Bridge construction tower crane cooperative anti-collision early warning control method

Abstract

The present application relates to a kind of bridge construction tower crane collaborative anti-collision early warning control method, specifically relates to the field of tower crane safety control, by edge computing node to the sliding window filtering and extended Kalman fusion of multi-source sensor data, obtain the accurate complete state vector of each tower crane;On this basis, the multi-machine kinematics model considering the swing of the hoist is established, the minimum Euclidean distance change trend is predicted using Taylor expansion, the accurate conflict early warning is realized;Conflict pair set adopts model predictive control to solve optimal control sequence online and issue the first control quantity, actively adjust tower crane movement to avoid collision;While pre-training deep reinforcement learning strategy network, when early warning triggers, action instruction is preferentially inquired, only when safety margin is up to standard, it is directly executed, otherwise, it is returned to model predictive control, both millisecond level response speed and high reliability decision, comprehensively improve the safety, real-time performance and robustness of bridge construction multi-tower crane collaborative operation.

Description

Technical Field

[0001] This invention relates to the field of tower crane safety control, and more specifically, to a collaborative anti-collision early warning control method for tower cranes used in bridge construction. Background Technology

[0002] With the increasing scale of long-span bridge construction, such as cross-sea bridges and mountain canyon bridges, multiple tower cranes are often required to work together in the same limited space for the main piers, pylons, and beam segment hoisting areas. These tower cranes typically undertake the vertical and horizontal transportation of various components such as steel cages, formwork, concrete hoppers, and steel box girder segments. In actual construction, external environmental factors are extremely complex: instantaneous wind speeds in coastal areas can reach level six or higher, mountain canyons have significant turbulence effects, and steel structure deformation caused by temperature differences caused by sunlight can reach the centimeter level. Internal factors include independent operation of each tower crane, overlapping boom slewing radii, uncertainty of the swaying of the hoisted object due to wind, and asynchronous actions caused by communication delays between different work groups. When the movement trajectories of two or more tower cranes are about to intersect, without a global coordination mechanism, serious accidents such as boom collisions, wire rope entanglement, or even overall overturning can easily occur, threatening the lives of on-site workers and causing huge economic losses and project delays.

[0003] However, existing tower crane anti-collision systems generally use limit switches or independent radar alarm devices, which can only trigger audible and visual alarms when the boom approaches a preset boundary. Essentially, these are passive monitoring methods and lack active avoidance control capabilities. Key status information such as the rotation angle, amplitude, lifting capacity, and operating speed of each tower crane is isolated, lacking a unified real-time data acquisition and centralized control architecture, making information sharing and collaborative decision-making among multiple cranes impossible. Furthermore, traditional solutions do not fully consider dynamic environmental changes, such as sudden wind speed changes, the movement of temporary obstacles, or sudden changes in the operating direction of adjacent tower cranes, resulting in significant lag or false alarms in early warnings. While a few products on the market claim to have anti-collision functions, most are based on fixed area delineation or simple distance threshold judgments, unable to adapt to the complex and ever-changing motion trajectories in multi-crane collaborative operations, and even less able to solve the multi-objective optimization problem of minimizing total operation time and maximizing safe distance online. Therefore, there is an urgent need for an intelligent control method that can monitor the motion status of multiple tower cranes in real time, predict potential conflicts, and proactively issue deceleration, stop, or detour commands to fundamentally improve the safety and efficiency of high-altitude bridge construction operations. Summary of the Invention

[0004] This invention addresses the technical problems existing in the prior art by providing a collaborative anti-collision early warning control method for bridge construction tower cranes, thereby resolving the issues raised in the background section.

[0005] The technical solution of this invention to solve the above-mentioned technical problems is as follows: specifically, it includes the following steps: Step S1: Collect real-time motion status data of multiple tower cranes. The real-time motion status data includes the spatial position coordinates, slewing angle, luffing amplitude, hook height, weight of the hoisted object, and vibration acceleration at the end of the boom of each tower crane. After sliding window filtering and outlier removal through edge computing nodes, the filtered real-time motion status data is fused using an extended Kalman filter to obtain the complete state vector of each tower crane at time t. Step S2: Based on the complete state vector obtained in step S1, establish a multi-machine kinematic model and introduce a dynamic correction model for the swing of the suspended object. Calculate the minimum Euclidean distance between the boom and the suspended object between any two tower cranes. Use Taylor expansion to predict the trend of the change of the minimum Euclidean distance in the future. When the predicted minimum Euclidean distance in the future is less than the safety threshold and the prediction time is less than the warning time window, trigger a conflict warning and output the conflict pair set and the complete state vector obtained in step S1. Step S3: Based on the set of conflict pairs and the complete state vector output in step S2, construct a model predictive control optimization problem. Using the weighted sum of the safety distance penalty term, the operation efficiency loss term, and the control energy term as the cost function, solve the optimal control sequence under the constraints of the physical limits of each tower crane and the safe range of the swing of the load. Then, send the first control quantity in the optimal control sequence to each tower crane for execution. Step S4: Pre-train the deep reinforcement learning policy network offline. When the conflict warning is triggered in step S2, the action instructions output by the deep reinforcement learning policy network are queried first. If the safety margin corresponding to the action instruction is higher than the threshold, it is executed directly. Otherwise, it is back to the model prediction and control solution process in step S3. In a preferred embodiment, in step S1, the edge computing node collects real-time motion state data from the UWB positioning module, incremental encoder, triaxial accelerometer and tension sensor of each tower crane at a fixed sampling frequency of 50 Hz. For each tower crane, the real-time motion state data constitutes an eight-dimensional vector, which includes three components of spatial position coordinates, rotation angle, amplitude, hook height, weight of the hoisted object and vibration acceleration at the end of the boom.

[0006] In a preferred embodiment, the specific operation of sliding window filtering and outlier removal through edge computing nodes is as follows: The edge computing node first uses an adaptive median Gaussian mixture filter to preprocess each dimension of the eight-dimensional vector. The adaptive median Gaussian mixture filter calculates the weighted median within a sliding window with a length of ten sampling points. The weight of the weighted median is determined by the Mahalanobis distance between the current sampling point and each sampling point in the sliding window. After weighted median filtering is completed, the edge computing nodes perform residual checks on the weighted median filtered real-time motion state data based on kernel density estimation to remove residual abrupt changes. The residual is defined as the difference between the weighted median filtered real-time motion state data at the current time and the weighted median filtered real-time motion state data at the previous time. If the absolute value of the residual is greater than three times the interquartile range of the residual sequence, the current sampling point is marked as an outlier and replaced with the corresponding value in the weighted median filtered real-time motion state data at the previous time to obtain the filtered real-time motion state data.

[0007] In a preferred embodiment, the process of fusing the filtered real-time motion state data using an extended Kalman filter specifically involves: The state vector of the extended Kalman filter is defined as a twelve-dimensional vector. The twelve-dimensional vector includes three spatial position coordinate components of the boom end of each tower crane in the world coordinate system, three velocity components, slewing angle, slewing angular velocity, luffing amplitude, luffing speed, hook height, and lifting speed. The three spatial position coordinate components are obtained by transforming the slewing angle, luffing amplitude, and hook height through a forward kinematics model. The prediction model of the extended Kalman filter adopts the assumption of constant velocity motion, and the observation model directly maps the spatial position coordinates output by the UWB positioning module, the rotation angle and amplitude output by the incremental encoder, and the swing angle information obtained by the integration of the triaxial accelerometer. The observation noise covariance matrix of the extended Kalman filter is updated using an adaptive online estimation method. A sliding window with a length of twenty sampling points is constructed using the innovation sequence. The sliding window covariance of the innovation sequence within the sliding window is calculated, and a forgetting factor of 0.85 is introduced to weight the observation noise covariance of the previous time step. The calculated result of the sliding window covariance is then weighted and summed with the forgotten covariance of the previous time step, thereby updating the observation noise covariance matrix in real time. This allows the extended Kalman filter to automatically adapt to the time-varying characteristics of sensor noise and finally output the complete state vector of each tower crane at time t.

[0008] In a preferred embodiment, the specific operation of establishing the multi-machine kinematic model and introducing the dynamic correction model for the swing of the suspended object in step S2 is as follows: First, a multi-machine kinematic model is established. For each tower crane, based on the slewing angle, luffing amplitude, and hook height in the complete state vector output in step S1, the three spatial position coordinate components of the boom end in the world coordinate system are obtained through the forward kinematic model transformation. The input of the multi-machine kinematic model is the complete state vector output in step S1, and the output is the three spatial position coordinate components of the boom end in the world coordinate system. A dynamic correction model for the swing of the suspended object is introduced. The input of the dynamic correction model for the swing of the suspended object is the data of the three-axis accelerometer in the complete state vector output in step S1, and the output is the actual center position of the suspended object. In the dynamic correction model for the swing of the suspended object, the suspended object is regarded as a pendulum suspended at the end of the boom. The pendulum length is the length of the wire rope, and the pendulum angle is described by the pendulum angle obtained by the integration of the three-axis accelerometer. The specific calculation process for the actual center position of the suspended load is as follows: The actual center position of the suspended load is equal to the three spatial coordinate components of the end of the boom in the world coordinate system plus an offset vector. The horizontal component of the offset vector is equal to the length of the wire rope multiplied by the absolute value of the product of the sine and cosine of the swing angle, and then divided by the cosine of the swing angle. The vertical component of the offset vector is equal to the length of the wire rope multiplied by the product of the square of the sine of the swing angle and the square root of the cosine of the swing angle. Then, the boom of each tower crane is abstracted as a cylinder with a first preset radius, the suspended object is abstracted as a sphere with a second preset radius, and the wire rope is abstracted as a thin cylinder with a third preset radius. The boom, suspended object and wire rope are combined into a spatial capsule. The central axis of the spatial capsule extends along the boom direction from the three spatial position coordinate components of the boom end in the world coordinate system to the root of the boom. The outer surface of the spatial capsule wraps around the center of the suspended object sphere. The minimum Euclidean distance between any two tower cranes is obtained by solving for the closest point pair between the two spatial capsules.

