A Multi-Operator Cooperative Path Planning Method Based on Wargaming Platform

Abstract

This invention discloses a multi-operator cooperative path planning method based on a wargaming platform, which addresses the problem of multi-operator cooperative planning for traversing dangerous areas, based on an improved A... * The algorithm implements multi-objective path planning. This method introduces time nodes, enabling operators to utilize time information for temporal and spatial coordination. It improves the evaluation function by introducing damage costs, achieving hazard avoidance for operators. Employing a coordinate rotation method, it optimizes operator paths one by one based on pre-planned results, reducing the search dimensionality, decreasing the number of search nodes, and improving planning efficiency. Experimental results show that this method can efficiently plan cooperative paths for operators, shorten operator maneuver time, and reduce operator damage costs.

Description

Technical Field

[0001] This invention relates to the field of wargaming and path planning technology, and in particular to a multi-operator collaborative path planning method based on a wargaming platform. Background Technology

[0002] Wargames (military simulation) are simulations of combat situations using specific rules. Generally, wargames serve three purposes: first, training officers' decision-making abilities in actual combat; second, familiarizing officers with certain operational strategies; and third, analyzing and simulating real-world strategic, operational, and combat situations to identify suitable tactics. It is evident that wargames play a crucial role in improving decision-making capabilities and optimizing tactical deployments. Currently, wargames are gradually becoming a research hotspot in China. By combining wargame concepts with modern information technologies such as modeling and simulation, computer networks, and parallel computing, wargame systems suitable for simulating modern warfare are being established.

[0003] The chessboard, pieces, and rules constitute the basic form of any board game, and wargames are no exception. The chessboard in wargames is called a wargame map. Wargame maps can be drawn to scale according to real terrain or can be virtual maps containing various terrain features. The pieces of each side are placed on specific grids, often composed of hexagonal grids, with different hexagonal grids containing different information. Wargame pieces represent specific combat units or battlefield events; pieces representing combat units are called "unit operators," and pieces representing battlefield events are called "event operators." Wargame rules are the fundamental principles guiding the implementation of wargame simulations and are the core of wargame simulations. The rationality of the rules directly affects the credibility of the simulation analysis results.

[0004] Path planning is a fundamental problem in wargaming, a basic capability of operators, and directly affects their operational efficiency and battlefield survivability. In wargaming, operators will perform various maneuver missions, with rapid traversal of threat zones being a common one. Rapidly traversing threat zones within a specified time and at minimal cost requires coordination and joint planning among operators. Collaborative path planning takes a holistic view, emphasizing cooperation among operators, comprehensively considering the relationships between them, and ensuring the overall consistency of the system. In complex and ever-changing environments, collaborative path planning not only enables operators to reach their target locations efficiently and safely but also contributes to the realization of overall tactical intentions and improves combat effectiveness. Therefore, exploring a path planning method with fast convergence speed, high accuracy, and strong coordination based on hexagonal grid wargaming maps is crucial.

[0005] Cooperative planning for traversing hazardous areas requires short timeframes and low damage, making it a typical multi-objective optimization problem. Scholars both domestically and internationally have conducted significant research on this issue. Currently, most existing techniques focus on path planning for a single operator, neglecting the cooperative nature of multi-operator maneuvers. Summary of the Invention

[0006] To address the shortcomings of existing technologies, this invention addresses the problem of multi-operator cooperative maneuvering in hexagonal grid networks. Based on the traditional A* algorithm, it introduces the concept of time nodes, using the common factor of the time consumed to traverse different hexagonal grids as the node period. This allows the A* algorithm to expand its search according to time nodes, thus achieving operator cooperation.

[0007] To achieve the above objectives, this invention provides a multi-operator cooperative path planning method based on a wargaming platform, comprising the following steps:

[0008] Step 1: Obtain actual task information and construct a hexagonal grid map, where one hexagonal grid corresponds to multiple time nodes;

[0009] Step 2: Construct the objective function for multi-operator cooperative path planning:

[0010] J = minf(L) i ,L i + )

[0011] Among them, L i + For the paths of operators other than the i-th operator, it is treated as a fixed value in each optimization;

[0012] Step 3: Plan the initial path for each operator;

[0013] Step 4: Each operator will be optimized and updated for i rounds using the improved A* algorithm, and the collaborative planning path will be output.

