Method and system for trajectory planning of a bridge crane

Abstract

The application relates to a bridge crane trajectory planning method and system, comprising the following steps: constructing a bridge crane system dynamics model based on trolley displacement, bridge displacement and rope length, and hook and load swing angles in a three-dimensional space, and setting a control target; designing an auxiliary signal according to trolley movement, bridge movement, rope length change, hook swing and load swing state variables, and converting constraints applied to the trolley, the bridge, the rope length and the hook and the load swing in the model into constraints on the auxiliary signal according to the control target; obtaining trajectory planning of the trolley, the bridge movement and the rope change according to the model result, and realizing positioning and swing suppression control of the bridge crane.

Description

Technical Field

[0001] This invention relates to the field of electromechanical system control technology, specifically to a method and system for planning the trajectory of a bridge crane. Background Technology

[0002] The statements in this section are merely background information related to the present invention and do not necessarily constitute prior art.

[0003] Bridge cranes are commonly used lifting equipment. Their control system is a typical multi-input multi-output and underactuated electromechanical system. The control input of a bridge crane is less than the degree of freedom of the system output. When the trolley and the bridge frame move simultaneously to lift large structural loads, the hook and load will swing in two stages in three-dimensional space, exhibiting complex double-spherical pendulum characteristics.

[0004] To improve operational efficiency, the length of the lifting rope changes during the movement of the trolley and bridge to complete the load lifting operation. At this time, the nonlinear coupling relationship between the driving state variables (trolley displacement, bridge displacement, and lifting rope length) and the non-driving state variables (swing angle of the hook and load in three-dimensional space) of the bridge crane is stronger, making dynamic modeling and anti-swing controller design more challenging.

[0005] Existing technologies have proposed various control methods for bridge crane systems. Based on whether or not system motion state feedback signals are included, the current methods can be divided into open-loop control and closed-loop control. Open-loop control methods include input shaping, smooth shaping, trajectory planning, etc., while closed-loop control methods include sliding mode control, fuzzy control, adaptive control, etc.

[0006] The inventors discovered that bridge crane control methods still have some problems to be solved in terms of high-performance nonlinear control of positioning and anti-sway functions. Existing bridge cranes only consider a maximum of six degrees of freedom (trolley movement, bridge frame movement, hook spherical oscillation, and load spherical oscillation), while ignoring the change in the length of the hoisting rope, thus failing to theoretically guarantee the transient control performance of the bridge crane across all states. Summary of the Invention

[0007] To address the technical problems described in the background, this invention provides a trajectory planning method and system for bridge cranes. This method fully considers the dynamic effects and state constraints of the double-spherical pendulum of the bridge crane. Based on the positions of the hook and load, a set of auxiliary signals is introduced, including trolley displacement, bridge frame displacement, rope length, hook swing angle, and load swing angle. By fully considering the state constraints, 13th-order polynomial functions are used to design the auxiliary signals, effectively solving the problems of trolley and bridge frame movement, rope length variation, and double-spherical pendulum suppression in bridge cranes.

[0008] To achieve the above objectives, the present invention adopts the following technical solution:

[0009] The first aspect of the present invention provides a method for planning the trajectory of a bridge crane, comprising the following steps:

[0010] Based on the trolley displacement, bridge frame displacement, and rope length, as well as the swing angle of the hook and load in three-dimensional space, a dynamic model of the bridge crane system is constructed, and control objectives are set.

[0011] Auxiliary signals are designed based on the state variables of trolley movement, bridge movement, rope length change, hook swing and load swing. According to the control objective, the constraints imposed on the trolley, bridge, rope length and hook and load swing in the model are transformed into constraints on the auxiliary signals.

[0012] Based on the model results, trajectory planning for the movement of the trolley, bridge frame, and suspension rope is obtained, enabling positioning and sway suppression control of the bridge crane.

