Track planning method and system for unmanned power line inspection machine

Abstract

The invention provides a trajectory planning method and system for an unmanned power line inspection machine, and the method comprises the steps: generating a candidate trajectory based on an arc interpolation method, and generating a discretized trajectory space through arc interpolation on the basis of considering the motion characteristics of an unmanned plane and the working characteristics of a laser radar; performing trajectory selection by taking a multi-index cost function as an optimization target; and a Nesterov acceleration technology and adaptive parameter adjustment are combined to adjust and optimize the adjacent beam method. According to the method, the technical problems of low calculation efficiency, low enforceability of the generated trajectory, poor trajectory cost quantification effect and slow optimization process are solved.

Description

Technical Field

[0001] The present invention relates to the field of intelligent inspection technology, and in particular to a trajectory planning method and system for an unmanned power line inspection machine. Background Art

[0002] In recent years, with the continuous development of intelligent inspection technology and the maturity of drone and unmanned vehicle technologies, more and more power companies have begun to use unmanned vehicles for inspections. However, current unmanned inspection solutions rely on offline path planning and high-precision positioning systems, making them inflexible and unable to adapt to diverse scenarios during aerial operations. Furthermore, they rely on "point-to-point" path planning and neglect velocity planning along that path, also known as trajectory planning. When unmanned vehicles inspect power line corridors, particularly around corners of power line towers, the lack of proper trajectory planning can lead to drastic speed fluctuations in order to adhere to the planned path. This can affect the imaging stability of the onboard recognition equipment, ultimately compromising inspection quality and making it difficult to meet the demands of today's precision inspection tasks. Therefore, planning smoother trajectories that better reflect the unmanned vehicle's motion characteristics, within the acceptable offset distance, is crucial for improving inspection quality, especially around corners of power line towers.

[0003] In current unmanned power line inspections, LiDAR (Light Detection and Ranging) systems have become one of the main sensing technologies widely used. LiDAR has high precision and strong anti-interference capabilities, and can provide more detailed three-dimensional spatial information, especially in complex power line inspection environments. In contrast, single-camera or infrared systems are easily affected by external factors such as lighting changes and weather conditions, and have poor accuracy and reliability. Therefore, the solution of the present invention is mainly based on unmanned equipment equipped with LiDAR systems. In addition, although modern drones are equipped with high-precision GPS systems, their accuracy in outdoor environments still has meter-level errors, especially in the complex terrain of power line towers and environments with strong electromagnetic interference. The accuracy is often difficult to meet the requirements of efficient inspections. Therefore, relying solely on GPS for offline planning is not feasible, and real-time planning must be combined to ensure the accuracy and stability of drone flights.

[0004] Most existing unmanned power line inspection solutions first plan an inspection route offline. This route typically abstracts power line towers as "points" and the power line corridors between them as "lines." Finally, GPS-based drones are controlled to follow the planned "point-to-point" route, with real-time planning assistance along the way to correct errors. However, this path planning method neglects the drone's inherent motion characteristics. Especially when turning or approaching a tower, the drone often needs to first come to rest at the tower before turning to adhere to the planned path. This process is not only inefficient but also increases unnecessary energy consumption. Furthermore, improper speed control during turning can lead to wobbling, reducing the measurement accuracy of sensors (such as lidar), impacting inspection quality. Sharp deceleration or acceleration can cause the drone to tilt forward or backward, causing the onboard lidar to change its scanning direction, thus affecting the spatial coordinate parameters of the power line being identified. These incorrect parameters, in turn, lead to incorrect speed commands from the drone, ultimately causing oscillation.

[0005] In most inspection environments, if the distance between the drone and power lines is within a certain range, it will not significantly affect the inspection results. However, within this allowable deviation, trajectory planning generates a smooth path that conforms to the drone's motion characteristics. This not only ensures inspection quality, but also improves the efficiency of drone inspections near corners by avoiding inefficient stationary turns, and correspondingly reduces energy consumption. Furthermore, this optimized trajectory planning method can better control the speed of the entire inspection process, avoiding the aforementioned "forward and backward tilt" problem, thereby improving inspection quality.

[0006] Trajectory planning near a tower corner involves two steps: path planning and velocity planning based on that path. Specifically, path planning requires generating a continuous and smooth curve based on two intersecting paths to avoid inefficient stationary turns at corners. To ensure path feasibility, the generated path must meet the UAV's kinematic constraints and inspection mission requirements, such as minimum turning radius, turning rate, and maximum lateral distance deviation. Currently, path generation methods primarily use polynomial interpolation or spline interpolation. Polynomial interpolation constructs a single, high-order polynomial to ensure that the trajectory precisely passes through all given key points. However, polynomial interpolation is prone to oscillation (especially when there are many points), and modifying any interpolated point can cause the entire trajectory to change, resulting in poor numerical stability. Spline interpolation, on the other hand, divides the entire trajectory into segments, fitting each segment with a low-order (usually cubic) polynomial while ensuring continuity in position, velocity, and acceleration between segments. This makes handling irregularly distributed points more complex, and conventional splines have limited control over physical properties such as trajectory curvature and acceleration, requiring additional optimization to meet higher-performance planning requirements.

[0007] Furthermore, given the necessity of real-time planning, the entire planning process must meet planning time requirements and take into account the real-time motion state of the unmanned vehicle. Current trajectory planning methods for quadratic objective functions often employ nonsmooth convex optimization methods or heuristic algorithms. Nonsmooth convex optimization typically involves modeling the trajectory planning problem as a convex optimization problem with nonsmooth terms. Trajectories are optimized using iterative solvers (such as subgradient methods and ADMM) to satisfy constraints (such as obstacle avoidance and speed limits). The general process involves first establishing the cost function and constraints, ensuring that the problem is convex, and then using a specific nonsmooth optimization algorithm to gradually approach the optimal solution. The drawback is that while convergence is guaranteed, the involvement of nonsmooth terms often results in slow iterations, and the accuracy of the solution is easily affected by parameter adjustments. Heuristic algorithms (such as genetic algorithms, particle swarm optimization, and ant colony algorithms) simulate biological behavior or swarm intelligence phenomena in nature to search for and optimize trajectories. The general process involves initializing a batch of candidate trajectory solutions, then iterating and updating them based on pre-defined evaluation metrics (such as trajectory length, smoothness, and safety) to gradually find a more optimal trajectory. The advantages of heuristic algorithms are their strong adaptability to complex and non-convex problems and their ease in escaping local optimality. However, their disadvantages are also obvious: slow convergence, lack of theoretical convergence guarantees, the final results are greatly affected by randomness, and the amount of computation is extremely large in high-dimensional trajectory space, making it difficult to directly apply to strictly real-time tasks.

[0008] The existing invention patent application document, "A Reactive Obstacle Avoidance Method for Unmanned Aerial Vehicles Based on Ultrasonic Sensors," with publication number CN115903905A, includes the following: real-time monitoring and recording of obstacles using ultrasonic sensors; modeling the obstacles to obtain an obstacle surface model; determining whether to perform obstacle plane fitting; performing deduplication on the obstacle surface model and determining whether the hazard has been resolved; determining the positional relationship of the drone's current direction of motion relative to the obstacle surface; calculating the corresponding obstacle avoidance trajectory, and performing obstacle avoidance according to obstacle planning. However, the aforementioned existing technology focuses on solving the obstacle avoidance problem for a single drone, emphasizing the utilization of multidimensional sensor data rather than trajectory planning. Its trajectory planning method primarily utilizes quadratic polynomial interpolation, which is not suitable for inspection scenarios in the relatively open areas of power line corridors.

[0009] The existing invention patent application document, "Method and System for Path Coordination of Civilian Heterogeneous Unmanned Clusters Based on Collaboration with and without UAVs," with publication number CN119126777A, includes the following steps: obtaining UAV collaborative flight missions, parsing the UAV collaborative flight missions, and establishing subtask entities; performing self-inspections on idle UAVs, establishing a feature set for the idle UAVs, performing feature matching, and establishing a UAV-subtask mapping; establishing a search cluster and a follower cluster; performing real-time environmental data collection based on pre-flight trajectories and using the search cluster; and adjusting the pre-flight trajectory to complete path coordination for the UAV collaborative flight mission. However, the aforementioned prior art focuses on solving the problem of collaborative obstacle avoidance for multiple UAVs. The algorithm used in this existing solution has low accuracy and stability, and is not suitable for inspection scenarios.