[0014] Furthermore, the time node includes two types of node information: the time sequence number t of the current node. k The hexagonal grid k where the node is located.

[0015] Furthermore, the specific steps in step 4 are as follows:

[0016] Step 4.1: Define and initialize the old list and the new list, and store the initial path planned in Step 3 in the new list;

[0017] Step 4.2: Initialize the number of training rounds i = 1;

[0018] Step 4.3: If the old list stores the path data of the operators before the latest round of optimization, delete the path data of all the original operators in the old list, save the path data of the new list to the old list, and initialize the operator index j = 1;

[0019] Step 4.4: Delete the path data of operator j in the new list, optimize and update the path of operator j based on the remaining operator data using the improved A* algorithm, and store the updated path data back into the new list;

[0020] Step 4.5: Determine whether all operators have completed the i-th round of updates. If they have, proceed to step 4.6. If they have not, set j = j + 1 and proceed to step 4.4.

[0021] Step 4.6: Traverse the new list and the old list, and compare the strings to determine whether the operator path information in the new list and the old list is the same, or whether the training round number i has reached the preset update round number. If the path information is the same or the maximum update round number has been reached, the path update of the i-th round is completed. Otherwise, let i = i + 1 and go to step 4.3.

[0022] Furthermore, the improved A* algorithm described in step 4.4 includes the following steps:

[0023] Step 4.4.1: Construct time nodes;

[0024] Step 4.4.2: Determine the time interval T based on the types of all operators, and obtain the time t required for the operator to traverse a hexagonal grid with terrain elevation of m using the following formula. m (k):

[0025] t m (k)=r m *T r m ∈N* (2)

[0026] Where k represents the hexagonal grid where the time node is located; r m This represents the number of time points required for the operator to traverse a hexagonal grid with terrain of elevation m.

[0027] Step 4.4.3: Define and initialize the open and close lists;

[0028] Step 4.4.4: Add the initial time node of the i-th operator to the open list;

[0029] Step 4.4.5: Determine if the open list is empty. If it is, the path planning of operator i fails and the target point cannot be reached. If not, there is a time node in the open list, and proceed to step 4.4.6.

[0030] Step 4.4.6: Select the time node with the smallest estimated cost from the open list, delete it from the open list, and store the time node in the close list;

[0031] Step 4.4.7: Find the set of time nodes A corresponding to the time nodes stored in the close list in step 4.4.6, select the time nodes that have not yet been evaluated from the set of time nodes A, and proceed to step 4.4.8;

[0032] Step 4.4.8: Based on the time sequence number t of the time node k Determine whether the time node for incomplete evaluation selected in step 4.4.7 is in the close list, and if so, proceed to step 4.4.10; otherwise, proceed to step 4.4.9.

[0033] Step 4.4.9: Based on the time sequence number t of the time node k Determine whether the time node for which the evaluation was not completed in step 4.4.7 is in the open list, and if it is not, proceed to step 4.4.10; if it is, update the relevant information of the time node and proceed to step 4.4.11.

[0034] Step 4.4.10: Add the time nodes selected in step 4.4.7 to the open list and update the relevant information of the time nodes;

[0035] Step 4.4.11: Determine whether all nodes in the time node set A have been completely determined. If yes, proceed to step 4.4.12; otherwise, proceed to step 4.4.7.

[0036] Step 4.4.12: Determine whether the spatial location information of all time nodes in the time node set A is the target point. If it is the target node, obtain the route of operator i by backtracking, the path optimization is completed, and the planned path is output; otherwise, proceed to step 4.4.6.

[0037] Furthermore, the node-related information updated in steps 4.4.9 and 4.4.10 includes:

[0038] 1) Time sequence number of the time node

[0039]

[0040] In the formula, r i This represents the number of time nodes required to traverse the i-th hexagonal grid in the shortest path from the starting point to hexagonal grid k.

