A multi-robot joint scheduling optimization method based on dynamic space-time graph

Abstract

The present invention discloses a multi-robot joint scheduling optimization method based on a dynamic space-time graph, comprising the following steps: obtaining initial parameters and initializing the time step; expanding the undirected original map in the time dimension using a special bridging structure based on the initial parameters to convert it into a directed dynamic space-time graph; constructing an integer linear programming mathematical model based on the directed dynamic space-time graph; solving the integer linear programming mathematical model using a branch-and-bound method to obtain edge variable values, and variable values ​​corresponding to task start points and task end points; determining the current number of completed tasks based on the variable value corresponding to the task end point; when the current number of completed tasks equals a preset number of tasks, obtaining task allocation status based on the variable values ​​corresponding to the task start points and task end points, and obtaining path planning status based on the edge variable values. Corresponding decision variables and constraints are designed for task allocation and path planning, respectively, so that complex collaborative scheduling problems can be solved with fewer mathematical constraints, effectively improving the quality of the solution.

Description

Technical Field

[0001] The present invention belongs to the field of robots, and in particular relates to a multi-robot joint scheduling optimization method based on a dynamic space-time graph. Background Art

[0002] With the advent of Industry 4.0, highly automated and intelligent workshop production models are gaining increasing attention. Intelligent production methods are gradually replacing traditional labor-intensive methods and becoming a key means for companies to reduce costs and increase profits. Material transportation is a core component of the manufacturing process. In traditional manufacturing, especially large-scale high-end equipment manufacturing, over 95% of the time is spent on material handling and distribution, leaving less than 5% for processing and assembly. Therefore, improving the efficiency of material transportation and distribution has become a major research hotspot in intelligent manufacturing.

[0003] The prototype of most material transportation problems is the Pick-up and Delivery Problem (PDP). Each transportation task consists of a starting point and a destination, requiring the transport vehicle to first reach the starting point and then the destination. This type of problem is widely encountered in real life, including but not limited to the aforementioned material distribution in smart manufacturing, such as the dispatching and routing decision-making systems for food delivery platform drivers, the integrated collaborative delivery routing planning system for e-commerce logistics pickup and delivery, and the Didi pick-up and drop-off order allocation and route planning system, among many other fields.

[0004] In the design of a collaborative scheduling system for pickup and delivery, path planning and task allocation are closely linked. Path planning is based on task allocation, and task allocation is directly influenced by the path planning results. If these two issues are considered separately, the scheduling problem across multiple transport carriers cannot be effectively solved. Instead of improving system performance, system performance may actually deteriorate or even fail. Therefore, for a multi-transporter system based on pickup and delivery, the most critical issue is how to collaboratively consider path planning and task allocation—the scheduling problem—to effectively improve solution quality.

[0005] Currently, domestic and international scholars have achieved significant research results on issues such as path planning, task allocation, and scheduling. However, most studies are often limited to considering one or two of these issues separately, and few consider all three together, which is not conducive to improving overall efficiency. Among them, some scholars have proposed a conflict-based minimum cost flow algorithm to solve these three problems, but they do not perform them simultaneously, so the results obtained are not optimal. Other scholars have proposed a conflict-based task search algorithm (TCBS), which combines the three problems of pickup and delivery, path planning, and task allocation by introducing task allocation into a conflict-search-based path planning strategy. However, this method has poor scalability and can only be adapted to small-scale problems.

[0006] In summary, current methods either cannot optimize simultaneously, lack scalability, or have too many constraints. Therefore, developing a method that does not increase model complexity while more rationally utilizing system resources and effectively improving solution quality is an urgent problem in this field. Summary of the Invention

[0007] In response to the above technical problems, the present invention provides a multi-robot joint scheduling optimization method based on a dynamic space-time graph.