[0013] Construct a dynamic model of the bridge crane system, including:

[0014] The positions of the hook and load in the three-dimensional coordinate system are determined, and the velocity signals of the hook and load are obtained by differentiation;

[0015] Based on the speed signals of the hook and load, and the masses of the trolley, bridge frame, hook, and load, the total kinetic energy of the bridge crane system is obtained;

[0016] A Lagrangian function is constructed using the total kinetic and potential energy of the bridge crane system. After solving the Lagrangian function, a dynamic model of the bridge crane with seven degrees of freedom is obtained, based on the trolley displacement, bridge frame displacement, rope length, hook and load swing angle.

[0017] Control objectives include:

[0018] Positioning constraints: the trolley and the bridge frame move from their initial positions to their target positions during the hoisting time, and the length of the hoisting rope changes from its initial length to its target length during the hoisting time.

[0019] Anti-sway restraint prevents the hook and load from swinging during the lifting time;

[0020] All conditions are constrained, and the speed and acceleration of the trolley, the speed and acceleration of the bridge, and the speed and acceleration of the change in the length of the suspension rope are all kept within the set range; the swing angle of the hook and the load in three-dimensional space are all kept within the set range.

[0021] Auxiliary signals are designed based on the state variables of trolley movement, bridge movement, rope length change, hook swing and load swing. According to the control objective, the constraints imposed on the trolley, bridge, rope length and hook and load swing in the model are transformed into constraints on the auxiliary signals.

[0022] The dynamic model of the bridge crane is transformed and the positions of the hook and the load are combined to obtain auxiliary signals including the displacement of the trolley, the displacement of the bridge frame, the length of the lifting rope, the sway of the hook, and the sway of the load.

[0023] Substituting the obtained auxiliary signals into the relational expression of the control target yields the positioning constraint control target, anti-sway constraint control target, and full-state constraint control target based on the proposed auxiliary signal representation.

[0024] The trolley displacement, bridge frame displacement, hoisting rope length, hook swing angle, load swing angle, and control objective in the dynamic model of the bridge crane are transformed into expressions for auxiliary signals and their different derivatives. The model results are obtained through a time optimization problem based on the auxiliary signals; including:

[0025] Based on the auxiliary signal represented by the polynomial curve, the positioning constraint control target is substituted into the polynomial curve to obtain the polynomial curve parameters;

[0026] Based on ensuring that the positioning constraint control objective, anti-sway constraint control objective, and all-state constraint control objective are met, a time optimization problem is constructed with the minimum hoisting time as the objective value.

[0027] The optimal value of hoisting time is obtained by solving the time optimization problem using the bisection method.

[0028] A second aspect of the present invention provides a system for implementing the above-described method, comprising:

[0029] The control target module is configured to: construct a dynamic model of the bridge crane system based on the trolley displacement, bridge frame displacement, and rope length, as well as the swing angle of the hook and load in three-dimensional space, and set the control target;

[0030] The model conversion module is configured to design auxiliary signals based on the state variables of trolley movement, bridge movement, rope length change, hook swing and load swing, and to convert the constraints applied to the trolley, bridge, rope length and hook and load swing in the model into constraints on the auxiliary signals according to the control objectives.

[0031] The trajectory planning module is configured to: obtain trajectory planning for the movement of the trolley, bridge frame and the changes in the hoisting rope based on the model results, so as to realize the positioning and sway suppression control of the bridge crane.

[0032] A third aspect of the present invention provides a computer-readable storage medium.

[0033] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps in the bridge crane trajectory planning method described above.

[0034] A fourth aspect of the present invention provides a computer device.

[0035] A computer device includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the steps in the bridge crane trajectory planning method described above.

[0036] Compared with existing technologies, one or more of the above technical solutions have the following beneficial effects:

[0037] 1. Taking into full account the dynamic effects and state constraints of the double spherical pendulum of the bridge crane, a dynamic model is constructed using seven degrees of freedom: trolley displacement, bridge frame displacement, rope length, hook swing angle, and load swing angle. The constraints applied to the trolley, bridge frame, rope length, hook, and load swing are transformed into constraints on auxiliary signals. Thus, the trajectory planning problem of the bridge crane is transformed into a time optimization problem related to the auxiliary signals. The solution effectively solves the problems of trolley and bridge frame movement, rope length variation, and double spherical pendulum suppression, and can theoretically guarantee the transient control performance of the bridge crane's full-state control.