[0041] 2) The actual cost incurred in reaching this node

[0042] g(k)=α*ξ(k)+(1-α)*c(k)α∈[0,1]

[0043] In the formula, α represents the weight of the time cost; ξ(k) represents the time cost from the starting node to node k, which is expressed by the number of time nodes traversed, i.e., ξ(k) = t k When the number of time nodes exceeds the limit, the time cost becomes infinite; c(k) represents the damage cost from the starting node to node k;

[0044] And the damage cost c at each time point in c(k) i for:

[0045]

[0046]

[0047] In the formula, This represents the expected damage caused by the enemy operator e to the multiple operators at time i; Indicates the position of our operator; n represents the position of the enemy operator; Indicates the type of the operator on your side; j e Indicates the type of the enemy operator; This indicates the estimated health of the player's own operator; b e This represents the health of the enemy operator e;

[0048] 3) The estimated cost of reaching the target point after this time node.

[0049] f(k) = g(k) + h(k)

[0050] In the formula, h(k) represents the estimated cost of reaching the target node from spatial node k, that is, the lower limit of the cost of reaching the target node from spatial node k;

[0051] and:

[0052]

[0053] In the formula, x and y are the abscissa and ordinate of the node in the Cartesian coordinate system, respectively; q d ,r d ,s d Let q represent the coordinates of the target node in the cube coordinate system. k ,r k ,s k These represent the coordinates of the cube coordinate system corresponding to the spatial node k.

[0054] Therefore, the multi-operator cooperative path planning method based on a wargaming platform described above has the following beneficial effects:

[0055] This invention addresses the problem of multi-operator collaborative traversal of danger zones in wargaming simulations by proposing an improved A* algorithm. By introducing time nodes, the traversal time is shortened, reducing operator damage costs and enabling collaborative cover during danger zone traversal. Furthermore, a coordinate rotation method is used to sequentially optimize the routes of operators, significantly reducing the number of nodes and improving computation speed. Finally, the optimal route for each individual operator is selected as the initial route for optimization, reducing the number of optimization iterations.

[0056] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0057] Figure 1 A flowchart for multi-operator collaborative planning;

[0058] Figure 2 Flowchart of the improved operator update method;

[0059] Figure 3 This is the initial distribution diagram for Experiment 1.

[0060] Figure 4 This is the route planning diagram for Experiment 1 using the A* algorithm.

[0061] Figure 5 This is a route planning diagram for the improved A* algorithm in Experiment 1.

[0062] Figure 6 This is the initial distribution diagram for Experiment 2.

[0063] Figure 7 This is the route planning diagram for the A* algorithm in Experiment 2.

[0064] Figure 8 This is the route planning diagram for the improved A* algorithm in Experiment 2. Detailed Implementation

[0065] In the description of this invention, it should also be noted that, unless otherwise expressly specified and limited, these eight embodiments are for illustrative purposes only and are not intended to limit the scope of the invention. Furthermore, it should be understood that after reading the teachings of this invention, those skilled in the art can make various alterations or modifications to the invention, and these equivalent forms also fall within the scope defined by the appended claims.

[0066] 1. Wargaming Environment

[0067] Multi-operator cooperative path planning is influenced by various factors, including terrain, operator mobility, enemy deployment location, and friendly force distribution. In wargaming simulations, these factors directly affect the speed and safety of operator maneuvers and must be fully considered.

[0068] The operator's field of view is affected by factors such as terrain, terrain features, and distance, and the range of the weapon carried by the operator varies. The operator can only damage operators that are simultaneously within its field of view and range. Each damage attack can only target one operator. The damage effect is increased when multiple operators are in the same square, and there is a cooldown interval between each operator's two attacks.

[0069] In actual simulations, multiple operators often need to be controlled by one operator to reach a predetermined location in the shortest possible time. This process must consider minimizing enemy attacks and reaching the predetermined destination from the starting point as quickly as possible while preserving as much manpower as possible. Within the allotted time, the earlier the destination is reached and the more operators that reach it, the better the mission is considered accomplished. During the simulation, enemy operators score points by damaging friendly operators, while friendly operators score points based on the time taken to traverse danger zones and their remaining value. Simultaneously, the simulation has a time limit; operators that fail to reach the target point within the time limit receive no points.