[0008] The technical solution adopted by the present invention to solve the technical problem is:

[0009] A multi-robot joint scheduling optimization method based on a dynamic space-time graph comprises the following steps:

[0010] Step S100: Obtain initial parameters and initialize the time step;

[0011] Step S200: Based on the initial parameters, a special bridge structure is used to expand the undirected original map G(V, E) in the time dimension, transforming it into a directed dynamic spatiotemporal graph G'=(V', E', C); where V is the original node set, E is the original edge set, V' is a node in the dynamic spatiotemporal graph, E' is an edge in the dynamic spatiotemporal graph, and C is the capacity set of the edges;

[0012] Step S300: constructing an integer linear programming mathematical model according to the directed dynamic space-time graph;

[0013] Step S400: Solving the integer linear programming mathematical model based on the branch and bound method to obtain edge variable values, variable values ​​corresponding to the task starting point, and variable values ​​corresponding to the task end point;

[0014] Step S500: Determine the number of currently completed tasks based on the variable value corresponding to the task endpoint. When the currently completed number of tasks is equal to the preset number of tasks, obtain the task allocation status based on the variable value corresponding to the task starting point and the variable value corresponding to the task endpoint, and obtain the path planning status based on the edge variable value.

[0015] Preferably, the initial parameters in step S100 include the starting coordinates of A transport robots, m pairs of task start / end coordinates and original map information.

[0016] Preferably, in step S200, V' includes the original node and time information, and E' is a directed edge including its previous and next nodes and time information, and points from the previous time node to the next time point.

[0017] Preferably, step S300 includes:

[0018] Step S310: In the dynamic spatiotemporal graph, construct an edge variable X for each edge e`∈E` a,j , where a represents the robot number and j represents the edge number;

[0019] Step S320: In the dynamic spatiotemporal graph, construct a point variable for the starting point of each task in Indicates that robot a is performing task o at time t i ; Build point variables for each task's endpoint in Indicates that robot a has completed task o at time t i ;

[0020] Step S330: setting node deadlock avoidance constraints, flow conservation constraints, opposite collision avoidance constraints, task execution constraints, task completion constraints, task→robot constraints, and robot→task constraints;

[0021] Step S340: Setting the objective function.

[0022] Preferably, in step S330:

[0023] The node deadlock avoidance constraint is the sum of the variables of the edges entering all points, that is, for each point, the X of all its incoming edges is a,j The sum is ≤1, specifically:

[0024]

[0025] Among them, δ + (v`(t)) represents the set of all edges entering v' at time t, e' jrepresents the j-th edge in the set, a represents the robot number, G` represents a directed dynamic spatiotemporal graph, A represents the number of robots, and T represents the total time step;

[0026] The flow conservation constraint is that for each point, the sum of the incoming flow = the sum of the outgoing flow, specifically:

[0027]

[0028] Among them, δ - (v`(t)) represents the set of all edges leaving point v' at time t;

[0029] The specific constraints for avoiding collisions are:

[0030]

[0031] Among them, (u'(t), v'(t+1)) and (v'(t), u'(t+1)) are two intersecting edges in the directed dynamic space-time graph G';

[0032] The specific task execution constraints are:

[0033]

[0034] Among them, i Represents the i-th task, which contains the starting and ending information of the i-th task;

[0035] The premise for the above equation to occur is:

[0036] 1) At time t+1, robot a just arrives at task o i Starting point i :

[0037]

[0038] Among them, i Represents the i-th task, which contains the task start and end information, i.e. o i =(s i ,g i ), s i represents the starting point of the i-th task, g i represents the end point of the i-th task, m represents the total number of tasks, e j ∈δ + (s' i e in (t+1)) j Indicates that at time t+1 all the slaves enter the i-th task o i Starting point s' i An edge in the set of edges of a point, x a,j Represents robot a about edge e jIf the variable is equal to 1, it means that the trajectory of robot a passes through this edge;

[0039] 2) And no tasks are executed at time t:

[0040]

[0041] The task completion constraints are as follows:

[0042]

[0043] The prerequisites for the above equation to occur are:

[0044] 1) At time t+1, robot a just arrives at task o i The end point g i :

[0045]

