A multi-unmanned aerial vehicle cooperative power inspection task planning method based on a multi-layer decoupling strategy

Abstract

This invention discloses a multi-UAV collaborative power line inspection task planning method based on a multi-layer decoupling strategy. A two-layer optimization model is constructed: the upper layer is a task allocation model, which determines the inspection points and access sequences for each UAV, considering task completion time and energy consumption; the lower layer is a global path planning model, which plans flight paths that satisfy dynamic constraints, minimum safe distance between UAVs, and joint reliability constraints of electromagnetic interference and communication quality. A multi-layer decoupling strategy is employed for hierarchical iterative solution: inter-layer decoupling uses an iterative feedback mechanism to transmit the actual cost of path planning feedback to the task allocation layer to correct the solution; intra-layer decoupling utilizes the augmented Lagrangian method to handle inter-UAV coupling constraints, transforming them into penalty terms added to the objective function, thereby decomposing the multi-UAV coupling problem into multiple single-UAV subproblems and solving them alternately. This invention effectively reduces problem complexity, balances global optimum and feasible solution quality, and significantly improves inspection efficiency and safety.

Description

Technical Field

[0001] This invention relates to the field of power line inspection technology, specifically to a multi-UAV collaborative power line inspection task planning method based on a multi-layer decoupling strategy. Background Technology

[0002] With the continuous increase in the scale and complexity of power inspection scenarios, UAV inspection has gradually become an important automation technology to replace traditional manual inspection due to its wide coverage, high efficiency and flexibility. UAV inspection task planning usually consists of two parts: task allocation and path planning. At present, the research on multi-UAV collaborative power inspection still has the following problems: (1) At the modeling level, it is difficult to simultaneously take into account complex factors such as energy consumption constraints, UAV dynamics, minimum safe distance between UAVs, and reliability of electromagnetic interference and communication analytical quantization relationship, and the feasibility of application needs to be improved. (2) At the solution level, the task planning and path planning problems are highly coupled, and the minimum safe distance constraint between UAVs and the inter-UAV communication requirement constraint in path planning usually make the path planning problem exhibit multi-UAV coupling characteristics, resulting in a large problem scale, strong nonlinearity and high solution complexity. Summary of the Invention

[0003] Purpose of the invention: The purpose of this invention is to provide a multi-UAV collaborative power line inspection task planning method based on a multi-layer decoupling strategy, which solves problems such as insufficient safe distance between UAVs, insufficient quantification of joint reliability of electromagnetic interference and communication, and high coupling of collaborative relationships; and solves the problem of high computational complexity of traditional optimization methods.

[0004] Technical solution: The present invention provides a multi-UAV collaborative power line inspection task planning method based on a multi-layer decoupling strategy, comprising:

[0005] Step 1: Construct a two-layer optimization model for multi-UAV collaborative power line inspection. The two-layer optimization model includes an upper-layer task allocation model and a lower-layer global path planning model. The task allocation model is used to determine the inspection points and access sequences to be visited by each UAV, taking into account task completion time and energy consumption constraints. The global path planning model is used to plan flight paths for each UAV that satisfy dynamic constraints, minimum safe distance constraints between UAVs, and joint reliability constraints that take into account the analytical quantification relationship between electromagnetic interference and communication quality.

[0006] Step 2: Solve the two-layer optimization model using a multi-layer decoupling strategy, which includes inter-layer decoupling and intra-layer decoupling. Inter-layer decoupling is achieved by building an iterative feedback mechanism between the task allocation model and the path planning model, passing the actual path cost fed back from the path planning model to the task allocation model to correct the task allocation scheme. Intra-layer decoupling is implemented within the path planning model by using the augmented Lagrangian method to handle the inter-drone coupling constraints, transforming the coupling constraints into penalty terms in the objective function, thereby decoupling the multi-drone coupled path planning problem into multiple single-drone path planning subproblems, and solving each single-drone subproblem alternately.

[0007] Furthermore, in step 1, the upper-level task allocation model takes minimizing the maximum task completion time among all drones as the optimization objective, determines the allocation relationship of each inspection point task among drones and the inspection point access order of each drone, and each task of each inspection point is assigned to only one drone for execution.

[0008] Furthermore, in step 1, the lower-level global path planning model aims to minimize the total energy consumption of all UAVs. It describes the three-dimensional flight trajectory of each UAV through discrete control points, plans a continuous flight path for each UAV that meets the dynamic constraints of flight altitude, speed, acceleration, turn angle and pitch angle, and ensures that each control point maintains a safe distance from static obstacles.

[0009] Furthermore, in step 2, during the inter-layer decoupling, the lower-layer path planning model feeds back the actual flight distance and actual flight time of each UAV between inspection points to the upper-layer task allocation model. The upper-layer task allocation model re-optimizes the task allocation scheme based on the actual path cost feedback, forming an iterative closed loop between the upper and lower layers until the relative change of the upper-layer objective function in two adjacent iterations is less than a preset threshold or the maximum number of iterations is reached.

[0010] Furthermore, in step 2, during the intra-layer decoupling, the inter-machine coupling constraints include the minimum safe distance constraint between UAVs and the communication rate constraint between UAVs; when solving each single-machine path planning sub-problem, the paths of the UAVs other than the current UAV are regarded as known quantities, and each UAV sub-problem is alternately optimized in turn, and the augmented Lagrange multiplier and penalty parameter are updated after each round of alternate optimization.

[0011] Furthermore, each single-machine path planning subproblem adopts a two-stage solution strategy: the first stage generates an initial path that satisfies the inspection point access sequence based on a preset search algorithm and performs smoothing; the second stage uses the initial path as the initial value and employs the particle swarm optimization algorithm to optimize and solve the problem, thereby obtaining a flight path that satisfies all single-machine constraints.

[0012] Furthermore, in step 2, the joint reliability constraints that take into account the analytical quantification relationship between electromagnetic interference and communication quality include: constructing electromagnetic risk field strength constraints based on the spatial electromagnetic field distribution to limit the electromagnetic risk at the locations along the UAV's flight path from exceeding a safety threshold; and constructing transmission rate constraints for air-to-ground and air-to-air communication links based on path loss, signal-to-interference-plus-noise ratio, and Shannon's formula to ensure that each UAV can maintain data communication with ground base stations or other UAVs at a rate no lower than the minimum requirement when flying along the planned path.

