Highway intelligent inspection path planning method based on single inspection vehicle and multiple unmanned aerial vehicles cooperation of capability restriction and robust time of flight

Abstract

The application relates to the technical field of intelligent highway inspection, and discloses a single-inspection-vehicle-multiple-unmanned-aircraft cooperative highway intelligent inspection path planning method based on capacity limitation and a robust flight time; in view of the problems that the prior art is insufficient in describing the energy supplement process of the unmanned aircraft, the resource utilization efficiency is low, and the flight time fluctuation is not fully considered, the application constructs a cooperative path planning model containing a partial charging and segmented linear charging mechanism, introduces cooperative scheduling of on-vehicle charging and parking point charging, and adopts a budget uncertainty set to describe the flight time robust constraint. Meanwhile, an adaptive large neighborhood search algorithm (FD-ALNS) based on feasibility decoding is designed to efficiently solve the problem. Experiments show that the application can obtain an optimal solution consistent with the exact solution in a small-scale example, and in the scene of a 102.6 km highway, 45 inspection points and 5 unmanned aircrafts, the total completion time is reduced by 34.33%, and the inspection efficiency, resource utilization rate and scheme stability are significantly improved.

Description

Technical Field

[0001] This invention relates to the field of intelligent highway inspection technology, and in particular to a single inspection vehicle-multiple UAV collaborative intelligent highway inspection path planning method based on capability-limited and robust flight time. Background Technology

[0002] Highways are vital infrastructure supporting regional economic connections, personnel flow, and logistics transportation, and their operational status directly impacts traffic efficiency and public safety. With the continuous increase in highway mileage and a large number of routes entering their long-term service phase, bridges, culverts, slopes, roadbeds, retaining walls, drainage facilities, and ancillary protective structures along the routes face problems such as aging, wear, erosion, deformation, and cracking, making inspection and maintenance tasks increasingly demanding.

[0003] Currently, highway inspections mainly rely on manual on-site checks, patrol vehicles along the route, and a small amount of fixed monitoring equipment. This approach has significant limitations in the highway environment: highways have high speeds, dense traffic flow, and strict on-site safety controls, making it difficult for inspection personnel to frequently enter dangerous areas such as shoulders, slopes, under bridges, culvert entrances, or near the median strip for close-up inspections; early-stage damage often manifests as minor cracks, localized erosion, slight component deformation, or superficial anomalies, which are difficult to identify promptly using only visual inspection and vehicle patrols; traditional inspection methods are easily affected by weather, visibility, work windows, and traffic conditions, resulting in low inspection efficiency, high operational risks, and significant long-term maintenance costs.

[0004] With the development of drone technology, some solutions have begun to incorporate drones as an auxiliary means of inspection. Drones, due to their advantages such as low-altitude maneuverability, diverse viewing angles, and ability to acquire high-resolution images and video data at close range, can conduct detailed inspections of bridge substructures, slope surfaces, tunnel entrances, drainage facilities, and other areas difficult for humans to access. This offers significant advantages in improving inspection coverage and reducing personnel risks. Related reviews indicate that drones are widely used in highway systems for traffic monitoring, infrastructure inspection, and safety assessment, and can be combined with intelligent identification and data analysis technologies to improve the digitalization and automation of inspections.

[0005] However, the widespread adoption of drones for long-distance highway inspections still faces practical bottlenecks. The most prominent limitation comes from the drones' own endurance: a single drone's range is limited by battery capacity, payload capacity, and environmental conditions, making it difficult to independently undertake long-distance continuous inspection tasks. Furthermore, the open environment of highway inspections means that changes in wind speed, local airflow, and weather disturbances can cause fluctuations in drone flight time, further affecting task coordination and recovery arrangements. Therefore, in practical engineering, drones often need to work in conjunction with ground inspection vehicles. The inspection vehicles handle long-distance mobility, takeoff and landing support, and energy resupply, while the drones are responsible for detailed inspections of the areas surrounding the docking points, thus forming an air-ground collaborative inspection model.

[0006] From the perspective of existing inspection models, most research and applications are still based on the assumption that "UAVs take off from and return from fixed ground base stations" or "complete tasks at fixed take-off and landing points." This is more suitable for point-based inspections of local structures such as bridges, slopes, and tunnel entrances. However, for scenarios like highways with long routes, numerous inspection points, and continuous tasks, the fixed base station model is often significantly limited by range and recovery distance. On the other hand, although some research has begun to consider the collaboration between ground vehicles and UAVs, related work is mostly focused on the organization of general patrols, traffic inspections, or pavement defect detection. Research on systematic path planning for long-distance, multi-segment, and continuous inspections of highway infrastructure remains relatively insufficient.

[0007] Most existing research on vehicle-drone collaboration simplifies the range problem to a maximum single flight time or a maximum total battery capacity, rarely delving into the dynamic recharging process of drones after recovery. In practical engineering, drones don't always need to be fully charged before departure; instead, they are often partially charged based on subsequent mission requirements. Furthermore, the charging process isn't always at a fixed rate but exhibits a phased characteristic of "pre-charging - fast charging - slow charging" depending on the battery status. In addition, drone recharging on inspection vehicles includes two typical methods: on-board charging while the inspection vehicle continues its journey, and docking point charging at designated stops. Existing research rarely integrates these recharging mechanisms into a unified model framework and lacks refined processing at the collaborative path planning level.

[0008] Furthermore, existing solutions generally fail to adequately address the uncertainty of flight time. The highway inspection environment is highly open, and the drone's flight is easily affected by wind field changes, local disturbances, and weather conditions, often resulting in a difference between the actual and nominal flight times. If mission scheduling is based solely on ideal flight times, issues such as arrival delays, disrupted time windows, delayed recovery times, and failures to connect subsequent mission segments can easily arise, thus affecting the stability of the entire inspection plan.

[0009] In summary, the existing technology has the following main drawbacks:

[0010] (1) The description of the recharging process under limited UAV endurance is insufficient. Existing solutions usually simplify the charging process to a fixed charging time or a single linear charging rate, which makes it difficult to truly reflect the segmented changes of UAV batteries in different power ranges, such as "pre-charge-fast charge-slow charge". They also fail to systematically depict the two types of recharging methods: on-board charging during the inspection vehicle's journey and charging at docking points. This can easily lead to a large deviation in the estimation of actual recharging time, making it difficult for the planning scheme to simultaneously meet the requirements of power constraints and timing coordination during implementation.

[0011] (2) It is difficult to reduce the number of UAVs by reasonably replenishing their power, resulting in low resource utilization efficiency. In long-distance, multi-point inspection tasks on highways, due to the limited endurance of a single UAV, if there is a lack of a refined power replenishment mechanism and dynamic task connection strategy, existing solutions often have to increase the number of UAVs to make up for the insufficient endurance of a single UAV, thereby ensuring that the task can be completed within the specified time. This approach will significantly increase equipment investment costs, on-site scheduling complexity, and system operation burden. Existing technologies have failed to fully utilize the role of inspection vehicles as mobile power replenishment platforms, and also lack a systematic model and scheduling method around the operating mechanism of "partial charging - multiple departures - multiple rounds of task execution".

[0012] (3) Insufficient consideration of flight time fluctuations leads to poor stability and practical feasibility of the scheme. Most existing multi-UAV inspection or vehicle-to-machine collaborative schemes are still based on ideal flight time for modeling and scheduling, and the handling of flight time uncertainty is relatively rough, lacking targeted robust constraint design. In actual implementation, problems such as UAV arrival time at inspection points being delayed, time window constraints being broken, UAVs failing to be recovered on time, and subsequent task chain failures are likely to occur, thus affecting the reliability and engineering applicability of the entire highway collaborative inspection scheme.

[0013] (4) Unified modeling is difficult and the solution is complex. Most existing vehicle-UAV collaborative research is based on fixed base stations or simplified power replenishment assumptions, and only plans local links in the UAV path or vehicle path. It does not integrate key factors such as "selection of inspection vehicle parking points, multi-UAV task allocation, partial charging and segmented linear charging process, on-board charging and parking point charging, flight time fluctuations and vehicle-UAV timing synchronization relationship" into the same optimization framework. Since these factors have significant time-power coupling characteristics, the problem is highly complex and belongs to a typical complex combinatorial optimization problem. If a general accurate algorithm is directly used, the solution time is often long and even difficult to converge on an engineering scale; while simple heuristic methods are difficult to simultaneously take into account the feasibility, stability and quality of the solution.

