A Multi-Vehicle Cooperative Path Planning Method Based on Two-Stage Spatiotemporal A-Satellite

Abstract

This invention relates to the field of autonomous mobile robot scheduling and control technology, specifically a multi-vehicle collaborative path planning method based on a two-stage spatiotemporal A-satellite architecture. The method employs a two-stage spatiotemporal A-satellite architecture: the first stage rapidly generates a reference shortest path; the second stage uses this path as an anchor point to overlay conflict costs for optimization, supplemented by an avoidance state machine to limit detour range. Simultaneously, it constructs a conflict cost quantification model based on path actions, contention areas, and time windows, and predicts deadlock pruning. This invention's hierarchical search ensures real-time scheduling response, controlled avoidance balances traffic efficiency with conflict avoidance requirements, and early deadlock identification reduces invalid computation. It can be applied to multi-AMR collaborative operation scenarios in warehousing, smart manufacturing workshops, and automated terminals, reducing vehicle waiting time and the probability of local deadlocks, and improving the overall scheduling stability and operational efficiency of multiple robots.

Description

Technical Field

[0001] This invention relates to the field of autonomous mobile robot scheduling and control technology, and in particular to a multi-vehicle collaborative path planning method based on a two-stage spatiotemporal A-satellite, which can be applied to multi-vehicle parallel operation scenarios such as warehousing and logistics systems, intelligent manufacturing workshops, and automated terminals. Background Technology

[0002] In scenarios such as warehousing and logistics, smart manufacturing, and automated terminals, multiple automated mobile warehouses (AMRs) often need to simultaneously perform tasks such as picking, handling, and delivering goods within the same topology map. With increasing operational density, situations such as path intersections, aisle encounters, and elevator cross-floor switching are becoming increasingly frequent. Path planning has evolved from a single-vehicle geometric pathfinding problem to a collaborative scheduling problem that requires consideration of both time dimensions and multi-vehicle interactions. Existing technologies typically employ the following path planning methods, but these still have significant shortcomings: (1) Perform only geometric shortest path planning These methods primarily rely on map connectivity, path length, or static obstacles, employing algorithms such as Dijkstra's algorithm and the traditional A* algorithm to solve for the geometrically shortest path. Essentially, they treat other vehicles as static occupied areas or simple no-entry zones, failing to predict future path occupancy relationships during the search process. When multiple AMRs encounter each other in narrow passages, intersections, or oncoming traffic areas, the system often only mitigates the problem by stopping, yielding, or replanning after the path has been assigned, resulting in long waiting times, low traffic efficiency, and a high risk of local deadlocks.

[0003] (2) Incorporate the conflict cost directly into a single search To improve multi-vehicle collaboration capabilities, some solutions simultaneously calculate the spatiotemporal conflict cost with all other AMRs during each node expansion in the A* search. While this approach can theoretically optimize both path length and conflict risk, the conflict cost is strongly correlated with search depth, action sequence, and the states of other vehicles. As a result, the search state space expands dramatically with the number of vehicles and map complexity, significantly increasing the time required for a single planning iteration. This makes it difficult to meet the millisecond to second-level real-time response requirements of warehouse operations.

[0004] (3) Imbalance between conflict avoidance and path efficiency If conflict avoidance completely deviates from the shortest path, the search branch is prone to excessive detours, and the path length and execution time become uncontrollable. If it strictly follows the geometric shortest path, it is difficult to give way to other vehicles with the necessary time and space resources. Existing technologies generally lack a method to uniformly embed "controlled avoidance with the reference shortest path as the anchor point" into the search cost function and branch pruning mechanism, and cannot establish a quantifiable and constrained balance between "necessary yielding" and "path efficiency".

[0005] In summary, there is an urgent need for a multi-vehicle collaborative path planning method that balances real-time planning, path efficiency, and early conflict avoidance. Summary of the Invention

[0006] The purpose of this invention is to overcome the problems of the prior art and provide a multi-vehicle collaborative path planning method based on a two-stage spatiotemporal A-satellite. This method addresses the issues of traditional single-stage path planning, which cannot simultaneously consider real-time planning response and pre-judgment of spatiotemporal conflicts among multiple vehicles; the computational power explosion of single-layer full-scale conflict search; the passive resolution of conflicts only after the fact by pure geometric pathfinding; long vehicle waiting times; frequent local deadlocks; and the lack of standardized and controlled avoidance constraint mechanisms in existing solutions, making it impossible to quantify and balance avoidance and detour efficiency with shortest path efficiency. Furthermore, it fails to remove deadlock branches in advance during the search phase, resulting in a large amount of invalid computation and high load on the scheduling server.

