An optimal scheduling search method for multi-robot cooperative system

Abstract

The present invention relates to the technical field of intelligent manufacturing systems, and discloses an optimal scheduling search method for a multi-robot coordination and cooperation system, including: constructing a timed Petri net model of the multi-robot coordination and cooperation system according to the robot resource usage and production process of the multi-robot coordination and cooperation system; constructing a state diagram under the fastest excitation strategy based on the timed Petri net model, and the state diagram retains the optimal state sequence with the shortest corresponding processing time; designing a state merging rule in combination with the structural information of the Petri net, eliminating redundant states that do not belong to the optimal state sequence, and reducing the scale of the state diagram; searching the state diagram through a global search to obtain the optimal scheduling solution of the system. The present invention constructs a timed Petri net model that effectively characterizes the conflict relationship of multi-robot resources and the logic and time relationship of processing events, and on this basis constructs and searches a state space containing an optimal processing event sequence, thereby obtaining an optimal scheduling strategy.

Description

Technical Field

[0001] The present invention relates to the technical field of intelligent manufacturing systems, and in particular to an optimal scheduling search method for a multi-robot coordinated cooperation system. Background Art

[0002] With the development of technologies such as big data, artificial intelligence, and industrial interconnection, intelligent robots are widely used in various links of intelligent manufacturing systems such as procurement, production, and distribution. However, as the participation of intelligent robots deepens, the increase in their number will inevitably cause a sharp increase in system states and even state explosion, which brings unprecedented challenges to the optimization and scheduling of intelligent manufacturing systems. In addition, intelligent manufacturing places high demands on the efficiency and flexibility of the system, which requires the system to reasonably allocate resources such as robots and flexibly arrange specific links of the production process to achieve the scheduling goal of the shortest production operation time.

[0003] In the intelligent manufacturing system with multiple robots, it involves not only the allocation of resources but also the scheduling of the production process. This requires the ability to accurately describe the parallel, sequential, selection, conflict and other event relationships of the system. As a formal modeling tool, Petri nets not only have rigorous mathematical expressions, but also vivid graphical representations, which can accurately describe the logical relationships between various events in the intelligent manufacturing system. In addition, considering the time constraints of events, timed Petri nets with time information are used here to construct the modeling language of the intelligent manufacturing system. On this basis, the finite state space representation method of the system can be further analyzed to solve the most efficient processing event sequence. In recent years, methods for using timed Petri nets for system scheduling optimization have been proposed for various manufacturing systems. Existing scheduling strategy research based on Petri nets and search methods such as heuristic search and greedy algorithm (such as Chinese invention patents CN118689172A, CN117421105A and CN117406684B) mainly relies on the time of the heuristic function using a reachable graph without time information. The neglect of time information increases the difficulty of designing the heuristic function on the one hand; on the other hand, it also causes the design of the heuristic function or the search strategy to be overly dependent on the specific system structure. Once the structure of the system changes, the efficiency of the search scheduling method is difficult to guarantee. In addition, the representation and simplification methods of conflicting relationships between resources and the representation and simplification methods of state space with time information are not clearly given, that is, the Petri net model construction and state space representation problems of multi-robot systems have not been solved.

[0004] In summary, existing methods are not suitable for solving the optimal scheduling problem of intelligent manufacturing systems with multi-robot resources, and it is difficult to meet the actual production needs of such systems. Summary of the invention

[0005] The purpose of the present invention is to solve the problems in the prior art.

[0006] The technical solution adopted by the present invention to solve the technical problem is: to provide an optimal scheduling search method for a multi-robot coordinated cooperation system, comprising the following steps:

[0007] According to the robot resource usage and production process of the multi-robot cooperative system, a place-timed Petri net model of the multi-robot cooperative system is constructed, in which the resource place represents the state of the robot resources, and the time added to the Petri net transition represents the time consumption of the production operation.

[0008] Based on the place timed Petri net model, a state diagram under the fastest excitation strategy is constructed, which retains the optimal state sequence with the shortest processing time.

[0009] The state merging rules are designed based on the structural information of Petri nets, and the redundant states that do not belong to the optimal state sequence are eliminated to reduce the size of the state diagram.

[0010] The optimal scheduling solution for the system can be obtained by searching the state diagram through global search.