[0070] Wargame environments are typically composed of hexagonal grids, with different grids containing different information, including terrain, features, and facilities. Terrain represents the relative elevation of a player's location to the lowest point on the map, affecting player movement, observation, and engagement with fire. Common features include woodlands, water bodies, soft ground, roads, and railways. Specific terrain features can influence player actions, such as reducing travel speed, altering observation distance, and decreasing attack effectiveness. Facilities are artificially created conditions in a specific area to achieve combat objectives, including roadblocks, indirect fire zones, minefields, etc., affecting player movement.

[0071] 2. The collaborative path planning method proposed in this invention

[0072] (1) Basic principles of A* algorithm

[0073] The A* algorithm combines heuristic search and conventional search, and is an extension of Dijkstra's algorithm. It is widely used in path planning problems. While ensuring that the shortest path is found, it effectively prunes redundant nodes to reduce the search space and improve search efficiency through heuristic information.

[0074] Currently, the A* algorithm is the most commonly used and efficient path planning algorithm in wargames, suitable for hexagonal grid environments. In wargames, each hexagonal grid is a spatial node. The A* algorithm finds the lower bound of the path cost passing through a spatial node k by constructing an evaluation function f(k). The evaluation function consists of two parts, and its general form is as follows:

[0075] f(k)=g(k)+h(k) (3)

[0076] In the formula, g(k) represents the minimum actual cost required to reach spatial node k from the starting node, and h(k) represents the estimated cost to reach the target node from spatial node k, that is, the lower limit of the cost of reaching the target node from spatial node k.

[0077] The A* algorithm uses the point with the smallest current evaluation function as the center and expands the search to the surrounding neighboring nodes, iterating continuously to search for new spatial nodes until the target node is found.

[0078] The estimated cost h(k) is used as heuristic information and is generally represented by Euclidean distance or Manhattan distance. In a hexagonal grid environment, the position of each cell is represented by coordinates (x, y). The minimum number of hexagonal cells required to reach the target node from the spatial node k is taken as the estimated cost h(k), as shown in equation (2):

[0079]

[0080] In the formula, x and y are the abscissa and ordinate of the node in the Cartesian coordinate system, respectively; q d ,r d ,s d Let q represent the coordinates of the target node in the cube coordinate system. k ,r k ,s k These represent the coordinates of the cube coordinate system corresponding to the spatial node k.

[0081] (2) Improved A* algorithm

[0082] In wargaming simulations, multiple operators traversing danger zones require coordination in both time and space. In the temporal dimension, operators should avoid alternating appearances within the enemy's field of vision to reduce the number of times the enemy operator can inflict damage. In the spatial dimension, multiple operators should avoid being located on the same grid to reduce the damage effect of the enemy operator.

[0083] Based on this, in order to achieve cooperation in the multi-operator maneuvering process in a hexagonal lattice network, the following concept is introduced:

[0084] ① Constructing time nodes

[0085] The traditional A* algorithm constructs an evaluation function for each spatial node that does not contain any time information. Therefore, it cannot accurately assess the damage cost incurred by the operator when passing through spatial node k, nor can it support multi-operator collaborative planning.

[0086] To address the aforementioned problems, this invention proposes the concept of a time node to replace the original spatial node, with one hexagonal grid corresponding to multiple time nodes to represent the spatial location of the operator at a given moment. The time node contains two types of information: the time sequence number t of the current node. k The hexagonal grid k where the node is located.

[0087] Because the terrain causes different types of operators to take different amounts of time to traverse different hexagonal grids, their common factor is taken as the time node period T, so that the time for the operator to traverse any hexagonal grid can be represented by an integer number of time node periods, as shown in equation (3):

[0088] t m (k)=r m *T r m ∈N* (5)

[0089] In the formula, t m r represents the time required for the operator to traverse a hexagonal grid with terrain elevation m; m This represents the number of time points required for the operator to traverse a hexagonal grid with terrain of elevation m.

[0090] By selecting a time node period T, it is ensured that information at every moment during the maneuver is recorded in the time node.

[0091] Therefore, the time sequence number for entering the hexagonal lattice k is:

[0092]

[0093] In the formula, r i This represents the number of time nodes required to traverse the i-th hexagonal grid in the shortest path from the starting point to hexagonal grid k.

[0094] ② Actual cost function

[0095] Traditional A* algorithms only consider path length. However, in real-world scenarios involving traversing hazardous areas, both time and safety factors need to be considered.

