Multi-machine suspension system obstacle avoidance planning method and system based on multi-level collaborative planning framework

Abstract

The invention belongs to the technical field of intelligent control and collaborative planning, and discloses a multi-machine suspension system obstacle avoidance planning method and system based on a multi-level collaborative planning framework, and the method comprises the steps: building a multi-machine coupling model comprising kinematics coupling and dynamics coupling based on the spatial configuration of a suspension system; based on a multi-machine coupling model containing kinematics coupling and dynamics coupling, the rope length, tension, the tail end of a crane and the position of a suspended object of the multi-machine suspension system are obtained; a global-local-collaborative three-level obstacle avoidance planning framework is constructed; based on a global-local-cooperative three-level obstacle avoidance planning framework, three-dimensional combined obstacle avoidance of a suspended object, a rope and a crane tail end is realized.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of intelligent control and collaborative planning, and particularly relates to a multi-machine suspension system obstacle avoidance planning method and system based on a multi-level collaborative planning framework. BACKGROUND

[0002] With the development of modern industrial equipment towards large-scale, the limitations of single crane in load capacity, operation flexibility and the like are increasingly highlighted, and a multi-machine suspension system has become the core equipment for realizing safe and efficient transportation of large-size and high-quality objects. However, as a typical under-constrained rigid-flexible coupling system, the system has key problems such as strong coupling between rope tension and suspension object position, high complexity of multi-body motion coupling, large calculation complexity of high-dimensional state space, and unperfected multi-rigid-body collaborative obstacle avoidance method, so that the traditional single-machine control method is difficult to meet the engineering application requirements of the system.

[0003] At present, there is no very accurate definition of the multi-machine suspension system, and a system that suspends an object by setting a rope or similar flexible connecting device above the object and realizes balance by using the dynamic response characteristics of the object is generally referred to as a suspension system.

[0004] In view of the height motion coupling characteristics of the multi-machine suspension system caused by the physical constraints of the rope, the existing researches have the bottleneck problems of excessive model simplification, limited planning range (only paying attention to the suspension object and ignoring the cooperation of the rope and the end of the crane), and missing of dynamic constraints in trajectory planning, which seriously restricts the safety and operation efficiency of the system under complex working conditions. Therefore, a multi-level planning framework that fuses the coupling relationship of the crane-rope-suspension object whole link and takes into account the dynamic feasibility is established, a multi-machine suspension system obstacle avoidance planning method and system based on a three-level obstacle avoidance planning framework is researched, and through the hierarchical progressive obstacle avoidance, path optimization and real-time trajectory correction mechanism, the collaborative regulation from the global path to the local execution is realized, which has important theoretical value and engineering significance for breaking through the motion coupling and dynamic constraints and improving the robustness of the system environmental adaptability and hoisting task completion. SUMMARY

[0005] To solve the problems in the prior art, the application provides a multi-machine suspension system obstacle avoidance planning method and system based on a multi-level collaborative planning framework, a multi-machine coupling model and a step-by-step iterative collaborative solving strategy are constructed, a three-level obstacle avoidance planning framework of "global-local-collaboration" is established, and three-dimensional joint obstacle avoidance of the suspension object, the rope and the end of the crane is realized.

[0006] To achieve the above object, the application provides the following scheme: The multi-machine suspension system obstacle avoidance planning method based on the multi-level collaborative planning framework comprises the following steps: Based on the spatial configuration of the suspension system, a multi-machine coupling model containing kinematic coupling and dynamic coupling is established; Based on the multi-machine coupling model containing kinematic coupling and dynamic coupling, the rope length, tension, crane end and suspended object position of the multi-machine suspension system are obtained; Based on the structural characteristics of the suspension system, a "global-local-collaborative" three-level obstacle avoidance planning framework is constructed; Based on the "global-local-collaborative" three-level obstacle avoidance planning framework, three-dimensional joint obstacle avoidance of the suspended object, rope and crane end is realized.

[0007] Preferably, the method for establishing a multi-machine coupling model containing kinematic coupling and dynamic coupling based on the spatial configuration of the suspension system comprises: Determine the typical configuration of the suspension system, and divide the typical configuration of the suspension system into three types of systems, i.e. rope driving, crane end driving and mixed driving, according to the driving mechanism; The kinematic geometric constraint equations of the three types of systems are established by using the closed-loop vector method; The dynamic force balance equations of the three types of systems are established based on the force screw balance equation; Integrate the kinematic geometric constraint equations and the dynamic force balance equations to form a multi-machine coupling model.

[0008] Preferably, the method for obtaining the rope length, tension, crane end and suspended object position of the multi-machine suspension system based on the multi-machine coupling model containing kinematic coupling and dynamic coupling comprises: Input the desired trajectory of the suspended object in the operation time domain , and set the total number of iterations and the convergence threshold value; the total operation time is discretized into equidistant time steps to generate a time sequence ; and define a multi-machine collaborative state vector containing the end position of the first crane, the rope length , the tension and the suspended object position ; based on the desired trajectory of the suspended object, map to the initial position of each crane end using inverse kinematics, and calculate the initial rope tension through the dynamic equation, verify and complete the initial value setting, and enter the loop solution in time step order; At each time step, each crane independently calculates the end position based on the current collaborative state vector through the inverse kinematics equation ; calculate the length of the rope in combination with the geometric constraint equation , and solve the rope tension through the dynamic equation , and update the cooperative state vector synchronously ; perform cooperative constraint checking: time synchronization constraint, space obstacle avoidance constraint, force balance constraint, and tension non-negative constraint If the solution satisfies all cooperative constraints, store the cooperative state vector of the current time step in the global database; if the constraints are not satisfied, apply a correction to the end position of the conflicting crane , recalculate the length of the rope and the tension , and verify the constraints again, complete the constraint checking, generate the global cooperative state vector , and use it as the initial value of the iteration at moment; Determine whether the current time step is less than the total number of steps , if , return to the time step and continue the iterative loop; if , output the final cooperative state vector, including the end position of each crane , the length of the rope , the tension of the rope , and the actual trajectory of the suspended object , which is the final motion result of the multi-crane suspension system.

[0009] Preferably, the "global-local-cooperative" three-level obstacle avoidance planning framework includes: global layer, local layer, and cooperative layer. The global layer is used to generate an optimal trajectory that satisfies the multi-crane cooperative constraint using a global obstacle avoidance algorithm. The local layer is used to deal with dynamic obstacles through a dynamic obstacle avoidance strategy. The cooperative layer is used to ensure the cooperation of multi-crane motion by adjusting the length of the rope and the end position of the crane.