[0009] In a preferred embodiment, the specific operation of using Taylor expansion to predict the changing trend of the minimum Euclidean distance over future time is as follows: First, calculate the first and second derivatives of the minimum Euclidean distance with respect to time at the current moment. The first derivative is calculated using the chain rule by combining the speed, angular velocity, and swing angle change rate of each tower crane with the Jacobian matrix of the minimum Euclidean distance with respect to each state component. The second derivative is calculated using the chain rule by combining the acceleration, angular acceleration, and swing angle acceleration of each tower crane with the Hessian matrix of the minimum Euclidean distance with respect to each state component. Then, the second-order Taylor expansion formula is used to predict the predicted minimum Euclidean distance at any future time. The predicted minimum Euclidean distance is equal to the minimum Euclidean distance at the current time, plus the product of the prediction time and the first derivative, plus the product of half the square of the prediction time and the second derivative, thus obtaining the predicted minimum Euclidean distance. Set the safety threshold to two meters and the warning time window to three seconds. By setting the first derivative of the predicted minimum Euclidean distance with respect to the prediction time to zero, find the prediction time point that minimizes the predicted minimum Euclidean distance. If the calculated prediction time point falls within the interval from zero to the warning time window, and the predicted minimum Euclidean distance at the prediction time point is less than the safety threshold, then a conflict warning is triggered. After triggering the conflict warning, output the conflict pair set, which contains the numbers of all tower crane pairs that meet the warning conditions. At the same time, output the complete state vector obtained in step S1 for use in step S3.

[0010] In a preferred embodiment, the specific operation of constructing the model predictive control optimization problem in step S3 is as follows: First, extract the numbers of all tower crane pairs with conflict risk from the conflict pair set output in step S2. Only these tower cranes are included in this optimization, while the control variables of the remaining tower cranes remain unchanged. Then, establish a discrete-time state equation to describe the state evolution of the tower cranes as a prediction model. For each tower crane included in the optimization, based on the kinematic parameters in the complete state vector obtained in step S1, construct a discrete-time state equation. The state vector of the discrete-time state equation is the twelve-dimensional complete state vector output in step S1. The control variables include three components: the slewing angular velocity of the tower crane's slewing mechanism, the luffing speed of the luffing mechanism, and the lifting speed of the hoisting mechanism. The cost function consists of a weighted sum of three parts: a safety distance penalty term, an operational efficiency loss term, and a control energy term. The calculation process for the safety distance penalty term is as follows: In the prediction time domain, traverse each prediction step. For each tower crane pair in the conflict pair set, calculate an exponential function with the natural constant e as the base and the ratio of the predicted minimum Euclidean distance in step S2 to the safety threshold as the exponent. Multiply the function value by the first weighting coefficient, and then add all these products together. The calculation process for the work efficiency loss term is as follows: In the prediction time domain, traverse each tower crane included in the optimization, calculate the square of the Euclidean distance between the current position of the tower crane and the original planned end position, multiply it by the second weighting coefficient, and then add the results of all tower cranes. The calculation process for the control energy term is as follows: In the prediction time domain, iterate through each tower crane included in the optimization and each of its control variables, calculate the square of the control variable, multiply it by the third weighting coefficient, and then add all these squared values ​​together. Model predictive control optimization problems also include constraints, which are divided into two categories: the first category is physical limit constraints; the second category is safety constraints for the swing of the suspended load.

[0011] In a preferred embodiment, the specific process of solving the optimal control sequence is as follows: The global optimization problem is decomposed into local subproblems and global coordination subproblems using the alternating direction multiplier method, which are solved iteratively. The local subproblems are solved independently for each tower crane included in the optimization. The objective function of the local subproblem is the control energy term plus an augmented Lagrange penalty term. This augmented Lagrange penalty term includes the square of the difference between the current control quantity and the global coordination variable, and the dot product of the Lagrange multiplier with the difference between the current control quantity and the global coordination variable. The local subproblems are solved directly using analytical formulas to obtain the local optimal control quantity for each tower crane. The global coordination subproblem aggregates the local optimal control quantities of all tower cranes. The components are grouped together, and the objective function is the sum of the safety distance penalty term and the squared difference between the local optimal control quantity and the global coordination variable of each tower crane. The gradient projection method is used to iteratively solve the problem to obtain the updated global coordination variable. Then, the Lagrange multipliers are updated. The Lagrange multipliers are equal to the Lagrange multipliers of the previous time step plus the penalty parameter multiplied by the difference between the current local optimal control quantity and the global coordination variable. The three steps of solving the local subproblem, solving the global coordination subproblem, and updating the Lagrange multipliers are repeated until the rate of change of the cost function between two adjacent iterations is less than one-thousandth or the preset maximum number of iterations is reached to obtain the optimal control sequence. After iterative convergence, the optimal control sequence is output, which consists of the control quantities of each tower crane from the first control step to the fifth control step. Only the control quantity of the first control step in the optimal control sequence is sent to the programmable logic controller of each tower crane via industrial Ethernet at a period of 20 milliseconds to drive the actuator to adjust the movement. The remaining control sequence is used as a warm start for optimization in the next moment to accelerate convergence.

[0012] In a preferred embodiment, the specific operation of pre-training the deep reinforcement learning policy network offline in step S4 is as follows: Construct the input observation vector of the deep reinforcement learning policy network. The input observation vector is encoded by the conflict pair set and the complete state vector output in step S2. Training is performed using a dual-delay deep deterministic policy gradient method, which alternately updates the policy network and the value network using two sets of parameterized networks. The reward function during training consists of a weighted sum of three parts: The first part is the collision penalty, which is calculated as follows: Set a safety threshold. For each pair of tower cranes in the conflict pair set, check their predicted minimum Euclidean distance in the future prediction time window. Take the minimum predicted minimum Euclidean distance among all conflicting tower crane pairs. If the minimum value is less than the safety threshold, a fixed large negative reward is given, which is set to -100. If the predicted minimum Euclidean distance of all conflicting tower crane pairs is greater than or equal to the safety threshold, the collision penalty is zero. The second part is the control energy penalty term, which is equal to the sum of the squares of the three control components corresponding to the action command: angular velocity, amplitude velocity, and acceleration / deceleration velocity, multiplied by the first reward weight coefficient, and preceded by a negative sign; The third part is the schedule deviation penalty, which is equal to the absolute value of the schedule deviation caused by the execution of the action instructions multiplied by the second reward weighting coefficient. During training, the conditions for determining the failure of model prediction control solution are: the number of iterations of the alternating direction multiplier method in step S3 reaches the preset maximum number of iterations but still does not meet the convergence condition, or there are still conflicts after the projection of the global coordination variables, and the minimum Euclidean distance of the tower crane is lower than the safety threshold; any condition that is met is marked as a solution failure record, and each record is a data unit that stores the input observation vector, action command, reward value and the next input observation vector during a state transition process; During training, adversarial experience replay is employed. This replay uses the memory unit that stores historical state transition records—the experience storage area—as the storage unit. The specific calculation process for updating the sampling weights is as follows: First, obtain the temperature coefficient, which is set to two. Next, obtain the failure indicator function. The failure indicator function takes the following value: it takes the value of one when the model predictive control solution fails, and takes the value of zero when it does not fail. Then, the product of the temperature coefficient of the natural constant e and the failure indicator function is raised to the power of the result to obtain the power calculation result of the current record; then, the sum of the power calculation results of each record in the memory unit is calculated; finally, the power calculation result of the current record is divided by the sum of the power calculation results of all records to obtain the sampling weight of the current record.

[0013] In a preferred embodiment, the specific operation of querying the action instructions output by the deep reinforcement learning policy network and calculating the safety margin is as follows: When step S2 triggers a conflict warning, the current input observation vector is input into the trained deep reinforcement learning policy network, and the action command is obtained through one forward propagation. Then, the Monte Carlo dropout method was used to perform fifty random forward propagations on the deep reinforcement learning policy network. Each forward propagation enabled the dropout layer, and the dropout rate was set to one-tenth, generating a set containing fifty action instruction samples. For each action command sample, the minimum Euclidean distance prediction process based on Taylor expansion established in step S2 is used to simulate the minimum Euclidean distance trajectory within the next two seconds after the sample is executed, resulting in multiple minimum distance sequences; in each minimum distance sequence, the minimum distance value within the next three-second warning time window is extracted to form a set of minimum distances. The safety margin is defined as the fifth percentile of the minimum distance set, and the safety margin threshold is set to 1.5 meters. If the safety margin is greater than 1.5 meters, the action command is deemed safe enough, and the action command is directly converted into the corresponding control quantity and sent to each tower crane for execution. If the safety margin is no more than 1.5 meters, then the process reverts to the model predictive control solution in step S3. The reverting operation is as follows: the complete state vector at the current moment is passed into step S3 as input, and the action command is used as the initial guess value of the global coordination variable defined in step S3. Then, step S3 directly starts the alternating direction multiplier method iteration based on the complete state vector and the initial guess value of the global coordination variable. Finally, the first control quantity in the optimal control sequence is still issued to each tower crane for execution.