[0096] This invention comprehensively considers both time and safety to construct a practical cost function. The practical cost function constructed for a single operator is as follows:

[0097] g(k)=α*ξ(k)+(1-α)*c(k)α∈[0,1](5)

[0098] In the formula, α represents the weight of the time cost, which is adjusted according to the urgency of crossing the danger zone; ξ(k) represents the time cost from the starting node to node k, which can be represented by the number of time nodes traversed, i.e., ξ(k) = t k When the number of time nodes exceeds the limit, the time cost becomes infinite; c(k) represents the damage cost from the starting node to node k.

[0099] The damage cost of each path is determined by the damage cost c at each time point. i Composition, c i The expression is as follows:

[0100]

[0101]

[0102] In the formula, Let $e$ be the expected damage inflicted by the enemy operator $e$ on multiple operators at time $i$, and $i$ be the position of the friendly operator. Enemy operator position n, friendly operator type Enemy operator type j e , Your own operator's estimated health The enemy operator e's health b e related.

[0103] ③ Coordinate rotation

[0104] The objective function for multi-operator cooperative path planning is:

[0105] J = minf(L1, L2, ..., L) n (7)

[0106] Where, f(L1,L2…L n ) is the cost of multi-operator path planning, representing the minimum total actual cost function for paths L1, L2…L with n operators. n The problem is related to n-dimensional optimization, which is difficult to solve using the traditional A* algorithm.

[0107] To reduce computational costs and the number of nodes, a coordinate rotation method is used to transform the multidimensional optimization problem (Equation 7) into a one-dimensional optimization problem:

[0108] J = minf(L) i ,L i + (8)

[0109] Among them, L i + The path to the operator other than the i-th operator is treated as a fixed value in each optimization.

[0110] Theorem 1 states that, given a fixed cost function, the result after the m-th iteration is no worse than the result of any previous iteration.

[0111] The proof of the theorem is as follows:

[0112] prove

[0113] Let the cost function before the p-th iteration be f(L). i ,L i + ) p-1 The cost function before the p-th iteration is f(L) j ,L j + ) p Because of L i The number of possible values ​​is finite, therefore there exists L. i p* Make:

[0114] f(L i ,L i + ) p-1 ≥f(L i p* ,L i + ) p-1

[0115] make

[0116] but

[0117] so,

[0118] J = f(L) j ,L j + ) p =f(L i ,L i + ) p-1 ≤f(L i ,L i + ) p-2 ≤…≤f(L1,L1 + )1≤f(L1,L2…L n )

[0119] Therefore, Theorem 1 holds. Q.E.D.

[0120] As shown in Theorem 1, this algorithm can converge to the optimal solution or a local optimal solution, thus ensuring the effectiveness of multi-operator cooperative path planning.

[0121] ④ Algorithm Flow

[0122] This invention proposes a multi-operator cooperative path planning method based on a wargaming platform, such as... Figure 1 As shown, it includes the following steps:

[0123] Step 1: Define an old list to store the path data of all operators before the latest round of optimization; and define a new list to store the updated path data of all operators.

[0124] Step 2: Plan the optimal route for each operator as the initial route and put it into the new list. Preferably, the traditional A* algorithm in the prior art can be used to plan the initial route for the operator.

[0125] Step 3: Initialize the number of training rounds i = 1;

[0126] Step 4: Remove all existing operator path data from the old list, save the path data from the new list to the old list, and initialize the operator index j = 1;

[0127] Step 5: Remove the path data of operator j from the new list. Based on the remaining operator data, optimize and update the path of operator j using the improved A* algorithm, and store the updated path data back into the new list.

[0128] Step 6: Determine whether all operators have completed the i-th round of updates. If they have, proceed to step 7. If they have not, then j = j + 1 and proceed to step 5.

[0129] Step 7: Iterate through each value in the new list and the old list, and compare the strings to determine whether the operator path information in the new list and the old list is the same, or whether the preset number of update rounds has been reached. If so, the path update is complete; otherwise, set i = i + 1 and go to step 4.

