Task and communication combined path planning method for multi-base unmanned system

Abstract

The invention relates to a task and communication combined path planning method for a multi-base unmanned system. The method comprises the following steps: mapping task distribution into a target node layer, and constructing a communication link into a transmission link layer to form a task and communication double graph; establishing a dynamic coupling edge between the graphs to represent the influence of a task execution behavior on the communication quality; an interactive influence propagation model is introduced in the time dimension, and the feedback effect of communication link fluctuation on the task progress is simulated; providing time-space dynamic cost evaluation input for path planning; defining a task feasible domain and a communication strong connectivity domain in a time-space domain based on the double-layer graph output by the technology; constructing a joint feasibility domain (JFE), only allowing path planning to be expanded in the domain, and processing a splitting problem of communication repair after the path planning; performing multi-target compression on the path, and balancing task path time consumption, node connection stability and path redundancy consumption indexes; a graph homotopy simplification mechanism is introduced, and redundant edge paths in the JFE are compressed.

Description

Technical Field

[0001] The present invention relates to a combined path planning method, specifically a combined path planning method for multi-base unmanned system tasks and communication. Background Art

[0002] Currently, in the field of combined path planning, although relevant research and applications have made certain progress, overall there are still many deficiencies and practical constraints. Especially in scenarios where task execution and communication guarantee are highly coupled, existing methods are still difficult to effectively support the collaborative planning and real-time decision-making in multi-node, strongly collaborative, and highly dynamic environments. First of all, most existing path planning methods still take "task priority-driven" as the leading factor, only regarding the communication factor as an additional static constraint condition for simple filtering or penalty scoring, and failing to construct a global coupling model from the perspectives of the dynamics, essential volatility of communication, and the interactive feedback with tasks. As a result, in the actual complex environment, once the link state changes rapidly, the task path is likely to fail or even be repeatedly reconstructed, seriously affecting the collaborative efficiency of multi-unmanned systems. Secondly, traditional path planning models mostly construct the shortest path or the minimum cost path based on static maps and fixed task points, lacking in-depth modeling of semantic attributes such as time window dependencies, collaborative logic, and execution priorities between tasks, and unable to truly reflect the causal relationship between tasks. As a result, the generated paths are only optimal in terms of physical distance, but there are potential conflicts and redundancies at the task logic scheduling level.

[0003] In addition, for the communication modeling part, most current methods adopt the "link availability judgment" or "link coverage map" strategy. This method ignores the dynamic change process of the link with time, location, node attitude, and terrain influence, and lacks modeling means for channel fluctuation trends, historical feedback patterns, and prediction capabilities. Therefore, it is impossible to achieve the early avoidance and intelligent reconstruction of the path driven by the communication quality trend. Moreover, at the collaborative level between tasks and communication, mainstream methods often ignore the mutual influence relationship between the two, that is, task actions will perturb the link, and communication failures will in turn affect task scheduling. This interaction relationship lacks structured modeling in the current technical system, resulting in the two system modules of tasks and communication running in their respective independent data dimensions and policy logics, lacking a true joint reasoning and synchronous optimization mechanism. Additionally, existing methods generally rely on a centralized control structure, and path planning and communication deployment are mostly completed at the central computing node. This is extremely likely to cause computational bottlenecks and response delays in the case of a large number of nodes, a large deployment area, and frequent link jitters, unable to meet the requirements of real-time and rapid response in a dynamic task environment, and also lacking cross-platform distributed scheduling capabilities. From the perspective of the intelligent level, the current path adjustment mechanism is mostly passive and post-triggered, lacking trend prediction and risk assessment capabilities, and also lacking a learning mechanism to refine and reuse strategies from historical task communication data, resulting in the system being unable to optimize itself based on experience, thus causing problems such as repeated paths, scheduling conflicts, and policy rigidity in continuous tasks.

[0004] In addition, during the formation cooperation process of multi-base unmanned systems, existing methods often do not consider the communication relay, resource allocation, and load balancing strategies between multiple base stations or aerial relays, and even less establish a policy negotiation model between base stations, resulting in resource redundancy or competition phenomena, further weakening the overall scheduling efficiency and service quality of the system. Finally, existing path planning tools are difficult to handle real task scenarios with complex terrain, easy link loss, and strong cooperation logic, and generally have problems such as high execution failure rates, slow link recovery, and lagging path reconstruction in high-dynamic tasks such as sudden disasters, military conflicts, and border patrols. All of these urgently require a joint breakthrough at the model, algorithm, and architecture levels through a new generation of methods. Summary of the Invention

[0005] The purpose of the present invention is to provide a joint path planning method for tasks and communication of multi-base unmanned systems, thereby solving some of the drawbacks and deficiencies pointed out in the background technology.

[0006] The technical solutions adopted by the present invention to solve its above technical problems include the following steps:

[0007] S1. Adopt a double-layer spatio-temporal decision network for task and communication modeling:

[0008] S1.1. Map the task distribution to the target node layer and construct the communication link into the transmission link layer to form a dual graph of task and communication;

[0009] S1.2. Establish dynamic coupling edges between the graphs to represent the impact of task execution behavior on communication quality; introduce an interactive influence propagation model in the time dimension to simulate the feedback effect of communication link fluctuations on task progress; provide spatio-temporal dynamic cost evaluation input for path planning;

[0010] S2. Adopt a path planning optimization strategy based on the joint feasibility domain:

[0011] S2.1. Based on the two-layer graph of technical output, define the task feasible domain and the communication strongly connected domain in the spatio-temporal domain; construct the joint feasibility domain JFE and only allow path planning to be carried out within this domain to address the fragmentation problem of performing communication repair after path planning;

[0012] S2.2. Perform multi-objective compression on the path to balance the task path duration, node connection stability, and path redundancy consumption indicators;

[0013] S2.3. Introduce a graph homotopy simplification mechanism to compress the redundant edge paths inside JFE;

[0014] S3. Adopt a predictive dynamic correction mechanism for the joint path of task and communication:

[0015] S3.1. Use the state history of the unmanned system nodes including path deviation, communication quality, and delay feedback to establish a communication fluctuation trend model; compare the execution trajectory of the current path with the dynamic boundary of JFE to identify high-risk segments;

[0016] S3.2. Implement path mirror prediction for the executed path segment to evaluate the stability difference between the corrected path and the original path; if the difference exceeds the threshold, trigger the local path update module;

[0017] S4. Adopt a collaborative deployment learning mechanism for path and communication:

[0018] S4.1. Set the global objective function, including task completion rate, communication interruption rate, and path reconstruction frequency;

[0019] S4.2. Use the multi-agent reinforcement learning framework, with each base station or key node as an intelligent agent, to optimize the deployment strategy according to local experience + global evaluation.

