A method for posture and height collaborative stabilization of cable-driven steel bar binding robot based on invariant kalman filter

Abstract

The application provides a cable-driven steel bar binding robot posture and height collaborative stability method based on an invariant Kalman filter, relates to the technical field of building construction automation and robot posture control, and acquires a posture rotation matrix, a vertical velocity and a fused height estimation value by collecting three-axis angular velocity, three-axis linear acceleration, double-sided laser distance, cable length and tension and other data of an end effector, performing extended rigid body motion group state modeling and invariant Kalman filter fusion processing, constructing posture geometric consistency indexes, cable-driven flexible coupling risk indexes and height energy dissipation indexes, and respectively comparing and judging the indexes with corresponding safety thresholds, respectively starting posture collaborative reconstruction, cable-driven flexible balance vibration suppression and height damping steady-state control strategies in abnormal conditions, and forming a closed-loop regulation mechanism. The method can effectively improve the posture and height estimation accuracy, suppress uneven cable stress and flexible vibration amplification, and enhance the system operation stability and operation safety.

Description

Technical Field

[0001] This invention relates to the field of construction automation and robot posture control technology, specifically to a method for cooperative stabilization of posture and height of a cable-driven rebar tying robot based on invariant Kalman filtering. Background Technology

[0002] Rebar tying is a crucial process in building construction, especially in high-rise buildings, prefabricated structures, and complex joint areas. The numerous rebar intersections, limited space, and high workload have historically made this work reliance on manual labor, resulting in high labor intensity, low efficiency, and significant safety risks associated with working at heights. To improve construction efficiency and reduce human risks, rebar tying robots are gradually becoming an important research direction in the field of intelligent construction.

[0003] Existing rebar tying robots mostly employ rigid robotic arm structures or mobile platforms with multi-joint actuators to complete the tying action. However, in large-span construction areas or high-altitude structural environments, rigid structure robots suffer from problems such as heavy weight, complex structure, inconvenient installation, and poor spatial adaptability. To address these issues, cable-driven parallel mechanisms, due to their advantages of light weight, ability to cover a large workspace, and good structural flexibility, have been introduced into rebar tying robot systems to achieve wide-range positioning and operation of the end effector.

[0004] However, cable-driven rebar tying robots are typical flexible drive systems, where the attitude and height control of their end effectors are highly dependent on the length coordination and tension distribution of multiple cables. In actual construction environments, factors such as cable elastic deformation, tension fluctuations, structural disturbances, and changes in construction loads can easily lead to the following technical problems: First, inconsistencies between attitude estimation errors and actual geometric states. Existing systems often use conventional extended Kalman filtering or simple attitude calculation methods for state estimation, failing to fully consider the group structure characteristics of rigid body motion. Under nonlinear coupling conditions, this can easily lead to error accumulation, causing attitude drift and increasing the risk of lateral overturning. Second, uneven stiffness in the cable-driven structure. Uneven tension distribution among multiple cables during dynamic operation can lead to equivalent stiffness imbalance, causing low-frequency oscillations, amplified flexible vibrations, and the risk of local cable overload, affecting tying accuracy and structural safety. Third, oscillations in dynamic height control. Due to unreasonable end-effector mass, cable flexibility, and control gain settings, vertical oscillations or height drift can easily occur, leading to increased tying point deviations and repeatability errors, thus affecting construction quality.

[0005] Existing technologies typically adjust attitude control, height control, or tension distribution independently, lacking a multi-index collaborative stabilization mechanism based on a unified state estimation framework. They also fail to form an integrated closed-loop risk assessment and adjustment system encompassing attitude, structure, and height, making it difficult to achieve long-term stable operation in complex construction environments. Summary of the Invention

[0006] The purpose of this invention is to provide a cooperative stabilization method for the posture and height of a cable-driven rebar tying robot based on invariant Kalman filtering, so as to solve the problems mentioned in the background art.

[0007] To achieve the above objectives, the present invention provides the following technical solution: A cooperative stabilization method for attitude and height of a cable-driven rebar tying robot based on invariant Kalman filtering, comprising the following steps: Step 1: Collect raw data of the three-axis angular velocity, three-axis linear acceleration, left-side distance, and right-side distance of the end effector of the cable-driven rebar tying robot; collect the length and tension data of the eight drive cables; and the laser installation spacing and target working height. Step 2: Perform extended rigid body motion group state modeling, invariant Kalman filter fusion processing, and dual-laser differential geometric solution processing on the original attitude inertia data and the original bilateral height data to obtain the filtered attitude rotation matrix, filtered vertical velocity, fused height estimate, geometric roll angle, filtered roll angle, and filtered pitch angle. Step 3: By calculating the attitude geometric consistency index and comparing it with the attitude consistency safety threshold, determine whether the attitude geometric consistency between the attitude estimation result of the cable-driven rebar binding robot end effector and the dual laser geometric constraints is qualified. If it is not qualified, a posture collaborative reconstruction strategy is given. Step 4: Calculate the cable-driven flexible coupling risk index and compare it with the cable-driven flexible coupling safety threshold to determine whether the force and length distribution of the eight steel cables of the cable-driven rebar binding robot are in a balanced state. If not, a cable-driven flexible equalization vibration suppression strategy is given. Step 5: Calculate the height energy dissipation index and compare it with the height stability safety threshold to determine whether the current height control of the cable-driven rebar tying robot's end effector is in a stable state. If not, apply a height damping steady-state control strategy.