[0013] Furthermore, the upper-level task allocation model of the two-level optimization model is a mixed-integer linear programming model, which is solved using a commercial solver; the lower-level global path planning model is transformed into multiple nonlinear programming subproblems after intra-layer decoupling, and is solved alternately using the augmented Lagrangian method, so as to reduce the overall solution scale and computational complexity while satisfying all complex constraints.

[0014] Beneficial effects: Compared with the prior art, the present invention has the following significant advantages:

[0015] (1) A two-layer optimization model for multi-UAV collaborative power inspection was constructed. The upper layer is a task allocation model that takes into account the task completion time and energy consumption constraints, and the lower layer is a global path planning model that comprehensively considers UAV dynamics, minimum safe distance between UAVs, and joint reliability constraints that take into account the analytical and quantitative relationship between electromagnetic interference and communication quality. It can simultaneously satisfy complex constraints such as minimum safe distance between UAVs and joint reliability constraints that take into account the analytical and quantitative relationship between electromagnetic interference and communication quality, thereby improving the effectiveness and accuracy of the power inspection task planning model.

[0016] (2) A model solution method based on a multi-layer decoupling strategy is proposed, where decoupling is reflected in two levels: first, an iterative feedback mechanism is constructed between the task allocation layer and the path planning layer to achieve inter-layer decoupling of task allocation and path cost; second, within the path planning layer, the augmented Lagrangian method is used to handle the coupling constraints of minimum safe distance between drones and inter-drone communication, decoupling the multi-UAV coupled path planning problem into multiple single-drone path planning subproblems to be solved alternately. This solution method can effectively reduce the problem size and computational complexity under complex constraints, and improve optimization efficiency and solution quality. Attached Figure Description

[0017] Figure 1 This is the multi-UAV collaborative inspection path of the present invention;

[0018] Figure 2 This is the tree-type communication structure of the present invention;

[0019] Figure 3 This relates to the two-layer coupling relationship of the task planning model in this invention;

[0020] Figure 4 This is the solution process for the lower-level path planning model of the present invention;

[0021] Figure 5 This is the inspection scenario setting of the present invention;

[0022] Figure 6 This is a three-dimensional path trajectory diagram of multiple unmanned aerial vehicles (UAVs) according to the present invention;

[0023] Figure 7 This is the normalized electromagnetic risk distribution of the present invention;

[0024] Figure 8 This is the communication rate distribution of the present invention. Detailed Implementation

[0025] The technical solution of the present invention will be further described below with reference to the accompanying drawings.

[0026] This invention provides a multi-UAV collaborative power line inspection task planning method based on a multi-layer decoupling strategy, comprising:

[0027] Step 1: Construct the task planning model as a two-layer model. The upper-layer model is the task allocation problem, aiming to determine the inspection points and access sequences required for each UAV, and to execute tasks at the visited inspection points. The lower-layer model is the path planning problem, aiming to plan the minimum energy consumption flight strategy for the UAVs, ensuring avoidance of static obstacles, preventing collisions between UAVs, satisfying the dynamic constraints of the UAVs, and simultaneously satisfying the joint reliability constraints considering the analytical quantification relationship between electromagnetic interference and communication quality. This includes the following steps:

[0028] Step 1.1 Model scene setup.

[0029] This invention considers the following scenario of multi-UAV collaborative power line inspection: all UAVs take off from the same base and return to the base after the mission is completed; there are N... UAV drones and N target There are several inspection points, including but not limited to power towers, combiner boxes, and photovoltaic arrays; known static obstacles exist in the environment, such as mountains, buildings, and towers; online dynamic obstacle avoidance and real-time replanning are not considered; task allocation and path planning are completed before the task begins; the UAV dynamics model is approximated as a discrete-time model, with the flight trajectory discretely described by control points. Specifically, for example... Figure 1As shown, the multi-UAV collaborative inspection path consists of a UAV base, inspection points, control points, and the flight paths of each UAV. UAVs depart from the same base, sequentially visit corresponding inspection points according to the upper-level task allocation, and return to the base after completing their inspection tasks. Each flight path is discretely represented by several control points, with adjacent control points forming a local flight trajectory. Different UAV paths correspond to different inspection point visit sequences. By optimizing the spatial location of the control points, it is possible to ensure that UAVs complete their inspection tasks sequentially while meeting constraints such as obstacle avoidance, minimum safe distance between UAVs, dynamic feasibility, and electromagnetic interference and communication reliability. Therefore, Figure 1 The control points in the model are not only the core decision-making objects of the lower-level path planning model, but also important intermediate variables connecting the task allocation results and the actual flight trajectory.

[0030] Step 1.2 Upper-level task allocation model.

[0031] The objective function is as follows: The goal of the upper-level model is to minimize the total task completion time Z. task It consists of the mission execution time and flight time of each drone, and is specifically determined by the maximum mission completion time among all drones:

[0032] ;

[0033] ;

[0034] In the formula: T i x represents the mission completion time for drone i; ijl The variable is 0-1, indicating whether drone i performs task l at inspection point j; c ijk N is a 0-1 variable, representing whether drone i traverses the path from node j to node k; target This represents the total number of inspection points, numbered 1, 2, …, N. target Let the drone base be denoted as node 0. Therefore, path indices j and k can be found in the set {0, 1, 2, …, N}. target Values ​​are taken from}; N j,task Let j be the total number of tasks at inspection point j. l {1, 2, …, N j,task};T task (j,l) represents the execution time required for task l at inspection point j; T ijk Let c be the flight time of UAV i from node j to node k, provided by the lower-level path planning model. When j=0 or k=0, c ijk T ijkThese represent the path selection variables and flight time associated with the drone base, respectively.

[0035] Constraints: Each task is assigned to one drone:

[0036] ;

[0037] Where: N UAV The total number of drones, .

[0038] Each drone must perform at least one task:

[0039] ;

[0040] The drone must depart from the base and eventually return to the base:

[0041] ;

[0042] ;

[0043] A drone is only allowed to choose its path to or from a given inspection point if it has been assigned at least one inspection task. In other words, the sum of path selection variables cannot exceed the sum of task assignment variables for that inspection point.

