Task scheduling method for towed multi-AGV system based on multi-layer unidirectional graph

Abstract

The present invention discloses a method for task scheduling of a trailer-type multi-AGV system based on a multi-layer unidirectional graph, which belongs to the technical field of production scheduling. The present invention combines the layout and geometric constraints of the physical space, considers the characteristics of the trailer-type multi-AGV system when performing material distribution, constructs a multi-layer unidirectional graph to ensure the conflict-free operation of the trailer-type multi-AGV system, models the uncertainty of the distribution time through the translation gamma distribution, and establishes a task scheduling model to minimize the early lag penalty for the trailer-type multi-AGV system to complete all distribution tasks, thereby obtaining the task execution route assigned to each trailer-type AGV. The present invention solves the task scheduling decision-making problem of the trailer-type multi-AGV system, reduces the investment cost of enterprises in the process of intelligent transformation, ensures the coordinated and conflict-free operation of the trailer-type multi-AGV system, ensures the stability and timeliness of material distribution, and can effectively reduce production costs and improve logistics efficiency and production efficiency.

Description

Technical Field

[0001] The invention relates to a task scheduling method for a towed multi-AGV system based on a multi-layer unidirectional graph, belonging to the technical field of production scheduling. Background Art

[0002] As market competition becomes increasingly fierce and customer personalized needs increase, more and more manufacturing companies are gradually adopting personalized customized production models. In order to improve the flexibility of the system and adapt to the needs of personalized customized production, the material distribution system of enterprises gradually adopts multi-AGV (Automated Guided Vehicle) system solutions. Using highly intelligent and flexible AGV as transportation equipment, combined with corresponding intelligent scheduling models and optimization algorithms, the multi-AGV material distribution system has the ability to drive automatically, actively avoid obstacles, and distribute materials in a timely and accurate manner, which can achieve high automation and intelligence in the entire process of material distribution.

[0003] Although the multi-AGV system is developing rapidly and is technically sufficient to support the intelligent upgrading and transformation of the manufacturing industry's material distribution system, traditional enterprises still use traditional manual transportation methods and rely on traditional trailer vehicles to transport materials after considering the high investment cost of purchasing multiple industrial AGVs. In order to promote the upgrading and transformation of manufacturing enterprises, enterprises combine intelligent AGVs with traditional trailer vehicles, using laser-guided AGVs as the front of the vehicle to tow a certain number of trailers to form multi-load trailer AGVs.

[0004] In the trailer-type multi-AGV system, it is necessary to pay attention to the constraints of the workshop environment on the physical properties of the trailer-type AGV. The longer the trailer-type AGV is, the larger the required turning radius is. Limited by the width of the aisle in the production workshop, the maximum length of the trailer-type AGV allowed to pass through different turning points is also different. In addition, the trailer-type AGV is connected or unloaded during the material distribution process to load and unload materials, and its length is constantly changing. Therefore, the trailer-type AGV with dynamically changing length, combined with environmental constraints, and conflict-free path planning has become one of the problems that the trailer-type multi-AGV system needs to solve.

[0005] On the other hand, considering the waiting or lag time in the process of multiple AGVs coordinating with each other and avoiding conflicts, the delivery time between two task points is uncertain, which affects the task scheduling results. Under the condition of multi-AGV collaboration without conflict, considering the time uncertainty, delivering each known task to the corresponding demand point within a non-strictly constrained time window has also become an urgent problem to be solved in the task scheduling of the trailer multi-AGV system. Summary of the invention

[0006] The purpose of the present invention is to provide a method for task scheduling of a trailer-type multi-AGV system based on a multi-layer unidirectional graph. The present invention combines the layout and geometric constraints of the physical space, considers the characteristics of the trailer-type multi-AGV system when performing material distribution, constructs a multi-layer unidirectional graph to ensure the conflict-free operation of the trailer-type multi-AGV system, models the uncertainty of the distribution time through the translation gamma distribution, and establishes a task scheduling model to minimize the early lag penalty for the trailer-type multi-AGV system to complete all distribution tasks, thereby obtaining the task execution route assigned to each trailer-type AGV. The present invention solves the task scheduling decision-making problem of the trailer-type multi-AGV system, reduces the investment cost of enterprises in the process of intelligent transformation, ensures the coordinated and conflict-free operation of the trailer-type multi-AGV system, ensures the stability and timeliness of material distribution, and can effectively reduce production costs and improve logistics efficiency and production efficiency.