[0008] Further, step one includes: S11. Real-time monitoring of the attitude changes and instantaneous motion state of the end effector of the cable-driven rebar tying robot is performed. By installing a six-axis inertial measurement unit (IMU) at the geometric center of the end effector, raw data of the three-axis angular velocities during the operation are continuously collected, including roll rate, pitch rate, and yaw rate; as well as raw data of the three-axis linear accelerations, including linear acceleration in the X-axis direction, linear acceleration in the Y-axis direction, and linear acceleration in the Z-axis direction. A unified timestamp is added to each set of data to establish a raw attitude inertial dataset. S12. Real-time monitoring of the absolute height and lateral tilt of the end effector relative to the ground is performed by installing a laser rangefinder at the left and right symmetrical positions at the bottom of the end effector, continuously collecting the distance values ​​on the left and right sides, and adding a unified timestamp to the distance measurement data to establish a raw dataset of bilateral height. S13. Real-time monitoring of the length changes of the eight drive cables is carried out by installing a high-precision rotary encoder at the output shaft of the drive motor corresponding to each cable, collecting the length data of each cable in real time, recording the corresponding timestamp, and establishing the original dataset of cable length. S14. Real-time monitoring of the stress state of the eight drive cables is carried out by installing tension sensors at the fixed end or tension end of each cable, continuously collecting the tension value of each cable, and adding a uniform time identifier to establish the original dataset of cable stress. S15. Obtain the installation distance between the left and right laser rangefinders through structural calibration during the installation phase, and set the target operating height during the control system initialization phase to establish a system reference parameter dataset.

[0009] Furthermore, step two includes: S21. Based on the roll change rate, pitch change rate, yaw change rate, linear acceleration in the X-axis direction, linear acceleration in the Y-axis direction, and linear acceleration in the Z-axis direction of the original attitude inertia dataset, the invariant Kalman filter method of extended rigid body motion group state modeling is used to perform attitude prediction and invariant error correction processing to obtain the filtered attitude rotation matrix. S22. Based on the linear acceleration in the Z-axis direction in the original attitude inertia dataset, and combined with the left and right distance values ​​in the original bilateral height dataset as observation constraints, the invariant Kalman filter method of extended rigid body motion group state modeling is used to estimate the velocity state and compensate for the gravity component to obtain the filtered vertical velocity. S23. Based on the left and right distance values ​​in the original bilateral height dataset, and combined with the linear acceleration in the Z-axis direction in the original attitude inertial dataset, the height fusion estimation method of invariant Kalman filtering is used to perform observation update and state fusion processing to obtain the fused height estimate. S24. Based on the left and right distance values ​​in the original dual-sided height dataset, and combined with the installation distance between the left and right laser rangefinders in the system reference parameter dataset, the dual-laser differential geometric solution method is used to perform lateral tilt inversion calculation to obtain the geometric roll angle. S25. Based on the filtered attitude rotation matrix, the attitude angle decomposition process is performed by using the rotation matrix to Euler angle conversion method to obtain the filtered roll angle. S26. Based on the filtered attitude rotation matrix, the attitude angle decomposition process is performed by using the rotation matrix to Euler angle conversion method to obtain the filtered pitch angle.

[0010] Furthermore, step three includes: S31. After dimensionless processing of the obtained filtered roll angle, geometric roll angle and filtered pitch angle, the attitude difference weighted calculation is performed to obtain the attitude geometric consistency index.

[0011] Furthermore, step three also includes: S32. By setting a preset attitude consistency safety threshold and comparing the attitude geometric consistency index with the attitude consistency safety threshold, the first evaluation result is obtained, including: When the attitude geometric consistency index is less than or equal to the attitude consistency safety threshold, it indicates that the attitude geometric consistency between the attitude estimation result of the cable-driven rebar tying robot end effector and the dual laser geometric constraints is qualified, and continuous monitoring is required. When the attitude geometric consistency index exceeds the attitude consistency safety threshold, it indicates that the attitude geometric consistency between the attitude estimation result of the cable-driven rebar tying robot's end effector and the dual-laser geometric constraints is unqualified. This poses risks of lateral overturning, cable force redistribution, tying positioning accuracy deviation, and height estimation error amplification. This triggers the first warning command and generates the first strategy: initiate attitude and height collaborative constraint control, limit the output of the end effector's horizontal displacement command, and generate an attitude coupling correction amount based on the fused height estimate and filtered vertical velocity to drive the cable to perform synchronous retrieval and release for attitude reconstruction. After the adjustment is completed, the attitude geometric consistency index is recalculated until it is less than or equal to the attitude consistency safety threshold.

[0012] Furthermore, step four includes: S41. Based on the tension values ​​of eight steel cables in the original dataset of steel cable stress, the tension dispersion is analyzed and processed by the statistical standard deviation calculation method to obtain the tension dispersion. S42. Based on the length data of eight steel cables in the original dataset of steel cable lengths, the length dispersion is analyzed using the statistical standard deviation calculation method to obtain the length dispersion.

[0013] Furthermore, step four also includes: S43. After dimensionless processing of the obtained tension dispersion and length dispersion, the dispersion weighted calculation is performed to obtain the cable-driven flexible coupling risk index.

[0014] Furthermore, step four also includes: S44. By setting a safety threshold for cable-driven flexible coupling and comparing the cable-driven flexible coupling risk index with the cable-driven flexible coupling safety threshold, the second evaluation results are obtained, including: When the cable-driven flexible coupling risk index is less than or equal to the cable-driven flexible coupling safety threshold, it indicates that the force and length distribution of the eight steel cables of the cable-driven rebar binding robot are in a balanced state, and continuous monitoring is required. When the cable-driven flexible coupling risk index exceeds the cable-driven flexible coupling safety threshold, it indicates that the eight cables of the cable-driven rebar binding robot are unevenly distributed in terms of force or length. This presents risks of unbalanced equivalent stiffness of the cable-driven structure, amplification of attitude and height control coupling, and local overload of the cables. This triggers a second warning command and generates a second strategy: Using the average tension of the eight cables as the target, tension regression control is implemented on cables with large tension deviations to converge the tension of each cable towards the overall average. Adaptive attenuation is applied to the current attitude control gain and height control gain according to the control gain correction principle, which is inversely proportional to the cable-driven flexible coupling risk index. This reduces the system's rapid response to errors and suppresses the amplification effect of flexible vibration caused by structural stiffness imbalance. Large-amplitude rapid adjustment commands in the height direction are restricted to reduce the peak vertical acceleration. The system is then recalculated until the cable-driven flexible coupling risk index is less than or equal to the cable-driven flexible coupling safety threshold.

