Bridge machine double-hook cooperative lifting trajectory planning method considering space-time coupling constraints

Abstract

The application belongs to the field of hoisting trajectory planning, and particularly discloses a method for planning a double-hook coordinated hoisting trajectory of a bridge girder erection machine considering space-time coupling constraints, which comprises the following steps: constructing a kinematic model of the bridge girder erection machine and a three-dimensional obstacle geometric model of a hoisting operation environment to form a multi-dimensional configuration space; generating a hoisting operation sequence according to the type attribute of a component to be hoisted; in the global path planning stage, a global path planning algorithm based on sampling is used to search and sample in the multi-dimensional configuration space, and a double-hook kinematic coordination constraint detection mechanism is implanted to obtain an initial collision-free path; in the local trajectory optimization stage, a trajectory smoothing model based on quadratic programming is constructed, a smooth and synchronous time-state trajectory is generated by minimizing jerk and introducing a synchronization error hard constraint. The application effectively solves the space-time coordination and anti-swing control problems in the double-hook hoisting operation, and realizes the optimal balance between efficiency and safety.

Description

Technical Field

[0001] This invention belongs to the field of hoisting trajectory planning, and more specifically, relates to a method for collaborative hoisting trajectory planning of a bridge erecting machine with dual hooks that considers spatiotemporal coupling constraints. Background Technology

[0002] Bridge erecting machines are core equipment for precast beam erection in large-scale infrastructure construction such as high-speed railways and highways. With increasingly stringent requirements for efficiency and safety in engineering construction, the automation and intelligentization of bridge erecting machines have become an inevitable trend in the industry. In traditional bridge erecting machine hoisting operations, operators primarily rely on visual observation and manual operation of remote controls to control the movement of the trolley, crane, and lifting mechanism. This operating mode has many drawbacks. First, manual operation is inefficient and limited by the operator's experience and fatigue, making it difficult to ensure consistency in continuous hoisting operations. Second, for the installation of large, irregularly shaped components such as piers and cap beams, high-precision coordinated movements of two trolleys are often required in confined spaces, such as aerial attitude adjustment and synchronous double-hook translation. Manual operation is highly susceptible to component collisions or equipment damage due to improper coordination. Third, the underactuated system composed of flexible cables suspending heavy loads has inherent swaying characteristics, and manual operation struggles to accurately suppress residual load swaying, posing significant safety hazards.

[0003] While existing path planning technologies have been widely applied in mobile robots and robotic arms, their direct application to bridge erecting machines still faces significant challenges. Traditional path planning algorithms typically simplify the work object as a single point mass, neglecting the complex geometric constraints of a dual-hook system. For example, the front and rear trolleys of the bridge erecting machine run on the same track, requiring constant maintenance of a safe distance to prevent collisions, while simultaneously maintaining a specific spacing to balance the load. These dynamic geometric constraints are difficult to handle effectively in traditional sampling algorithms. Furthermore, traditional trajectory smoothing methods only consider kinematic constraints, neglecting dynamic response, resulting in discontinuous trajectory acceleration that can easily induce violent swaying of the load. Current academic research largely focuses on anti-sway control for single hooks, lacking a systematic solution for the entire process of dual-hook collaborative lifting operations. Therefore, there is an urgent need for a bridge erecting machine lifting trajectory planning method that can comprehensively consider spatial obstacle avoidance, dual-hook collaborative constraints, and dynamic stability. Summary of the Invention

[0004] To address the aforementioned deficiencies or improvement needs of existing technologies, this invention provides a method for planning the collaborative lifting trajectory of a bridge erecting machine with dual hooks, considering spatiotemporal coupling constraints. The purpose is to solve the spatiotemporal coordination problem in the lifting operation of a bridge erecting machine with dual hooks and improve the safety of the lifting operation.

[0005] To achieve the above objectives, according to one aspect of the present invention, a method for planning the collaborative lifting trajectory of a bridge erecting machine with dual hooks, considering spatiotemporal coupling constraints, is proposed, comprising the following steps:

[0006] S1. Construct the kinematic model of the bridge erecting machine and the three-dimensional obstacle geometry model of the hoisting operation environment to form a multi-dimensional configuration space;

[0007] S2. Generate a hoisting operation sequence based on the type and attributes of the component to be hoisted. This hoisting operation sequence contains several sequentially executed action primitives.

[0008] S3. Based on the hoisting operation sequence, a sampling-based global path planning algorithm is used to search and sample in the multi-dimensional configuration space to generate an initial collision-free path connecting the starting state and the target state; and during the search and sampling process, invalid sampling points that violate the physical distance constraint between the two trolleys or cause the cable tilt angle to be too large are eliminated through dual hook collaborative constraint detection.