[0007] The present invention is achieved through the following specific technical solutions:

[0008] A task scheduling method for a trailer-type multi-AGV system based on a multi-layer unidirectional graph: First, a topological unidirectional map is constructed according to the actual layout of the physical space, and the maximum length table of the trailer-type AGVs that are allowed to turn and pass through each node is determined. On this basis, a multi-layer unidirectional graph is constructed to ensure that the trailer-type AGVs with variable lengths can operate normally, and the conflicts and deadlocks of the trailer-type AGVs are resolved through the waiting strategy, and the distance matrix between nodes is constructed; then, on the basis of the multi-layer unidirectional graph and the distance matrix between nodes, the uncertainty of the delivery time is modeled by the shifted gamma distribution, the uncertainty caused by factors such as the waiting strategy is resolved, a reasonable estimate of the trailer-type AGV delivery time is obtained, and the advance-delay penalty value of material delivery is determined; finally, a task scheduling model is established to minimize the advance-delay penalty for the trailer-type multi-AGV system to complete all delivery tasks, and the task execution route assigned to each trailer-type AGV is obtained.

[0009] A method for scheduling tasks of a towed multi-AGV system based on a multi-layer unidirectional graph of the present invention comprises the following steps:

[0010] Step 1: According to the actual layout of the physical space, a topological one-way map is constructed to determine the maximum length table of the trailer AGVs that are allowed to turn and pass through each node. On this basis, a multi-layer one-way graph is constructed to ensure that the trailer AGVs with variable lengths can operate normally in the system. The conflict and deadlock of the trailer AGVs are resolved through the waiting strategy, and the distance matrix between nodes is constructed;

[0011] Step 1.1: For the layout of the physical space, important locations are abstracted into nodes, represented by v, where the set of all channel intersection nodes is V c , the set of all task requirement nodes is V k , the set of nodes where the warehouse entrance and exit are located is V p, the set of all nodes V = V p ∪V k ∪V c , abstract the road into edges, represented by z, and the set is Z, and construct a topological map to ensure that there is a reachable path between any two road nodes, and each edge allows vehicles to enter and exit normally;

[0012] Step 1.2: Based on the topological map constructed in step 1.1, specify that the direction of each edge is unidirectional, that is, any node v i With adjacent nodes v j The edge z between i,j For a unidirectional edge, construct an environmental unidirectional graph G 0 ;

[0013] Each edge allows multiple tractor-trailer AGVs to exist at the same time, but the interval between each tractor-trailer AGV must be greater than the specified safe driving distance. In the one-way graph, the conflict problem of all tractor-trailer AGVs is solved by the waiting strategy.

[0014] Step 1.3: Based on the topological map constructed in step 1.1 and the geometric constraints of the actual physical space, determine the maximum length table of the towed AGV that is allowed to turn and pass through each channel intersection node;

[0015] Step 1.4: According to the maximum length table of the trailer AGVs allowed to turn and pass through each node of the channel intersection created in step 1.3, determine the maximum length of the trailer AGV as m, and consider the trailer AGVs with a length of n (1≤n≤m) in turn, and select the trailer AGVs from the channel intersection node set V c The nodes whose maximum length of the trailer AGV that is allowed to turn and pass is greater than or equal to n are selected to form a set

[0016] Combined with the initial unidirectional graph G constructed in step 1.2 0 , delete G 0 Divide the collection The edge outside the midpoint will make the towed AGV turn if and only if the set When the middle node is used as the starting point of a one-way edge, the towed AGV is allowed to turn;

[0017] Construct the unidirectional graph G in sequence n , ensuring that the trailer AGV with a length of n can operate normally in this one-way graph;

[0018] Step 1.5: Construct a multi-layer unidirectional graph G from the m unidirectional graphs obtained in step 1.4, G = {G 1 ,G 2 ,…G m};

[0019] To avoid deadlock and environmental constraints on the path of the towed AGV, the towed AGV with a length of n (1≤n≤m) is only allowed to move in the one-way graph G n Run on;

[0020] Step 1.6: Based on the multi-layer unidirectional graph in step 1.5, use d ij n It represents a towed AGV with a length of n (1≤n≤m) from task node i to task node j (i, j∈V k ), and construct the distance matrix D between task nodes n ;

[0021] Step 2: Based on the multi-layer unidirectional graph constructed in step 1 and the distance matrix between task nodes, the uncertainty of delivery time is modeled by translating the gamma distribution to solve the uncertainty caused by factors such as waiting strategy, obtain a reasonable estimate of the delivery time of the trailer AGV, determine the penalty value of advance and delay for material delivery, and ensure that the material transportation task is completed within the non-strictly constrained time window of the demand point;

[0022] Step 2.1: The time uncertainty modeling is completed by introducing a distribution function that describes the uncertain delivery time. The time u of the trailer AGV to deliver a unit distance is set to satisfy the translation gamma distribution of u~gamma(α,β,δ), where α is the shape parameter, β is the scale parameter, and δ is the translation amount.