[0038] 2. The constructed dynamic model includes three driving state variables: trolley displacement, bridge displacement, and rope length; and four non-driving state variables: the swing angle of the hook and load in three-dimensional space, thus taking into account more system degrees of freedom and more complex dynamic characteristics of the double spherical pendulum and variable rope length.

[0039] 3. The full state variables of the bridge crane are described by a set of auxiliary signals. By analyzing the nonlinear coupling relationship between the driving state variables and the non-driving state variables, each state variable is represented as a combination of the auxiliary signal and its derivatives of different orders. Thus, the trajectory planning problem of the bridge crane is transformed into a time optimization problem related to the auxiliary signals and solved.

[0040] 4. In the process of solving the problem, the polynomial-based optimization trajectory planning control strategy not only reduces the hoisting time and improves the operating efficiency of the bridge crane, but also ensures that all state variables meet the constraints, thereby improving the safety performance of the bridge crane operation. Attached Figure Description

[0041] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0042] Figure 1 This is a schematic diagram of a seven-degree-of-freedom bridge crane structure provided in one or more embodiments of the present invention;

[0043] Figure 2 This is a schematic diagram of the control system of a bridge crane provided in one or more embodiments of the present invention;

[0044] Figure 3 This is a flowchart of solving the time optimization problem in equation (56) in one or more embodiments of the present invention;

[0045] Figures 4(a)-4(i) This is a comparison chart of the simulation results of the trajectory planning method provided by one or more embodiments of the present invention with the driving state variables of the EI shaper, the smoothing shaper and the EAB controller.

[0046] Figures 5(a)-5(d) This is a comparison chart of simulation results of the trajectory planning method provided by one or more embodiments of the present invention with the non-driving state variables of the EI shaper, smoothing shaper and EAB controller;

[0047] Figures 6(a)-6(b) This is a comparison chart of the trajectory planning method provided by one or more embodiments of the present invention with the simulation results of the hook and load trajectory of the EI shaper, smoothing shaper and EAB controller. Detailed Implementation

[0048] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0049] It should be noted that the following detailed descriptions are exemplary and intended to provide further illustration of the invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0050] As described in the background section, existing bridge crane control systems only consider six degrees of freedom (trolley movement, bridge frame movement, hook spherical oscillation, and load spherical oscillation), neglecting the change in rope length. This leads to the need for further improvement in the dynamic modeling of three-dimensional bridge cranes with double spherical oscillation and variable rope length characteristics. Moreover, considering the bounded nature of the motor driving force of the bridge crane, the driving state variables (velocity and acceleration of trolley / bridge frame movement, and velocity and acceleration of rope length change) should all be kept within a certain range. Considering the safety of hoisting operations, the non-driving state variables (swing angle of the hook / load in three-dimensional space) should also be limited to a reasonable range. However, existing technologies cannot theoretically guarantee the transient control performance of all state variables of the bridge crane.

[0051] Therefore, the following embodiments provide a trajectory planning method and system for bridge cranes, which fully considers the dynamic effects and state constraints of the double spherical pendulum of the bridge crane. Based on the positions of the hook and the load, a set of auxiliary signals (seven degrees of freedom) including trolley displacement, bridge frame displacement, rope length, hook swing angle and load swing angle are introduced.

[0052] Based on full consideration of state constraints, auxiliary signals were designed using 13th-order polynomial functions, which effectively solved the problems of movement of bridge crane trolley and bridge frame, change of suspension rope length and suppression of double spherical pendulum.