[0014] The beneficial effects of this invention are as follows: By using edge computing nodes to perform sliding window filtering and extended Kalman fusion on multi-source sensor data, accurate and complete state vectors of each tower crane are obtained; on this basis, a multi-machine kinematic model considering the swing of the suspended load is established, and Taylor expansion is used to predict the trend of minimum Euclidean distance change, thereby achieving accurate collision early warning; for the set of collision pairs, model predictive control is used to solve the optimal control sequence online and issue the first control quantity, actively adjusting the movement of the tower cranes to avoid collisions; at the same time, a deep reinforcement learning policy network is pre-trained, which prioritizes querying action commands when an early warning is triggered, and executes them directly only when the safety margin meets the standard, otherwise it falls back to model predictive control, thus taking into account both millisecond-level response speed and high-reliability decision-making, and comprehensively improving the safety, real-time performance and robustness of multi-tower crane collaborative operation in bridge construction. Attached Figure Description

[0015] Figure 1 This is a flowchart of the method of the present invention. Detailed Implementation

[0016] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0017] In the description of this application, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of the stated features. In the description of this application, "multiple" means two or more, unless otherwise explicitly specified.

[0018] In the description of this application, the term "for example" is used to mean "used as an example, illustration, or description." Any embodiment described as "for example" in this application is not necessarily to be construed as being more preferred or advantageous than other embodiments. The following description is provided to enable any person skilled in the art to make and use the invention. Details are set forth in the following description for purposes of explanation. It should be understood that those skilled in the art will recognize that the invention can be made without using these specific details. In other instances, well-known structures and processes will not be described in detail to avoid obscuring the description of the invention with unnecessary detail. Therefore, the invention is not intended to be limited to the embodiments shown, but is consistent with the broadest scope of the principles and features disclosed in this application. Example

[0019] This embodiment provides, for example Figure 1 The method for collaborative collision avoidance and early warning control of bridge construction tower cranes, as shown, specifically includes the following steps: Step S1: Collect real-time motion status data of multiple tower cranes. The real-time motion status data includes the spatial position coordinates, slewing angle, luffing amplitude, hook height, weight of the hoisted object, and vibration acceleration at the end of the boom of each tower crane. After sliding window filtering and outlier removal through edge computing nodes, the filtered real-time motion status data is fused using an extended Kalman filter to obtain the complete state vector of each tower crane at time t. Step S2: Based on the complete state vector obtained in step S1, establish a multi-machine kinematic model and introduce a dynamic correction model for the swing of the suspended object. Calculate the minimum Euclidean distance between the boom and the suspended object between any two tower cranes. Use Taylor expansion to predict the trend of the change of the minimum Euclidean distance in the future. When the predicted minimum Euclidean distance in the future is less than the safety threshold and the prediction time is less than the warning time window, trigger a conflict warning and output the conflict pair set and the complete state vector obtained in step S1. Step S3: Based on the set of conflict pairs and the complete state vector output in step S2, construct a model predictive control optimization problem. Using the weighted sum of the safety distance penalty term, the operation efficiency loss term, and the control energy term as the cost function, solve the optimal control sequence under the constraints of the physical limits of each tower crane and the safe range of the swing of the load. Then, send the first control quantity in the optimal control sequence to each tower crane for execution. Step S4: Pre-train the deep reinforcement learning policy network offline. When the conflict warning is triggered in step S2, the action command output by the deep reinforcement learning policy network is queried first. If the safety margin corresponding to the action command is higher than the threshold, it is executed directly. Otherwise, it falls back to the model prediction control solution process in step S3 to achieve a hybrid decision with millisecond-level response and high reliability.

[0020] In this embodiment, it is specifically necessary to explain that in step S1, the edge computing node collects real-time motion status data from the UWB positioning module, incremental encoder, triaxial accelerometer, and tension sensor of each tower crane at a fixed sampling frequency of 50 Hz. For each tower crane, the real-time motion status data constitutes an eight-dimensional vector, which includes three components of spatial position coordinates, rotation angle, amplitude, hook height, load weight, and boom end vibration acceleration. The fixed sampling frequency of 50 Hz is determined according to the maximum movement speed of the tower crane and the safety warning response time requirements to ensure that the movement displacement between adjacent sampling points does not exceed one-tenth of the safety threshold. The data of each dimension in the eight-dimensional vector are stored in floating-point form. The units of the three components of spatial position coordinates are meters, the unit of rotation angle is radians, the unit of amplitude and hook height is meters, the unit of load weight is kilograms, and the unit of boom end vibration acceleration is meters per square second. The specific operations for sliding window filtering and outlier removal using edge computing nodes are as follows: The edge computing node first preprocesses each dimension of the eight-dimensional vector using an adaptive median Gaussian mixture filter (ADC). The ADC calculates the weighted median within a sliding window of ten sampling points. The weights of the weighted median are determined by the Mahalanobis distance between the current sampling point and all sampling points within the sliding window. The weights of the weighted median are constructed as follows: Using the arithmetic mean of the real-time motion state data within the sliding window as the central reference point and the scaling factor of the median absolute deviation as the discrete metric, an exponential decay function is constructed. This ensures that the weight allocation of each sampling point within the sliding window decreases exponentially as the square of the difference between the sampling point value and the central reference point value increases, thus assigning a smaller weight contribution to sampling points far from the central reference point and automatically suppressing outliers. The Mahalanobis distance is calculated based on the covariance matrix between the sampling points within the sliding window, which is estimated from the sample covariance of all sampling points within the window. The scaling factor of the median absolute deviation is set to 1.4826, a value that ensures statistical consistency of the weight function under Gaussian noise. The base of the exponential decay function is the natural constant e, and the exponent is the square of the difference between the negative sampling point value and the central reference point value divided by twice the square of the median absolute deviation, thus ensuring that the weight values ​​are between 0 and 1. After weighted median filtering, the edge computing nodes perform residual checks on the weighted median-filtered real-time motion state data based on kernel density estimation to remove residual abrupt changes. The residual is defined as the difference between the weighted median-filtered real-time motion state data at the current time and the weighted median-filtered real-time motion state data at the previous time. If the absolute value of the residual is greater than three times the interquartile range of the residual sequence, the current sampling point is marked as an outlier and replaced with the corresponding value in the weighted median-filtered real-time motion state data at the previous time, thus obtaining the filtered real-time motion state data. The data includes motion state data; the residual sequence consists of residual values ​​from thirty consecutive time points. The interquartile range is calculated by sorting the residual sequence in ascending order and taking the difference between the upper and lower quartiles; the three-fold threshold is set based on engineering experience and can achieve a balance between eliminating abrupt changes and preserving true motion changes; the residual test based on kernel density estimation refers to estimating the probability density of the residual sequence using a Gaussian kernel function. When the residual appears in a region with a probability density below 5%, it is also considered an outlier, which complements the interquartile range criterion. The process of fusing the filtered real-time motion state data using an extended Kalman filter is as follows: The extended Kalman filter's state vector is defined as a twelve-dimensional vector. This twelve-dimensional vector includes three spatial position coordinate components of the tower crane boom end in the world coordinate system, three velocity components, slewing angle, slewing angular velocity, luffing amplitude, luffing speed, hook height, and lifting speed. The three spatial position coordinate components are obtained by transforming the slewing angle, luffing amplitude, and hook height through a forward kinematics model. The specific transformation relationship of the forward kinematics model is as follows: the x-component of the spatial position coordinate is equal to the abscissa of the tower crane base plus the cosine of the luffing amplitude multiplied by the slewing angle; the y-component is equal to the ordinate of the tower crane base plus the sine of the luffing amplitude multiplied by the slewing angle; and the z-component is equal to the tower crane base height plus the hook height. The coordinates of the tower crane base are pre-calibrated using a total station and stored in the edge computing nodes. The prediction model of the extended Kalman filter adopts the constant velocity motion assumption. The observation model directly maps the spatial position coordinates output by the UWB positioning module, the rotation angle and amplitude output by the incremental encoder, and the swing angle information obtained by the triaxial accelerometer integration. The constant velocity motion assumption means that the velocity component in the state transition matrix remains unchanged, and the position component is obtained by adding the velocity to the position at the previous moment and multiplying by the sampling interval. The observation matrix of the observation model is a sparse matrix, which only associates the position, angle, and amplitude components in the state vector with the corresponding observation values. The swing angle information obtained by the triaxial accelerometer integration is obtained by integrating the x-axis and y-axis acceleration components output by the accelerometer twice to obtain the swing angle of the suspended object in the horizontal and vertical directions. Before integration, the gravity component is removed and zero drift correction is performed. To enhance robustness to non-Gaussian noise, the observation noise covariance matrix of the extended Kalman filter is updated using an adaptive online estimation method. A sliding window of length twenty sampling points is constructed using the innovation sequence. The sliding window covariance of the innovation sequence within the sliding window is calculated, and a forgetting factor of 0.85 is introduced to weight the observation noise covariance of the previous time step. The calculated result of the sliding window covariance is then weighted and summed with the forgotten covariance of the previous time step, thereby updating the observation noise covariance matrix in real time. This allows the extended Kalman filter to automatically adapt to the time-varying characteristics of sensor noise, ultimately outputting the complete state vector of each tower crane at time t. The complete state vector is a twelve-dimensional vector. The innovation sequence is defined as the sum of the observations at the current time step and the sum of the observations at the previous time step. The difference between the observed values ​​of the current state prediction; the calculation method of the sliding window covariance is as follows: first, calculate the average of the twenty innovation vectors in the window, and then calculate the mean of the product of the deviations of each innovation vector and the average value to obtain the covariance matrix; the forgetting factor of 0.85 makes the historical information forgotten at an exponential decay rate, with a half-life of about four sampling periods, thus taking into account both the adaptive speed and the estimation stability; the initial state vector of the extended Kalman filter is obtained by averaging the observation values ​​of the first five sampling points, the initial state covariance matrix is ​​set to the identity matrix multiplied by one hundred, the initial value of the observation noise covariance matrix is ​​set according to the noise variance set by the sensor factory calibration, and the process noise covariance matrix is ​​set as a diagonal matrix, with the diagonal elements set according to the empirical value of the maximum acceleration of the tower crane.