[0010] Preferably, based on the "global-local-cooperative" three-level obstacle avoidance planning framework, the method for three-dimensional joint obstacle avoidance of the suspended object, the rope, and the end of the crane includes: Based on the kinematic-dynamic coupling characteristics, the tensioned rope is abstracted as a spatial vector, the crane end and the suspended object are regarded as rigid bodies, and the multi-crane cooperative constraint is embedded. A rope vector-rigid body hybrid model is constructed, and a convex optimization + semi-definite programming algorithm is used to fuse the rope length, crane workspace, and obstacle geometric constraints to calculate the collision-free feasible region. Design the objective function of the suspension system, use intelligent optimization algorithm to solve the multi-objective optimization problem, generate the initial global trajectory of the suspended object, and discretize it into time sequence sub-targets; Based on the initial global trajectory of the suspended object, a global-local-collaborative three-level planning framework is embedded: for the spatial characteristics of the rope vector, the vector field method is used to realize rope obstacle avoidance through vector constraint avoidance strategy; for the virtual formation configuration of the crane, a space-time collaborative model is constructed and a space-time parallel collaborative strategy is used to optimize the time sequence and spatial trajectory; for the force-position coupling characteristics of the system, a force-position collaborative model is designed and a hierarchical search-step optimization strategy is used to refine the motion planning, and finally the obstacle avoidance planning results covering the rope, the crane end and the hybrid driving mode are output.

[0011] The application also provides a multi-machine suspension system obstacle avoidance planning system based on a multi-level collaborative planning framework, which is used to implement the method described above, and comprises a first construction module, a decoupling module, a second construction module and an obstacle avoidance module. The first construction module is used to establish a multi-machine coupling model containing kinematic coupling and dynamic coupling based on the spatial configuration of the suspension system. The decoupling module is used to obtain the rope length, tension, crane end and suspended object position of the multi-machine suspension system based on the multi-machine coupling model containing kinematic coupling and dynamic coupling. The second construction module is used to construct a "global-local-collaborative" three-level obstacle avoidance planning framework based on the structural characteristics of the suspension system. The obstacle avoidance module is used to realize three-dimensional joint obstacle avoidance of the suspended object, the rope and the crane end based on the "global-local-collaborative" three-level obstacle avoidance planning framework.

[0012] Preferably, the first construction module comprises a division unit, a kinematics unit, a dynamics unit and an integration unit. The division unit is used to determine the typical configuration of the suspension system, and divide the typical configuration of the suspension system into three types of systems, i.e., rope driving, crane end driving and hybrid driving, according to the driving mechanism. The kinematics unit is used to establish the kinematic geometric constraint equation of the three types of systems by using the closed-loop vector method. The dynamics unit is used to establish the dynamic force balance equation of the three types of systems based on the force screw balance equation. The integration unit is used to integrate the kinematic geometric constraint equation and the dynamic force balance equation to form the multi-machine coupling model.

[0013] Preferably, the process of obtaining the rope length, tension, crane end and suspended object position of the multi-machine suspension system based on the multi-machine coupling model containing kinematic coupling and dynamic coupling comprises: inputting the desired trajectory of the suspended object in the work time domain and setting the total number of iterations and the convergence threshold; setting the total work duration discretization is equidistant time steps , generating time series ; and defining a multi-machine cooperative state vector , containing the end position of the first crane, the rope length , the tension and the suspended object position ; based on the desired trajectory of the suspended object, using inverse kinematics to map to the initial position of each crane end , and calculating the initial rope tension through the dynamics equation , verifying after completing the initial value setting, entering the loop in time step order to solve; At each time step, each crane independently calculates the end position based on the current cooperative state vector through the inverse kinematics equation; combined with the geometric constraint equation to calculate the rope length , and then solve the rope tension through the dynamics equation, and update the cooperative state vector synchronously; perform cooperative constraint checking: time synchronization constraint, space obstacle avoidance constraint, force balance constraint, tension non-negative constraint; If the solution satisfies all cooperative constraints, store the cooperative state vector of the current time step in the global database; if the constraints are not satisfied, apply a correction to the end position of the conflicting crane , recalculate the rope length and tension , and verify the constraints again, complete the constraint checking, and generate the global cooperative state vector , and use it as the initial value of the iteration at ; Determine whether the current time step is less than the total number of steps , if , return to the time step and continue the loop iteration; if , output the final cooperative state vector, including the end position of each crane , the rope length , the rope tension and the actual trajectory of the suspended object , which is the final motion result of the multi-machine suspension system.

[0014] Preferably, the "global-local-cooperative" three-level obstacle avoidance planning framework includes: global layer, local layer and cooperative layer. The global layer is used to generate an optimal trajectory that satisfies the multi-machine cooperative constraint using a global obstacle avoidance algorithm; a local layer for dealing with dynamic obstacles by dynamic obstacle avoidance strategy; a coordination layer for ensuring the coordination of multi-machine motion by adjusting the length of the rope and the position of the end of the crane.

[0015] Preferably, the obstacle avoidance module comprises a modeling unit, a calculation unit, a generation unit and a planning unit. The modeling unit is used for abstracting the tensioned rope as a spatial vector, regarding the end of the crane and the suspended object as rigid bodies, and embedding multi-machine coordination constraints based on the kinematics-dynamics coupling characteristics. The calculation unit is used for constructing a rope vector-rigid body hybrid model, fusing the rope length, the crane workspace and the obstacle geometric constraints by a convex optimization + semi-definite programming algorithm, and calculating the collision-free feasible region. The generation unit is used for designing the objective function of the suspension system, solving the multi-objective optimization problem by using an intelligent optimization algorithm, generating the initial global trajectory of the suspended object, and discretizing the initial global trajectory into time sequence sub-targets. The planning unit is used for embedding a global-local-coordination three-level planning framework based on the initial global trajectory of the suspended object: for the spatial characteristics of the rope vector, the vector field method is used to realize the rope obstacle avoidance by the vector constraint obstacle avoidance strategy; for the virtual formation configuration of the crane, a space-time coordination model is constructed and the time sequence and spatial trajectory are optimized by the space-time parallel coordination strategy; for the force-position coupling characteristics of the system, a force-position coordination model is designed and the motion planning is refined by the hierarchical search-step optimization strategy, and finally the obstacle avoidance planning results covering the rope, the end of the crane and the hybrid driving mode are output.

[0016] Compared with the prior art, the present application has the following beneficial effects: (1) The kinematics-dynamics coupling model of three types of suspension systems (rope / end / hybrid driving) is constructed. The closed loop vector method and the force screw balance equation are used to reveal the coupling relationship between the motion parameters and the rope tension, and a consistency iteration algorithm is designed to reduce the complexity of the solution, thereby providing theoretical constraints and calculation basis for obstacle avoidance planning.