[0053] Without approximate simplification, an accurate dynamic model of a seven-DOF bridge crane with a double-spherical pendulum and variable rope length effects is established using the Lagrangian method. Based on this, a set of auxiliary signals containing various state variables is constructed. Constraints applied to the trolley, bridge frame, rope length, hook, and load swing are transformed into constraints on the auxiliary signals. This transforms the trajectory planning problem of the bridge crane into a time optimization problem related to the auxiliary signals, which is then solved using the bisection method. The proposed trajectory planning method not only shortens the hoisting time but also ensures that all state variables satisfy the constraints. Simulation results demonstrate the accuracy of the dynamic model and the effectiveness of the trajectory planning method.

[0054] Example 1:

[0055] The trajectory planning method for bridge cranes includes the following steps:

[0056] A dynamic model of a bridge crane system with a double spherical pendulum and variable rope length effect was established and analyzed based on the Lagrange method. The model contains seven degrees of freedom: trolley displacement, bridge frame displacement, rope length, and the swing angle of the hook and load in three-dimensional space.

[0057] Considering both driving and non-driving state constraints, auxiliary signals are introduced to represent the state variables of trolley movement, bridge frame movement, rope length change, hook sway, and load sway. The constraints applied to the trolley, bridge frame, rope length, and hook and load sway are transformed into constraints on the auxiliary signals. Thus, the trajectory planning problem of the bridge crane is transformed into a time optimization problem related to the auxiliary signals and solved using the bisection method to complete the trajectory planning of the trolley and bridge frame movement and the rope change.

[0058] The above trajectory planning control method enables precise positioning and sway suppression control of the bridge crane.

[0059] Specifically:

[0060] (1) Dynamic model and analysis:

[0061] like Figure 1 The seven-degree-of-freedom bridge crane system in three-dimensional space is shown in Table 1. The relevant physical parameters and definitions of the bridge crane system are shown in Table 1.

[0062] Table 1: System Parameters

[0063] parameter Physical meaning unit <![CDATA[M1]]> trolley quality kg <![CDATA[M2]]> The sum of the mass of the trolley and the cable tray kg <![CDATA[m1,m2]]> Hook, load mass kg x,y Trolley and bridge displacement m <![CDATA[l1,l2]]> Length of slings and rigging m <![CDATA[θ1,θ2,θ3,θ4]]> Hook and load three-dimensional swing angle deg <![CDATA[F x ,F y ,F z ]]> Trolley, cable tray, and suspension rope control force N g gravitational acceleration <![CDATA[m / s 2 ]]>

[0064] The hook position (x1, y1, z1) and the load position (x2, y2, z2) are defined in the O-XYZ three-dimensional coordinate system as follows:

[0065]

[0066]

[0067] Differentiating equations (1) and (2) respectively, we can obtain the speed signals of the hook and the load:

[0068]

[0069]

[0070] The total kinetic energy K of a bridge crane system can be expressed as the sum of the kinetic energies of the trolley, bridge frame, hook, and load:

[0071]

[0072] The total potential energy P of the bridge crane system can be calculated as follows:

[0073] P=m1gz1+m2gz2=-(m1+m2)gl1cosθ1cosθ2-m2gl2cosθ3cosθ4 (6)

[0074] Define the Lagrange function And calculate the following equation:

[0075]

[0076] Solving equation (7) yields the dynamic equations of the seven-degree-of-freedom bridge crane, as shown in equations (8)-(14):

[0077] The dynamic equation related to the trolley displacement x is:

[0078]

[0079] The dynamic equation related to the cable tray displacement y is:

[0080]

[0081] The dynamic equations related to the length l1 of the suspension rope are:

[0082]

[0083] The dynamic equation related to the hook swing angle θ1 is:

[0084]

[0085] The dynamic equation related to the hook swing angle θ2 is:

[0086]

[0087] The dynamic equation related to the load swing angle θ3 is:

[0088]

[0089] The dynamic equation related to the load swing angle θ4 is:

[0090]

[0091] (2) Control Target

[0092] For a seven-freedom bridge crane system, the control objective of this embodiment is as follows:

[0093] Positioning. The trolley and bridge frame move from their initial positions (x0, y0) to their target positions (x, y0) within the hoisting time T. d ,y d The length of the lifting rope changes from its initial length l during the lifting time T. 10 Change to target length l 1d ,Right now:

[0094]

[0095] Anti-sway. The hook and load stop swinging within the lifting time T, that is:

[0096]

[0097] Full-state constraints. Driving state variables such as trolley speed. acceleration Cable tray speed acceleration The rate of change of the length of the suspension rope acceleration All should be kept within a certain range; non-driven state quantities such as the swing angles θ1(t) and θ2(t) of the hook in three-dimensional space, and the swing angles θ3(t) and θ4(t) of the load in three-dimensional space should also be limited to a reasonable range, that is:

[0098]

[0099] Where, k v and k a The upper limit of the velocity and acceleration of the trolley, bridge, and suspension rope length changes is represented by k. θ This indicates the upper limit of the swing angle of the hook and load.

[0100] (3) Model transformation

[0101] To more clearly illustrate the trajectory planning process, Figure 2 A schematic diagram of the trajectory planning method is shown. Under the anti-sway control, the swing amplitude of the hook and load is small. At this time, the dynamic model of the bridge crane (11)-(14) can be reasonably linearly approximated as follows:

[0102]

[0103]

[0104]

[0105]

[0106] By combining equations (1) and (2) and considering the above linear approximation conditions, a set of auxiliary signals containing each state variable can be constructed:

[0107]

[0108] Taking the second-order time derivative of equation (22) yields:

[0109]

[0110] Substituting equation (23) into equations (18) and (20) respectively, we get:

[0111]

[0112]

[0113] Substituting the second-order time derivative of equation (25) into equation (24), we get:

[0114]

[0115] Similarly, substituting (23) into equations (19) and (21) respectively and resolving them, we can obtain:

[0116]

[0117]

[0118] Substituting equations (25)-(28) into equation (22), we can obtain the trolley displacement x, the bridge displacement y, and the suspension rope length l1, which are expressed using the proposed auxiliary signals as follows:

[0119]

[0120]

[0121] l1=-z2-l2 (31)

[0122] Substituting equations (29)-(31) into equation (15), we can obtain the following representation of the positioning control target using the proposed auxiliary signal:

[0123]

[0124]

[0125] Substituting equations (25)-(28) into equation (16), the anti-sway control target can be represented by the proposed auxiliary signal as follows:

[0126]

[0127]

[0128]

[0129]

[0130] Substituting equations (25)-(31) into equation (17), we obtain the full-state constraint control target represented by the proposed auxiliary signals, namely, representing the trolley speeds respectively. and acceleration Cable tray speed and acceleration The rate of change of the length of the suspension rope and acceleration Both remain within a certain range; the swing angles θ1(t) and θ2(t) of the hook in three-dimensional space, and the swing angles θ3(t) and θ4(t) of the load in three-dimensional space, are as follows:

[0131] Cart speed The constraints are expressed as follows:

[0132]

[0133] Car acceleration The constraints are expressed as follows:

[0134]

[0135] Cable tray speed The constraints are expressed as follows:

[0136]

[0137] Cable tray acceleration The constraints are expressed as follows:

[0138]

[0139] Speed ​​of change of rope length The constraints are:

[0140]

[0141] Acceleration of change in rope length The constraints are:

[0142]

[0143] The constraint condition for the hook swing angle θ1(t) is:

[0144]

[0145] The constraint condition for the hook swing angle θ2(t) is:

[0146]

[0147] The constraint condition for the load swing angle θ3(t) is:

[0148]

[0149] The constraint condition for the load swing angle θ4(t) is:

[0150]

[0151] In this embodiment, the driving state quantities (trolley displacement x, bridge frame displacement y, and rope length l1) and non-driving state quantities (hook swing angles θ1, θ2 and load swing angles θ3, θ4) of the bridge crane, as well as the control objective, are all equivalently converted into expressions for the auxiliary signals x2, y2, z2 and their different derivatives.