[0044] ;

[0045] ;

[0046] Drones will not form a self-loop at inspection points:

[0047] ;

[0048] To prevent drones from forming sub-loops between several inspection points that bypass the base, an auxiliary sequence variable u is introduced. ij Encode the path sequence to eliminate sub-loops:

[0049] ;

[0050] ;

[0051] Drones have an upper limit on energy consumption, and the energy consumption calculation takes into account the effects of flight distance and flight time:

[0052] ;

[0053] In the formula: α is the energy consumption coefficient per unit flight distance; β is the energy consumption coefficient per unit flight time; γ is the energy consumption coefficient per unit mission execution time, used to characterize the energy consumption of the UAV during hovering inspection; d ijk The flight distance of UAV i from node j to node k is provided by the lower-level path planning model; For drones The upper limit of energy consumption.

[0054] Step 1.3 Lower-level path planning model.

[0055] To characterize the trajectory of a drone, this invention sets up core variables: , is a continuous variable, representing the position coordinates of the u-th control point of UAV i on the path from node j to node k, where x, y, and z represent the components along the x-axis, y-axis, and z-axis, respectively.

[0056] Objective function: The goal of the lower-level problem is to minimize the total energy consumption of all drones. The objective function is:

[0057] ;

[0058] ;

[0059] ;

[0060] In the formula: Z energy N represents the total energy consumption of all drones; control This represents the total number of control points on a path. u {1, 2, …, N control}; This represents the Euclidean distance between adjacent control points; For drones In the path segment Upper From the first control point to the... Flight speed between control points.

[0061] Constraints:

[0062] (1) Minimum obstacle distance constraint.

[0063] The minimum distance between each control point and an obstacle must be greater than a safe value to ensure that the flight path does not collide with the obstacle.

[0064] ;

[0065] In the formula: O m Let r be the position coordinates of the m-th obstacle; m d is the radius of the m-th obstacle; safe This is the minimum safe distance.

[0066] (2) Minimum safe distance constraints between UAVs.

[0067] To establish the correspondence between control point indices and actual flight times, let the starting time of UAV i in the overall mission execution process of path segment (j, k) be . The flight time corresponding to the u-th control point on this path segment is denoted as . :

[0068] ;

[0069] Among them, the start time The sequence of UAV inspection points is determined recursively by the preceding flight time and mission execution time; q is the index of the path segment between control points, and for the u-th control point on the path segment, 1≤q≤u-1.

[0070] Let the global time sampling set be: ,in, This represents the total number of global time sampling points. For the first There are several global time sampling times, and in this invention, the interval between global sampling times is set to 3 seconds. For drone i at global time The position, which is determined by the control point trajectory of UAV i. The minimum safe distance constraint between machines can be expressed as follows, obtained through time mapping and piecewise linear interpolation:

[0071] ;

[0072] In the formula: d min Minimum safe distance between drones; This indicates another drone that is different from drone i, and .

[0073] UAV dynamics constraints: including upper and lower limits for flight altitude, speed, acceleration, turn angle, and pitch angle.

[0074] ;

[0075] ;

[0076] ;

[0077] ;

[0078] ;

[0079] In the formula: z max , z min These are the maximum and minimum flight altitudes for the drone, respectively. This represents the speed of UAV i at the u-th control point on the path from node j to node k; , These are the maximum and minimum flight speeds of the drone, respectively. a represents the acceleration of UAV i at the u-th control point on the path from node j to node k; max , a min These are the maximum and minimum flight accelerations of the drone, respectively. θ is the turning angle of the drone. max This represents the maximum steering angle. γ is the pitch angle of the drone; max This represents the maximum pitch angle.

[0080] Among them, the flight speed of the drone and acceleration Location coordinates There is a relationship between them:

[0081] ;

[0082] Drone turning angle Pitch angle with position coordinates There is a relationship between them:

[0083] ;

[0084] ;

[0085] In the formula: and The horizontal displacement between the u-th control point and the (u+1)-th control point is calculated using the following formula: , ; The vertical displacement between the u-th control point and the (u+1)-th control point is calculated using the following formula: .

[0086] Joint reliability constraints considering the analytical quantification relationship between electromagnetic interference and communication quality: In power line inspection scenarios, complex electromagnetic environments exist around power equipment. Converter stations, substations, and high-voltage equipment may generate high-frequency electromagnetic interference such as partial discharge, corona discharge, and power electronic switch transients. On the one hand, the electromagnetic environment may interfere with the UAV flight control system, increasing operational risks during inspections. On the other hand, the UAV's flight attitude data, collected visible light image data, or point cloud data need to be transmitted to the base station via wireless communication links. If the quality of the communication link is ignored, problems may arise where the path is reachable but the data is difficult to transmit back in a timely manner. Therefore, this invention constructs joint reliability constraints considering the analytical quantification relationship between electromagnetic interference and communication quality.

[0087] Define the spatial electromagnetic risk field strength index:

[0088] ;

[0089] In the formula: For position The spatial electromagnetic risk field strength index; , Positions The electric and magnetic field strengths, where the spatial electric and magnetic field strength distributions are pre-acquired before mission planning. Discrete spatial sampled values ​​can be obtained through analytical calculations, finite element electromagnetic field simulations, or on-site measurements based on parameters such as the spatial location, operating voltage, and current of the power equipment in the scenario. A continuous three-dimensional electromagnetic field distribution function is then constructed using spatial spline interpolation. lim B is the normalized reference value for electric field strength. lim This is a normalized reference value for the magnetic field strength; and These are the electric field risk and magnetic field risk weighting coefficients, respectively, satisfying... , , . The larger the value, the higher the electromagnetic risk associated with that spatial location.

[0090] To ensure the electromagnetic safety of drones during flight, the following requirements must be met:

[0091] ;

[0092] In the formula: This is the threshold for the electromagnetic risk field strength in space.

[0093] In power line inspection scenarios, due to factors such as communication distance, terrain obstruction, and local electromagnetic interference, some drones may not be able to maintain reliable direct communication with ground base stations throughout the entire inspection process.