[0017] (2) The vector-rigid body hybrid model is established, and the obstacle avoidance is converted into a multi-objective optimization problem of a multi-vector-multi-rigid body system. A three-level framework of "global planning-local adjustment-coordination consistency" is designed, the collision-free feasible region is solved by convex optimization, the space-time coordination and safety constraints are integrated, and a unified solution method is formed.

[0018] In summary, through the vector-rigid body coupling modeling and the three-level planning framework, the dynamics constraints and the coordinated obstacle avoidance planning problem of the multi-machine suspension configuration are solved. BRIEF DESCRIPTION OF DRAWINGS

[0019] In order to more clearly illustrate the technical solutions of the present application, the following briefly introduces the drawings needed to be used in the embodiments, obviously, the drawings described in the following embodiments are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without any creative labor.

[0020] Figure 1 For the embodiment of the present application, the flowchart of the multi-machine suspension system obstacle avoidance planning method based on the multi-level collaborative planning framework is shown. Figure 2 For the embodiment of the present application, the flowchart of the multi-machine coupling model solving is shown. Figure 3 For the embodiment of the present application, the three-level planning framework of the suspension system is shown. DETAILED DESCRIPTION

[0021] The technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application, obviously, the described embodiments are only some embodiments of the present application, not all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without any creative labor are within the protection scope of the present application.

[0022] In order to make the above-mentioned purposes, features and advantages of the present application more obvious and easy to understand, the present application will be further described in detail below with reference to the drawings and specific embodiments.

[0023] Embodiment one As shown in the figure, the present application provides a multi-machine suspension system obstacle avoidance planning method based on a multi-level collaborative planning framework, which comprises: Figure 1 Based on the spatial configuration of the suspension system, a multi-machine coupling model containing kinematic coupling and dynamic coupling is established; Based on the multi-machine coupling model containing kinematic coupling and dynamic coupling, the rope length, tension, and the position of the end of the crane and the suspended object of the multi-machine suspension system are obtained; Based on the structural characteristics of the suspension system, a three-level obstacle avoidance planning framework of "global-local-collaboration" is constructed; Based on the three-level obstacle avoidance planning framework of "global-local-collaboration", three-dimensional joint obstacle avoidance of the suspended object, the rope and the end of the crane is realized. Specific implementation process:

[0024] ​In multi-crane suspension systems, the positions of the crane ends are usually variable because they need to work together to adjust the position and attitude of the suspended object. In some cases, the positions of the crane ends may be fixed, such as aerial work (building exterior maintenance), underground work (oil and mine exploitation), and mountain rescue. According to the driving method, fixed-base multi-crane suspension systems are divided into three types: (1) Rope-driven multi-crane suspension system: the position and attitude of the suspended object are adjusted by changing the length of the rope, which is practical and accurate.

[0025] (2) End-driven multi-crane suspension system: the position of the suspended object is changed by adjusting the position of the crane end itself while keeping the length of the rope constant, which is relatively simple and intuitive.

[0026] (3) Hybrid-driven multi-crane suspension system: a method of adjusting both the length of the rope and the position of the crane end is used to achieve comprehensive control of the position and attitude of the suspended object, taking into account the advantages of the first two methods.

[0027] Kinematic coupling analysis: For a multi-crane suspension system, the position of the crane end is uniquely determined by the position of the suspended object and the unit vector of the rope : where is the transformation matrix of the coordinate system relative to , is the position of the connection point between the suspended object and the rope in , and is the length of the rope.

[0028] As can be seen from equation (1), there is a coupling relationship between the position of the crane end, the length of the rope, and the position of the suspended object in the suspension system. When one crane adjusts its position, the other cranes will move cooperatively through the rope constraint, forming a coupling effect like "pulling one hair and moving the whole body". Taking the first rope as an example, its length change rate k is: Equation (2) shows the coupling relationship between the length change rate of the rope and the end velocity of the crane , the velocity of the suspended object . The relative motion between the crane end and the suspended object directly affects the tension state of the rope.

[0029] From the perspective of driving method, for a rope-driven system, the length of the rope ​​For control input, the end-effector position of the crane is given by equation (1). In the end-driven mode, the rope must satisfy the constraint of constant length, i.e. where, is the connection point of the rope and the suspended object, is the vector of the rope connecting the crane and the suspended object. The hybrid-driven mode requires the simultaneous optimization of and , which reflects the deep coupling of the rope constraint and the driving strategy.

[0030] In summary, multiple cranes are connected to the same object through ropes, and the position adjustment of any crane will affect the motion constraints of other cranes through the ropes, forming a strong coupling relationship. For example, the change in the end position of a crane will change the length and direction of the corresponding rope, and then cause the change in the pose of the suspended object, forcing other cranes to adjust their positions synchronously to maintain the system configuration. This coupling effect does not exist in traditional single robot systems, and it is an inherent kinematic characteristic of multi-crane suspension systems. Through kinematic coupling analysis, the design of multi-crane coordination algorithms can be guided, and the coupling relationship can be used to adjust the motion of multiple cranes simultaneously to avoid the imbalance of the suspended object caused by single crane adjustment.

[0031] Dynamic coupling analysis: In a multi-crane suspension system, kinematic coupling describes the geometric relationship between the crane end, the rope, and the suspended object, while dynamic coupling reveals the inherent relationship between force and motion. The system must satisfy the force and torque balance equations. These equations not only reflect the driving effect of rope tension on object motion, but also reflect the dynamic coupling effect between cranes through the rope, i.e. the motion change of a single crane will affect the force state and motion trajectory of other cranes through tension transmission. The dynamic coupling relationship is reflected through the following equations: where, and are the velocity and angular velocity vectors of the suspended object, respectively, is the rope tension vector, is the gravity acceleration vector, is the vector between the center of mass of the suspended object and the connection point of the rope, is the number of cranes, is the mass of the suspended object, is the moment of inertia.

[0032] From equation (3), it can be seen that the dynamic coupling mainly reflects the distribution and transmission of the suspended object's gravity among multiple cranes through the ropes. The gravity of the suspended object is balanced by the tension of all the ropes, forming a coupling relationship between gravity and tension. Specifically, the tension of each rope depends not only on its own length and direction, but also on the changes in the tension of other ropes: when a crane adjusts its position, causing the length of its corresponding rope to change, the tension of that rope changes, which in turn triggers a redistribution of tension in other ropes to maintain the overall force balance of the multi-crane suspension system.