[0010] In summary, the existing technology has technical problems such as low computational efficiency, low executable ability of generated trajectories, poor trajectory cost quantification effect, and slow optimization process. Summary of the Invention

[0011] The technical problem to be solved by the present invention is: how to solve the technical problems in the prior art of low computational efficiency, low executable capability of generated trajectories, poor trajectory cost quantization effect, and slow optimization process.

[0012] The present invention solves the above technical problems by adopting the following technical solutions: A trajectory planning method for an unmanned power line inspection machine includes:

[0013] S1. Perform platform coordinate system transformation, calculate power line parameters near the corner, generate candidate trajectories based on circular interpolation, generate initial candidate trajectory space based on UAV motion characteristics information and lidar working characteristics information, and process to obtain discrete candidate trajectory space;

[0014] S2. Define a multi-index cost function, use the multi-index cost function as the optimization target, and select the optimal trajectory from the discrete subsequent trajectory space;

[0015] S3. Combine Nesterov acceleration technology with adaptive parameter adjustment to tune the neighboring beam method and solve the function. Specifically, based on the multi-index cost function, the cost function problem is analyzed, and a convex optimization method is introduced for non-smooth scenarios. The tuning direction is updated according to historical information. The neighboring beam method based on multi-step acceleration is executed, combined with the finite difference method, to approximate the subgradient.

[0016] The present invention focuses on the trajectory planning problem in the power line corner environment. First, the planning problem near the corner is modeled based on the arc interpolation method and the characteristics of the inspection equipment. At the same time, combined with the requirements of the fine inspection task, a variety of optimization indicators are comprehensively considered to define and conditionally constrain the optimization target, namely the cost function. In addition, considering the complexity of problem solving, the present invention proposes a neighboring beam method based on multi-step acceleration based on the convex optimization method to solve the planning problem. And finally verified: the inspection trajectory planned based on the method of the present invention can greatly improve the inspection stability and inspection efficiency of the unmanned vehicle during the inspection process, especially in the corner environment, and meet the quality requirements of the fine inspection task of real-time planning. Different from the existing technology that focuses on the problem of aerial obstacle avoidance, the present invention focuses on the power line inspection scenario, aiming to improve the technical problems of the motion stability and inspection time efficiency of the unmanned vehicle at the corners of the power line corridor.

[0017] In a more specific technical solution, in the platform coordinate system transformation of S1, the point cloud coordinates in the laser radar coordinate system are set as: P LiDAR =(x L ,y L ,y L ), use the following logic to obtain the transformed point cloud coordinates P in the drone body coordinate system UM =(x B ,y B ,y B ):

[0018] P UM =R pose ·(P LiDAR -offest)#(1)

[0019] Where R pose The yaw angle R z (θ), pitch angle R Y (φ) and roll angle R X (η) transformation matrix;

[0020] Using the following logic, we can express the transformation matrix R pose :

[0021] R pose =R z (θ)·R Y (φ)·R X (η)#(2)

[0022] Where R X (η), R Y (φ), R z (θ) are the matrices for rotation around the X, Y, and Z axes respectively;

[0023] Using the following logic, we can express the matrix R for rotation around the X, Y, and Z axes: X (η), R Y (φ), R z (θ):

[0024]

[0025] In a more specific technical solution, S1 processes the converted point cloud coordinates to identify the spatial position of the power lines during the process of calculating the parameters related to the power lines near the corners;

[0026] For the converted point cloud data, the power lines are separated from the background through the point cloud segmentation algorithm;

[0027] The point cloud of the power lines is fitted using a spatial fitting algorithm to obtain the spatial geometric parameters of the power lines. The spatial geometric parameters include: the three-dimensional coordinates of the cables, the direction vectors, and the angles between the power line corridors.

[0028] Merge the lines with the same direction vector and abstract the power line corridor into one line;

[0029] When two power lines with different direction vectors are identified, it is determined that the drone has patrolled near the corner.

[0030] For at least two power line corridors near the tower corner, in the UAV coordinate system, let the i-th line of the power line corridor at time k be: The power line corridors are expressed using the following logic:

[0031]

[0032] Where, for At some point, is the direction vector;

[0033] For the intersection of the two lines at the corner, use the following logic to express the distance along the X axis in the drone coordinate system:

[0034]

[0035] Where, The power line currently tracked by the drone, is another line parameter identified;

[0036] Assuming the power line corridor is parallel to the ground, the angle formula is:

[0037]

[0038] In a more specific technical solution, in the process of generating the initial candidate trajectory space in S1, circular arc interpolation is used to optimize the initial power line path to generate a smooth path suitable for the UAV motion characteristics;

[0039] Define e as the maximum lateral distance deviation between the UAV and the power line corridor, r e is the radius of the current arc, It is the tangent point of the arc and the straight line, and the turning point where the drone starts to turn; define Path e is the smooth path under the lateral deviation e, The kth frame is when the machine reaches the inflection point Distance on the X axis; for a path with a deviation error of e, the following logic is used to calculate the radius r of the current arc e :

[0040]

[0041] Get the inflection point P corresponding to the radius r T The parameter values ​​and

[0042]

[0043] On the planned path, the speed information is combined to form a trajectory; the planned path includes: a straight line part and an arc part;

[0044] For the arc part, use the following logic to define the linear velocity of the drone at the kth frame and angular velocity The relationship when the radius is r makes the drone patrol along the arc:

[0045]

[0046] Based on the current planned path Path e ,The unmanned vehicle plans its own speed in each unit of time, based on its own state information, turning point distance and turning speed;

[0047] Define a unit time as a frame f; use the following logic to determine the speed change planned in the kth frame under the planned path

[0048]

[0049] The speed of the drone in the next frame is:

[0050]

[0051] Where r e is the radius under the lateral deviation e, rUM The minimum turning radius of the unmanned vehicle is set to the initial radius when the trajectory is planned in the kth frame. The radius within these two radius lengths All are candidate radii, corresponding to the path is the candidate path; on the subsequent path, the speed planning information is combined to generate the initial candidate trajectory space.

[0052] This paper addresses the problem of generating candidate trajectories based on raw power lines and proposes a candidate trajectory generation method based on circular interpolation. This method, taking into account the characteristics of drone motion and lidar operating characteristics, generates a discretized trajectory space through circular interpolation, significantly reducing the calculation of meaningless trajectories and improving computational efficiency. Furthermore, the generated trajectories are consistent with the characteristics of the task execution machine, ensuring their feasibility and providing a stable foundation for subsequent trajectory selection.

[0053] In a more specific technical solution, in S1, spatial discretization is performed based on the LiDAR working characteristics, and the discrete candidate trajectory space is obtained; wherein, the definition is the distance between the i-th inflection point and the unmanned machine in the k-th frame, and we get and and The relationship is:

[0054]

[0055] Define the minimum turning radius r of the unmanned vehicle UM The corresponding inflection point distance at the kth frame is get

[0056] In a more specific technical solution, the following logic is used to define a multi-index cost function:

[0057] min Cost=A*v * +B*w * +C*t * #(15)

[0058] Where, v * Indicates the cumulative rate of change of linear velocity in a corner environment, w * Expressed as the cumulative rate of change of angular velocity, t * It is expressed as relative time efficiency. A, B, and C are weight coefficients.

[0059] The state change of each time frame from the current position of the UAV to the inflection point position is accumulated and calculated to obtain the cumulative linear velocity change rate;

[0060] In the kth frame, for a certain trajectory Its turning linear velocity at the inflection point is Plan to slow down before reaching the turning point;

[0061] According to different frames k, different lines i and different speeds j, the cumulative amount of linear velocity change v is distinguished * , recover from the turning state to the straight state, from Acceleration to deceleration Using the following logic, determine the i-th path from the k-th frame to the turning point with a turning speed of Cumulative rate of change of linear velocity

[0062]

[0063] Where, From formula (12), we can get Δv MAX is the maximum linear speed per frame;

[0064] Calculate the cumulative rate of change of angular velocity; use the following logic, for the path and angular velocity Cumulative amount of angular velocity change rate under

[0065]

[0066] In a more specific technical solution, in S2, the relative time efficiency is calculated, wherein, the currently selected The radius is Then use the following logic to find the time in the turning state

[0067]

[0068] From equations (12), (13), and (14), calculate the speed of the straight-line state

[0069]

[0070] Where, Indicates the distance between unmanned vehicles in the kth frame The X-axis distance of the inflection point, Indicates that the inflection point is reached after the Kth frame, and arg min(·) represents the K that minimizes the expression;

[0071] Make up extra time Get for and the turning speed is Next time

[0072]

[0073] Define the minimum inspection time at the corner as t base According to formula (11), let the maximum angular acceleration of the unmanned machine be Δw MAX , then when the turning speed is When t base :

[0074] t base =tc e,e +ts e,e #(twenty one)

[0075] Where, tc e,e and ts e,e The calculation of is obtained by transforming formula (18) and (19);

[0076] According to the minimum inspection time t at the corner base ,for and the turning speed is Next time Use the following logic to find the path and turning speed Relative time efficiency under

[0077]

[0078] According to the path and turning speed Relative time efficiency under Finding Value At the minimum value of the entire corner, the optimal trajectory is planned.

