A rigid light-bar trajectory optimization method and system combining a nonlinear dynamic model and an adaptive grid enumeration strategy

Abstract

This invention belongs to the field of rigid light rod trajectory optimization technology, aiming to solve the problems of numerical convergence instability, parameter sensitivity, and poor suppression effect in existing anti-sway technologies. It provides a rigid light rod trajectory optimization method and system that combines a nonlinear dynamic model and an adaptive mesh enumeration strategy. By constructing a physical model of the rigid light rod system, a nonlinear dynamic equation characterizing the coupling relationship between the link angle and the hoisting moving platform is derived. Multiple candidate solutions are generated by discretizing the total motion time, and a velocity trajectory is constructed using a cubic polynomial. The peak velocity and acceleration sequence of the hoisting moving platform are adaptively adjusted based on displacement deviation. The residual oscillation parameters of the load are extracted using the nonlinear dynamic equation, and the total motion time is adaptively adjusted. Candidate solutions are screened through preset acceleration and angle constraints, and the optimal solution is selected with the goal of minimizing the total motion time. This invention can achieve efficient, low-oscillation, and precise hoisting control.

Description

Technical Field

[0001] This invention belongs to the field of rigid light rod trajectory optimization technology, specifically involving a rigid light rod trajectory optimization method and system that combines a nonlinear dynamics model and an adaptive mesh enumeration strategy. Background Technology

[0002] With the rapid development of new energy vehicles, the safety and stability of battery packs, as a core component of these vehicles, directly affect the vehicle's range and operating efficiency. However, during battery pack replacement, due to the underactuated characteristics of the system, rapid changes in the speed of the steel cable can easily cause significant load swings, leading to increased battery pack collision risk, decreased positioning accuracy, and reduced safety.

[0003] To address the above issues, current electronic anti-sway devices rely on sensors and complex calculations, resulting in poor reliability and high costs; mechanical anti-sway devices, on the other hand, suffer from insufficient flexibility and difficult maintenance due to their complex structure.

[0004] Researchers' in-depth study of rope anti-sway technology for bridge cranes has revealed that multi-constraint time-optimal trajectory planning methods under the assumption of rigid light bars theoretically have the potential to improve existing problems. However, these methods generally suffer from unstable numerical convergence and sensitivity to engineering parameters, making it difficult to meet the real-time and robustness requirements of high-frequency battery replacement. Furthermore, when considering minimizing transport time and full-state constraints, existing speed curve optimization techniques can only provide limited load sway suppression effects. Summary of the Invention

[0005] To address the problems of unstable numerical convergence, sensitivity to engineering parameters, and limited load sway suppression effect in existing rope anti-sway technology for bridge cranes, this invention provides a rigid light rod trajectory optimization method and system that combines a nonlinear dynamic model and an adaptive mesh enumeration strategy.

[0006] This invention is achieved using the following technical solution: a method for optimizing the trajectory of a rigid light rod by combining a nonlinear dynamic model and an adaptive mesh enumeration strategy, comprising the following steps: A physical model of a rigid light rod system is constructed. The structure in the physical model of the rigid light rod system includes load, linkage, hoisting and moving platform and frame. The basic parameters, motion state variables and structural relationships of the model are defined, and the kinematic geometric relationships of load, linkage and hoisting and moving platform are derived. Based on the kinematic geometry of the load, linkage, and hoisting mobile platform, the Lagrangian quantity of the rigid light link system is obtained, and the nonlinear dynamic equation of the rigid light link system characterizing the coupling relationship between the linkage angle and the hoisting mobile platform is derived through the Euler-Lagrangian equation. The total motion time of the rigid light bar system is discretized, and multiple candidate solutions are generated, consisting of discrete peak speed of the hoisting moving platform, load acceleration time, and load constant speed time. For each candidate solution, a high-density grid is used for discretization enumeration. Based on the preset boundary conditions, the velocity trajectory of the hoisting mobile platform corresponding to each candidate solution is constructed using a cubic polynomial. The velocity and acceleration trajectory expressions of the hoisting mobile platform at the current moment are derived. The peak velocity of the hoisting mobile platform is adaptively adjusted by the displacement deviation of the hoisting mobile platform. At the same time, the discretized acceleration sequence of the hoisting mobile platform obtained based on the acceleration trajectory expression is updated. Based on the discretized acceleration sequence and nonlinear dynamic equations of the hoisting mobile platform, the angular trajectory expression and angular velocity expression of the link are derived, and the load residual oscillation swing angle and angular velocity value are extracted from them. The total motion time of the rigid light rod system is adaptively adjusted according to the load residual oscillation swing angle and angular velocity. Determine whether the candidate solutions after parameter adjustment meet the preset acceleration and angle constraints; By comparing the total motion time of the rigid light bar system corresponding to all candidate solutions that satisfy the constraints, the candidate solution that minimizes the total motion time of the rigid light bar system is selected as the optimal solution of the rigid light bar system.