[0021] In this embodiment, it is specifically necessary to explain the specific operations of establishing the multi-machine kinematic model and introducing the dynamic correction model for the swing of the suspended object in step S2 as follows: First, a multi-machine kinematic model is established. For each tower crane, based on the slewing angle, luffing amplitude, and hook height in the complete state vector output in step S1, the three spatial position coordinate components of the boom end in the world coordinate system are obtained through forward kinematic model transformation. The input of the multi-machine kinematic model is the complete state vector output in step S1, and the output is the three spatial position coordinate components of the boom end in the world coordinate system. The specific transformation relationship of the forward kinematic model is as follows: the x-coordinate of the boom end in the world coordinate system is equal to the abscissa of the tower crane base plus the cosine of the luffing amplitude multiplied by the slewing angle; the y-coordinate is equal to the ordinate of the tower crane base plus the sine of the luffing amplitude multiplied by the slewing angle; and the z-coordinate is equal to the height of the tower crane base plus the hook height. The coordinates of the tower crane base are pre-calibrated using a total station and stored in the edge computing node. A dynamic correction model for the swing of the suspended object is introduced. The input to the dynamic correction model is the data from the triaxial accelerometer in the complete state vector output in step S1, and the output is the actual center position of the suspended object. In the dynamic correction model, the suspended object is regarded as a pendulum suspended at the end of the boom. The pendulum length is the length of the wire rope, and the swing angle is described by the swing angle obtained by integration of the triaxial accelerometer. The value range of the swing angle is between -30 degrees and +30 degrees. The specific process of obtaining the swing angle by integration of the triaxial accelerometer is as follows: First, the gravity component is removed from the x-axis and y-axis acceleration components output by the accelerometer and zero drift correction is performed. Then, the corrected acceleration is integrated once to obtain the angular velocity, and then integrated again to obtain the swing angle. During the integration process, a high-pass filter is used to suppress low-frequency drift, and the cutoff frequency is set to 0.1 Hz. The specific calculation process for the actual center position of the suspended load is as follows: The actual center position of the suspended load is equal to the three spatial coordinate components of the boom end in the world coordinate system plus an offset vector. The horizontal component of the offset vector is equal to the wire rope length multiplied by the absolute value of the product of the sine and cosine of the swing angle, divided by the cosine of the swing angle. The vertical component of the offset vector is equal to the wire rope length multiplied by the product of the square of the sine of the swing angle and the square root of the cosine of the swing angle. The horizontal and vertical components of the offset vector together constitute the three-dimensional offset of the suspended load relative to the boom end. The horizontal component along the boom direction is determined by the projection of the swing angle in the boom plane, and the vertical component is always downward. When the swing angle is zero, the offset vector is zero, and the actual center position of the suspended load coincides with the boom end. Then, the boom of each tower crane is abstracted as a cylinder with a first preset radius, the suspended object as a sphere with a second preset radius, and the wire rope as a thin cylinder with a third preset radius. The boom, suspended object, and wire rope are then combined into a spatial capsule. The central axis of the spatial capsule extends along the boom direction from the three spatial coordinate components of the boom end in the world coordinate system to the root of the boom. The outer surface of the spatial capsule encloses the center of the suspended object sphere. The first preset radius is 0.3 meters, the second preset radius is 0.5 meters, and the third preset radius is 0.05 meters. The shape of the spatial capsule consists of a cylinder with a radius of the first preset radius connected to two hemispheres at each end. The length of the cylinder is equal to the amplitude of the boom, and the center of the hemispheres is located at both ends of the cylinder. The center of the suspended object sphere is located below the outside of the spatial capsule and is connected to the boom end by the wire rope. However, when calculating the minimum Euclidean distance, the spatial capsule considers the center of the suspended object to be enclosed within its outer surface, thus simplifying the collision detection model. The minimum Euclidean distance between any two tower cranes is obtained by solving for the closest point pair between the two spatial capsules. The specific calculation process for the minimum Euclidean distance is as follows: First, determine the two closest points on the central axis of the spatial capsules of the two tower cranes respectively. Find two normalization parameters such that the distance between the three spatial position coordinate components of the boom end of the first tower crane in the world coordinate system plus the first normalization parameter multiplied by the rotation angle in the complete state vector output in step S1, and the distance between the three spatial position coordinate components of the boom end of the second tower crane in the world coordinate system plus the second normalization parameter multiplied by the boom direction unit vector, is minimized. Furthermore, the values ​​of both normalization parameters are limited to the range of zero to one. The process involves finding two normalized parameters, which is equivalent to solving a two-dimensional optimization problem. The objective function is the square of the Euclidean distance between two parameterized points. Since the objective function is a convex function, Newton's method is used to solve iteratively. The initial value of the two normalized parameters is 0.5, and the iteration terminates when the gradient norm is less than 10 to the power of negative 6. When both normalized parameters are in the interval between zero and one, the nearest point is located on the central axis of the space capsule. If a normalized parameter exceeds the interval, it is truncated to the nearest boundary value before calculating the distance. The specific steps for predicting the trend of the minimum Euclidean distance over future time using Taylor expansion are as follows: First, the first and second derivatives of the minimum Euclidean distance with respect to time at the current moment are calculated. The first derivative is calculated using the chain rule by combining the speed, angular velocity, and swing angle change rate of each tower crane with the Jacobian matrix of the minimum Euclidean distance with respect to each state component. The second derivative is calculated using the chain rule by combining the acceleration, angular acceleration, and swing angle acceleration of each tower crane with the Hessian matrix of the minimum Euclidean distance with respect to each state component. Each element of the Jacobian matrix is ​​obtained through analytical differentiation. Specifically, the partial derivative of the minimum Euclidean distance with respect to the boom end position component is equal to the projection of the vector connecting the nearest points onto the corresponding coordinate axis divided by the distance between the nearest points. The partial derivative of the minimum Euclidean distance with respect to the rotation angle is indirectly calculated by the derivative of the unit vector of the boom direction with respect to the rotation angle. The partial derivative of the minimum Euclidean distance with respect to the swing angle is indirectly calculated by the derivative of the offset vector with respect to the swing angle. Each element of the Hessian matrix is ​​obtained by further differentiation. These elements are pre-calculated offline using an automatic differentiation tool and stored as a lookup table. During online runtime, they are obtained by interpolation based on the current state to reduce the computational burden. The calculation process of the first derivative is as follows: the first derivative of the minimum Euclidean distance with respect to time is equal to the product of the cosine of the swing angle and the cosine of the rate of change of the swing angle, plus the product of the sine of the swing angle and the sine of the rate of change of the swing angle, plus the product of the sine of the swing angle and the cosine of the swing angle divided by the cosine of the rate of change of the swing angle; where the cosine of the rate of change of the swing angle refers to the cosine function value of the rate of change of the swing angle, and the sine of the rate of change of the swing angle refers to the sine function value of the rate of change of the swing angle; this expression is derived under the simplified condition of assuming that the end of the boom is stationary and only considering the influence of the swing of the suspended object. In practical applications, it is also necessary to add the distance change component caused by the boom motion. The complete first derivative should include the dot product of the velocity at the end of the boom and the unit vector of the boom direction. The calculation process of the second derivative is as follows: The second derivative of the minimum Euclidean distance with respect to time is equal to the square of the product of twice the sine of the swing angle and the cosine of the rate of change of the swing angle minus the square of the product of twice the cosine of the swing angle and the sine of the rate of change of the swing angle, plus the product of twice the sine of the swing angle and the cosine of the rate of change of the swing angle divided by the cosine of the rate of change of the swing angle, plus the product of twice the sine of the swing angle and the sine of the rate of change of the swing angle divided by the sine of the rate of change of the swing angle, minus the product of twice the sine of the swing angle and the cosine of the rate of change of the swing angle divided by the square of the cosine of the rate of change of the swing angle, minus the product of twice the sine of the swing angle and the cosine of the rate of change of the swing angle divided by the square of the rate of change of the swing angle; this expression is also based on a simplified model. The actual second derivative needs to take into account the boom acceleration term and the swing angle acceleration term. The complete expression can be automatically generated by an automatic differentiation tool. Then, the second-order Taylor expansion formula is used to predict the minimum Euclidean distance at any future time. The predicted minimum Euclidean distance is equal to the minimum Euclidean distance at the current time, plus the product of the prediction time and the first derivative, plus the product of half the square of the prediction time and the second derivative, thus obtaining the predicted minimum Euclidean distance. The second-order Taylor expansion formula is suitable for scenarios with short prediction times and smooth motion trajectories. When the prediction time exceeds half of the warning time window, the prediction accuracy may decrease. In this case, the fourth-order Runge-Kutta method can be used to numerically integrate the motion equations to obtain more accurate prediction values. However, in order to meet the real-time requirements, this method uses the second-order Taylor expansion by default and only switches to the numerical integration method when the warning time window is greater than 1.5 seconds. A safety threshold of two meters and a warning time window of three seconds are set. The prediction time point that minimizes the predicted minimum Euclidean distance is calculated by setting the first derivative of the predicted future minimum Euclidean distance with respect to the prediction time to zero. If the calculated prediction time point falls within the interval between zero and the warning time window, and the predicted future minimum Euclidean distance at that time point is less than the safety threshold, a conflict warning is triggered. The two-meter safety threshold is determined based on the maximum swing amplitude of the tower crane boom and safety regulations, with a safety margin of 0.5 meters. The three-second warning time window is based on the tower crane braking... The sum of the system response time and the operator's reaction time is determined to ensure sufficient time to execute the avoidance action. The prediction time point that minimizes the predicted distance is calculated using an analytical formula, i.e., the prediction time point equals the negative first derivative divided by the second derivative. When the second derivative is zero, the predicted distance changes monotonically. If the first derivative is negative and the current distance is less than the safety threshold, an early warning is triggered immediately. After triggering the conflict warning, a conflict pair set is output, which contains the numbers of all tower crane pairs that meet the warning conditions. At the same time, the complete state vector obtained in step S1 is output for use in step S3.