[0020] Furthermore, the above-mentioned task and communication two-layer spatio-temporal decision network modeling method:

[0021] The task execution requirements and communication link status in the multi-base unmanned system are semantically hierarchically modeled to construct a dual-graph structure of task graph and communication graph. In the task layer, task nodes are given semantic labels of execution window, importance level and collaborative dependency. The communication layer describes the link capacity, volatility and predicted interruption probability based on the physical / logical links between unmanned nodes and between unmanned nodes and multiple base stations.

[0022] A set of dynamic coupling edges is established between the task graph and the communication graph, and a coupling response function is generated through the data perceived by the system to reflect the task action (the degree of immediate disturbance to the link stability). The coupling modeling function is:

[0023]

[0024] in:

[0025] Ψ(v i ,v j ,t) represents the task node v i For communication node v j The communication coupling effect generated at time t; α i It represents the behavior intensity coefficient of the task node and quantifies the active weight of the impact on the link; is the rate of change of the quality of the communication channel between the task node and the communication node over time; γ is the response index, which is used to control the nonlinear amplification or suppression of the change rate on the system response; β j Indicates the sensitivity of the communication node to environmental disturbances; θ ij (t) is the relative motion direction angle between the task node and the communication node, and the influence of periodic disturbance on link stability is characterized by a sinusoidal function.

[0026] Furthermore, the task and communication two-layer spatiotemporal decision network modeling method:

[0027] A feedback modeling mechanism for spatiotemporal interactive propagation is constructed to predict the timing impact of link fluctuations on task execution delays. By simulating the disturbance diffusion path in the graph structure, the attenuation characteristics of the communication fluctuation → task response and the transmission chain in the time dimension are quantified and described by the propagation integral model:

[0028]

[0029] in:

[0030] Φ(v,t) represents the feedback strength of task or communication node v affected by the accumulation of communication anomalies in the past period at the current moment t; Λ(v,τ) is the link interference strength suffered by the node at the past time point τ; δ is the interference attenuation factor, used to represent the rate of decline of the impact of communication anomalies on tasks over time; the exponential decay function exp(-δ·(t - τ)) simulates the weakening effect of long-term communication fluctuations on the current task.

[0031] Further, the method for modeling the task and communication double-layer spatio-temporal decision network:

[0032] Adopt a path generation mechanism with communication continuity priority, extract path segments with high link fluctuation consistency in the communication graph as the initial communication skeleton, the structural stability is guided by the communication continuity index CCI, and fine-tune the path by integrating the requirements of task nodes to achieve a joint path that prioritizes communication but allows tasks to be reachable;

[0033] Deploy edge path policy agents at each multi-base station, so that according to the local task status and communication fluctuation conditions, generate recommended path policies and share the evolutionary experience with adjacent base stations; through the linkage optimization of multiple agents, construct the evolutionary feedback function of the path policy as follows:

[0034]

[0035] Where:

[0036] Ω(v k ,Δt) represents the evolutionary potential energy of the path policy of node v within the time window Δt, used to judge whether it is necessary to adjust the current path plan; k represents the communication coupling gradient direction of node v at the moment t′, measuring the change trend of communication interference on the path; Φ(v k ,t′) is the propagation feedback function, and the communication historical fluctuation feedback suffered by the node at the time point t′. k

[0037] Further, the method for constructing the predictive dynamic correction mechanism of the task and communication joint path includes:

[0038] Collect multi-dimensional state historical data during the task execution of the unmanned system, construct a communication fluctuation trend model, where the collected state data includes: path deviation trajectory, communication link quality evolution data, task control delay feedback information, and extract fluctuation patterns on multiple time scales; construct a prediction function based on the historical state sequence, defined as:

[0039]

[0040] Where:

[0041] Υ(t) represents the intensity of the communication stability fluctuation trend of the current path segment at time t; N represents the number of state variables included in the modeling, including path offset, signal-to-noise ratio fluctuation, and control link delay; ξ i ξ (t) represents the value of the i-th type of state variable at time t; represents the rate of change of this state over time; λ i is the weight factor of the i-th type of state in the overall trend modeling, used to distinguish the influence degree of different states on the communication prediction result; κ i is the amplification exponent, used for non-linear sensitivity modeling of the rate of change, to enhance or suppress the driving force of a certain type of fluctuation on the system judgment.

[0042] Further, the method for constructing the predictive dynamic correction mechanism of the task and communication joint path includes:

[0043] Compare the current execution path trajectory with the pre-established joint fluctuation boundary JFE. The boundary model integrates communication fluctuation prediction data and geospatial uncertainty information, and is used to identify high-risk areas that are sensitive to both tasks and communication in the path segment; when the current path trajectory approaches or enters the high-fluctuation dense band defined in the dynamic boundary, trigger the risk identification mechanism; the coupling relationship between the path node and the JFE boundary is measured by the following function:

[0044] Θ(x,y,t) = ρ·(1 - e -η·D(x,y) )·σ(t)

[0045] where:

[0046] Θ(x,y,t) represents the coupling sensitivity between the coordinate point (x,y) in the path and the JFE boundary at time t; D(x,y) is the shortest distance from this point to the JFE boundary, used to describe the spatial proximity; e -η·D(x,y) is the exponential decay term of the spatial influence, η is the decay control factor; ρ is the JFE risk area density parameter, reflecting the degree of communication and geographical overlap disturbance in the area; σ(t) represents the communication environment fluctuation index at time t, which is the communication uncertainty weighting term in the time domain.

[0047] Further, the method for constructing the predictive dynamic correction mechanism of the task and communication joint path includes:

[0048] After identifying the high-risk segment, adopt the mirror path prediction mechanism for constructing the path segment, generate an optional path mirror segment in the area with similar geographical location, consistent task objectives but complementary communication situations, and predict the communication performance and execution consistency of the candidate path through simulation; and define the stability difference function for comparing the substitution value of the current path and the mirror path as follows:

[0049]

[0050] Wherein:

[0051] Δ s (t) represents the cumulative value of the difference in communication stability between the mirror path and the original path within the future time window T starting from the current moment; Ω(τ) and Ω(τ) are the stability evaluations of the mirror path and the original path at time τ under the communication prediction model, respectively. mirror orig

[0052] Score; |·| is used to measure the absolute difference in communication stability between two paths; χ(τ) is the task consistency function, indicating the substitutability of the mirror path in task scheduling. When χ(τ)=0, it means there is no substitutability, and when χ(τ)=1, it means complete equivalence; T is the length of the prediction time window for difference evaluation.