[0015] Furthermore, step five includes: S51. By obtaining the filtered vertical velocity and the fused height estimate, and combining them with the target working height, the height energy dissipation index is calculated after dimensionless processing.

[0016] Furthermore, step five also includes: S52. By setting a high stability safety threshold and comparing the high energy dissipation index with the high stability safety threshold, the third evaluation results are obtained, including: When the height energy dissipation index is less than or equal to the height stability safety threshold, it indicates that the end effector of the cable-driven rebar tying robot is in a stable state of height control and will be continuously monitored. When the height energy dissipation index exceeds the height stability safety threshold, it indicates that the end effector of the cable-driven rebar tying robot is not in a stable state in terms of current height control, and there is a risk of accumulated tying position errors and additional structural impact loads. This triggers the third warning command and generates a third strategy: increase the virtual damping coefficient in the vertical direction, reduce the height control proportional gain, and reduce the vertical response sensitivity; limit the output of rapid displacement commands in the height direction to suppress the peak vertical acceleration; reduce the overall system response frequency; and recalculate the height energy dissipation index after adjustment until the height energy dissipation index is ≤ the height stability safety threshold.

[0017] Compared with the prior art, the beneficial effects of the present invention are: This invention utilizes an invariant Kalman filter fusion process to extend rigid body motion group state modeling, unifying the modeling and observation constraint fusion of inertial data and dual-laser height data. Simultaneously, it introduces geometric roll angles to verify the consistency of the filtered attitude results. This effectively suppresses the error accumulation problem caused by traditional Euler angle linearization, improves the stability and anti-interference capability of attitude and height estimation, and thus enhances the binding and positioning accuracy.

[0018] This invention also constructs a cable-driven flexible coupling risk index to quantitatively evaluate the tension and length dispersion of the eight steel cables, and implements a tension regression and control gain adaptive attenuation strategy under abnormal conditions. This can effectively avoid problems such as uneven stress on the steel cables, imbalance of equivalent stiffness, and amplification of flexible vibration, reduce the risk of local overload of the steel cables, and improve the overall structural safety and operational stability of the system.

[0019] This invention also establishes an attitude geometric consistency index, a cable-driven flexible coupling risk index, and an altitude energy dissipation index, and combines them with corresponding safety thresholds for hierarchical judgment and closed-loop adjustment, forming a closed-loop stability control system from state estimation, risk assessment to strategy execution and index recalculation. This achieves coordinated stability control of attitude and altitude, reduces overturning risk and impact load risk, and improves operational continuity and system reliability. Attached Figure Description

[0020] Figure 1 This is a schematic diagram of the overall method flow of the present invention. Detailed Implementation

[0021] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0022] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein, and those skilled in the art can make similar extensions without departing from the spirit of the invention. Therefore, the invention is not limited to the specific embodiments disclosed below.

[0023] Example 1 Please see Figure 1 This invention provides a technical solution: a method for cooperative stabilization of posture and height of a cable-driven rebar tying robot based on invariant Kalman filtering, the specific steps of which include: Step 1: Collect raw data of the three-axis angular velocity, three-axis linear acceleration, left-side distance, and right-side distance of the end effector of the cable-driven rebar tying robot; collect the length and tension data of the eight drive cables; and the laser installation spacing and target working height. Step 2: Perform extended rigid body motion group state modeling, invariant Kalman filter fusion processing, and dual-laser differential geometric solution processing on the original attitude inertia data and the original bilateral height data to obtain the filtered attitude rotation matrix, filtered vertical velocity, fused height estimate, geometric roll angle, filtered roll angle, and filtered pitch angle. Step 3: By calculating the attitude geometric consistency index and comparing it with the attitude consistency safety threshold, determine whether the attitude geometric consistency between the attitude estimation result of the cable-driven rebar binding robot end effector and the dual laser geometric constraints is qualified. If it is not qualified, a posture collaborative reconstruction strategy is given. Step 4: Calculate the cable-driven flexible coupling risk index and compare it with the cable-driven flexible coupling safety threshold to determine whether the force and length distribution of the eight steel cables of the cable-driven rebar binding robot are in a balanced state. If not, a cable-driven flexible equalization vibration suppression strategy is given. Step 5: Calculate the height energy dissipation index and compare it with the height stability safety threshold to determine whether the current height control of the cable-driven rebar tying robot's end effector is in a stable state. If not, apply a height damping steady-state control strategy.

[0024] In this embodiment, three types of state evaluation indicators are constructed: attitude geometric consistency index, cable-driven flexible coupling risk index, and height energy dissipation index. These indicators are then compared with their corresponding safety thresholds to achieve real-time identification and closed-loop control of attitude estimation deviation, uneven cable stress, and height oscillation risks. This enables timely collaborative correction in the early stages of risk formation, effectively reducing overturning risks and structural impact loads, and improving the overall stability and safety reliability of the cable-driven rebar binding robot during operation.

