Eight-rope suspension non-impact motion trajectory planning and mechanics analysis method

Abstract

The application provides an eight-rope suspension non-impact motion trajectory planning and mechanical analysis method, and relates to the electric digital data processing technical field.The application collects the geometric size and mass of a load, the physical properties of eight suspension ropes and the three-dimensional coordinates of anchoring points, and obtains the start and end positions and reference speed parameters of the load motion.Through calculation of the non-impact trajectory continuity coefficient, the rope tension feasibility balance coefficient and the rope real form consistency coefficient, and evaluation, corresponding motion time and speed correction, zero space solution amplitude reduction and initial rope length fine adjustment are carried out.Finally, the discrete time sequence output of the rope length and tension is formed, which is used for reverse correction of the suspension structure and parameters to realize closed-loop feedback control.The method can ensure the stable load motion, balanced rope tension and mechanical consistency of the suspension system, and improve the system operation safety and reliability.

Description

Technical Field

[0001] This invention relates to the technical field, specifically to a method for planning and analyzing the trajectory of an eight-rope suspension system without impact. Background Technology

[0002] Rope-driven parallel mechanisms are widely used in large equipment control, space operation platforms, stages, and special lifting systems due to their advantages such as lightweight structure, large workspace, low inertia, and high load capacity. These systems typically achieve position and attitude control of the driven carrier through the coordinated action of multiple flexible ropes. Their operational safety and control accuracy largely depend on the rationality of rope tension distribution and the continuous stability of the motion trajectory.

[0003] In existing technologies, trajectory planning and tension distribution for rope-driven systems are generally based on ideal geometric models or simplified static equilibrium assumptions, treating the rope as an inextensible ideal constraint element, or solving and verifying the tension only at a single moment. These methods fail to adequately reflect the actual mechanical changes of the rope under the influence of its own weight, elastic elongation, and structural coupling in practical applications, easily leading to significant discrepancies between theoretical calculations and actual operating conditions.

[0004] Furthermore, since ropes can only withstand tension but not compression, existing trajectory planning methods often require the introduction of a tensile feasibility assessment or the post-hoc elimination of solutions with negative tension when solving for tension distribution. However, such assessments are mostly based on static or instantaneous conditions and lack constraints on the continuity of the entire trajectory process. This can easily lead to sudden tension changes, concentrated loads, or hidden instability risks during trajectory switching or local attitude changes, affecting the stability and safety of the system operation.

[0005] Meanwhile, under multi-rope redundant drive conditions, tension distribution often presents multiple solutions. Existing technologies handle these multiple solutions in a rather crude manner, often relying on empirical weights, manual parameter adjustments, or a single optimization objective. They lack a collaborative evaluation mechanism for rope tension balance, consistency of actual shape, and impact-free trajectory characteristics, making it difficult to establish quantifiable, verifiable, and traceable effectiveness screening criteria. Summary of the Invention

[0006] The purpose of this invention is to provide a method for planning and analyzing the motion trajectory of an eight-rope suspension without impact, in order to solve the problems mentioned in the background art.

[0007] To achieve the above objectives, the present invention provides the following technical solution:

[0008] A method for planning and analyzing the impact-free motion trajectory of an eight-rope suspension system, comprising the following steps:

[0009] Step 1: Collect the geometric dimensions and mass information of the suspended load, the physical property parameters of the eight suspension ropes, the three-dimensional spatial coordinates of the rope anchor points, and the start and end positions and motion parameters of the load.

[0010] Step 2: Perform electrical digital data processing on the collected data to obtain the maximum jerk parameter, rope tension parameter, average tension of eight ropes, actual mechanical length parameter of the rope, and geometric straight length parameter;

[0011] Step 3: Calculate the continuity coefficient of the non-impact trajectory and compare it with the continuity threshold of the non-impact trajectory to determine whether the current trajectory meets the requirements of non-impact motion under the jerk continuity constraint. If it does, generate a continuity validity mark; if it does not, give an adjustment strategy of extending the motion time and reducing the reference motion speed.

[0012] Step 4: Calculate the rope tension feasibility balance coefficient and compare it with the tension feasibility balance threshold to determine whether the current tension distribution scheme meets the requirements for rope tension feasibility balance. If it does, generate a tension balance validity mark; if it does not, apply a strategy of decreasing the zero-space solution vector magnitude by a preset ratio.

[0013] Step 5: Calculate the rope's true shape consistency coefficient and compare it with the rope's true shape consistency threshold to determine whether the rope's mechanical analysis results are consistent with the actual suspension state. If they are, generate a shape consistency validity mark; if they are, provide a mechanical error correction strategy.

[0014] Step Six: By summarizing the analysis results that satisfy continuity, tension balance and morphological consistency, a time-series output of rope length and tension is generated. The results are then used to reverse-correct the structure and parameter configuration, thereby constructing a closed-loop feedback mechanism for impact-free motion planning and mechanical analysis of the eight-rope suspension system.

[0015] Further, step one includes:

[0016] S11. Real-time monitoring of the structural state of the suspended load is carried out by collecting the geometric dimension information of the load through offline measurement of the load before the load is transported; and by collecting the mass data of the suspended load by setting up a weighing device before the load is lifted.

[0017] S12. The physical properties of the eight suspension ropes are monitored uniformly. The tensile stiffness parameters of each rope are collected by reading the factory technical parameters of the ropes; the self-weight parameters of each rope are collected by calibrating the weight per unit length of the ropes; and the initial length data of each rope is collected by measuring the initial state of the ropes after installation.

[0018] S13. Real-time monitoring of the spatial position of the eight rope anchor points is carried out by deploying spatial positioning and measurement equipment at each anchor point and collecting three-dimensional coordinate data of each anchor point in a unified spatial coordinate system.

[0019] S14. Monitor the motion of the suspended load by reading the task planning system to collect the starting and ending coordinates of the load's motion; and collect the reference motion speed parameters and the number of trajectory discrete points of the load by reading the task planning parameters.