[0014] Therefore, there is an urgent need for a single inspection vehicle-multiple UAV collaborative intelligent inspection path planning method for highways based on capability-constrained and robust flight time, in order to improve the overall efficiency, feasibility and resource utilization of long-distance, multi-point inspection tasks on highways. Summary of the Invention

[0015] The purpose of this invention is to overcome the problems of existing highway inspection vehicle-multi-UAV collaborative path planning methods, such as insufficient characterization of the dynamic refueling process under limited UAV endurance, low resource utilization efficiency, and insufficient consideration of flight time fluctuations. This invention provides a single inspection vehicle-multi-UAV collaborative intelligent highway inspection path planning method and system based on limited capabilities and robust flight time, in order to reduce the total operation completion time and improve the stability of the scheme and the level of resource utilization.

[0016] To achieve the above objectives, the present invention provides the following technical solution: A collaborative intelligent highway inspection path planning method based on capability-constrained and robust flight time single inspection vehicle-multi-UAVs includes the following steps: S1. Obtain highway inspection task information The task information includes a set of alternative parking points for the inspection vehicle, a set of inspection points, the earliest and latest service times for each inspection point, the battery capacity of the drone and the initial power of each drone, the energy consumption per unit distance of the drone, and the segmented linear charging parameters of the drone. The segmented linear charging parameters include the pre-charge rate, the fast charge rate, the slow charge rate, and the critical power level for switching from pre-charge to fast charge and the critical power level for switching from fast charge to slow charge. S2. Construct a collaborative inspection path planning model Using a single inspection vehicle as a ground-based mobile command and supply platform and multiple UAVs as aerial inspection execution units, a collaborative inspection path planning model is constructed with the objective function of minimizing the total operation completion time. The model includes inspection vehicle path constraints, inspection vehicle time recursion constraints, UAV path constraints, UAV takeoff and inspection vehicle synchronization constraints, UAV robust time propagation constraints to describe flight time fluctuations, UAV charging constraints, flight arc power transfer constraints, and piecewise linear partial charging constraints based on the cumulative charging time function. The piecewise linear partial charging constraint is expressed through a cumulative charging time function. accomplish:

[0017] in, q1 represents the critical charge level for switching from pre-charge to fast charge, and q2 represents the critical charge level for switching from fast charge to slow charge. The charging rates are for pre-charge, fast charge, and slow charge, respectively; and the charging time meets the following requirements:

[0018] in, For drones Arrive at the parking spot And the battery level before charging; For drones At the parking spot The battery level when the inspection vehicle leaves after charging; For drones at parking spots Charging time; The drone charging constraints include: Charging power balance and its upper limit ; Recover synchronization constraints ; Dock duration constraints ; Power boundary ; and on-board charging constraints And its lower limit inequality, thereby realizing the coordinated scheduling of on-vehicle charging (energy replenishment while driving) and docking point charging (node ​​energy replenishment).

[0019] The robust time propagation constraint for the UAV uses a budget uncertainty set to describe flight time fluctuations, including: Unperturbed recursion: Robust recursion: Monotonicity constraint: Time window constraint: and Where G is the robust layer set, controlling the maximum number of flight segments that deteriorate. ; The maximum number of flight arcs that can be allowed to deteriorate is set; For drones in the inspection vehicle arc Inside, when the maximum allowed When the flight arc deteriorates, the node is reached. The worst arrival time; For drones in the inspection vehicle arc Inside, when the maximum allowed When the flight arc deteriorates, the node is reached. The worst arrival time; For drones in the inspection vehicle arc Inside, when the maximum allowed When the flight arc deteriorates, the node is reached. The worst arrival time is determined by the above recursive relationship, ensuring that the time window requirements of each inspection point are still met even in the worst flight scenario. For nodes Service hours; Nominal flight time; This represents the maximum deviation in flight time. For drones Is it in the patrol vehicle arc? Inspection arc within the corresponding interval If yes, it is 1; otherwise, it is 0. For drones Is it in the arc? Corresponding inspection points within the area Yes, it is 1; no, it is 0. Inspection point The earliest service time; Inspection point Latest service hours; S3. The model is solved using an adaptive large neighborhood search algorithm based on feasibility decoding: The algorithm adopts a two-layer encoding structure, with the outer layer encoding the inspection vehicle docking sequence and the inner layer encoding the interval task matrix, where each element represents the ordered inspection task chain undertaken by a certain UAV in the interval between two adjacent actual docking points.

[0020] The feasibility decoding process includes: recursively tracing each operational area forward along the inspection vehicle parking sequence, recursively tracing the flight, service, and recovery processes according to the task chain sequence, and recording the battery level before charging at each parking point. , leaving the battery and interval flight power The system adopts an on-demand energy replenishment rule, determining energy replenishment based on the minimum starting power required for the next stage of the task, prioritizing onboard charging, and arranging charging at rest stops only when insufficient; it employs an early-stop feasibility check, immediately terminating decoding if a time window is violated, power is insufficient, or the timing is infeasible.

[0021] The initial solution construction includes a Split rescue mechanism: when a task point cannot find a feasible insertion position under the current docking structure, a new intermediate docking point is added near the highway projection of the task point or within the bottleneck section, splitting the original section into two shorter sections, adding a new row dimension to the path matrix, and then retrying to insert the task point.

[0022] The adaptive large neighborhood search algorithm includes the following destructive operators: random removal operator, robust urgent removal operator, charging criticality removal operator, and greedy marginal cost removal operator; and the following repair operators: greedy repair operator, Regret2 repair operator, anchored interval repair operator, and energy balance repair operator. The algorithm employs a simulated annealing acceptance criterion: if the new solution's objective value is better than the current solution, it is unconditionally accepted; otherwise, it is rejected probabilistically. Accept inferior solutions, among which, Let f(X) be the objective function value of the current solution, and f(X') be the objective function value of the candidate solution. The current temperature parameter is used; at the same time, a weight adaptive update mechanism based on search segments is used to dynamically adjust the operator selection weights.

[0023] S4. Perform the inspection task according to the solution results: The inspection vehicle only stops at the actual selected docking point, the UAV takes off, inspects and recovers in each section, and charges on the vehicle or at the docking point according to the energy replenishment arrangement. After completing the operation of all inspection points, it returns to the destination.

[0024] As a preferred technical solution, the collaborative inspection path planning model selects actual stops from a pre-set set of alternative stops, including service areas, toll stations, management stations, emergency parking lanes, maintenance work areas, or permitted temporary work points; the inspection vehicle travels along the highway and only stops at the actual stops to support the drone in performing inspection tasks within the interval between adjacent actual stops.

[0025] As a preferred technical solution, the system incorporates a Split rescue mechanism and feasibility decoding rules for on-demand energy replenishment; the piecewise linear partial charging constraint is based on a cumulative charging time function. To achieve this, the flight time robust constraint employs a budget uncertainty set, and the flight arc charge transfer satisfies... and And continuous constraints on cross-interval power generation.

[0026] Furthermore, the present invention also provides a system for implementing the above method, comprising: a perception layer for acquiring highway inspection task information; a model building module for constructing the collaborative inspection path planning model; a solution module for generating the optimal inspection vehicle stopping sequence and the task chain of each UAV interval using the adaptive large neighborhood search algorithm based on feasibility decoding; and an execution module for controlling the driving of the inspection vehicle and the take-off, landing, inspection, recovery, and recharging operations of multiple UAVs according to the solution results.

[0027] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0028] (1) Significantly reduce the total operation completion time and improve inspection efficiency. By employing a piecewise linear partial charging function and on-demand energy replenishment rules, the slow charging wait caused by fully charging after each recovery is avoided. Priority is given to synchronous energy replenishment via on-board charging, significantly reducing stop time. In a large-scale simulation (102.6 km highway, 38 candidate stop points, 45 inspection points, and 5 drones), the optimized total completion time was reduced from 371.24 min to 243.81 min, a reduction of 34.33%.

[0029] (2) High accuracy in charging time estimation and reliable task connection. The cumulative charging time function of this invention divides the charging process into three segments: pre-charging, fast charging, and slow charging, and uses different charging rates for each segment. The segmented processing of six charging scenarios fully covers all possible start and end charge ranges, avoiding errors caused by fixed charging time or a single linear rate, and making the task timing recursion more consistent with the actual charging pattern.

[0030] (3) High resource utilization efficiency and reduced number of drones required. By employing an on-demand charging strategy and coordinating on-board and docking station charging, a single drone can launch and perform multiple missions within a single inspection task, reducing reliance on the total number of drones. In the case study, five drones completed full coverage of 45 inspection points, with a total on-board charging capacity of 243.3 units, effectively replacing some docking station charging and reducing equipment investment costs.

[0031] (4) The scheme has strong stability and good adaptability to complex environments. A robust flight time constraint based on the budget uncertainty set is introduced to ensure that the scheme can still meet the time window requirements and recovery continuity under worst-case disturbances such as wind speed and airflow. Sensitivity analysis shows that when the robust budget Γ increases from 0 to 4, the completion time increases from 213.46 min to 247.46 min; when the flight time deviation ratio δ increases from 0.05 to 0.25, the completion time increases from 236.33 min to 251.86 min, providing a quantitative basis for the trade-off between robustness and efficiency in engineering.