[0046] Among them, e j ∈δ + (g' i e in (t+1)) j Indicates that at time t+1 all the slaves enter the i-th task o i The end point g' i An edge in the set of edges of a point, x a,j Represents robot a about edge e j If the variable is equal to 1, it means that the trajectory of robot a passes through this edge;

[0047] 2) At time t, robot a is performing task o i :

[0048]

[0049] Task → Robot Constraints are:

[0050]

[0051] Robot → Task constraints are as follows:

[0052]

[0053] Preferably, step S340 is specifically as follows:

[0054]

[0055] Preferably, step S500 further includes:

[0056] When the number of currently completed tasks is not equal to the preset number of tasks, the time step is iterated and the process returns to step S200 until the minimum time step that just completes all tasks is found.

[0057] The above method uses network flow theory to design corresponding decision variables and constraints for task allocation and path planning respectively, while satisfying the basic network flow capacity constraints and flow conservation constraints. In this way, the task allocation and path planning problem of multiple transport robots is transformed into a multi-commodity network flow problem with special constraints, thereby solving complex collaborative scheduling problems with fewer mathematical constraints, effectively improving the solution quality. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Figure 1 A flowchart of a multi-robot joint scheduling optimization method based on a dynamic space-time graph provided by one embodiment of the present invention;

[0059] Figure 2 A flowchart of a multi-robot joint scheduling optimization method based on a dynamic spatiotemporal graph provided by one embodiment of the present invention;

[0060] Figure 3 Schematic diagram of initial information in one embodiment of the present invention;

[0061] Figure 4 A schematic diagram of constructing a dynamic space-time graph in one embodiment of the present invention;

[0062] Figure 5 Schematic diagram of the conversion of the original map transport robot route to the dynamic spatiotemporal graph network flow in one embodiment of the present invention. DETAILED DESCRIPTION

[0063] In order to enable those skilled in the art to better understand the technical solution of the present invention, the present invention is further described in detail below with reference to the accompanying drawings.

[0064] In one embodiment, Figure 1 and Figure 2 As shown, a multi-robot joint scheduling optimization method based on a dynamic space-time graph includes the following steps:

[0065] Step S100: Obtain initial parameters and initialize the time step.

[0066] In one embodiment, the initial parameters in step S100 include A transport robot starting point coordinates, m pairs of task start / end point coordinates, and original map information.

[0067] Specifically, load the initial parameters (A transport robot starting coordinates, m pairs of task start / end coordinates, original map information, and specific information such as Figure 3The number of robots A may not be equal to the number of tasks m, that is, one robot can perform multiple tasks, thus achieving optimal efficiency. Figure 5 As shown in the figure, the robot is restricted to move on the guide rail, which is divided into sections with sections as edges and section endpoints as nodes. The entire guide rail system forms a network. The robot loads items from one node according to the task requirements and then transports them to another node for unloading.

[0068] Step S200: Based on the initial parameters, a special bridging structure is used to expand the undirected original map G(V,E) in the time dimension to transform it into a directed dynamic space-time graph G`=(V`,E`,C); wherein V is the original node set, E is the original edge set, V` is the node in the dynamic space-time graph, E` is the edge in the dynamic space-time graph, and C is the capacity set of the edge.

[0069] In one embodiment, in step S200, V' includes the original node and time information, and E' is a directed edge including its previous and next nodes and time information, and points from the previous time node to the next time point.

[0070] Specifically, a special bridging structure is used to expand the undirected original map G(V,E) in the time dimension (based on the time step T) to transform it into a directed dynamic space-time graph G`=(V`,E`,C). V is the original node set, E is the original edge set, V` is the node in the dynamic space-time graph (including the original node and time information), E` is the edge in the dynamic space-time graph (a directed edge, including its previous and next nodes, time information, pointing from the previous time point to the next time point), and C is the capacity set of the edge (all 1). The specific process is as follows Figure 4 As shown, the space-time graph is constructed by discretizing time, for example, into t=0, t=1, and t=2 in the embodiment of the present invention, and then replicating the route map at each time point. Directed edges are connected between route maps at different time points to represent the robot's possible positional movements between those time points. It can be shown that the robot's movements on the original map are equivalent to the network flows on the space-time graph, as shown in Figure 5. Because the space-time graph is dynamically and iteratively constructed during the decision-making process, the present invention refers to it as a dynamic space-time graph.