[0033] In summary, the coupling of kinematics and dynamics manifests as a tension-pose coupling: the distribution of rope tension and the pose of the suspended object (the end of the crane) influence each other. On the one hand, the size and direction of the tension directly determine the force state of the suspended object, and unbalanced tension can cause the suspended object to lose stability. On the other hand, changes in the pose of the suspended object change the geometric constraints of the ropes, which in turn trigger a redistribution of tension. For example, when the suspended object undergoes a small displacement, the force direction of each rope changes, and the tension distribution adjusts accordingly. This coupling has nonlinear characteristics, increasing the difficulty of control.

[0034] System coupling characteristic analysis and solution: The coupling characteristics of the multi-crane suspension system arise from mechanical connections, forming a "motion constraint-dynamic response" closed loop, and any component change will trigger a chain reaction: 1. Crane-rope coupling: kinematics: the position of the crane end directly determines the vector direction and length of the rope. Dynamics: rope tension acts on the end of the crane, interfering with the motion trajectory; adjustment of a single crane will affect other cranes through the tension chain. 2. Rope-suspended object coupling: statics: the vector sum of the tension of each rope needs to balance the weight of the object, and uneven tension causes the object's attitude to deviate. Dynamics: dynamic changes in tension directly drive the object's acceleration; rope elastic deformation causes tension fluctuations and energy conversion between the object's swing. 3. Motion coupling between cranes: force transmission: any crane position adjustment will change the distribution of rope tension, forcing other cranes to adjust simultaneously to maintain force balance. Motion coordination: the positions of multiple crane ends need to satisfy geometric constraints to avoid rope interference.

[0035] Multi-crane coupling modeling and characteristic analysis: In the multi-crane suspension system, cranes, ropes, and suspended objects are deeply coupled through kinematic geometric constraints and dynamic force balance equations. A unified model that integrates both is needed to accurately describe the interaction between system components. The motion of a single crane is not only driven by its own control input, but also interacts with the motion states of other cranes and suspended objects through the tension chain: kinematics determines the pose geometric relationship, and dynamics dominates the transmission of force and acceleration. The coupling of the two is the root of the system's strong nonlinear characteristics. By accurately modeling the coupling relationship between cranes, the mutual influence between them can be accurately reflected in the obstacle avoidance planning process.

[0036] The cranes, the ropes and the suspended object are related by kinematic and dynamic equations - the end position of the crane determines the direction of the rope vector, and the rope tension affects the motion of the suspended object. Based on the moving platform-stationary platform architecture, a multi-coupling model integrating kinematics and dynamics is constructed. The end positions of the three cranes are defined as the moving platform, and the connection points of the three ropes and the suspended object are defined as the stationary platform. 、 and 、 and

[0037] A coordinate system is established at the center of gravity of the moving platform , and a coordinate system is established at the center of gravity of the stationary platform . is the vector from to the end of the crane, is the vector from to the connection point of the rope and the stationary platform, and where is the position vector of the stationary platform relative to the moving platform in , is the position vector of the stationary platform relative to the inertial coordinate system in , and is the position vector of the inertial coordinate system relative to the moving platform in . The subscripts in equation (5) have the same meaning.

[0038] In , the rope vector is: where is a known parameter. and are determined using equations (4) and (5), and

[0039] ​​​Core coupling mechanism: rope length / tension and platform pose affect each other, forming a closed loop of "pose change → tension adjustment → pose re-adjustment". 1. Forward influence (tension → pose): the size / direction of the rope tension directly determines the force state of the suspended object, sudden changes in tension break the force balance, causing the object to translate or tilt (e.g. a crane speeding up too quickly causes the object to tilt to that side), uneven tension causes attitude instability and rope entanglement risk. 2. Reverse influence (pose → tension): changes in the object's pose change the direction and length of the rope's force, forcing the tension to redistribute. When avoiding obstacles, the crane adjusts its position → the tension chain changes → the object's pose changes, forming a strong coupling. 3. Solution and optimization: given the desired trajectory of the static platform, solve for the dynamic platform pose, optimize the crane's end position, and calculate the tension in real time to ensure that the rope remains taut under gravity. Multiple machines need to work together to optimize the algorithm, and obstacle avoidance and pose stability need to be achieved simultaneously.

[0040] Step-by-step iterative collaborative solution strategy design: The step-by-step iterative collaborative solution strategy breaks down the complex global optimization problem into multiple local sub-problems, achieving collaborative solution of rope length, tension, crane end position, and suspended object position. The calculus idea in mathematical analysis is introduced into the coupling analysis of the suspension system, and the iterative method is used to solve the multi-machine coupling model. The solution process is shown in Figure 2 , and the solution steps are as follows: (1) First, perform initialization operations, input the desired trajectory of the suspended object in the work time domain , and set the total number of iterations and the convergence threshold; then discretize the total work duration into equally spaced time steps , generate the time sequence , and define the multi-machine collaborative state vector (which contains the end position of the th crane, rope length, tension, and suspended object position). Based on the desired trajectory of the suspended object, use inverse kinematics to map to the initial position of each crane end , and calculate the initial rope tension , verify , and complete the initial value setting for iteration, entering the loop solution in time step order.

[0041] (2) At each time step, each crane independently calculates the end position based on the current collaborative state vector through the inverse kinematics equation (which must satisfy the crane workspace constraints, i.e. the crane's reachable space); combined with the geometric constraint equation to calculate the rope length , and then solve the rope tension , the cooperative state vector is updated synchronously . After that, cooperative constraint checking is performed: time synchronization constraint, space obstacle avoidance constraint, force balance constraint, and tension non-negative constraint, etc.

[0042] (3) If the solution satisfies all cooperative constraints, the cooperative state vector of the current time step is stored in the global database; if the constraints are not satisfied, a correction is applied to the end position of the conflicting crane, the rope length and tension are recalculated, and the constraints are verified again. After completing the constraint checking, the global cooperative state vector is generated and used as the initial value of the iteration at .

[0043] (4) It is determined whether the current time step is less than the total number of steps . If , the time step continues to loop iteration; if , the final cooperative state vector is output, including the end position of each crane , rope length , rope tension , and actual trajectory of the suspended object , i.e., the final motion result of the multi-crane suspension system.

[0044] The integration of the step-by-step iterative cooperative solving strategy and the multi-crane coupling model is the key to achieving efficient cooperation of the multi-crane suspension system. The multi-crane coupling model describes the kinematic and dynamic relationships between the cranes, ropes, and suspended objects, while the step-by-step iterative cooperative solving strategy provides a feasible method for solving the multi-crane coupling model. In the integration process, the global constraints in the multi-crane coupling model are first converted into boundary conditions for local optimization of each crane, and then the dynamic updating of model parameters is achieved through iterative calculation to ensure that the motion of each crane is consistent with the overall state of the system.