[0020] Furthermore, step two includes:

[0021] S21. Based on the starting point and ending point coordinates of the load motion, a three-dimensional vector difference and normalization processing method is used to perform vector operations on the starting point and ending point coordinates to obtain the unit vector of the load motion direction, and the spatial straight-line distance parameter between the starting point and the ending point is calculated simultaneously.

[0022] S22. Based on the reference motion velocity parameters of the load and the number of discrete points of the trajectory, and combined with the spatial straight-line distance parameters between the starting point and the ending point, the total motion time parameters of the load are constructed using time scale mapping and equal interval discretization methods, and the corresponding discrete time vector is generated.

[0023] S23. Based on discrete-time vectors, a seventh-order polynomial trajectory modeling method is adopted. Under the boundary constraints of zero starting and ending position, velocity, acceleration, and jerk, a non-impact displacement function of the load along the motion direction is constructed. The third-order time derivative of the non-impact displacement function is then performed to extract the jerk parameters corresponding to each discrete moment. At the same time, extreme value analysis is performed on the jerk parameters to obtain the maximum jerk parameter.

[0024] S24. Based on the unit vector of the load motion direction and the non-impact displacement function, the vector mapping and spatial coordinate reconstruction method is used to map the one-dimensional displacement parameters to three-dimensional space, obtain the three-dimensional spatial coordinate parameters of the load centroid at each discrete moment, and form the three-dimensional spatial trajectory matrix of the load centroid.

[0025] S25. Based on the three-dimensional spatial trajectory matrix of the load centroid and combined with the geometric dimension information of the load, the geometric pose mapping and rigid body translation calculation method is used to calculate the spatial coordinate parameters of the eight vertices of the load at each discrete moment.

[0026] S26. Based on the spatial coordinate parameters of the eight vertices and combined with the three-dimensional coordinate data of the anchoring points, a spatial vector connection and geometric relationship modeling method is used to construct the spatial connection relationship of "anchoring point - load vertex" for each rope at each discrete moment; a geometric distance calculation method is used to calculate the length state of each rope at each discrete moment and obtain the geometric straight line length parameters of each rope.

[0027] S27. Based on the geometric straight length parameters of each rope, combined with the rope tensile stiffness parameters, unit length self-weight parameters and initial length data, the elastic elongation modeling and static equilibrium analysis methods are used to construct the force and deformation relationship expressions of the rope at each discrete time, calculate the corresponding real mechanical length parameters and tension parameters of each rope, and further calculate the average tension of the eight ropes.

[0028] Furthermore, step three includes:

[0029] S31. After dimensionless processing of the obtained maximum jerk parameters, the continuity coefficient of the impact-free trajectory is calculated.

[0030] Furthermore, step three also includes:

[0031] S32. By setting a preset threshold for the continuity of the non-impact trajectory, and comparing and analyzing the continuity coefficient of the non-impact trajectory with the threshold for the continuity of the non-impact trajectory, the first evaluation result is obtained, including:

[0032] When the continuity coefficient of the non-impact trajectory is greater than or equal to the continuity threshold of the non-impact trajectory, it indicates that the current trajectory meets the requirements of non-impact motion under the jerk continuity constraint, and a continuity validity mark is generated for continuous monitoring;

[0033] When the continuity coefficient of the impact-free trajectory is less than the continuity threshold of the impact-free trajectory, it indicates that the current trajectory does not meet the requirements for impact-free motion under the jerk continuity constraint. There is a risk of impact caused by a sudden increase in rope transient tension, amplification of structural dynamic response, or instability in the tracking of the control system. This triggers the first warning command and generates the first strategy: adjust the motion time by increasing the total motion time parameter of the load while keeping the start and end positions unchanged, so as to reduce the amplitude of higher-order derivatives in the seventh-order polynomial trajectory; adjust the reference velocity by reducing the reference motion velocity and recalculating the time scale mapping relationship; perform a joint adjustment by simultaneously adjusting the total motion time parameter of the load and the reference motion velocity, and regenerating the seventh-order polynomial trajectory function that satisfies the boundary continuity constraint; after adjustment, recalculate until the continuity coefficient of the impact-free trajectory is greater than or equal to the continuity threshold of the impact-free trajectory.

[0034] Furthermore, step four includes:

[0035] S41. Based on the continuous validity label, the rope tension feasibility balance coefficient is calculated by combining the obtained tension parameter of the i-th rope and the average tension of the eight ropes at each discrete moment of the trajectory, after dimensionless processing.

[0036] Furthermore, step four also includes:

[0037] S42. By setting a preset tension feasibility balance threshold and comparing the rope tension feasibility balance coefficient with the tension feasibility balance threshold, the second evaluation result is obtained, including:

[0038] When the rope tension feasibility balance coefficient is greater than or equal to the tension feasibility balance threshold, it means that the current tension distribution scheme meets the requirements of rope tension feasibility balance, and a tension balance effectiveness mark is generated for continuous monitoring.

[0039] When the rope tension feasibility balance coefficient is less than the tension feasibility balance threshold, it indicates that the current tension distribution scheme does not meet the requirements for rope tension feasibility balance, and there are engineering risks caused by local rope slack, rope tension overload, or rope tension distribution imbalance. This triggers a second warning instruction and generates a second strategy: the overall amplitude of the null solution vector is adjusted by decreasing it by a preset percentage to reduce the probability of negative tension and extreme off-center load in the tension distribution; after the null solution amplitude adjustment is completed, the tension distribution results of each rope are regenerated while keeping the force and moment balance constraints unchanged; the adjustment is repeated until the rope tension feasibility balance coefficient is greater than or equal to the tension feasibility balance threshold.

[0040] Furthermore, step five includes:

[0041] S51. Based on the tension balance effectiveness marker, the rope's true shape consistency coefficient is calculated by combining the obtained true mechanical length parameter of the i-th rope and the corresponding geometric straight line length parameter at each trajectory discrete moment, after dimensionless processing.