[0032] (5) The algorithm has high solution accuracy, and the solution is consistent with the exact solution in small-scale scenarios. In six sets of tests on large-scale examples (2-3 UAVs, 5-7 inspection points), the optimal target value obtained by the FD-ALNS algorithm of this invention is completely consistent with the optimal solution given by the Gurobi solver, verifying the high accuracy and feasibility of the algorithm.

[0033] (6) The algorithm has high solution efficiency and meets the real-time requirements of engineering. In small-scale examples, the FD-ALNS solution time is only 0.43 to 0.91 seconds, which is far better than Gurobi's 18.13 to 675.27 seconds. In large-scale examples, it can provide high-quality solutions within a reasonable time, meeting the needs of rapid planning for long-distance highway inspection.

[0034] (7) The resource sensitivity analysis is clear, guiding actual allocation. Sensitivity analysis of the number of drones shows that when the number of drones increases from 4 to 9, the cumulative reduction in completion time is 10.71%. However, the marginal benefit slows down when the number of drones exceeds 7 (the reduction is only 0.02% when increasing from 7 to 8 drones), providing a scientific basis for the number of drones to be configured in actual engineering projects. Sensitivity analysis of charging capacity shows that when the charging capacity coefficient λ increases from 0.80 to 1.20, the completion time decreases from 252.32 min to 221.62 min, a reduction of 12.16%, indicating that improving charging efficiency is an important direction for optimizing system performance.

[0035] (8) The algorithm has strong adaptability and high search efficiency. This invention dynamically adjusts the selection weights of the destruction / repair operators by using a simulated annealing acceptance criterion and a weight adaptive update mechanism based on search fragments. This allows the search process to initially favor diverse perturbations and gradually shift towards more refined operators, effectively avoiding local optima stagnation. When the global optimum is not refreshed after multiple consecutive iterations, the temperature is automatically increased and the structure-level destruction operator is invoked for reheating, enhancing the global exploration capability.

[0036] In summary, this invention outperforms existing technologies in terms of operational efficiency, resource utilization, solution reliability, solution accuracy and speed, and engineering applicability, providing an efficient, stable, and feasible intelligent path planning solution for long-distance, multi-point, and continuous inspection tasks on highways. Attached Figure Description

[0037] Figure 1 This is a diagram illustrating the overall technical architecture of the present invention; Figure 2 This is a schematic diagram of the piecewise linear charging function in Embodiment 1 of the present invention; Figure 3 This is a large-scale calculation example of the road network and inspection point distribution map of Embodiment 3 of the present invention; Figure 4 This is a visualization of the solution results for a large-scale computational example in Embodiment 3 of the present invention; Figure 5 This is a graph showing the sensitivity analysis results of the number of drones in Embodiment 4 of the present invention; Figure 6 This is a graph showing the sensitivity analysis results of the algorithm parameters in Embodiment 4 of the present invention. Detailed Implementation

[0038] To make the technical means, creative features, objectives, and effects of this invention easier to understand, the invention is further described below with reference to specific embodiments. It should be noted that the specific embodiments described herein are for illustrative purposes only and are not intended to limit the invention.

[0039] This invention is achieved through the following technical solution. (See...) Figure 1 Addressing the long-distance, continuous inspection scenarios of highways, this invention utilizes a highway inspection vehicle as a ground-based mobile command and supply platform, and multiple drones as aerial inspection execution units, constructing a collaborative inspection system of "inspection vehicle mobility along the route - drone segmented operation - dynamic recharging - re-departure." Specifically, alternative stopping points such as service areas, toll stations, management stations, emergency parking lanes, maintenance work areas, or permitted temporary work points are pre-set on the target highway section. The inspection vehicle travels along the main line according to the planned route, stopping only at the actual stopping points selected by the optimized model. The drones, using the inspection vehicle as a mobile base, take off from a specific actual stopping point and sequentially visit inspection points such as bridges, culverts, slopes, retaining walls, drainage facilities, and roadbed defects within the assigned section according to the assigned task chain. After completing tasks such as photography, video acquisition, surveying, or other inspections, they rejoin the inspection vehicle at a subsequent actual stopping point and are then retrieved. Compared with the traditional "fixed base station - single flight - return and recovery" method, this invention combines the movement of inspection vehicles along the route with the multi-round operation of UAVs to break down the inspection task that originally spanned a long route into several continuously connected operation sections. This expands the overall inspection coverage and improves the system's resource utilization efficiency under the premise that the endurance of a single UAV is limited.

[0040] Within the aforementioned collaborative framework, this invention does not merely optimize the paths of inspection vehicles or drones locally, but rather integrates and jointly models the inspection vehicle docking decisions, multi-drone task allocation, flight path arrangement, recharging process, and vehicle-drone timing relationship. Addressing the common limitation of drone endurance during long-distance inspections, this invention introduces a partial charging mechanism. Instead of requiring drones to be fully charged after each recovery, it recharges on demand based on the minimum energy level required for subsequent tasks. Simultaneously, considering the actual charging pattern of drone batteries ("pre-charge - fast charge - slow charge"), a piecewise linear partial charging function is constructed to uniformly characterize the dynamic recharging process of drones during both the inspection vehicle docking and vehicle-flying phases. In other words, drones can charge at the docking point when the inspection vehicle is stopped, or they can charge while the inspection vehicle is in motion; both methods constitute the recharging method for drones during continuous inspections. On the other hand, considering the impact of wind speed changes, local airflow disturbances, and weather conditions on flight time in the open environment of highways, this invention further introduces robust flight time constraints to ensure that the obtained inspection scheme can still meet the requirements of mission completion, time window constraints, and UAV recovery and connection under adverse flight conditions. Based on this, with the minimum total operation completion time of the entire inspection mission as the optimization objective, a capability-constrained collaborative path planning model is formed that simultaneously considers docking, flight, refueling, and uncertainties.

[0041] Given that the aforementioned joint optimization problem simultaneously involves inspection vehicle docking selection, multi-UAV task chain construction, piecewise linear partial charging, and flight time robustness constraints, exhibiting significant time-power coupling characteristics and high solution complexity, directly employing general-purpose precise algorithms is insufficient to meet the requirements for rapidly generating scheduling schemes in engineering scenarios. Therefore, this invention proposes an adaptive large neighborhood search method based on feasibility decoding at the algorithmic level. This method employs a two-layer encoding structure of "outer layer docking decision - inner layer UAV task orchestration," where the outer layer describes the docking skeleton of the inspection vehicle along the highway, and the inner layer describes the inspection task chain of each UAV within its corresponding operating section. When evaluating candidate solutions, instead of directly using charging quantity and charging stage switching as explicit search variables, the feasibility decoder recursively calculates the arrival and departure times of the inspection vehicle, the worst-case arrival time of the UAV, the interval recovery time, power evolution, and charging duration along the docking sequence, thereby completing the feasibility verification and target evaluation of the candidate solutions. To obtain high-quality solutions, the algorithm first uses a "sparse initialization + greedy insertion + Split Rescue Mechanism" approach to generate an initial feasible solution. Then, it performs an iterative search process of "destruction-repair-acceptance-adaptive update" around the current solution: In the destruction phase, operators such as random removal, robust urgent removal, charging criticality removal, greedy marginal cost removal, and docking point deletion and insertion perturbation are designed for capability-constrained scenarios. In the repair phase, operators such as greedy repair, Regret-2 repair, anchored interval repair, and energy balance repair are used to reconstruct incomplete solutions. In the solution acceptance phase, simulated annealing is introduced to enhance the ability to escape local optima. In the operator selection phase, an adaptive adjustment is achieved through a weight update mechanism based on historical performance. Therefore, this invention can embed piecewise linear partial charging constraints and flight time robust constraints into the search process without significantly increasing the algorithm's implementation complexity, ultimately obtaining a patrol vehicle-multi-UAV cooperative path scheme that balances feasibility, stability, and operational efficiency.

[0042] Example 1: Model Building and Algorithm Design This embodiment describes in detail the collaborative inspection path planning model constructed by the present invention and the proposed adaptive large neighborhood search algorithm (FD-ALNS) based on feasibility decoding.

[0043] 1.1 Model Symbols The symbols of the collaborative inspection path planning model constructed in this invention are summarized in Table 1.

[0044] Table 1 Summary of Model Symbols

[0045]

[0046] 1.2 Objective Function (1) (2) Equation (1) indicates that the optimization objective of the model is to minimize the total inspection time. Equation (2) indicates that the completion time is not less than the time it takes for the inspection vehicle to complete the task.

[0047] 1.3 Constraints 1.3.1 Inspection vehicle route constraints (3) (4) (5) (6) (7) (8) Equation (3) indicates that the inspection vehicle must start from the starting point. Equation (4) indicates that the inspection vehicle must reach the destination.