[0079] This invention, within the permissible deviation range, generates a smooth path through trajectory planning that conforms to the drone's motion characteristics. This not only ensures inspection quality but also improves inspection efficiency near corners by avoiding inefficient stationary steering, thereby reducing energy consumption. Furthermore, this optimized trajectory planning method allows for better speed control throughout the inspection process, avoiding the aforementioned "forward and backward tilt" problem and thus improving inspection quality.

[0080] In a more specific technical solution, in S2, constraints are set, wherein the constraints include: autocorrelation constraint, maximum speed constraint, maximum turning linear speed constraint, and corner trajectory constraint:

[0081] In the straight state, any k-th frame, for the selected and The solution is to calculate the change in each frame when the drone performs speed planning. Set the following restrictions:

[0082]

[0083] For the angular velocity change per frame, we have:

[0084]

[0085] Define the maximum speed constraint, for all have:

[0086]

[0087] Define the maximum turning linear speed constraint for choose have:

[0088]

[0089] Define corner trajectory constraints, including:

[0090] The turning radius is calculated by equations (10) and (14). The numerical range of the turning radius is less than or equal to r under the maximum lateral distance. e , and is greater than or equal to the minimum turning radius r UM :

[0091]

[0092] Inflection point distance, for one frame have:

[0093]

[0094] The trajectory space is defined using equations (9) to (14); the cost function is defined using equations (15) to (22); and the constraints are defined using equations (23) to (28), thus obtaining the trajectory planning model in the corner environment.

[0095] This paper proposes a multi-index cost function as an optimization objective to provide a basis for trajectory selection. This cost function integrates multiple key factors, including linear velocity stability, angular velocity stability, and inspection efficiency, and provides a method for calculating these factors, thereby quantifying the cost of each trajectory.

[0096] In a more specific technical solution, in the finite difference method of S3, the value of the subgradient is estimated by calculating the rate of change of the objective function under small perturbations:

[0097]

[0098] The Neighboring Beam Method, based on Nesterov multi-step acceleration, is combined with the finite difference method and the NAG method based on interpolated momentum estimation to improve the solution speed. Furthermore, the parameters are adjusted step by step based on this acceleration algorithm to reduce oscillation. The following are specific strategies for this problem: using the momentum term to predict the next position, calculating the gradient at the next position and updating the momentum; and the interpolated momentum estimation strategy, which selects an interpolated point between the current point and the predicted point to calculate the momentum.

[0099] To address the problem of solving functions in trajectory planning, this paper further proposes a neighboring beam method based on multi-step acceleration. This algorithm improves on the neighboring beam method by combining Nesterov acceleration technology with adaptive parameter adjustment. This allows the algorithm to quickly find the optimal solution while ensuring convergence stability, thereby accelerating the optimization process and improving computational efficiency.

[0100] In a more specific technical solution, a trajectory planning system for an unmanned power line inspection machine includes:

[0101] The candidate trajectory generation module is used to transform the platform coordinate system, calculate the parameters related to the power lines near the corners, and generate candidate trajectories based on the circular interpolation method. Based on the UAV motion characteristics information and the lidar working characteristics information, the initial candidate trajectory space is generated through circular interpolation, and the discrete candidate trajectory space is obtained through processing;

[0102] The cost function definition module is used to define a multi-index cost function, use the multi-index cost function as the optimization target, and select the optimal trajectory from the discrete subsequent trajectory space. The cost function definition module is connected to the candidate trajectory generation module;

[0103] The function solving module combines Nesterov acceleration technology with adaptive parameter adjustment to optimize the neighboring beam method for function solving. This module analyzes the cost function problem based on a multi-metric cost function, introduces convex optimization methods for non-smooth scenarios, and updates the optimization direction based on historical information. It also implements the neighboring beam method based on multi-step acceleration, combined with the finite difference method, to approximate subgradients. The function solving module is connected to the cost function definition module.

[0104] Compared with the prior art, the present invention has the following advantages:

[0105] The present invention focuses on the trajectory planning problem in the power line corner environment. First, the planning problem near the corner is modeled based on the arc interpolation method and the characteristics of the inspection equipment. At the same time, combined with the requirements of the fine inspection task, a variety of optimization indicators are comprehensively considered to define and conditionally constrain the optimization target, i.e. the cost function. In addition, considering the complexity of problem solving, the present invention proposes a neighboring beam method based on multi-step acceleration based on the convex optimization method to solve the planning problem. It is finally verified that the inspection trajectory planned by the method of the present invention can greatly improve the inspection stability and efficiency of the unmanned vehicle during the inspection process, especially in the corner environment, and meet the quality requirements of the fine inspection task of real-time planning.

[0106] This paper addresses the problem of generating candidate trajectories based on raw power lines and proposes a candidate trajectory generation method based on circular interpolation. This method, taking into account the characteristics of drone motion and lidar operating characteristics, generates a discretized trajectory space through circular interpolation, significantly reducing the calculation of meaningless trajectories and improving computational efficiency. Furthermore, the generated trajectories are consistent with the characteristics of the task execution machine, ensuring their feasibility and providing a stable foundation for subsequent trajectory selection.

[0107] This invention, within the permissible deviation range, generates a smooth path through trajectory planning that conforms to the drone's motion characteristics. This not only ensures inspection quality but also improves inspection efficiency near corners by avoiding inefficient stationary steering, thereby reducing energy consumption. Furthermore, this optimized trajectory planning method allows for better speed control throughout the inspection process, avoiding the aforementioned "forward and backward tilt" problem and thus improving inspection quality.

[0108] This paper proposes a multi-index cost function as an optimization objective to provide a basis for trajectory selection. This cost function integrates multiple key factors, including linear velocity stability, angular velocity stability, and inspection efficiency, and provides a method for calculating these factors, thereby quantifying the cost of each trajectory.

[0109] To address the problem of solving functions in trajectory planning, this paper further proposes a neighboring beam method based on multi-step acceleration. This algorithm improves on the neighboring beam method by combining Nesterov acceleration technology with adaptive parameter adjustment. This allows the algorithm to quickly find the optimal solution while ensuring convergence stability, thereby accelerating the optimization process and improving computational efficiency.

[0110] The present invention solves the technical problems existing in the prior art, such as low computational efficiency, low executable capability of generated trajectories, poor trajectory cost quantization effect, and slow optimization process. BRIEF DESCRIPTION OF THE DRAWINGS

[0111] Figure 1This is a schematic diagram of the basic steps of a trajectory planning method for an unmanned power line inspection machine according to embodiment 1 of the present invention;

[0112] Figure 2 Schematic diagram of the circular interpolation method according to embodiment 1 of the present invention;

[0113] Figure 3 This is a schematic diagram of planning in the linear velocity direction of Example 1 of the present invention;

[0114] Figure 4 This is a schematic diagram of candidate trajectory planning according to Example 1 of the present invention;

[0115] Figure 5 Schematic diagram of radar point cloud return for each frame in Example 1 of the present invention;

[0116] Figure 6 Schematic diagram of the discretized trajectory space of Example 1 of the present invention;

[0117] Figure 7 This is a schematic diagram of the accumulation process in a straight line state according to Example 1 of the present invention;

[0118] Figure 8 Schematic diagram of the relationship between speed and cost under a determined path according to embodiment 1 of the present invention;

[0119] Figure 9 Schematic diagrams of three situations of the gradient relationship between the current point and the next iteration point in Example 1 of the present invention;

[0120] Figure 10 This is a schematic diagram of the operation process of the simulation experiment platform of Example 2 of the present invention;

[0121] Figure 11 This is a schematic diagram of a power line inspection scenario according to Embodiment 2 of the present invention;

[0122] Figure 12 This is a schematic diagram of a specific experimental scheme of Example 2 of the present invention;

[0123] Figure 13 Schematic diagram of the experimental results of Example 2 of the present invention. DETAILED DESCRIPTION

[0124] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0125] Example 1

[0126] like Figure 1 As shown, the present invention provides a trajectory planning method for an unmanned power line inspection machine, comprising the following basic steps:

[0127] S1. Perform platform coordinate system transformation, calculate parameters related to power lines near the corners, generate candidate trajectories based on circular interpolation, and generate the initial candidate trajectory space by circular interpolation, taking into account the UAV motion characteristics and lidar working characteristics, to obtain a discrete candidate trajectory space.