[0042] Furthermore, step five also includes:

[0043] S52. By setting a preset rope true shape consistency threshold, and comparing and analyzing the rope true shape consistency coefficient with the rope true shape consistency threshold, the third evaluation results are obtained, including:

[0044] When the rope's true shape consistency coefficient is greater than or equal to the rope's true shape consistency threshold, it indicates that the rope's mechanical analysis results are consistent with the actual suspension state, generating a shape consistency validity mark for continuous monitoring.

[0045] When the rope's true shape consistency coefficient is less than the rope's true shape consistency threshold, it indicates that the rope's mechanical analysis results are not consistent with the actual suspension state. This suggests a risk of mechanical errors due to amplified sag effects caused by the rope's own weight, inaccurate estimation of local effective length, or unreasonable spatial layout of anchor points. This triggers a third warning instruction and generates a third strategy: based on the acquired geometric straight length parameters, the initial length data of the corresponding rope is finely adjusted by a preset percentage to reduce the relative deviation between the true mechanical length and the geometric length; while keeping the three-dimensional coordinate data of the anchor points and the load centroid trajectory matrix unchanged, the geometric straight length parameters, true mechanical length parameters, and tension parameters of each rope at the corresponding trajectory discrete time are updated and recalculated until the rope's true shape consistency coefficient is greater than or equal to the rope's true shape consistency threshold.

[0046] Furthermore, step six includes:

[0047] S61. Based on the continuity validity marker, tension balance validity marker and morphology consistency validity marker, the true mechanical length parameters, tension parameters and the average tension of the eight ropes are combined to output a unified result and form the corresponding discrete time series result.

[0048] S62. Based on the corresponding discrete time series results, the load geometry information, rope physical property parameters and anchor point three-dimensional coordinate data are corrected for the motion control, structural design and on-site debugging of the guidance suspension system. A closed-loop feedback process for the impact-free motion trajectory planning and mechanical analysis of the eight-rope suspension system is constructed.

[0049] Compared with the prior art, the beneficial effects of the present invention are:

[0050] This invention unifies the acquisition and processing of multi-source information, including load geometry, mass parameters, rope physical properties, and anchor point spatial coordinates. Based on electro-digital data processing, it constructs a complete parameter model of an eight-rope suspension system, achieving a fully digital description from structural input and motion tasks to mechanical analysis. Compared to traditional methods relying on empirical settings or single-parameter assumptions, this invention significantly improves the accuracy and consistency of trajectory planning and tension calculation results, providing a reliable data foundation for subsequent impact-free trajectory generation and mechanical evaluation.

[0051] This invention also constructs a continuity coefficient for the impact-free trajectory by modeling with a seventh-order polynomial and introducing jerk constraints during trajectory planning, combined with dimensionless processing of the maximum jerk parameter, and achieves quantitative evaluation of trajectory continuity based on a threshold determination mechanism. This process relies on electronic digital data processing to automatically analyze and iteratively adjust discrete time series, effectively suppressing transient impacts, tension abrupt changes, and amplification of structural dynamic response during motion, significantly improving the stability and safety of the suspension system.

[0052] This invention also addresses the issue of multiple tension solutions caused by underdetermined force and moment balance in an eight-rope system by constructing evaluation coefficients from two dimensions: tension feasibility equilibrium and consistency of the rope's true shape. A closed-loop correction mechanism is then formed through effectiveness labeling and a graded adjustment strategy. Through continuous verification and correction of the tension distribution results and the rope's true mechanical length, the risks of rope slack, overload, and shape distortion can be effectively reduced, making the final output trajectory and mechanical analysis results closer to actual engineering conditions. This improves the system's engineering applicability and reliability under complex working conditions. Attached Figure Description

[0053] Figure 1 This is a schematic diagram of the overall method flow of the present invention. Detailed Implementation

[0054] 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.

[0055] 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.

[0056] Example 1

[0057] Please see Figure 1 This invention provides a technical solution: a method for planning and analyzing the trajectory of an eight-rope suspension system without impact, the specific steps of which include:

[0058] Step 1: Collect the geometric dimensions and mass information of the suspended load, the physical property parameters of the eight suspension ropes, the three-dimensional spatial coordinates of the rope anchor points, and the start and end positions and motion parameters of the load.

[0059] Step 2: Perform electrical digital data processing on the collected data to obtain the maximum jerk parameter, rope tension parameter, average tension of eight ropes, actual mechanical length parameter of the rope, and geometric straight length parameter;

[0060] Step 3: Calculate the continuity coefficient of the non-impact trajectory and compare it with the continuity threshold of the non-impact trajectory to determine whether the current trajectory meets the requirements of non-impact motion under the jerk continuity constraint. If it does, generate a continuity validity mark; if it does not, give an adjustment strategy of extending the motion time and reducing the reference motion speed.

[0061] Step 4: Calculate the rope tension feasibility balance coefficient and compare it with the tension feasibility balance threshold to determine whether the current tension distribution scheme meets the requirements for rope tension feasibility balance. If it does, generate a tension balance validity mark; if it does not, apply a strategy of decreasing the zero-space solution vector magnitude by a preset ratio.

[0062] Step 5: Calculate the rope's true shape consistency coefficient and compare it with the rope's true shape consistency threshold to determine whether the rope's mechanical analysis results are consistent with the actual suspension state. If they are, generate a shape consistency validity mark; if they are, provide a mechanical error correction strategy.

[0063] Step Six: By summarizing the analysis results that satisfy continuity, tension balance and morphological consistency, a time-series output of rope length and tension is generated. The results are then used to reverse-correct the structure and parameter configuration, thereby constructing a closed-loop feedback mechanism for impact-free motion planning and mechanical analysis of the eight-rope suspension system.

[0064] In this embodiment, by performing electro-digital data processing on the multi-source parameters of the eight-rope suspension system and constructing a closed-loop feedback mechanism under the triple constraints of trajectory continuity, tension balance, and rope shape consistency, the system can identify the failure risk of non-impact trajectories and mechanical distribution in real time during load movement and automatically provide targeted adjustment strategies, thereby significantly improving the safety, stability, and engineering adaptability of the suspension system.