[0011] Preferably, the method of constructing a timed Petri net model of a multi-robot coordination and cooperation system according to the robot resource usage and production process of the multi-robot coordination and cooperation system comprises the following steps:

[0012] The sequential and parallel structure of the system's Petri net is built according to the production process, where the structure of transition connected to place and then connected to transition corresponds to the start action, progress state, and end action of a certain production operation, and the specific time of the place is the specific time consumption of the production operation corresponding to the place;

[0013] Analyze the conflict relationship between resources and construct the minimum conflict library set. There is a robot resource competition between the production operations corresponding to any two libraries in the set. There is a library that is not in the set, and its corresponding production operation does not conflict with the production operation corresponding to a library in the set.

[0014] A Petri conflict structure is constructed based on the minimum conflict place set; a conflict resource place is constructed for each minimum conflict place set, and the conflict resource place represents the robot resources that will be contended for by the processing operations corresponding to all places in the minimum conflict place set; the Petri conflict structure is constructed, including directed arcs starting from the conflict resource place and terminating at the start transition of each place in the minimum conflict place set, and directed arcs starting from the end transition of each place in the minimum conflict place set and terminating at the resource place;

[0015] The start and end places of the multi-robot coordination and cooperation system are constructed to represent the start and end states of the system production, respectively. The number of tokens placed in the start place is the total batch number of production tasks; the initial number of tokens in each resource place is 1, indicating that the robot resources are idle and can be used.

[0016] Preferably, the construction of a state diagram under the fastest excitation strategy based on the library-place timed Petri net model comprises the following steps:

[0017] Determine the state representation form of the timed Petri net of the library, state Include logo , Remaining delay , Time consumption of current state ; Initial state ,in, is the initial identifier, is the initial residual delay, The time consumption for the initial state;

[0018] According to the fastest excitation strategy, the evolution rules of the state are formalized, and the logical conditions and time conditions for enabling transitions are given, as well as the rules for the evolution of the state with time and transition excitation;

[0019] Starting from the initial state, combined with the evolution rules of the state under the fastest excitation strategy, a bounded state space graph is constructed as the state graph under the fastest excitation strategy.

[0020] Preferably, the state representation form of the timed Petri net of the determination library includes:

[0021] Define the remaining delay function , which means that the library is collected Mapping to a real matrix ,in, represents all sets, is the maximum number of tokens in the Petri net; Each token in the library is associated with a decreasing clock. When the token enters the library, its corresponding clock increases from the initial value Start decreasing, where It is a library Fixed delay of ; residual delay function General library place Mapped to a Dimensional vector , where the elements Indicates Enter the library The remaining delay of the token is sorted in descending order. ;

[0022] For the initial state , given any and any :if but , Indicates the initial residual delay The jth entry into the library The remaining delay of the token; if ,but ,in For the initial identification.

[0023] Preferably, the logic conditions and time conditions for enabling the transition include: Start from the creation time, after time unit, change The conditions that can be triggered are , that is, any forward place of the transition There are available tokens in all of them, and the number of available tokens is greater than or equal to the number of transitions from the library to The arc weight ;

[0024] The rules for the evolution of the state over time and transition stimulation include: In Status The following can be stimulated, The time interval is expressed as:

[0025] ;

[0026] Among them, Remaining delay Determine according to the following rules: Any token that has been in its location since the moment it was created will be The remaining delay in minus If the value of is non-negative, the token is The remaining delay in minus The value of the token is The residual delay in is zero otherwise; Any token that was just placed in the library when it was triggered, The remaining delay in is equal to the initial delay .

[0027] Preferably, the constructing of the bounded state space graph comprises the following steps:

[0028] Input the timed Petri net model of the multi-robot collaborative system;

[0029] According to the initial identification Hekushu Fixed delay Determine the initial state , and Place in state collection and the state table middle;

[0030] When the status table When it is not empty, the status table The first state in Take out and enable transition by stimulating , construct the state All subsequent status ,in, ,express By stimulating the transition t , , according to calculated;

[0031] Determine the status Whether to place in the state collection In; if the state set Existence status , then let , do not change the status Place in collection Otherwise, the status Place in collection In , ;

[0032] Transition between structural states and transfer time ;

[0033] Output bounded state space graph .

[0034] Preferably, reducing the size of the state diagram comprises the following steps:

[0035] Define the paths in the Petri net and their time costs;

[0036] According to the structural information and time information of the Petri net, construct To the target state The first time cost estimation function , the time estimation function is less than or equal to the actual time cost from the current state to the target state , ; represents the key place set, Represents the target library set;

[0037] According to the structural information and time information of the Petri net, construct To the target state The second time cost estimation function , the time estimation function is greater than or equal to the actual time cost from the current state to the target state , , Represents the target place set A place in the

[0038] According to the first time cost estimation function and the second time cost estimation function Merge states to reduce the size of the state diagram.