[0007] Preferably, the basic parameters of the rigid light rod system physical model include the link length, the mass of the hoisting platform, and the load mass; the motion parameters include the link angle, the coordinates of the hoisting platform, the load coordinates, the angular velocity of the link, the angular acceleration of the link, the velocity of the hoisting platform, and the angular acceleration of the hoisting platform, wherein the link angle refers to the distance between the link and the load. The angle between the axes in the positive direction is defined as vertically downwards. The positive direction of the axis is horizontal to the right. In the positive axis direction, the coordinates of the hoisting and moving platform refer to the coordinates of the connection point between the connecting rod and the hoisting and moving platform, and the load coordinates refer to the coordinates of the connection point between the connecting rod and the load; structural association refers to the connection relationship between the connecting rod, the hoisting and moving platform, and the load.

[0008] Preferably, the Lagrangian of the rigid light rod system is obtained by solving for the kinetic energy of the hoisting platform and the load, as well as the potential energy of the rigid light rod; the Euler-Lagrangian equations are applied to the generalized coordinate link angles to simplify and obtain the nonlinear dynamic equations of the rigid light rod system; the expression of the nonlinear dynamic equations is: In the formula, This represents the angular acceleration of the connecting rod. This indicates the acceleration of the hoisting mobile platform; Indicates the angle of the link; Indicates the length of the link; It represents the acceleration due to gravity.

[0009] Preferably, during the velocity trajectory of the hoisting mobile platform, the velocity and acceleration trajectory expressions of the hoisting mobile platform at the current moment corresponding to the acceleration phase are as follows: In the formula, Indicates the current time; This indicates the adjusted peak speed of the hoisting mobile platform; The scaling factor representing the normalization time; Indicates the duration of load acceleration; The constant speed phase corresponds to the speed of the hoisting mobile platform at the current moment. Hengwei acceleration =0; Based on symmetry, the expressions for the velocity and acceleration trajectory of the hoisting mobile platform at the current moment corresponding to the deceleration phase can be derived similarly as follows: The speed of the hoisting mobile platform at the current moment corresponds to the load residual oscillation phase. The acceleration is always 0. It is 0.

[0010] Preferably, the displacement deviation of the hoisting mobile platform is the deviation between the actual displacement and the target displacement. By adjusting the peak speed of the hoisting mobile platform without changing the time parameters of the acceleration and deceleration phases, closed-loop compensation of the displacement error can be achieved. The adjusted expression for the peak speed of the hoisting mobile platform is: In the formula, The peak speed of the hoisting mobile platform before adjustment. For error rate; In the formula, This represents the actual displacement. For the target displacement; For effective exercise time, , This indicates the duration of uniform load movement.

[0011] Preferably, the total motion time of the rigid light bar system is adaptively adjusted based on the load residual oscillation angle and angular velocity. The expression is: In the formula, This refers to the linkage angle at the end of the motion phase of the hoisting mobile platform. This represents the maximum amplitude of the residual load oscillation angle. The link angular velocity at the end of the motion phase of the hoisting mobile platform. The residual angular velocity of the load at the end of the motion phase of the hoisting mobile platform; It is preset Penalty function; It is preset Penalty constant; Indicates when If true, it is returned a value of 1; if false, it is returned a value of 0. It is the preset load residual oscillation angular velocity threshold.