[0065] Example 2

[0066] Please see Figure 1 In this embodiment, as explained in Embodiment 1, specifically, step one includes:

[0067] S11. Real-time monitoring of the structural state of the suspended load is carried out by collecting the geometric dimension information of the load through offline measurement of the load before the load is transported; and by collecting the mass data of the suspended load by setting up a weighing device before the load is lifted.

[0068] S12. The physical properties of the eight suspension ropes are monitored uniformly. The tensile stiffness parameters of each rope are collected by reading the factory technical parameters of the ropes; the self-weight parameters of each rope are collected by calibrating the weight per unit length of the ropes; and the initial length data of each rope is collected by measuring the initial state of the ropes after installation.

[0069] S13. Real-time monitoring of the spatial position of the eight rope anchor points is carried out by deploying spatial positioning and measurement equipment at each anchor point and collecting three-dimensional coordinate data of each anchor point in a unified spatial coordinate system.

[0070] S14. Monitor the motion of the suspended load by reading the task planning system to collect the starting and ending coordinates of the load's motion; and collect the reference motion speed parameters and the number of trajectory discrete points of the load by reading the task planning parameters.

[0071] In this embodiment, by uniformly and systematically collecting the suspended load, rope physical properties, anchor point spatial location, and motion task parameters, complete and accurate basic data support is provided for subsequent trajectory planning and mechanical analysis. This effectively avoids tension calculation deviations and motion planning distortions caused by incomplete or inconsistent initial parameters, thereby improving the reliability and engineering applicability of the overall analysis results of the eight-rope suspension system.

[0072] Example 3

[0073] Please see Figure 1 In the explanation of Example 2, this embodiment specifically includes the following steps:

[0074] S21. Based on the starting point and ending point coordinates of the load motion, a three-dimensional vector difference and normalization processing method is used to perform vector operations on the starting point and ending point coordinates to obtain the unit vector of the load motion direction, and the spatial straight-line distance parameter between the starting point and the ending point is calculated simultaneously.

[0075] S22. Based on the reference motion velocity parameters of the load and the number of discrete points of the trajectory, and combined with the spatial straight-line distance parameters between the starting point and the ending point, the total motion time parameters of the load are constructed using the time scale mapping and equal interval discretization method, denoted as T, and the corresponding discrete time vector is generated, denoted as tk.

[0076] S23. Based on the discrete-time vector tk, a seventh-order polynomial trajectory modeling method is adopted. Under the boundary constraints of zero starting and ending positions, velocity, acceleration, and jerk, a non-impact displacement function of the load along the motion direction is constructed. The third-order time derivative of the non-impact displacement function is then performed to extract the jerk parameter corresponding to each discrete moment, denoted as j(tk). Simultaneously, extreme value analysis is performed on the jerk parameter to obtain the maximum jerk parameter, denoted as j(tk). ;

[0077] S24. Based on the unit vector of the load motion direction and the non-impact displacement function, the vector mapping and spatial coordinate reconstruction method is used to map the one-dimensional displacement parameters to three-dimensional space, obtain the three-dimensional spatial coordinate parameters of the load centroid at each discrete moment, and form the three-dimensional spatial trajectory matrix of the load centroid.

[0078] S25. Based on the three-dimensional spatial trajectory matrix of the load centroid and combined with the geometric dimension information of the load, the geometric pose mapping and rigid body translation calculation method is used to calculate the spatial coordinate parameters of the eight vertices of the load at each discrete moment.

[0079] S26. Based on the spatial coordinate parameters of the eight vertices and combined with the three-dimensional coordinate data of the anchoring points, a spatial vector connection and geometric relationship modeling method is used to construct the spatial connection relationship between the anchoring point and the load vertex for each rope at each discrete moment. A geometric distance calculation method is used to calculate the length state of each rope at each discrete moment, obtaining the geometric straight-line length parameters of each rope, denoted as... ;

[0080] S27. Based on the geometric straight-line length parameters of each rope By combining the tensile stiffness parameters, unit weight parameters, and initial length data of the rope, and employing elastic elongation modeling and static equilibrium analysis methods, expressions for the force-deformation relationship of the rope at each discrete moment are constructed. The actual mechanical length parameters corresponding to each rope are then calculated, denoted as... and tension parameters, denoted as Furthermore, the average tension of the eight ropes was calculated and denoted as... ;

[0081] In the process of elastic elongation modeling and static equilibrium analysis, since the eight-rope force and moment equilibrium constraint equations are in underdetermined form, the tension solution has multiple solutions under the premise of satisfying the overall force and moment equilibrium conditions; among them, the tension change component that does not affect the force and moment equilibrium result of the system is defined as the null space solution vector corresponding to the underdetermined equilibrium equations.

[0082] In this embodiment, by performing unified electronic and digital data processing on the load motion trajectory, rope spatial geometry, and tension distribution, trajectory planning calculation, rope length calculation, and static balance analysis are completed collaboratively within the same data framework. This not only accurately characterizes the variation range of eight rope tensions under multiple solution conditions, but also effectively improves the consistency and repeatability of trajectory continuity analysis and tension calculation results, thereby enhancing the engineering reliability of mechanical analysis of complex suspension systems.

[0083] Example 4

[0084] Please see Figure 1In the explanation of Example 3, this embodiment specifically includes the following steps:

[0085] S31. Obtain the maximum jerk parameter After dimensionless processing, the continuity coefficient of the impact-free trajectory is calculated and denoted as WGL, as shown in the following formula:

[0086]

[0087] In the formula, jallow represents the maximum jerk threshold. Based on the dynamic analysis and statistical analysis of safety design parameters of the eight-rope suspension system and the load-bearing structure, the jerk limit value corresponding to the allowable stress range of the structure is extracted. Combined with the experience judgment of professional technicians, a reasonable maximum jerk judgment value is determined. Referring to suspension system design specifications, structural dynamics safety standards, and performance parameters provided by equipment manufacturers, these standards usually specify the maximum allowable jerk or jerk amplitude range of the structure. This threshold is used to effectively distinguish whether the load motion trajectory may cause impact or abnormal structural response, ensuring the motion stability and structural safety of the eight-rope suspension system.