[0094] Therefore, such as Figure 2 As shown, this invention pre-constructs a tree-like communication structure consisting of a ground base station, a relay communication UAV, and a mission-executing UAV. The ground base station serves as the root node of the communication network, the relay communication UAV as an intermediate forwarding node, and the mission-executing UAV as leaf nodes. The communication topology is predetermined before mission planning and remains unchanged during mission execution. The relay communication UAV only handles communication data reception, forwarding, and link maintenance, and does not participate in the allocation and execution of inspection tasks. The mission-executing UAV is responsible for completing the inspection tasks and data collection. Its communication parent node is uniquely determined by the pre-defined communication structure; that is, each mission-executing UAV establishes an uplink communication link with only one designated relay communication UAV or ground base station, and does not simultaneously establish connections with multiple relay nodes. Inspection data is transmitted upwards level by level according to the pre-defined tree structure: mission-executing UAVs directly connected to the ground base station directly transmit data back to the ground base station; mission-executing UAVs connected to relay communication UAVs first send data to their designated relay communication UAV, which then forwards it to the ground base station.

[0095] It should be noted that the communication topology used in this invention is predetermined before mission planning. Each mission-performing UAV establishes an uplink communication link with only one designated parent node, which can be a ground base station or a relay communication UAV. Therefore, for mission-performing UAVs and relay communication UAVs that communicate directly with ground base stations, only air-to-ground communication link constraints need to be met; for mission-performing UAVs that communicate via relay UAVs, only the corresponding air-to-air communication link constraints need to be met.

[0096] The quality of UAV communication links is affected by a combination of factors, including spatial distance, background noise, co-channel interference, and high-frequency electromagnetic environment. (Location: [omitted]) The path loss and signal-to-interference-plus-noise ratio (SINNR) between the drone and the base station (air-to-ground link) are denoted as follows: , At global time From position drones The drone at the location The path loss and signal-to-interference-plus-noise ratio (SINNR) of an air-to-air link are denoted as follows: , :

[0097] ;

[0098] ;

[0099] ;

[0100] ;

[0101] In the formula: For communication carrier frequency; For position Distance to base station; The signal power emitted by UAV i; For the transmit antenna gain of UAV i, This refers to the receiving antenna gain of the ground base station. For relay drones The receiving antenna gain; N0 is the noise power spectral density; B c For communication bandwidth; This is interference with co-channel communication. For in position Communication interference caused by high-frequency electromagnetic environments is represented as:

[0102] ;

[0103] ;

[0104] In the formula: For position Location, communication frequency band The equivalent electromagnetic noise power spectral density in the vicinity, Equation (34) is the fitting function used in this invention; This is the electric field interference calibration coefficient; This is the magnetic field interference calibration coefficient; , These are the effective threshold coefficients for electric and magnetic fields, respectively. For in position Communication interference caused by high-frequency electromagnetic environments has the same expression; only the following needs to be changed: Replace with .

[0105] It should be noted that Equation (34) adopts a quadratic fitting form because the interference power formed after the external electromagnetic field couples into the communication receiving device is related to the mean square value of the induced voltage or induced current, and the test results show that the quadratic fitting has high fitting accuracy. , This can be determined through on-site communication testing: For At a fixed carrier frequency Communication bandwidth B c Transmit and receive distance Under these conditions, the electric field strength is gradually changed, and the signal-to-interference-plus-noise ratio is recorded simultaneously. The index defines the electric field strength at which the signal-to-interference-plus-noise ratio (SNR) changes by more than 10% compared to the SNR without electric field strength as the interference-effective electric field strength, and then compares it with E. lim By analogy .for At a fixed carrier frequency Communication bandwidth B c Transmit and receive distance Under these conditions, the magnetic field strength is gradually changed, and the signal-to-interference-plus-noise ratio is recorded simultaneously. The index defines the magnetic field strength at which the signal-to-interference-plus-noise ratio (SNR) changes by more than 10% compared to the SNR without magnetic field strength as the effective magnetic field strength for interference. This is then compared with B. lim By analogy After determining the effective threshold coefficients of electric and magnetic fields, based on the measured interference power within the frequency band under different electric and magnetic field conditions, using equation (34) as the regression model, and fitting it with the non-negative least squares method, the following parameters are obtained: and Furthermore, a spatial interpolation method (in this invention, inverse distance weighted interpolation is used, with a distance power exponent of 2 and a search point count of 10) is employed to construct a continuous three-dimensional spatial distribution function in order to obtain the values ​​of the corresponding parameters at any location.

[0106] Based on Shannon's formula, the position is... The communication transmission rate between the drone and the base station can be expressed as: At global time From position The drone i to the location is drones The communication transmission rate can be expressed as :

[0107] ;

[0108] ;

[0109] To ensure reliable transmission of inspection data, under a fixed communication topology, each uplink communication link should meet the following requirements:

[0110] ;

[0111] ;

[0112] In the formula: For drones To the base station (denoted as Minimum data transmission rate requirements; For drones To drones The minimum data transmission rate requirement. Therefore, when a UAV directly connects to a ground base station, its communication quality depends on the distance between the UAV and the base station and the electromagnetic interference it experiences; when a UAV is relayed by another UAV, its communication quality depends on the positions of both the sending UAV and the relay UAV, as well as the electromagnetic interference it experiences. In the example of this invention, the air-to-ground link and the air-to-air link adopt the same minimum communication rate requirement, i.e. .

[0113] Step 2: Model transformation and solution based on decoupling strategy, including the following steps:

[0114] Step 2.1 Model coupling relationship.

[0115] The model proposed in this invention consists of a mixed-integer bi-level nonlinear programming problem at the upper level and a nonlinear programming problem at the lower level. Therefore, this model belongs to mixed-integer bi-level nonlinear programming (MIBNLP), which is an NP-hard problem.

[0116] Model coupling relationships are as follows Figure 3 As shown: The upper layer (task allocation model) provides x to the lower layer (path planning model). ijl With c ijk The value of is used to determine the inspection points and access sequence that each drone in the lower layer needs to visit. The lower layer (path planning model) provides the upper layer (task allocation model) with the path length d for each drone. ijk With path flight time T ijk Therefore, the results of upper-level task allocation affect the starting and ending points of lower-level path planning, and the quality of lower-level path planning affects the selection of upper-level task allocation schemes.

[0117] Step 2.2 Overall solution process.