[0007] The above objectives are achieved through the following technical solutions: A multi-vehicle cooperative path planning method based on a two-stage spatiotemporal satellite A includes the following steps: Step (1) Receive AMR planning request and verify topology map constraint nodes, initialize conflict prediction context, and load path action sequence and time prediction information of other AMRs in the field; Step (2) Perform the first stage A* search without introducing the cost of spatiotemporal conflict, and generate the reference shortest path; Step (3) Execute the second stage conflict optimization A* search, using the reference shortest path as the anchor point, configure the avoidance state machine to control the detour range, and synchronously calculate the spatiotemporal conflict cost to select the best node for expansion; Step (4) Output the final planned path. If a deadlock conflict is identified or no feasible path is found after the second stage search iteration reaches the upper limit, the upper-level scheduling module is triggered to perform replanning or adjust the AMR running priority. Step (5) After the single path planning is completed, clean up the conflict prediction context cache.

[0008] As a further optimization of this method, the AMR planning request in step (1) includes applying for a unique AMR identifier, a starting point node, and a target endpoint node; the topology map constraint nodes include necessary vertices of branch roads and blocking nodes; the conflict prediction context stores the complete path action sequence of the remaining AMRs and the time prediction data of each action.

[0009] As a further optimization of this method, the two judgment conditions triggered by the upper-level scheduling module in step (1) are: the number of search iterations in the second stage reaches the preset upper limit and the reference shortest path is output back; the conflict cost calculation process identifies deadlock conflicts that cannot be resolved by waiting.

[0010] As a further optimization of this method, when initializing the conflict prediction context in step (1), the path action sequence of the remaining AMRs, the estimated arrival time of each action, and the estimated departure time of each action are uniformly stored in a temporary cache. If the temporary cache is only retained within the life cycle of a single path planning process, it will not be persistently stored.

[0011] As a further optimization of this method, the evaluation function of the first stage A* search in step (2) is F1(n)=G(n)+H(n); where G(n) is the cumulative time cost from the starting point to the current node n, and G(n) is calculated based on the AMR local action sequence and time prediction model; H(n) is the heuristic time cost from the current node n to the target node. In the same floor scenario, H(n) is calculated by dividing the Euclidean distance by the maximum allowable speed of AMR. In the cross-floor scenario, H(n) is superimposed with the elevator group connectivity heuristic cost and the elevator switching prediction time.

[0012] As a further optimization of this method, the evaluation function of the second-stage conflict optimization A* search in step (3) is F2(n)=G(n)+H(n)+C(n), where C(n) is the spatiotemporal conflict weighted waiting cost; the second stage pre-sets an upper limit for the number of iterations, which is 5000 times. When the number of iterations reaches the upper limit and no conflict-free feasible path is found, the reference shortest path generated in the first stage is backed up and a warning mark is marked on the output path.

[0013] As a further optimization of this method, the avoidance state machine maintains an avoidance state and an avoidance count value for each adjacent node to be expanded. The avoidance state includes the shortest path state, the avoidance state, and the avoidance completion state. The avoidance count is configured with a preset threshold value of 1. When a node deviates from the ordered sequence of the reference shortest path, the avoidance count value is incremented by 1. After the avoidance count reaches the preset threshold, all subsequent expanded nodes must pass through the next node of the reference shortest path in sequence. In the avoidance completion state, when a node deviates from the reference shortest path or backtracks to a previously traversed node, the search branch is pruned.

[0014] As a further optimization of this method, the calculation of the spatiotemporal conflict cost C(n) in step (3) includes the following steps: the application AMR to be evaluated path and all other planned paths of AMR are discretized into node action and line segment action sequences, and the estimated arrival and departure times corresponding to each group of actions are recorded; the actions of the application AMR and other AMRs are compared one by one to identify conflict action pairs that occupy the same spatial resources; the spatially continuous conflict actions are merged into a single contention area; for each contention area, the time interval [T_start, T_end] for the application AMR and the corresponding other AMR occupying the contention area is calculated respectively; the single-area waiting cost is calculated based on the overlap relationship between the two sets of time intervals; all contention areas and all other AMRs are traversed, and the maximum value of all single-area waiting cost values ​​is taken as the spatiotemporal conflict cost C(n); conflicts that cannot be resolved by time waiting are identified, and the corresponding search branches are terminated.