[0088] The physical principle behind the formula: The maximum jerk (i.e., the rate of change of acceleration) generated by the load during trajectory motion directly determines the transient impact force on the suspension rope and load-bearing structure. `jallow` is the maximum jerk threshold that the structure can withstand, determined by the dynamic safety design parameters of the suspension rope and load-bearing structure. The overall form of the formula reflects the "safety margin": when the maximum jerk is close to the allowable value, the coefficient approaches 0, indicating a high impact risk; when the jerk is far below the allowable value, the coefficient approaches 1, indicating a smooth and safe trajectory. The ratio of the maximum jerk to the allowable jerk is used to measure the dynamic smoothness of the trajectory, thereby evaluating whether the load will generate an impact during movement in the suspension system.

[0089] In this embodiment, by performing dimensionless processing on the maximum jerk parameter and constructing an impact-free trajectory continuity coefficient, the trajectory jerk level can be directly quantitatively compared with the structural safety design threshold, thereby intuitively reflecting the continuity and smoothness of the trajectory, effectively reducing the impact risk caused by excessive acceleration, and improving the safety and reliability of the motion planning of the eight-rope suspension system.

[0090] Example 5

[0091] Please see Figure 1 In the explanation of Embodiment 4, specifically, step three further includes:

[0092] S32. By setting a preset threshold for the continuity of the impact-free trajectory, denoted as Wth, and comparing the continuity coefficient WGL of the impact-free trajectory with the threshold Wth, the first evaluation result is obtained, including:

[0093] When the continuity coefficient WGL of the non-impact trajectory is greater than or equal to the continuity threshold Wth of the non-impact trajectory, it means that the current trajectory meets the requirements of non-impact motion under the jerk continuity constraint, and a continuity validity mark is generated for continuous monitoring.

[0094] When the continuity coefficient of the impact-free trajectory WGL is less than the continuity threshold Wth, it indicates that the current trajectory does not meet the requirements for impact-free motion under the jerk continuity constraint. There is a risk of impact caused by a sudden increase in rope transient tension, amplification of structural dynamic response, or instability in the tracking of the control system. This triggers the first warning command and generates the first strategy: adjust the motion time by increasing the total motion time parameter T of the load while keeping the start and end positions unchanged, so as to reduce the amplitude of the higher-order derivatives in the seventh-order polynomial trajectory; adjust the reference velocity by reducing the reference motion velocity and recalculating the time scale mapping relationship; perform a joint adjustment by simultaneously adjusting the total motion time parameter T of the load and the reference motion velocity, and regenerating the seventh-order polynomial trajectory function that satisfies the boundary continuity constraint; after adjustment, recalculate until the continuity coefficient of the impact-free trajectory WGL is greater than or equal to the continuity threshold Wth.

[0095] The method for obtaining the impact-free trajectory continuity threshold Wth is as follows: Through statistical analysis of a large amount of impact-free motion trajectory data, the key parameter ranges for satisfying and not satisfying acceleration continuity are extracted. Combined with the experience judgment of professional technicians, a reasonable critical judgment value is determined. Referring to mechanical system dynamics analysis standards and technical parameters provided by equipment manufacturers, these standards typically define a safe threshold range for acceleration continuity. This threshold is used to effectively distinguish between the normal operating trajectory of the equipment and potential impact risk states, ensuring the smooth operation of the system and structural safety.

[0096] In this embodiment, by performing electrical digital data processing on the maximum jerk parameter and introducing a non-impact trajectory continuity coefficient, a quantitative assessment and threshold determination of the high-order continuity of the trajectory is achieved. This enables real-time and objective identification of whether the trajectory meets the requirements for non-impact motion, and automatically triggers coordinated adjustment of motion time and reference speed when the conditions are not met. This effectively suppresses the sudden increase in rope transient tension and the amplification of structural dynamic response, thereby improving the safety and stability of the eight-rope suspension system during motion.

[0097] Example 6

[0098] Please see Figure 1 In the explanation of Example 5, specifically, step four includes:

[0099] S41. Based on the continuity validity marker, by combining the obtained tension parameter of the i-th rope at each discrete time tk of the trajectory... and the average tension of the eight ropes After dimensionless processing, the feasibility balance coefficient of rope tension is calculated and denoted as SZJ, as shown in the following formula:

[0100]

[0101] In the formula, This indicates an indicator function used to constrain the rope to a state where it is only under tension.

[0102] The physical principle of the formula: indicator function Ensure that only ropes under tension are considered, and eliminate the interference of slack ropes on the equilibrium calculation; It reflects the relative magnitude of the deviation of the tension of each rope from the average value; 1 minus the deviation ratio is the tension balance degree: the smaller the deviation, the closer the rope tension feasibility balance coefficient SZJ is to 1; the larger the deviation or the occurrence of negative tension, the smaller the rope tension feasibility balance coefficient SZJ is; by normalizing the deviation of the tension of each rope from the average tension, the tension balance of the eight-rope system is evaluated, thereby ensuring reasonable force distribution and avoiding local overload or slack.

[0103] In this embodiment, by introducing a rope tension feasibility balance coefficient under the continuity validity label constraint, the relative deviation between the tension of each rope and the average tension is quantified dimensionlessly. Combined with the tension state constraint, a unified assessment of the rationality of tension distribution is achieved, thereby effectively avoiding the occurrence of rope slack or overload and improving the stability and engineering safety of the tension distribution of the eight-rope suspension system.

[0104] Example 7

[0105] Please see Figure 1 In the explanation of Example Six, specifically, step four further includes:

[0106] S42. By setting a preset tension feasibility balance threshold, denoted as Sth, and comparing the rope tension feasibility balance coefficient SZJ with the tension feasibility balance threshold Sth, the second evaluation results are obtained, including:

[0107] When the rope tension feasibility balance coefficient SZJ ≥ tension feasibility balance threshold Sth, it means that the current tension distribution scheme meets the requirements of rope tension feasibility balance, and a tension balance effectiveness mark is generated for continuous monitoring.