[0152] Next, we will plan x2, y2, z2 to achieve the equivalent control objectives represented by equations (32)-(47).

[0153] (4) Time-optimized trajectory design based on 13th degree polynomial curve

[0154] The expressions for x², y², z² based on the 13th-degree polynomial curve are as follows:

[0155]

[0156]

[0157]

[0158] Among them, τ=t / T, 0≤t≤T, α i ,β i ,η i (i = 0, 1, 2, 3... 13) are the parameters of the polynomial curve to be determined.

[0159] Substituting equation (32) into equations (48)-(50) and calculating, we get:

[0160] α i =β i =η i =0, i=0,1,2,3,4,5,6. (51)

[0161] Therefore, the first six time derivatives of equations (48)-(50) are calculated as follows:

[0162]

[0163]

[0164]

[0165] Where j = 1, 2, 3... 6.

[0166] Substituting equation (33) into equations (52)-(54), the remaining polynomial parameters can be obtained as follows:

[0167] α7=β7=η7=1716, α8=β8=η8=-9009,

[0168] α9=β9=η9=20020,α 10 =β 10 =η 10 =-24024,

[0169] α 11 =β 11 =η 11 =16380,α 12 =β 12 =η 12 =-6006,

[0170] α 13 =β 13 =η 13 =924. (55)

[0171] After calculating all the polynomial curve parameters, the hoisting time T needs to be determined to complete the trajectory planning. Next, while ensuring that the inequality constraints (38)-(47) are satisfied, the hoisting time T will be minimized as much as possible to improve the operating efficiency of the bridge crane. Here, the following time optimization problem is constructed:

[0172] min T,subject to(38)-(47) (56)

[0173] The time optimization problem shown in equation (56) is solved using the bisection method. The flowchart of the solution process is as follows: Figure 3 As shown, T up ,T low , These represent the upper limit, lower limit, and optimal value of the hoisting time T to be optimized, respectively, and ε represents the maximum permissible error for time optimization.

[0174] (5) Simulation verification

[0175] The effectiveness of the trajectory planning method for a seven-DOF bridge crane was verified using simulation. The system parameters of the bridge crane and... Figure 3 The input parameters are set as follows:

[0176] M1=3kg, M2=6.5kg, m1=1kg, m2=1kg, l2=0.2m, g=9.8m / s 2 ,

[0177] k v =0.5m / s,k a =0.5m / s 2 ,k θ =2deg,T low =2s,T up =10s, ε=0.01s,

[0178] x0=y0=0m,l 10 =0.1m,x d =y d =1m,l 1d =0.8m.

[0179] This embodiment will verify the effectiveness of the trajectory planning method (the method presented in this paper) by comparing it with existing technologies such as the extra-insensitive (EI) shaper, the smooth shaper, and the energy-analysis-based (EAB) controller. Specifically, none of the above three control methods considers variations in the suspension rope length. For ease of comparison, the EI shaper and the smooth shaper use an average suspension rope length l1 = 0.45m to estimate the natural frequency of load swaying to design the trolley motion, bridge motion, and load lifting / lowering shaper; the EAB controller adds a traditional proportional-derivative (PD) controller to the original trolley controller and bridge controller to drive the load lifting / lowering motion. The simulation verification results of the above three comparison methods and the trajectory planning method designed in this embodiment are as follows: Figures 4(a)-6(b) As shown.

[0180] In this paper, the simulation results are represented by solid lines for the EI shaper, by single-point dashed lines “…” for the smoothing shaper, by dashed lines “-----” for the EAB controller, and by single-point dashed lines “﹎” for the method in this embodiment (the method in this paper).

[0181] Depend on Figures 4(a)-4(i) The simulation results of the driving state variables show that all control methods can accurately drive the trolley and bridge to the target position, and the load to fall to the target position. Except for the trolley acceleration and rope length change acceleration driven by the EAB controller, which are greater than 0.5 m / s². 2 Except for exceeding the driving state constraints, the trajectory planning method in this embodiment and the other comparative control methods can effectively ensure that the driving state meets the constraints. The hoisting times for the trajectory planning method, EI shaper, smoothing shaper, and EAB controller in this embodiment are 4.91s, 4.28s, 5.83s, and 8.34s, respectively. The hoisting time of the trajectory planning method proposed in this embodiment is second only to the EI shaper, effectively reducing hoisting time and improving work efficiency compared to other control methods.