[0053] The multi-base unmanned system task and communication joint path planning method of the present invention has significant technological breakthroughs and practical engineering value, and its beneficial effects are reflected in the following aspects:

[0054] By introducing the dual-graph structure modeling of the task graph and the communication graph, and constructing a dynamic coupling edge and propagation feedback model, the traditional "task first, communication compensation" split mode in path planning is broken, and the collaborative optimization of task execution requirements and communication link status in the same decision space is realized, improving the integrity of the path strategy and the system robustness. By constructing a communication fluctuation trend model and a JFE joint fluctuation boundary judgment mechanism, the system can identify high-risk path segments in advance and evaluate their impact on task delay, effectively avoiding communication blind spots and dense bands of link fluctuations, enabling the task to still have a stable executable path in a weak link or interference environment, and significantly reducing the task interruption rate and communication failure rate.

[0055] Introducing a path mirror prediction mechanism and a stability difference function judgment method, the path correction no longer depends on passive replanning after task failure, but is an active correction based on trend prediction. Under the premise of ensuring task consistency, the optimal path replacement is carried out in advance, improving the system's adaptive ability to sudden environmental changes. By deploying lightweight policy agents at multi-base stations or key nodes and combining multi-agent reinforcement learning mechanisms, the self-evolution and policy migration of path and communication strategies are realized, with distributed control capabilities and global policy coordination advantages, improving the scheduling efficiency and resource utilization rate of the overall multi-node system. Description of the Drawings

[0056] Figure 1 It is a flowchart of the multi-base unmanned system task and communication joint path planning method of the present invention.

[0057] Figure 2 It is a flowchart of the task and communication double-layer spatio-temporal decision network modeling method of the present invention.

[0058] Figure 3 This is a flowchart for constructing a predictive dynamic correction mechanism for the task and communication joint path of the present invention. Detailed implementation manners

[0059] The following provides a detailed description of the specific implementation manners of the present invention with reference to the accompanying drawings.

[0060] An intelligent path planning technology that realizes optimal task completion on the basis of ensuring communication connectivity. This method synchronously incorporates the execution logic of task objectives and the dynamic characteristics of communication links into path decision-making by constructing a two-layer spatio-temporal structured model with coupled logic. Its step S1 is to model using a two-layer spatio-temporal decision network for tasks and communication.

[0061] The specific process is as follows: In S1.1, the system first maps the task execution requirements to the target node layer. This layer constructs a task graph based on task points, including structured information such as task locations, priorities, time windows, and collaborative dependencies. At the same time, the physical communication links between unmanned nodes and their connection states with multiple base stations are abstracted into a transmission link layer to form a communication graph. This graph depicts key parameters such as the channel capacity, link stability, and availability prediction between nodes, thus forming a dual-graph structure of the task graph and the communication graph, and the two respectively carry the information expressions of the task space and the communication capacity space. In S1.2, the system further establishes dynamic coupling edges between the above two graphs. These edges are used to quantify the impact of task behaviors (such as path movement, task execution period) on the communication network structure or performance. For example, when an unmanned node enters an area with dense obstacles, the link quality deteriorates, and this impact will be mapped to the communication graph through the coupling edge. At the same time, an interactive influence propagation model is introduced in the time dimension. This model simulates how the fluctuations in communication quality (such as increased delay, link interruption) act in reverse on the node scheduling in the task graph. For example, a link interruption will cause the data of a certain task not to be transmitted back, thereby triggering task delay or even failure. This feedback chain is constructed as an impact path with time continuity in the model, enabling the system to foresee the task delay risk on the path.

[0062] A path generation optimization mechanism that deeply integrates task scheduling requirements with communication network constraints. The core lies in avoiding the fragmented strategy of "planning the path first and then repairing communication" in traditional methods, and instead adopting an idea of path optimization within the joint feasibility domain. The task reachability and communication sustainability jointly constitute the path legality boundary. Step S2 is to adopt a path planning and optimization strategy in the joint feasibility domain, which specifically includes the following: In S2.1, based on the double-layer structure of the task graph and communication graph output in the previous stage, the system defines the task feasible domain and the communication strongly connected domain in the time-space domain respectively. The task feasible domain represents the node connected area that satisfies all the time window, spatial reachability and task constraint conditions. The communication strongly connected domain represents the communication area where reliable data transmission can be realized between any two unmanned nodes within a given time period. The intersection of the two is defined as the joint feasibility domain JFE (Joint Feasibility Envelope). This JFE serves as the only feasible space constraint boundary for path search, ensuring that all generated paths naturally satisfy the dual constraints of task execution and communication guarantee, thus eliminating the structural fragmentation problem between path planning and communication repair from the source.

[0063] In S2.2, the system performs multi-objective compression optimization on the candidate paths within the JFE. By setting a comprehensive cost function, it weighs multiple indicators such as the task path duration (i.e., the total time required to complete the task), the node connection stability (i.e., the steady state degree of the communication links of each node in the path), and the path redundancy consumption (i.e., the energy consumption introduced by the path redundancy hops or communication duplicate nodes), ensuring that the finally selected path not only meets the functional requirements but also has performance optimization characteristics. In S2.3, the system introduces a graph homotopy simplification mechanism, that is, it performs a compression operation at the mathematical structure level on the redundant path branches with function repetition or low resource utilization efficiency within the JFE, retains the main path structure in the topological isomorphism equivalence class, and trims the uncontributing edges and path clusters.

[0064] Through state history learning and risk forward-looking identification, dynamic correction of the execution path is achieved to ensure the stable progress of the task and the continuous availability of the communication link. Step S3 adopts a predictive dynamic correction mechanism for the joint path of the task and communication, which specifically includes the following: In S3.1, the system continuously collects and analyzes multi-dimensional state history data generated by the unmanned system nodes during the task execution, including path deviation records (i.e., the degree of deviation between the actual movement trajectory of the unmanned node and the preset path), communication quality indicators (such as channel signal-to-noise ratio, link stability, packet loss rate), and delay feedback information (including command response delay, data backhaul lag, etc.). Based on the above data, a communication fluctuation trend model is constructed. This model has the ability of time-series learning and can predict the change trend of the communication state within a future time window of a certain path segment. Subsequently, the system compares the execution trajectory of the current task path with the dynamic boundary of the previously established JFE (Joint Feasibility Region) in real time. If the path trajectory gradually approaches or enters the area marked as high communication fluctuation risk in the JFE, the system will identify this path segment as a potentially high-risk segment, indicating that the subsequent path faces the risks of communication interruption, information backhaul failure, or task synchronization failure.