[0118] To address the proposed MIBNLP problem, this invention designs a hierarchical iterative solution strategy, with the overall solution process as follows:

[0119] (1) Using the A* algorithm, the approximate shortest paths between the base node and each inspection point, as well as between any two inspection points, are pre-calculated to obtain the distance matrix D. The UAV flight speed is taken as... In this way, the approximate flight time between each node is calculated, and the time matrix T is obtained;

[0120] (2) For the upper-level task allocation model, the task allocation scheme and inspection point access sequence for each UAV are obtained by solving the distance matrix D and the time matrix T. ijl c ijk ;

[0121] (3) For the lower-level path planning model, based on the task allocation scheme x ijl With inspection point access sequence c ijk The solution is performed to obtain the flight path of each UAV that satisfies the dynamic and safety constraints, and the distance matrix D and time matrix T are updated.

[0122] (4) Feed back the updated D and T from the lower layer to the upper layer, resolve the upper layer model and form an iteration until the number of iterations reaches the preset upper limit K. max Or the upper-level objective function Z task The relative change between two consecutive iterations is below a given threshold:

[0123] ;

[0124] In the formula: , ε represents the upper-level objective function values ​​for the k-th and (k-1)-th iterations, respectively; upper This is the convergence threshold for the outer loops of the upper and lower layers.

[0125] Step 2.3 Solve the upper-level model.

[0126] In the upper-level task allocation model, the total task completion time Z task To represent the max nonlinear term, this invention introduces an auxiliary variable T. a Perform a linearization equivalent transformation:

[0127] ;

[0128] ;

[0129] After linearization, all objective functions and constraints are transformed into linear forms. Therefore, the model is transformed into a mixed integer linear programming (MILP) problem, which can be solved using commercial solvers such as Gurobi.

[0130] Step 2.4 Solve the lower-level model.

[0131] In the lower-level path planning model, there are coupling constraints between UAVs: the safe distance constraint between UAVs (Equation (18)) requires that two UAVs cannot be too close, while the communication rate constraint between UAVs (Equations (31)-(32), (36), (38)) requires that two UAVs cannot be too far apart (only for UAVs performing tasks that communicate through relay UAVs, there are communication rate constraints between relay UAVs and UAVs performing tasks). These two types of constraints jointly limit the relative positions between UAVs, thus forming a coupling relationship between them. If all UAVs are directly optimized together, the problem size and solution complexity will increase significantly. To this end, this invention adopts the augmented lagrangian method (ALM) to transform the coupling constraints between UAVs into a penalty term in the objective function, thereby decoupling the originally coupled multi-UAV path planning problem into multiple single-UAV subproblems, and thus solving each subproblem independently.

[0132] Solving the single-machine path planning problem: For the coupling constraints between UAVs, namely the safety distance constraint between UAVs (Equation (18)) and the communication rate constraint between UAVs (Equations (31)-(32), (36), (38)), they can be uniformly written in vector form. The equality constraints can be split into two inequality constraints: greater than or equal to and less than or equal to. The sign of the greater than or equal to constraint is reversed, thus unifying it into the less than or equal to form:

[0133] ;

[0134] In the formula: p i For drone i at global time Location The vector formed by them For the drone i′ at global time Location The vector formed by these vectors. For drones With drones The vector function composed of inter-machine coupling constraints includes the inter-machine minimum safe distance constraint violation function and the air-to-air communication rate constraint violation function; when When the condition is met, it indicates that all inter-machine coupling constraints are satisfied.

[0135] Introducing the inequality Lagrange multiplier vector λ i,i' and penalty parameter ρ(λ) i,i' Construct the augmented Lagrangian function L for the coupling constraints between UAVs (≥0 and ρ>0):

[0136] ;

[0137] In the formula, Indicates the vector Each component in the equation is compared with 0: components less than 0 are assigned 0, while components greater than or equal to 0 retain their original values. When the inter-machine coupling constraint is satisfied, The penalty term L has no penalty effect; however, when the inter-machine coupling constraint is not satisfied, L will increase rapidly, thereby driving the optimization process to generate a path that satisfies the inter-machine coupling constraint.

[0138] Furthermore, the augmented Lagrangian function L of the coupling constraints between UAVs is embedded into the lower-level objective function Z. lower :

[0139] ;

[0140] In the formula: Z lower The objective function value is the lower-level objective function value after adding the inter-machine coupling augmented Lagrange term. The subproblem objective function of a single UAV i is Equation (44), and the constraints are Equations (16)-(17), (19)-(30), (33)-(34), (35), and (37). Among them, the paths of the other UAVs can be regarded as known quantities, thereby achieving decoupling of the multi-UAV path planning problem.

[0141] This single-machine subproblem belongs to a nonlinear optimization problem. This invention designs the following two-stage solution strategy: In stage one, for the inspection point visit sequence of UAV i, A... * The algorithm calculates the paths between adjacent inspection points and smooths the paths using spline interpolation to obtain a set of control point vectors p. i (0) In phase two, using p obtained in phase one... i (0) The initial solution is obtained using the particle swarm optimization algorithm.

[0142] Solving the multi-machine path planning problem: This invention constructs an iterative solution mechanism at the multi-machine level, performs alternating optimization on each UAV subproblem, and updates the Lagrange multipliers and penalty parameters after each iteration, thereby gradually approximating the multi-machine cooperative feasible solution that satisfies the inter-machine coupling constraints.

[0143] The specific solution process for the multi-machine path planning problem is as follows:

[0144] (a) for λ i,i' Initialize with ρ.

[0145] This invention initializes the Lagrange multipliers. Set the penalty parameter ρ to zero. (1) For a positive integer:

[0146] ;

[0147] ;

[0148] In the formula: the superscript 1 is the value applied to the first augmented Lagrange iteration after initialization.

[0149] (b) Solve the individual subproblems according to the order of the drones.

[0150] In the r-th iteration, when solving the path planning subproblem of UAV i, the paths of the other UAVs are considered as known quantities, denoted as the set. ,Right now Indicates the first In the round of iterations, except for drones The collection of other drone paths:

[0151] ;

[0152] The updated preceding drone uses the first The latest path is used in the first round, while subsequent drones that have not yet been updated still use the path from the previous round, i.e., the first... Round path. Based on this, the individual subproblems corresponding to each UAV are solved sequentially to obtain the path planning results for each UAV in the r-th iteration.

[0153] (c) Update λ i,i' With ρ.

[0154] Lagrange multiplier λ i,i' The update method is as follows:

[0155] ;

[0156] This update method can guarantee λ i,i' It is always non-negative. If an inter-machine coupling constraint is violated in the current iteration, its corresponding multiplier will increase, and a stronger penalty will be imposed in the next iteration; conversely, if the constraint has been satisfied, the multiplier will not increase.