[0048] Equations (5) and (6) represent variables. With variables The relationship between them is that if the inspection vehicle chooses to stop, then the inspection vehicle has a departure arc and an entry arc at that point.

[0049] Equation (7) indicates that the inspection vehicle must stop at the starting point and the end point.

[0050] Equation (8) represents the flow conservation at intermediate parking points, ensuring the flow balance of the inspection vehicle at the visited points.

[0051] 1.3.2 Inspection vehicle time recursion constraint (9) Equation (9) indicates that if the inspection vehicle starts from... Drive to If you reach the point, then you will arrive. The time of arrival is: Adding the moment to Point waiting time and The travel time of the segment.

[0052] 1.3.3 UAV Path Constraints (10) (11) (12) (13) (14) Equation (10) represents the coupling between the UAV and the inspection vehicle, that is, the UAV in The prerequisite for a section to have an inspection task is that the inspection vehicle passes through. Segment. Equation (11) represents the UAV in the interval. The prerequisite for selecting the flight arc is that the UAV has a flight mission in that interval. Equation (12) is the coverage constraint, indicating that each inspection point is inspected by the UAV exactly once. Equation (13) indicates that the UAV is in the interval The start and end point constraints. Equation (14) represents the flow balance of the UAV in the inspection mission.

[0053] 1.3.4 The drone takes off in sync with the inspection vehicle (15) (16) (17) Equations (15) and (16) together indicate that the takeoff time of the UAV is the same as the departure time of the inspection vehicle at that point. Equation (17) indicates that the UAV does not need to be inspected at the alternative parking point of the inspection vehicle.

[0054] 1.3.5 Robust Time Advancement for Unmanned Aerial Vehicles (18) (19) (20) Equation (18) represents the time recursion formula under undisturbed conditions, that is, the time of arrival at the later point is equal to the time of arrival at the earlier point plus the inspection time at the earlier point and the flight time between the two points. Equation (19) represents the robust flight time recursion formula for the UAV. Equation (20) indicates monotonicity, that is, the worst arrival time cannot be smaller.

[0055] (twenty one) (twenty two) (twenty three) Equation (21) defines the inspection point coverage variable; Equations (22) and (23) together represent the time window constraint of the inspection point, that is, the time when the UAV arrives at the inspection point is later than the lower bound of the inspection point time window, and the time when the inspection is completed is earlier than the upper bound of the time window.

[0056] 1.3.6 UAV charging constraints (twenty four) (25) (26) Equation (24) indicates the time relationship between the UAV and the inspection vehicle charging, that is, the departure time of the inspection vehicle must be later than the recovery time of the UAV. Equation (25) indicates that the parking time of the inspection vehicle at the alternative point is not less than the charging time of the UAV at that point. Equation (26) indicates the charging capacity boundary of the UAV.

[0057] 1.3.7 Flight Arc Electricity Transfer (27) (28) (29) (30) (31) Equations (27) and (28) represent the recursive formula for the power consumption of the UAV during flight, i.e., the power consumption at the later point is the power consumption of the UAV at the earlier point minus the power consumption consumed during flight between the two points. Equations (29) and (30) represent the power consumption of the UAV at the beginning and end of the interval, i.e., the power consumption of the UAV when it starts charging is the same as the power consumption of the UAV when it returns to the inspection vehicle after completing its mission; the same applies to the end point. Equation (31) represents the initial energy of the UAV.

[0058] (32) (33) (34) (35) Equations (32) and (33) represent the cross-interval continuous constraint of the UAV's power. Equations (34) and (35) represent the UAV's power in the arc... While traveling with the vehicle, the vehicle can continue charging on board; and the charging time shall not exceed the travel time of the inspection vehicle in that arc.

[0059] 1.4 Detailed Explanation of Piecewise Linear Partial Charging Mechanism In a collaborative inspection scenario involving inspection vehicles and drones, the inspection vehicle's docking time is limited. Whether the drone needs to be fully charged depends not on the battery capacity limit itself, but primarily on the actual energy requirements of its subsequent tasks. Requiring the drone to be fully charged after each recovery would, on the one hand, prolong the inspection vehicle's waiting time at the parking point, reducing overall operational efficiency; on the other hand, it could lead to unnecessary charging processes, increasing charging costs and affecting the flexibility of subsequent collaborative scheduling. Therefore, a partial charging strategy is adopted: when the drone's remaining battery power is insufficient to support the next stage of the inspection task, it can return to the inspection vehicle early to recharge. However, it does not need to reach a full charge at the end of charging; its battery level only needs to meet the requirements of subsequent tasks. This strategy better aligns with the operational characteristics of "on-demand charging and dynamic connection."

[0060] Considering the balance between charging efficiency and battery life, this invention does not employ constant current fast charging or constant voltage slow charging alone, but instead chooses a combined charging strategy of constant current fast charging and constant voltage slow charging. Under this strategy, the drone charging process can be summarized into two main stages: In the first stage, the battery undergoes constant current fast charging at a high charging rate to quickly restore usable power; when the power reaches a certain voltage threshold, approximately 80% of the rated power, the charging rate begins to decrease, and then the second stage of constant voltage slow charging is initiated to achieve deeper energy replenishment. This "fast at the beginning, slow at the end" approach improves energy replenishment efficiency within a limited docking time and avoids excessive damage to battery performance caused by continuous high-power charging. Furthermore, for batteries in a deeply discharged state, directly entering the fast charging stage may cause additional damage to the battery, thereby affecting its safety and lifespan. To better conform to actual charging patterns, a pre-charging stage is further introduced before the constant current fast charging. In other words, when the drone's remaining battery power is low, a lower charging rate is used for pre-charging to gradually restore the battery to a suitable range for fast charging, and then the process transitions to constant current fast charging and constant voltage slow charging stages. Thus, the charging process constructed by this invention actually consists of three stages: pre-charging, fast charging, and slow charging.

[0061] Segmented charging process, assuming These represent the charging rates during drone pre-charging, constant current fast charging, and constant voltage slow charging, respectively. Indicates the rated capacity of the drone battery. This is the critical charge level to begin fast charging. The critical charge level to begin slow charging depends on the drone's position at the node. Battery level before charging begins With the remaining power after charging is complete Depending on the location, the piecewise linear partial charging strategy can be divided into the following six cases.

[0062] Scenario 1: When This indicates that the drone's battery level is within the deep discharge range both before and after charging. At this point, the drone only needs to replenish its power within the pre-charge range, therefore the entire charging process only includes the pre-charge phase.

[0063] Scenario 2: When This indicates that the drone's initial battery level is still in the deep discharge range, but the target battery level has exceeded the upper limit of the pre-charge range but has not yet entered the slow charge range. At this point, the charging process should first perform pre-charge, and then proceed until the battery level reaches the target level. Then, it switches to the constant current fast charging stage until the target battery level is reached.

[0064] Scenario 3: When This indicates that the drone was still in the deep discharge range at the start, while the target battery level was... and Between. At this point, the drone needs to go through three stages in sequence: first, pre-charge to Then, it is fast charged using a constant current method until... Finally, the battery is replenished to the target level using a constant voltage slow charging method.

[0065] Scenario 4: When This indicates that the drone's battery level remained within the middle range before and after charging. Since this range corresponds to the constant current fast charging stage, the drone only needs to perform constant current fast charging throughout the entire charging process.

[0066] Scenario 5: When This indicates that the drone's initial battery level is in the fast charging range, while the target battery level is in the slow charging range. At this point, the charging process first uses constant current fast charging, and when the battery level reaches... Then, switch to constant voltage slow charging until the target battery level is reached.

[0067] Scenario 6: When This indicates that the drone's battery level remained at a certain level before and after charging. and Between these two periods. Since this range corresponds to the constant voltage slow charging stage, the entire charging process only involves constant voltage slow charging.

[0068] As can be seen from the six scenarios above, the constructed partial charging mechanism does not simply view the charging process as a linear mapping of "the time required to replenish a certain amount of electricity." Instead, it dynamically determines which charging stages the drone will undergo based on the differences between the initial and target states, and calculates the actual charging time accordingly. The advantage of this approach is that it can reflect the differences in charging efficiency under different SOC ranges while maintaining the computability of the model, thus providing a foundation for subsequent optimization solutions.

[0069] Based on this, the present invention defines a cumulative charging time function. Used to indicate that the battery level increases from 0 to... The required cumulative charging time. The cumulative charging time function is written as: (36) The meaning of this function is as follows: the first term represents the cumulative charging time required when the battery level is in the first interval; the second term represents the additional cumulative time after the battery level enters the second interval; and the third term represents the corresponding cumulative time after the battery level further enters the third interval. As long as the drone is located on the inspection vehicle's onboard platform and connected to the charging device, regardless of whether the inspection vehicle is parked or in motion, its recharging process follows the same cumulative charging time function.