[0025] Example 2 Please see Figure 1 In this embodiment, as explained in Embodiment 1, specifically, step one includes: S11. Real-time monitoring of the attitude changes and instantaneous motion state of the end effector of the cable-driven rebar tying robot is performed. By installing a six-axis inertial measurement unit (IMU) at the geometric center of the end effector, raw data of the three-axis angular velocities during the operation are continuously collected, including roll rate (ωx), pitch rate (ωy), and yaw rate (ωz); and raw data of the three-axis linear accelerations, including linear acceleration in the X-axis direction (ax), linear acceleration in the Y-axis direction (ay), and linear acceleration in the Z-axis direction (az). A unified timestamp is added to each set of data to establish a raw attitude inertial dataset. S12. Real-time monitoring of the absolute height and lateral tilt of the end effector relative to the ground is carried out by installing a laser rangefinder at the left and right symmetrical positions at the bottom of the end effector, continuously collecting the distance value on the left side (hL) and the distance value on the right side (hR), and adding a unified timestamp to the distance measurement data to establish a raw dataset of bilateral height. S13. Real-time monitoring of the length changes of the eight drive cables is carried out by installing a high-precision rotary encoder at the output shaft of the drive motor corresponding to each cable, collecting the length data of each cable in real time, denoted as L, and recording the corresponding timestamp to establish the original dataset of cable length. S14. Real-time monitoring of the stress state of the eight drive cables is carried out by installing tension sensors at the fixed end or tension end of each cable, continuously collecting the tension value of each cable, recording it as T, and adding a uniform time identifier to establish the original dataset of cable stress. S15. Obtain the installation distance between the left and right laser rangefinders through structural calibration during the installation phase, denoted as W, and set the target operating height during the control system initialization phase, denoted as Href, to establish a system reference parameter dataset.

[0026] In this embodiment, by synchronously collecting the three-axis angular velocity data, three-axis linear acceleration data, left and right side distance data of the end effector, as well as the length and tension data of the eight steel cables, and establishing a dataset with a unified time reference, and introducing the laser installation spacing and target working height as system reference parameters, unified time-series management of multi-source information on attitude, height and cable force status is achieved. This provides a complete and reliable data foundation for subsequent state modeling and fusion estimation, thereby improving the accuracy and real-time performance of system state identification.

[0027] Example 3 Please see Figure 1 In the explanation of Example 2, this embodiment specifically includes the following steps: S21. Based on the roll change velocity ωx, pitch change velocity ωy, yaw change velocity ωz, linear acceleration ax in the X-axis direction, linear acceleration ay in the Y-axis direction, and linear acceleration az in the Z-axis direction from the original attitude inertial dataset, the invariant Kalman filter method of extended rigid body motion group state modeling is used to perform attitude prediction and invariant error correction processing, and the filtered attitude rotation matrix is ​​obtained, denoted as Rest. S22. Based on the linear acceleration az in the Z-axis direction in the original attitude inertia dataset, and combined with the left distance hL and right distance hR in the original bilateral height dataset as observation constraints, the invariant Kalman filter method of extended rigid body motion group state modeling is used to estimate the velocity state and compensate for the gravity component, and obtain the filtered vertical velocity, denoted as VZest. S23. Based on the left distance value hL and the right distance value hR in the original bilateral height dataset, and combined with the linear acceleration az in the Z-axis direction in the original attitude inertial dataset, the height fusion estimation method of invariant Kalman filtering is used to perform observation update and state fusion processing to obtain the fused height estimate, denoted as Hest. S24. Based on the left-side distance value hL and right-side distance value hR in the original dual-sided height dataset, and combined with the installation distance W between the left and right laser rangefinders in the system reference parameter dataset, a dual-laser differential geometric solution method is used to perform lateral tilt inversion calculation to obtain the geometric roll angle, denoted as... geo; S25. Based on the filtered attitude rotation matrix Rest, the attitude angle decomposition process is performed using the rotation matrix to Euler angle transformation method to obtain the filtered roll angle, denoted as . est; S26. Based on the filtered attitude rotation matrix Rest, the attitude angle decomposition process is performed using the rotation matrix to Euler angle conversion method to obtain the filtered pitch angle, denoted as θest.

[0028] In this embodiment, by extending the state modeling of rigid body motion groups with invariant Kalman filtering fusion processing, an integrated estimation of attitude prediction, invariant error correction, gravity component compensation, and height observation fusion is achieved. At the same time, the geometric roll angle is obtained by dual-laser differential geometric calculation, forming a geometric constraint verification mechanism for the filtered attitude results. This improves the accuracy and consistency of the attitude rotation matrix, vertical velocity, and fused height estimates, and enhances the robustness and stability of the system under nonlinear motion and external disturbance conditions.

[0029] Example 4 Please see Figure 1 In the explanation of Example 3, this embodiment specifically includes the following steps: S31. Obtain the filtered roll angle est, geometric roll angle After dimensionless processing of geo and the filtered pitch angle θest, attitude difference weighted calculation is performed to obtain the attitude geometric consistency index, denoted as PGI, as shown in the following formula:

[0030] In the formula, w1 and w2 represent weighting coefficients.

[0031] : Characterizes the impact of roll angle estimation bias on attitude consistency, and has a high weight; roll angle directly affects end-effector lateral stability and anti-overturning capability, and the difference between it and the dual-laser geometric solution result reflects the core degree of attitude estimation error and is a key indicator for judging lateral instability risk. : Characterizes the impact of pitch angle on attitude consistency, and has the second highest weight; pitch changes will cause altitude estimation coupling error and tethering positioning offset, but have a relatively small impact on lateral rollover, so its weight is slightly lower than that of the roll angle difference item. This formula is essentially a linear representation model of the energy of attitude estimation error; the roll angle estimation error reflects the degree of deviation from the lateral geometric constraint, and the pitch angle reflects the degree of longitudinal attitude coupling; by performing dimensionless weighted superposition of the two types of attitude components, the spatial attitude error is uniformly mapped into a single risk index, thereby achieving a quantitative expression of attitude geometric consistency.