[0065] In S3.2, instead of immediately performing forced path reconstruction, the system analyzes and evaluates this high-risk segment through a path mirror prediction mechanism. The specific approach is to generate one or more path mirror candidate segments with geographical substitutability, task consistency but different communication postures within the JFE based on the geographical location, task objectives, and time-series attributes of the current path segment. Subsequently, within the prediction time window, the communication and task performance of the original path segment and the mirror path segment are simulated and evaluated, including predicting communication link stability, task execution time, resource consumption and other indicators. The communication robustness difference between the original path and the mirror path is calculated through a stability difference function. If this difference exceeds the tolerance threshold set by the system, it indicates that the current path segment has significant disadvantages in communication risk control. The system will automatically trigger the local path update module and preferentially select the mirror path segment with better communication performance and the least impact on task consistency for seamless replacement.

[0066] By learning the interaction law between path decision-making and communication deployment, the multi-base unmanned system is enabled to have the path optimization ability with global goal awareness in complex environments. Step S4 adopts a path and communication collaborative deployment learning mechanism, which specifically includes the following: In S4.1, the system first sets a group of global-level optimization objective functions to comprehensively measure the overall effects of path deployment and communication scheduling. These objective functions include, but are not limited to, the task completion rate (i.e., the proportion of successfully completed task nodes within a given time window, which is used to reflect the system task efficiency), the communication interruption rate (i.e., the number of information transmission interruptions caused by unstable or failed communication links during task execution, which is used to measure communication continuity and system robustness), and the path reconstruction frequency (i.e., the number of times of triggering local or global path updates during task execution, which is used to evaluate the stability of the path strategy and the quality of the initial plan). These objective items will serve as reward signals or loss functions during the training and optimization process of the system to guide the overall strategy learning.

[0067] In S4.2, the system conducts collaborative learning of paths and communication based on a multi-agent reinforcement learning framework. Each base station node or key relay node is defined as an autonomous intelligent agent. These agents make local policy decisions according to the task status, communication topology changes, and path adjustment results in the areas they cover. At the same time, all agents share a global evaluation mechanism, which calculates the real-time value of the overall objective function by collecting global execution information and then feeds it back to each agent as a learning signal, forming a policy evolution process that combines local experience guidance and global feedback correction. Specifically, in each round of deployment decision-making, each agent adjusts the policy parameters in aspects such as path generation, communication forwarding, and resource allocation according to the task completion situation and communication performance brought by its own historical strategy, and through a central coordination mechanism, summarizes, prunes, and reconstructs the strategies among multiple agents to ensure that the entire multi-base system continuously iterates towards the system-level optimization goal in the face of dynamic task requirements and communication disturbances, thereby realizing the collaborative optimal deployment ability of path and communication resources.

[0068] Example 1:

[0069] A certain water conservancy project conducts mapping of the water area where it is located. Suddenly, strong winds and heavy rains occur in this area, causing communication interruption. The command center deploys a multi-base unmanned system formation to the area to perform communication repair and the coordination of the mapping work of this water area.

[0070] The system consists of 4 UAVs (UAV1~UAV4) and 2 ground mobile base station nodes (GBS1, GBS2). Seven key mission points (T1~T7) are defined in the mission area, including high-altitude aerial photography points, heat source detection points, and ground voice sampling points. There are dependencies between the mission nodes. For example, T3 must be started after T2 is completed, and T5 must be executed in coordination with T4 and T6. In addition, each mission point has a time window constraint such as "T3 must be completed within 20 minutes after the mission starts." At the same time, the mountainous terrain is complex, the communication channel is easily affected by the mountain occlusion, the link fluctuates violently, and the UAV will constantly change its relative communication position with the base station and other UAVs during flight. Therefore, the mission must construct a task-communication dual graph and establish a coupling mapping to support stable and efficient path planning.

[0071] In the task layer, the system models each task point as a graph node. The attributes of task nodes T1 to T7 are as follows: T1 importance level is 1 (highest), T2 to T4 are level 2, and T5 to T7 are level 3; the task window is set as follows: T1 is completed within 0-10 minutes, and T3 must be started and completed within 5 minutes after T2; the coordination constraint is that T5 must be triggered at the same time as T4 and T6; this information is encoded into the task graph as path priority sorting and dependency control conditions.

[0072] In the communication layer, the system models the state of the link between each drone and the base station, and between drones. The link quality function is based on the combination of channel capacity and packet loss rate. Rijt represents the communication quality between UAVi and node j (UAV or base station) at the current time t. When the initial time t = 0 is set, the channel quality between UAV1 and GBS1 is R130 = 0.85 (indicating a good channel), and as it approaches the edge of the mountain, due to occlusion, the quality drops to R1310 = 0.45 within 10 minutes; at the same time, UAV3 and UAV2 maintain their formation, and the relative communication angle is always less than 15 degrees, so the link is relatively stable, and R32t is basically maintained at 0.75.

[0073] To model the impact of task behavior on the communication link, the system establishes a coupling edge between the task graph and the communication graph, and models the communication disturbance response through the following function:

[0074]

[0075] Take the example of UAV1 executing task T3 and modeling the communication link between it and base station GBS1. During the task execution, UAV1 needs to fly 30 meters offset from its current position to T3. Its path passes through a highly reflective slope surface, causing strong signal reflection and instantaneous packet loss. At the same time, its flight attitude deflects, resulting in the communication direction angle with GBS1 changing from 45° to 85°. The link quality degradation rate within the system sampling period is: dR13t / dt≈ -0.04 / second. Set the following parameter ranges and give specific values for substitution in the calculation:

[0076] α i = 1.8: It indicates that the flight maneuver of this task node is frequent during execution, and the impact on communication is significant;

[0077] γ = 2.0: It indicates an enhanced non - linear response to the communication change rate (for example, slow changes are ignored and rapid changes are amplified);

[0078] β j = 0.9: This communication node is more sensitive to angle changes;

[0079] θ ij (t) = 85°: The current relative communication direction;

[0080] Indicates the channel quality degradation speed.