[0128] During the platform coordinate system conversion process in this embodiment, in addition to installing lidar on drones for power line inspections, unmanned vehicles equipped with airborne lidar are also used in some low-altitude scenarios. Regardless of the type of inspection equipment used, the workflow is primarily divided into three phases: data acquisition, environmental perception, and trajectory planning. During data acquisition, the drone uses its onboard lidar system to acquire high-resolution point cloud data of its surroundings. The lidar generates a three-dimensional point cloud of the target environment by emitting a laser beam and measuring the time and intensity of the return signal. This point cloud data is recorded relative to the lidar's body coordinate system. Therefore, before trajectory planning, it is necessary to ensure that the lidar coordinate system is consistent with the drone's coordinate system.

[0129] Specifically, considering that the laser radar is fixed in both position and scanning angle relative to the inspection equipment, there is a fixed coordinate conversion relationship between the two. The X-axis of the laser radar coordinate system is parallel to the Z-axis of the drone coordinate system and has the same direction, the Y-axis is parallel to the Y-axis of the drone coordinate system and has the opposite direction, and the Z-axis is parallel to the X-axis of the drone coordinate system but has the opposite direction. In this case, assuming that the installation error angle of the laser radar sensor is (η, φ, θ), the position offset is offest = (Δx, Δy, Δz), and the point cloud coordinates in the laser radar coordinate system are P LiDAR =(x L ,y L ,y L ), then the coordinates of these point clouds in the drone body coordinate system are P UM =(x B ,y B ,y B ) can be calculated using the following formula:

[0130] P UM =R pose ·(P LiDAR -offest)#(1)

[0131] Among them, R pose The yaw angle R z (θ), pitch angle R Y (φ) and roll angle RX (η) is a transformation matrix. Usually, this matrix can be expressed as:

[0132] R pose =R z (θ)·R Y (φ)·R X (η)#(2)

[0133] Among them, R X (η), R Y (φ), R z (θ) are the matrices rotating around the X, Y, and Z axes, namely:

[0134]

[0135] In the process of calculating the relevant parameters of the power lines near the corners of this embodiment, in order to identify the spatial position of the power lines, the processing of point cloud data is also an important step. First, for the point cloud data after the above-mentioned conversion of the coordinate system, the power lines are separated from the background by a point cloud segmentation algorithm, usually filtered and extracted based on the height and density characteristics of the points and the linear distribution characteristics of the power lines. Subsequently, the extracted power line point cloud is fitted by a spatial fitting algorithm (such as the least squares method or the random sampling consistency algorithm RANSAC) to calculate the spatial geometric parameters of the power lines, including the three-dimensional coordinates of the cables, the direction vectors, and the angles between the power line corridors. At the same time, in order to facilitate subsequent trajectory planning, it is also necessary to merge the lines with the same direction vectors, so that the power line corridors are abstracted into one line. When two power lines with different direction vectors are identified, it means that the drone has inspected near the corner.

[0136] Specifically, in order to focus on the proposed trajectory planning problem, the following assumptions are made in this embodiment: the above-mentioned point cloud data processing can stably and correctly calculate the power line parameters of different direction vectors; the unmanned machine is regarded as a massless point, and the dynamic state information of the machine can be obtained in real time, including the current linear velocity, angular velocity, unit maximum acceleration, etc.; at the same time, the power line tower is abstracted as a point, and the two adjacent power line corridors based on the tower are regarded as two intersecting lines, and the power line corridors are always parallel to the ground.

[0137] Since the unmanned machine always establishes a coordinate system based on itself as the origin per unit time, the parameter calculation varies with the change of unit time. Therefore, the following parameter calculations are all based on the kth frame as the basic premise. If the kth frame is not marked, it means that the parameter calculation is constant in the entire corner environment. For multiple power line corridors near the tower corner, in the unmanned machine coordinate system, it is assumed that the i-th line at time k is Then its expression is:

[0138]

[0139] in for At some point, is the direction vector. From this, we can infer that the distance between the intersection point (tower) of the two lines at the corner in the X-axis direction in the unmanned vehicle coordinate system is:

[0140]

[0141] in The power line currently tracked by the drone, is another line parameter identified. Based on the assumption that the power line corridor is always parallel to the ground, the angle formula of the turning angle can be obtained:

[0142]

[0143] In the operation of generating the initial candidate trajectory space in this embodiment, after obtaining the specific power line parameters, angle information, and intersection information near the corner, the original power line path can be optimized through interpolation to generate a smooth path that is more in line with the movement characteristics of the drone.

[0144] like Figure 2 As shown, in this embodiment, circular interpolation is used to generate candidate paths. The core idea of ​​circular interpolation is to use a circle to make two intersecting power lines near a corner tangent. The arc between the two tangent points and the original straight line form a new path, and this path is smooth and differentiable. Figure 2 This is a schematic diagram of the interpolation method. The bold path in the figure is the new path planned by the circular interpolation method. Since the generated path is easier for unmanned vehicles to track in actual applications and conforms to the motion characteristics of unmanned vehicles, it can reduce instability and tracking accuracy during movement. The definition of e in the figure is the maximum lateral distance deviation between the unmanned vehicle and the power line corridor. This deviation is generally set according to the requirements of the inspection task. e is the radius of the arc, It is the tangent point of the arc and the straight line, and also the turning point where the drone starts turning. e is the smooth path under the lateral deviation e, The kth frame is when the machine reaches the inflection point The distance on the X-axis is easy to infer For a path with a deviation error of e, r can be calculated by the following formula e :

[0145]

[0146] Thus, we get the inflection point P corresponding to r t , and

[0147]

[0148] In this embodiment, the velocity information is combined with the planned path to form a trajectory. The path can be divided into a straight line part and an arc part. For the arc part, in order to allow the unmanned vehicle to patrol along the arc, the linear velocity at the kth frame is and angular velocity The relationship when the radius is r is:

[0149]

[0150] When the unmanned vehicle reaches the turning point and starts to turn, the frequent changes in speed will cause more oscillations than the straight part. Therefore, the angular velocity at this time is generally constant. From the formula, we can know that the linear velocity at this time is also constant. In the straight part, the speed of the unmanned vehicle at the kth moment is defined as Due to the limitations of the machine's hardware performance, its linear speed during turning must be less than or equal to the current speed, that is, Therefore, before the drone reaches the turning point, it is necessary to plan the linear speed to ensure that the speed change distribution is as uniform as possible, so as to meet the turning speed requirements when the drone reaches the turning point, and avoid the "forward and backward tilt" phenomenon caused by drastic changes in speed. Figure 3 , based on the path Path e The unmanned vehicle plans its speed per unit time based on its state information, turning point distance, and turning speed. This unit time is determined by the mechanical characteristics of the vehicle itself and the round-trip latency of the onboard LiDAR data. Therefore, the size of the unit time also affects the speed planning decision. Define a unit time as a frame f; The speed change planned in the kth frame under this path is given by:

[0151]

[0152] Then the speed of the drone for the next frame is:

[0153]

[0154] During the inspection process, e is the maximum lateral deviation, and r is the maximum radius allowed under this deviation. The smaller the radius, the closer the corresponding arc is to the intersection point, and the smaller the lateral distance deviation. Therefore, the paths composed of these radii and their arcs are all qualified candidate paths.

[0155] like Figure 4 As shown, in this embodiment, r e is the radius under the lateral deviation e, r UM The minimum turning radius of the unmanned vehicle is set to the initial radius when the trajectory is planned in the kth frame. The radius within these two radius lengths All are candidate radii, and their corresponding paths All of them are candidate paths; combining the above speed planning information on these paths, the initial candidate trajectory space is generated.