[0023] The probability density function of the shifted gamma distribution u~gamma(α,β,δ) is shown in formula (1):

[0024]

[0025] The cumulative distribution function of the shifted gamma distribution u~gamma(α,β,δ) is shown in formula (2):

[0026]

[0027] Step 2.2: Based on the translation gamma distribution of u constructed in step 2.1 and the additivity of the translation gamma distribution, the random delivery time T of the trailer AGV from task node i to task node j is ij , satisfying T ij ~gamma(d ij α,β,d ij δ);

[0028] Step 2.3: T constructed according to step 2.2 ij The translation gamma distribution of the trailer AGV numbered a starts from the warehouse and arrives at a task node k (k∈V k ) The time required τ k(X) is shown in formula (3):

[0029]

[0030] Among them, R ka is the set of all material demand points that the trailer AGV numbered a passes through before completing task k, including task node k and warehouse; ija is a decision variable. If the trailer AGV numbered a delivers the materials of task node i, and the next task node numbered is j, then x ija =1, otherwise x ija =0; X is the sum of all decision variables x ija The set of components represents the task scheduling scheme of the towed multi-AGV system, X = {x ija |i,j∈V P ∪V k ,a∈A}, A is the set of towed AGVs; L ija (X) is the vehicle length of the trailer AGV numbered a when it delivers from node i to node j, which is related to the task scheduling scheme of the trailer multi-AGV system. ija (X) is shown in formula (4):

[0031]

[0032] Among them, |R ka | represents the set R ka The number of nodes in the

[0033] τ k (X) is transformed into the form shown in formula (5):

[0034]

[0035] Among them, θ k represents the uncertain part of the delivery time, satisfying θ k ~gamma(α',β);

[0036] in,

[0037] Step 2.4: The time τ required for the trailer AGV numbered a to reach the demand point k from the warehouse obtained in step 2.3 k (X), combined with the time window requirement for material delivery [e k ,l k ], determine the penalty value caused by the advance and lag of the towed AGV;

[0038] Among them, e k Indicates the start time of the time window, l kIndicates the end time of the time window;

[0039] Preferably, based on the quadratic loss function, determining the penalty value generated by the advance and lag of the trailer AGV includes the following steps:

[0040] When the trailer AGV numbered a undertakes material transportation task k, the penalty E for physically delivering the material ahead of the time window is ka (X) As shown in formula (6):

[0041]

[0042] in, The lower bound of the uncertain part of the delivery time is determined by the shifted gamma distribution. The probability density function f is determined according to formula (1) in step 2.1, and the cumulative distribution function F is determined according to formula (2) in step 2.1;

[0043] Among them, θ k Obey the shifted gamma distribution, determine the probability density function f according to formula (1) in step 2.1, and determine the cumulative distribution function F according to formula (2) in step 2.1;

[0044] Among them, a 0 、a 1 、a 2 is the coefficient of the quadratic loss function;

[0045] Similarly, the penalty D for delaying the physical delivery within the time window is ka (X) As shown in formula (7):

[0046]

[0047] in, represents the upper bound of the uncertain part of the delivery time, which obeys the shifted gamma distribution. The probability density function f is determined according to formula (1) in step 2.1, and the cumulative distribution function F is determined according to formula (2) in step 2.1;

[0048] Among them, θ k Obey the shifted gamma distribution, determine the probability density function f according to formula (1) in step 2.1, and determine the cumulative distribution function F according to formula (2) in step 2.1;

[0049] Among them, a 0 、a 1 、a 2 is the coefficient of the quadratic loss function;

[0050] Step 3: Based on the advance-delay penalty value obtained in step 2, a task scheduling model is established to minimize the advance-delay penalty for the trailer multi-AGV system to complete all delivery tasks, and the task execution route assigned to each trailer AGV is determined;

[0051] Step 3.1: According to the lead-lag penalty E obtained in step 1.4 ka (X), D ka (X), the optimization goal is to minimize the lead-lag penalty of the trailer multi-AGV system to complete all delivery tasks, and the constraint condition is the trailer AGV transportation limit. The task scheduling model is established as follows:

[0052] The objective function is shown in formula (8):

[0053]

[0054] The constraints are shown in equations (9) to (15):

[0055]

[0056]

[0057]

[0058]

[0059]

[0060]

[0061] x ija ∈{0,1},i∈V p ∪V k ,j∈V p ∪V k ,a∈A (15)

[0062] Among them, Q represents the maximum number of tasks that the trailer AGV can carry, and B represents any task that satisfies A set of |B| represents the number of nodes in B; x 0ka 、x k0a By x ija It is a decision variable. If the next task node of the trailer AGV numbered a from the warehouse is numbered k, then x 0ka =1, otherwise x 0ka =0, if x 0ka The trailer AGV numbered a returns to the warehouse after completing the transportation task of task node k. Then x k0a =1, otherwise x k0a =0;

[0063] Step 3.2: Based on the task scheduling model constructed in step 3.1, a simulated annealing algorithm is preferably used to determine the task scheduling scheme of the trailer multi-AGV system, that is, the task execution route assigned to each trailer AGV.