[0070] Therefore, if the drone is at the point The battery levels before and after charging are respectively and The actual charging time can then be expressed as the difference between the two corresponding cumulative charging times: (37) Meanwhile, the battery level before and after charging meets the following requirements: (38) Figure 2 A schematic diagram of Equation (36) is given, reflecting the three-stage charging pattern of "pre-charge-fast charge-slow charge".

[0071] 1.5 FD-ALNS Algorithm Design This invention employs an adaptive large neighborhood search algorithm based on feasibility decoding (FD-ALNS). The algorithm flow is as follows.

[0072] The established capability-constrained inspection vehicle-UAV cooperative path planning model simultaneously incorporates inspection vehicle parking decisions, UAV task allocation, piecewise linear charging decisions, and robust flight time constraints, exhibiting significant multi-layered coupling characteristics. If a precise algorithm is directly applied, the solution time will rapidly increase with the number of candidate parking points, inspection points, and UAVs, failing to meet the demands of rapid scheduling scheme generation in engineering scenarios. Therefore, a Feasibility-Decoding Adaptive Large Neighborhood Search (FD-ALNS) algorithm is proposed. This algorithm retains core ideas such as dual-layer encoding, destruction-repair iteration, adaptive operator selection, and simulated annealing acceptance mechanisms. It also embeds the newly added piecewise linear partial charging constraints and robust flight time constraints into the decoding and fitness evaluation stages, thereby improving adaptability to capability-constrained scenarios without significantly increasing algorithm complexity.

[0073] Based on the above characteristics, during the search process, the algorithm still focuses on optimizing the inspection vehicle docking sequence and the UAV's task chain within the area, without directly making decisions regarding charging quantity or charging phase switching. Instead, during the decoding phase, it recursively calculates the inspection vehicle arrival time, UAV flight time within the area, worst-case recovery time, power evolution, and charging time based on the task order implied in the candidate solutions, and performs feasibility verification and objective function evaluation accordingly. This avoids the rapid expansion of the search space due to too many new capability variables, thereby improving the algorithm's implementation efficiency and practical operability.

[0074] 1.5.1 Dual-layer coding A candidate solution is represented using a two-layer coding method that separates the "outer layer docking decision" and the "inner layer UAV mission orchestration". The outer layer coding describes the docking framework of the inspection vehicle along the route, which can be represented as the inspection vehicle docking sequence, denoted as: (39) in and These correspond to the starting and ending points, respectively. The middle element represents the actual stop selected by the inspection vehicle from the set of candidate stops, and the stops are arranged in order of the route's travel direction. The outer sequence describes the overall operational framework of the inspection vehicle and determines that the entire route is divided into several adjacent work zones. The inner layer encoding is used to describe the inspection task chain undertaken by the UAV within each interval, which can be represented as an interval task matrix: (40) in, Indicates that the drone u is in the interval The sequence of inspection tasks undertaken within the matrix. Each element in the matrix is ​​an ordered task chain, with its implicit starting point being the starting parking point of the interval. The implied endpoint is the stop at the end of the section. This is used to describe the takeoff, inspection, and recovery process of the corresponding UAV within that range. This representation can decompose the complex vehicle-to-machine (V2X) coordination problem into two levels: "docking skeleton selection" and "task orchestration within the range," which facilitates subsequent neighborhood search operations.

[0075] 1.5.2 Feasibility Decoding Feasibility decoding is the core component of the lightweight adaptive large neighborhood search algorithm. Its role is to recursively deduce the time, battery level, and recharging status of the inspection vehicle and the drone based on the implicit docking structure and task execution order of the candidate solutions, without setting explicit decision variables for charging capacity and charging phase switching. This allows for the feasibility assessment and objective function evaluation of the candidate solutions. For any given candidate solution, the algorithm decodes each operational interval sequentially from front to back according to the inspection vehicle docking sequence, and within each interval, it recursively deduces the corresponding flight process, service process, and recovery process according to the drone task chain order. In this way, the highly coupled "docking-flight-charging-robust time" relationship in the original problem can be uniformly incorporated into the decoder for processing, without explicitly recording complex state variables at the encoding level.

[0076] The inspection vehicle was placed at the rest stop. The arrival time is The actual stop time at this point is Then its departure time is For intervals If drone If a vehicle is assigned to execute a corresponding task chain, its takeoff time is taken as the time the inspection vehicle leaves. The moment and with As the starting point of the task chain, with As the endpoint of the task chain, the flight and operations are completed in a predetermined order along the inspection points in the chain. This invention employs a conservative worst-case assessment rule for processing UAV flight time, that is, for all flight arcs involved in the task chain, the flight time is superimposed on the flight time. The maximum flight time deviation is calculated, and based on this, the worst arrival time and worst completion time of the drone at each mission point are recursively calculated. Since the initial docking points are relatively sparse, some mission points far from highways may be affected by the drone's limited range. The inability to insert the solution into any position in the matrix leads to the failure of solution construction.

[0077] Split Rescue Mechanism. (When a mission point...) When a path cannot be filled into the current path matrix, the algorithm no longer forces backtracking, but instead actively triggers a topological transformation of the outer structure: at the distance point Within the nearest interval, from the candidate set Search for an optimal new docking point Insert it into the sequence This operation splits the original interval into two shorter intervals, correspondingly affecting the path matrix. The algorithm adds new row dimensions to create new takeoff and landing opportunities, making previously infeasible mission points meet the endurance constraint. It alternates between matrix filling and split rescue until all mission points are successfully assigned, ensuring a complete, feasible, and high-quality initial solution is output.

[0078] Regarding power recursion, the decoder records the drone's power level before charging at each parking point, the power level upon leaving the parking point, and the power level changes during the interval flight. When the drone performs an interval task, its power level decreases linearly with the flight arc according to the energy consumption per unit distance. When the drone is located on the inspection vehicle's onboard platform and connected to the charging device, the power level that can be recovered under a given charging time is calculated in reverse based on the cumulative charging time function established in this invention. The charging amount is not used as an explicit search object; instead, a deterministic rule of "on-demand energy replenishment" is used to update the power level status during the decoding stage. Specifically, after the drone completes the current interval task and is retrieved to the inspection vehicle, the decoder calculates the minimum starting power level required to perform the task in the next stage based on the energy requirements of the assigned task in the next stage. If the current remaining power level already meets the requirement, no additional energy replenishment is needed at the current node. If the current remaining power level is insufficient, the available charging time during the subsequent travel with the inspection vehicle is used to recover the power level. Only when the vehicle charging is still insufficient to bring the power level to the minimum level required for the next stage task is the necessary node charging time arranged at the current parking point. This embodiment 1 does not employ a strategy of "fully charging after each recovery," but rather "charging only until sufficient to support the execution of the next stage of the task." Since the decoder advances segment by segment according to this rule at each parking point, it can ensure the continuous feasibility of the global task chain's power supply without increasing the charging decision dimension, and naturally embed the segmented linear partial charging mechanism into the search process.

[0079] To improve decoding efficiency, an "early-stop feasibility check" strategy is adopted: throughout the decoding process, the arrival and departure times of the inspection vehicle, the worst-case service time of the UAV, the recovery time, and the battery status at the start and end points of the interval are updated segment by segment according to the docking sequence, and these updates jointly determine the objective function value of the candidate solution. If a candidate solution encounters any of the following situations during the forward recursion, it is immediately determined to be infeasible: first, a task point violates the time window constraint under the worst-case flight condition; second, a UAV, after completing the current interval task and utilizing node charging and vehicle charging, still cannot reach the minimum starting battery required for its next stage task; third, the subsequent timing relationship derived from waiting and recharging cannot continue to meet the continuous operation requirements of the inspection vehicle and the UAV. To improve search efficiency, this invention further adopts an "early-stop feasibility check" mechanism, that is, once any of the above infeasibility situations are found in the forward recursion, the calculation after that position is immediately terminated and an infeasibility mark is returned, thereby reducing the number of invalid evaluations in the neighborhood search.

[0080] 1.5.3 Initial Solution Construction Under the aforementioned coding structure, an initial solution is constructed using the approach of "sparse initialization + greedy insertion + split rescue". The fundamental premise of this strategy is that in capability-constrained scenarios, setting too many stopping points in the initial stage, while improving feasibility, significantly increases the number of stops for the inspection vehicle and the search space size. Conversely, if the stopping structure is too sparse, excessively long intervals may lead to insufficient drone endurance, insufficient refueling opportunities, or exceeding the robustness window. To achieve a balance between these two factors, the initial solution first retains the start and end points from the set of candidate stopping points, and then evenly selects a small number of intermediate stopping points according to the route mileage, forming a relatively sparse but fundamentally supportive initial stopping sequence. This process establishes a relatively simple outer operational framework, providing a basic interval framework for subsequent task insertion, while minimizing unnecessary structural complexity.