[0009] S4. Based on the initial collision-free path, with position sequence, velocity sequence and acceleration sequence as decision variables, and the objective function being the comprehensive optimization of trajectory smoothness, tracking accuracy and energy consumption, and the extreme values ​​of position, velocity, acceleration and the synchronization error of the two hooks being transformed into linear constraints, a quadratic programming model is constructed and solved to obtain the time state trajectory.

[0010] As a further preferred step, step S3 uses the batch heuristic tree (BIT) algorithm for global path planning based on sampling. Specifically, it first searches in the multidimensional configuration space to obtain an elliptic heuristic set, and then performs elliptic heuristic sampling to obtain an initial collision-free path.

[0011] As a further preferred step, step S3, the dual-hook collaborative constraint detection includes: obtaining the three-dimensional position of the two trolleys equipped with dual hooks in the world coordinate system through forward kinematics calculation based on the configuration state of the current sampling point; calculating the Euclidean distance between the two trolleys, and determining whether the Euclidean distance is within the closed interval formed by the preset minimum safe anti-collision distance and the maximum allowable distance of the main beam span; if it is within the closed interval and neither trolley exceeds its respective mechanical limit boundary, then the sampling point is determined to be valid, otherwise it is discarded.

[0012] As a further optimization, step S4 uses the comprehensive optimization of trajectory smoothness, tracking accuracy, and energy consumption as the objective function, expressed as:

[0013]

[0014] in, The acceleration term characterizes the smoothness of the trajectory; For path tracking, it represents the trajectory tracking accuracy; The velocity regularization term characterizes the system's energy consumption.

[0015] The above objective function J Integrate into a standard secondary programming form:

[0016]

[0017] in, X These are decision variables, which include position sequences, velocity sequences, and acceleration sequences; This is a Hessian matrix, with its diagonal blocks corresponding to... , , The weighting coefficients of the three items; f It is a linear target vector.

[0018] As a further preferred embodiment, step S4 converts the extreme values ​​of position, velocity, acceleration, and the synchronization error of the two hooks into linear constraints, expressed as follows:

[0019]

[0020] Where L is the lower bound vector and U is the upper bound vector; A The constraint matrix contains dynamic constraints, physical limit constraints, and cooperative synchronization constraints. The dynamic constraints are discretized Newtonian kinematic equations used to constrain the state evolution relationship between adjacent time steps. The physical limit constraints limit the position, velocity, and acceleration extreme values ​​of the mechanism's physical performance. The cooperative synchronization constraints are represented as a linear combination of the position deviations of the two hooks, used to constrain the synchronization error at any time.

[0021] As a further preferred option, the following steps are also included:

[0022] S5. Perform dynamic simulation based on the time-state trajectory to obtain the maximum swing angle, synchronization error, and cable tension during the hoisting operation. If any of the maximum swing angle, synchronization error, or cable tension exceeds the preset safety threshold, adjust the weight coefficients or kinematic parameters in the Hessian matrix and return to step S4 to replan the time-state trajectory until the safety threshold is met. The kinematic parameters include geometric dimensions, maximum velocity, maximum acceleration, and maximum jerk.

[0023] As a further preferred step, in step S5, the system state equation is derived using the Lagrange equation to establish a coupled double pendulum dynamic model. The state equation considers the nonlinear coupling effect of the hook swing and the load rotation around the center of mass, as well as the Coriolis force caused by the change in cable length. The time state trajectory is input into the coupled double pendulum dynamic model for dynamic simulation. The integration process of the dynamic simulation adopts the fourth-order Runge-Kutta method.

[0024] As a further preferred option, the following steps are also included:

[0025] S6. For the time-state trajectory that meets the safety threshold in step S5, further perform layered collision detection, including: for the time-state trajectory, use axis-aligned bounding box (AABB) for coarse detection; if the coarse detection fails, return directly to step S3; if the coarse detection passes, use oriented bounding box (OBB) and separating axis theorem (SAT) for fine detection, and determine whether a collision occurs by whether the projected intervals overlap; if no collision occurs, the process ends; if a collision occurs, return to step S3.

[0026] As a further preferred step, in step S2, the type attributes of the components to be hoisted include piers, cap beams, and beam segments. For pier components, the hoisting operation sequence is as follows: positioning the trolley, simultaneous lifting of the front and rear trolleys with double hooks, simultaneous longitudinal movement of the two trolleys, independent lowering of the rear trolley, unhooking of the rear trolley, and independent lowering of the front trolley. For cap beam components, the hoisting operation sequence is as follows: positioning the trolley, lifting of the front trolley with a single hook, longitudinal movement of the front trolley, 90-degree rotation of the secondary lifting device, and precise positioning and lowering. For beam segment components, the hoisting operation sequence is as follows: positioning the trolley, lifting the front end of the front trolley, lifting the rear end of the rear trolley, simultaneous longitudinal movement of the two trolleys, and simultaneous lowering of the two trolleys.