[0156] In this embodiment, spatial discretization is performed based on the operating characteristics of LiDAR. The drone's perception of the environment relies on the point cloud data returned by the LiDAR. There is a certain delay between the radar emitting a laser beam and the return of the point cloud data. After the radar returns the data, it will perform the next scan. Based on this operating principle, this article refers to the time interval between two radar data returns as a frame f (the unit time mentioned above). The specific time of a frame is the delay of the radar return data.

[0157] like Figure 5 As shown, in this embodiment, the unmanned vehicle can only perceive the relative state of the fuselage and the power line corridor after obtaining the data returned by the radar, and plan according to its own motion state; before the next radar data is returned, the unmanned vehicle will perform inspection operations according to the planned trajectory plan.

[0158] Therefore, between the completion of trajectory planning and the return of the next LiDAR data, the drone cannot perceive the environment during this period, nor can it determine the exact distance to the turning point, and therefore cannot make a turn. Only when the LiDAR data returns can the drone determine whether to turn or implement a linear speed planning strategy based on its distance to the turning point. In short, the drone can only change its state at the position it reaches at the beginning or end of a frame; other positions within the frame cannot be changed.

[0159] In summary, in order to meet the working characteristics, this embodiment combines the characteristics of the laser radar and the arc interpolation method to generate a candidate trajectory space. The discretized trajectory space is as follows Figure 6 As shown, is the distance between the i-th inflection point and the unmanned machine in the k-th frame, so and and The relationship is:

[0160]

[0161] Define the minimum turning radius r of the unmanned vehicle UM The corresponding inflection point distance at the kth frame is Easy to know

[0162] S2. Define a multi-index cost function and use the multi-index cost function as the optimization target to select trajectories;

[0163] In this embodiment, a key step in establishing the trajectory planning model is determining the optimization objective, or cost function. Within the candidate trajectory space obtained in step S1, different trajectories have different planning schemes and costs. The goal of trajectory planning is to create a trajectory that conforms to the unmanned vehicle's motion characteristics and LiDAR requirements in cornering environments while minimizing the cost. Therefore, this embodiment considers multiple metrics to evaluate and analyze the cost of each trajectory, ultimately selecting the optimal trajectory.

[0164] Specifically, dramatic speed changes near corners have a significant impact on radar recognition accuracy. Therefore, when constructing the cost function, we must first ensure that the linear and angular speed changes are as low as possible throughout the entire process, allowing the unmanned vehicle to perform inspections stably. At the same time, to avoid inefficient inspections near corners due to excessively slow speeds, this cost function also uses time as one of the optimization indicators. The optimization objective formula is as follows:

[0165] min Cost=A*v * +B*w * +C*t * #(15)

[0166] Among them, v * Indicates the cumulative rate of change of linear velocity in a corner environment. Similarly, w * Expressed as the cumulative rate of change of angular velocity, t * It is expressed as relative time efficiency. A, B, and C are weight coefficients, which are adjusted according to the different inspection task objectives.

[0167] In this embodiment, the cumulative linear velocity change rate is calculated. Specifically, throughout the inspection process, the unmanned vehicle's motion state is divided into a straight-line state and a turning state. As mentioned above, frequent speed changes should be avoided as much as possible in the turning state. This is to ensure accurate tracking of the planned trajectory, and frequent speed changes in the turning state are more likely to cause oscillations. Therefore, in the turning state, the unmanned vehicle's motion state is relatively stable. In the straight-line state, since the current unmanned vehicle's linear velocity may not meet the turning speed requirements at the inflection point, deceleration or acceleration planning is required when necessary. Considering that the precise inspection task places high demands on the unmanned vehicle's motion state changes at each moment during the inspection process, it is necessary to accumulate the state changes in each time frame from the unmanned vehicle's current position to the inflection point position, rather than estimating the global state changes.

[0168] In this embodiment, the accumulation process in the straight line state is as follows: Figure 7 As shown, in the kth frame, for a certain trajectory Its turning linear velocity at the inflection point is Since the linear speed of the unmanned machine at this time Therefore, it is necessary to plan the deceleration before reaching the turning point. Since the drone dynamically adjusts the speed change according to its own state and environmental information in each frame, and the turning speed at the turning point also affects the cumulative amount, the cumulative linear speed change rate v * It should be distinguished according to different frames k, different lines i and different speeds j, so The meaning is that the i-th path from the k-th frame to the turning point and the turning speed is At the same time, after returning from the turning state to the straight state, it is also necessary to Acceleration to deceleration but The formula is:

[0169]

[0170] in According to formula (12), Δv MAX Determined by the mechanical characteristics of the unmanned machine, it means the maximum linear velocity per frame. Use Δv MAX The speed other than the previous frame speed can limit the excessive changes of the drone to a greater extent and avoid oscillation.

[0171] In this embodiment, the cumulative amount of the angular velocity change rate is calculated. Specifically, in the turning state, the speed in both directions should be kept as stable as possible. Therefore, for the angular velocity, the cumulative amount of its change rate is mainly concentrated in two moments, one is when the unmanned vehicle reaches the turning point and turns, and the other is when it reaches the other line and changes from the turning state to the straight state. Therefore, for the path and angular velocity Cumulative amount of angular velocity change rate under for:

[0172]

[0173] In this embodiment, relative time efficiency is calculated. Specifically, before reaching the turning point, the time calculation is mainly divided into two parts: one is the time calculation in the turning state; the other is the straight state. The straight state is further divided into the time spent on deceleration planning from the current position of the unmanned vehicle to the turning point, and the time spent on acceleration planning after the turn. However, the two parts of the latter are the same because the distance and the absolute value of the acceleration are the same. In the turning state, since the linear speed is constant, the time is relatively easy to calculate. Assuming that the selected The radius is The time in the turning state for:

[0174]

[0175] In a straight line state, since the speed of each frame before reaching the turning point is variable, the distance traveled in each frame after the speed changes is also different. It is difficult to directly calculate the speed of the straight line state from the current speed, the turning speed at the turning point and the distance to the turning point through the formula Therefore, it is necessary to reversely calculate from equations (12), (13), and (14):

[0176]

[0177] in, Indicates the distance between unmanned vehicles in the kth frame The X-axis distance of the inflection point, =(arg min(·)) represents the Kth frame after which the inflection point is reached. This means that the number of frames required to reach the inflection point starting from the kth frame is the minimum. Furthermore, since the drone calculates time for each frame based on its current motion state and relative position to the environment, this state may have evolved from the deceleration plan of the previous state. The calculation of time efficiency differs from the aforementioned calculation of speed stability, which focuses more on the changes between frames. The time efficiency of the entire turn should be considered, so additional time is required. Its meaning is the time from reaching the corner to the kth frame. and the turning speed is Next time for:

[0178]

[0179] Under the premise of ensuring the stability of the unmanned vehicle's motion, choosing different paths and different turning speeds will affect the inspection time. The relative time efficiency is the ratio between the delay caused by the currently selected planning scheme and the minimum delay scheme at the entire corner. This optimization indicator is mutually exclusive with the above two indicators to prevent the inspection time efficiency from being low due to excessive consideration of motion stability. The minimum inspection time at the corner is defined as t base , which represents the minimum inspection time around the entire corner and therefore does not change with each frame. For an unmanned vehicle arriving near a corner, the closest inflection point is the Path under the lateral error e. e At the same speed, the closer the inflection point is, the lower the time it takes to turn the corner. Therefore, t base Must appear in Path eAt the same time, for a trajectory, the angular velocity only affects the steering of the unmanned vehicle, and the linear velocity affects the time it takes for the unmanned vehicle to complete the trajectory tracking. According to formula (11), assuming that the maximum angular velocity of the unmanned vehicle is Δw MAX , then when the turning speed is When t base Minimum. So we get t base formula:

[0180] t base =tc e,e +ts e,e #(twenty one)

[0181] where tc e,e and ts e,e The calculation of is derived from equations (18) and (19). Then, for the selected path and turning speed Relative time efficiency under for:

[0182]

[0183] In summary, in the kth frame, select as well as Its cost is To find the minimum value of the entire corner, not only does it need to compare the costs under different paths and different speeds in each frame, but it also needs to be compared with the optimal solution of the historical frame to plan the optimal trajectory.