[0039] Preferably, the defining of the paths and their time costs in the Petri net comprises the following steps:

[0040] Defining Paths , where all the libraries , and satisfy Make and Established, among which, , I represents the total number of places in the path, and They represent the forward incidence matrix and backward incidence matrix of the Petri net model respectively;

[0041] path The first and last nodes of and ,path The time cost is: ,in ;

[0042] Define the key place set and the target place set; given a transition and a state ,satisfy and The library place of is defined as the key library place, and the key library place set is recorded as ; For a given target ID , define the set of libraries containing tokens as the target library set .

[0043] Preferably, the first time cost estimation function and the second time cost estimation function Merge the statuses. The merging rules are as follows:

[0044] If for the newly generated state If there is a state Make , then let , do not change the status Place in collection middle;

[0045] If for the newly generated state If there is a state Make , then the state From the collection Remove it and change the status Place in collection and the state table middle;

[0046] If for the newly generated state , does not exist Make or If established, the state Place in collection and the state table middle.

[0047] Preferably, the search of the state diagram through global search can obtain the optimal scheduling plan of the system, specifically: according to the initial situation and processing objectives of the actual system, the initial state and target state of the Petri net model are given, and the minimum completion time is used as the scheduling goal. The Dijkstra algorithm is used to construct a bounded state diagram or a reduced bounded state diagram, and the transition excitation trajectory containing time information from the initial state of the system to the target state is searched. The excitation trajectory takes the shortest time and corresponds to the processing event sequence with the shortest completion time.

[0048] The present invention has the following beneficial effects:

[0049] (1) For the production operation of multiple robot resources, the Petri net model of the system is constructed in combination with the production process. The system's competition for robot resources is described through the system's minimum conflict library set and the resource library is constructed. In this way, the system's logical relationships such as parallelism, sequence, and conflict, as well as time constraints such as the time consumption of production operations are vividly and intuitively represented, laying a model foundation for the subsequent design of the optimal scheduling strategy;

[0050] (2) Based on the system's place timed Petri net model, the present invention provides a method for representing a bounded state space. The state diagram contains the optimal trajectory from the initial state to the target state. By searching the state diagram, it is possible to obtain a processing time sequence with the shortest completion time.

[0051] (3) For large-scale systems, the present invention reduces the bounded state graph and designs two state evaluation functions. These two evaluation functions can eliminate certain states that do not belong to the optimal trajectory, thereby reducing the scale of the state graph while ensuring that the optimal trajectory is retained. By searching the reduced state graph, the processing event sequence with the minimum completion time can be obtained more quickly.

[0052] The present invention is further described in detail below in conjunction with the accompanying drawings and embodiments, but the present invention is not limited to the embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 A method step diagram of an embodiment of the present invention;

[0054] Figure 2 is a detailed flow chart of an embodiment of the present invention;

[0055] Figure 3 A schematic diagram of a multi-robot coordination and cooperation system according to an embodiment of the present invention;

[0056] Figure 4 This is a timed Petri net model of a library of a multi-robot coordination and cooperation system according to an embodiment of the present invention. DETAILED DESCRIPTION

[0057] See also Figure 1 and Figure 2 The method step diagram and detailed flow chart of the embodiment of the present invention are shown, which include the following steps:

[0058] S101, constructing a place-timed Petri net model of the multi-robot coordination and cooperation system according to the robot resource usage and production process of the multi-robot coordination and cooperation system, wherein the resource place represents the state of the robot resources, and adding time to the Petri net transition represents the time consumption of the production operation;

[0059] S102, constructing a state diagram under the fastest excitation strategy based on the place timed Petri net model, the state diagram retains the optimal state sequence with the shortest processing time;

[0060] S103, designing a state merging rule based on the structural information of the Petri net, removing redundant states that do not belong to the optimal state sequence, and reducing the size of the state diagram;

[0061] S104, searching the state diagram through global search can obtain the optimal scheduling solution of the system.

[0062] Specifically, in this embodiment, the optimal scheduling state space construction and search for multi-machine coordinated cooperation are obtained through the following hardware specifications: CPU i9-12900K 3.20 GHz, RAM 64.0GB.