[0027] According to another aspect of the present invention, a bridge erecting machine dual-hook collaborative hoisting trajectory planning system considering spatiotemporal coupling constraints is provided, including a processor, the processor being used to execute the above-described bridge erecting machine dual-hook collaborative hoisting trajectory planning method considering spatiotemporal coupling constraints.

[0028] In summary, compared with the prior art, the above-described technical solutions conceived by this invention mainly possess the following technical advantages:

[0029] 1. By introducing geometrical coordination constraint detection of dual hooks at the global planning layer and introducing hard constraints of synchronization error at the local optimization layer, precise coordination of dual trolleys in complex lifting operations is achieved, effectively preventing the risk of collision or tearing of load between the two trolleys and solving the problem of dual hook coordination.

[0030] 2. By adopting OSQP trajectory optimization that combines jerk minimization, the generated trajectory has extremely high smoothness, suppressing residual load sway from the source. Compared with traditional trapezoidal velocity planning, the swing angle amplitude is significantly reduced, thereby improving the stability of hoisting operations.

[0031] 3. By introducing a double pendulum dynamics model for verification, the planning system is made to consider not only "geometric reachability" but also "dynamic stability", which effectively avoids safety accidents caused by improper trajectory planning and enhances system safety.

[0032] 4. The parameterized job sequence generation mechanism based on component type enables the method to flexibly adapt to the hoisting needs of various components such as piers, cap beams, and beam segments, and has broad engineering application value, thus improving the adaptability of the method. Attached Figure Description

[0033] Figure 1 This is a schematic diagram of the trajectory planning method for collaborative lifting of a bridge erecting machine with dual hooks, considering spatiotemporal coupling constraints, as an embodiment of the present invention.

[0034] Figure 2 This is a simplified geometric model diagram of the bridge erecting machine and its working environment according to an embodiment of the present invention.

[0035] Figure 3 This is a schematic diagram of the sampling principle of BIT* global path planning considering double hook constraints in an embodiment of the present invention.

[0036] Figure 4 This is a schematic diagram of the trajectory smoothing process based on quadratic programming in an embodiment of the present invention.

[0037] Figure 5 This is a schematic diagram illustrating the mechanical relationship between the trolley, the cable, and the load in an embodiment of the present invention. Detailed Implementation

[0038] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0039] This invention provides a method for planning the collaborative lifting trajectory of a bridge erecting machine with dual hooks, considering spatiotemporal coupling constraints. Figure 1 As shown, it includes the following steps:

[0040] S1. Construct the task and environment model. Construct the kinematic model of the bridge erecting machine and the three-dimensional obstacle geometry model of the hoisting operation environment to form a multi-dimensional configuration space.

[0041] Furthermore, the kinematic model encompasses the kinematic relationships of the main trolley traveling mechanism, the front trolley traveling mechanism, the rear trolley traveling mechanism, the hoisting mechanism, and the secondary lifting device rotation mechanism. The front and rear trolleys are each equipped with independent hook systems to achieve high-precision coordinated lifting, while the main trolley traveling mechanism is primarily responsible for the lateral displacement of the bridge erecting machine's main body on the bridge. Simultaneously, the kinematic constraints of the bridge erecting machine are initialized, including the geometric dimensions, maximum speed, maximum acceleration, and jerk limits of each mechanism. When constructing the 3D obstacle geometry model, a 3D grid map or bounding box model of the working environment is established in real time based on point cloud data acquired by LiDAR or visual sensors, thereby identifying and marking the precise spatial location and 3D geometric dimensions of each obstacle in the environment.

[0042] In some embodiments, refer to Figure 2 The geometric model of the bridge erecting machine shown is used for kinematic parameter definition and modeling. The main structure of the bridge erecting machine includes the main beam, outriggers, and front and rear trolleys running on the main beam track. First, a global world coordinate system W is established, with the origin located at the ground projection point at one end of the main beam. The X-axis extends longitudinally along the main beam, the Y-axis extends laterally perpendicular to the main beam, and the Z-axis extends vertically upward. Based on mechanical limits, the working space range of the main beam is set, for example, X-axis -15 meters to 15 meters, Y-axis -10 meters to 15 meters, and Z-axis -10 meters to 15 meters. The physical motion capability of each mechanism is limited by motor power and mechanical strength. In this embodiment, the maximum speed of the main trolley is set to 2.0 meters per second, and the maximum acceleration is 0.5 meters per second squared; the maximum speed of the trolley is set to 1.5 meters per second, and the maximum acceleration is 0.3 meters per second squared; the maximum speed of the hoisting mechanism is set to 0.5 meters per second. These parameters constitute the boundary range for subsequent trajectory planning.