[0045] Multi-level cooperative obstacle avoidance planning framework construction: Multi-crane suspension system transmits the motion and force of cranes to the suspended object through multiple ropes. Collision may occur between any two of the crane, rope, suspended object and obstacle, making the obstacle avoidance planning different from the traditional single rigid body obstacle avoidance planning. On the one hand, the obstacle avoidance planning of multi-crane suspension system needs to consider the optimality of global trajectory, the adaptability of local dynamic environment and the coordination of multi-crane obstacle avoidance. Therefore, a three-level planning framework of global-local-coordination is proposed. The global planning algorithm is responsible for generating collision-free motion trajectory, and the local planning algorithm optimizes and adjusts the end position of the crane or the length of the rope, so as to achieve safe and efficient obstacle avoidance in complex environment. On the other hand, each crane in the multi-crane suspension system has independence, and each crane is connected through the rope and the same suspended object. The kinematic and dynamic coupling characteristics make the system have integrity. Therefore, a multi-vector-multi-rigid body model obstacle avoidance planning framework of multi-crane suspension system is constructed, and through the hierarchical decoupling and collaborative optimization mechanism, the coordinated planning of the suspended object, the crane and the rope is realized.

[0046] In summary, the multi-level coordination of obstacle avoidance planning of fixed-base multi-crane suspension system mainly reflects in four dimensions: (1) According to the driving mode, it is divided into rope driving, crane end driving and hybrid driving three levels; (2) According to the type of obstacle, it is divided into static obstacle and dynamic obstacle two levels; (3) According to the planning method, it is divided into global planning, local planning and coordination planning three levels; (4) According to the obstacle avoidance object, it is divided into suspended object obstacle avoidance, rope obstacle avoidance and crane obstacle avoidance three levels.

[0047] The global-local-coordination three-level planning framework is shown as Figure 3 In the obstacle avoidance planning of multi-crane suspension system, global obstacle avoidance planning is the key to deal with complex coupled constraints. It not only provides a unified time and space reference for multi-crane motion, but also ensures the feasibility of the generated trajectory on the physical level by integrating system kinematics and dynamics constraints. Although the actual environment may contain dynamic obstacles, the basic trajectory generated by global planning is still an important reference for local dynamic adjustment. It reduces the computational burden of local planning by avoiding static obstacle dense areas in advance, and provides an initial coordination scheme for multi-crane coordination. Without global planning, it may fall into the local optimal trap, leading to multi-crane motion conflict or system instability. Therefore, global planning is the basis for multi-crane suspension system to achieve safe and efficient hoisting.

[0048] ​For multi-machine suspension system, the local dynamic obstacle avoidance method quickly generates adjustment scheme by dynamically updating obstacle position combined with efficient optimization algorithm, ensuring the safety of the system in emergency. The combination of local planning and global planning forms a "rough planning-fine adjustment" planning framework: global planning provides a stable basic framework, local planning handles real-time disturbance, and both are indispensable. Especially in multi-machine cooperation, local planning also needs to consider the motion coordination between cranes, for example, when a crane slows down to avoid obstacles, local planning needs to adjust the speed of adjacent cranes synchronously to avoid sudden changes in rope tension caused by excessive speed difference. Therefore, local obstacle avoidance planning is a key method for multi-machine suspension system to achieve reliable operation in dynamic environment.

[0049] Since the global planning cannot well avoid moving obstacles in the environment, the trajectory of the local planning does not satisfy the global optimality. Therefore, the deficiencies of the global planning and local planning algorithms are improved to meet the practical application requirements of the multi-machine suspension system. The optimal or better trajectory is generated in the known environment by using the global planning algorithm, and then the real-time adjustment is performed by using the local planning algorithm, solving the problems of global planning unable to avoid dynamic obstacles and local planning trajectory easily falling into local optimum. For this purpose, a three-level planning framework of global-local-coordination is proposed, and the three-level planning framework realizes multi-machine cooperative obstacle avoidance through hierarchical interaction: the global layer generates the optimal basic trajectory based on the static environment, providing the overall motion framework for the system; the local layer detects dynamic obstacles in real time, generates local adjustment amount through intelligent optimization algorithm, and corrects the basic trajectory to avoid sudden obstacles; the coordination layer realizes the synchronization of multi-machine states through the information interaction mechanism, ensures that the motion speed and position deviation of each crane are maintained within the allowed range, and avoids secondary collision. When the three-level planning framework is executed, the basic trajectory is generated by the global planning, the trajectory is adjusted by detecting dynamic obstacles in real time, and finally the coordination layer ensures the consistency of multi-machine action. The planning framework decomposes the high-dimensional coupled problem into three sub-problems of trajectory generation, dynamic obstacle avoidance and multi-machine coordination, which not only guarantees the global optimality, but also improves the adaptability to environmental changes.

[0050] In the planning framework, global planning is responsible for generating a collision-free trajectory, while local planning generates a specific local motion trajectory considering dynamic obstacle factors based on the global trajectory, ensuring that the suspended object can safely and effectively reach the target position. This decoupling method reduces the planning complexity while ensuring trajectory feasibility and system stability. The three-level planning framework combines global and local planning, ensuring the global optimality and stability of multi-machine motion, and giving the system the agility to respond to dynamic changes, providing a complete solution for multi-machine suspension obstacle avoidance in complex environments.

[0051] Suspension system obstacle avoidance planning scheme: The structural characteristics of the multi-machine suspension system determine that its obstacle avoidance planning needs to break through the traditional single-rigid-body obstacle avoidance idea: the rope exists rigid constraints as a spatial vector in the tension state, the crane and the suspended object are kinematically constrained as rigid bodies, and the force and position spaces coincide (force balance and position motion are coupled), so force balance, tension constraints and obstacle avoidance safety need to be considered simultaneously. In view of this characteristic, the obstacle avoidance planning framework of the multi-machine suspension system is constructed to realize the coordinated planning of the suspended object trajectory, the crane end motion and the rope vector. The key steps include: (1) Based on the kinematic-dynamic coupling characteristics, the tensioned rope is abstracted as a spatial vector (constraint length and direction), the crane end and the suspended object are regarded as rigid bodies (which need to satisfy the workspace and obstacle avoidance safety distance), and the multi-machine collaborative constraints are embedded to lay the constraint foundation for subsequent obstacle avoidance planning.

[0052] (2) A three-dimensional environmental model of the rope, crane and suspended object is constructed. Through convex optimization + semi-definite programming algorithm, the collision-free feasible region is calculated by integrating the rope length, crane workspace, obstacle geometry and other constraints to ensure that the initial solution meets the physical feasibility and reduces the search range of subsequent optimization.