[0032] In this embodiment, by performing dimensionless and weighted difference calculations on the filtered roll angle, geometric roll angle, and filtered pitch angle, an attitude geometric consistency index is constructed. This enables a quantitative representation of the degree of deviation between the attitude estimation result and the geometric constraints. It can transform the attitude error, which was originally difficult to judge directly, into an index parameter that can be judged by thresholds, thereby improving the sensitivity and predictability of attitude anomaly identification and providing a clear basis for triggering subsequent collaborative control strategies.

[0033] Example 5 Please see Figure 1 In the explanation of Example 4, specifically, step three further includes: S32. By setting a preset attitude consistency safety threshold, denoted as Pth, and comparing the attitude geometric consistency index PGI with the attitude consistency safety threshold Pth, the first evaluation results are obtained, including: When the attitude geometric consistency index PGI ≤ attitude consistency safety threshold Pth, it indicates that the attitude geometric consistency between the attitude estimation result of the cable-driven rebar tying robot end effector and the dual laser geometric constraints is qualified, and continuous monitoring is required. When the attitude geometric consistency index PGI > attitude consistency safety threshold Pth, it indicates that the attitude geometric consistency between the attitude estimation result of the cable-driven rebar tying robot's end effector and the dual-laser geometric constraints is unqualified. This poses risks of lateral overturning, cable force redistribution, tying positioning accuracy deviation, and height estimation error amplification. This triggers the first warning command and generates the first strategy: initiate attitude and height collaborative constraint control, limit the output of the end effector's horizontal displacement command, and generate an attitude coupling correction amount based on the fused height estimate and filtered vertical velocity to drive the cable to perform synchronous retrieval and release for attitude reconstruction. After the adjustment is completed, the attitude geometric consistency index is recalculated until the attitude geometric consistency index PGI ≤ attitude consistency safety threshold Pth.

[0034] The method for obtaining the attitude consistency safety threshold Pth is as follows: Through extensive comparative statistical analysis of the attitude estimation data and dual-laser geometric calculation results of the cable-driven rebar tying robot during multi-condition operations, the distribution range of the attitude geometric consistency index in the normal stable state and the attitude instability critical state is extracted. Combined with the structural overturning margin analysis results and the engineering experience of professional technicians, a reasonable attitude consistency critical judgment value is determined. At the same time, the threshold range is checked and corrected with reference to the equipment structural design parameters, steel cable safety factor and on-site construction stability requirements, so as to effectively distinguish between the attitude estimation error acceptable state and the state with overturning risk.

[0035] In this embodiment, by comparing the attitude geometric consistency index with a preset safety threshold, real-time judgment and graded response to attitude anomalies are achieved. When the attitude deviation exceeds the limit, attitude and height collaborative reconstruction control is automatically initiated, and after adjustment, the index is recalculated to form a closed-loop control mechanism. This mechanism can intervene in time before the overturning trend and positioning error increase, effectively reducing the risk of lateral instability and the risk of height error amplification, and improving the safety and continuous stability of the operation process.

[0036] Example 6 Please see Figure 1 In the explanation of Example 5, specifically, step four includes: S41. Based on the tension values ​​T of eight steel cables in the original dataset of steel cable stress, the tension dispersion is analyzed by using the statistical standard deviation calculation method to obtain the tension dispersion, denoted as σT. S42. Based on the length data L of eight steel cables in the original dataset of steel cable lengths, the length dispersion is analyzed using the statistical standard deviation calculation method to obtain the length dispersion, denoted as σL.

[0037] In this embodiment, by performing statistical standard deviation analysis on the tension values ​​and length data of the eight steel cables, the tension dispersion and length dispersion are obtained, thereby achieving a quantitative characterization of the equilibrium of the force and geometric distribution of the steel cables. This can transform the problem of uneven force distribution, which was originally difficult to judge intuitively, into a calculable discrete index, thereby improving the ability to identify changes in the equivalent stiffness of cable-driven structures and potential imbalance trends.

[0038] Example 7 Please see Figure 1 In the explanation of Example Six, specifically, step four further includes: S43. After dimensionless processing of the obtained tension dispersion σT and length dispersion σL, a dispersion weighted calculation is performed to obtain the cable-driven flexible coupling risk index, denoted as FCI, as shown in the following formula:

[0039] In the formula, a1 and a2 represent weighting coefficients.

[0040] The stress dispersion characterizes the impact of flexible coupling risk and has a dominant weight; the stress distribution directly determines the equivalent stiffness and stress equilibrium state of the cable-driven structure, and is a key factor affecting vibration amplification and local overload. : Characterizes the impact of length dispersion on the risk of flexible coupling, accounting for auxiliary weight; length difference reflects geometric configuration deviation and attitude coupling degree, which has an indirect impact on stiffness change, so its weight is relatively low; Tension dispersion reflects the degree of uneven force distribution, while length dispersion reflects the geometric deviation of the structure. Together, they determine the balance of the system's equivalent stiffness matrix. By linear weighted superposition, the uneven mechanical distribution and geometric configuration deviation are uniformly characterized as a flexible coupling risk index, thereby achieving a comprehensive quantification of the amplification trend of structural vibration.

[0041] In this embodiment, by dimensionless and weighted fusion of tension dispersion and length dispersion, a cable-driven flexible coupling risk index is constructed, which realizes a comprehensive quantitative assessment of the coupling effect of uneven cable stress and geometric deviation. This can more comprehensively reflect the overall flexibility imbalance of the cable-driven system and improve the accuracy of judging the structural stiffness imbalance and coupled vibration risk.