[0043] The front trolley and rear trolley share the load. To ensure operational safety, critical geometric constraints must be set. To prevent mechanical collisions between the two trolleys during high-speed operation, a minimum safe distance between the front and rear hooks must be established. For example, 5 meters. To ensure that the stress on the main beam structure is within the allowable range and to prevent structural deformation due to excessive moment, a maximum allowable spacing is set. For example, 25 meters. Obstacles in the environment, such as bridge piers and existing beams, are abstracted as axis-aligned bounding boxes (AABBs) or oriented bounding boxes (OBBs), and stored in the environment map for use by the planning algorithm.

[0044] S2. Generate a component-oriented hoisting operation sequence. Based on the type and attributes of the component to be hoisted, call the preset hoisting strategy library to generate a hoisting operation sequence. This hoisting operation sequence contains several sequentially executed action primitives. Each action primitive explicitly specifies the mechanism object participating in the action and the collaborative hoisting mode.

[0045] In response to the diversity of objects that bridge erecting machines can operate on, the system has a built-in expert knowledge base (i.e., a lifting strategy library) for different component types. Based on the input type of component to be lifted, the corresponding operation template can be automatically matched, and the complex lifting task can be decomposed into a series of standardized action primitive sequences.

[0046] Furthermore, the type attributes of components include at least three types: piers, cap beams, and beam segments.

[0047] For pier components, due to their typically high height and unstable center of gravity, the installation accuracy requirements are extremely high. The generated hoisting sequence is as follows: The main trolley is positioned, and moves to the beam-retrieving point, at which point the trolley and hoisting mechanism remain stationary; the front and rear trolleys simultaneously lift the pier with their hooks, activating the double-hook coordination marker, and the front and rear trolleys execute the synchronous double-hook lifting action, raising the pier to a safe height. During this process, the system monitors the load distribution of the two hooks in real time; the two trolleys move longitudinally synchronously, moving to above the installation position. During this process, the speed of the front and rear trolleys must be strictly kept consistent to prevent the pier from tilting or swaying in the air; the rear trolley is lowered independently, performing a single-action lowering action, coordinating with the micro-movements of the front trolley to adjust the pier from a horizontal to a vertical position; the rear trolley is unhooked, and the front trolley is lowered independently, continuing to lower until the pier is accurately seated on the base.

[0048] For the cap beam component, since the cap beam is usually placed horizontally and needs to be rotated in the air to adjust its orientation, the resulting hoisting operation sequence is as follows: positioning of the main trolley; single-hook lifting of the front trolley, lifting the cap beam's center of gravity position by a single point; longitudinal movement of the front trolley, moving the front trolley longitudinally to the obstacle avoidance area to avoid existing piers; rotation of the secondary lifting device by ninety degrees, during which the main trolley and the trolley are locked in place, and only the rotation mechanism moves; precise positioning and lowering to the top of the pier.

[0049] For bridge girder components, this is the most common working condition for bridge erecting machines, requiring high coordination between the front and rear trolleys. The resulting hoisting sequence is as follows: positioning the main trolley; the front trolley lifts the front end, moves to the front lifting point of the girder and lifts it; the rear trolley lifts the rear end, moves to the rear lifting point of the girder and lifts it; the two trolleys move synchronously longitudinally, and after ensuring the component is securely mounted, the front and rear trolleys enter the stage of synchronous longitudinal movement. This stage requires not only positional synchronization but also strict matching of speed and acceleration; the two trolleys lower the girder synchronously.

[0050] S3. Global path planning considering collaborative constraints. Based on the hoisting operation sequence, a collision-free geometric path is generated. The path describes the front / rear trolleys of the bridge erecting machine, the hooks, and the components being hoisted. A sampling-based global path planning algorithm is used to search in the multi-dimensional configuration space to generate an initial collision-free path connecting the starting state and the target state. During the search and sampling process, invalid sampling points that violate the physical distance constraints between the two trolleys or cause excessive cable inclination angles are eliminated through dual-hook collaborative constraint detection.