[0053] (3) The objective function of the suspension system is designed, and intelligent optimization algorithms (such as MGEA, SDBO) are used to solve the multi-objective optimization problem to generate the initial global trajectory of the suspended object, and it is discretized into time sequence sub-targets (trajectory points are divided according to the period) to provide a reference for local obstacle avoidance. Specifically, the optimization model and the objective function design include: The obstacle avoidance planning of the multi-machine suspension system is based on the generated collision-free feasible region to realize global trajectory design and local dynamic adjustment in stages. First, intermediate target points are set in the feasible region, and a global trajectory from the starting point to the ending point is generated by heuristic algorithm to ensure that the points on the trajectory are located within the feasible region and meet the multi-machine collaborative constraints. Then, for dynamic environment, local planning strategy (such as IAPF algorithm) is used to adjust the trajectory in real time to ensure that it avoids dynamic obstacles while not exceeding the boundary of the feasible region.

[0054] The idea of obstacle avoidance planning for the multi-machine suspension system is to transform the motion coordination problem of the suspended object, rope and crane end into a multi-objective optimization problem, so its obstacle avoidance planning includes problem definition, objective function and optimization algorithm, and the core is to construct an objective function that includes trajectory quality and constraint satisfaction. Typical optimization objectives include path length, trajectory smoothness, tension balance, etc., which are combined into a comprehensive objective function by weighted summation. The constraint conditions are embedded into the optimization model as inequality constraints using the penalty function method, and the optimal trajectory is solved by convex optimization or nonlinear programming algorithm.

[0055] In the multi-machine suspension system, the availability and safety of the system are the main targets, and multiple optimization objectives are integrated, including the trajectory length of the suspended object , the height of the suspended object , the length of the rope , the rate of change of the rope tension , the curvature of the crane end trajectory and the penalty function , the optimal trajectory is solved in the solution set of the motion trajectory. The objective function comprehensively evaluates the advantages and disadvantages of the solution by integrating multiple objectives, avoiding one-sidedness caused by a single objective. The objective function established is as follows: In the formula, is the weight coefficient of each optimization objective.

[0056] In the formula, represents the coordinates of the discrete points of the suspended object, represents the total number of discrete points.

[0057] In the formula, represents the coordinates of the discrete points, represents the coordinates of the reference plane.

[0058] In formula (11), is the motion time.

[0059] In the formula, the curvature radius of the crane end trajectory is , the distance between the adjacent two points is , and the change of the included angle between the connecting line of the adjacent two points and the tangent at the point on the trajectory is .

[0060] In the formula, is the penalty factor, represents the number of collisions between the motion trajectory and the obstacle.

[0061] The multi-objective weight needs to be determined comprehensively combining the engineering safety and efficiency requirements. The Analytic Hierarchy Process (AHP) can integrate field experience through expert scoring and reduce subjectivity through consistency check. The weight in formula (7) is determined by the following specific steps: (1) Construction of the judgment matrix For example, in the mixed driving (static) working condition of the rope and the end of the crane, 6 targets are scored by expert evaluation to build a judgment matrix A.

[0062] (2) Weight calculation Calculate the maximum eigenvalue of the judgment matrix and the corresponding eigenvector, and obtain the weight vector after normalization , wherein the trajectory length weight and the collision penalty weight .

[0063] (3) Consistency check Calculate the consistency index: Find the random consistency index: ( by table lookup); Calculate the consistency ratio: Through the test, the rationality of the weight distribution is ensured.

[0064] Therefore, the objective function expression is: The formula embodies the principle of "efficiency first, safety bottom".

[0065] For different application scenarios, the obstacle avoidance strategy needs to be designed hierarchically (embedded global-local-collaborative three-level planning framework): according to the spatial characteristics of the rope vector, the vector field method is used to realize rope obstacle avoidance through vector constraint obstacle avoidance strategy; for the virtual formation configuration of the crane, a space-time collaborative model is built and a space-time parallel collaborative strategy is used to optimize the time sequence and spatial trajectory; for the force-position coupling characteristics of the system, a force-position collaborative model is designed and a hierarchical search-step optimization strategy is used to refine the motion planning, and finally the obstacle avoidance planning results covering the rope, the end of the crane and the mixed driving mode are output.

[0066] The hierarchical obstacle avoidance method of the multi-machine suspension system obstacle avoidance planning includes a global-local-collaborative three-level planning framework, considers the overall planning of the suspended objects, cranes and ropes in the multi-machine suspension system, and uses intelligent optimization algorithms and collaborative obstacle avoidance strategies to handle the interaction between multiple rigid bodies, ensuring the generation of collision-free trajectories while ensuring the stability and efficiency of the system.

[0067] Embodiment two The application also provides a multi-machine suspension system obstacle avoidance planning system based on a multi-level collaborative planning framework, which is used to implement the method of embodiment one, and the system comprises a first construction module, a decoupling module, a second construction module and an obstacle avoidance module. The first building module is used to establish a multi-machine coupling model that includes kinematic coupling and dynamic coupling based on the spatial configuration of the suspension system. The decoupling module is used to obtain the rope length, tension, crane end position and suspended object position of a multi-machine suspension system based on a multi-machine coupling model that includes kinematic coupling and dynamic coupling. The second building module is used to construct a three-level obstacle avoidance planning framework of "global-local-cooperative" based on the structural characteristics of the suspension system; The obstacle avoidance module is used to achieve three-dimensional joint obstacle avoidance of suspended objects, ropes and crane ends based on a three-level obstacle avoidance planning framework of "global-local-cooperative".

[0068] In this embodiment, the first construction module includes: a partitioning unit, a kinematic unit, a dynamic unit, and an integration unit; The division unit is used to determine the typical configuration of the suspension system and classify the typical configuration of the suspension system into three types of systems based on the drive mechanism: rope drive, crane end drive, and hybrid drive. Kinematic unit, used to establish the kinematic geometric constraint equations of three types of systems using the closed-loop vector method; The dynamic unit is used to establish the dynamic force balance equations for three types of systems based on the force spinor balance equation. The integration unit is used to integrate kinematic geometric constraint equations and dynamic force balance equations to form a multi-machine coupled model.