[0130] The update process of the operator update method (improved A* algorithm) described in step 5 is as follows: Figure 2 As shown. First, construct time nodes. Each time node contains two types of information: the current node's time sequence number t. k First, determine the hexagonal grid k where the node is located; second, set up an open list and a close list: the open list includes all time nodes to be examined. The hexagonal grids where these time nodes are located may become the hexagonal grids in the optimal path of this operator, but further evaluation is still needed; the close list includes all hexagonal grids that have been evaluated. The minimum cost from the initial node to the nodes in the close list has been determined and no additional evaluation is needed.

[0131] The estimated cost consists of the actual cost and the estimated cost. The estimated cost is the distance from the hexagonal grid where the node is located to the target point. The actual cost consists of three parts: the first part is the time cost, which is determined by the time from the start time to the current time; the second part is the damage cost, which is determined by the number of attacks suffered by all friendly operators from the start time to the current time; and the third part is the overlap cost, which is caused by the friendly operator being attacked and other friendly operators in the same grid during the time period from the start time to the current time.

[0132] Specifically, step 5 includes the following steps:

[0133] Step 5.1: Determine the time interval T based on the types of all operators, including armored vehicles, unmanned armored vehicles, tanks, infantry, drones, and helicopters;

[0134] Since each operator has a time value across each hexagonal grid, the time interval T can be determined by taking the common factor of all values;

[0135] Step 5.2: Define and initialize the open and close lists;

[0136] Step 5.3: Add the initial time node of the i-th operator to the open list;

[0137] Step 5.4: Determine if the open list is empty. If it is, the path planning of operator i fails and the target point cannot be reached. If not, there is a time node in the open list, and proceed to step 5.5.

[0138] Step 5.5: Select the time node with the smallest estimated cost f from the open list, delete it from the open list, and move the time node into the close list;

[0139] Step 5.6: Find the set A of the next time points corresponding to the time point moved into the close list in step 5.5, select the time points that have not yet been judged from the set A, and go to step 5.7.

[0140] The set of time nodes for the next moment refers to the spatial locations that a node can reach in the next moment. The set of time nodes is constructed by determining whether a node can reach the adjacent cell of the next moment. When determining, if any adjacent cell cannot be reached, the set of time nodes includes the current hexagonal cell of the next moment; if a certain adjacent cell can be reached, the set of time nodes includes that adjacent cell of the next moment.

[0141] Step 5.7: Determine whether the time node selected in Step 5.6 is in the close list based on the time sequence number of the time node and the hexagonal grid it is located in. If yes, proceed to Step 5.10; otherwise, proceed to Step 5.8.

[0142] Step 5.8: Determine whether the time node selected in Step 5.6 is in the open list based on the time sequence number of the time node and the hexagonal grid it is located in. If not, proceed to Step 5.9; if it is, update the relevant information of the time node and proceed to Step 5.10.

[0143] Step 5.9: Add the time nodes selected in Step 5.6 to the open list and update the relevant information of the time nodes;

[0144] The relevant information of the node to be updated includes: ① the time span t from the moment of entering the hexagonal grid where the time node is located to the current time of the time node; ② the actual cost g that has been incurred to reach the time node; ③ the estimated cost f of reaching the target point by passing through the time node;

[0145] Step 5.10: Determine whether all nodes in the time node set A have been completely determined. If yes, proceed to step 5.11; otherwise, proceed to step 5.6.

[0146] Step 5.11: Determine whether each time node in the time node set A is a target node. If it is a target node, obtain the route of operator i by backtracking, the path optimization is completed, and the planned path is output; otherwise, proceed to step 5.5.

[0147] Example 1

[0148] The effectiveness of the proposed method was verified on the "Temple Calculation - Land Combat Commander" platform. Path planning experiments with and without coordination were conducted under identical conditions, comparing time and damage costs to verify the effectiveness of coordination.

[0149] To verify the effectiveness of the collaborative algorithm, a total of 3 sets of experiments were set up in two experimental scenarios. In each experimental environment, 3 red team operators were set up to perform the task of traversing the danger zone, and 3 blue team operators were set up to perform the task of interception and destruction.

[0150] Experiment 1 was conducted in scenario 1, with a time limit of 800 seconds for the operator to reach the target point. The information settings for the red and blue operators and the target point in scenario 1 are shown in Table 1. Figure 3 The image intuitively shows the spatial relationship between the red and blue operators at their initial positions, and the observation range of the blue operator basically covers the shortest path from the red operator to the target point.