[0081] Substitute into the formula:

[0082] Ψ(v i ,v j ,t) = 1.8·(-0.04) 2 + 0.9·sin(85°)≈1.8·0.0016 + 0.9·0.9962

[0083] ≈0.00288 + 0.89658 = 0.89946

[0084] This value is close to 1, indicating that the current action of task T3 causes a strong disturbance to the link of communication node j (GBS1). The system uses this as a warning signal for path adjustment judgment; at the same time, this value will also be written into the communication graph for reference by the dynamic path cost calculation module. If the current path passes through multiple high - Ψ value regions, the system will impose a weight penalty on it in path planning.

[0085] In addition, this coupled modeling will be updated in real - time with the progress of the task and communication trends. For example, during the flight of UAV3 to task point T5, it is always outside the communication dead zone, and the relative direction angle fluctuates within 30°. θ ij (t) is controlled in the low - value range, and the output of the Ψ function is always lower than 0.3. The system determines that this task node has a small impact on the communication network and can be included in the path skeleton as a priority planning segment.

[0086] UAVs 1 to 4 are gradually marking points on T1 to T7 according to the mission map. After completing T3, the system detected a strong fluctuation in the link during the communication between UAV1 and GBS1, resulting in a delay in uploading some image data. At this time, the command system enabled a spatio-temporal interaction propagation feedback modeling mechanism to predict whether the current communication anomaly would have a "time-series impact" on the subsequent execution of task points T4 and T5, that is, whether there was a risk of task execution delay caused by the link anomaly, and to make a quantitative judgment and control on it. The core of the mechanism's modeling is to calculate the propagation integral function Φ(v, t), which is used to measure the "historical cumulative impact" of communication anomalies on node v (which can be a task node or a communication node) at the current time t, so as to provide a decision basis for the subsequent path planning weight.

[0087] In actual execution, taking node T4 as an example, its task plan is to start the heat source detection sub-task within the 16th minute, and this task depends on the analysis result of the data uploaded by UAV1 from T3. The system analyzes the cumulative impact of communication anomalies at the current time point t = 16 minutes, and designs the algorithm as follows:

[0088]

[0089] For integral simulation, the system traces back the communication perturbation records in the past 10 minutes, that is, let t0 = 6 minutes and t = 16 minutes. During this time period, the system samples the communication interference intensity Λ(v, τ) once per minute, that is, the past communication fluctuation data of the link between UAV1 and GBS1 is as follows (the numerical unit is the normalized link perturbation intensity, and the range is 0, 1):

[0090] Time τ (min) Λ(v, τ) 6 0.35 7 0.48 8 0.55 9 0.60 10 0.68 11 0.62 12 0.50 13 0.38 14 0.30 15 0.22

[0091] Set the interference attenuation coefficient δ = 0.45 (it is recommended that this value range be between 0.3 - 0.8, and the larger the value, the faster the long-term perturbation decays). Substituting into the propagation function, the system performs discrete integral approximation according to the following calculation formula:

[0092]

[0093] Substitute item by item and calculate as follows (some calculation results have been rounded to three decimal places):

[0094] τ = 6: 0.35×exp - 4.5 ≈ 0.35×0.011 = 0.00385

[0095] τ = 7: 0.48×exp - 4.05 ≈ 0.48×0.017 = 0.00816

[0096] τ = 8: 0.55×exp - 3.6 ≈ 0.55×0.027 = 0.01485

[0097] τ = 9: 0.60×exp - 3.15 ≈ 0.60×0.043 = 0.0258

[0098] τ = 10: 0.68×exp - 2.7 ≈ 0.68×0.067 = 0.04556

[0099] τ = 11: 0.62×exp - 2.25 ≈ 0.62×0.105 = 0.0651

[0100] τ = 12: 0.50×exp - 1.8 ≈ 0.50×0.165 = 0.0825

[0101] τ = 13: 0.38×exp - 1.35 ≈ 0.38×0.259 = 0.09842

[0102] τ = 14: 0.30×exp - 0.9 ≈ 0.30×0.407 = 0.1221

[0103] τ = 15: 0.22×exp - 0.45 ≈ 0.22×0.637 = 0.14014

[0104] Sum up the above values:

[0105] Φ(v, 16) ≈ 0.00385 + 0.00816 + 0.01485 + 0.0258 + 0.04556 + 0.0651 + 0.0825 + 0.09842

[0106] + 0.1221 + 0.14014 ≈ 0.60648

[0107] Finally, we get Φ(v, 16) ≈ 0.61. A value close to 1 indicates that "the historical communication fluctuations have a medium - level negative impact on the execution of the current task T4". The system sets a threshold value Φ = 0.5 according to experience. If the propagation function exceeds this threshold,

[0108] threshold

[0109] it is determined that there is a risk of delay in the current task, and the communication cost part in the path weight model is amplified, so that the path planning algorithm avoids such fluctuating links and preferentially selects other routes or scheduling time windows.

[0110] In actual planning, this propagation feedback mechanism has a significant impact on path selection. For example, in the original plan, UAV3 was to rendezvous with UAV1 at T5 after T4 to complete the collaborative shooting task. However, due to the poor communication stability of the T4 path, the system rescheduled UAV4 to undertake the T4 task and directly transmit data back through its link with GBS2, while UAV1 was redirected to execute T6 instead. This adjustment not only reduces communication risks but also maintains the integrity of the task collaboration chain, ensuring that the overall task execution progress is not affected by early communication anomalies in a chain reaction, fully demonstrating the key regulatory role of the propagation integration model in the dynamic evolution of the task-communication dual graph.

[0111] Currently, the multi-base unmanned system formation has completed mission marking from T1 to T4. There was a serious communication fluctuation event in the T3 path segment, and the propagation integration feedback value obtained in the T4 node evaluation has exceeded the system threshold. At this time, the command system aims to ensure that the path selection for subsequent key tasks T5, T6, and T7 can not only maintain the mission completion rate but also minimize the risks of delays and interruptions caused by link fluctuations. In particular, T5 and T6 have a collaborative execution relationship and have extremely high requirements for timing and link synchronization.

[0112] In this mechanism, the system first performs link state trend analysis in the communication graph, evaluating the communication fluctuation consistency of each link within a fixed past time window to calculate the communication continuity index CCI. Suppose the system observes that the CCI of the link from unmanned node UAV3 to GBS2 within the past 10 minutes is 0.89 (the value range is between 0 and 1, where 1 indicates the smallest fluctuation and extremely stable), while the CCI of the link from UAV2 to GBS1 is only 0.53. Then the system preferentially selects the path segment with a higher CCI value to construct the "communication skeleton" and expands based on the communication line of UAV3 as the path foundation.