[0069] In this embodiment, based on a multi-machine coupling model that includes kinematic coupling and dynamic coupling, the process of obtaining the rope length, tension, and the positions of the crane end and the suspended object in a multi-machine suspension system includes: Input the desired trajectory of the suspended object in the operation time domain. And set the total number of iterations. With convergence threshold; total job duration Discretize into equidistant time steps Generate time series And define the multi-machine cooperative state vector. , including the The end position of the platform crane Rope length ,tension and the position of the suspended object Based on the desired trajectory of the suspended object, inverse kinematics is used to... Mapped to the initial position of each crane end The initial rope tension was calculated using the dynamic equations. ,verify After setting the initial values ​​for the iteration, the loop is entered in the order of time steps to solve the problem; Within each time step, each crane operates based on its current cooperative state vector. The end position can be independently calculated using inverse kinematic equations. ; Calculate the rope length using geometric constraint equations Then, the rope tension is solved using the dynamic equations. Synchronously update the cooperative state vector Perform collaborative constraint checks: time synchronization constraints, spatial obstacle avoidance constraints, force balance constraints, and tension non-negativity constraints; If the solution satisfies all cooperative constraints, the cooperative state vector at the current time step will be... Store in the global database; if constraints are not met, apply a correction to the end position of the conflicting crane. Recalculate the rope length With tension The constraints are verified again, and after the constraint check is completed, a global cooperative state vector is generated. and take it as Initial values ​​for iteration at time step; Determine the current time step Is it less than the total number of steps? ,like Then return to the time step and continue the loop iteration; if Then the final cooperative state vector is output, including the position of each crane end. Rope length Rope tension and the actual trajectory of the suspended object That is, the final motion result of the multi-machine suspension system.

[0070] In this embodiment, the "global-local-cooperative" three-level obstacle avoidance planning framework includes: a global layer, a local layer, and a cooperative layer; The global layer is used to generate the optimal trajectory that satisfies the multi-machine cooperative constraints using a global obstacle avoidance algorithm. The local layer is used to deal with dynamic obstacles through dynamic obstacle avoidance strategies. The coordination layer is used to ensure the coordination of multiple machine movements by adjusting the rope length and the position of the crane end.

[0071] In this embodiment, the obstacle avoidance module includes: a modeling unit, a calculation unit, a generation unit, and a planning unit; The modeling unit is used to abstract the tension rope into a spatial vector based on the kinematic-dynamic coupling characteristics, treat the crane end and the suspended object as rigid bodies, and embed multi-machine collaborative constraints. The computational unit is used to construct a hybrid model of rope vector-rigid body. It calculates the collision-free feasible region by integrating rope length, crane workspace, and obstacle geometric constraints through convex optimization and semidefinite programming algorithms. A generating unit is configured to design a target function of the suspension system, solve a multi-objective optimization problem by using an intelligent optimization algorithm, and generate an initial global trajectory of the suspended object; A planning unit is configured to embed a global-local-collaborative three-level planning framework based on the initial global trajectory of the suspended object: for the spatial characteristics of the rope vector, a vector field method is used to realize rope obstacle avoidance through a vector constraint obstacle avoidance strategy; for the virtual formation configuration of the crane, a space-time collaborative model is constructed and a space-time parallel collaborative strategy is used to optimize the time sequence and spatial trajectory; for the force-position coupling characteristics of the system, a force-position collaborative model is designed and a hierarchical search-step optimization strategy is used to refine the motion planning, and finally the obstacle avoidance planning results covering the rope, the end of the crane and the hybrid driving mode are output.

[0072] The above-described embodiments are merely descriptions of the preferred modes of the present application and are not intended to limit the scope of the present application. Various modifications and improvements to the technical solutions of the present application made by those of ordinary skill in the art without departing from the design spirit of the present application shall fall within the scope of protection of the present application as defined by the claims.

Claims

1. A multi-machine suspension system obstacle avoidance planning method based on a multi-level cooperative planning framework, characterized in that, The method comprises: Based on the spatial configuration of the suspension system, a multi-machine coupling model containing kinematic coupling and dynamic coupling is established; Based on the multi-machine coupling model containing kinematic coupling and dynamic coupling, the length, tension, and position of the rope and the end of the crane of the multi-machine suspension system are obtained; Based on the structural characteristics of the suspension system, a three-level obstacle avoidance planning framework of "global-local-collaboration" is constructed; Based on the three-level obstacle avoidance planning framework of "global-local-collaboration", three-dimensional joint obstacle avoidance of the suspended object, the rope, and the end of the crane is realized.

2. The method of claim 1, wherein, The method for establishing a multi-machine coupling model containing kinematic coupling and dynamic coupling based on the spatial configuration of the suspension system comprises: Determine the typical configuration of the suspension system, and divide the typical configuration of the suspension system into three types of systems, i.e., rope-driven, end-of-crane-driven, and hybrid-driven, according to the driving mechanism; Use the closed-loop vector method to establish the kinematic geometric constraint equations of the three types of systems; Based on the force spinor balance equation, the dynamic force balance equation of the three types of systems is established; Integrate the kinematic geometric constraint equations and the dynamic force balance equations to form a multi-machine coupling model.

3. The method of claim 1, wherein, The method for obtaining the length, tension, and position of the rope and the end of the crane of the multi-machine suspension system based on the multi-machine coupling model containing kinematic coupling and dynamic coupling comprises: Inputting desired trajectory of suspended object within operation time domain , and setting total iteration times , and setting convergence threshold; setting total operation time , and discretizing into equidistant time steps , and generating time series ; and defining multi-machine cooperative state vector , containing end position , rope length , tension , and suspended object position of the first crane; based on desired trajectory of suspended object, mapping to initial position of each crane end by inverse kinematics , and calculating initial rope tension by dynamics equation , verifying , and completing initial value setting, entering loop solving in time step order Within each time step, each crane operates based on its current cooperative state vector. The end position can be independently calculated using inverse kinematic equations. ; Calculate the rope length using geometric constraint equations Then, the rope tension is solved using the dynamic equations. Synchronously update the cooperative state vector Perform collaborative constraint checks: time synchronization constraints, spatial obstacle avoidance constraints, force balance constraints, and tension non-negativity constraints; If the solution satisfies all cooperative constraints, the cooperative state vector at the current time step will be... Store in the global database; if constraints are not met, apply a correction to the end position of the conflicting crane. Recalculate the rope length With tension The constraints are verified again, and after the constraint check is completed, a global cooperative state vector is generated. and take it as Initial values ​​for iteration at time step; determine if the current time step is less than the total number of steps , if , return to the time step and continue the loop iteration; if , output the final cooperative state vector, including the end-of-cable position , cable length , cable tension , and actual trajectory of the suspended object , i.e., the final motion results of the multi-crane suspended system.

4. The method of claim 1, wherein, The three-level obstacle avoidance planning framework of "global-local-collaboration" comprises a global layer, a local layer, and a collaboration layer; The global layer is used to generate an optimal trajectory that satisfies the multi-machine collaboration constraint by using a global obstacle avoidance algorithm; The local layer is used to deal with dynamic obstacles through a dynamic obstacle avoidance strategy; The collaboration layer is used to ensure the collaboration of multi-machine motion by adjusting the length of the rope and the position of the end of the crane.

