no-collision zones and angle baselines is as follows: The coating contact restriction zone, hole edge contact control zone, and incident angle in the penetration plan from the scene model are used to calibrate the hole boundary related to the penetration plan on-site; the hole boundary is located at three points using the through-hole center coordinate system, and the projection of the hole axis onto the hole boundary plane is determined as the zero angle; angle baselines are drawn on the hole boundary plane according to the incident angle of each target in the penetration plan; the safety clearance of the coating contact restriction zone and surrounding obstacles is projected onto the hole boundary and its adjacent accessible surface to form a continuous no-collision zone boundary, which is clearly marked on-site with weather-resistant markings or removable patches, ensuring that the operator maintains a spatial clearance from the no-collision zone when executing the specified incident angle and penetration depth, preventing contact with the fireproof coating and surrounding obstacles; The specified timing for installing and removing the guide is as follows: Based on the penetration plan and the coverage arc length of the high-risk hole edge, determine the incident side and its coverage area where the detachable bell-shaped guide needs to be installed; complete the installation of the guide before inserting the first rebar using the coverage area on the incident side, and only begin advancing after the inner edge of the guide and the hole axis are aligned; the guide can only be removed after all rebars that need to pass through the coverage area have passed and their advancement depth exceeds the end point of the guide's coverage; it is prohibited to install or remove the guide during the advancement of any rebar, and it is prohibited to remove it prematurely while the guide's coverage area is still referenced by subsequent entries in the penetration plan, in order to avoid changes in the contact boundary and friction parameters, which could lead to inconsistencies between the on-site execution and the penetration plan.

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