[0015] As a further optimization of this method, the calculation formula for the waiting cost of a single contention area is c=w×Δt, where w is the preset waiting weight coefficient, with a value of 0.8, and Δt is the waiting time required for subsequent AMR. The avoidance number threshold, the preset waiting weight coefficient w, and the upper limit of the second-stage search iteration are all configurable parameters.

[0016] As a further optimization of this method, when cleaning up the conflict prediction context cache in step (5), all temporary records of contention areas, the time-occupied window array of each AMR, and the temporary calculation variables of the conflict cost C(n) corresponding to each node are cleared simultaneously.

[0017] This invention provides a multi-vehicle collaborative path planning method based on a two-stage spatiotemporal A* search architecture. It splits the baseline path solution and conflict optimization calculation into a two-stage hierarchical spatiotemporal A* search architecture, achieving millisecond-level real-time path planning in high-density scenarios. By constraining the maximum number of detours using an avoidance state machine, it achieves a quantitative balance between conflict avoidance and path travel efficiency. Furthermore, by using a conflict cost model based on contention regions and time windows to pre-predict conflicts and identify deadlocks, it enables early pruning of invalid search branches, reducing scheduling computational power consumption, and overall decreasing AMR waiting time and local deadlock failures, thus improving the stability of multi-robot collaborative scheduling operations. Attached Figure Description

[0018] Figure 1 This is a schematic diagram of the overall process of multi-vehicle cooperative path planning in the multi-vehicle cooperative path planning method based on a two-stage spatiotemporal A-satellite as described in this invention. Figure 2 This is a schematic diagram of path action contention area identification and conflict cost C(n) calculation in a multi-vehicle cooperative path planning method based on a dual-stage spatiotemporal A-satellite as described in this invention. Figure 3This is a schematic diagram of the process for determining the avoidance state of the relative reference shortest path in a multi-vehicle cooperative path planning method based on a two-stage spatiotemporal A-satellite as described in this invention. Detailed Implementation

[0019] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments. The described embodiments are merely some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0020] This solution provides a multi-vehicle collaborative path planning method based on a two-stage spatiotemporal A-satellite. The whole is composed of three coupled parts: a two-stage progressive spatiotemporal A-search architecture, a state machine for avoiding relative shortest paths, and a conflict cost quantification model based on path actions and time occupancy windows. It is accompanied by a complete process of iterative over-limit degradation, deadlock branch pruning, upper-level scheduling linkage, and cache cleanup.

[0021] In this embodiment, the requesting AMR is the robot that initiates the planning request; other AMRs are robots with planned paths in the field that participate in conflict assessment; the reference shortest path is the node sequence output by the conflict-free search in the first stage, which serves as the optimization anchor point in the second stage; the conflict cost C(n) is the weighted maximum waiting time cost caused by the requesting AMR competing for resources with other AMRs when it travels to node n.

[0022] The overall process is as follows Figure 1 As shown, the sequence is as follows: receiving planning requests, verifying constraint nodes, initializing conflict context, first-stage reference path A* search, second-stage conflict optimization A* search, outputting marked paths, and clearing the cache. Among these: The first stage is the reference shortest path stage, with the evaluation function F1(n) = G(n) + H(n), and the conflict cost C(n) is not calculated throughout. G(n) is the cumulative time cost from the starting point to the current node n, calculated based on the AMR action sequence and time prediction model; H(n) is the destination-inspired time cost, calculated by dividing the Euclidean distance by the maximum travel speed for single-floor scenarios, and adding elevator connectivity cost and elevator switching time across floors. This stage does not require traversing all vehicles to calculate conflicts, and quickly outputs the time-optimal baseline path.

[0023] The second stage is the conflict optimization stage, with the evaluation function F2(n) = G(n) + H(n) + C(n). Using the reference path from the first stage as the search anchor, it updates the avoidance state, accumulates conflict costs, and prunes deadlock branches while expanding adjacent nodes. This stage has a preset iteration limit of 5000 times. If no feasible path is found after reaching the limit, it directly downgrades to outputting the reference shortest path and adds a warning flag.