[0108] When the rope tension feasibility balance coefficient SZJ < the tension feasibility balance threshold Sth, it indicates that the current tension distribution scheme does not meet the requirements for rope tension feasibility balance, and there are engineering risks caused by local rope slack, rope tension overload, or rope tension distribution imbalance. This triggers a second warning instruction and generates a second strategy: the overall amplitude of the null space solution vector is adjusted by decreasing it by a preset percentage to reduce the probability of negative tension and extreme off-center load in the tension distribution; after the null space solution amplitude adjustment is completed, the tension distribution results of each rope are regenerated while keeping the force and moment balance constraints unchanged; the adjustment is repeated until the rope tension feasibility balance coefficient SZJ ≥ the tension feasibility balance threshold Sth.

[0109] The method for obtaining the tension feasibility balance threshold Sth is as follows: By analyzing a large amount of rope tension distribution data, key parameter ranges are extracted for when tension balance is satisfied and not satisfied. Combined with the judgment and experience of professional technicians, a reasonable critical value is determined. Referring to industry standards and performance parameters provided by equipment manufacturers, these standards typically provide reasonable tension balance requirements and define the safe range of rope tension distribution. This threshold is used to effectively distinguish whether the tension distribution meets the tensile feasibility requirements, thereby ensuring balanced force on the rope and safe operation of the system.

[0110] In this embodiment, by setting a tension feasibility equilibrium threshold and introducing an adaptive adjustment mechanism based on the decreasing amplitude of the null solution vector, the generation of negative tension and extreme off-center load can be automatically suppressed without destroying the overall force and torque balance constraints. This enables dynamic correction and convergence of the tension distribution scheme, thereby significantly improving the stress reliability and operational safety of the eight-rope suspension system under complex working conditions.

[0111] Example 8

[0112] Please see Figure 1 In the explanation of Example 7, specifically, step five includes:

[0113] S51. Based on the tension balance effectiveness marker, by combining the obtained true mechanical length parameter of the i-th rope at each discrete trajectory time tk. and the corresponding geometric line length parameters After dimensionless processing, the consistency coefficient of the rope's true shape is calculated and denoted as ZXY, as shown in the following formula:

[0114]

[0115] The physical principle behind the formula: It represents the actual mechanical length of the i-th rope at discrete time (considering the elastic elongation and stress of the rope). This represents the geometric straight-line length (the theoretical straight-line distance from the anchor point to the load apex). The formula assesses the consistency between the rope's mechanical state and its theoretical geometric shape by comparing the relative difference between the actual length and the geometric length. The smaller the difference, the higher the consistency coefficient ZXY of the rope's actual shape, indicating good consistency between the rope's stress and geometric arrangement. A large difference may indicate sag, local length estimation errors, or unreasonable anchor point layout.

[0116] In this embodiment, by introducing a rope true shape consistency coefficient based on the relative deviation between the true mechanical length and the geometric straight length, the shape difference caused by rope self-weight sag and elastic elongation is quantitatively evaluated. This can effectively reflect the degree of matching between the mechanical modeling results and the actual suspension state, thereby improving the accuracy and engineering applicability of rope stress analysis and shape prediction.

[0117] Example 9

[0118] Please see Figure 1 In the explanation of Embodiment Eight, specifically, step five further includes:

[0119] S52. By setting a preset rope true shape consistency threshold, denoted as Zth, and comparing the rope true shape consistency coefficient ZXY with the rope true shape consistency threshold Zth, the third evaluation results are obtained, including:

[0120] When the rope's true shape consistency coefficient ZXY ≥ the rope's true shape consistency threshold Zth, it indicates that the rope's mechanical analysis results are consistent with the actual suspension state, generating a shape consistency validity mark for continuous monitoring.

[0121] When the rope's true shape consistency coefficient ZXY < the rope's true shape consistency threshold Zth, it indicates that the rope's mechanical analysis results are not consistent with the actual suspension state. There is a risk of mechanical errors caused by amplified sag effects due to the rope's own weight, inaccurate estimation of local effective length, or unreasonable spatial layout of anchor points. This triggers a third warning instruction and generates a third strategy: based on the acquired geometric straight length parameters, the initial length data of the corresponding rope is finely adjusted by a preset percentage to reduce the relative deviation between the true mechanical length and the geometric length; while keeping the three-dimensional coordinate data of the anchor points and the load centroid trajectory matrix unchanged, the geometric straight length parameters, true mechanical length parameters, and tension parameters of each rope at the corresponding trajectory discrete time are updated and recalculated until the rope's true shape consistency coefficient ZXY ≥ the rope's true shape consistency threshold Zth.

[0122] The method for obtaining the rope's true shape consistency threshold Zth is as follows: Through statistical evaluation of a large amount of rope shape analysis data, the key difference range between the rope's true shape and its geometric shape is extracted. Combined with the judgment of technical experts, a reasonable judgment threshold is determined. Referencing the technical specifications provided by the rope manufacturer and relevant industry standards, these standards typically stipulate the consistency requirements between rope mechanical analysis and actual suspension conditions. This threshold is used to effectively distinguish the degree of matching between the rope's mechanical analysis results and its actual shape, ensuring the reliability of the rope's stress state and the safe operation of the system.

[0123] In this embodiment, by evaluating the consistency between the rope mechanical analysis results and the actual suspension state in real time, and by fine-tuning the initial length of the rope when it is unqualified, the risk of mechanical deviation caused by the amplification of sag effect and local length error can be effectively reduced, thereby improving the force accuracy and motion stability of the eight-rope suspension system.

[0124] Example 10

[0125] Please see Figure 1 In the explanation of Embodiment Nine, specifically, step six includes:

[0126] S61. Based on the continuity validity marker, tension balance validity marker and morphology consistency validity marker, the true mechanical length parameters, tension parameters and the average tension of the eight ropes are combined to output a unified result and form the corresponding discrete time series result.