[0051] Furthermore, the global path planning algorithm employs an improved batch heuristic tree BIT* algorithm, such as... Figure 3 As shown, this algorithm combines the sampling efficiency of RRT with the heuristic search advantages of A, enabling it to quickly find a path approximating the optimum in a high-dimensional configuration space. First, an elliptic heuristic set is constructed, with the sampling range defined within a hyperellipsoid centered at the start and end points to improve search efficiency. Then, elliptic heuristic sampling is performed to obtain an initial collision-free path. During the sampling and expansion phase of the algorithm, not only is conventional obstacle collision detection (e.g., standard geometric interference checks) performed, but a specialized dual-hook collaborative constraint detection mechanism is also introduced. This mechanism calculates the positions of the preceding and following vehicles corresponding to the sampling points in real time, verifying whether they meet the minimum anti-collision distance and maximum span constraints. This directly eliminates physically inoperable sampling points, ensuring that the generated global path is geometrically feasible. Furthermore, the process of dual-hook collaborative constraint detection is as follows: based on the configuration state of the current sampling point, the three-dimensional positions of the front and rear trolleys in the world coordinate system are obtained through forward kinematics calculation; the Euclidean distance between the front and rear trolleys is calculated, and it is determined whether the Euclidean distance is within the closed interval formed by the preset minimum safe anti-collision distance and the maximum allowable distance of the main beam span; if it is within the interval and neither trolley exceeds its respective mechanical limit boundary, the sampling point is determined to be valid, otherwise it is discarded.

[0052] Specifically, to avoid blindly searching the entire configuration space, this invention introduces the elliptic heuristic set Informed Subset. For example... Figure 3 As shown by the dashed ellipse in the image, the sampling range is limited to the initial configuration. and target configuration Within the hyperellipsoid with focus , this elliptical domain defines a region that may contain better solutions, its boundary defined by the current optimal path length. Confirmed. Sampling point. The formula for generating it is:

[0053]

[0054] in, Center of the ellipse This is a rotation matrix used to rotate uniformly sampled points within a unit sphere. Mapped into an ellipse with the line connecting the start and end points as its axis; The ellipse is a diagonal matrix, which determines the lengths of its axes. As the optimization process progresses, the cost of the current optimal path... As it continues to decrease, the elliptic domain gradually shrinks as... Figure 3 As shown by the dashed line, this accelerates the algorithm's convergence to the theoretically optimal path.

[0055] After generating sampling points, in addition to conventional obstacle collision detection, this invention incorporates key collaborative constraint detection logic, such as... Figure 3 The invalid sampling points are marked in the image. This is a rejection sampling strategy. For each sampling point, representing a state of the system, the position of the front cart is first calculated using the forward kinematics equations. and the position of the rear car Then, calculate the Euclidean distance between the two workshops. :

[0056]

[0057] Next, determine whether the distance satisfies the condition. If the calculated distance If the distance is less than 5 meters, it is considered a potential collision risk; if If the distance exceeds 25 meters, it is considered to be beyond the load-bearing capacity of the main beam. In both cases, the sampling point is directly marked as invalid and removed from the search tree. This ensures that the planned path is always geometrically safe.

[0058] S4. Local Trajectory Optimization Based on Quadratic Programming. The initial collision-free path consists of a series of discrete waypoints with discontinuous velocity profiles. Direct execution would lead to frequent motor starts and stops. Therefore, the quadratic programming (QP) method is used to transform it into a smooth time-state trajectory, introducing a time dimension into the trajectory.

[0059] Using discrete path points obtained from global path planning as reference input, a quadratic programming model based on the OSQP solver is constructed. A decision variable vector in the entire time domain is defined, and quadratic objective functions for trajectory smoothness, tracking accuracy, and energy consumption are constructed. The kinematic differential equations are discretized into linear equality constraints, and the extreme values ​​of position, velocity, acceleration, and double hook synchronization error are transformed into linear inequality constraints to construct the quadratic programming model. The numerical solver is then called to solve the quadratic programming model, generating a continuous, smooth time-state trajectory that meets the synchronization requirements.

[0060] Furthermore, such as Figure 4 As shown, the construction and solution of the quadratic programming model includes:

[0061] S41. Define the decision variable vector across the entire time domain;

[0062] To describe the complete dynamics of the system, let the trajectory prediction time domain be... The time step is Define the decision variable vector Includes the future Position sequence at each time point velocity sequence and acceleration sequence : The dimension of this vector is It covers all the kinematic information needed for trajectory planning.

[0063] S42. Construct a quadratic objective function:

[0064] The objective function aims to achieve a balance between smoothness, tracking accuracy, and energy consumption.

[0065]

[0066] Among them, the acceleration term This is key to suppressing swaying. By minimizing the rate of change of acceleration, i.e., the jerk, a continuous acceleration curve can be generated, thus avoiding the impact of pulsed acceleration on the flexible cable system. The calculation formula is:

[0067]

[0068] Path tracking item This ensures that the optimized trajectory does not deviate from the collision-free reference path generated by global planning. .

[0069] Let the time domain of trajectory prediction be T, the discretization time step (sampling interval) be Δt, and the total number of steps be N = T / Δt. Representing the first Position, velocity, and acceleration at each moment.

[0070] velocity regularization term It is used to suppress excessive speed and reduce system energy consumption.