[0024] like Figure 3The diagram illustrates the avoidance status determination process for this scheme. This process controls the detour extent of each expanded node in the second phase, distinguishing three working states and setting pruning rules. The three working states are: shortest path state, avoidance state, and avoidance completed state. The process begins by expanding adjacent nodes and updating the avoidance state. First, it checks if the current node is proceeding in an orderly manner along the reference shortest path. If so, the shortest path state is maintained, and the avoidance count remains unchanged. If it deviates from the baseline path, it switches to the avoidance state, and the avoidance count increments by 1. Then, it checks if the avoidance count reaches a preset threshold of 1. If not, it allows continued expansion of the search branch. If the threshold is reached, it enters the avoidance completed state. Afterward, all nodes must strictly proceed along the reference shortest path sequentially. If a node deviates from the baseline path or reverts to a historical node in the avoidance completed state, it is considered an avoidance overflow, and the invalid branch is directly pruned.

[0025] like Figure 2 As shown, it is divided into three parts: (a) a schematic diagram of path actions and contention areas, (b) a schematic diagram of time occupancy window and waiting cost calculation, and (c) a complete calculation step of conflict cost.

[0026] This model transforms multi-vehicle resource contention into a numerical cost that can participate in the A* evaluation function. The steps include: The first step is to discretize the motion path, breaking down all AMR paths into node and line segment motion sequences, and recording the estimated entry and exit time of each motion. The second step is spatial conflict identification, which involves comparing the actions of two vehicles in pairs and marking conflicting action pairs that occupy the same space. The third step is to merge contested areas, integrating continuous conflicting actions into a unified contested area. Step 4: Calculate the time occupancy window [T_start, T_end] for the two vehicles corresponding to the contention area; Step 5: Quantify the waiting cost of a single region. The cost is 0 when the window does not overlap. When the window overlaps, calculate the waiting time Δt for the following vehicle. The cost of a single region is c = w × Δt, where w takes the value 0.8. Step 6: Summarize the global conflict cost and take the maximum value of c corresponding to all contested regions and all other AMRs as C(n); Step 7: Deadlock Identification. If a conflict cannot be resolved by waiting and occurred before the current time, a deadlock is identified, and the search branch is terminated. This method does not limit the specific implementation of the merging algorithm within the contention region; the focus is on quantifying "spatial conflict + temporal overlap + waiting time" into a cost term C(n) that can participate in A* search.

[0027] Example 1 This embodiment discloses the complete planning process of this method, including: Step S1: Receive the AMR planning request, which includes robot identifier, start point, end point, and a list of static blocking nodes. Verify the topology map and lock the necessary vertices of the branch roads as driving constraints. Step S2: Initialize the conflict prediction context cache, read the path action sequences and time prediction data of all other AMRs that have been planned in the field, and store the action sequences, estimated arrival times and estimated departure times into a temporary cache that is only effective for a single planning session, without persistent storage. Step S3: Execute as follows Figure 1 The first stage A* search shown only uses F1(n)=G(n)+H(n) to expand nodes, does not calculate the conflict cost throughout, and outputs the reference shortest path node sequence; Step S4: Execute as follows Figure 1 The second-stage conflict-optimized A* search, as shown, anchors to the reference path output from the first stage. For each expanded adjacent node, it first runs the following... Figure 3 The avoidance state determination logic shown updates the avoidance state, and then follows... Figure 2 The complete steps shown calculate the conflict cost C(n) of the current node, and use F2(n)=G(n)+H(n)+C(n) to filter the optimal expansion branch; set the iteration limit to 5000 times, and if there is no feasible path after the iteration is exhausted, backtrack to the baseline path and mark a warning; Step S5: Output the complete node path, if... Figure 2 The conflict cost calculation process shown identifies deadlock conflicts and simultaneously carries a deadlock flag. Step S6: The upper-layer scheduling module receives the path and flags. If a warning or deadlock flag is present, it initiates global replanning or adjusts the AMR running priority. Step S7: Clear the conflict prediction context cache, synchronously delete the contention area record, time-occupied window array, and temporary calculation variables of each node C(n), and the single planning process ends.

[0028] Example 2 This embodiment discloses the two-stage search and avoidance state machine operation logic of the present method. like Figure 1 and Figure 3 As shown, G(n) is calculated based on the AMR segmented driving action and kinematic time prediction model; H(n) is calculated differently for each floor, with the Euclidean distance divided by the maximum driving speed for a single floor, and the estimated time for elevator door opening and closing and transfers is superimposed across floors.