[0182] Figures 5(a)-5(d) The simulation results for non-driven state variables are shown. Taking the load swing angle θ3 as an example, the maximum load swing angle θ3 driven by the EI shaper, smooth shaper, EAB controller, and trajectory planning method of this embodiment are 3.63deg, 2.46deg, 5.39deg, and 1.97deg, respectively. Under the three comparative control methods, the hook and load swing angles not only exceed the non-driven state constraints that ensure lifting safety, but also still have residual swing for a long time after the bridge crane stops running. In comparison, the trajectory planning method of this embodiment ensures that the hook and load swing angles are always within the non-driven state constraints (±2deg) during crane operation and there is no obvious residual swing, effectively ensuring the safe and efficient operation of the bridge crane. Moreover, Figures 6(a)-6(b) This represents the hoisting trajectory of the hook and load within a three-dimensional space, clearly demonstrating the operation process of hoisting the load under the planning method designed in this embodiment.

[0183] The above process establishes for the first time an accurate dynamic model of a seven-degree-of-freedom underactuated bridge crane. The model includes three driving state variables: trolley displacement, bridge displacement, and rope length; and four non-driving state variables: the swing angle of the hook and load in three-dimensional space. The dynamic model established in this disclosure considers more system degrees of freedom and more complex dynamic characteristics of the double-spherical pendulum and variable rope length.

[0184] The above process designs a novel set of auxiliary signals to describe the system's full state variables. By analyzing the nonlinear coupling relationship between the driving and non-driving state variables, each state variable is represented as a combination of the auxiliary signal and its derivatives of different orders. Thus, the trajectory planning problem of the bridge crane is transformed into a time optimization problem related to the auxiliary signals and solved.

[0185] The proposed polynomial-based optimized trajectory planning control strategy not only reduces hoisting time and improves the operating efficiency of bridge cranes, but also ensures that all state variables meet the constraints, thereby improving the safety performance of bridge crane operations.

[0186] Example 2:

[0187] A system for implementing the above method includes:

[0188] The control target module is configured to: construct a dynamic model of the bridge crane system based on the trolley displacement, bridge frame displacement, and rope length, as well as the swing angle of the hook and load in three-dimensional space, and set the control target;

[0189] The model conversion module is configured to design auxiliary signals based on the state variables of trolley movement, bridge movement, rope length change, hook swing and load swing, and to convert the constraints applied to the trolley, bridge, rope length and hook and load swing in the model into constraints on the auxiliary signals according to the control objectives.

[0190] The trajectory planning module is configured to: obtain trajectory planning for the movement of the trolley, bridge frame and the changes in the hoisting rope based on the model results, so as to realize the positioning and sway suppression control of the bridge crane.

[0191] Example 3:

[0192] This embodiment provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps in the bridge crane trajectory planning method described in Embodiment 1 above.

[0193] Example 4:

[0194] This embodiment provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, it implements the steps in the bridge crane trajectory planning method described in Embodiment 1 above.

[0195] The steps or modules involved in Embodiments 2 to 4 above correspond to those in Embodiment 1. For specific implementation details, please refer to the relevant description section of Embodiment 1. The term "computer-readable storage medium" should be understood as a single medium or multiple media including one or more instruction sets; it should also be understood as including any medium capable of storing, encoding, or carrying an instruction set for execution by a processor and enabling the processor to perform any of the methods in this invention.