[0081] After constructing the initial docking sequence, the algorithm pre-sorts all task points to be inspected. It adopts a sorting principle of "time window urgency first, geometric location second," meaning it prioritizes task points with earlier latest service times and smaller schedulable margins. When multiple task points are similar in time urgency, a secondary sort is performed based on their geometric projection position relative to the highway, nominal flight distance, or spatial clustering characteristics of their area. This approach aims to place tightly constrained tasks as early as possible, preventing them from losing feasibility opportunities during subsequent insertion due to excessive occupation of available intervals and locations. It also helps to allocate tasks within the same area to adjacent intervals, thereby improving the spatial compactness of the task chain.

[0082] Subsequently, the algorithm inserts task points one by one according to the above sorting results. For any task to be inserted, it enumerates the possible insertion range, the UAVs that can perform the task, and the possible insertion positions in the corresponding task chain, and calls the feasibility decoding module to evaluate the candidate structure after insertion. The evaluation here is not based solely on nominal flight distance or local path increment, but comprehensively considers the impact of insertion on the inspection vehicle timing, UAV task chain order, subsequent recharging arrangements, and the feasibility of the time window under the worst-case flight scenario. If an insertion position is not feasible after decoding, it is directly eliminated; if there are multiple feasible positions, the position with the smallest objective function increment is selected for insertion. Although this initial solution construction adopts a greedy approach, since each insertion step is based on a complete feasibility check, it can better adapt to the coupling relationship between "docking-flight-charging-robust time".

[0083] When a task cannot find a feasible insertion location within the current docking structure, the algorithm automatically triggers the Split rescue mechanism. The basic idea is to add a new intermediate docking point near the highway projection of the task, or within its associated bottleneck section, splitting the originally excessively long operational section into two shorter sections, and then re-attempting to insert the task. This mechanism is necessary because in capacity-constrained scenarios, an overly sparse initial docking structure often leads to problems such as insufficient endurance, excessively long recovery wait times, insufficient node refueling time, and exceeding time windows in worst-case flight scenarios. By introducing a new docking point, not only can the interval flight distance be shortened, releasing new takeoff, landing, and recovery opportunities, but additional refueling nodes and timing adjustment space can also be added, thereby restoring the insertion possibility of previously infeasible tasks.

[0084] In summary, the designed initial solution construction method does not aim to generate a high-quality optimal structure in the initial stage, but rather to quickly form a complete, feasible initial solution with certain optimization potential at a low construction cost. On the one hand, sparse initialization helps control the number of docking points and avoids premature expansion of the outer structure; on the other hand, the greedy insertion and split rescue mechanism based on feasibility decoding can gradually supplement the necessary structural degrees of freedom when encountering capacity bottlenecks, so that the initial solution maintains good simplicity and has a feasible basis for adapting to capacity-constrained scenarios. This design also provides a stable starting point for subsequent destruction-repair search and enables structural perturbation and task-level reconstruction to be carried out efficiently under a unified coding framework.

[0085] 1.5.4 Destruction Operator A two-tiered destruction mechanism is employed, with destruction priority guided by "capability bottlenecks." Task-level destruction operators primarily operate on the interval task matrix. This system is used to reallocate UAV task chains. At the task level, it employs four types of disruptive operators: random removal, robust urgent removal, charging critical removal, and greedy marginal cost removal. These four operators complement each other: random removal maintains the diversity of the search process; robust urgent removal and charging critical removal address robust time bottlenecks and charging critical removal, respectively; and greedy marginal cost removal directly weakens high-cost blocking tasks in the current solution, thereby improving the effectiveness of subsequent repairs and the overall convergence quality of the algorithm. The structural disruptive operators primarily operate on the docking sequence. It is used to change the parking frame of the inspection vehicle.

[0086] For mission-level destruction, the following four types of operators are used.

[0087] First, randomly remove operators. Let the set of assigned task points in the current solution be... The scale of a single act of destruction is Random removal operator from Randomly selected with uniform probability The operator identifies a task point and removes it from its original drone task chain, adding it to the unassigned task set. This operator does not rely on any structural information, nor does it target any specific bottleneck. Its main function is to continuously inject random perturbations into the search process, preventing the algorithm from remaining in a narrow neighborhood near the current docking skeleton and task arrangement pattern for an extended period.

[0088] Second, robust urgent removal operators. While some task points may be successfully served under nominal flight conditions, under worst-case flight perturbations, they approach or even nearly violate the upper bound of the time window, thus becoming critical nodes affecting the robust feasibility of the current solution. Therefore, we define task points... The latest service time is After robust feasibility decoding of the current solution, its worst arrival time is denoted as . Then define the task point. The robust relaxation is: (41) when The smaller the value, the more urgent the task point is in the worst-case scenario, and the greater the threat to the robust feasibility of the current solution. The robust urgency removal operator is based on... The task points are sorted from smallest to largest, and priority is given to releasing some of the task points with the smallest robust relaxation. The basic idea of ​​this operator is to prioritize attacking the "vulnerable points" in the current solution that are most likely to induce robust window overflow, so that the repair operator can relocate these high-risk tasks under new interval allocation, task order and UAV assignment, thereby improving the timing feasibility of the new solution under the worst flight scenario.

[0089] Calculate the time window relaxation of each task point under the worst-case flight scenario, and prioritize removing the task points with the smallest relaxation. Since robust time is considered, the real constraint on solution feasibility is often not the nominal service time, but the worst arrival time. Therefore, this operator can release "robust bottlenecks" more effectively.

[0090] Third, a charging critical removal operator is designed to target and mitigate the energy replenishment bottleneck in the current solution. It should be noted that in capability-constrained scenarios, the adverse impact of a particular task point on the solution quality is not solely determined by its marginal energy consumption; more importantly, it may cause the UAV to require energy replenishment beyond the critical range of the charging segment after recovery. Especially when the existence of a task point pushes subsequent energy replenishment from the pre-charging or fast-charging range into the slow-charging range, although the energy increment itself may be limited, the resulting increase in replenishment time can be significant, further extending the inspection vehicle's waiting time at the parking point and compressing the operational time margin for subsequent segments. To characterize this feature, a task point is defined... The marginal energy consumption increment is The resulting marginal charging time increment is And define the indicator variables: Then construct task points Charging threshold score: (42) in These are non-negative weight parameters. The charging critical removal operator is based on... The algorithm sorts tasks from highest to lowest score, prioritizing the removal of tasks with higher scores. The essence of this operator is not simply removing high-energy-consuming tasks, but rather prioritizing the release of tasks most detrimental to the recharging process—those critical tasks that significantly increase node charging time, induce slow charging tails, or exacerbate subsequent recharging pressure. This approach allows the repair phase to reduce docking waiting losses caused by the non-linearity of segmented charging by reconstructing the task chain or adjusting interval divisions, thereby improving the synchronization efficiency between the inspection vehicle and the drone.

[0091] The operator identifies and prioritizes removing task points that cause drones to have low remaining battery at the end of a range, requiring additional docking for recharging. By breaking up high-energy-consuming task chains, this provides greater flexibility for subsequent reconfiguration.

[0092] Fourth, the greedy marginal cost removal operator, starting from the overall quality of the current solution, comprehensively evaluates the marginal negative contribution of each task point to the total completion time, robust feasibility, and energy replenishment pressure. Specifically, for each assigned task point in the current solution... Temporarily remove it from its drone mission chain, and while keeping the order of other missions unchanged, call the feasibility decoding module to recalculate the system state. If the mission point is removed... If, subsequently, the total system completion time decreases significantly, the worst-case time window relaxation is improved, or the charging waiting pressure is significantly reduced, then it indicates that the task point is a high-cost blocking point in the current solution. Based on this, let... Indicates removal of task point The decrease in total completion time. Indicates the amount of robust relaxation improvement. To represent the decrease in replenishment pressure, the task point is defined. The Greedy Removal rating is: (43) in, These are the weighting parameters. Then, according to... The algorithm sorts tasks from largest to smallest, prioritizing the removal of the highest-scoring tasks. The core idea of ​​this operator is a greedy destruction strategy focused on the quality of the current solution; that is, in each destruction step, it prioritizes releasing tasks that "most improve the current solution after removal." Because it employs forward feasibility decoding, many poor structures do not originate from individual task points being too far apart, but rather from the combined effects of delayed recovery, longer energy replenishment, and subsequent cascading compression induced by a particular task point. Therefore, greedy marginal cost removal can more directly identify key blocking tasks in the current locally optimal structure and provide greater optimization space for subsequent repairs.