[0113] Subsequently, integrating the requirements of the task graph in the path planning engine, the system conducts spatial reachability and time window adaptability analysis for task nodes T5 - T7. The system discovers that if UAV3 is used as the main executor to complete the collaborative tasks of T5 and T6, its path needs to deviate by 15 meters to bypass a mountain reflection area and is still reachable within the time window, and the overall communication stability is controllable. Therefore, the system determines that this path is the result of joint optimization and meets the planning criteria of "communication first + task feasible".

[0114] After this path is selected, to cope with subsequent path changes and environmental disturbances, the system deploys edge path strategy agents Agent-G1 and Agent-G2 at multiple base stations (GBS1 and GBS2) respectively. Based on the communication graph data and task graph status collected locally, they collaboratively construct a path strategy evaluation model and conduct self-evolving learning. To further evaluate whether the current path should be adjusted or optimized, the system calls the path strategy evolution feedback function:

[0115]

[0116] In practical applications, taking the node v k = T6 and the evaluation time window Δt = 5 minutes as an example, the system collects the following continuous 5-minute data:

[0117]

[0118] Among them, represents the change gradient of the communication coupling strength in the T6 path, and the recommended value range is set to 0, 0.5. The larger the value, the greater the instability fluctuation of the communication environment; Φ(v k , t′) is the communication history fluctuation propagation feedback function at the corresponding moment, and the recommended value range is 0, 1. The larger the value, the more significant the cumulative impact of historical anomalies of this node.

[0119] Substitute the data into the evolution potential energy function:

[0120]

[0121] Finally, it is calculated that Ω(T6, 5) = 0.0717. The system sets the policy correction threshold to 0.08 (the recommended range is 0.05, 0.1, dynamically adjusted according to the task urgency). Since the current value is slightly lower than the threshold, the system determines that the path does not trigger an adjustment for the time being, and only records this path segment as the "status of continuous monitoring required". The edge agent Agent-G2 will continue to collect the link status and recalculate the Ω value within the subsequent time window. Through this mechanism, the system successfully realizes the dynamic construction and evolution adjustment of the communication stability priority path, avoids system instability caused by frequent reconstruction of the task path, ensures the reachability of the task nodes and the coherence of the collaborative execution between tasks, and further improves the reliability of the collaborative path planning of the entire multi-base unmanned system in a high-risk and weak signal environment.

[0122] Example 2:

[0123] Based on Example 1, as the multi-base unmanned system (including UAV1 - UAV4 and ground base stations GBS1, GBS2) has completed most of the mission path segments from T1 to T6, the system enters the critical final stage. Among them, Task Point T7 involves performing a voice recognition and thermal imaging fusion sampling task in a canyon area, and the task has extremely high dependence on real-time data upload and control feedback. Previously, due to a significant link fluctuation in Path Segment T3, subsequent nodes faced uncertainty in scheduling. Therefore, before planning the path of T6→T7, the command system decides to call the predictive dynamic correction mechanism for the joint path of tasks and communication proposed in the present invention to predict the trend of communication stability, so as to ensure the communication continuity and execution reliability of the final critical mission segment. The core of this mechanism is to construct a communication fluctuation trend model through historical state data, identify the stability change trend of the current path, discover risks in advance and adjust the path strategy accordingly.

[0124] In actual deployment, the system collected the state data of UAV3 (currently executing the T6→T7 segment) in the past 10 minutes, which involved three core state variables: path offset ξ1(t), communication signal-to-noise ratio fluctuation ξ2(t), and control link command delay ξ3(t), corresponding to N = 3 types of state variables. The data is as follows:

[0125] Time t (min) <![CDATA[ξ1(t): Path offset (m)]]> <![CDATA[ξ2(t): Signal-to-noise ratio fluctuation (dB)]]> <![CDATA[ξ3(t): Instruction delay (ms)]]> 10 2.0 3.1 55 11 3.2 4.0 60 12 4.5 5.8 74 13 5.1 6.5 88 14 5.9 6.2 96 15 6.5 6.8 110

[0126] The system extracts the time change rate by calculating the approximation of the derivative of each state variable Respectively:

[0127] Path offset change rate:

[0128] Signal-to-noise ratio change rate:

[0129] Delay change rate:

[0130] The system further sets the following model parameters (the value ranges are all within the scope recommended by the present invention):

[0131] λ1 = 0.6, λ2 = 0.9, λ3 = 1.1, that is, the delay and signal-to-noise ratio fluctuation are considered to have a more significant impact on communication stability prediction;

[0132] κ1 = 1.2, κ2 = 1.5, κ3 = 1.8, that is, different types of fluctuations are designed with non-linear amplification coefficients according to sensitivity (the recommended range is 1.0 - 2.0).

[0133] Substitute into the prediction function:

[0134]

[0135] Finally, the obtained trend value Υ(t) ≈ 128.13, which is much higher than the system's preset dynamic fluctuation risk threshold Υ th = 50, indicating that the communication status change trend of the current path segment has been in a severe fluctuation state. The system immediately marks this path segment as "predicted unstable" and triggers the path mirror selection mechanism to generate an alternative path 30 meters to the east from within the JFE feasibility domain. It is estimated that its signal-to-noise ratio is more stable and the delay response is lower. After re-evaluation, Υ(t) drops to 52.7. Although it is still near the threshold, it is already within the controllable range. The system finally decides to adjust the path to the mirror path segment, and at the same time, the edge agent Agent-G2 synchronously synchronizes this adjustment experience to GBS1 for subsequent reference in the T7 path correction learning.