[0071] Step S300: constructing an integer linear programming mathematical model according to the directed dynamic space-time graph.

[0072] In one embodiment, step S300 includes:

[0073] Step S310: In the dynamic spatiotemporal graph, construct an edge variable X for each edge e`∈E` a,j , where a represents the robot number and j represents the edge number.

[0074] Specifically, the edge number consists of the edge start point, edge end point, and time step. a,j Equal to 1 means robot a passes through edge e` j , equal to 0 means not passed.

[0075] Step S320: In the dynamic spatiotemporal graph, construct a point variable for the starting point of each task in Indicates that robot a is performing task o at time t i ; Build point variables for each task's endpoint in Indicates that robot a has completed task o at time t i .

[0076] Specifically, if If it is equal to 1, it means it is being transported, and if it is equal to 0, it means it is not being transported. Figure 5 The dynamic space-time diagram needs to be point 5 t0 , 5 t1 , 5 t2 , 5 t3 , 3 t0 , 3 t1 , 3 t2 , 3 t3 Create a point variable P. Equal to 1 means it has been completed, and 0 means it has not been completed. Figure 5 The dynamic space-time diagram needs to be point 2 t0 , 2 t1 , 2 t2 , 2 t3 、 1 t0 、1 t1 、1 t2 、1 t3 Create a point variable D.

[0077] Step S330: Set node deadlock avoidance constraints, flow conservation constraints, opposite collision avoidance constraints, task execution constraints, task completion constraints, task→robot constraints, and robot→task constraints.

[0078] In one embodiment, in step S330:

[0079] The node deadlock avoidance constraint is the sum of the variables of the edges entering all points, that is, for each point, the X of all its incoming edges is a,j The sum is ≤1, specifically:

[0080]

[0081] Among them, δ +(v`(t)) represents the set of all edges entering v' at time t, e' j represents the j-th edge in the set, a represents the robot number, G` represents a directed dynamic space-time graph, A represents the number of robots, and T represents the total time step.

[0082] Specifically, Figure 5 Point 5 t1 For example, the effect of this constraint is that at the same time point, only one robot can enter point 5 if and only if t1 In this algorithm, each edge in the graph G' contains A variables, such as e' j Contains x 1,j 、x 2,j Equal variables, when x 1,j =1, it means robot 1 passes through edge e' j .

[0083] The flow conservation constraint is that for each point, the sum of the incoming flow = the sum of the outgoing flow, specifically:

[0084]

[0085] Among them, δ - (v`(t)) represents the set of all edges leaving point v' at time t;

[0086] Specifically, Figure 5 Point 5 t1 For example, the effect of this constraint is that for point 5 t1 , the robot (a1) must drive out of this point at the next time point after entering the point.

[0087] The specific constraints for avoiding collisions are:

[0088]

[0089] Among them, (u'(t), v'(t+1)) and (v'(t), u'(t+1)) are two intersecting edges in the directed dynamic space-time graph G'.

[0090] Specifically, u and v are two adjacent points in the graph G, and the graph G' is formed by expanding the graph G in the time dimension. Therefore, (u'(t), v'(t+1)) and (v'(t), u'(t+1)) are two intersecting edges in the directed dynamic space-time graph G'.

[0091] like Figure 4 As shown in the bridge structure in Figure 3, this constraint is used to avoid directional collisions between the two robots in the original map.

[0092] The specific task execution constraints are:

[0093]

[0094] Among them, i Represents the i-th task, which contains the starting and ending information of the i-th task;

[0095] The premise for the above equation to occur is:

[0096] 1) At time t+1, robot a just arrives at task o i Starting point i :

[0097]

[0098] Among them, i Represents the i-th task, which contains the starting and ending information of the i-th task, i.e. o i =(s i ,g i ), s i represents the starting point of the i-th task, g i represents the end point of the i-th task, m represents the total number of tasks, e j ∈δ + (s' i e in (t+1)) j Indicates that at time t+1 all the slaves enter the i-th task o i Starting point s' i An edge in the set of edges of a point, x a,j Represents robot a about edge e j If it is equal to 1, it means that the trajectory of robot a passes through this edge.