[0029] In the second phase, each node expansion is executed as follows: Figure 3The avoidance determination process is as follows: If a node moves forward in an orderly manner along the reference path, it maintains the shortest path state and the number of avoidances remains unchanged; if it deviates from the baseline path, it enters the avoidance state and the number of avoidances is incremented by 1; if the number of avoidances reaches the threshold of 1, the avoidance completion state is switched, and subsequent nodes are forced to move forward in sequence along the reference path; if detour or backtracking occurs after the avoidance is completed, the branch is pruned directly.

[0030] Example 3 This embodiment discloses a complete example of conflict cost calculation for this method. like Figure 2 As shown, taking the conflict between applying for an AMR and other AMRs on the N5-N6 road section as an example, the calculation process is as follows: The first step is to discretize the paths of the two vehicles into a standardized sequence of actions and record the estimated entry and exit times for each action. The second step identifies spatial conflicts in actions on road segments N5 to N6 and merges them to generate, as shown below. Figure 2 (a) shows the contested area R1; The third step is to calculate the time window occupied by the two vehicles in R1, request the AMR window [10:00:05, 10:00:12], and the other AMR windows [10:00:08, 10:00:15], corresponding to... Figure 2 (b) shows the time interval; The fourth step is to identify the overlapping window interval from 10:00:08 to 10:00:12, with a waiting time of Δt = 4 seconds. Substituting this into the formula, we get c = 0.8 × 4 = 3.2 seconds. The fifth step involves traversing all contested areas and other vehicles, taking the maximum single-area cost as the current node C(n); if the conflict cannot be resolved waitingly, proceed as follows... Figure 2 (c) shows the deadlock determination rule that prunes the search branch.

[0031] Example 4 This embodiment uses a real-world application in a warehouse as an example. The warehouse topology nodes include N1, N2, N3, N4, N5, N6, N7, N8, and N9. The starting point for applying for AMR_A is N1, and the ending point is N9. Other AMR_B nodes continue to operate in N4-N7.

[0032] The first stage output references the shortest path N1→N3→N5→N7→N9; When expanding to node N5 in the second phase, it is done through methods such as... Figure 2 The logic identifies a conflict in the contention region R1, and calculates C(n) = 3.2 seconds. The system generates a bypass branch that passes through N2, and executes as follows: Figure 3 The avoidance state logic shown is that when the number of avoidances accumulates to a threshold of 1, the avoidance is completed and then the search is forced along N7→N9. The final output path is N1→N2→N4→N6→N8→N9, with no deadlock indicator.

[0033] It should be noted that, as an alternative implementation, the above-mentioned avoidance number threshold, waiting weight w, and second-stage iteration upper limit are configurable parameters; the calculation formulas of G(n), H(n), and C(n), the contention region merging algorithm, and the path action discrete rules can be replaced by equivalent alternatives.

[0034] The above description is merely illustrative of the embodiments of the present invention and is not intended to limit the present invention. For those skilled in the art, any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A multi-vehicle cooperative path planning method based on a two-stage spatiotemporal satellite A, characterized in that, Includes the following steps: Step (1) Receive AMR planning request and verify topology map constraint nodes, initialize conflict prediction context, and load path action sequence and time prediction information of other AMRs in the field; Step (2) Perform the first stage A* search without introducing the cost of spatiotemporal conflict, and generate the reference shortest path; Step (3) Execute the second stage conflict optimization A* search, using the reference shortest path as the anchor point, configure the avoidance state machine to control the detour range, and synchronously calculate the spatiotemporal conflict cost to select the best node for expansion; Step (4) Output the final planned path. If a deadlock conflict is identified or no feasible path is found after the second stage search iteration reaches the upper limit, the upper-level scheduling module is triggered to perform replanning or adjust the AMR running priority. Step (5) After the single path planning is completed, clean up the conflict prediction context cache.

2. The multi-vehicle cooperative path planning method based on a two-stage spatiotemporal A-satellite as described in claim 1, characterized in that, The AMR planning request in step (1) includes the application for a unique AMR identifier, the starting point node, and the target endpoint node; the topology map constraint nodes include the vertices that must be passed through the branch roads and the blocking nodes; the conflict prediction context stores the complete path action sequence of the remaining AMRs and the time prediction data of each action.