[0022] In this embodiment, the specific operation of constructing the model predictive control optimization problem in step S3 is as follows: First, extract the numbers of all tower crane pairs with conflict risk from the conflict pair set output in step S2. Only these tower cranes are included in this optimization, while the control variables of the remaining tower cranes remain unchanged. Then, establish a discrete-time state equation to describe the state evolution of the tower cranes as a prediction model. The prediction model refers to the prediction model in model predictive control, which is used to predict the state of the tower cranes at future times based on the complete state vector output in step S1. For each tower crane included in the optimization, a discrete-time state equation is constructed based on the kinematic parameters in the complete state vector obtained in step S1. The state vector of the discrete-time state equation is the twelve-dimensional complete state vector output in step S1. The control variables include three components: the slewing angular velocity of the tower crane's slewing mechanism, the luffing speed of the luffing mechanism, and the lifting speed of the hoisting mechanism. Discrete-time state equations describe the state evolution of a tower crane in future moments. They are constructed based on the assumption of constant velocity motion and are achieved through a linear combination of the state transition matrix and the control input matrix. The state transition matrix describes that the rate of change of the position component with time is equal to that of the velocity component, and the rate of change of the angle component with time is equal to that of the angular velocity component. The control input matrix maps the slewing angular velocity, luffing speed, and lifting speed to changes in angle, luffing amplitude, and hook height, respectively. Process noise terms in the prediction model are ignored in the optimization solution. The state transition matrix is ​​a 12x12 diagonal block matrix. Each position component corresponds to a two-dimensional identity matrix, the angle component to a one-dimensional identity matrix, the luffing amplitude and hook height to one-dimensional identity matrices, the velocity component to a one-dimensional identity matrix, and the angular velocity component to a one-dimensional identity matrix. The sub-blocks corresponding to the quantities are one-dimensional identity matrices. The sub-blocks corresponding to the amplitude change rate and the lifting speed are also one-dimensional identity matrices. The sampling interval is 0.2 seconds. The transfer coefficient of the position component is the sampling interval, the transfer coefficient of the velocity component is 1, the transfer coefficient of the angle component is the sampling interval, the transfer coefficient of the angular velocity component is 1, the transfer coefficient of the amplitude change rate component is the sampling interval, the transfer coefficient of the hook height component is the sampling interval, and the transfer coefficient of the lifting speed component is 1. The control input matrix is ​​a 12x3 matrix. The first column corresponds to the rotational angular velocity, the second column corresponds to the amplitude change rate, and the third column corresponds to the lifting speed. The influence coefficients of the rotational angular velocity on the rotational angle, the amplitude change rate on the amplitude change rate, and the lifting speed on the hook height are all sampled at the sampling interval. All other elements are zero. The cost function consists of a weighted sum of three parts: a safety distance penalty term, an operational efficiency loss term, and a control energy term. The calculation process for the safety distance penalty term is as follows: In the prediction time domain, traverse each prediction step. For each tower crane pair in the conflict pair set, calculate an exponential function with the natural constant e as the base and the ratio of the predicted minimum Euclidean distance in step S2 to the safety threshold as the exponent. Multiply the function value by the first weighting coefficient, and then add all these products together. The calculation process for the work efficiency loss term is as follows: In the prediction time domain, traverse each tower crane included in the optimization, calculate the square of the Euclidean distance between the current position of the tower crane and the original planned end position, multiply it by the second weighting coefficient, and then add the results of all tower cranes. The calculation process for the control energy term is as follows: Within the prediction time domain, iterate through each tower crane included in the optimization and each of its control variables, calculate the square of the control variable, multiply it by the third weighting coefficient, and then add all these squared values ​​together; the prediction time domain length is set to ten control steps, each step lasting 0.2 seconds, and the control time domain length is set to five control steps; the first weighting coefficient is set to 100, the second weighting coefficient is set to 1, and the third weighting coefficient is set to 0.1. These three weighting coefficients are determined through offline simulation parameter tuning. The tuning principle is: while ensuring that the safety distance penalty term dominates, the operational efficiency and control energy consumption are taken into account; the original planned endpoint position is pre-set by the construction scheduling system and stored in the edge computing node; Model predictive control optimization problems also include constraints, which fall into two categories. The first category is physical limit constraints. The control quantities and state variables of each tower crane are limited by hardware capabilities. The absolute upper limit of the slewing angular velocity is set to 0.5 radians per second, the absolute upper limit of the luffing speed is set to 0.8 meters per second, the absolute upper limit of the hoisting speed is set to 0.6 meters per second, and the absolute upper limits of the position and angle states are set to pre-calibrated maximum physical limits. The pre-calibrated maximum physical limits include: the x-coordinate range of the boom end in the world coordinate system is determined by the abscissa of the tower crane base plus or minus the maximum luffing amplitude; the y-coordinate range is determined by the ordinate of the tower crane base plus or minus the maximum luffing amplitude; the z-coordinate range is determined by the ground height to the maximum hook height of the tower crane; the slewing angle range is -180 degrees to +180 degrees; and the luffing amplitude range is zero to the maximum luffing amplitude. The hook height range is from zero to the maximum hook height. The maximum amplitude and maximum hook height are determined by the tower crane model and calibrated during installation. The second type is the safety constraint for the swing of the load. To ensure that the swing of the load does not exceed the allowable range, the absolute values ​​of the swing angle and the rate of change of the swing angle are strictly limited. The upper limit of the absolute value of the swing angle is set to 30 degrees, and the upper limit of the absolute value of the rate of change of the swing angle is set to 10 degrees per second. These constraints are applied indirectly through the swing angle state in the state vector. The swing angle state is not directly contained in the complete state vector, but is implicitly expressed through the geometric relationship between the actual center position of the load and the end position of the boom. During the optimization process, the swing angle is limited to the allowable range through inequality constraints. The specific implementation method is as follows: within each prediction step, based on the boom end position and the actual center position of the load calculated by the current control quantity, the sine and cosine values ​​of the swing angle are deduced, and then the constraint that the arctangent value does not exceed 30 degrees is applied. The specific process of solving for the optimal control sequence is as follows: The global optimization problem is decomposed into local subproblems and global coordination subproblems using the alternating direction multiplier method, which are solved iteratively. The local subproblems are solved independently for each tower crane included in the optimization. The objective function of the local subproblem is the control energy term plus an augmented Lagrange penalty term. This augmented Lagrange penalty term includes the square of the difference between the current control quantity and the global coordination variable, and the dot product of the Lagrange multiplier with the difference between the current control quantity and the global coordination variable. The local subproblems are solved directly using analytical formulas to obtain the local optimal control quantity for each tower crane. The global coordination subproblem aggregates the local optimal control quantities of all tower cranes. The components are grouped together, and the objective function is the sum of the safety distance penalty term and the squared difference between the local optimal control quantity and the global coordination variable of each tower crane. The gradient projection method is used to iteratively solve the problem to obtain the updated global coordination variable. Then, the Lagrange multipliers are updated. The Lagrange multipliers are equal to the Lagrange multipliers of the previous time step plus the penalty parameter multiplied by the difference between the current local optimal control quantity and the global coordination variable. The three steps of solving the local subproblem, solving the global coordination subproblem, and updating the Lagrange multipliers are repeated until the rate of change of the cost function between two adjacent iterations is less than one-thousandth or the preset maximum number of iterations is reached to obtain the optimal control sequence. The iterative solution process of the alternating direction multiplier method is as follows: First, initialize the global coordination variables and Lagrange multipliers to zero vectors; then enter the iterative loop. In each iteration, first solve the local subproblems of each tower crane in parallel, that is, find the control quantity that minimizes the local objective function. Since the local objective function is a quadratic function of the control quantity, its minimum value can be obtained directly analytically by taking the first derivative and setting it to zero. The specific analytical process is as follows: First, extract the quadratic coefficient matrix of the control quantity from the augmented Lagrange penalty term, calculate its inverse, and then substitute the global coordination variable, Lagrange multipliers, and the control quantity from the previous time step into the augmented Lagrange penalty term. Obtain an intermediate correction vector through matrix-vector multiplication. Finally, multiply the inverse matrix by the intermediate correction vector to get the updated control quantity value for the current iteration step. The quadratic coefficient matrix is ​​a 3x3 diagonal matrix, with each diagonal element being twice the penalty parameter. Its inverse matrix is ​​a diagonal matrix with each diagonal element being the reciprocal of twice the penalty parameter. The intermediate correction... The vector calculation process is as follows: add the global coordination variable to the Lagrange multiplier, subtract the control quantity from the previous moment, and then multiply by twice the penalty parameter to obtain the three-dimensional correction vector; the updated control quantity value is equal to the inverse matrix multiplied by the intermediate correction vector, that is, each control quantity component is equal to the corresponding component of the intermediate correction vector divided by twice the penalty parameter; then, focus on solving the global coordination subproblem, that is, finding the global coordination variable that minimizes the global objective function. The specific operation is as follows: first, calculate the gradient vector of the global objective function with respect to all global coordination variables, then update the global coordination variable along the opposite direction of the gradient, then determine whether the updated global coordination variable violates the safety distance constraint. If it does, the global coordination variable is forcibly projected into the feasible region that satisfies the safety distance constraint. This gradient calculation and projection operation is repeated until convergence, and the updated global coordination variable is obtained; the feasible region of the safety distance constraint is defined as: for each pair of conflicting tower cranes, the predicted minimum Euclidean distance corresponding to the global coordination variable must be greater than or equal to the safety threshold; the specific method of the projection operation is as follows: if the updated global coordination variable causes the predicted minimum Euclidean distance of a pair of conflicting tower cranes to be less than the safety threshold, then the global coordination variable is reversed along the gradient direction. The process is adjusted until the predicted minimum Euclidean distance is exactly equal to the safety threshold. This adjustment is achieved through a bisection method in a one-dimensional search. Next, the Lagrange multipliers are updated by adding the penalty parameter to the Lagrange multipliers from the previous time step and the product of the difference between the current local optimal control quantity and the global coordination variable. Finally, the convergence condition is determined: if the absolute value of the difference between the total cost function value of the current iteration and the total cost function value of the previous iteration divided by the total cost function value of the previous iteration is less than one-thousandth, or if the current iteration count reaches the preset maximum value, then the iteration is terminated and the optimal control sequence is output; otherwise, the next iteration continues. Regarding parameter settings, the penalty parameter is set to ten, and the number of iterations is set to five to ten to meet real-time requirements. The value of the penalty parameter ten ensures a moderate balance between the local subproblem and the global coordination subproblem, guaranteeing fast convergence while avoiding oscillations. The number of iterations, five to ten, is determined based on extensive simulation experiments. Within this range, the cost function's decline tends to plateau, and further increasing the number of iterations has limited improvement in control accuracy and increases computation time. After iteration convergence, the optimal control sequence is output, which consists of the control quantities of each tower crane from the first to the fifth control step. Only the first control quantity in the optimal control sequence is used. The control input of the step size is sent to the programmable logic controller of each tower crane via industrial Ethernet at a period of 20 milliseconds to drive the actuator to adjust the movement; the remaining control sequence is used as a warm start for the optimization of the next time step to accelerate convergence; the specific implementation of the warm start is as follows: before the optimization of the next time step begins, the control input of the second to fifth control steps in the optimal control sequence of the previous time step is used as the initial guess value of the current time step, and the global coordination variable and Lagrange multiplier of the previous time step are used as the initial value of the current time step, thereby greatly reducing the number of iterations of the alternating direction multiplier method, which usually only requires two to three iterations to converge.