[0196] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A trajectory planning method for bridge cranes, characterized in that, Includes the following steps: Based on the trolley displacement, bridge frame displacement, and rope length, as well as the swing angle of the hook and load in three-dimensional space, a dynamic model of the bridge crane system is constructed, and control objectives are set. Auxiliary signals are designed based on the state variables of trolley movement, bridge movement, rope length change, hook swing and load swing. According to the control objective, the constraints imposed on the trolley, bridge, rope length and hook and load swing in the model are transformed into constraints on the auxiliary signals. Based on the model results, trajectory planning for the movement of the trolley, bridge frame, and suspension rope is obtained, enabling positioning and sway suppression control of the bridge crane; The construction of the dynamic model of the bridge crane system includes: The positions of the hook and load in the three-dimensional coordinate system are determined, and the velocity signals of the hook and load are obtained by differentiation; Based on the speed signals of the hook and load, and the masses of the trolley, bridge frame, hook, and load, the total kinetic energy of the bridge crane system is obtained; Using the total kinetic and potential energy of the bridge crane system, a Lagrangian function is constructed. After solving the Lagrangian function, a dynamic model of the bridge crane with seven degrees of freedom is obtained, based on the trolley displacement, bridge frame displacement, rope length, hook and load swing angle. The control objectives include positioning constraints, anti-sway constraints, and full-state constraints. The positioning constraints are that the trolley and the bridge frame move from their initial positions to their target positions during the hoisting time, and the length of the hoisting rope changes from its initial length to its target length during the hoisting time. Anti-sway constraint means that the hook and load stop swinging during the lifting time; The full-state constraints are as follows: the speed and acceleration of the trolley, the speed and acceleration of the bridge, and the speed and acceleration of the change in the length of the suspension rope are all kept within the set range; the swing angles of the hook and the load in three-dimensional space are all kept within the set range. Auxiliary signals are designed based on the state variables of trolley movement, bridge frame movement, rope length change, hook sway, and load sway. According to the control objective, the constraints imposed on the trolley, bridge frame, rope length, and hook and load sway in the model are transformed into constraints on the auxiliary signals; including: The dynamic model of the bridge crane is transformed and the positions of the hook and the load are combined to obtain auxiliary signals including the displacement of the trolley, the displacement of the bridge frame, the length of the lifting rope, the sway of the hook, and the sway of the load. Substituting the obtained auxiliary signals into the relational formula of the control target, we obtain the positioning constraint control target, anti-sway constraint control target, and full-state constraint control target based on the proposed auxiliary signal representation. The trolley displacement, bridge frame displacement, hoisting rope length, hook swing angle, load swing angle, and control target in the dynamic model of the bridge crane are transformed into expressions of auxiliary signals and their different derivatives. The model results are obtained by solving a time optimization problem based on the auxiliary signals. Based on the auxiliary signal represented by the polynomial curve, the positioning constraint control target is substituted into the polynomial curve to obtain the polynomial curve parameters.

2. The bridge crane trajectory planning method as described in claim 1, characterized in that, Based on ensuring that the positioning constraint control objective, anti-sway constraint control objective, and all-state constraint control objective are met, a time optimization problem is constructed with the minimum hoisting time as the objective value. The optimal value of hoisting time is obtained by solving the time optimization problem using the bisection method.

3. A bridge crane trajectory planning system, used to implement the bridge crane trajectory planning method as described in claim 1 or 2, characterized in that, include: The control target module is configured to: construct a dynamic model of the bridge crane system based on the trolley displacement, bridge frame displacement, and rope length, as well as the swing angle of the hook and load in three-dimensional space, and set the control target; The model conversion module is configured to design auxiliary signals based on the state variables of trolley movement, bridge movement, rope length change, hook swing and load swing, and to convert the constraints applied to the trolley, bridge, rope length and hook and load swing in the model into constraints on the auxiliary signals according to the control objectives. The trajectory planning module is configured to: obtain trajectory planning for the movement of the trolley, bridge frame and the changes in the hoisting rope based on the model results, so as to realize the positioning and sway suppression control of the bridge crane.

4. A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the bridge crane trajectory planning method as described in claim 1 or 2 above.

5. A computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the steps of the bridge crane trajectory planning method as described in claim 1 or 2.

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