[0184] In this embodiment, constraints are set. Specifically, autocorrelation constraints are defined. Autocorrelation constraints are mainly the dynamic constraints of the unmanned vehicle itself and the mechanical characteristics of the laser radar. Different machines and equipment have different constraints. The main constraints are as follows:

[0185] The maximum acceleration per frame is the maximum acceleration under the premise of ensuring the smooth operation of the unmanned vehicle. In the straight state, for any k-th frame, and The solution is to calculate the change in each frame when the drone performs speed planning. There are the following restrictions:

[0186]

[0187] Similarly, for the change in angular velocity per frame, we have:

[0188]

[0189] Specifically, the maximum speed constraint is defined. If speed planning is not performed before reaching the turning point, the unmanned vehicle will always maintain the initial linear speed for inspection. Therefore, the initial linear speed is the maximum linear speed of the unmanned vehicle during the entire inspection process. have:

[0190]

[0191] Since the angular velocity changes after reaching the inflection point and remains unchanged during the entire turning state, the maximum angular velocity constraint is equivalent to equation (24).

[0192] Specifically, the maximum turning linear speed constraint is defined, the maximum turning linear speed It is affected not only by the current speed, but also by the radius corresponding to the turning point. In order to track the planned arc, the turning speed cannot exceed the product of the radius and the maximum angular velocity per frame. choose have:

[0193]

[0194] In this embodiment, corner trajectory constraints are defined. Specifically, the corner trajectory constraints are mainly based on the maximum lateral error e required by the inspection task and the relative state of the unmanned vehicle with respect to the power line when operating in a corner environment. The main constraints are:

[0195] Turning radius. The candidate radius of each frame will be slightly different according to the motion state of the unmanned vehicle and the relative position of the power line. It can be derived and calculated by equations (10) and (14). Its value range should be less than or equal to r under the maximum lateral distance. e , and is greater than or equal to the minimum turning radius r UM :

[0196]

[0197] The inflection point distance, the farthest inflection point candidate must not only be less than the distance from the current drone to the intersection, but also be less than or equal to the inflection point distance corresponding to the minimum turning radius. At the same time, the inflection point distance must also be greater than the inflection point distance corresponding to the maximum lateral error. have:

[0198]

[0199] Through the above analysis and modeling, the trajectory planning model in the complete corner environment is expressed as follows:

[0200] Trajectory space: defined by the above equations (9) to (14);

[0201] Cost function (optimization objective): defined by equations (15) to (22) above;

[0202] Constraints: defined by the above equations (23) to (28).

[0203] S3. Combine Nesterov acceleration technology with adaptive parameter adjustment to tune the neighboring beam method and solve the function.

[0204] In this embodiment, based on the above model, the specific cost of each trajectory can be quantified through the cost function, and the optimal trajectory can be planned. Since the trajectory planning model is discretized, all possible paths and possible speed plans based on these paths can be enumerated through exhaustive enumeration, and in theory, the trajectory with the lowest cost can be found. However, this method has extremely high computational complexity. Not only does it take a long time to traverse the trajectory space, but it also often requires a large amount of computing resources when calculating the cost function value, resulting in low efficiency in practical applications and difficulty in meeting the needs of real-time planning. Therefore, a relatively efficient solution is needed to solve this trajectory planning problem. To this end, it is first necessary to analyze the original planning problem and, based on the analysis results, abstract the original planning problem into an optimization problem that is easier to solve.

[0205] In this embodiment, the cost function problem is analyzed; specifically, within a certain frame, the process of planning the optimal trajectory first iterates through each turning point and the corresponding radius, and at the same time exhaustively enumerates the turning speed based on each turning point to find the trajectory with the lowest cost. For most quadratic cost function expressions, their function properties are often expressed as overall convex function properties or partially convex function properties. In order to further analyze the function characteristics and thus optimize the computational efficiency, this section studies the relationship between speed and cost under a certain path, such as Figure 8 As shown, the vertical axis is the kth frame as well as The cost value at the time of The enumeration iteration step is 0.01m / s.

[0206] Through analysis, it was found that the objective function is a non-smooth convex function, which means that although it satisfies convexity, it may not be differentiable at certain points, resulting in the optimization method being less effective than expected. For example, the gradient descent method relies on gradient calculation to update the iteration points, but at non-smooth points, the gradient may not exist or change dramatically, causing the optimization process to oscillate or converge slowly. Similarly, the Newton method relies on the Hessian matrix to calculate the Newton step size, but for non-smooth functions, the Hessian matrix may be unavailable or difficult to calculate. Therefore, purely gradient-based methods are not effective, and it is necessary to introduce convex optimization methods for non-smooth scenarios.

[0207] Common non-smooth convex optimization methods include ADMM, subgradient methods, and neighboring bundle methods. Compared to ADMM, neighboring bundle methods primarily leverage historical information to clarify the optimization update direction and improve optimization stability. Compared to simple subgradient methods, neighboring bundle methods construct better linear approximations by maintaining a set of historical subgradients, thereby reducing oscillations and accelerating convergence. Therefore, this section uses a trajectory planning method based on the neighboring bundle method to solve this optimization problem and find the minimum cost solution.

[0208] In this embodiment, a multi-step accelerated neighboring bundle method is implemented. Specifically, the core idea of ​​the original neighboring bundle method is to use the target value information and gradient information of historical points as "bundles" in each iteration, and use these bundles to construct a linear approximation function of the optimization objective. At the same time, to control the stability of the optimization and ensure that the new point does not deviate too far, a neighboring term is added to avoid oscillation. Then, the subproblem is solved to obtain a new iteration point. If the new point can significantly reduce the cost function value, the point is accepted and the bundle is updated. Otherwise, the neighboring parameters are adjusted and the iteration continues.

[0209] Although it is more stable in converging to the optimal solution than purely gradient-based methods, its bundle update process is also based on the gradient information of the function. To address the problem of non-differentiable functions and the difficulty in obtaining subgradients, this paper combines the finite difference method to approximate the subgradient. Specifically, the finite difference method estimates the value of the subgradient by calculating the rate of change of the objective function under small perturbations. The formula is as follows:

[0210]

[0211] In addition, there are still some problems when using the neighboring bundle method to optimize this problem. First, although this method is relatively stable for non-smooth optimization problems, its solution speed still has room for improvement compared to smooth optimization methods. Especially in the case of relatively complex cost functions in this article, frequent calculation of function values ​​will lead to large optimization delays. Secondly, during the parameter update process, the traditional neighboring bundle method usually relies on fixed neighboring parameters, or is reduced according to a fixed step size, which makes it difficult to stably approach the optimal solution in the later stage of optimization. Therefore, this paper proposes a multi-step acceleration based neighboring bundle method (Multi Step Acceleration based Proximal Bundle Method, MSA-PB). On the basis of combining the finite difference method, a NAG method based on interpolation momentum estimation is proposed to improve the solution speed; and based on this acceleration algorithm, the parameters are adjusted step by step to reduce oscillations. The following is a specific strategy for the above problems.

[0212] In this embodiment, a multi-step acceleration strategy is adopted. In this embodiment, the neighboring beam method usually needs to solve a subproblem in each iteration, which leads to high computational cost and slow convergence. Therefore, in order to accelerate the optimization process, this chapter considers introducing the Nesterov Accelerated Gradient (NAG) method. NAG introduces a momentum term when updating parameters, allowing the optimization path to converge more quickly toward the optimal solution. Its basic idea is to first use the momentum term to predict the next step position, then calculate the gradient at that position and update the momentum, thereby introducing a certain degree of foresight in the update direction and significantly accelerating the convergence process.

[0213] Specifically, the NAG method has a fast convergence rate for smooth convex optimization problems. However, considering that in non-smooth or high-curvature environments, the discontinuity of gradient information may lead to uncertainty in the update rate. Especially in the late convergence stage, directly calculating the gradient at the prediction point may skip the optimal solution. Therefore, to alleviate this problem, based on the NAG method, an interpolation momentum estimation strategy is introduced. Specifically, an interpolation point is selected between the current point and the prediction point to calculate its momentum, thereby appropriately reducing the forward estimation error during the optimization process and improving the smoothness of convergence. By adjusting the interpolation coefficient, a better balance can be achieved between accelerated convergence and optimization stability, making this method more robust for non-smooth convex optimization problems. The specific process is shown in Algorithm 1.