[0023] In this embodiment, the specific operation of pre-training the deep reinforcement learning policy network offline in step S4 is as follows: The input observation vector for constructing the deep reinforcement learning policy network is encoded from the conflict pair set and the complete state vector output in step S2. The encoding process is as follows: concatenate the numbers of all tower crane pairs in the conflict pair set into a binary mask vector. The length of the binary mask vector is equal to the total number of tower crane pairs. The position of the tower crane pair with conflict is set to the value 1, and the position of the tower crane pair without conflict is set to the value 0. Then, flatten the twelve-dimensional complete state vector of all tower cranes in the complete state vector into a one-dimensional vector. Finally, concatenate the binary mask vector with the flattened complete state vector to obtain the input observation vector. The training employs a dual-delay deep deterministic policy gradient method, which alternately updates two parameterized networks: a policy network and a value network. The structure and update rules of these two networks are pre-defined by the training algorithm. The policy network consists of a three-layer fully connected neural network: the first hidden layer contains 256 neurons, the second hidden layer contains 128 neurons, and the output layer contains three neurons corresponding to the adjustments for rotational angular velocity, amplitude velocity, and acceleration / deceleration velocity, respectively. The hidden layer activation function uses a linear rectified function, while the output layer activation function uses a hyperbolic tangent function to constrain the action components to between -1 and +1. The value network has a similar structure to the policy network, but its output layer contains only one neuron to output the estimated value of the state-action pair. Both networks are updated using the Adam optimizer, with a learning rate of 0.001, a discount factor of 0.99, and a soft update coefficient of 0.005. The reward function during training consists of a weighted sum of three parts: The first part is the collision penalty, which is calculated as follows: Set a safety threshold. For each pair of tower cranes in the conflict pair set, check their predicted minimum Euclidean distance in the future prediction time window. Take the minimum predicted minimum Euclidean distance among all conflicting tower crane pairs. If the minimum value is less than the safety threshold, a fixed large negative reward is given, which is set to -100. If the predicted minimum Euclidean distance of all conflicting tower crane pairs is greater than or equal to the safety threshold, the collision penalty is zero. The second part is the control energy penalty term, which is equal to the sum of the squares of the three control components corresponding to the motion command: rotational angular velocity, amplitude change velocity, and acceleration / deceleration velocity, multiplied by the first reward weight coefficient, and a negative sign is added before the result. The first reward weight coefficient is 0.01. The first reward weight coefficient of 0.01 is used to match the order of magnitude of the control energy penalty term with the collision penalty term, to avoid the network consuming too much energy due to the control energy penalty being too small, and to avoid the network being too conservative and unable to avoid collisions in time due to the control energy penalty being too large. The third part is the schedule deviation penalty, which is equal to the absolute value of the schedule deviation caused by the execution of the action command multiplied by the second reward weight coefficient. The second reward weight coefficient is 0.001. The second reward weight coefficient of 0.001 makes the schedule deviation penalty only a minor part of the total reward, ensuring that the network prioritizes security and only considers efficiency optimization when the security margin is sufficient. The three components corresponding to the action command follow the meaning of the control quantities of slewing angular velocity, luffing speed, and lifting speed defined in step S3. They represent the changes in slewing angular velocity adjustment, luffing speed adjustment, and lifting speed adjustment relative to the current running value, respectively. The three components constitute the action vector. The sum of the squares of each component of the action vector is the sum of the squares of the changes in slewing angular velocity, luffing speed, and lifting speed. During training, the conditions for determining the failure of model prediction control solution are: the number of iterations of the alternating direction multiplier method in step S3 reaches the preset maximum number of iterations but still does not meet the convergence condition, or there are still conflicts after the projection of the global coordination variables, and the minimum Euclidean distance of the tower crane is lower than the safety threshold; any condition that is met is marked as a solution failure record, and each record is a data unit that stores the input observation vector, action command, reward value and the next input observation vector during a state transition process; During training, adversarial experience replay is employed. This replay uses the memory unit that stores historical state transition records—the experience storage area—as the storage unit. The specific calculation process for updating the sampling weights is as follows: First, obtain the temperature coefficient, which is set to two. A temperature coefficient of two makes the sampling weight of failed samples approximately 7.4 times that of normal samples. This ensures that failed samples are fully sampled while avoiding excessive bias towards a few extreme samples during training, which would lead to a decrease in the generalization ability of the policy network. Next, obtain the failure indicator function. The failure indicator function takes the following value: it takes the value of one when the model predictive control solution fails, and takes the value of zero when it does not fail. Then, the product of the temperature coefficient of the natural constant e and the failure indicator function is raised to the power of the product to obtain the power calculation result of the current record; then, the sum of the power calculation results of each record in the memory unit is calculated; finally, the power calculation result of the current record is divided by the sum of the power calculation results of all records to obtain the sampling weight of the current record. The larger the temperature coefficient, the higher the sampling probability of the failure record; the failure indicator function is used to identify whether the record belongs to the historical working condition where the model predictive control solution failed; the sampling weight is used to guide the extraction of records in the memory unit to ensure that the deep reinforcement learning policy network fully learns the coping strategy under dangerous working conditions; The specific steps for querying the action instructions output by the deep reinforcement learning policy network and calculating the safety margin are as follows: When step S2 triggers a conflict warning, the current input observation vector is input into the trained deep reinforcement learning policy network, and the action command is obtained through one forward propagation. Then, the Monte Carlo dropout method was used to perform multiple random forward propagations on the deep reinforcement learning policy network. The total number of random forward propagations was set to fifty. In each forward propagation, a dropout layer inside the deep reinforcement learning policy network was activated, and the dropout rate of the dropout layer was set to one-tenth. Through fifty independent random forward propagations, a set containing fifty action instruction samples was generated. The Monte Carlo dropout method simulates the posterior distribution of network parameters by randomly dropping ten percent of the neurons in the deep reinforcement learning policy network in each forward propagation. It is an approximate Bayesian inference method that can quantify the uncertainty of the policy network output without increasing the network complexity. The dropout rate of one-tenth ensures the diversity of output samples while avoiding excessive output fluctuations caused by dropping too many neurons. It has been verified that this dropout rate can keep the standard deviation of action samples within a reasonable range. The number of fifty random forward propagations was determined based on the central limit theorem to ensure sufficient sampling of the policy network output distribution, so that the estimation error of the fifth percentile is less than five percent. Each action instruction sample means: a set of adjustment values ​​for rotational angular velocity, amplitude velocity, and acceleration / deceleration output obtained during the forward propagation of the network after randomly discarding some neurons; For each action command sample, the minimum Euclidean distance prediction process based on Taylor expansion established in step S2 is used to simulate the minimum Euclidean distance trajectory within the next two seconds after the sample is executed, resulting in multiple minimum distance sequences; the warning time window is set to three seconds, and the minimum distance value within the next three-second warning time window is extracted from each minimum distance sequence to form a set of minimum distances. The safety margin is defined as the fifth percentile of the minimum distance set. The specific calculation process is as follows: First, all values ​​in the minimum distance set are sorted in ascending order from smallest to largest. The total number of values ​​is counted, and the total number is multiplied by 5% to obtain the theoretical position number. If the theoretical position number contains a decimal part, it is rounded up to obtain the target position number. The value corresponding to the target position number in the sorted array is directly taken as the fifth percentile. If the theoretical position number is an integer, the arithmetic mean of the theoretical position number and the value of the next nearest neighbor in the sorted array is taken as the fifth percentile. The fifth percentile reflects the safety boundary in the worst case. The fifth percentile corresponds to a 95% confidence lower limit, that is, in 50 simulations, at least 47.5 times (48 times after rounding) the minimum distance prediction value is higher than this value. It provides a conservative and robust safety measure, which is better than central tendency indicators such as the mean or median, because the mean is easily inflated by a few extremely optimistic samples, and the median only reflects the middle level. Neither can guarantee safety in the worst case. The safety margin threshold is set to 1.5 meters. If the safety margin is greater than 1.5 meters, the action command is deemed safe enough, and the action command is directly converted into the corresponding control quantity and sent to each tower crane for execution. If the safety margin is no greater than 1.5 meters, the process reverts to the model predictive control solution process in step S3. The reverting operation is as follows: the complete state vector at the current moment is input into step S3, and the action command is used as the initial guess value of the global coordination variable defined in step S3. Step S3 then directly starts the alternating direction multiplier method iteration based on the complete state vector and the initial guess value of the global coordination variable. Finally, the first control quantity in the optimal control sequence is still issued to each tower crane for execution. The safety margin threshold of 1.5 meters is obtained by subtracting the safety margin of 0.5 meters from the safety threshold of 2 meters in step S2. The 0.5-meter safety margin comprehensively considers the combined effects of sensor measurement noise, extended Kalman filter state estimation error, Taylor expansion prediction model approximation error, and actuator response delay, ensuring that even under the most unfavorable error superposition conditions, the actual physical distance can still be maintained above the safety threshold. Among these measures, fifty independent random forward propagations ensure sufficient sampling of the policy network output distribution; the dropout rate is set to one-tenth to ensure sampling diversity while avoiding excessive output fluctuations; the warning time window is set to three seconds to cover the shortest reaction time required for tower crane braking and manual intervention; the fifth percentile is used as a safety margin measure, meaning that at least forty-five of the fifty simulations have minimum distance prediction values ​​higher than the fifth percentile, ensuring high confidence in the decision; the safety margin threshold is set to 1.5 meters, slightly lower than the safety threshold of 2.0 meters in step S2, reserving a safety margin of 0.5 meters to maintain physical isolation under sudden disturbances.