[0093] For structural-level failure, two types of operators are set: First, the docking point deletion operator. For an intermediate parking point in the current parking sequence, the algorithm comprehensively evaluates its task load, energy replenishment contribution, and the resulting waiting cost, prioritizing the deletion of parking points with "low task load, limited energy replenishment, and high parking cost." In the scenario where the capabilities of this invention are limited, deleting an intermediate parking point not only changes the task organization of its adjacent intervals but may also further affect the time-series recursion and power recovery process of multiple intervals after the deleted point. The reason is that once the parking point is removed, the two adjacent intervals will be merged, and the original node energy replenishment opportunity will disappear, which may change the remaining power of the subsequent drones, the parking time of the inspection vehicle, and the latest service state of the suffix intervals. Therefore, after executing the parking point deletion, the algorithm first releases the tasks of the adjacent intervals directly related to the parking point back to the unallocated set; then, it re-decodes the entire suffix solution after the deletion position to check whether the new time-energy recursion chain is still feasible. If infeasibility persists in the suffix interval due to insufficient energy replenishment, excessive waiting time, or worsening worst-case arrival time, then some tasks in the relevant downstream bottleneck intervals are further released and redistributed by subsequent repair operators. Through this "local deletion - suffix re-decoding - expanding the release range when necessary" approach, the structural-level destruction operator can more realistically reflect the chain reaction of docking structure adjustments on global feasibility, thereby providing a more effective search space for subsequent reconstruction.

[0094] Secondly, a stop point insertion perturbation operator is used. For intervals where the worst-case recovery time is too long, the power recovery is insufficient, or the robustness time pressure is too high, a new stop point is inserted near the midpoint of the interval or in a task-intensive area, and some tasks in that area are released for redistribution. This operator is equivalent to actively creating new energy replenishment and synchronization opportunities on the outer structure, which helps to break through local optima under capacity-constrained conditions.

[0095] 1.5.5 Repair Operator The goal of the repair phase is to reinsert unassigned tasks into the current solution, while balancing total completion time, robust feasibility, and energy replenishment during the insertion process. Four types of repair operators are constructed.

[0096] First, a greedy repair operator. For each unassigned task point, it enumerates its feasible insertion positions in each interval and each UAV task chain, calls the decoder to calculate the objective function increment after insertion, and selects the position with the smallest increment to perform the insertion. This operator is simple to implement and suitable for quickly restoring feasible solutions.

[0097] Second, the Regret-2 repair operator. It calculates the cost difference between the optimal and suboptimal insertion positions for each task point, prioritizing the insertion of the task with the highest "regret value" to reduce the risk of being forced into high-cost positions later. Considering that some task points are subject to both time windows and energy replenishment constraints, this operator can better handle tightly constrained tasks.

[0098] Third, the anchored interval repair operator. This limits the search range of the task to be inserted to the interval where its highway projection is located and a few adjacent intervals, thereby reducing blind evaluation of invalid locations at long distances and improving decoding efficiency.

[0099] Fourth, the energy balance repair operator. When evaluating the insertion cost, in addition to the total completion time increment, a penalty term for the minimum remaining power at the end of the interval and a term for the expected energy replenishment pressure in the next interval are added, making the algorithm tend to generate a solution with a more balanced power distribution after the interval ends. This operator can reduce the probability of frequent subsequent triggering of energy replenishment waiting or structural rescue.

[0100] When the aforementioned conventional repair strategies fail to find a feasible insertion location for a given task point, the algorithm automatically triggers the Split rescue mechanism: a new docking point is added near the task point or within its bottleneck interval, splitting the original interval into two shorter intervals, and the insertion feasibility is re-evaluated through the decoder. If the candidate solution remains infeasible after repair and rescue, it is discarded, and the current solution is retained for the next iteration. The "rescue triggering conditions" here include three categories: first, nominal flight is feasible but the robust time exceeds the window; second, the remaining battery power after flight is insufficient and the recharging time after recovery is insufficient; and third, insertion causes the inspection vehicle to wait too long at a certain docking point. Thus, in this invention, Split rescue is no longer just about solving the "insufficient range" problem, but is extended to a unified feasibility recovery mechanism oriented towards the triple coupling constraints of "range-charging-robust time".

[0101] 1.5.6 Acceptance Criterion and Operator Adaptation Mechanism In the main search loop, the algorithm alternates between "destruction-repair" operations according to the standard ALNS procedure, and uses simulated annealing to determine whether to accept a new solution. Let the current solution be... The candidate solution is The objective function values ​​are respectively and .like If the solution is positive, then the new solution is accepted unconditionally; otherwise, it is determined by probability. (44) Accept inferior solutions, among which The current temperature parameter is used and gradually decreased. This mechanism maintains necessary perturbations during the search process, preventing the algorithm from prematurely stalling due to a narrow feasible region under limited capabilities.

[0102] To improve the adaptability of different operators at different stages, a weight adaptive update mechanism based on search segments is continued. Specifically, the entire iterative process is divided into several equal-length segments, and the number of calls and scores of each disruptive and repairing operator are recorded within each segment. If an operator generates a new globally optimal solution, it is given the highest reward; if it improves the current solution, it is given the second-highest reward; if its generated inferior solution is accepted, it is given a lower reward. After the segment ends, the weights of each operator are adjusted according to a smooth update rule, and an operator is selected in the next segment using a roulette wheel algorithm. This mechanism enables the algorithm to favor diverse perturbations in the early stages of the search and gradually favor more refined operators in the later stages.

[0103] Furthermore, to avoid lingering near local extrema for extended periods, a stagnation criterion and a reheating mechanism are implemented. When the global optimum is not reached after several consecutive iterations, the temperature parameter is temporarily increased, and the structure-level disruption operator is invoked first to apply a strong perturbation to the docking sequence, thereby restoring the algorithm's global exploration capability.

[0104] Example 2: Small-scale case verification This embodiment is used to verify the solution accuracy of the proposed model and algorithm.

[0105] Experimental setup: The route is 45 km long and has a number of drones. 2-3 aircraft, number of parking spots selected There are 5-7 inspection points. There are 5-7 drones. The drone has a full-charge range of 40 km and a flight speed of [missing information]. The patrol vehicle's speed is km / h. km / h. The standardized battery capacity for drones is... The energy consumption per unit distance is 2.5 units / km, and the initial battery power of the drones is uniformly set at... Charging cutoff point , Charging rate =20 units / h, =80 units / hour =30 units / hour. The maximum deviation in flight time is taken as 15% of the nominal flight time. =2 The service time for each inspection point is 5 minutes, and the time window width is uniformly 50 minutes. FDALNS has a maximum of 800 iterations, and the initial temperature... 80, Cooling coefficient 0.985. Each test case was run independently 10 times and the average was taken to mitigate the impact of randomness. The maximum Gurobi time was 3600 seconds, and the optimality gap tolerance was 0.00%.

[0106] Results: As shown in Table 2, FD-ALNS obtained the optimal solution consistent with Gurobi in all 6 sets of examples, with a solution time of 0.43 to 0.91 s, which is much better than Gurobi's 18 to 675 s.

[0107] Table 2 Comparison of solutions from Gurobi and FD-ALNS in small-scale examples.

[0108] Example 3: Large-scale test case verification This embodiment simulates a real long-distance highway inspection scenario.

[0109] Experimental setup: A 102.6 km long highway, adaptively generating 38 compliant candidate stops ( Figure 3 Randomly generated within a 10 km offset range on both sides of the highway. There are 45 inspection points, with each point serving for 1-3 minutes. There are 5 drones, with a maximum of 1500 iterations for FD-ALNS, an initial temperature of 80°C, a cooling coefficient of 0.985, and a stagnation and reheat threshold of 150°C.

[0110] Results: See below for the optimized docking sequence and task allocation. Figure 4 The total completion time decreased from 371.24 min in the initial solution to 243.81 min, a reduction of 34.33%. The inspection vehicle travel time was 78.43 min. Detailed results are shown in Table 3.

[0111] Table 3 Results of the Large-Scale Case Study

[0112] The charging status of each drone is shown in Table 4. The number of times the drone was charged at the dock was 2 to 4 times, and the number of times it was charged on the vehicle was 0 to 2 times, which reflects the dual-mode coordination.

[0113] Table 4. Drone Charging Analysis Table

[0114] Example 4: Sensitivity Analysis Keep other parameters constant, and change the number of drones respectively. Robust budgeting Flight time deviation ratio Charging capacity scaling factor and simulated annealing initial temperature Analyze the changes in completion time. (See) Figure 5 , Figure 6 ) Number of drones: 4 → 9, with a cumulative decrease in completion time of 10.71%; 7 → 8, with a decrease of only 0.02%, indicating a slowdown in marginal returns.

[0115] Robust Budget : 0→4, completion time 213.46→247.46 min, monotonically increasing.

[0116] Flight time deviation ratio : 0.05→0.25, completion time 236.33→251.86 min, monotonically increasing.

[0117] Charging capacity scaling factor : 0.80→1.20, completion time 252.32→221.62 min, a decrease of 12.16%.