[0063] See also Figure 3 FIG. 1 is a schematic diagram of a multi-robot collaborative system according to an embodiment of the present invention. The system includes a robot responsible for handling , and , the machine responsible for processing , , and , loading station , , and unloading station , , , and the workpiece to be processed. The system produces three types of products: A, B, and C.

[0064] The specific processing of A products is divided into , , Three production operations, the workpieces to be processed are loaded at the loading station Enter the production line of product A, where The robot corresponds to the workpiece to be processed From the loading station Transport to the machine , it takes 8s; Corresponding to the workpiece in the machine Medium processing, taking 34s; Corresponding to the robot The workpiece is removed from the machine Transport to unloading station , which takes 5 seconds.

[0065] The specific processing of B products is divided into , , , , Five production operations, the workpieces to be processed are loaded at the loading station Enter the production line of product B, where The robot corresponds to the workpiece to be processed From the loading station Transport to the machine or , it takes 4 seconds; Corresponding to the workpiece in the machine or Medium processing, taking 32s or 23s; Corresponding to the robot The workpiece is removed from the machine or Transport to the machine or , taking 8s or 6s; Corresponding to the workpiece in the machine or Medium processing, taking 38s or 20s; Corresponding to the robot The workpiece is removed from the machine or Transport to unloading station , which takes 5 seconds.

[0066] The specific processing of C products is divided into , , , , Five production operations, the workpieces to be processed are loaded at the loading station Enter the production line of product C, where The robot corresponds to the workpiece to be processed From the loading station Transport to the machine , it takes 5 seconds; Corresponding to the workpiece in the machine Medium processing, taking 22 seconds; Corresponding to the robot The workpiece is removed from the machine Transport to the machine , it takes 4 seconds; Corresponding to the workpiece in the machine Medium processing, taking 17s; Corresponding to the robot The workpiece is removed from the machine Transport to unloading station , which takes 6 seconds.

[0067] Each robot , and Only one workpiece can be moved at a time, and each processing machine , , and Only one workpiece can be processed at a time. In summary, the process and time consumption of the multi-robot production system for three types of products are shown in Table 1.

[0068] Table 1 Process technology of multi-robot production system for three types of products:

[0069]

[0070] Specifically, the library timed Petri net model of the multi-robot collaborative operation system obtained in step S101 in this embodiment can be found in Figure 4 As shown in the figure, it includes the timed Petri net model of the robot operation system corresponding to the production process, and the state control place part which uses the resource place to represent the robot resources. Corresponding to production operations , its delay ; Library Corresponding to production operations And delay Library Corresponding to production operations use , whose delay is ; Library Corresponding to production operations And delay According to the occupation of resources such as robots by production operations, the largest collection of warehouses is , corresponding to the structure control library .

[0071] Specifically, S104 of this embodiment is based on the initial situation and processing objectives of the actual system, given the initial state and target state of the Petri net model, with the minimum completion time as the scheduling goal, and the Dijkstra algorithm is used to construct a bounded state graph or a reduced bounded state graph, to search for a transition excitation trajectory containing time information from the initial state of the system to the target state. The excitation trajectory takes the shortest time and corresponds to a processing event sequence with the shortest completion time.

[0072] As shown in Table 2, the batch The six different values ​​are set to show the completion time and the number of states searched by the scheduling strategy obtained by searching the bounded state graph and the reduced state graph. For these experiments, the number of searched states is limited to a maximum of 150,000. Therefore, if the size of a state graph exceeds 150,000, the program will terminate, and Table 2 uses " / " to represent the size of the state graph.

[0073] Table 2 shows the scheduling results of different batches obtained by searching the state diagram:

[0074] In the first three groups of experiments, the scheduling strategy with the shortest completion time can be found by searching the two state graphs, but it is obvious that the size of the reduced state graph is significantly reduced; in the last three groups of experiments, as the batch size increases, the number of states of the bounded state graph exceeds 150,000, while the number of states of the reduced state graph is less than 150,000, and the optimal scheduling strategy with the shortest completion time can be found.