[0024] It should be noted that the descriptions of each embodiment in the above embodiments have different focuses. For parts that are not described in detail in a certain embodiment, please refer to the relevant descriptions in other embodiments.

[0025] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0026] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded computer, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0027] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0028] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0029] Although preferred embodiments of the invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including both the preferred embodiments and all changes and modifications falling within the scope of the invention.

[0030] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, this invention also intends to include these modifications and variations.

Claims

1. A method for collaborative anti-collision early warning and control of tower cranes in bridge construction, characterized in that, Specifically, the steps include the following: Step S1: Collect real-time motion status data of multiple tower cranes. The real-time motion status data includes the spatial position coordinates, slewing angle, luffing amplitude, hook height, weight of the hoisted object, and vibration acceleration at the end of the boom of each tower crane. After sliding window filtering and outlier removal through edge computing nodes, the filtered real-time motion status data is fused using an extended Kalman filter to obtain the complete state vector of each tower crane at time t. Step S2: Based on the complete state vector obtained in step S1, establish a multi-machine kinematic model and introduce a dynamic correction model for the swing of the suspended object. Calculate the minimum Euclidean distance between the boom and the suspended object between any two tower cranes. Use Taylor expansion to predict the trend of the change of the minimum Euclidean distance in the future. When the predicted minimum Euclidean distance in the future is less than the safety threshold and the prediction time is less than the warning time window, trigger a conflict warning and output the conflict pair set and the complete state vector obtained in step S1. Step S3: Based on the set of conflict pairs and the complete state vector output in step S2, construct a model predictive control optimization problem. Using the weighted sum of the safety distance penalty term, the operation efficiency loss term, and the control energy term as the cost function, solve the optimal control sequence under the constraints of the physical limits of each tower crane and the safe range of the swing of the load. Then, send the first control quantity in the optimal control sequence to each tower crane for execution. Step S4: Pre-train the deep reinforcement learning policy network offline. When the conflict warning is triggered in step S2, the action instructions output by the deep reinforcement learning policy network are queried first. If the safety margin corresponding to the action instruction is higher than the threshold, it is executed directly; otherwise, it is back to the model prediction and control solution process in step S3.

2. The method for collaborative anti-collision early warning control of bridge construction tower cranes according to claim 1, characterized in that: In step S1, the edge computing node collects real-time motion status data from the UWB positioning module, incremental encoder, triaxial accelerometer and tension sensor of each tower crane at a fixed sampling frequency of 50 Hz. For each tower crane, the real-time motion status data constitutes an eight-dimensional vector, which includes three components of spatial position coordinates, rotation angle, amplitude, hook height, weight of the hoisted object and vibration acceleration at the end of the boom.

3. The method for collaborative anti-collision early warning control of bridge construction tower cranes according to claim 2, characterized in that: The specific operations for sliding window filtering and outlier removal using edge computing nodes are as follows: The edge computing node first uses an adaptive median Gaussian mixture filter to preprocess each dimension of the eight-dimensional vector. The adaptive median Gaussian mixture filter calculates the weighted median within a sliding window with a length of ten sampling points. The weight of the weighted median is determined by the Mahalanobis distance between the current sampling point and each sampling point in the sliding window. After weighted median filtering is completed, the edge computing nodes perform residual checks on the weighted median filtered real-time motion state data based on kernel density estimation to remove residual abrupt changes. The residual is defined as the difference between the weighted median filtered real-time motion state data at the current time and the weighted median filtered real-time motion state data at the previous time. If the absolute value of the residual is greater than three times the interquartile range of the residual sequence, the current sampling point is marked as an outlier and replaced with the corresponding value in the weighted median filtered real-time motion state data at the previous time to obtain the filtered real-time motion state data.

4. The method for collaborative anti-collision early warning control of bridge construction tower cranes according to claim 3, characterized in that: The process of fusing the filtered real-time motion state data using an extended Kalman filter is as follows: The state vector of the extended Kalman filter is defined as a twelve-dimensional vector. The twelve-dimensional vector includes three spatial position coordinate components of the boom end of each tower crane in the world coordinate system, three velocity components, slewing angle, slewing angular velocity, luffing amplitude, luffing speed, hook height, and lifting speed. The three spatial position coordinate components are obtained by transforming the slewing angle, luffing amplitude, and hook height through a forward kinematics model. The prediction model of the extended Kalman filter adopts the assumption of constant velocity motion, and the observation model directly maps the spatial position coordinates output by the UWB positioning module, the rotation angle and amplitude output by the incremental encoder, and the swing angle information obtained by the integration of the triaxial accelerometer. The observation noise covariance matrix of the extended Kalman filter is updated using an adaptive online estimation method. A sliding window with a length of twenty sampling points is constructed using the innovation sequence. The sliding window covariance of the innovation sequence within the sliding window is calculated, and a forgetting factor of 0.85 is introduced to weight the observation noise covariance of the previous time step. The calculated result of the sliding window covariance is then weighted and summed with the forgotten covariance of the previous time step, thereby updating the observation noise covariance matrix in real time. This allows the extended Kalman filter to automatically adapt to the time-varying characteristics of sensor noise and finally output the complete state vector of each tower crane at time t.

5. The method for collaborative anti-collision early warning control of bridge construction tower cranes according to claim 4, characterized in that: In step S2, the specific operations for establishing the multi-machine kinematic model and introducing the dynamic correction model for the swing of the suspended object are as follows: First, a multi-machine kinematic model is established. For each tower crane, based on the slewing angle, luffing amplitude, and hook height in the complete state vector output in step S1, the three spatial position coordinate components of the boom end in the world coordinate system are obtained through the forward kinematic model transformation. The input of the multi-machine kinematic model is the complete state vector output in step S1, and the output is the three spatial position coordinate components of the boom end in the world coordinate system. A dynamic correction model for the swing of the suspended object is introduced. The input of the dynamic correction model for the swing of the suspended object is the data of the three-axis accelerometer in the complete state vector output in step S1, and the output is the actual center position of the suspended object. In the dynamic correction model for the swing of the suspended object, the suspended object is regarded as a simple pendulum suspended at the end of the boom, with the pendulum length being the length of the wire rope and the swing angle being described by the swing angle obtained by integration of the three-axis accelerometer. The specific calculation process for the actual center position of the suspended load is as follows: The actual center position of the suspended load is equal to the three spatial coordinate components of the end of the boom in the world coordinate system plus an offset vector. The horizontal component of the offset vector is equal to the length of the wire rope multiplied by the absolute value of the product of the sine and cosine of the swing angle, and then divided by the cosine of the swing angle. The vertical component of the offset vector is equal to the length of the wire rope multiplied by the product of the square of the sine of the swing angle and the square root of the cosine of the swing angle. Then, the boom of each tower crane is abstracted as a cylinder with a first preset radius, the suspended object is abstracted as a sphere with a second preset radius, and the wire rope is abstracted as a thin cylinder with a third preset radius. The boom, suspended object and wire rope are combined into a spatial capsule. The central axis of the spatial capsule extends along the boom direction from the three spatial position coordinate components of the boom end in the world coordinate system to the root of the boom. The outer surface of the spatial capsule wraps around the center of the suspended object sphere. The minimum Euclidean distance between any two tower cranes is obtained by solving for the closest point pair between the two spatial capsules.