[0064] Beneficial effects:

[0065] 1. The present invention discloses a method for scheduling tasks of a trailer-type multi-AGV system based on a multi-layer one-way graph. The multi-layer one-way graph is constructed according to the actual layout of the physical space, and the trailer-type AGV with variable length is applied to the manufacturing workshop, which can reduce the investment cost of the enterprise in the process of intelligent transformation, and solve the conflict and deadlock of the trailer-type AGV through the waiting strategy, so as to ensure the coordinated and conflict-free operation of the system;

[0066] 2. The present invention discloses a method for scheduling tasks of a towed multi-AGV system based on a multi-layer unidirectional graph, which models the uncertainty of delivery time by translating the gamma distribution, can effectively solve the uncertainty caused by factors such as waiting strategies, and ensure the robustness of the task scheduling method;

[0067] 3. The present invention discloses a task scheduling method for a trailer-type multi-AGV system based on a multi-layer unidirectional graph, establishes a task scheduling model, minimizes the lead-lag penalty for the trailer-type multi-AGV system to complete all distribution tasks, obtains the task execution route assigned to each trailer-type AGV, and ensures the stability and timeliness of material distribution. BRIEF DESCRIPTION OF THE DRAWINGS

[0068] Figure 1 It is a flowchart of a method for scheduling tasks of a towed multi-AGV system based on a multi-layer unidirectional graph according to the present invention;

[0069] Figure 2 It is the actual layout of the workshop;

[0070] Figure 3 It is the key node diagram of the workshop;

[0071] Figure 4 It is a one-way graph of the workshop G 1 ;

[0072] Figure 5 It is a one-way diagram of the workshop G 2 ;

[0073] Figure 6 It is a one-way graph of the workshop G 3 ;

[0074] Figure 7 It is a one-way graph of the workshop G 4 ;

[0075] Figure 8 It is the flow chart of simulated annealing algorithm. DETAILED DESCRIPTION

[0076] In order to better illustrate the purpose and advantages of the present invention, the invention is further described below with reference to the accompanying drawings and examples.

[0077] Embodiment 1:

[0078] As attached Figure 1 As shown, the main process of the task scheduling method of a trailer-type multi-AGV system based on a multi-layer unidirectional graph of the present invention is as follows: first, according to the actual layout of the physical space, a topological unidirectional map is constructed to determine the maximum length table of the trailer-type AGVs that are allowed to turn and pass through each node, and on this basis, a multi-layer unidirectional graph is constructed to ensure that the trailer-type AGVs with variable lengths can operate normally, and the conflicts and deadlocks of the trailer-type AGVs are resolved through the waiting strategy, and the distance matrix between nodes is constructed; then, on the basis of the multi-layer unidirectional graph and the distance matrix between nodes, the uncertainty of the delivery time is modeled by translating the gamma distribution to resolve the uncertainty caused by factors such as the waiting strategy, obtain a reasonable estimate of the trailer-type AGV delivery time, and determine the advance lag penalty value of material delivery; finally, a task scheduling model is established to minimize the advance lag penalty for the trailer-type multi-AGV system to complete all delivery tasks, and obtain the task execution route assigned to each trailer-type AGV.

[0079] This embodiment is an application of the present invention to the production layout and logistics requirements of an assembly workshop of an agricultural machinery manufacturing enterprise. Figure 2 As shown, in the assembly workshop of the agricultural machinery manufacturing enterprise, there are final assembly lines and sub-assembly lines. Different components are assembled at different assembly stations and finally assembled on the final assembly line. During the product assembly process, a large number of different types of materials need to be transported to the assembly stations.

[0080] The specific steps of applying the present invention to the assembly workshop of the agricultural machinery manufacturing enterprise are as follows:

[0081] Step 1: According to the actual layout of the assembly workshop, a topological one-way map is constructed to determine the maximum length table of the trailer AGV that is allowed to turn through each node. On this basis, a multi-layer one-way graph is constructed to ensure that the trailer AGV with variable length can operate normally in the system, and the conflict and deadlock of the trailer AGV are resolved through the waiting strategy, and the distance matrix between nodes is constructed;

[0082] Step 1.1: Layout of the assembly workshop, such as Figure 3 As shown in the figure, the important locations of the assembly workshop are abstracted into nodes, represented by v, where the set of all channel intersection nodes is V c , the set of all task requirement nodes is V k , the set of nodes where the warehouse entrance and exit are located is V p , the set of all nodes V = Vp ∪V k ∪V c , abstract the road into edges, represented by z, and the set is Z, and construct a topological map: nodes numbered 1 to 30 represent the intersection nodes of the channel, and nodes numbered 31 to 57 represent the loading and unloading points in the layout, that is, the task requirement nodes. Nodes 1 and 24 correspond to the import and export of the material warehouse respectively. All materials in the production system enter the assembly workshop from node 1, and the trailer AGV returns to the warehouse from node 24. There are situations in the system where the loading and unloading points coincide with the intersection of the channel, such as nodes 21 and 49;