[0042] Example 8 Please see Figure 1 In the explanation of Example 7, specifically, step four further includes: S44. By setting a preset safety threshold for cable-driven flexible coupling, denoted as Fth, and comparing the cable-driven flexible coupling risk index FCI with the cable-driven flexible coupling safety threshold Fth, the second evaluation results are obtained, including: When the cable-driven flexible coupling risk index FCI is less than or equal to the cable-driven flexible coupling safety threshold Fth, it indicates that the force and length distribution of the eight steel cables of the cable-driven rebar binding robot are in a balanced state, and continuous monitoring is required. When the cable-driven flexible coupling risk index FCI > the cable-driven flexible coupling safety threshold Fth, it indicates that the eight cables of the cable-driven rebar binding robot are unevenly distributed in terms of force or length. This presents risks of uneven equivalent stiffness of the cable-driven structure, amplification of attitude and height control coupling, and local overload of the cables. This triggers a second warning command and generates a second strategy: using the average tension of the eight cables as the target, tension regression control is performed on cables with large tension deviations to converge the tension of each cable towards the overall average; according to the control gain correction principle that is inversely proportional to the cable-driven flexible coupling risk index, the current attitude control gain and height control gain are adaptively attenuated to reduce the system's rapid response to errors and suppress the amplification effect of flexible vibration caused by structural stiffness imbalance; large-amplitude rapid adjustment commands in the height direction are restricted to reduce the peak value of vertical acceleration; after adjustment, the calculation is repeated until the cable-driven flexible coupling risk index FCI ≤ the cable-driven flexible coupling safety threshold Fth.

[0043] The method for obtaining the safety threshold Fth of cable-driven flexible coupling is as follows: By statistically analyzing the tension and length distribution data of eight steel cables under different loads and attitude conditions, the variation range of tension dispersion and length dispersion under structural equilibrium and stiffness imbalance critical states is extracted. Combined with the allowable stress of the steel cables, the analysis results of the equivalent stiffness model of the structure, and on-site commissioning experience, the critical judgment value of cable-driven flexible coupling risk is determined. The threshold is verified by referring to the steel cable manufacturing parameters and safety operation specifications to distinguish between the stress equilibrium operation state and the state with local overload or vibration amplification risk.

[0044] In this embodiment, by comparing the cable-driven flexible coupling risk index with a preset safety threshold, the system can identify and control the imbalance of the cable's stress and length distribution in real time. When the risk exceeds the limit, the system can automatically initiate the tension regression and adaptive attenuation strategy of control gain, and then recalculate the index until it returns to the safe range. This effectively suppresses the amplification of flexible vibration and local overload, and improves the stress balance and system operation stability of the cable-driven structure.

[0045] Example 9 Please see Figure 1 In the explanation of Embodiment Eight, specifically, step five includes: S51. Using the obtained filtered vertical velocity VZest and fused height estimate Hest, combined with the target working height Href, after dimensionless processing, the height energy dissipation index, denoted as HEI, is calculated as follows:

[0046] In the formula, s1 and s2 represent weighting coefficients.

[0047] The vertical velocity of the filter represents the impact of height stability and has a high weight; the vertical velocity of the filter directly reflects the kinetic energy level of the system and is the core indicator reflecting the height oscillation trend. The height deviation characterizes the impact of height deviation on stability and has the second highest weight. Height deviation reflects the degree of accumulation of positional errors and is directly related to construction accuracy, but its immediate responsiveness to oscillation trends is slightly lower than that of the velocity term. This formula is based on the principles of energy dissipation and dynamic system stability; vertical velocity corresponds to the kinetic energy component, and height deviation corresponds to the potential energy shift component; by weighting and fusing the kinetic energy and potential energy terms, a comprehensive quantification of the dynamic energy state of the height system is achieved, which can effectively characterize the oscillation amplification or height drift trend.

[0048] In this embodiment, by performing dimensionless weighted fusion of the filtered vertical velocity and the fused height estimate, a height energy dissipation index is constructed, which realizes a comprehensive quantitative characterization of height deviation and vertical motion trend. This can unify height error and oscillation trend into a identifiable indicator, improve the ability to identify height drift and vertical oscillation risks in advance, and provide a clear basis for height stability control.

[0049] Example 10 Please see Figure 1 In the explanation of Embodiment Nine, specifically, step five further includes: S52. By setting a high stability safety threshold, denoted as Hth, and comparing the high energy dissipation index HEI with the high stability safety threshold Hth, the third evaluation results are obtained, including: When the height energy dissipation index HEI ≤ the height stability safety threshold Hth, it indicates that the end effector of the cable-driven rebar tying robot is in a stable state of height control and is continuously monitored. When the height energy dissipation index HEI > the height stability safety threshold Hth, it indicates that the current height control of the end effector of the cable-driven rebar tying robot is not in a stable state, and there is a risk of accumulated tying position error and additional impact load on the structure. This triggers the third warning command and generates a third strategy: increase the virtual damping coefficient in the vertical direction, reduce the height control proportional gain, and reduce the vertical response sensitivity; limit the output of rapid displacement commands in the height direction to suppress the peak vertical acceleration; reduce the overall system response frequency; after the adjustment is completed, recalculate the height energy dissipation index until the height energy dissipation index HEI ≤ the height stability safety threshold Hth.

[0050] The method for obtaining the height stability safety threshold Hth is as follows: By statistically analyzing the vertical velocity and height deviation data of the end effector under different binding cycles and different height control response conditions, the range of the height energy dissipation index in the stable convergence state and the critical state of oscillation amplification is extracted. Combined with the structural impact load test results and construction positioning accuracy requirements, a reasonable height stability critical judgment value is determined. At the same time, the threshold range is comprehensively checked with reference to the dynamic response characteristic parameters of the equipment and the safety operation standards, so as to effectively distinguish the height stable operation state from the state with oscillation or drift risk.

[0051] In this embodiment, by comparing the height energy dissipation index with the preset height stability safety threshold, the risk of height oscillation and drift is determined in real time. When the limit is exceeded, the damping enhancement and response suppression adjustment mechanism is automatically activated. At the same time, the closed-loop control process is formed by recalculating the index, which can effectively reduce the risk of vertical impact load and position error accumulation, and improve the stability and operation accuracy of the end effector height control.