[0151] Table 1 Initial position distribution of operators in Experiment 1

[0152]

[0153] In Experiment 1, path planning was performed using two strategies: no collaboration and multi-operator collaboration. The path planning results are as follows: Figure 4 , Figure 5 As shown in the diagram, in the uncoordinated planning route, the red operators, influenced by their starting positions, disperse and traverse the danger zone, entering the attack range of different blue operators. Red operators 2 and 3 both choose to detour to reduce the time exposed to the damage range of the blue operators. In the coordinated planning, the red operators move closer together, concentrating their traversal of the danger zone, and are differentiated in terms of time to avoid stacking and reduce damage costs. Table 2 shows the time cost and the number of attacks by the blue operators under the two planning methods. From a time perspective, the coordinated planning route shortens the red operators' maneuver time, reducing the total time by 11.6%. From a safety perspective, the red operators in the uncoordinated planning route are attacked by blue operators 2 and 3, reaching 8 attacks in total. The red operators in the coordinated planning route are only attacked by blue operator 2. The red operators fully utilize the firepower vacuum period of the blue operators, reducing detours and quickly traversing the danger zone, achieving tactical cover and evasion.

[0154] Table 2 Time Cost Table for Experiment 1 Path Planning

[0155]

[0156] Example 2

[0157] Experiment 2 was conducted in scenario 2, with a time limit of 800 seconds for the operator to reach the target point. Table 3 shows the information settings for the red and blue operators and the target point in scenario 2. Figure 6 It visually demonstrates the spatial relationship between the red and blue operators at their initial positions.

[0158] Table 3 Initial position distribution of operators in Experiment 2

[0159]

[0160] Figure 7 The experiment demonstrates the path without collaborative planning in Experiment 2. The red operator traverses the danger zone according to its individual optimal path and is destroyed by all the blue operators. Among them, red operator 1 is destroyed by 2 blue operators. Figure 8 The path of cooperative planning in Experiment 2 is shown. Red operators 1 and 3 move closer to each other and cooperate to pass through the danger zone. The time and damage details of Experiment 2 are shown in Table 4. Cooperative planning reduced the total time by 12.5%. The time cost of red operator 1 increased slightly, while the time cost of the other red operators decreased significantly. The red operators successfully avoided the damage range of blue operator 1 and were only damaged by two blue operators. Due to time constraints, red operator 2 could not cooperate. The other red operators achieved tactical cover and avoidance with each other and cooperated to cross the danger zone.

[0161] Example 3

[0162] Experiment 3 was conducted in Scenario 1, with a total of 7 comparative experiments to verify the impact of task time requirements on collaboration. The time and damage data for Experiment 3 are recorded in Tables 4 and 5, respectively. Analysis of the data in Tables 4 and 5 shows that when task time is too tight, operators can only proceed along the shortest path; the route is fixed, and collaboration is impossible. When there is no time limit, operators can avoid damage by spending a lot of time detouring, thus eliminating the need for collaboration. However, in most cases, tasks have appropriate time requirements; in these situations, collaborative planning can reduce both time and damage costs.

[0163] Table 4 Time Cost Table for Experiment 3

[0164]

[0165] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A multi-agent cooperative path planning method based on a board game platform, characterized in that, The method comprises the following steps: Step 1: obtaining actual task information and constructing a hexagonal grid map, wherein one hexagonal grid corresponds to multiple time nodes; Step 2: constructing a target function of multi-operator cooperative path planning: ； in, For the first The paths of operators other than the one operator are treated as fixed values ​​in each optimization. Step 3: planning an initial path for each operator; Step 4: performing multiple rounds of optimization and update on each operator by using the improved A* algorithm, and outputting a cooperative planning path; The improved A* algorithm comprises the following steps: Step 4.4.1: constructing time nodes; Step 4.4.2: Determine the time interval T according to the type of all operators, the time needed for the operator to cross the terrain relief is obtained by the following formula : ； wherein, represents the hexagonal cell in which the time node is located; represents the number of time nodes that the operator needs to go through when crossing the hexagonal cell whose terrain topography is . Step 4.4.3: defining and initializing an open list and a close list; Step 4.4.4: putting the time node of the initial time of the i th operator into the open list; Step 4.4.5: judging whether the open list is empty, if yes, the path planning of the operator i fails and the target point cannot be reached; if not, there is a time node in the open list, and step 4.4.6 is entered; Step 4.4.6: selecting a time node with the minimum estimated cost value from the open list, deleting the time node from the open list, and storing the time node in the close list; Step 4.4.7: finding the time node set A of the next time corresponding to the time node stored in the close list in step 4.4.6, selecting a time node which has not been evaluated from the time node set A, and turning to step 4.4.8; Step 4.4.8: Time series of time stamps according to time node and the hexagonal grid it belongs to Determine if the time node selected in step 4.4.7 is in the close list. If yes, go to step 4.4.10, if no, go to step 4.4.