[0157] The penalty parameter ρ is updated as follows:

[0158] ;

[0159] ;

[0160] In the formula: 0 < κ < 1 is the reduction factor; μ > 1 is the magnification factor; Indicates the first Drones in round of iteration With drones The maximum value of the inter-machine coupling constraint function between them; ε (r) Let be the maximum positive value among all UAV pairs and all inter-UAV coupling constraint function values ​​in the r-th iteration, i.e., the maximum constraint violation amount in this iteration. Equation (49) shows that if the new iteration's There was a significant decrease compared to the previous round, while ρ remained unchanged; if If the decrease is not significant, increase ρ to enhance the objective function's rejection of infeasible solutions.

[0161] (d) Convergence judgment.

[0162] The convergence criterion for the lower-level model in the r-th iteration is reaching the maximum number of iterations. Or, the difference between two consecutive objective functions is less than a threshold:

[0163] ;

[0164] In the formula: , These are the lower-level objective function values ​​for the r-th and (r-1)-th iterations, respectively; The lower-level convergence threshold is set as follows: if the convergence criterion is met, the loop exits and ends; otherwise, r = r + 1, and the process returns to (b). In summary, the solution process for the lower-level path planning model is as follows: Figure 4 As shown.

[0165] Simulation Experiment: To verify the applicability of the multi-layer decoupling strategy proposed in this invention to multi-UAV collaborative power line inspection tasks, a three-dimensional simulation scenario of a suburban power transmission line corridor was constructed. The inspection area was established in a three-dimensional Cartesian coordinate system, with a horizontal range of 8000 m × 8000 m and a flight altitude constraint of 25~130 m. A unified UAV take-off and landing base was set up in the scenario, and all UAVs departed from the base and returned to the base after completing their respective inspection tasks. The inspection scenario constructed by this invention is as follows: Figure 5 As shown. Figure 5 The inspection area includes a suburban power transmission line corridor, which runs in a southwest-northeast direction and then bends back in the northern region. Inspection points are set up along the line, with a converter station in the north and a substation in the east. Some areas include maintenance equipment areas, mountainous forest areas, steep slopes, and tree obstacles that need to be avoided. The UAV take-off and landing base and communication base station are located in the south-central part of the scene, and are used to handle mission departure, return, and inspection data transmission. Figure 5 Obstacles are represented by a center point and a circular radius, with the radius characterizing the restricted area or the scope of safety impact. Power facilities such as converter stations, substations, and towers are important source terms for electromagnetic risk and communication reliability analysis.

[0166] In this invention, the number of drones is set to 4, the number of inspection points is set to 22, the number of obstacles is set to 7, and each inspection point includes 1 to 3 inspection tasks.

[0167] It should be noted that the example in this invention represents a specific scenario of the proposed tree-shaped communication structure. In the example, all four UAVs participate in the inspection task allocation and path planning as mission-executing UAVs. No dedicated relay communication UAV is set up, and each UAV establishes a communication link directly with the ground base station according to a pre-determined communication relationship.

[0168] The 22 inspection points mainly correspond to the locations of power transmission line towers and auxiliary power equipment. The inspection tasks include typical power inspection items such as tower body, insulators, conductor sag, hardware connections, tree obstructions in passageways, and infrared thermography of equipment. The coordinates of the inspection points, task information, and spatial parameters of obstacles are shown in Tables 1 and 2, respectively.

[0169] Table 1. Inspection Point Coordinates and Task Information ;

[0170] Table 2 Obstacle Spatial Parameters ;

[0171] The model and algorithm parameter settings are shown in Tables 3 and 4, respectively. It should be noted that when calculating flight time, the flight speed of the path segment must meet the following conditions: Table 3 This only indicates the minimum speed of the drone during mission execution or hovering, and is not used for calculating flight time on path segments. In the table, "e" indicates scientific notation to base 10; for example, 2.0e4 means 2.0 × 10⁻⁴. 4 1.0e-3 means 1.0 × 10 -3 .

[0172] Table 3 Model Parameter Settings

[0173] Table 4 Algorithm Parameter Settings ;

[0174] Regarding the hardware and software simulation platform, the operating system used is Windows 11, the CPU is a 12th Gen Intel(R) Core(TM) i5-12490F, and the memory is 16 GB. This invention is based on MATLAB 2024a for simulation. The upper-level model is modeled using YALMIP and solved using the Gurobi solver, while the lower-level model is solved using the proposed ALM-based iterative decoupling strategy.

[0175] Simulation Results and Analysis: After completing the upper and lower layer feedback iterations, the task allocation and access order obtained by the upper layer model are shown in Table 5.

[0176] Table 5. Results of UAV Task Allocation ;

[0177] Table 5 shows that the 22 inspection points were assigned to 4 UAVs, with each UAV undertaking 11, 12, 9, and 11 tasks respectively, and task execution times of 111, 122, 98, and 112 minutes respectively, indicating that the workload was not significantly concentrated on a single UAV. Considering the actual flight time after feedback from the lower layer, the total task times for the 4 UAVs were 124.17, 135.47, 111.66, and 125.81 minutes respectively, with the maximum task completion time being 135.47 minutes. The energy consumption of each UAV was lower than the upper limit of 12000 given in Table 3, with the highest being UAV 4 at 10276.97, still retaining a margin of 1723.03. Overall, the upper-layer model is able to strike a balance between the spatial distribution of inspection points, task execution time, and path cost feedback, resulting in a relatively balanced inspection load for each UAV.

[0178] The lower-level model plans a three-dimensional flight path for each UAV that satisfies obstacle avoidance and dynamic constraints, based on the inspection point visit sequence output by the upper-level model. Figure 6 The final obtained 3D path trajectories of the multiple UAVs are shown. From Figure 6 It can be seen that each drone departs from the base and eventually returns to the base, with its trajectory forming several spatially adjacent inspection loops according to the assigned inspection point sequence. Different trajectories require detours near obstacles and high-risk equipment, indicating that the lower-level model can adjust its flight path based on terrain, obstacles, and environmental constraints.

[0179] To further quantify the results of the lower-level path planning, Table 6 provides key statistics for each UAV, including path length, dynamics indicators, electromagnetic risks, and communication rates.