[0075] The above are only preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. An optimal scheduling search method for a multi-robot coordination system, characterized in that: The following steps are involved: According to the robot resource usage and production process of the multi-robot cooperative system, a place-timed Petri net model of the multi-robot cooperative system is constructed, in which the resource place represents the state of the robot resources, and the time added to the Petri net transition represents the time consumption of the production operation. Based on the place timed Petri net model, a state diagram under the fastest excitation strategy is constructed, which retains the optimal state sequence with the shortest processing time. The state merging rules are designed based on the structural information of Petri nets, and the redundant states that do not belong to the optimal state sequence are eliminated to reduce the size of the state diagram. The optimal scheduling scheme of the system is obtained by searching the reduced-scale state graph through global search; The method of constructing a state diagram under the fastest excitation strategy based on the place-timed Petri net model includes the following steps: Determine the state representation form of the place timed Petri net, the state s = (m, v, g) includes the identifier m, the remaining delay v, and the time consumption g of the current state; the initial state s0 = (m0, v0, 0), where m0 is the initial identifier, v0 is the initial remaining delay, and g0 = 0 is the time consumption of the initial state; According to the fastest excitation strategy, the evolution rules of the state are formalized, and the logical conditions and time conditions for enabling transitions are given, as well as the rules for the evolution of the state with time and transition excitation; Starting from the initial state, combined with the evolution rules of the state under the fastest excitation strategy, a bounded state space diagram is constructed as the state diagram under the fastest excitation strategy; The reducing the size of the state diagram comprises the following steps: Define the paths in the Petri net and their time costs; According to the structural information and time information of the Petri net, construct a transition from the current state s to the target state s g The first time cost estimation function h1(s,s g ), the time estimation function is less than or equal to the actual time cost h from the current state to the target state * (s,s g ), represents the key place set, P g represents the target library set; π represents the path, ＊ π and π ＊ represents the first node and the last node of the path π, τ(π) represents the time cost of the path π; According to the structural information and time information of the Petri net, construct a transition from the current state s to the target state s g The second time cost estimation function h2(s,s g ), the time estimation function is greater than or equal to the actual time cost h from the current state to the target state * (s,s g ), p′ represents the target library set P g A library in the According to the first time cost estimation function h1(s,s g ) and the second time cost estimation function h2(s,s g ) to merge states and reduce the size of the state diagram.

2. The optimal scheduling search method for a multi-robot coordination and cooperation system according to claim 1, characterized in that: The method of constructing a timed Petri net model of a multi-robot coordination and cooperation system according to the robot resource usage and production process of the multi-robot coordination and cooperation system comprises the following steps: The sequential and parallel structure of the system's Petri net is built according to the production process, where the structure of transition connected to place and then connected to transition corresponds to the start action, progress state, and end action of a certain production operation, and the specific time of the place is the specific time consumption of the production operation corresponding to the place; Analyze the conflict relationship between resources and construct the minimum conflict library set. There is a robot resource competition between the production operations corresponding to any two libraries in the set. There is a library that is not in the set, and its corresponding production operation does not conflict with the production operation corresponding to a library in the set. A Petri conflict structure is constructed based on the minimum conflict place set; a conflict resource place is constructed for each minimum conflict place set, and the conflict resource place represents the robot resources that will be contended for by the processing operations corresponding to all places in the minimum conflict place set; the Petri conflict structure is constructed, including directed arcs starting from the conflict resource place and terminating at the start transition of each place in the minimum conflict place set, and directed arcs starting from the end transition of each place in the minimum conflict place set and terminating at the resource place; The start and end places of the multi-robot coordination and cooperation system are constructed to represent the start and end states of the system production, respectively. The number of tokens placed in the start place is the total batch number of production tasks; the initial number of tokens in each resource place is 1, indicating that the robot resources are idle and can be used.

3. The optimal scheduling search method for a multi-robot coordination and cooperation system according to claim 1, characterized in that: The state representation form of the determined library timed Petri net includes: Define the residual delay function v:P→R K , which means mapping the place set P to the real matrix R K , where R represents all sets and K is the maximum number of tokens in the Petri net; each token in a place in P is associated with a decreasing clock. When a token enters a place, its corresponding clock decreases from the initial value d(p), where d(p) is the fixed delay of place p; the residual delay function v maps place p to a K-dimensional vector v(p), where the element v(p)[i] represents the residual delay of the i-th token entering place p, and is arranged in descending order of value, 1≤i≤K; For the initial state s0=(m0,v0,0), given any p∈P and any j∈{1,2,...,K}: if j≤m0(p), then v0(p)[j]=d(p), v0(p)[j] represents the residual delay of the jth token entering place p in the initial residual delay v0; if j>m0(p), then v0(p)[j]=0, ​​where m0 is the initial identifier.