[0099] Specifically, The variable is associated with the starting point si of the i-th task at time t+1 in the graph G'. A value of 1 indicates that robot a is executing the i-th task at time t+1, and a value of 0 indicates that the i-th task is not executed.

[0100] 2) No tasks are executed at time t

[0101]

[0102] Specifically, if Figure 5 In the dynamic space-time diagram, at time t1, robot a1 arrives at the starting point 5 of task o1, ​​and does not perform any task at time t0. So the point variable will be set to 1.

[0103] The task completion constraints are as follows:

[0104]

[0105] The prerequisites for the above equation to occur are:

[0106] 1) At time t+1, robot a just arrives at task o i The end point g i :

[0107]

[0108] Among them, e j ∈δ + (g' i e in (t+1)) j Indicates that at time t+1 all the slaves enter the i-th task o i The end point g' i An edge in the set of edges of a point, x a,j Represents robot a about edge e j If the variable is equal to 1, it means that the trajectory of robot a passes through this edge;

[0109] 2) At time t, robot a is performing task o i :

[0110]

[0111] Specifically, if Figure 5 In the dynamic space-time diagram, at time t3, robot a1 reaches the end point 1 of task o1, ​​and at time t2 is performing task o1. So the point variable It will be set to 1, indicating that at time t3, robot a1 has completed task o1.

[0112] Task → Robot Constraints are:

[0113]

[0114] Specifically, any task at any time is either completed, being executed by a robot, or not yet executed. This constraint is explained in three cases: ① When the task has been completed, such as Figure 5 In the original map, when robot a1 reaches the end point 3 of task 1 from point 4, the corresponding point 3 in the dynamic space-time graph t2 D a1,(o1,t2) The variable will be assigned a value of 1 and will remain so until the end of the schedule. After that, even if any robot reaches the starting point of Task 1, its corresponding P variable will not be assigned a value of 1, thus preventing the same task from being executed multiple times. Figure 5 In the original map, when robot a1 arrives at the starting point 5 of task 1 from point 4, the corresponding point 5 in the dynamic space-time grapht1 P a1,(o1,t1) The variable will be assigned a value of 1 and will remain so until Task 1 is completed. At this point, even if other robots reach the end point of Task 1, their corresponding D variables will not be assigned a value of 1, thus avoiding errors in determining whether the task is complete. ③ If a task has not yet been completed, the P and D variables corresponding to its starting and end points are both assigned a value of 0, waiting for robots to arrive to perform the task.

[0115] Robot → Task constraints are as follows:

[0116]

[0117] Specifically, any robot can only execute one task at any time, or it has completed the task. Figure 5 As shown in the dynamic time-space diagram, for each time step t, there are two task starting points and their variables P. If one of them is assigned a value of 1, the other must be equal to 0. Assuming that robot a1 is performing task o1, ​​then at time step t2, the variable Pa1, (o1, t2) corresponding to the starting point 5 of task 1 will be assigned a value of 1. At this time, even if robot a1 passes the starting point s2 of task o2, its corresponding variable P a1,(o2,t2) It will not be assigned a value of 1, thus ensuring that the robot can only perform one task at a time.

[0118] Step S340: Setting the objective function. Further, step S340 is specifically as follows:

[0119]

[0120] Specifically, as limited by the previous constraints, for each task, when it is completed, the D variable value corresponding to the task endpoint will remain 1 until the end of the scheduling. Therefore, it is natural to use the maximization of the sum of all D variables in the last time step T as the objective function.

[0121] Task allocation is introduced into the problem model by setting decision variables P and D, task-robot assignment constraints, and task start / completion constraints. Path planning is introduced into the problem model by designing decision variables X, task-edge constraints, flow-edge constraints, node deadlock avoidance constraints, and opposite-direction collision avoidance constraints. The corresponding optimization objective function is also designed, and one or more objective functions can be selected for joint optimization based on actual needs.