[0071] These items are integrated into a standard QP format: Where X is the decision variable, This is a Hessian matrix, with its diagonal blocks corresponding to the weight coefficients of the three terms mentioned above. f The target vector is a linear vector containing the product of the reference path coordinates and their corresponding weight coefficients; this is achieved by designing a matrix. sum vector To minimize jerk and path tracking errors.

[0072] S43, Inject hard constraints:

[0073] To ensure physical feasibility, strict linear constraints must be imposed. The speed and acceleration limits of each mechanism, as well as the synchronization error requirements between the two hooks, are transformed into linear constraints. Linear constraints include dynamic constraints, physical limit constraints, and cooperative synchronization constraints.

[0074] Dynamic constraints utilize Euler's difference equations to constrain adjacent states, such as... This is in the matrix It exhibits a specific sparse block structure.

[0075] Physical limit constraints restrict the speed and acceleration at each moment to within the allowable range of the motor, for example, the speed is between -2.0 and 2.0.

[0076] Cooperative synchronization constraints are applied to the double-hook synchronization phase, where the marked cooperative action primitives are defined in the matrix. A linear constraint row is added to the double hook position difference, ensuring that the deviation of the difference between the front and rear hook positions from the preset distance at any given time is limited to a closed interval formed by positive and negative synchronization tolerance thresholds; the constraint row is as follows:

[0077]

[0078] in, For preset spacing, , These are the positions of the front and rear hooks, respectively. The preset synchronization tolerance threshold, such as 0.1 meters, is used to constrain the absolute deviation between the difference in the positions of the two hooks and the preset distance at any given time to be within the allowable range.

[0079] S44. The constructed QP problem is fed into the numerical solver OSQP. This solver uses the Alternating Direction Multiplier Method (ADMM) algorithm for fast iterative solution, and finally outputs a smooth and synchronous time-state continuous trajectory.

[0080] S5. Verification of the dynamic stability of the double pendulum. A coupled double pendulum dynamic model is established, including the swing angle of the main hook, the swing angle of the auxiliary hook, and the yaw angle of the load. The system state equation is derived using the Lagrange equation, which considers the nonlinear coupling effect of the hook swing and the rotation of the load around the center of mass, as well as the Coriolis force caused by the change in cable length. The time state trajectory is input into the coupled double pendulum dynamic model for dynamic simulation. The maximum swing angle, synchronization error, and cable tension during the lifting operation are calculated using the numerical integration method. If the simulation results exceed the preset safety threshold, the current trajectory is determined to be unsafe. The weight parameters or kinematic parameters of the local optimization layer are automatically adjusted, and the process returns to step S4 for replanning until all stability requirements are met. Finally, an executable control command sequence is output.

[0081] Furthermore, the integration process of the dynamic simulation adopts the fourth-order Runge-Kutta method; the safety thresholds include the maximum permissible swing angle, the maximum permissible load tilt angle, and the minimum cable tension.

[0082] Specifically, to ensure that the generated trajectory does not cause dangerous load swings, this invention introduces a double pendulum dynamics model for verification. For example... Figure 5 As shown, the model details the mechanical relationship between the trolley, cable, and load.

[0083] First, Lagrange dynamics modeling is performed. This is based on the Lagrange equations. The state equations of the system are derived. For example... Figure 5 As shown, the system is subject to gravity. Cable tension and inertial force The function of the front hook. For the front hook, its swing angle... The second-order differential equation is:

[0084]

[0085] in: It is the acceleration due to gravity. For the length of the rope, Input acceleration for the car. This is the air drag coefficient. This term characterizes the coupling torque generated by the movement of the rear hook on the front hook due to the rigid connection of the load. This term makes the dynamic behavior of the double-hook system much more complex than that of the single-hook system.

[0086] Then, stability verification and backtracking are performed. For example, the smooth acceleration curve generated in step S4 is used. Substituting these values ​​into the above equation and performing numerical integration yields the swing angle response curve. Check the maximum swing angle throughout the entire process. ,like An acceleration greater than 5 degrees indicates that while the trajectory is smooth, it is still too aggressive for the current rope length and may cause a safety hazard. If the verification fails, a backtracking mechanism is automatically triggered; specific adjustment strategies include reducing the maximum allowable acceleration in the local optimization layer. Or increase the jerk weights in the Hessian matrix. After adjusting the parameters, return to step S4 to re-optimize the trajectory. This closed-loop mechanism ensures that the final output command sequence is absolutely safe in terms of dynamics.