5. The method of claim 1, wherein, The method for realizing three-dimensional joint obstacle avoidance of the suspended object, the rope, and the end of the crane based on the three-level obstacle avoidance planning framework of "global-local-collaboration" comprises: Based on the kinematic-dynamic coupling characteristics, the tensioned rope is abstracted as a spatial vector, the end of the crane and the suspended object are regarded as rigid bodies, and the multi-machine collaboration constraint is embedded; A rope vector-rigid body hybrid model is constructed, and a collision-free feasible region is calculated by combining the rope length, the crane workspace, and the obstacle geometric constraint through convex optimization + semi-definite programming algorithm; A target function of the suspension system is designed, and an intelligent optimization algorithm is used to solve the multi-objective optimization problem to generate an initial global trajectory of the suspended object; Based on the initial global trajectory of the suspended object, the three-level planning framework of global-local-collaboration is embedded: for the spatial characteristics of the rope vector, the vector field method is used to realize rope obstacle avoidance through vector constraint obstacle avoidance strategy; for the virtual formation configuration of the crane, a time-space collaboration model is constructed and a time-space parallel collaboration strategy is used to optimize the time sequence and spatial trajectory; for the force-position coupling characteristics of the system, a force-position collaboration model is designed and a hierarchical search-step optimization strategy is used to refine the motion planning, and finally the obstacle avoidance planning results covering the rope, the end of the crane, and the hybrid driving mode are output.

6. A multi-robot suspension system obstacle avoidance planning system based on a multi-level cooperative planning framework, the system being configured to implement the method of any one of claims 1-5, wherein, The system comprises a first construction module, a decoupling module, a second construction module, and an obstacle avoidance module; The first construction module is used to establish a multi-machine coupling model containing kinematic coupling and dynamic coupling based on the spatial configuration of the suspension system; The decoupling module is configured to obtain rope length, tension, crane end and suspended object position of the multi-machine suspension system based on a multi-machine coupling model containing kinematic coupling and dynamic coupling. The second construction module is configured to construct a "global-local-collaborative" three-level obstacle avoidance planning framework based on structural characteristic features of the suspension system. The obstacle avoidance module is configured to realize three-dimensional joint obstacle avoidance of the suspended object, the rope and the crane end based on the "global-local-collaborative" three-level obstacle avoidance planning framework.

7. The system of claim 6, wherein, The first construction module comprises a division unit, a kinematics unit, a dynamics unit and an integration unit. The division unit is configured to determine typical configurations of the suspension system, and divide the typical configurations of the suspension system into three types of systems, i.e., rope driving, crane end driving and hybrid driving, according to driving mechanisms. The kinematics unit is configured to establish kinematic geometric constraint equations of the three types of systems by using a closed-loop vector method. The dynamics unit is configured to establish dynamic force balance equations of the three types of systems based on force screw balance equations. The integration unit is configured to integrate the kinematic geometric constraint equations and the dynamic force balance equations to form the multi-machine coupling model.

8. The system of claim 6, wherein, The process of obtaining rope length, tension, crane end and suspended object position of the multi-machine suspension system based on the multi-machine coupling model containing kinematic coupling and dynamic coupling comprises: Input the desired trajectory of the suspended object in the operation time domain. And set the total number of iterations. With convergence threshold; total job duration Discretize into equidistant time steps Generate time series And define the multi-machine cooperative state vector. , including the The end position of the platform crane Rope length ,tension and the position of the suspended object Based on the desired trajectory of the suspended object, inverse kinematics is used to... Mapped to the initial position of each crane end The initial rope tension was calculated using the dynamic equations. ,verify After setting the initial values ​​for the iteration, the loop is entered in the order of time steps to solve the problem; Within each time step, each crane operates based on its current cooperative state vector. The end position can be independently calculated using inverse kinematic equations. ; Calculate the rope length using geometric constraint equations Then, the rope tension is solved using the dynamic equations. Synchronously update the cooperative state vector Perform collaborative constraint checks: time synchronization constraints, spatial obstacle avoidance constraints, force balance constraints, and tension non-negativity constraints; If the solution satisfies all cooperative constraints, the cooperative state vector at the current time step will be... Store in the global database; if constraints are not met, apply a correction to the end position of the conflicting crane. Recalculate the rope length With tension The constraints are verified again, and after the constraint check is completed, a global cooperative state vector is generated. and take it as Initial values ​​for iteration at time step; determine if the current time step is less than the total number of steps , if then return the time step to continue the loop iteration; if , then output the final cooperative state vector, including the end-of-cable position , cable length , cable tension , and actual trajectory of the suspended object , i.e., the final motion results of the multi-crane suspended system.

9. The system of claim 6, wherein, The "global-local-collaborative" three-level obstacle avoidance planning framework comprises a global layer, a local layer and a collaborative layer. The global layer is configured to generate an optimal trajectory satisfying multi-machine collaborative constraints by using a global obstacle avoidance algorithm. The local layer is configured to cope with dynamic obstacles by using a dynamic obstacle avoidance strategy. The collaborative layer is configured to ensure the collaboration of multi-machine movement by adjusting rope length and crane end position.

10. The system of claim 6, wherein, The obstacle avoidance module comprises a modeling unit, a calculation unit, a generation unit and a planning unit. The modeling unit is configured to abstract a tensioned rope as a spatial vector, a crane end and a suspended object as rigid bodies based on kinematic-dynamic coupling characteristics, and embed multi-machine collaborative constraints. The calculation unit is configured to construct a rope vector-rigid body hybrid model, and calculate a collision-free feasible region by fusing rope length, crane workspace and obstacle geometric constraints through a convex optimization + semi-definite programming algorithm. The generation unit is configured to design an objective function of the suspension system, and solve a multi-objective optimization problem by using an intelligent optimization algorithm to generate an initial global trajectory of the suspended object. The planning unit is configured to embed a global-local-collaborative three-level planning framework based on the initial global trajectory of the suspended object: a vector constraint obstacle avoidance strategy is used to realize rope obstacle avoidance based on spatial characteristics of the rope vector; a time-space collaborative model is constructed and a time-space parallel collaborative strategy is used to optimize time sequence and spatial trajectory for crane virtual formation configuration; a force-position collaborative model is designed and a hierarchical search-step optimization strategy is used to refine motion planning for force-position coupling characteristics of the system, and finally an obstacle avoidance planning result covering the rope, the crane end and the hybrid driving mode is output.

Images