[0180] Table 6 Results of the Lower-Level Path Planning Model ;

[0181] As shown in Table 6, the maximum speed of all four drones is 15 m / s, and the absolute value of their maximum acceleration is 3 m / s². 2 The maximum turning angle was 18.07° and the maximum pitch angle was 4.38°, both of which did not exceed the upper limit of the constraints set in Table 3, indicating that the planned path met the requirements for the dynamic feasibility of the UAV. The maximum electromagnetic risk of each UAV was less than 1.0, and the minimum communication rate was not less than 10 Mbit / s, indicating that the planning results could take into account both electromagnetic safety and communication reliability requirements.

[0182] Furthermore, Figure 7 and Figure 8 The normalized electromagnetic risk distribution and communication rate distribution after superimposing the UAV trajectory are shown respectively. Figure 7 It can be seen that high electromagnetic risk values ​​are mainly concentrated near the northern converter station and the eastern substation, with the normalized risk approaching 1 in some areas. When passing near high-risk areas, the planned trajectory did not directly cross the risk peak center, but instead detoured along areas with lower risk gradients. The maximum electromagnetic risks of the four UAVs in Table 6 are 0.47, 0.86, 0.81, and 0.57, respectively, all less than the risk threshold of 1 set in Table 3. UAV2 and UAV3, due to their role at the northern inspection point, have relatively higher maximum risks, but still possess positive margins. This result indicates that after introducing electromagnetic risk constraints into the lower-level objective function, path planning can actively avoid areas with high electromagnetic interference.

[0183] Depend on Figure 8 It is known that communication speed is affected by factors such as base station distance, terrain obstruction, and electromagnetic interference, resulting in low communication speed zones in the northern part of the map and in areas with partial obstruction. The minimum communication speeds of the four UAVs along their final trajectories were 22.45, 10.41, 10.91, and 22.20 Mbit / s, respectively, all above the minimum communication requirement of 10 Mbit / s. UAV2 and UAV3, located near the high-risk northern area, had minimum communication speeds close to the lower limit of the constraint, indicating that this area is sensitive to communication reliability. UAV1 and UAV4, being farther from the high-interference area, had relatively greater communication margins. In summary... Figure 7 , Figure 8 It can be seen that the proposed model can strike a balance between path length, electromagnetic risk and communication reliability, so that the inspection trajectory can take into account both environmental safety and data transmission requirements.

[0184] This invention employs an iterative feedback mechanism between upper and lower layers, feeding back the actual flight distance matrix D and the actual flight time matrix T obtained from the lower-level path planning to the upper-level task allocation model, thereby continuously refining the task allocation results. Statistical results of the iterative feedback process between upper and lower layers are shown in Table 7.

[0185] Table 7 Statistics of iterative feedback process between upper and lower layers ;

[0186] As shown in Table 7, the value of the upper-level objective function Z decreases with each iteration. task The time gradually decreased from 148.62 minutes in the first round to 135.47 minutes in the fourth round, indicating that the actual flight distance and time fed back by the lower-level path planning can effectively correct the upper-level task allocation results. Meanwhile, the lower-level objective function value Z... energyThe value decreased from 42186.54 to 40325.29. In the fourth iteration, the relative change rate of the upper-layer objective function between two adjacent iterations was 5.51e-3, which is less than the outer-layer convergence threshold of 1.0e-2 set in Table 4. Therefore, the upper and lower layer feedback iterations are considered to have converged. This result shows that the proposed upper and lower layer decoupled feedback mechanism can obtain stable task allocation and path planning results within a finite number of iterations.

[0187] To further analyze the role of ALM in the decoupling of multiple UAV paths in the lower layer, Table 8 presents the statistics of the lower layer ALM iteration process.

[0188] Table 8 Statistics of the lower-level ALM iteration process ;

[0189] As shown in Table 8, in the first and second iterations, due to the ongoing adjustment of task allocation and path costs, there were certain safety distance violations between UAV trajectories. ALM converged after three iterations in each iteration. In the third iteration, the path structure was relatively stable, and ALM only needed two iterations to eliminate the safety distance violation. In the fourth iteration, the initial trajectories met the minimum safety distance requirement between UAVs, and ALM converged within one iteration. As ALM iterations progressed, the minimum inter-UAV distance gradually increased and exceeded the d set in Table 3. min =50 m, the maximum default amount eventually dropped to 0, indicating that the augmented Lagrange penalty can effectively push the trajectory away from the potential conflict area.

[0190] From the overall process, as the number of iterations between the upper and lower layers increases, the number of iterations required for the lower-level ALM gradually decreases from 3 to 1, indicating that the feedback updates between the upper and lower layers can improve the quality of the initial values ​​for the lower-level path planning, enabling the subsequent ALM decoupling solution to reach a feasible state more quickly. This result verifies that the multi-layer decoupling strategy proposed in this invention has good collaborative convergence characteristics between the task allocation layer and the path planning layer.

[0191] Comparative Experiment: To further verify the effectiveness of the established model and solution strategy, this invention sets up a comparative experiment under the same calculation examples, parameters and constraint thresholds.

[0192] To verify the necessity of considering various key constraints and energy consumption factors in this invention, a comparative experiment at the model level was conducted. All models adopted the same multi-layer decoupled solution process as this invention, and the results are shown in Table 9.

[0193] Table 9 Comparison results at the model level ;

[0194] As shown in Table 9, after ignoring dynamic constraints, the path length of M2 is shortened by 3.11% compared to M1, and the upper-level objective function decreases by 2.62%. However, the maximum speed, maximum acceleration, and maximum steering angle all exceed the range given in Table 3, indicating that relying solely on the geometric shortest path reduces the dynamic executability of the trajectory. When energy consumption is not considered, the upper-level objective function of M3 further decreases to 128.84 min, but the lower-level objective function value increases to 43372.65, an increase of 7.56% compared to M1. Furthermore, the maximum energy consumption per unit exceeds the 12000 range limit, indicating that simply pursuing rapid task completion weakens the sustainability of the solution under energy consumption constraints. After removing the minimum safe distance constraint between units in M4, the minimum inter-unit distance decreases to 31.84 m, indicating a significant risk of close-range collisions. After removing the electromagnetic risk constraint in M5, the maximum normalized electromagnetic risk reaches 1.18. After removing the communication reliability constraint in M6, the minimum communication rate decreases to 7.86 Mbit / s. Therefore, in the model of this invention, constraints on dynamics, energy consumption, safe distance, electromagnetic risk, and communication reliability all play a necessary role in ensuring the engineering feasibility of the multi-UAV inspection scheme.