[0087] S6. Layered Collision Detection. For the time-state trajectory that meets the safety threshold in step S5, further layered collision detection is performed to ensure that the "swept volume" generated by the load due to inertia will not collide with obstacles during actual hoisting. To improve collision detection efficiency, a layered collision detection method from coarse to fine is adopted, including:

[0088] First, a rapid coarse check is performed. For the time-state trajectory, an axis-aligned bounding box (AABB) is used for coarse checking. The system encloses the main beam, end beam, trolley, lifting device, and load in a minimum cuboid parallel to their coordinate axes. If the AABBs of two objects do not overlap, the coarse check is considered successful; if the coarse check fails, the process returns directly to step S3. If the coarse check passes, a precise check is performed using an oriented bounding box (OBB) and the separating axis theorem (SAT). The overlap of the projected regions is used to determine if a collision has occurred; if no collision occurs, the process ends; if a collision occurs, the process returns to step S3.

[0089] Specifically, the reason for the detection failure is usually that although the static path did not collide, the load swing amplitude was too large, causing the "dynamic envelope space" it swept to touch the obstacle. This means that the current "path corridor" is too narrow. In order to plan a new path, parameters must be adjusted to "guide" or "force" S3 to be farther away from the obstacle. Specifically, the coordinate area where the collision occurred can be marked as a "high cost" or "no-go zone" in the configuration space, and the system will automatically avoid the "bumped" area and find different S3 paths.

[0090] This invention also provides a bridge erecting machine dual-hook collaborative lifting trajectory planning system considering spatiotemporal coupling constraints, wherein a processor is used to execute the aforementioned bridge erecting machine dual-hook collaborative lifting trajectory planning method considering spatiotemporal coupling constraints. The system runs on the onboard high-performance industrial control computer of the bridge erecting machine, and its core logic architecture is designed as a closed-loop feedback control mode. The system first receives externally input work task instructions, and after a series of planning and verification steps, finally outputs servo control instructions that can be directly executed by the underlying PLC.

[0091] In summary, this invention realizes a fully automated planning method from task decision-making to low-level control. Specifically, a parameterized operation sequence generation mechanism based on component characteristics achieves standard decoupling of complex hoisting processes; the improved BIT* global planning algorithm quickly searches for collision-free safe channels that satisfy the geometric cooperative constraints of the double hooks in the multi-dimensional configuration space; the local trajectory optimization strategy based on quadratic programming (OSQP) eliminates the impact of sudden velocity changes on the mechanical structure from the kinematic source by minimizing the jerk objective function, and uses linear inequality hard constraints to forcibly ensure the synchronous motion accuracy of the two trolleys during the dynamic process; finally, the double pendulum dynamics verification module adds a safety barrier to the system, effectively avoiding the risk of dynamic instability caused by improper parameter settings. This method, while ensuring obstacle avoidance safety, can control the synchronization error of the double hooks to the centimeter level, and the load swing amplitude is significantly reduced compared to traditional methods, effectively improving the efficiency and safety of bridge erecting machine hoisting operations.

[0092] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements 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 method for planning the collaborative lifting trajectory of a bridge erecting machine with two hooks, considering spatiotemporal coupling constraints, characterized in that, Includes the following steps: S1. Construct the kinematic model of the bridge erecting machine and the three-dimensional obstacle geometry model of the hoisting operation environment to form a multi-dimensional configuration space; S2. Generate a hoisting operation sequence based on the type and attributes of the component to be hoisted. This hoisting operation sequence contains several sequentially executed action primitives. S3. Based on the hoisting operation sequence, a sampling-based global path planning algorithm is used to search and sample in the multi-dimensional configuration space to generate an initial collision-free path connecting the starting state and the target state. During the search and sampling process, invalid sampling points that violate the physical distance constraint between the two trolleys or cause excessive cable inclination angle are eliminated through dual hook collaborative constraint detection. The dual-hook collaborative constraint detection includes: obtaining the three-dimensional position of the two trolleys equipped with dual hooks in the world coordinate system through forward kinematics calculation based on the configuration state of the current sampling point; calculating the Euclidean distance between the two trolleys and determining whether the Euclidean distance is within the closed interval formed by the preset minimum safe anti-collision distance and the maximum allowable distance of the main beam span; if it is within the closed interval and neither trolley exceeds its respective mechanical limit boundary, the sampling point is determined to be valid; otherwise, it is discarded. S4. Based on the initial collision-free path, with position sequence, velocity sequence and acceleration sequence as decision variables, and with the comprehensive optimization of trajectory smoothness, tracking accuracy and energy consumption as the objective function, and with the extreme values ​​of position, velocity, and acceleration and the synchronization error of the two hooks transformed into linear constraints, a quadratic programming model is constructed and solved to obtain the time state trajectory. The extreme values ​​of position, velocity, and acceleration, as well as the synchronization error of the two hooks, are transformed into linear constraints, expressed as follows: Where L is the lower bound vector and U is the upper bound vector; X These are decision variables, which include position sequences, velocity sequences, and acceleration sequences; A The constraint matrix contains dynamic constraints, physical limit constraints, and cooperative synchronization constraints. Dynamic constraints are discretized Newtonian kinematic equations used to constrain the state evolution relationship between adjacent time steps. Physical limit constraints limit the position, velocity, and acceleration extreme values ​​of the mechanism's physical performance. Cooperative synchronization constraints are represented as a linear combination of the positional deviations of the two hooks, used to constrain the synchronization error at any given time. Specifically: , For preset spacing, , These are the positions of the front and rear hooks, respectively. This is the preset synchronization tolerance threshold.