3. The multi-vehicle cooperative path planning method based on a two-stage spatiotemporal A-satellite as described in claim 1, characterized in that, The two types of judgment conditions that trigger the upper-level scheduling module in step (1) are: the number of search iterations in the second stage reaches the preset upper limit and the reference shortest path is output back; The conflict cost calculation process identifies deadlock conflicts that cannot be resolved by waiting.

4. The multi-vehicle cooperative path planning method based on a two-stage spatiotemporal A-satellite as described in claim 1, characterized in that, When initializing the conflict prediction context in step (1), the path action sequence of the remaining AMRs, the estimated arrival time of each action, and the estimated departure time of each action are stored in a temporary cache. If the temporary cache is only retained within the life cycle of a single path planning process, it will not be persistently stored.

5. The multi-vehicle cooperative path planning method based on a two-stage spatiotemporal A-satellite as described in claim 1, characterized in that, In step (2), the evaluation function of the first stage A* search is F1(n)=G(n)+H(n); where G(n) is the cumulative time cost from the starting point to the current node n, and G(n) is calculated based on the AMR local action sequence and time prediction model; H(n) is the heuristic time cost from the current node n to the target node. In the same floor scenario, H(n) is calculated by dividing the Euclidean distance by the maximum allowable travel speed of AMR. In the cross-floor scenario, H(n) is superimposed with the elevator group connectivity heuristic cost and the elevator switching prediction time.

6. The multi-vehicle cooperative path planning method based on a two-stage spatiotemporal A-satellite as described in claim 5, characterized in that, In step (3), the evaluation function of the second stage conflict optimization A* search is F2(n)=G(n)+H(n)+C(n), where C(n) is the spatiotemporal conflict weighted waiting cost; the second stage pre-sets an upper limit for the number of iterations, which is 5000 times. If no conflict-free feasible path is found after the upper limit of the number of iterations is reached, the reference shortest path generated in the first stage is backed up and a warning mark is marked on the output path.

7. The multi-vehicle cooperative path planning method based on a two-stage spatiotemporal A-satellite as described in claim 6, characterized in that, The avoidance state machine maintains the avoidance state and the number of avoidances for each adjacent node to be expanded; the avoidance state includes the shortest path state, the avoidance state, and the avoidance completed state; the number of avoidances is configured with a preset threshold, which is set to 1. When a node deviates from the ordered sequence of the reference shortest path, the number of avoidances increments by 1; after the number of avoidances reaches a preset threshold, all subsequent extended nodes must pass through the next node of the reference shortest path in sequence. If a node deviates from the reference shortest path or reverts to a previously visited node when the avoidance is complete, prune that search branch.

8. The multi-vehicle cooperative path planning method based on a two-stage spatiotemporal satellite A, as described in claim 7, is characterized in that... The calculation of the spatiotemporal conflict cost C(n) in step (3) includes the following steps: the path to be evaluated for the application AMR and all other planned paths of the AMR are discretized into node action and line segment action sequences, and the estimated arrival and departure times corresponding to each group of actions are recorded; Each AMR request is compared with the actions of other AMRs to identify conflicting action pairs that occupy the same spatial resource; spatially consecutive conflicting actions are merged into a single contention zone; for each contention zone, the time interval [T_start, T_end] for requesting an AMR and the corresponding other AMR occupying the contention zone is calculated; the single-zone waiting cost is calculated based on the overlap relationship between the two sets of time intervals; all contention zones and all other AMRs are traversed, and the maximum value of all single-zone waiting costs is taken as the spatiotemporal conflict cost C(n); conflicts that cannot be resolved by time waiting are identified, and the corresponding search branch is terminated.

9. A multi-vehicle cooperative path planning method based on a two-stage spatiotemporal A-satellite as described in claim 8, characterized in that, The formula for calculating the waiting cost of a single contention zone is c=w×Δt, where w is the preset waiting weight coefficient, with a value of 0.8, and Δt is the waiting time required for subsequent AMR. The avoidance number threshold, the preset weight coefficient w, and the upper limit of the second-stage search iteration are all configurable parameters.

10. The multi-vehicle cooperative path planning method based on a two-stage spatiotemporal A-satellite as described in claim 1, characterized in that, When cleaning up the conflict prediction context cache in step (5), all temporary records of contention areas, the time-occupied window array of each AMR, and the temporary calculation variables of the conflict cost C(n) corresponding to each node are cleared simultaneously.

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