[0052] It should be noted that all calculation formulas in this application employ regression analysis, including but not limited to machine learning algorithms, to deeply analyze the collected parameters and identify their natural trends and interrelationships. Specialized software, such as Python's Scikit-learn library or the R language, is used to automatically generate mathematical models that match the data. Then, cross-validation and other methods are used to objectively evaluate the model performance, and continuous feedback and optimization are combined to ensure that the created formulas truly reflect the inherent laws of the data, thereby guaranteeing their effectiveness and accuracy. In all calculation formulas in this application, the parameters in each formula undergo dimensionless processing within a consistent range to ensure that different physical quantities are compared on the same scale; dimensionless processing techniques include, but are not limited to, min-max-normalization and Z-score standardization. The algorithm of this invention is implemented as a Python script. Before executing the core logic, the program first executes a data loading module (e.g., using the widely used pandas library in Python) configured to read the aforementioned spreadsheet file and load its contents into the program's working memory (e.g., a DataFrame data structure). Subsequent algorithm steps will directly query and retrieve the required configuration parameters from this in-memory data structure.

[0053] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A method for cooperative stabilization of posture and height of a cable-driven rebar tying robot based on invariant Kalman filtering, characterized in that, The specific steps include: Step 1: Collect raw data of the three-axis angular velocity, three-axis linear acceleration, left-side distance, and right-side distance of the end effector of the cable-driven rebar tying robot; collect the length and tension data of the eight drive cables; and the laser installation spacing and target working height. Step 2: Perform extended rigid body motion group state modeling, invariant Kalman filter fusion processing, and dual-laser differential geometric solution processing on the original attitude inertia data and the original bilateral height data to obtain the filtered attitude rotation matrix, filtered vertical velocity, fused height estimate, geometric roll angle, filtered roll angle, and filtered pitch angle. Step 3: By calculating the attitude geometric consistency index and comparing it with the attitude consistency safety threshold, determine whether the attitude geometric consistency between the attitude estimation result of the cable-driven rebar binding robot end effector and the dual laser geometric constraints is qualified. If it is not qualified, a posture collaborative reconstruction strategy is given. Step 4: Calculate the cable-driven flexible coupling risk index and compare it with the cable-driven flexible coupling safety threshold to determine whether the force and length distribution of the eight steel cables of the cable-driven rebar binding robot are in a balanced state. If not, a cable-driven flexible equalization vibration suppression strategy is given. Step 5: Calculate the height energy dissipation index and compare it with the height stability safety threshold to determine whether the current height control of the cable-driven rebar tying robot's end effector is in a stable state. If not, apply a height damping steady-state control strategy.

2. The method for cooperative stabilization of attitude and height of a cable-driven rebar tying robot based on invariant Kalman filtering according to claim 1, characterized in that: Step one includes: S11. Real-time monitoring of the attitude changes and instantaneous motion state of the end effector of the cable-driven rebar tying robot is performed. By installing a six-axis inertial measurement unit (IMU) at the geometric center of the end effector, raw data of the three-axis angular velocities during the operation are continuously collected, including roll rate, pitch rate, and yaw rate; as well as raw data of the three-axis linear accelerations, including linear acceleration in the X-axis direction, linear acceleration in the Y-axis direction, and linear acceleration in the Z-axis direction. A unified timestamp is added to each set of data to establish a raw attitude inertial dataset. S12. Real-time monitoring of the absolute height and lateral tilt of the end effector relative to the ground is performed by installing a laser rangefinder at the left and right symmetrical positions at the bottom of the end effector, continuously collecting the distance values ​​on the left and right sides, and adding a unified timestamp to the distance measurement data to establish a raw dataset of bilateral height. S13. Real-time monitoring of the length changes of the eight drive cables is carried out by installing a high-precision rotary encoder at the output shaft of the drive motor corresponding to each cable, collecting the length data of each cable in real time, recording the corresponding timestamp, and establishing the original dataset of cable length. S14. Real-time monitoring of the stress state of the eight drive cables is carried out by installing tension sensors at the fixed end or tension end of each cable, continuously collecting the tension value of each cable, and adding a uniform time identifier to establish the original dataset of cable stress. S15. Obtain the installation distance between the left and right laser rangefinders through structural calibration during the installation phase, and set the target operating height during the control system initialization phase to establish a system reference parameter dataset.

3. The method for cooperative stabilization of attitude and height of a cable-driven rebar tying robot based on invariant Kalman filtering according to claim 2, characterized in that: Step two includes: S21. Based on the roll change rate, pitch change rate, yaw change rate, linear acceleration in the X-axis direction, linear acceleration in the Y-axis direction, and linear acceleration in the Z-axis direction of the original attitude inertia dataset, the invariant Kalman filter method of extended rigid body motion group state modeling is used to perform attitude prediction and invariant error correction processing to obtain the filtered attitude rotation matrix. S22. Based on the linear acceleration in the Z-axis direction in the original attitude inertia dataset, and combined with the left and right distance values ​​in the original bilateral height dataset as observation constraints, the invariant Kalman filter method of extended rigid body motion group state modeling is used to estimate the velocity state and compensate for the gravity component to obtain the filtered vertical velocity. S23. Based on the left and right distance values ​​in the original bilateral height dataset, and combined with the linear acceleration in the Z-axis direction in the original attitude inertial dataset, the height fusion estimation method of invariant Kalman filtering is used to perform observation update and state fusion processing to obtain the fused height estimate. S24. Based on the left and right distance values ​​in the original dual-sided height dataset, and combined with the installation distance between the left and right laser rangefinders in the system reference parameter dataset, the dual-laser differential geometric solution method is used to perform lateral tilt inversion calculation to obtain the geometric roll angle. S25. Based on the filtered attitude rotation matrix, the attitude angle decomposition process is performed by using the rotation matrix to Euler angle conversion method to obtain the filtered roll angle. S26. Based on the filtered attitude rotation matrix, the attitude angle decomposition process is performed by using the rotation matrix to Euler angle conversion method to obtain the filtered pitch angle.