[0083] Step 1.2: Based on the topological map constructed in step 1.1, specify that the direction of each edge is unidirectional and construct the environmental unidirectional graph G 0 ;

[0084] Step 1.3: Based on the topological map constructed in step 1.1 and the geometric constraints of the assembly workshop, determine the maximum length table of the trailer AGV that is allowed to turn through each channel intersection node, as shown in Table 1:

[0085] Table 1 The maximum length of each channel intersection node that allows the towed AGV to turn and pass

[0086]

[0087] Step 1.4: According to the maximum length table of trailer AGVs allowed to turn and pass through each channel intersection node created in step 1.3, determine that the maximum length of the trailer AGV in the trailer multi-AGV system is 4, and consider the trailer AGVs with a length of n (1≤n≤4) in turn, and select the trailer AGVs from the channel intersection node set V c The nodes whose maximum length of the trailer AGV that is allowed to turn and pass is greater than or equal to n are selected to form a set V n c ;

[0088] Combined with the initial unidirectional graph G constructed in step 1.2 0 , delete G 0 Medium Collection V n c The edges outside the node that will make the towed AGV turn, and then build a one-way graph G 1 , G 2 , G 3 , G 4 , the one-way diagrams of each layer are as shown in the attached Figure 4 To Attachment Figure 7 As shown;

[0089] Step 1.5: Construct a multi-layer unidirectional graph G from the four unidirectional graphs obtained in step 1.4, G = {G 1 ,G 2 ,G3 ,G 4}, the length of the trailer AGV is n (1≤n≤4) is only allowed in the one-way graph G n Run on;

[0090] Step 1.6: Based on the multi-layer unidirectional graph in step 1.5, construct the distance matrix D between task nodes for each towed AGV with a length of n (1≤n≤4) n ,The distance table between task nodes is shown in Table 2:

[0091] Table 2 Distance table between task nodes

[0092]

[0093] Step 2: Based on the multi-layer unidirectional graph constructed in step 1 and the distance matrix between task nodes, the uncertainty of delivery time is modeled by translating the gamma distribution to solve the uncertainty caused by factors such as waiting strategy, obtain a reasonable estimate of the delivery time of the trailer AGV, determine the penalty value of advance and delay for material delivery, and ensure that the material transportation task is completed within the non-strictly constrained time window of the demand point;

[0094] Step 2.1: Set the time u of the trailer AGV to deliver a unit distance to satisfy the translation gamma distribution of u~gamma(α,β,δ), model the time uncertainty, and determine the shape parameter α to be 1, the scale parameter β to be 0.25, and the translation δ to be 0.75 through parameter selection and optimization verification;

[0095] The probability density function of the shifted gamma distribution u~gamma(α,β,δ) is shown in formula (1):

[0096]

[0097] The cumulative distribution function of the shifted gamma distribution u~gamma(α,β,δ) is shown in formula (2):

[0098]

[0099] According to equations (1) and (2), the probability density function of the time u~gamma(1,0.25,0.75) for the distribution unit distance is obtained as f(u)=16e 3-4u , cumulative distribution function F(u) = 1-e 3-4u ;

[0100] Step 2.2: Based on the shifted gamma distribution of u constructed in step 2.1 and the additivity of the shifted gamma distribution, the random delivery time T of the trailer AGV from node i to node j is ij , satisfying the shifted gamma distribution T ij~gamma(d ij ,0.25,0.75d ij );

[0101] Step 2.3: T constructed according to step 2.2 ij The translation gamma distribution of the AGV numbered a is obtained when the trailer AGV starts from the warehouse and arrives at a certain task node k (k∈V k ) The time required τ k (X) is shown in formula (3):

[0102]

[0103] Among them, R ka is the set of all material demand points that the trailer AGV numbered a passes through before completing task k, including task node k and warehouse; ija is a decision variable. If the trailer AGV numbered a delivers the materials of task node i, and the next task node numbered is j, then x ija =1, otherwise x ija =0; X is the sum of all decision variables x ija The set of components represents the task scheduling scheme of the towed multi-AGV system, X = {x ija |i,j∈V P ∪V k ,a∈A}, A is the set of towed AGVs; L ija (X) is the vehicle length of the trailer AGV numbered a when it delivers from node i to node j, which is related to the task scheduling scheme of the trailer multi-AGV system. ija (X) is shown in formula (4):

[0104]

[0105] Among them, |R ka | represents the set R ka The number of nodes in the

[0106] τ k (X) is transformed into the form shown in formula (5):

[0107]

[0108] Among them, θ k represents the uncertain part of the delivery time, θ k ~gamma(α',β);