[0136] Since the trend prediction model Υ(t) was used in the previous stage to determine that there is a high communication fluctuation risk in this path, the system further calls the joint fluctuation boundary JFE model for space-state coupling analysis to determine whether the current path segment has entered the high-risk area where communication and task sensitivity are superimposed. This JFE boundary is constructed by superimposing historical communication fluctuation data with geographical high-interference factors (such as mountain blockage, multipath reflection areas, wind disturbance, etc.), and the task area is marked and classified by grids to form a risk density map. The system makes a decision on whether to trigger the correction mechanism for the path based on the spatial position relationship between the path nodes and the JFE and the communication fluctuation intensity, using the following coupling function:

[0137] Θ(x,y,t) = ρ·(1 - e -η·D(x,y) )·σ(t)

[0138] The system selects three key position nodes from the path segment T6→T7 for real-time evaluation: P1(110,65), P2(130,72), P3(148,81). According to the GIS terrain data and the JFE boundary map, the system calculates their minimum distances to the nearest JFE boundary point as: D(P1) = 22 meters, D(P2) = 10 meters, D(P3) = 4 meters. The geographical information system has evaluated the risk density parameter ρ = 0.85 in this area. This value indicates that there is a coupling phenomenon of frequent communication fluctuations and terrain disturbances in this area, and the recommended value range is [0.5, 1.0]. The spatial exponential decay factor η = 0.12 (recommended range [0.1, 0.3], and the larger the value, the more likely the path points close to the JFE boundary in space are to be affected by amplified risks). At the same time, the system judges through the communication environment fluctuation prediction module that the communication uncertainty index at the current moment t = 17 minutes is σ(t) = 0.93 (range 0 - 1, indicating that the environmental disturbance is close to the peak).

[0139] Substitute the data into the function one by one:

[0140] 1. For P1(110,65):

[0141] Θ1 = 0.85·(1 - e -0.12·22 )·0.93 = 0.85·(1 - e -2.64 )·0.93 ≈ 0.85·(1 - 0.071)·0.93

[0142] ≈ 0.85·0.929·0.93 ≈ 0.735

[0143] 2. For P2130, 72:

[0144] Θ2 = 0.85·(1 - e -0.12·10 )·0.93 = 0.85·(1 - e -1.2 )·0.93 ≈ 0.85·(1 - 0.301)·0.93

[0145] ≈ 0.85·0.699·0.93 ≈ 0.553

[0146] 3. For P3148, 81:

[0147] Θ3 = 0.85·(1 - e -0.12·4 )·0.93 = 0.85·(1 - e -0.48 )·0.93 ≈ 0.85·(1 - 0.619)·0.93

[0148] ≈ 0.85·0.381·0.93 ≈ 0.302

[0149] System comparison results and threshold setting Θ th = 0.6, that is, path nodes with coupling strength greater than this value will be marked as "risk intrusion points", and dynamic avoidance or replanning is required. Thus, the coupling strength of node P1 reaches 0.735, exceeding the threshold, triggering the risk identification mechanism; P2 is an edge point, approaching the warning line; P3 is in the safe area. Therefore, the system marks the first half of the path T6 → T7 as a "potentially unsafe section" and immediately enters the path mirror replacement process. The system replans a new path segment of 115, 60 → 133, 67 → 150, 75 outside the JFE safety boundary, recalculates its communication fluctuation trend and task delay impact, and finally evaluates that its stability is improved by 28%, and the task time delay risk is reduced to half of the original path. This path change information is synchronized to the edge intelligent agents of GBS1 and GBS2, and the policy evolution weight is updated, enabling the subsequent path evaluation process to quickly avoid the JFE high-density risk area.

[0150] As the multi-base unmanned system completes the task marking at point T6 and prepares to execute the acquisition task at point T7, during the process, the system determines through the JFE model that there is a high communication coupling sensitivity risk in the path segment T6→T7, especially the coupling intensity Θ1 = 0.735 > 0.6 at the middle segment P1 node, which triggers the risk identification mechanism.

[0151] According to the predictive dynamic correction mechanism for the task and communication joint path proposed by the present invention, the system needs to find a feasible "mirror path" for this path segment without interrupting the execution of the original task sequence, that is, an alternative segment with similar geographical accessibility, consistent task objectives, but better communication situation, and conduct quantitative evaluation to decide whether to perform local path replacement.

[0152] First, the system retrieves a new path segment that meets the mirror conditions from the JFE feasibility domain: a detour segment that offsets from the current node P1(110,65) to P1'(114,62) and passes through nodes P2'(133,68), P3'(150,76), etc. This mirror path has an offset in the range of 15 - 20 meters from the original path in space, but avoids the high-fluctuation dense band of JFE, and at the same time avoids mountain passes and low-altitude channel blind spots. Then, through the communication prediction module, the system models the communication stability scores Ω(τ) of the mirror path and the original path segment respectively within the prediction time window T = 6 minutes and at time τ = 17 to 23 minutes, and the results are as follows:

[0153] Time τ (min) <![CDATA[Ω orig (τ)|]]> <![CDATA[Ω mirror (τ)]]> χ(τ) 17 0.82 0.65 1 18 0.87 0.60 1 19 0.91 0.59 1 20 0.95 0.58 1 21 0.90 0.56 1 22 0.85 0.55 1 23 0.83 0.54 1

[0154] Note: The value range of Ω(τ) is [0,1]. The higher the value, the more unstable the communication state, and 0 represents the optimal state; it is recommended to set the replacement evaluation threshold Δ s (t) > 0.15 triggers path update; χ(τ) = 1 indicates that the mirror path is completely substitutable in terms of task timing, objectives, data types, etc.

[0155] Substitute into the stability difference function:

[0156]

[0157] In discrete approximate calculation, take Δt = 1 minute, T = 6:

[0158]

[0159] Finally, obtain Δ s(17) ≈ 0.295, which greatly exceeds the set trigger threshold of 0.15. According to the policy logic set by the present invention, the system will determine that this original path segment shows significant disadvantages within the future time window, the communication fluctuation is unacceptable, and the mirror path has 100% task substitutability. Therefore, the local path update module is immediately triggered to use the mirror path P1' → P3' to replace the original path segment P1 → P3.

[0160] The updated path information is synchronized to all participating agents (UAV3, GBS2, Agent - G1, Agent - G2), and written into the system experience pool as a "communication - guided path evolution event" for future similar scenarios to refer to; in this correction, the task delay is reduced by about 2.4 minutes on average, and the image transmission success rate is increased from 72% to over 95%, significantly improving the continuity and anti - interruption ability of task execution, and ensuring the smooth upload of key data of Task T7 to the command center.

[0161] In summary, this example fully demonstrates the feasibility and necessity of the predictive dynamic correction mechanism of the present invention in actual combat tasks from the full process of communication risk identification → mirror path construction → differential function quantification → replacement judgment decision. The formula modeling has a clear structure and the physical meaning of the parameters is clear, and it can be directly embedded into the system decision logic to achieve automatic path safety assessment and update control.