[0122] Step S400: Solving the integer linear programming mathematical model based on the branch and bound method to obtain edge variable values, variable values ​​corresponding to the task starting point, and variable values ​​corresponding to the task end point.

[0123] Specifically, to achieve higher accuracy, the present invention uses a branch-and-bound algorithm to solve the problem decision model. First, the entire solution space is branched, repeatedly dividing the solution space into smaller and smaller subsets. Each subset is then bounded, calculating a target bound for the solution set within the subset. Finally, pruning is performed. After each branch, if the target value of the known feasible solution set fails to meet the current bound, the subset is discarded. By discarding many subsets through these operations, the solution to the problem approaches the optimal solution. Repeating these three operations will yield the optimal solution for the model. The optimal solution includes the variable values ​​corresponding to the task start and end points, as well as the edge variable values. For example, in an example with three pairs of task start and end points, and the local graph is expanded three times in the time dimension, the algorithm sets variables p1, p2, ..., p9 for each of the nine task start points in the dynamic spatiotemporal graph. Similarly, variables d1, d2, ..., d9 are set for each of the nine task start points. Variables x1, ..., xn are set for all edges in the graph.

[0124] Step S500: Determine the number of currently completed tasks based on the variable value corresponding to the task endpoint. When the currently completed number of tasks is equal to the preset number of tasks, obtain the task allocation status based on the variable value corresponding to the task starting point and the variable value corresponding to the task endpoint, and obtain the path planning status based on the edge variable value.

[0125] Specifically, when the number of completed tasks currently equals the preset number, the task allocation status is determined based on the values ​​of the P and D variables, and the path planning status is determined based on the value of the X variable. For example, robot a1 begins executing task o1 at time step t1 and completes it at time step t3. Path planning status can also be determined, indicating which edge robot a1 passes at a certain time step. Finally, the task allocation and path planning results are output.

[0126] Furthermore, step S500 also includes: when the number of currently completed tasks is not equal to the preset number of tasks, iterating the time step and returning to step S200 until the minimum time step that just completes all tasks is found.

[0127] Specifically, if Figure 5 As shown, when T=3, at time step t3, the objective function value is obviously only equal to 1 (because only task 1 has been completed), which is not equal to the number of tasks 2. Therefore, it is necessary to increase the time step T by 1 and repeat steps S200 to S400 until all tasks are completed.

[0128] Because the joint scheduling problem of a multi-transport robot system based on a pickup and delivery mode is very complex, it is difficult to simply describe it using mathematical formulas and models. However, when the capacity of each edge in the network flow graph is 1, the multi-commodity network flow problem can be regarded as a multi-path planning problem. This invention uses network flow theory to design corresponding decision variables and constraints for task allocation and path planning, respectively, while satisfying the basic network flow capacity limit and flow conservation limit. This transforms the multi-transport robot task allocation and path planning problem into a multi-commodity network flow problem with special constraints, thereby solving the complex collaborative scheduling problem with fewer mathematical constraints, effectively improving the solution quality.

[0129] The above describes in detail the multi-robot joint scheduling optimization method based on a dynamic spatiotemporal graph provided by the present invention. This article uses specific examples to illustrate the principles and implementation methods of the present invention. The description of the above examples is only intended to help understand the core concept of the present invention. It should be noted that those skilled in the art can make various improvements and modifications to the present invention without departing from the principles of the present invention, and such improvements and modifications also fall within the scope of protection of the claims of the present invention.