[0109] in,

[0110] Step 2.4: This embodiment sets a set of static task scheduling test cases according to the actual material transportation needs of the assembly workshop. The case includes 20 tasks with non-strict time window requirements. The specific task nodes and time window constraints are shown in Table 3. The initial time of the system is set to 0. There are 7 trailer AGVs in the system, and the maximum length of each trailer AGV is 4;

[0111] Table 3 Static task scheduling test case table

[0112]

[0113]

[0114] According to the time τ required for the trailer AGV numbered a to reach the demand point k from the warehouse obtained in step 2.3 k (X), combined with the time window requirements for material delivery [e k ,l k ], preferably, based on the quadratic loss function, the penalty value generated by the advance and lag of the towed AGV is determined;

[0115] Among them, e k Indicates the start time of the time window, l k Indicates the end time of the time window;

[0116] When the trailer AGV numbered a undertakes material transportation task k, the penalty E for physically delivering the material ahead of the time window is ka (X) As shown in formula (6):

[0117]

[0118] in, The lower bound of the uncertain part of the delivery time is determined by the shifted gamma distribution. The probability density function f is determined according to formula (1) in step 2.1, and the cumulative distribution function F is determined according to formula (2) in step 2.1;

[0119] Among them, θ k Obey the shifted gamma distribution, determine the probability density function f according to formula (1) in step 2.1, and determine the cumulative distribution function F according to formula (2) in step 2.1;

[0120] Among them, a 0 、a 1 、a 2 is the coefficient of the quadratic loss function. After parameter selection and optimization verification, the coefficient a of the quadratic loss function is determined. 0 The value is 0, a 1 The value is 1, a 2 The value is 0;

[0121] Similarly, the penalty D for delaying the physical delivery within the time window is ka (X) As shown in formula (7):

[0122]

[0123] in, represents the upper bound of the uncertain part of the delivery time, which obeys the shifted gamma distribution. The probability density function f is determined according to formula (1) in step 2.1, and the cumulative distribution function F is determined according to formula (2) in step 2.1;

[0124] Step 3: Based on the advance-delay penalty value obtained in step 2, a task scheduling model is established to minimize the advance-delay penalty for the trailer multi-AGV system to complete all delivery tasks, and the task execution route assigned to each trailer AGV is determined;

[0125] Step 3.1: According to the lead-lag penalty E obtained in step 1.4 ka (X), D ka (X), the optimization goal is to minimize the lead-lag penalty of the trailer multi-AGV system to complete all delivery tasks, and the constraint condition is the trailer AGV transportation limit. The task scheduling mathematical model is established as follows:

[0126] The objective function is shown in formula (8):

[0127]

[0128] The constraints are shown in equations (9) to (15):

[0129]

[0130]

[0131]

[0132]

[0133]

[0134]

[0135] x ija ∈{0,1},i∈V p ∪V k ,j∈V p ∪V k ,a∈A (15)

[0136] Among them, Q represents the maximum number of tasks that the trailer AGV can carry, and B represents any task that satisfies A set of, |B| represents the number of nodes in B;

[0137] Step 3.2: Based on the task scheduling model constructed in step 3.1, a simulated annealing algorithm is preferably used to determine the task scheduling scheme, that is, the task execution route assigned to each trailer AGV;

[0138] The simulated annealing algorithm process is as follows Figure 8 As shown, the specific implementation steps are:

[0139] (1) Set the main control parameters of simulated annealing, including the initial temperature T 0 , End temperature T end , temperature proportional decrease rate κ (0<κ<1) and maximum number of iterations Iter max ; Let temperature T = T 0 , Iteration number Iter = 1;

[0140] (2) Randomly generate initial input value X 0 , let X = X 0 , determine the energy value of the initial value, that is, the objective function value f(X);

[0141] (3) Transform the current input value X to generate a new input value X′, which corresponds to the new task allocation scheme of the trailer multi-AGV system;

[0142] (4) Calculate the new objective function value f(X′), the energy difference between the new input value and the current input value △f = f(X′)-f(X);

[0143] (5) If △f<0, then X=X′; otherwise,

[0144] (6) Take a random number R = random(0,1) in the range (0,1). If P>R, then X = X′.

[0145] (7) If Iter <Iter max , then Iter = Iter + 1, and repeat (3) to (8), otherwise, go to (8);

[0146] (8) If T>T end , then T = κT, and repeat (2) to (6), otherwise, go to (9);

[0147] (9) Output X and objective function value f(X);

[0148] The result obtained by the simulated annealing algorithm is the task scheduling solution. Taking the task scheduling test case in step 2.4 as an example, the result is:

[0149] X=[0 8 16 19 20 0 2 0 1 9 11 17 0 3 10 0 5 7 0 6 13 15 18 0 4 12 140];

[0150] The numbers represent the task numbers in the case of step 2.4, and the corresponding execution routes of each towed AGV task are shown in Table 4 below:

[0151] Table 4 Task execution route of trailer AGV

[0152]

[0153] The specific description above further illustrates the purpose, technical solutions and beneficial effects of the invention in detail. It should be understood that the above is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for scheduling tasks of a towed multi-AGV system based on a multi-layer unidirectional graph, characterized in that: Firstly, according to the actual layout of the physical space, a topological one-way map is constructed to determine the maximum length table of the trailer AGV that is allowed to turn and pass through each node. On this basis, a multi-layer one-way graph is constructed to ensure that the trailer AGV with variable length can operate normally, and the conflict and deadlock of the trailer AGV are resolved through the waiting strategy, and the distance matrix between nodes is constructed; then, based on the multi-layer one-way graph and the distance matrix between nodes, the uncertainty of the delivery time is modeled by the shifted gamma distribution to resolve the uncertainty caused by the waiting strategy factors, obtain a reasonable estimate of the trailer AGV delivery time, and determine the advance and delay penalty value of material delivery; finally, a task scheduling model is established to minimize the advance and delay penalty for the trailer multi-AGV system to complete all delivery tasks, and obtain the task execution route assigned to each trailer AGV; The method comprises the following steps: Step 1: According to the actual layout of the physical space, a topological one-way map is constructed to determine the maximum length table of the trailer AGVs that are allowed to turn and pass through each node. On this basis, a multi-layer one-way graph is constructed to ensure that the trailer AGVs with variable lengths can operate normally in the system. The conflict and deadlock of the trailer AGVs are resolved through the waiting strategy, and the distance matrix between nodes is constructed; Step 1.1: For the layout of the physical space, important locations are abstracted into nodes, represented by v, where the set of all channel intersection nodes is V c , the set of all task requirement nodes is V k , the set of nodes where the warehouse entrance and exit are located is V p , the set of all nodes V = V p ∪V k ∪V c , abstract the road into edges, represented by z, and the set is Z, and construct a topological map to ensure that there is a reachable path between any two road nodes, and each edge allows vehicles to enter and exit normally; Step 1.2: Based on the topological map constructed in step 1.1, specify that the direction of each edge is unidirectional, that is, any node v i With adjacent nodes v j The edge z between i,j For unidirectional edges, construct the environmental unidirectional graph G0; Each edge allows multiple tractor-trailer AGVs to exist at the same time, but the interval between each tractor-trailer AGV must be greater than the specified safe driving distance. In the one-way graph, the conflict problem of all tractor-trailer AGVs is solved by the waiting strategy. Step 1.3: Based on the topological map constructed in step 1.1 and the geometric constraints of the actual physical space, determine the maximum length table of the towed AGV that is allowed to turn and pass through each channel intersection node; Step 1.4: According to the maximum length table of the trailer AGVs allowed to turn and pass through each node of the channel intersection created in step 1.3, determine the maximum length of the trailer AGV as m, and consider the trailer AGVs with length n in turn, where 1≤n≤m, and select the maximum length of the trailer AGVs from the channel intersection node set V. c The nodes whose maximum length of the trailer AGV that is allowed to turn and pass is greater than or equal to n are selected to form a set Combined with the initial unidirectional graph G0 constructed in step 1.2, delete the set except The edge outside the midpoint will make the towed AGV turn if and only if the set When the middle node is used as the starting point of a one-way edge, the towed AGV is allowed to turn; Construct the unidirectional graph G in sequence n , ensuring that the trailer AGV with a length of n can operate normally in this one-way graph; Step 1.5: Construct a multi-layer unidirectional graph G from the m unidirectional graphs obtained in step 1.4, where G = {G1, G2, …G m }; To avoid deadlock and environmental constraints on the path of the tractor-trailer AGV, the tractor-trailer AGV with a length of n is only allowed to move in the one-way graph G. n Run on, where 1≤n≤m; Step 1.6: Based on the multi-layer unidirectional graph in step 1.5, use d ij n represents the shortest distance from task node i to task node j of a towed AGV with a length of n, where 1≤n≤m, i,j∈V k , construct the distance matrix D between task nodes n ; Step 2: Based on the multi-layer unidirectional graph constructed in step 1 and the distance matrix between task nodes, the uncertainty of delivery time is modeled by translating the gamma distribution to solve the uncertainty caused by waiting strategy factors, obtain a reasonable estimate of the delivery time of the trailer AGV, determine the penalty value of advance and delay for material delivery, and ensure that the material transportation task is completed within the non-strictly constrained time window of the demand point; Step 2.1: The time uncertainty modeling is completed by introducing a distribution function that describes the uncertain delivery time. The time u of the trailer AGV to deliver a unit distance is set to satisfy the translation gamma distribution of u~gamma(α,β,δ), where α is the shape parameter, β is the scale parameter, and δ is the translation amount. The probability density function of the shifted gamma distribution u~gamma(α,β,δ) is shown in formula (1): The cumulative distribution function of the shifted gamma distribution u~gamma(α,β,δ) is shown in formula (2): Step 2.2: Based on the translation gamma distribution of u constructed in step 2.1 and the additivity of the translation gamma distribution, the random delivery time T of the trailer AGV from task node i to task node j is ij , satisfying T ij ~gamma(d ij α,β,d ij δ); Step 2.3: T constructed according to step 2.2 ij The time τ required for a trailer AGV numbered a to reach a task node k from the warehouse is k (X) is shown in formula (3): Where k∈V k , R ka is the set of all material demand points that the trailer AGV numbered a passes through before completing task k, including task node k and warehouse; ija is a decision variable. If the trailer AGV numbered a delivers the materials of task node i, and the next task node numbered is j, then x ija =1, otherwise x ija =0; X is the sum of all decision variables x ija The set of components represents the task scheduling scheme of the towed multi-AGV system, X = {x ija |i,j∈V P ∪V k ,a∈A}, A is the set of towed AGVs; L ija (X) is the vehicle length of the trailer AGV numbered a when it delivers from node i to node j, which is related to the task scheduling scheme of the trailer multi-AGV system. ija (X) is shown in formula (4): Among them, |R ka | represents the set R ka The number of nodes in the τ k (X) is transformed into the form shown in formula (5): Among them, θ k represents the uncertain part of the delivery time, satisfying θ k ~gamma(α',β); in, Step 2.4: The time τ required for the trailer AGV numbered a to reach the demand point k from the warehouse obtained in step 2.3 k (X), combined with the time window requirements for material delivery [e k ,l k ], determine the penalty value caused by the advance and lag of the towed AGV; Among them, e k Indicates the start time of the time window, l k Indicates the end time of the time window; Step 3: Based on the advance-delay penalty value obtained in step 2, a task scheduling model is established to minimize the advance-delay penalty for the trailer multi-AGV system to complete all delivery tasks, and the task execution route assigned to each trailer AGV is obtained; Step 3.1: According to the lead-lag penalty E obtained in step 2.4 ka (X), D ka (X), the optimization goal is to minimize the lead-lag penalty of the trailer multi-AGV system to complete all delivery tasks, and the constraint condition is the trailer AGV transportation limit. The task scheduling model is established as follows: The objective function is shown in formula (6): The constraints are shown in equations (7) to (13): x ija ∈{0,1},i∈V p ∪V k ,j∈V p ∪V k ,a∈A(13)where Q represents the maximum number of tasks that the towed AGV can carry, and B represents any task that satisfies A set of |B| represents the number of nodes in B; x 0ka 、x k0a By x ija It is a decision variable. If the next task node of the trailer AGV numbered a from the warehouse is numbered k, then x 0ka =1, otherwise x 0ka =0, if x 0ka The trailer AGV numbered a returns to the warehouse after completing the transportation task of task node k. Then x k0a =1, otherwise x k0a =0; Step 3.2: According to the task scheduling model constructed in step 3.1, determine the task scheduling scheme of the trailer multi-AGV system, that is, the task execution route assigned to each trailer AGV.