[0195] To verify the effectiveness of the multi-layer decoupled solution framework of this invention, four solution strategies were further designed for comparison. S1 is the upper and lower layer feedback and lower-layer ALM decoupling strategy proposed in this invention; S2 encodes the task allocation variables and path control point variables into a centralized joint optimization problem; S3 retains the upper and lower layer feedback, but the lower layer does not use ALM decoupling, instead performing joint optimization of the path variables of multiple UAVs; S4 adopts a unidirectional phased solution, that is, first completes the task allocation based on the initial approximate distance matrix, and then performs a lower-layer path planning, without feeding back the actual distance matrix D and flight time matrix T to the upper layer. The comparison results are shown in Table 10.

[0196] Table 10 Comparison Results at the Solution Strategy Level ;

[0197] As shown in Table 10, the centralized joint optimization method S2 achieves a slightly better objective function value and path length than S1, but its computation time reaches 1546.8 s, approximately 3.69 times that of S1. This is because the centralized method simultaneously searches for discrete task assignment variables and continuous path control variables, significantly increasing the variable dimensionality and constraint coupling, resulting in higher solution costs. Although S3 retains the upper and lower layer feedback mechanism, the lower layer does not perform ALM decoupling, and multiple UAV path control points still need to be jointly searched, with a computation time of 932.4 s, approximately 2.23 times that of S1, and Z... energyCompared to S1, the computation time is increased by 1.16%. S4, due to performing only one task allocation and path planning operation, has the shortest computation time, but its upper-level objective function value, lower-level objective function value, and total path length increase by 5.09%, 4.42%, and 4.34%, respectively, compared to S1. This result indicates that without feedback from the lower-level actual flight cost to the upper-level task allocation, the initial approximate distance matrix will lead to a deviation between the task allocation and the actual path cost. In summary, the S1 strategy proposed in this invention maintains the feasibility of complete constraints while achieving near-centralized joint optimization planning quality with lower computational cost, demonstrating the trade-off between solution quality and computational efficiency achieved by decoupling upper-level feedback and lower-level ALM.

Claims

1. A multi-UAV collaborative power line inspection task planning method based on a multi-layer decoupling strategy, characterized in that, include: Step 1: Construct a two-layer optimization model for multi-UAV collaborative power line inspection. This model includes an upper-layer task allocation model and a lower-layer global path planning model. The task allocation model determines the inspection points and access sequences for each UAV, taking into account task completion time and energy consumption constraints. The global path planning model plans flight paths for each UAV that satisfy dynamic constraints, minimum safe distance constraints between UAVs, and joint reliability constraints considering the analytical quantization relationship between electromagnetic interference and communication quality. The lower-layer global path planning model aims to minimize the total energy consumption of all UAVs, describing the three-dimensional flight trajectory of each UAV through discrete control points. The UAV planning ensures continuous flight paths that meet dynamic constraints on flight altitude, speed, acceleration, turn angle, and pitch angle, and maintains safe distances between each control point and static obstacles. Joint reliability constraints considering the analytical quantification relationship between electromagnetic interference and communication quality include: electromagnetic risk field strength constraints based on spatial electromagnetic field distribution to limit electromagnetic risks at locations along the UAV flight path from exceeding a safe threshold; and transmission rate constraints for air-to-ground and air-to-air communication links based on path loss, signal-to-interference-plus-noise ratio, and Shannon's formula to ensure that each UAV can maintain data communication with ground base stations or other UAVs at a rate not lower than the minimum required rate while flying along the planned path. Step 2: Solve the two-layer optimization model using a multi-layer decoupling strategy, which includes inter-layer decoupling and intra-layer decoupling. Inter-layer decoupling is achieved by building an iterative feedback mechanism between the task allocation model and the path planning model, transmitting the actual path cost from the path planning model to the task allocation model to correct the task allocation scheme. Intra-layer decoupling is implemented within the path planning model, using the augmented Lagrangian method to handle the inter-UAV coupling constraints, transforming the coupling constraints into penalty terms in the objective function, thus decoupling the multi-UAV coupled path planning problem into multiple single-UAV path planning sub-problems, which are then solved alternately. In inter-layer decoupling, the lower-level path planning model decouples each UAV... The actual flight distance and time of the drone between inspection points are fed back to the upper-level task allocation model. The upper-level task allocation model re-optimizes the task allocation scheme based on the actual path cost feedback, forming an iterative closed loop between the upper and lower layers until the relative change of the upper-level objective function in two adjacent iterations is less than a preset threshold or the maximum number of iterations is reached. In the intra-layer decoupling, the inter-machine coupling constraints include the minimum safe distance constraint between drones and the communication rate constraint between drones. When solving each single-drone path planning sub-problem, the paths of other drones besides the current drone are regarded as known quantities, and each drone sub-problem is alternately optimized in turn. After each round of alternate optimization, the augmented Lagrange multiplier and penalty parameters are updated.

2. The multi-UAV collaborative power line inspection task planning method based on a multi-layer decoupling strategy according to claim 1, characterized in that, In step 1, the upper-level task allocation model aims to minimize the maximum task completion time among all drones, and determines the allocation relationship of each inspection point task among drones and the order in which each drone visits the inspection points. Each task at each inspection point is assigned to only one drone for execution.

3. The multi-UAV collaborative power line inspection task planning method based on a multi-layer decoupling strategy according to claim 1, characterized in that, Each single-machine path planning subproblem adopts a two-stage solution strategy: the first stage generates an initial path that satisfies the inspection point access sequence based on a preset search algorithm and performs smoothing; the second stage uses the initial path as the initial value and employs the particle swarm optimization algorithm to optimize and solve the problem, thereby obtaining a flight path that satisfies all single-machine constraints.

4. The multi-UAV collaborative power line inspection task planning method based on a multi-layer decoupling strategy according to claim 1, characterized in that, The upper-level task allocation model of the two-level optimization model is a mixed-integer linear programming model, which is solved using a commercial solver; The lower-level global path planning model is transformed into multiple nonlinear programming subproblems after intra-layer decoupling. These subproblems are solved alternately using the augmented Lagrangian method to reduce the overall solution size and computational complexity while satisfying all complex constraints.

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