9. Step 4.4.9: Time series number according to time node and the hexagonal grid in which it is located Determine whether the time node selected in step 4.4.7 is not yet evaluated in the open list. If not, go to step 4.4.

10. If so, update the relevant information for this time node and go to step 4.4.

11. Step 4.4.10: putting the time node selected in step 4.4.7 into the open list, and updating the related information of the time node; Step 4.4.11: judging whether all nodes in the time node set A have been judged, if yes, step 4.4.12 is entered, if not, step 4.4.7 is performed; Step 4.4.12: judging whether the spatial position information of all time nodes in the time node set A is the target point, if yes, the target point is reached, the route of the operator i is obtained through backtracking, the path optimization is completed, and the planning path is output; if not, step 4.4.6 is entered; In step 4.4.9 and step 4.4.10, the updated node related information comprises: 1) time sequence number of the time node ； In the formula, represents the number of time nodes that need to be experienced in the shortest path from the starting point to the hexagonal grid of the u-th hexagonal grid. 2) actual cost generated by reaching the hexagonal grid k ； In the formula, represents the weight of time cost; represents the time cost from the starting point to the hexagonal grid k, which is represented by the number of time nodes experienced, that is When the number of time nodes exceeds the limit, the time cost becomes infinite; represents the damage cost from the starting point to the hexagonal grid ; and the damage cost of each time node in is: ； wherein, represents the enemy operator the damage expectation of the multi-operator at time t; represents the friendly operator position; represents the enemy operator position; represents the friendly operator type; represents the enemy operator type; represents the friendly operator estimated blood; represents the enemy operator blood; 3) estimated cost of reaching the target point through the time node ； In the formula, represents the estimated cost of reaching the target node from the hexagonal grid , i.e. the cost lower bound of reaching the target node from the hexagonal grid . And: ； In the formula, respectively represent the horizontal and vertical coordinates of the Cartesian coordinate system of the node; respectively represent the coordinates of the cubic coordinate system corresponding to the target node, respectively represent the coordinates of the cubic coordinate system corresponding to the hexagonal lattice k.

2. The multi-agent cooperative pathfinding method based on a board game platform according to claim 1, wherein, The time node includes two node information, respectively, the time sequence number of the current node , the hexagonal grid where the node is located .

3. The multi-agent cooperative pathfinding method based on a board game platform of claim 2, wherein, The specific operation steps of step 4 are as follows: Step 4.1: defining and initializing an old list and a new list, and storing the initial path planned in step 3 in the new list; Step 4.2: initializing the training round number p = 1; Step 4.3: if the path data of the operator before the latest round of optimization is stored in the old list, deleting all path data of the original operator in the old list, saving the path data of the new list to the old list, and initializing the operator serial number j = 1; Step 4.4: deleting the path data of the j th operator in the new list, optimizing and updating the path of the j th operator by using the improved A* algorithm according to the data of the other remaining operators, and storing the updated path data in the new list again; Step 4.5: Determine whether all operators have completed the pth round of updating. If yes, go to step 4.

6. If not, let j = j + 1 and go to step 4.

4. Step 4.6: Traverse the new list and the old list, and determine whether the path information of the operators in the new list and the old list is the same through string comparison, or whether the training round p has reached the preset updating round. If the path information is the same or the maximum updating round has been reached, the pth round of path updating is completed. Otherwise, let p = p + 1 and go to step 4.3.

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