Claims

1. A joint path planning method for multi-base unmanned systems tasks and communications, characterized in that The following steps are involved: S1. Modeling using a two-layer spatiotemporal decision network for tasks and communications: S1.1, map the task distribution to the target node layer, and construct the communication link to the transmission link layer to form a dual graph of task and communication; S1.

2. Establish dynamic coupling edges between graphs to represent the impact of task execution behavior on communication quality; introduce interactive influence propagation model in the time dimension to simulate the feedback effect of communication link fluctuation on task progress; provide spatiotemporal dynamic cost evaluation input for path planning; S2. Path planning optimization strategy using joint feasibility domain: S2.

1. Based on the two-layer graph output by the technology, the task feasible domain and the communication strong connected domain are defined in the time and space domain; a joint feasibility domain JFE is constructed, and path planning is only allowed to be carried out in this domain, so as to deal with the split problem of communication repair after path planning; S2.2, perform multi-objective compression on the path to balance the task path time consumption, node connection stability, and path redundancy consumption indicators; S2.3, introduce graph homotopy simplification mechanism to compress redundant edge paths inside JFE; S3. Predictive dynamic correction mechanism using joint task and communication paths: S3.

1. Use the state history of the unmanned system nodes including path deviation, communication quality, and delayed feedback to establish a communication fluctuation trend model; compare the execution trajectory of the current path with the dynamic boundary of the JFE to identify high-risk segments; S3.2, implement path mirror prediction for the executed path segment, and evaluate the stability difference between the modified path and the original path; if the difference exceeds a threshold, trigger the local path update module; S4. Adopt path and communication collaborative deployment learning mechanism: S4.

1. Setting the global objective function, including task completion rate, communication interruption rate, and path reconstruction frequency; S4.

2. Using the multi-agent reinforcement learning framework, each base station or key node acts as an intelligent agent to optimize the deployment strategy based on local experience + global evaluation.

2. The multi-base unmanned system task and communication joint path planning method according to claim 1, characterized in that The task and communication two-layer spatiotemporal decision network modeling method: The task execution requirements and communication link status in the multi-base unmanned system are semantically modeled in a hierarchical manner to construct a dual-graph structure of the task graph and the communication graph. In the task layer, the task nodes are given semantic labels such as execution window, importance level, and collaborative dependency. The communication layer describes the link capacity, volatility, and predicted interruption probability based on the physical / logical links between the unmanned nodes and between the unmanned nodes and multiple base stations.

3. The multi-base unmanned system task and communication joint path planning method according to claim 2, wherein The task and communication two-layer spatiotemporal decision network modeling method: A feedback modeling mechanism for spatiotemporal interactive propagation is constructed to predict the timing impact of link fluctuations on task execution delays. By simulating the disturbance diffusion path in the graph structure, the attenuation characteristics of the communication fluctuation → task response and the transmission chain in the time dimension are quantified and described by the propagation integral model: in: Φ(v, t) represents the feedback intensity of task or communication node v affected by the accumulation of communication anomalies over a past period of time at the current moment t; Λ(v, τ) is the link interference intensity suffered by the node at the past time point τ; δ is the interference attenuation factor, used to represent the rate at which the impact of communication anomalies on tasks decays over time; the exponential decay function exp(-δ·(t - τ)) simulates the weakening effect of long-term communication fluctuations on the current task.

4. The multi-base unmanned system task and communication joint path planning method according to claim 3, wherein The task and communication double-layer spatio-temporal decision network modeling method: Adopt a path generation mechanism with communication continuity priority, extract path segments with relatively high link fluctuation consistency in the communication graph as the initial communication skeleton, the structural stability is guided by the communication continuity index CCI, and fine-tune the path by integrating the requirements of task nodes to achieve a joint path that prioritizes communication but allows tasks to be reachable; deploy edge path strategy agents at each multi-base station, so that according to the local task status and communication fluctuation conditions, generate recommended path strategies and share evolutionary experience with adjacent base stations.

5. The multi-base unmanned system task and communication joint path planning method according to claim 1, characterized in that The construction method of the predictive dynamic correction mechanism for the task and communication joint path includes: Collect multi-dimensional state historical data during the task execution of the unmanned system, construct a communication fluctuation trend model, where the collected state data includes: path deviation trajectory, communication link quality evolution data, task control delay feedback information, and extract fluctuation patterns on multiple time scales; construct a prediction function based on the historical state sequence, defined as: Where: Υ(t) represents the intensity of the communication stability fluctuation trend of the current path segment at time t; N represents the number of state variables included in the modeling, including path offset, signal-to-noise ratio fluctuation, and control link delay; ξ i (t) represents the value of the i-th type of state variable at time t; represents the rate of change of this state over time; λ i is the weight factor of the i-th type of state in the overall trend modeling, used to distinguish the influence degree of different states on the communication prediction result; κ i is the amplification exponent, used for non-linear sensitivity modeling of the rate of change, to enhance or suppress the driving force of a certain type of fluctuation on the system judgment.

6. The multi-base unmanned system task and communication joint path planning method according to claim 5, characterized in that The construction method of the predictive dynamic correction mechanism for the task and communication joint path includes: Compare the current execution path trajectory with the pre-established joint fluctuation boundary JFE. The boundary model integrates communication fluctuation prediction data and geospatial uncertainty information, and is used to identify high-risk areas in the path segment that are sensitive to both tasks and communication; when the current path trajectory approaches or enters the high-fluctuation dense zone defined in the dynamic boundary, trigger the risk identification mechanism.

7. The multi-base unmanned system task and communication joint path planning method according to claim 6, wherein The construction method of the predictive dynamic correction mechanism for the task and communication joint path includes: After identifying the high-risk segment, adopt a mirror path prediction mechanism for constructing path segments, generate optional path mirror segments in areas with similar geographical locations, the same task objectives but complementary communication situations, and predict the communication performance and execution consistency of the candidate path through simulation; and compare the alternative values of the current path and the mirror path by defining a stability difference function as follows: Where: Δ s (t) represents the cumulative value of the difference in communication stability between the mirror path and the original path within the future time window T starting from the current moment; Ω(τ) and Ω(τ) are the stability evaluations of the mirror path and the original path under the communication prediction model at time τ, respectively. mirror orig Points; |·| is used to measure the absolute difference in communication stability between two paths; χ(τ) is the task consistency function, indicating the substitutability of the mirror path in task scheduling. When χ(τ) = 0, it means there is no substitutability, and when χ(τ) = 1, it means complete equivalence; T is the prediction time window length for difference evaluation.

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