Claims

1. A multi-robot joint scheduling optimization method based on dynamic spatiotemporal graph, characterized in that: The method comprises the following steps: Step S100: Obtain initial parameters and initialize the time step; Step S200: Expand the undirected original map G(V, E) in the time dimension using a special bridging structure based on the initial parameters to transform it into a directed dynamic spatiotemporal graph G'=(V', E', C); where V is the original node set, E is the original edge set, V' is a node in the dynamic spatiotemporal graph, E' is an edge in the dynamic spatiotemporal graph, and C is the capacity set of the edges; Step S300: constructing an integer linear programming mathematical model according to the directed dynamic space-time graph; Step S300 includes: Step S310: In the dynamic spatiotemporal graph, construct an edge variable X for each edge e`∈E` a,j , where a represents the robot number and j represents the edge number; Step S320: In the dynamic spatiotemporal graph, construct a point variable for the starting point of each task in Indicates that robot a is performing the i-th task oi at time t; construct a point variable for the end point of each task in Indicates that robot a has completed the i-th task oi at time t; Step S330: setting node deadlock avoidance constraints, flow conservation constraints, opposite collision avoidance constraints, task execution constraints, task completion constraints, task→robot constraints, and robot→task constraints; Step S340: setting the objective function; Step S400: Solving the integer linear programming mathematical model based on the branch and bound method to obtain edge variable values, variable values ​​corresponding to the task starting point, and variable values ​​corresponding to the task end point; Step S500: Determine the number of currently completed tasks based on the variable value corresponding to the task endpoint. When the currently completed number of tasks is equal to the preset number of tasks, obtain the task allocation status based on the variable value corresponding to the task starting point and the variable value corresponding to the task endpoint, and obtain the path planning status based on the edge variable value.

2. The method according to claim 1, characterized in that The initial parameters in step S100 include A transport robot starting point coordinates, m pairs of task start / end point coordinates and original map information.

3. The method according to claim 2, characterized in that In step S200, V' includes the original node and time information, and E' is a directed edge, including its previous and next nodes and time information, and points from the previous time node to the next time point.

4. The method according to claim 3, characterized in that In step S330: The node deadlock avoidance constraint is to constrain the sum of the variables of the edges entering all points, that is, for each point, the X of all its incoming edges is a,j The sum is ≤1, specifically: Among them, δ + (v`(t)) represents the set of all edges entering v' at time t, e' j represents the j-th edge in the set, a represents the robot number, G` represents a directed dynamic spatiotemporal graph, A represents the number of robots, and T represents the total time step; The flow conservation constraint is that for each point, the sum of its incoming edge flows = the sum of its outgoing edge flows, specifically: Among them, δ - (v`(t)) represents the set of all edges leaving point v' at time t; The specific constraints for avoiding collisions are: Among them, (u'(t), v'(t+1)) and (v'(t), u'(t+1)) are two intersecting edges in the directed dynamic space-time graph G'; The task execution constraints are specifically: Among them, i Represents the i-th task, which contains the starting and ending information of the i-th task; The premise for the above equation to occur is: 1) At time t+1, robot a just arrives at task o i Starting point i : Among them, i Represents the i-th task, which contains the starting and ending information of the i-th task, i.e. o i =(s i ,g i ), s i represents the starting point of the i-th task, g i represents the end point of the i-th task, m represents the total number of tasks, e j ∈δ + (s' i e in (t+1)) j Indicates that at time t+1 all the slaves enter the i-th task o i Starting point s' i An edge in the set of edges of a point, x a,j Represents robot a about edge e j If the variable is equal to 1, it means that the trajectory of robot a passes through this edge; 2) And no tasks are executed at time t: The task completion constraints are specifically: The prerequisites for the above equation to occur are: 1) At time t+1, robot a just arrives at task o i The end point g i : Among them, e j ∈δ + (g' i e in (t+1)) j Indicates that at time t+1 all the slaves enter the i-th task o i The end point g' i An edge in the set of edges of a point, x a,j Represents robot a about edge e j If the variable is equal to 1, it means that the trajectory of robot a passes through this edge; 2) At time t, robot a is performing task o i : The task→robot constraints are specifically: The robot→task constraints are specifically: 。 5. The method according to claim 4, characterized in that Step S340 is specifically as follows: 。 6. The method according to claim 5, characterized in that Step S500 further includes: When the current number of completed tasks is not equal to the preset number of tasks, the time step is iterated and the process returns to step S200 until the minimum time step for completing all tasks is found.

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