[0012] Compared with the prior art, the beneficial effects of the present invention are: This application constructs a physical model of a rigid light-bar system, including a load, connecting rods, a hoisting mobile platform, and a frame. It accurately derives the kinematic geometric relationships of each component and, based on this, constructs the Lagrangian quantities of the rigid light-bar system. Using the Euler-Lagrangian equations, it derives nonlinear dynamic equations characterizing the coupling relationship between the connecting rod angles and the hoisting mobile platform, providing a precise theoretical foundation for system motion analysis and control. Simultaneously, by discretizing the total motion time to generate multiple candidate solutions, it employs high-density grid discretization and enumeration combined with cubic polynomials to construct velocity trajectories. Based on displacement deviations, it adaptively adjusts the peak velocity and acceleration sequences of the hoisting mobile platform. Furthermore, it extracts residual load oscillation parameters using the nonlinear dynamic equations and adaptively adjusts the total motion time, effectively suppressing residual load oscillations and improving positioning accuracy. Finally, by screening candidate solutions through preset acceleration and angle constraints and selecting the optimal solution with the goal of minimizing the total motion time, it significantly improves the efficiency and accuracy of hoisting operations while ensuring the safe and stable operation of the system, achieving efficient, low-oscillation, and precise hoisting control. Attached Figure Description

[0013] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0014] Figure 1 This is a schematic diagram of the physical model structure of the rigid light rod system of the present invention; Figure 2 This is a flowchart of the algorithm execution of the present invention. Detailed Implementation

[0015] The technical solutions of the embodiments of the present invention will be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other implementation methods obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0016] It should be noted that the structures, proportions, sizes, etc., shown in the accompanying drawings of this specification are only for the purpose of assisting those skilled in the art in understanding and reading the content disclosed in the specification, and are not intended to limit the conditions under which the present invention can be implemented. Therefore, they have no substantial technical significance. Any modifications to the structure, changes in the proportional relationships, or adjustments to the size, without affecting the effects and objectives that the present invention can produce, should fall within the scope of the technical content disclosed in the present invention. It should be noted that in this specification, relational terms such as "first" and "second" are only used to distinguish one entity from several other entities, and do not necessarily require or imply any actual relationship or order between these entities.

[0017] This invention provides an embodiment: like Figure 1 , 2 As shown, a method for optimizing the trajectory of a rigid light rod by combining a nonlinear dynamic model and an adaptive mesh enumeration strategy includes the following steps: S1: Construct a physical model of a rigid light rod system. The structure in the rigid light rod system physical model includes load, linkage, hoisting and moving platform and frame. Define the basic parameters, motion state variables and structural relationships of the model, and derive the kinematic geometric relationships of load, linkage and hoisting and moving platform.

[0018] In this embodiment, the load is a battery pack; the basic parameters of the rigid light rod system physical model include the link length. Quality of hoisting mobile platform Load quality Motion parameters include link angles. Coordinates of the hoisting mobile platform Load coordinates The angular velocity of the connecting rod, the angular acceleration of the connecting rod, the speed of the hoisting moving platform, and the angular acceleration of the hoisting moving platform, where the connecting rod angle refers to the angle between the connecting rod and the angular velocity of the connecting rod. The angle along the positive direction of the axis. The value is not greater than 90°; vertical downward is defined as... The positive direction of the axis is horizontal to the right. In the positive axis direction, the hoisting and moving platform coordinates refer to the coordinates of the connection point between the connecting rod and the hoisting and moving platform, while the load coordinates refer to the coordinates of the connection point between the connecting rod and the load; structural association refers to the connection relationship between the connecting rod, the hoisting and moving platform, and the load. Initially, the hoisting and moving platform is located at the coordinate origin; the connecting rod and... The axes coincide, at this time The angle is 0°. After the hoisting begins, the hoisting platform moves along... Movement in the positive direction of the axis. Define the motion state quantity as a function of time. The relationships of change are as follows: ; according to Figure 1 From the geometric relationships shown, the load coordinates, i.e., the coordinates of the connection point between the link and the load, can be easily obtained. It can be represented as: The velocity at the connection point between the link and the load is expressed as: In the formula, This is the horizontal component of the velocity at the connection point between the link and the load. This is the vertical component of the velocity at the connection point between the link and the load; The horizontal component of the velocity at the connection point between the connecting rod and the hoisting mobile platform; Let be the angular acceleration of the connecting rod.