[0127] S62. Based on the corresponding discrete time series results, the load geometry information, rope physical property parameters and anchor point three-dimensional coordinate data are corrected for the motion control, structural design and on-site debugging of the guidance suspension system. A closed-loop feedback process for the impact-free motion trajectory planning and mechanical analysis of the eight-rope suspension system is constructed.

[0128] In this embodiment, by comprehensively analyzing the results of continuity, tension balance, and morphological consistency, accurate time-series data is generated, which can provide real-time feedback for the motion control, structural design, and on-site debugging of the suspension system, ensuring system optimization and adjustment, thereby improving the operating accuracy and stability of the eight-rope suspension system.

[0129] 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.

[0130] 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.

[0131] 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 planning and analyzing the impact-free motion trajectory of an eight-rope suspension system, characterized in that, The specific steps include: Step 1: Collect the geometric dimensions and mass information of the suspended load, the physical property parameters of the eight suspension ropes, the three-dimensional spatial coordinates of the rope anchor points, and the start and end positions and motion parameters of the load. Step 2: Perform electrical digital data processing on the collected data to obtain the maximum jerk parameter, rope tension parameter, average tension of eight ropes, actual mechanical length parameter of the rope, and geometric straight length parameter; Step 3: Calculate the continuity coefficient of the non-impact trajectory and compare it with the continuity threshold of the non-impact trajectory to determine whether the current trajectory meets the requirements of non-impact motion under the jerk continuity constraint. If it does, generate a continuity validity mark; if it does not, give an adjustment strategy of extending the motion time and reducing the reference motion speed. Step 4: Calculate the rope tension feasibility balance coefficient and compare it with the tension feasibility balance threshold to determine whether the current tension distribution scheme meets the requirements for rope tension feasibility balance. If it does, generate a tension balance validity mark; if it does not, apply a strategy of decreasing the zero-space solution vector magnitude by a preset ratio. Step 5: Calculate the rope's true shape consistency coefficient and compare it with the rope's true shape consistency threshold to determine whether the rope's mechanical analysis results are consistent with the actual suspension state. If they are, generate a shape consistency validity mark; if they are, provide a mechanical error correction strategy. Step Six: By summarizing the analysis results that satisfy continuity, tension balance and morphological consistency, a time-series output of rope length and tension is generated. The results are then used to reverse-correct the structure and parameter configuration, thereby constructing a closed-loop feedback mechanism for impact-free motion planning and mechanical analysis of the eight-rope suspension system.

2. The method for planning and analyzing the impact-free motion trajectory of an eight-rope suspension system according to claim 1, characterized in that: Step one includes: S11. Real-time monitoring of the structural state of the suspended load is carried out by collecting the geometric dimension information of the load through offline measurement of the load before the load is transported; and by collecting the mass data of the suspended load by setting up a weighing device before the load is lifted. S12. The physical properties of the eight suspension ropes are monitored uniformly. The tensile stiffness parameters of each rope are collected by reading the factory technical parameters of the ropes; the self-weight parameters of each rope are collected by calibrating the weight per unit length of the ropes; and the initial length data of each rope is collected by measuring the initial state of the ropes after installation. S13. Real-time monitoring of the spatial position of the eight rope anchor points is carried out by deploying spatial positioning and measurement equipment at each anchor point and collecting three-dimensional coordinate data of each anchor point in a unified spatial coordinate system. S14. Monitor the motion of the suspended load by reading the task planning system to collect the starting and ending coordinates of the load's motion; and collect the reference motion speed parameters and the number of trajectory discrete points of the load by reading the task planning parameters.

3. The method for planning and analyzing the impact-free motion trajectory of an eight-rope suspension system according to claim 2, characterized in that: Step two includes: S21. Based on the starting point and ending point coordinates of the load motion, a three-dimensional vector difference and normalization processing method is used to perform vector operations on the starting point and ending point coordinates to obtain the unit vector of the load motion direction, and the spatial straight-line distance parameter between the starting point and the ending point is calculated simultaneously. S22. Based on the reference motion velocity parameters of the load and the number of discrete points of the trajectory, and combined with the spatial straight-line distance parameters between the starting point and the ending point, the total motion time parameters of the load are constructed using time scale mapping and equal interval discretization methods, and the corresponding discrete time vector is generated. S23. Based on discrete-time vectors, a seventh-order polynomial trajectory modeling method is adopted. Under the boundary constraints of zero starting and ending position, velocity, acceleration, and jerk, a non-impact displacement function of the load along the motion direction is constructed. The third-order time derivative of the non-impact displacement function is then performed to extract the jerk parameters corresponding to each discrete moment. At the same time, extreme value analysis is performed on the jerk parameters to obtain the maximum jerk parameter. S24. Based on the unit vector of the load motion direction and the non-impact displacement function, the vector mapping and spatial coordinate reconstruction method is used to map the one-dimensional displacement parameters to three-dimensional space, obtain the three-dimensional spatial coordinate parameters of the load centroid at each discrete moment, and form the three-dimensional spatial trajectory matrix of the load centroid. S25. Based on the three-dimensional spatial trajectory matrix of the load centroid and combined with the geometric dimension information of the load, the geometric pose mapping and rigid body translation calculation method is used to calculate the spatial coordinate parameters of the eight vertices of the load at each discrete moment. S26. Based on the spatial coordinate parameters of the eight vertices and combined with the three-dimensional coordinate data of the anchoring points, a spatial vector connection and geometric relationship modeling method is used to construct the spatial connection relationship of "anchoring point - load vertex" for each rope at each discrete moment; a geometric distance calculation method is used to calculate the length state of each rope at each discrete moment and obtain the geometric straight line length parameters of each rope. S27. Based on the geometric straight length parameters of each rope, combined with the rope tensile stiffness parameters, unit length self-weight parameters and initial length data, the elastic elongation modeling and static equilibrium analysis methods are used to construct the force and deformation relationship expressions of the rope at each discrete time, calculate the corresponding real mechanical length parameters and tension parameters of each rope, and further calculate the average tension of the eight ropes.