4. The method for cooperative stabilization of attitude and height of a cable-driven rebar tying robot based on invariant Kalman filtering according to claim 3, characterized in that: Step three includes: S31. After dimensionless processing of the obtained filtered roll angle, geometric roll angle and filtered pitch angle, the attitude difference weighted calculation is performed to obtain the attitude geometric consistency index.

5. The method for cooperative stabilization of attitude and height of a cable-driven rebar tying robot based on invariant Kalman filtering according to claim 4, characterized in that: Step three also includes: S32. By setting a preset attitude consistency safety threshold and comparing the attitude geometric consistency index with the attitude consistency safety threshold, the first evaluation result is obtained, including: When the attitude geometric consistency index is less than or equal to the attitude consistency safety threshold, it indicates that the attitude geometric consistency between the attitude estimation result of the cable-driven rebar tying robot end effector and the dual laser geometric constraints is qualified, and continuous monitoring is required. When the attitude geometric consistency index exceeds the attitude consistency safety threshold, it indicates that the attitude geometric consistency between the attitude estimation result of the cable-driven rebar tying robot's end effector and the dual-laser geometric constraints is unqualified. This poses risks of lateral overturning, cable force redistribution, tying positioning accuracy deviation, and height estimation error amplification. This triggers the first warning command and generates the first strategy: initiate attitude and height collaborative constraint control, limit the output of the end effector's horizontal displacement command, and generate an attitude coupling correction amount based on the fused height estimate and filtered vertical velocity to drive the cable to perform synchronous retrieval and release for attitude reconstruction. After the adjustment is completed, the attitude geometric consistency index is recalculated until it is less than or equal to the attitude consistency safety threshold.

6. The method for cooperative stabilization of attitude and height of a cable-driven rebar tying robot based on invariant Kalman filtering according to claim 5, characterized in that: Step four includes: S41. Based on the tension values ​​of eight steel cables in the original dataset of steel cable stress, the tension dispersion is analyzed and processed by the statistical standard deviation calculation method to obtain the tension dispersion. S42. Based on the length data of eight steel cables in the original dataset of steel cable lengths, the length dispersion is analyzed using the statistical standard deviation calculation method to obtain the length dispersion.

7. The method for cooperative stabilization of attitude and height of a cable-driven rebar tying robot based on invariant Kalman filtering according to claim 6, characterized in that: Step four also includes: S43. After dimensionless processing of the obtained tension dispersion and length dispersion, the dispersion weighted calculation is performed to obtain the cable-driven flexible coupling risk index.

8. The method for cooperative stabilization of attitude and height of a cable-driven rebar tying robot based on invariant Kalman filtering according to claim 7, characterized in that: Step four also includes: S44. By setting a safety threshold for cable-driven flexible coupling and comparing the cable-driven flexible coupling risk index with the cable-driven flexible coupling safety threshold, the second evaluation results are obtained, including: When the cable-driven flexible coupling risk index is less than or equal to the cable-driven flexible coupling safety threshold, it indicates that the force and length distribution of the eight steel cables of the cable-driven rebar binding robot are in a balanced state, and continuous monitoring is required. When the cable-driven flexible coupling risk index exceeds the cable-driven flexible coupling safety threshold, it indicates that the eight cables of the cable-driven rebar binding robot are unevenly distributed in terms of force or length. This presents risks of unbalanced equivalent stiffness of the cable-driven structure, amplification of attitude and height control coupling, and local overload of the cables. This triggers a second warning command and generates a second strategy: Using the average tension of the eight cables as the target, tension regression control is implemented on cables with large tension deviations to converge the tension of each cable towards the overall average. Adaptive attenuation is applied to the current attitude control gain and height control gain according to the control gain correction principle, which is inversely proportional to the cable-driven flexible coupling risk index. This reduces the system's rapid response to errors and suppresses the amplification effect of flexible vibration caused by structural stiffness imbalance. Large-amplitude rapid adjustment commands in the height direction are restricted to reduce the peak vertical acceleration. The system is then recalculated until the cable-driven flexible coupling risk index is less than or equal to the cable-driven flexible coupling safety threshold.

9. The method for cooperative stabilization of attitude and height of a cable-driven rebar tying robot based on invariant Kalman filtering according to claim 8, characterized in that: Step five includes: S51. By obtaining the filtered vertical velocity and the fused height estimate, and combining them with the target working height, the height energy dissipation index is calculated after dimensionless processing.

10. The method for cooperative stabilization of attitude and height of a cable-driven rebar tying robot based on invariant Kalman filtering according to claim 9, characterized in that: Step five also includes: S52. By setting a high stability safety threshold and comparing the high energy dissipation index with the high stability safety threshold, the third evaluation results are obtained, including: When the height energy dissipation index is less than or equal to the height stability safety threshold, it indicates that the end effector of the cable-driven rebar tying robot is in a stable state of height control and will be continuously monitored. When the height energy dissipation index exceeds the height stability safety threshold, it indicates that the end effector of the cable-driven rebar tying robot is not in a stable state in terms of current height control, and there is a risk of accumulated tying position errors and additional structural impact loads. This triggers the third warning command and generates a third strategy: increase the virtual damping coefficient in the vertical direction, reduce the height control proportional gain, and reduce the vertical response sensitivity; limit the output of rapid displacement commands in the height direction to suppress the peak vertical acceleration; reduce the overall system response frequency; and recalculate the height energy dissipation index after adjustment until the height energy dissipation index is ≤ the height stability safety threshold.

Images