[0019] S2: Based on the kinematic geometry of the load, linkage, and hoisting platform, the Lagrangian quantities of the rigid light link system are obtained, and the nonlinear dynamic equations of the rigid light link system characterizing the coupling relationship between the linkage angle and the hoisting platform are derived through the Euler-Lagrangian equations.

[0020] By solving for the kinetic energy of the hoisting platform and the load, as well as the potential energy of the rigid light rod, the Lagrangian of the rigid light rod system is obtained: kinetic energy of the load for: Kinetic energy of the hoisting mobile platform for: by The horizontal plane containing the axis is the zero potential energy surface, and the system's potential energy is... It can be represented as: Obtain the Lagrangian of the rigid light rod system : For generalized coordinate link angles Applying the Euler-Lagrange equations, the nonlinear dynamic equations of the rigid light rod system are simplified to obtain the following expression: In the formula, This represents the angular acceleration of the connecting rod. This indicates the acceleration of the hoisting mobile platform; Indicates the angle of the link; Indicates the length of the link; It represents the acceleration due to gravity.

[0021] S3: Discretize the total motion time of the rigid light rod system and generate multiple candidate solutions consisting of discrete peak speed of the hoisting moving platform, load acceleration time and load uniform speed time, thus transforming the continuous dynamics problem into a discrete form that is easy to calculate.

[0022] The total motion time interval of the rigid light bar system Discretization, corresponding discrete time nodes for: in, The number of discrete time segments. To discretize the time step, This represents the total motion time of the rigid light rod system (including the time when the residual load oscillation ends).

[0023] A search grid can be formed within the following given range: in, It is the peak speed of the discrete hoisting mobile platform. , These are the preset minimum and maximum peak speeds of the hoisting mobile platform. The number of sampling points for the peak speed of the hoisting mobile platform; It is the discrete load acceleration time. , These are the preset minimum and maximum load acceleration times, respectively. The number of sampling points for the load acceleration duration; It is the discrete uniform load duration. , These are the preset minimum and maximum durations of uniform load speed. The number of sampling points for the duration of uniform load movement; This is a candidate solution. The peak speed constraint condition for the hoisting mobile platform is: , This is the value corresponding to the preset peak speed of the hoisting mobile platform.

[0024] S4: For each candidate solution, a high-density grid is used for discretization enumeration. Based on the preset boundary conditions, the velocity trajectory of the hoisting mobile platform corresponding to each candidate solution is constructed using a cubic polynomial. The velocity and acceleration trajectory expressions of the hoisting mobile platform at the current moment are derived. The peak velocity of the hoisting mobile platform is adaptively adjusted by the displacement deviation of the hoisting mobile platform. At the same time, the discretized acceleration sequence of the hoisting mobile platform obtained based on the acceleration trajectory expression is updated.

[0025] Set the speed of the hoisting mobile platform With the current time The changing cubic polynomial is: in, The scaling factor for normalized time. The speed of the hoisting mobile platform at the current moment; The acceleration of the hoisting mobile platform at the current moment, These are unknown parameters; their specific values ​​will be obtained through subsequent calculations.

[0026] Let's first discuss the acceleration phase. To ensure the smoothness of the velocity trajectory, the cubic polynomial must satisfy the following boundary constraints: Among them, when hour, ;when hour, ; This refers to the adjusted peak speed of the hoisting mobile platform.

[0027] Substituting the values, we obtain the coefficient matrix: The specific solution to the coefficient matrix is: A cubic polynomial is used as a smoothing factor to avoid abrupt acceleration changes caused by linear speed changes, ensuring continuous acceleration and improving motion stability and mechanical lifespan.

[0028] During the speed trajectory of the hoisting mobile platform, the acceleration phase The corresponding expressions for the velocity and acceleration trajectory of the hoisting mobile platform at the current moment are: In the formula, Indicates the current time; This indicates the adjusted peak speed of the hoisting mobile platform; The scaling factor representing the normalization time; Indicates the duration of load acceleration; Uniform speed phase The corresponding speed of the hoisting mobile platform at the current moment Hengwei acceleration =0; Based on symmetry, the deceleration phase can be derived similarly. The corresponding expressions for the velocity and acceleration trajectory of the hoisting mobile platform at the current moment are: Residual oscillation phase of load The corresponding speed of the hoisting mobile platform at the current moment The acceleration is always 0. It is 0.