2. A method for scheduling tasks of a towed multi-AGV system based on a multi-layer unidirectional graph as claimed in claim 1, characterized in that: Based on the quadratic loss function, the penalty value generated by the advance and lag of the trailer AGV is determined, including the following steps: When the trailer AGV numbered a undertakes material transportation task k, the penalty E for physically delivering the material ahead of the time window is ka (X) As shown in formula (14): in, The lower bound of the uncertain part of the delivery time is determined by the shifted gamma distribution. The probability density function f is determined according to formula (1) in step 2.1, and the cumulative distribution function F is determined according to formula (2) in step 2.1; Among them, θ k Obey the shifted gamma distribution, determine the probability density function f according to formula (1) in step 2.1, and determine the cumulative distribution function F according to formula (2) in step 2.1; Among them, a0, a1, and a2 are the coefficients of the quadratic loss function; Similarly, the penalty D for delaying the physical delivery within the time window is ka (X) As shown in formula (15): in, represents the upper bound of the uncertain part of the delivery time, which obeys the shifted gamma distribution. The probability density function f is determined according to formula (1) in step 2.1, and the cumulative distribution function F is determined according to formula (2) in step 2.1; Among them, θ k Obey the shifted gamma distribution, determine the probability density function f according to formula (1) in step 2.1, and determine the cumulative distribution function F according to formula (2) in step 2.1; Among them, a0, a1, and a2 are the coefficients of the quadratic loss function.

3. A method for scheduling tasks of a towed multi-AGV system based on a multi-layer unidirectional graph as claimed in claim 1, characterized in that: In step 3.2, the simulated annealing algorithm is applied to determine the task scheduling scheme of the trailer multi-AGV system, that is, the task execution route assigned to each trailer AGV.

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