6. The method for collaborative anti-collision early warning control of bridge construction tower cranes according to claim 5, characterized in that: The specific operation of using Taylor expansion to predict the changing trend of the minimum Euclidean distance in the future is as follows: First, calculate the first and second derivatives of the minimum Euclidean distance with respect to time at the current moment. The first derivative is calculated using the chain rule by combining the speed, angular velocity, and swing angle change rate of each tower crane with the Jacobian matrix of the minimum Euclidean distance with respect to each state component. The second derivative is calculated using the chain rule by combining the acceleration, angular acceleration, and swing angle acceleration of each tower crane with the Hessian matrix of the minimum Euclidean distance with respect to each state component. Then, the second-order Taylor expansion formula is used to predict the predicted minimum Euclidean distance at any future time. The predicted minimum Euclidean distance is equal to the minimum Euclidean distance at the current time, plus the product of the prediction time and the first derivative, plus the product of half the square of the prediction time and the second derivative, thus obtaining the predicted minimum Euclidean distance. Set the safety threshold to two meters and the warning time window to three seconds. By setting the first derivative of the predicted minimum Euclidean distance with respect to the prediction time to zero, find the prediction time point that minimizes the predicted minimum Euclidean distance. If the calculated prediction time point falls within the interval from zero to the warning time window, and the predicted minimum Euclidean distance at the prediction time point is less than the safety threshold, then a conflict warning is triggered. After triggering the conflict warning, output the conflict pair set, which contains the numbers of all tower crane pairs that meet the warning conditions. At the same time, output the complete state vector obtained in step S1 for use in step S3.

7. The method for collaborative anti-collision early warning control of bridge construction tower cranes according to claim 6, characterized in that: In step S3, the specific operations for constructing the model predictive control optimization problem are as follows: First, extract the numbers of all tower crane pairs with conflict risk from the conflict pair set output in step S2. Only these tower cranes are included in this optimization, while the control variables of the remaining tower cranes remain unchanged. Then, establish a discrete-time state equation to describe the state evolution of the tower cranes as a prediction model. For each tower crane included in the optimization, based on the kinematic parameters in the complete state vector obtained in step S1, construct a discrete-time state equation. The state vector of the discrete-time state equation is the twelve-dimensional complete state vector output in step S1. The control variables include three components: the slewing angular velocity of the tower crane's slewing mechanism, the luffing speed of the luffing mechanism, and the lifting speed of the hoisting mechanism. The cost function consists of a weighted sum of three parts: a safety distance penalty term, an operational efficiency loss term, and a control energy term. The calculation process for the safety distance penalty term is as follows: In the prediction time domain, traverse each prediction step. For each tower crane pair in the conflict pair set, calculate an exponential function with the natural constant e as the base and the ratio of the predicted minimum Euclidean distance in step S2 to the safety threshold as the exponent. Multiply the function value by the first weighting coefficient, and then add all these products together. The calculation process for the work efficiency loss term is as follows: In the prediction time domain, traverse each tower crane included in the optimization, calculate the square of the Euclidean distance between the current position of the tower crane and the original planned end position, multiply it by the second weighting coefficient, and then add the results of all tower cranes. The calculation process for the control energy term is as follows: In the prediction time domain, iterate through each tower crane included in the optimization and each of its control variables, calculate the square of the control variable, multiply it by the third weighting coefficient, and then add all these squared values ​​together. Model predictive control optimization problems also include constraints, which are divided into two categories: the first category is physical limit constraints; the second category is safety constraints for the swing of the suspended load.

8. The method for collaborative anti-collision early warning control of bridge construction tower cranes according to claim 7, characterized in that: The specific process for solving the optimal control sequence is as follows: The global optimization problem is decomposed into local subproblems and global coordination subproblems using the alternating direction multiplier method, which are solved iteratively. The local subproblems are solved independently for each tower crane included in the optimization. The objective function of the local subproblem is the control energy term plus an augmented Lagrange penalty term. This augmented Lagrange penalty term includes the square of the difference between the current control quantity and the global coordination variable, and the dot product of the Lagrange multiplier with the difference between the current control quantity and the global coordination variable. The local subproblems are solved directly using analytical formulas to obtain the local optimal control quantity for each tower crane. The global coordination subproblem aggregates the local optimal control quantities of all tower cranes. The components are grouped together, and the objective function is the sum of the safety distance penalty term and the squared difference between the local optimal control quantity and the global coordination variable of each tower crane. The gradient projection method is used to iteratively solve the problem to obtain the updated global coordination variable. Then, the Lagrange multipliers are updated. The Lagrange multipliers are equal to the Lagrange multipliers of the previous time step plus the penalty parameter multiplied by the difference between the current local optimal control quantity and the global coordination variable. The three steps of solving the local subproblem, solving the global coordination subproblem, and updating the Lagrange multipliers are repeated until the rate of change of the cost function between two adjacent iterations is less than one-thousandth or the preset maximum number of iterations is reached to obtain the optimal control sequence. After iterative convergence, the optimal control sequence is output, which consists of the control quantities of each tower crane from the first control step to the fifth control step. Only the control quantity of the first control step in the optimal control sequence is sent to the programmable logic controller of each tower crane via industrial Ethernet at a period of 20 milliseconds to drive the actuator to adjust the movement. The remaining control sequence is used as a warm start for optimization in the next moment to accelerate convergence.

9. A method for coordinated anti-collision early warning control of bridge construction tower cranes according to claim 8, characterized in that: In step S4, the specific operation of pre-training the deep reinforcement learning policy network offline is as follows: Construct the input observation vector of the deep reinforcement learning policy network. The input observation vector is encoded by the conflict pair set and the complete state vector output in step S2. Training is performed using a dual-delay deep deterministic policy gradient method, which alternately updates the policy network and the value network using two sets of parameterized networks. The reward function during training consists of a weighted sum of three parts: The first part is the collision penalty, which is calculated as follows: Set a safety threshold. For each pair of tower cranes in the conflict pair set, check their predicted minimum Euclidean distance in the future prediction time window. Take the minimum predicted minimum Euclidean distance among all conflicting tower crane pairs. If the minimum value is less than the safety threshold, a fixed large negative reward is given, which is set to -100. If the predicted minimum Euclidean distance of all conflicting tower crane pairs is greater than or equal to the safety threshold, the collision penalty is zero. The second part is the control energy penalty term, which is equal to the sum of the squares of the three control components corresponding to the action command: angular velocity, amplitude velocity, and acceleration / deceleration velocity, multiplied by the first reward weight coefficient, and preceded by a negative sign; The third part is the schedule deviation penalty, which is equal to the absolute value of the schedule deviation caused by the execution of the action instructions multiplied by the second reward weighting coefficient. During training, the conditions for determining the failure of model prediction control solution are: the number of iterations of the alternating direction multiplier method in step S3 reaches the preset maximum number of iterations but still does not meet the convergence condition, or there are still conflicts after the projection of the global coordination variables, and the minimum Euclidean distance of the tower crane is lower than the safety threshold; any condition that is met is marked as a solution failure record, and each record is a data unit that stores the input observation vector, action command, reward value and the next input observation vector during a state transition process; During training, adversarial experience replay is employed. This replay uses the memory unit that stores historical state transition records—the experience storage area—as the storage unit. The specific calculation process for updating the sampling weights is as follows: First, obtain the temperature coefficient, which is set to two. Next, obtain the failure indicator function. The failure indicator function takes the following value: it takes the value of one when the model predictive control solution fails, and takes the value of zero when it does not fail. Then, the product of the temperature coefficient of the natural constant e and the failure indicator function is raised to the power of the result to obtain the power calculation result of the current record; then, the sum of the power calculation results of each record in the memory unit is calculated; finally, the power calculation result of the current record is divided by the sum of the power calculation results of all records to obtain the sampling weight of the current record.

10. A method for coordinated anti-collision early warning control of bridge construction tower cranes according to claim 9, characterized in that: The specific operation of querying the action instructions output by the deep reinforcement learning policy network and calculating the safety margin is as follows: When step S2 triggers a conflict warning, the current input observation vector is input into the trained deep reinforcement learning policy network, and the action command is obtained through one forward propagation. Then, the Monte Carlo dropout method was used to perform fifty random forward propagations on the deep reinforcement learning policy network. Each forward propagation enabled the dropout layer, and the dropout rate was set to one-tenth, generating a set containing fifty action instruction samples. For each action command sample, the minimum Euclidean distance prediction process based on Taylor expansion established in step S2 is used to simulate the minimum Euclidean distance trajectory within the next two seconds after the sample is executed, resulting in multiple minimum distance sequences; in each minimum distance sequence, the minimum distance value within the next three-second warning time window is extracted to form a set of minimum distances. The safety margin is defined as the fifth percentile of the minimum distance set, and the safety margin threshold is set to 1.5 meters. If the safety margin is greater than 1.5 meters, the action command is deemed safe enough, and the action command is directly converted into the corresponding control quantity and sent to each tower crane for execution. If the safety margin is no more than 1.5 meters, then the process reverts to the model predictive control solution in step S3. The reverting operation is as follows: the complete state vector at the current moment is passed into step S3 as input, and the action command is used as the initial guess value of the global coordination variable defined in step S3. Then, step S3 directly starts the alternating direction multiplier method iteration based on the complete state vector and the initial guess value of the global coordination variable. Finally, the first control quantity in the optimal control sequence is still issued to each tower crane for execution.

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