[0029] The displacement deviation of the hoisting mobile platform is the deviation between the actual displacement and the target displacement. By adjusting the peak speed of the hoisting mobile platform without changing the time parameters of the acceleration and deceleration phases, closed-loop compensation of the displacement error can be achieved. Since the velocity changes during acceleration and deceleration are preset to a smooth shape, their corresponding displacement contributions are equivalent to those at peak velocity. run and The resulting displacement.

[0030] Effective exercise time can be obtained for: In the formula, The load deceleration time is given by the symmetry of the system engineering: .

[0031] The adjusted expression for the peak speed of the hoisting mobile platform is: In the formula, The peak speed of the hoisting mobile platform before adjustment is equivalent to ; For error rate; In the formula, This represents the actual displacement. For the target displacement; For effective exercise time, , This indicates the duration of uniform load movement.

[0032] S5: Based on the discretized acceleration sequence and nonlinear dynamic equations of the hoisting mobile platform, the angular trajectory expression and angular velocity expression of the connecting rod are derived, and the load residual oscillation swing angle and angular velocity value are extracted from them. The total motion time of the rigid light rod system is adaptively adjusted according to the load residual oscillation swing angle and angular velocity.

[0033] Based on discretized acceleration sequences The angle sequence of the connecting rod is derived through nonlinear dynamic equations. Specifically: Numerical integration of angular velocity and angle yields: For all Discretized acceleration sequences can be obtained through repeated iterations. The angle trajectory of the lower link and angular velocity expression.

[0034] An adaptive rest time compensation mechanism based on the maximum swing angle is introduced to effectively solve the positioning error problem caused by residual load oscillation after the deceleration phase.

[0035] The total motion time of the rigid light bar system is adaptively adjusted based on the load residual oscillation angle and angular velocity. The expression is: In the formula, This refers to the linkage angle at the end of the motion phase of the hoisting mobile platform. This represents the maximum amplitude of the residual load oscillation angle. The link angular velocity at the end of the motion phase of the hoisting mobile platform. The residual angular velocity of the load at the end of the motion phase of the hoisting mobile platform; It is preset Penalty function; It is preset Penalty constant; Indicates when If true, it is returned a value of 1; if false, it is returned a value of 0. It is the preset load residual oscillation angular velocity threshold.

[0036] S6: Determine whether the candidate solution after parameter adjustment meets the preset acceleration and angle constraints.

[0037] The preset acceleration and angle constraints are as follows: .

[0038] in, The maximum amplitude of the load residual oscillation angle preset by the user. The maximum peak acceleration value of the hoisting mobile platform is preset for the user.

[0039] S7: Compare the total motion time of the rigid light bar system corresponding to all candidate solutions that satisfy the constraints, and select the candidate solution that minimizes the total motion time of the rigid light bar system as the optimal solution of the rigid light bar system.

[0040] The present invention also provides a rigid light rod trajectory optimization system that combines a nonlinear dynamics model and an adaptive mesh enumeration strategy, including a physical modeling module configured to construct a physical model of a rigid light rod system including load, linkage, hoisting mobile platform and frame; The dynamics modeling module, connected to the physical modeling module, is configured to obtain the nonlinear dynamic equations of a rigid light rod system. The candidate solution generation module is configured to discretize the total motion time of the rigid light bar system and enumerate and generate multiple candidate solutions; The trajectory optimization and parameter adjustment module, connected to the candidate solution generation module and the dynamic modeling module, is configured to perform trajectory fitting for each candidate solution, adaptively adjust the peak speed of the hoisting mobile platform according to the displacement deviation, and generate the corresponding discretized acceleration sequence. The residual oscillation suppression and total time optimization module, connected to the trajectory optimization and parameter adjustment module, is configured to receive the adjusted acceleration sequence and nonlinear dynamic equation, solve for the linkage motion trajectory and extract the load residual oscillation swing angle and angular velocity value, and adaptively optimize the total motion time of the rigid light rod system based on the load residual oscillation swing angle and angular velocity value. The constraint judgment module, connected to the residual oscillation suppression and total duration optimization module, is configured to judge whether the candidate solution after parameter adjustment meets the preset acceleration and angle constraint conditions. The optimal solution selection module, connected to the constraint judgment module, is configured to select the candidate solution that minimizes the total motion time of the rigid light bar system from all candidate solutions that satisfy the constraint conditions as the optimal solution of the rigid light bar system.