[0214] Algorithm 1 NAG method based on interpolation momentum estimation

[0215]

[0216]

[0217] In this embodiment, an adaptive step size strategy is adopted; in this embodiment, after the Nesterov multi-step acceleration method is introduced, the solution speed of the algorithm is significantly improved. However, this acceleration process also introduces multiple parameters, including momentum coefficient and step size parameter, which have an important impact on the convergence direction and stability of the algorithm during the optimization process. Specifically, the iterative step size of the Nesterov acceleration method can effectively speed up the convergence speed in the early stage of convergence, but when approaching the optimal solution, an excessively large step size may cause the solution to oscillate near the optimal solution or even deviate from the optimal solution. Therefore, in order to achieve more stable convergence when approaching the optimal solution, it is necessary to adaptively adjust the step size.

[0218] In order to effectively adjust the step size parameters, this embodiment proposes an adaptive step size shrinking strategy based on gradient information. The core idea of ​​this strategy is to dynamically adjust the step size parameters by analyzing the gradient relationship between the current point and the next iteration point, thereby achieving more stable convergence when approaching the optimal solution. Specifically, after calculating the next iteration point, according to the gradient relationship between the current point and the next iteration point, it can be divided into the following three situations: Figure 9 shown.

[0219] The first case is Figure 9 As shown in (a), the gradient signs of the current iteration point and the next iteration point are consistent and the absolute value of the gradient of the next iteration point is smaller. This indicates that the algorithm is still approaching the minimum value and the optimization direction is correct. At this time, there is no need to reduce the step size parameter. Continue to maintain a larger step size to accelerate convergence. The second case is as follows Figure 9 As shown in (b), the signs of the gradients at the current iteration point and the next iteration point are inconsistent, but the absolute value of the gradient at the next iteration point is smaller. This indicates that the algorithm may have skipped the minimum point, but is still near the minimum. In this case, the momentum coefficient and step size need to be appropriately reduced to avoid oscillation caused by an excessively large step size. If the third situation occurs, that is, Figure 9 As shown in (c) in the figure, the gradient signs are inconsistent and the absolute value of the gradient at the next iteration point is larger. This indicates that the algorithm may have deviated from the optimal solution. Continuing to iterate may lead to increased oscillation. In this case, it is necessary to reduce both the proximity coefficient and the momentum coefficient at the same time to stabilize the optimization direction and avoid further deviation from the optimal solution.

[0220] In summary, the complete multi-step accelerated neighboring beam method is shown in Algorithm 2. First, the current momentum information is obtained based on Algorithm 1. This momentum information is then used to replace the subgradient of the subproblem in the original neighboring beam method. Solving this subproblem yields the next iteration point. Based on the relationship between the target value and the gradient of the next iteration point and the current point, a decision is made as to whether to accept the iteration point and whether to change the parameters.

[0221] Algorithm 2: Flow of the neighboring beam method based on multi-step acceleration

[0222]

[0223] Example 2

[0224] In order to verify the performance of this method, in this embodiment, a simulation experiment platform is built based on an actual unmanned inspection vehicle, and the advantages and disadvantages of the trajectory planning inspection scheme proposed by the present invention and the traditional inspection method are compared based on this experimental platform. The operation process of the simulation experiment platform is as follows: Figure 10As shown in the figure, considering that it is difficult to visually observe the planned motion trajectory on a real device, and the power line parameters constructed by the power line extraction and fitting modules may be inaccurate, which may affect the subsequent trajectory planning results, a simulation experimental platform was constructed. This platform is built in the ROS environment and uses Gazebo and RViz for simulation and visualization. This experimental platform is deployed on a real physical machine running Ubuntu 18.04, with an Intel(R) Core(TM) i5-10500 CPU @ 3.10GHz and 16GB of RAM. The ROS system version is Melodic Morenia. The Gazebo version is 9.16.0. The RViz version is consistent with ROS.

[0225] The core purpose of this experiment is to verify the performance of the trajectory planning algorithm in power line inspection scenarios, especially near the corners of power line towers. Therefore, the design of the experimental scenario focuses on simulating different corner types near the corners of power line towers to comprehensively evaluate the adaptability and stability of the trajectory planning algorithm in complex corner environments. This experiment selected three typical corner types for simulation. These three corner types are more common in power line inspection scenarios, such as Figure 11 The following diagrams illustrate the scenarios, each including the angle between the two power lines and other parameters. The LiDAR scanning range was set to 5-10 meters in the X direction, 1-2 meters in the Y direction, and 5-10 meters in the Z direction, depending on the initial speed and mission. For each scenario, the unmanned vehicle was subjected to multiple experiments at initial speeds of 0.3 to 1.2 m / s to comprehensively verify the algorithm's performance.

[0226] During the experiment, the trajectory planning-based inspection solution optimized the drone's trajectory around corners, resulting in smoother overall motion. However, this also resulted in a significant lateral offset error. In contrast, while the traditional inspection solution experienced some offset at corners due to braking and deceleration, the magnitude of the offset was relatively small. To ensure fairness in the experiment, the offset distance of the trajectory planning solution was adjusted to be consistent with that of the traditional inspection solution at the same initial speed, thus ensuring comparability of the experimental results.

[0227] Specific experimental plans include Figure 12As shown: First, under different initial speeds, the lateral offset distance generated by the traditional inspection scheme at the corner is recorded. Then, under the same initial speed conditions, the inspection scheme based on trajectory planning is set to the same offset distance to ensure that the lateral offsets of the two schemes are consistent. In order to comprehensively evaluate the performance of the two schemes, this paper adopts normalized weighted indicators for integrated analysis: that is, for the three factors of linear velocity change variance, angular velocity change variance and inspection time in the entire corner environment, the proportion of the measured values ​​of the two schemes to the sum of the two is calculated respectively, and finally the comprehensive performance score is obtained by weighting. The lower the score, the better the comprehensive performance. The evaluation function formula is as follows, where A, B, and C are the coefficients of the cost function, i.e., the corresponding terms of formula (15), Var(V i ), Var(W i ) represents the variance of the linear / angular velocity samples of the i-th solution, T i is the time consumed by the solution near the corner.

[0228]

[0229] According to the experimental results Figure 13 As can be seen, the current trajectory planning-based inspection solution outperforms the traditional solution in all scenarios and at all initial speeds, demonstrating its overall superiority. Furthermore, significant performance differences between the two solutions can be observed across all scenarios and speeds. Specifically, the trajectory planning-based inspection solution achieved maximum performance improvements of 52.77%, 36.59%, and 32.07% in the three scenarios and in the comprehensive comparison, respectively.

[0230] In summary, the present invention focuses on the trajectory planning problem in the power line corner environment. First, the planning problem near the corner is modeled based on the arc interpolation method and the characteristics of the inspection equipment. At the same time, combined with the requirements of the fine inspection task, a variety of optimization indicators are comprehensively considered to define and conditionally constrain the optimization target, i.e., the cost function. In addition, considering the complexity of problem solving, the present invention proposes a neighboring beam method based on multi-step acceleration based on the convex optimization method to solve the planning problem. And finally verified: the inspection trajectory planned based on the method of the present invention can greatly improve the inspection stability and inspection efficiency of the unmanned vehicle during the inspection process, especially in the corner environment, and meet the quality requirements of the fine inspection task of real-time planning.

[0231] This paper addresses the problem of generating candidate trajectories based on raw power lines and proposes a candidate trajectory generation method based on circular interpolation. This method, taking into account the characteristics of drone motion and lidar operating characteristics, generates a discretized trajectory space through circular interpolation, significantly reducing the calculation of meaningless trajectories and improving computational efficiency. Furthermore, the generated trajectories are consistent with the characteristics of the task execution machine, ensuring their feasibility and providing a stable foundation for subsequent trajectory selection.

[0232] This invention, within the permissible deviation range, generates a smooth path through trajectory planning that conforms to the drone's motion characteristics. This not only ensures inspection quality but also improves inspection efficiency near corners by avoiding inefficient stationary steering, thereby reducing energy consumption. Furthermore, this optimized trajectory planning method allows for better speed control throughout the inspection process, avoiding the aforementioned "forward and backward tilt" problem and thus improving inspection quality.

[0233] This paper proposes a multi-index cost function as an optimization objective to provide a basis for trajectory selection. This cost function integrates multiple key factors, including linear velocity stability, angular velocity stability, and inspection efficiency, and provides a method for calculating these factors, thereby quantifying the cost of each trajectory.