4. The optimal scheduling search method for a multi-robot coordination and cooperation system according to claim 1, characterized in that: The logic conditions and time conditions for enabling the transition include: starting from the moment when the state s = (m, v, g) is generated, after δ time units, the condition that the transition t can be triggered is At this time, any forward place p∈·t of the transition has available tokens, and the number of available tokens is greater than or equal to the arc weight Pre(p,t) from the place to transition t. The rules for the evolution of the state over time and transition stimulation include: if the transition e k+1 In status k The k+1th time interval can be expressed as: Among them, the k+1th residual delay v k+1 Determine according to the following rules: k Any token that has been in its location since the moment it was created, if the token is in v k The residual delay in minus δ k+1 If the value of is non-negative, the token is k The residual delay in minus δ k+1 The value of the token in v k+1 The residual delay in e is zero otherwise. k+1 Any token that was just placed in the library when it was triggered, which is in v k+1 The residual delay in is equal to the initial delay d(p).

5. The optimal scheduling search method for a multi-robot coordination and cooperation system according to claim 1, characterized in that: The construction of the bounded state space graph comprises the following steps: Input the timed Petri net model of the multi-robot collaborative system; Determine the initial state s0 = (m0, v0, 0) according to the initial identifier m0 and the fixed delay d(p) of the library place p, and place s0 in the state set S and the state table L; When the state table L is not empty, the first state s in the state table L is * =(m * ,v * ,g * ) is taken out, and the state s is constructed by stimulating the enabling transition t. * All subsequent states s ** =(m ** ,v ** ,g ** ), where m * [t>m ** , indicating m * By stimulating the transition t is transformed into m ** , v ** According to v * calculated; Determine the status ** =(m ** ,v ** ,g ** ) is placed in the state set S; if there is a state s'=s in the state set S ** , then let s ** =s', do not change the state s ** Place it in the set S; otherwise, the state s ** Placed in the set S, that is, S←S∪{s ** }, L←L∪{s ** }; Transition between structural statesΩ(s * ,s ** )←t and the transfer time B(s * ,s ** )←δ; Output bounded state space graph (S,Ω,B,s0).

6. The optimal scheduling search method for a multi-robot coordination and cooperation system according to claim 1, characterized in that: Defining the paths and their time costs in the Petri net includes the following steps: Defining Paths Among them, all libraries And satisfy Make and Established, where i = 1, 2, ..., I-1, I represents the total number of places in the path, Pre and Post represent the forward and backward incidence matrices of the Petri net model respectively; The first and last nodes of a path π are represented as ＊ π and π ＊ , the time cost of path π is: in Define the key place set and the target place set; given a transition t and a state s = (m, v, g), satisfying m(p) ≠ 0 and The library place of is defined as the key library place, and the key library place set is recorded as For a given target ID m g , define the set of libraries containing tokens as the target library set P g ={p∈P|m g (p)≠0}.

7. The optimal scheduling search method for a multi-robot coordination and cooperation system according to claim 1, characterized in that: According to the first time cost estimation function h1(s,s g ) and the second time cost estimation function h2(s,s g ) to merge the states. The merging rules are as follows: If for a newly generated state s, there exists a state s′=(m′,v′,g′)∈S such that h1(s′,s g )+g′≥h2(s,s g )+g, then let s=s', and do not place state s in the set S; If for a newly generated state s, there exists a state s′=(m′,v′,g′)∈S such that h1(s,s g )+g≥h2(s′,s g )+g′, then remove state s′ from set S and place state s in set S and state table L; If for the newly generated state s, there is no state s′=(m′,v′,g′)∈S such that h1(s,s g )+g≥h2(s′,s g )+g′orh1(s′,s g )+g′≥h2(s,s g )+g holds, then the state s is placed in the set S and the state table L.

8. The optimal scheduling search method for a multi-robot coordination and cooperation system according to claim 1, characterized in that: The optimal scheduling scheme of the system is obtained by searching the state diagram through global search, specifically: according to the initial situation and processing objectives of the actual system, the initial state and target state of the Petri net model are given, and the minimum completion time is used as the scheduling goal. The Dijkstra algorithm is used to search for the transition excitation trajectory containing time information from the initial state of the system to the target state on the basis of the reduced bounded state diagram. The excitation trajectory takes the shortest time and corresponds to the processing event sequence with the shortest completion time.

Images