[0041] The above description is merely a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A rigid light-bar trajectory optimization method combining a nonlinear dynamics model and an adaptive grid enumeration strategy, characterized in that, Includes the following steps: A physical model of a rigid light rod system is constructed. The structure in the physical model of the rigid light rod system includes load, linkage, hoisting and moving platform and frame. The basic parameters, motion state variables and structural relationships of the model are defined, and the kinematic geometric relationships of load, linkage and hoisting and moving platform are derived. Based on the kinematic geometry of the load, linkage, and hoisting mobile platform, the Lagrangian quantity of the rigid light link system is obtained, and the nonlinear dynamic equation of the rigid light link system characterizing the coupling relationship between the linkage angle and the hoisting mobile platform is derived through the Euler-Lagrangian equation. The total motion time of the rigid light bar system is discretized, and multiple candidate solutions are generated, consisting of discrete peak speed of the hoisting moving platform, load acceleration time, and load constant speed time. For each candidate solution, a high-density grid is used for discretization enumeration. Based on the preset boundary conditions, the velocity trajectory of the hoisting mobile platform corresponding to each candidate solution is constructed using a cubic polynomial. The velocity and acceleration trajectory expressions of the hoisting mobile platform at the current moment are derived. The peak velocity of the hoisting mobile platform is adaptively adjusted by the displacement deviation of the hoisting mobile platform. At the same time, the discretized acceleration sequence of the hoisting mobile platform obtained based on the acceleration trajectory expression is updated. Based on the discretized acceleration sequence and nonlinear dynamic equations of the hoisting mobile platform, the angular trajectory expression and angular velocity expression of the link are derived, and the load residual oscillation swing angle and angular velocity value are extracted from them. The total motion time of the rigid light rod system is adaptively adjusted according to the load residual oscillation swing angle and angular velocity. Determine whether the candidate solutions after parameter adjustment meet the preset acceleration and angle constraints; By comparing the total motion time of the rigid light bar system corresponding to all candidate solutions that satisfy the constraints, the candidate solution that minimizes the total motion time of the rigid light bar system is selected as the optimal solution of the rigid light bar system.

2. The method for optimizing the trajectory of a rigid light rod by combining a nonlinear dynamic model and an adaptive mesh enumeration strategy according to claim 1, characterized in that: The basic parameters of the rigid light rod system physical model include the link length, the mass of the hoisting platform, and the load mass; the motion parameters include the link angle, the coordinates of the hoisting platform, the load coordinates, the angular velocity of the link, the angular acceleration of the link, the velocity of the hoisting platform, and the angular acceleration of the hoisting platform. The link angle refers to the distance between the link and the load. The angle between the axes in the positive direction is defined as vertically downwards. The positive direction of the axis is horizontal to the right. In the positive axis direction, the coordinates of the hoisting and moving platform refer to the coordinates of the connection point between the connecting rod and the hoisting and moving platform, and the load coordinates refer to the coordinates of the connection point between the connecting rod and the load; structural association refers to the connection relationship between the connecting rod, the hoisting and moving platform, and the load.

3. The method for optimizing the trajectory of a rigid light rod by combining a nonlinear dynamic model and an adaptive mesh enumeration strategy according to claim 2, characterized in that: By solving for the kinetic energy of the hoisting platform and the load, as well as the potential energy of the rigid light rod, the Lagrangian quantity of the rigid light rod system is obtained. Applying the Euler-Lagrangian equations to the generalized coordinate link angles, the nonlinear dynamic equations of the rigid light rod system are simplified to obtain the following expression: In the formula, This represents the angular acceleration of the connecting rod. This indicates the acceleration of the hoisting mobile platform; Indicates the angle of the link; Indicates the length of the link; It represents the acceleration due to gravity.