2. The method for planning the collaborative lifting trajectory of a bridge erecting machine with dual hooks, considering spatiotemporal coupling constraints, as described in claim 1, is characterized in that... Step S3: The sampling-based global path planning algorithm uses the batch heuristic tree (BIT) algorithm. Specifically, it first searches in the multidimensional configuration space to obtain an elliptic heuristic set, and then performs elliptic heuristic sampling to obtain an initial collision-free path.

3. The method for planning the collaborative lifting trajectory of a bridge erecting machine with dual hooks, considering spatiotemporal coupling constraints, as described in claim 1, is characterized in that... Step S4, with the objective function being the optimal combination of trajectory smoothness, tracking accuracy, and energy consumption, is expressed as: in, The acceleration term characterizes the smoothness of the trajectory; For path tracking, it represents the trajectory tracking accuracy; The velocity regularization term characterizes the system's energy consumption. The above objective function J Integrate into a standard secondary programming form: in, This is a Hessian matrix, with its diagonal blocks corresponding to... , , The weighting coefficients of the three items; f It is a linear target vector.

4. The method for planning the collaborative lifting trajectory of a bridge erecting machine with dual hooks, considering spatiotemporal coupling constraints, as described in claim 1, is characterized in that... It also includes the following steps: S5. Perform dynamic simulation based on the time-state trajectory to obtain the maximum swing angle, synchronization error, and cable tension during the hoisting operation. If any of the maximum swing angle, synchronization error, or cable tension exceeds the preset safety threshold, adjust the weight coefficients or kinematic parameters in the Hessian matrix and return to step S4 to replan the time-state trajectory until the safety threshold is met. The kinematic parameters include geometric dimensions, maximum velocity, maximum acceleration, and maximum jerk.

5. The method for planning the collaborative lifting trajectory of a bridge erecting machine with dual hooks, considering spatiotemporal coupling constraints, as described in claim 4, is characterized in that... Step S5: Use the Lagrange equation to derive the system state equation and establish a coupled double pendulum dynamic model; the state equation considers the nonlinear coupling effect of the hook swing and the load rotation around the center of mass, as well as the Coriolis force caused by the change in cable length. The time-state trajectory is input into the coupled double pendulum dynamic model for dynamic simulation. The integration process of the dynamic simulation adopts the fourth-order Runge-Kutta method.

6. The method for planning the collaborative lifting trajectory of a bridge erecting machine with dual hooks, considering spatiotemporal coupling constraints as described in claim 4, is characterized in that... It also includes the following steps: S6. For the time-state trajectory that meets the safety threshold in step S5, further perform layered collision detection, including: for the time-state trajectory, use axis-aligned bounding box (AABB) for coarse detection; if the coarse detection fails, return directly to step S3; if the coarse detection passes, use oriented bounding box (OBB) and separating axis theorem (SAT) for fine detection, and determine whether a collision occurs by whether the projected intervals overlap; if no collision occurs, the process ends; if a collision occurs, return to step S3.

7. The method for planning the collaborative lifting trajectory of a bridge erecting machine with dual hooks, considering spatiotemporal coupling constraints, as described in any one of claims 1-6, is characterized in that... Step S2: The types and attributes of the components to be hoisted include piers, cap beams, and beam segments. For pier components, the hoisting sequence is as follows: positioning the trolley, simultaneous lifting of the front and rear trolleys with double hooks, simultaneous longitudinal movement of both trolleys, independent lowering of the rear trolley, unhooking of the rear trolley, and independent lowering of the front trolley. For cap beam components, the hoisting sequence is as follows: positioning the trolley, lifting of the front trolley with a single hook, longitudinal movement of the front trolley, 90-degree rotation of the secondary lifting device, and precise positioning and lowering. For beam segment components, the hoisting sequence is as follows: positioning the trolley, lifting the front end of the front trolley, lifting the rear end of the rear trolley, simultaneous longitudinal movement of both trolleys, and simultaneous lowering of both trolleys.

8. A bridge erecting machine dual-hook collaborative lifting trajectory planning system considering spatiotemporal coupling constraints, characterized in that, Includes a processor for executing the bridge erecting machine dual-hook collaborative hoisting trajectory planning method considering spatiotemporal coupling constraints as described in any one of claims 1-7.

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