[0118] Simulated annealing initial temperature : =40 is optimal (235.52 min), and too low or too high will lead to a decrease in performance.

[0119] Example 5: System Configuration

[0120] The present invention also provides a system for implementing the above method, comprising:

[0121] Perception layer: Acquires highway inspection task information (alternative stop points, inspection points, time windows, battery parameters, segmented charging parameters, etc.).

[0122] Model building module: Constructs a collaborative path planning model that minimizes the total completion time, including the constraints of equations (1) to (38).

[0123] Solution module: The model is solved using the FD-ALNS algorithm, and it has built-in Split rescue and on-demand power replenishment decoding rules.

[0124] Execution module: Controls the movement of the inspection vehicle and the take-off, landing, inspection, recovery, and recharging of multiple drones. The inspection vehicle only stops at the actually selected stops (service areas, toll stations, management stations, emergency parking lanes, etc.), supporting the drones to perform tasks within the interval between adjacent stops.

[0125] In summary, the present invention has the following beneficial effects:

[0126] High accuracy: Obtains the optimal solution that is consistent with the exact solution in small-scale scenarios.

[0127] High efficiency: The solution time is reduced by two orders of magnitude, and the completion time for large-scale scenarios is reduced by 34.33%.

[0128] Resource conservation: Partial charging and on-vehicle / parking point coordination reduce the configuration requirements of drones.

[0129] High robustness: The flight time robust constraint ensures that the time window is still satisfied under the worst disturbance.

[0130] Parameter guidance: Sensitivity analysis provides a quantitative basis for engineering configuration.

[0131] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the present invention as claimed. The scope of protection of this invention is defined by the appended claims and their equivalents.

Claims

1. A single-inspection-vehicle-multi-UAV collaborative intelligent inspection path planning method for highways based on capability-constrained and robust flight time, characterized in that, Includes the following steps: S1. Obtain highway inspection task information, which includes a set of alternative stopping points for inspection vehicles, a set of inspection points, time window constraints for inspection points, UAV battery capacity and initial charge, UAV energy consumption per unit distance, and UAV segmented linear charging parameters; the UAV segmented linear charging parameters include pre-charge rate, fast charge rate, slow charge rate, and stage boundary charge. S2. Using a single inspection vehicle as a ground-based mobile command and supply platform and multiple drones as aerial inspection execution units, a collaborative inspection path planning model is constructed. The model aims to minimize the total operation completion time and includes inspection vehicle path constraints, inspection vehicle time recursion constraints, drone path constraints, drone takeoff and inspection vehicle synchronization constraints, drone robust time advancement constraints, drone charging constraints, flight arc power transfer constraints, and piecewise linear partial charging constraints. The drone robust time advancement constraints include flight time robust constraints. S3. The collaborative inspection path planning model is solved by using an adaptive large neighborhood search algorithm based on feasibility decoding to obtain the optimal inspection vehicle stopping sequence and the inspection task chain of each UAV in each section. S4. Perform the inspection task according to the solution results.

2. The method according to claim 1, characterized in that: The piecewise linear partial charging constraint is expressed through a cumulative charging time function. accomplish: in, q1 represents the critical charge level for switching from pre-charge to fast charge, and q2 represents the critical charge level for switching from fast charge to slow charge. The charging rates for pre-charge, fast charge, and slow charge are respectively; and the charging time meets the following requirements: in, For drones Arrive at the parking spot And the battery level before charging; For drones At the parking spot The battery level when the inspection vehicle leaves after charging; For drones at parking spots Charging time.

3. The method according to claim 1, characterized in that, The drone charging constraints include: in, For drones exist The battery level was replenished. For drone battery capacity; To check if the inspection vehicle is The value for docking is 1 if yes, and 0 if no. The arrival point of the inspection vehicle The moment; For the inspection vehicle at the point The duration of the stop; For drones in the inspection vehicle arc Inside, when the maximum allowed When the flight arc deteriorates, the node is reached. The worst arrival time; For drones Is it in the patrol vehicle arc? If there is an inspection task within the corresponding interval, the value is 1; otherwise, the value is 0. To check if the inspection vehicle is moving in an arc , is 1 if yes, 0 if no; This refers to the travel time of the inspection vehicle. It is a sufficiently large constant.

4. The method according to claim 1, characterized in that, The robust time propagation constraints for the UAV include: in, ; The maximum number of flight arcs that can be allowed to deteriorate is set; For drones in the inspection vehicle arc Inside, when the maximum allowed When the flight arc deteriorates, the node is reached. The worst arrival time; For nodes Service hours; Nominal flight time; This represents the maximum deviation in flight time. For drones Is it in the patrol vehicle arc? Inspection arc within the corresponding interval If yes, it is 1; otherwise, it is 0. For drones Is it in the arc? Corresponding inspection points within the area Yes, it is 1; no, it is 0. Inspection point The earliest service time; Inspection point The latest service time.

5. The method according to claim 1, characterized in that, The adaptive large neighborhood search algorithm based on feasibility decoding adopts a two-layer encoding structure: the outer layer encoding is the inspection vehicle docking sequence, and the inner layer encoding is the interval task matrix, where each element represents the ordered inspection task chain undertaken by a certain UAV in the interval between two adjacent actual docking points. The feasibility decoding process includes forward deducing each work area along the inspection vehicle parking sequence, deducing the flight, service and recovery process according to the task chain sequence, and recording the battery level before charging at each parking point, the battery level upon departure and the battery level during flight within the area. The system adopts an on-demand energy replenishment rule: energy replenishment is determined based on the minimum starting power required for the next stage of the task, with priority given to using onboard charging, and charging at rest stops arranged only when insufficient; an early-stop feasibility check is adopted, and decoding is immediately terminated if a time window is violated, power is insufficient, or the timing is infeasible.

6. The method according to claim 1, characterized in that, The initial solution construction of the adaptive large neighborhood search algorithm includes a Split rescue mechanism: when a task point cannot find a feasible insertion position under the current docking structure, a new intermediate docking point is added near the highway projection of the task point or within the bottleneck interval, splitting the original interval into two shorter intervals, adding a new row dimension to the path matrix, and then retrying to insert the task point.

7. The method according to claim 1, characterized in that, The adaptive large neighborhood search algorithm includes the following destruction operators: random removal operator, robust urgent removal operator, charging criticality removal operator, and greedy marginal cost removal operator; and the following repair operators: greedy repair operator, Regret-2 repair operator, anchored interval repair operator, and energy balance repair operator. The algorithm employs a simulated annealing acceptance criterion: if a candidate solution's objective value is superior to the current solution, it is accepted unconditionally; otherwise, it is accepted based on probability. Accept inferior solutions, among which, The objective function value of the current solution. The objective function value for the candidate solution. This refers to the current temperature parameter. Furthermore, a weight adaptive update mechanism based on search fragments is adopted to dynamically adjust the operator selection weights.

8. A single-inspection vehicle-multi-UAV collaborative intelligent highway inspection path planning system based on capability-constrained and robust flight time for implementing the method of claim 1, characterized in that: It includes a perception layer, a model building module, a solution module, and an execution module; The perception layer is used to acquire highway inspection task information, including the set of alternative stopping points for inspection vehicles, the set of inspection points and their time window constraints, and the parameters of the drone battery and piecewise linear charging. The model building module is used to build a collaborative inspection path planning model with the goal of minimizing the total operation completion time. The model includes inspection vehicle path constraints, inspection vehicle time recursion constraints, UAV path constraints, UAV take-off and inspection vehicle synchronization constraints, flight time robustness constraints, UAV charging constraints, flight arc power transfer constraints, and piecewise linear partial charging constraints. The solution module uses an adaptive large neighborhood search algorithm based on feasibility decoding to solve the model and generate the optimal inspection vehicle docking sequence and the task chain of each UAV interval; The execution module is used to control the movement of the inspection vehicle and the take-off, landing, inspection, recovery and refueling operations of multiple UAVs according to the solution results.

9. The system according to claim 8, characterized in that: The collaborative inspection route planning model selects actual stops from a pre-set set of alternative stops, which include service areas, toll stations, management stations, emergency parking lanes, maintenance work areas, or permitted temporary work points. The inspection vehicle travels along the highway and only stops at designated stops to support the drone in carrying out inspection tasks within the area between adjacent stops.

10. The system according to claim 8, characterized in that: The piecewise linear partial charging constraint is based on the cumulative charging time function: And the charging time meets the following requirements: The flight time robust constraint adopts a budget uncertainty set and satisfies: The electric charge transfer in the flight arc satisfies: And cross-interval power continuity constraints: in, For drones in the arc ( Energy consumption between ) For drones In the interval Inner reach node The amount of electricity; The solution module incorporates a Split rescue mechanism and a feasibility decoding rule for on-demand energy replenishment.

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