4. The method for optimizing the trajectory of a rigid light rod by combining a nonlinear dynamic model and an adaptive mesh enumeration strategy according to claim 1, characterized in that: During the velocity trajectory of the hoisting mobile platform, the velocity and acceleration trajectory expressions for the hoisting mobile platform at the current moment corresponding to the acceleration phase are as follows: In the formula, Indicates the current time; This indicates the adjusted peak speed of the hoisting mobile platform; The scaling factor representing the normalization time; Indicates the duration of load acceleration; The constant speed phase corresponds to the speed of the hoisting mobile platform at the current moment. Hengwei acceleration =0; Based on symmetry, the expressions for the velocity and acceleration trajectory of the hoisting mobile platform at the current moment corresponding to the deceleration phase can be derived similarly as follows: The speed of the hoisting mobile platform at the current moment corresponds to the load residual oscillation phase. The acceleration is always 0. It is 0.

5. The method for optimizing the trajectory of a rigid light rod by combining a nonlinear dynamic model and an adaptive mesh enumeration strategy according to claim 4, characterized in that: The displacement deviation of the hoisting mobile platform is the deviation between the actual displacement and the target displacement. By adjusting the peak speed of the hoisting mobile platform without changing the time parameters of the acceleration and deceleration phases, closed-loop compensation of the displacement error can be achieved. The adjusted expression for the peak speed of the hoisting mobile platform is: In the formula, The peak speed of the hoisting mobile platform before adjustment. For error rate; In the formula, This represents the actual displacement. For the target displacement; For effective exercise time, , This indicates the duration of uniform load movement.

6. The method for optimizing the trajectory of a rigid light rod by combining a nonlinear dynamic model and an adaptive mesh enumeration strategy according to claim 1, characterized in that: The total motion time of the rigid light bar system is adaptively adjusted based on the load residual oscillation angle and angular velocity. The expression is: In the formula, This refers to the linkage angle at the end of the motion phase of the hoisting mobile platform. This represents the maximum amplitude of the residual load oscillation angle. The link angular velocity at the end of the motion phase of the hoisting mobile platform. The residual angular velocity of the load at the end of the motion phase of the hoisting mobile platform; It is preset Penalty function; It is preset Penalty constant; Indicates when If true, it is returned a value of 1; if false, it is returned a value of 0. It is the preset load residual oscillation angular velocity threshold.

7. A rigid light rod trajectory optimization system combining a nonlinear dynamic model and an adaptive mesh enumeration strategy, used to implement the rigid light rod trajectory optimization method combining a nonlinear dynamic model and an adaptive mesh enumeration strategy as described in any one of claims 1 to 6, characterized in that: This includes a physical modeling module, configured to build a physical model of a rigid light-bar system that includes loads, linkages, lifting and moving platforms, and frames; The dynamics modeling module, connected to the physical modeling module, is configured to obtain the nonlinear dynamic equations of a rigid light rod system. The candidate solution generation module is configured to discretize the total motion time of the rigid light bar system and enumerate and generate multiple candidate solutions; The trajectory optimization and parameter adjustment module, connected to the candidate solution generation module and the dynamic modeling module, is configured to perform trajectory fitting for each candidate solution, adaptively adjust the peak speed of the hoisting mobile platform according to the displacement deviation, and generate the corresponding discretized acceleration sequence. The residual oscillation suppression and total time optimization module, connected to the trajectory optimization and parameter adjustment module, is configured to receive the adjusted acceleration sequence and nonlinear dynamic equation, solve for the linkage motion trajectory and extract the load residual oscillation swing angle and angular velocity value, and adaptively optimize the total motion time of the rigid light rod system based on the load residual oscillation swing angle and angular velocity value. The constraint judgment module, connected to the residual oscillation suppression and total duration optimization module, is configured to judge whether the candidate solution after parameter adjustment meets the preset acceleration and angle constraint conditions. The optimal solution selection module, connected to the constraint judgment module, is configured to select the candidate solution that minimizes the total motion time of the rigid light bar system from all candidate solutions that satisfy the constraint conditions as the optimal solution of the rigid light bar system.

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