4. The method for planning and analyzing the impact-free motion trajectory of an eight-rope suspension system according to claim 3, characterized in that: Step three includes: S31. After dimensionless processing of the obtained maximum jerk parameters, the continuity coefficient of the impact-free trajectory is calculated.

5. The method for planning and analyzing the impact-free motion trajectory of an eight-rope suspension system according to claim 4, characterized in that: Step three also includes: S32. By setting a preset threshold for the continuity of the non-impact trajectory, and comparing and analyzing the continuity coefficient of the non-impact trajectory with the threshold for the continuity of the non-impact trajectory, the first evaluation result is obtained, including: When the continuity coefficient of the non-impact trajectory is greater than or equal to the continuity threshold of the non-impact trajectory, it indicates that the current trajectory meets the requirements of non-impact motion under the jerk continuity constraint, and a continuity validity mark is generated for continuous monitoring; When the continuity coefficient of the impact-free trajectory is less than the continuity threshold of the impact-free trajectory, it indicates that the current trajectory does not meet the requirements for impact-free motion under the jerk continuity constraint. There is a risk of impact caused by a sudden increase in rope transient tension, amplification of structural dynamic response, or instability in the tracking of the control system. This triggers the first warning command and generates the first strategy: adjust the motion time by increasing the total motion time parameter of the load while keeping the start and end positions unchanged, so as to reduce the amplitude of higher-order derivatives in the seventh-order polynomial trajectory; adjust the reference velocity by reducing the reference motion velocity and recalculating the time scale mapping relationship; perform a joint adjustment by simultaneously adjusting the total motion time parameter of the load and the reference motion velocity, and regenerating the seventh-order polynomial trajectory function that satisfies the boundary continuity constraint; after adjustment, recalculate until the continuity coefficient of the impact-free trajectory is greater than or equal to the continuity threshold of the impact-free trajectory.

6. The method for planning and analyzing the impact-free motion trajectory of an eight-rope suspension system according to claim 5, characterized in that: Step four includes: S41. Based on the continuous validity label, the rope tension feasibility balance coefficient is calculated by combining the obtained tension parameter of the i-th rope and the average tension of the eight ropes at each discrete moment of the trajectory, after dimensionless processing.

7. The method for planning and analyzing the impact-free motion trajectory of an eight-rope suspension system according to claim 6, characterized in that: Step four also includes: S42. By setting a preset tension feasibility balance threshold and comparing the rope tension feasibility balance coefficient with the tension feasibility balance threshold, the second evaluation result is obtained, including: When the rope tension feasibility balance coefficient is greater than or equal to the tension feasibility balance threshold, it means that the current tension distribution scheme meets the requirements of rope tension feasibility balance, and a tension balance effectiveness mark is generated for continuous monitoring. When the rope tension feasibility balance coefficient is less than the tension feasibility balance threshold, it indicates that the current tension distribution scheme does not meet the requirements for rope tension feasibility balance, and there are engineering risks caused by local rope slack, rope tension overload, or rope tension distribution imbalance. This triggers a second warning instruction and generates a second strategy: the overall amplitude of the null solution vector is adjusted by decreasing it by a preset percentage to reduce the probability of negative tension and extreme off-center load in the tension distribution; after the null solution amplitude adjustment is completed, the tension distribution results of each rope are regenerated while keeping the force and moment balance constraints unchanged; the adjustment is repeated until the rope tension feasibility balance coefficient is greater than or equal to the tension feasibility balance threshold.

8. The method for planning and analyzing the impact-free motion trajectory of an eight-rope suspension system according to claim 7, characterized in that: Step five includes: S51. Based on the tension balance effectiveness marker, the rope's true shape consistency coefficient is calculated by combining the obtained true mechanical length parameter of the i-th rope and the corresponding geometric straight line length parameter at each trajectory discrete moment, after dimensionless processing.

9. The method for planning and analyzing the impact-free motion trajectory of an eight-rope suspension system according to claim 8, characterized in that: Step five also includes: S52. By setting a preset rope true shape consistency threshold, and comparing and analyzing the rope true shape consistency coefficient with the rope true shape consistency threshold, the third evaluation results are obtained, including: When the rope's true shape consistency coefficient is greater than or equal to the rope's true shape consistency threshold, it indicates that the rope's mechanical analysis results are consistent with the actual suspension state, generating a shape consistency validity mark for continuous monitoring. When the rope's true shape consistency coefficient is less than the rope's true shape consistency threshold, it indicates that the rope's mechanical analysis results are not consistent with the actual suspension state. This suggests a risk of mechanical errors due to amplified sag effects caused by the rope's own weight, inaccurate estimation of local effective length, or unreasonable spatial layout of anchor points. This triggers a third warning instruction and generates a third strategy: based on the acquired geometric straight length parameters, the initial length data of the corresponding rope is finely adjusted by a preset percentage to reduce the relative deviation between the true mechanical length and the geometric length; while keeping the three-dimensional coordinate data of the anchor points and the load centroid trajectory matrix unchanged, the geometric straight length parameters, true mechanical length parameters, and tension parameters of each rope at the corresponding trajectory discrete time are updated and recalculated until the rope's true shape consistency coefficient is greater than or equal to the rope's true shape consistency threshold.

10. The method for planning and analyzing the impact-free motion trajectory of an eight-rope suspension system according to claim 9, characterized in that: Step six includes: S61. Based on the continuity validity marker, tension balance validity marker and morphology consistency validity marker, the true mechanical length parameters, tension parameters and the average tension of the eight ropes are combined to output a unified result and form the corresponding discrete time series result. S62. Based on the corresponding discrete time series results, the load geometry information, rope physical property parameters and anchor point three-dimensional coordinate data are corrected for the motion control, structural design and on-site debugging of the guidance suspension system. A closed-loop feedback process for the impact-free motion trajectory planning and mechanical analysis of the eight-rope suspension system is constructed.

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