[0234] To address the problem of solving functions in trajectory planning, this paper further proposes a neighboring beam method based on multi-step acceleration. This algorithm improves on the neighboring beam method by combining Nesterov acceleration technology with adaptive parameter adjustment. This allows the algorithm to quickly find the optimal solution while ensuring convergence stability, thereby accelerating the optimization process and improving computational efficiency.

[0235] The present invention solves the technical problems existing in the prior art, such as low computational efficiency, low executable capability of generated trajectories, poor trajectory cost quantization effect, and slow optimization process.

[0236] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the various embodiments of the present invention.

Claims

1. A trajectory planning method for an unmanned power line inspection machine, characterized in that: The method comprises: S1. Perform platform coordinate system transformation, calculate power line parameters near the corner, generate candidate trajectories based on circular interpolation, generate initial candidate trajectory space based on UAV motion characteristics information and lidar working characteristics information, and process to obtain discrete candidate trajectory space; S2. defining a multi-index cost function, using the multi-index cost function as an optimization target, and selecting an optimal trajectory from the discrete subsequent trajectory space; S3. Combining Nesterov acceleration technology with adaptive parameter adjustment, the neighboring beam method is tuned to solve the function. According to the multi-index cost function, the cost function problem is analyzed, and the convex optimization method in non-smooth scenarios is introduced to update the tuning direction according to historical information. The neighboring beam method based on multi-step acceleration is executed, combined with the finite difference method, to approximately calculate the subgradient.

2. The trajectory planning method for an unmanned power line inspection machine according to claim 1, characterized in that: In the platform coordinate system conversion of S1, the point cloud coordinates in the laser radar coordinate system are: LiDAR =(x L ,y L ,y L ), use the following logic to obtain the transformed point cloud coordinates P in the drone body coordinate system UM =(x B ,y B ,y B ): P UM =R pose ·(P LiDAR -offest)#(1) Where R pose The yaw angle R z (θ), pitch angle R Y (φ) and roll angle R X (η) transformation matrix; The transformation matrix R is expressed using the following logic: pose : R pose =R z (θ)·R Y (φ)·R X (h)#(2) Where R X (η), R Y (φ), R z (θ) are the matrices for rotation around the X, Y, and Z axes respectively; The following logic is used to express the matrix R rotating around the X, Y, and Z axes: X (η), R Y (φ), R z (θ):

3. The trajectory planning method for an unmanned power line inspection machine according to claim 1, characterized in that: In the process of calculating the parameters related to the power lines near the corner, the converted point cloud coordinates are processed to identify the spatial position of the power lines; Separating the power lines from the background using a point cloud segmentation algorithm for the converted point cloud data; Fitting the point cloud of the power line using a spatial fitting algorithm to obtain spatial geometric parameters of the power line, the spatial geometric parameters including: three-dimensional coordinates of the cable, direction vectors, and angles between power line corridors; Merge the lines with the same direction vector and abstract the power line corridor into one line; When the two power lines with different direction vectors are identified, it is determined that the drone has patrolled near a corner. For at least two power line corridors near the tower corner, in the unmanned vehicle coordinate system, let the i-th line of the power line corridor at time k be: The power line corridor is expressed using the following logic: Where, for At some point, is the direction vector; For the intersection of the two lines at the corner, the following logic is used to express the distance in the X-axis direction in the unmanned vehicle coordinate system: Where, The power line currently tracked by the drone, is another line parameter identified; Assuming that the power line corridor is parallel to the ground, the angle formula of the turning angle is obtained:

4. The trajectory planning method for an unmanned power line inspection machine according to claim 1, characterized in that: In the process of generating the initial candidate trajectory space in S1, the initial power line path is optimized by the circular interpolation to generate a smooth path suitable for the UAV motion characteristics; Define e as the maximum lateral distance deviation between the UAV and the power line corridor, r e is the radius of the current arc, It is the tangent point of the arc and the straight line, and the turning point where the drone starts to turn; define Path e is the smooth path under the lateral deviation e, The kth frame is the point where no machine reaches the inflection point Distance on the X axis; for a path with a deviation error of e, the following logic is used to calculate the radius r of the current arc e : Get the inflection point P corresponding to the radius r T The parameter values ​​and On the planned path, the speed information is combined to form a trajectory; wherein the planned path includes: a straight line portion and an arc portion; For the arc part, the linear velocity of the UAV at the kth frame is defined using the following logic: and angular velocity When the radius is r, the UAV patrols along the arc: Based on the current planned path Path e ,The unmanned vehicle plans its own speed in each unit of time, based on its own state information, turning point distance and turning speed; Define a unit time as a frame f; use the following logic to determine the speed change planned in the kth frame under the planned path The speed of the drone in the next frame is: Where r e is the radius under lateral deviation e, r UM The minimum turning radius of the unmanned vehicle is set to the initial radius when the trajectory is planned in the kth frame. The radius within these two radius lengths are all candidate radii, and the corresponding paths is the candidate path; on the subsequent path, combined with the speed planning information, the initial candidate trajectory space is generated.

5. The trajectory planning method for an unmanned power line inspection machine according to claim 1, characterized in that: In S1, spatial discretization is performed based on the LiDAR working characteristics to obtain the discrete candidate trajectory space; wherein, the definition is the distance between the i-th inflection point and the unmanned machine in the k-th frame, and we get and and The relationship is: Define the minimum turning radius r of the unmanned vehicle UM The corresponding inflection point distance at the kth frame is get 6. The trajectory planning method for an unmanned power line inspection machine according to claim 1, characterized in that: In S2, the multi-index cost function is defined using the following logic: min Cost=A*v * +B*w * +C*t * #(15) Where, v * Indicates the cumulative rate of change of linear velocity in a corner environment, w * Expressed as the cumulative rate of change of angular velocity, t * It is expressed as relative time efficiency. A, B, and C are weight coefficients. The state change of each time frame from the current position of the UAV to the inflection point position is accumulated and calculated to obtain the cumulative linear velocity change rate; In the kth frame, for a certain trajectory Its turning linear velocity at the inflection point is Plan to slow down before reaching the turning point; According to different frames k, different lines i and different speeds j, the cumulative amount of linear velocity change v is distinguished * , recover from the turning state to the straight state, from Acceleration to deceleration Using the following logic, determine the i-th path from the k-th frame to the turning point with a turning speed of Cumulative rate of change of linear velocity Where, From formula (12), we can get Δv MAX is the maximum linear speed per frame; Calculate the cumulative amount of angular velocity change rate; use the following logic, for the path and angular velocity The cumulative amount of the angular velocity change rate under 7. The trajectory planning method for an unmanned power line inspection machine according to claim 1, characterized in that: In S2, the relative time efficiency is calculated, wherein, the currently selected The radius is Then use the following logic to find the time in the turning state From equations (12), (13), and (14), calculate the speed of the straight-line state Where, Indicates the distance between unmanned vehicles in the kth frame The X-axis distance of the inflection point, Indicates that the inflection point is reached after the Kth frame, and arg min(·) represents the K that minimizes the expression; Make up extra time Get for and the turning speed is Next time Define the minimum inspection time at the corner as t base According to formula (11), let the maximum angular acceleration of the unmanned machine be Δw MAX , then when the turning speed is When t base : t base =tc e,e +ts e,e #(21) Where, tc e,e and ts e,e The calculation of is obtained by transforming formula (18) and (19); According to the minimum inspection time t at the corner base 、 and the turning speed is Next time Use the following logic to find the path and turning speed Relative time efficiency under According to the path and turning speed Relative time efficiency under Finding Value At the minimum value of the entire corner, the optimal trajectory is planned.

8. The trajectory planning method for an unmanned power line inspection machine according to claim 1, characterized in that: In S2, constraints are set, wherein the constraints include: autocorrelation constraint, maximum speed constraint, maximum turning linear speed constraint, and corner trajectory constraint: In the straight state, any k-th frame, for the selected and The solution is to calculate the change in each frame when the drone performs speed planning. Set the following restrictions: For the angular velocity change per frame, we have: Define the maximum speed constraint, for all have: Define the maximum turning linear speed constraint, for choose have: Defining the corner trajectory constraint includes: The turning radius is calculated by equations (10) and (14). The numerical range of the turning radius is less than or equal to r under the maximum lateral distance. e , and is greater than or equal to the minimum turning radius r UM : Inflection point distance, for one frame have: The trajectory space is defined using equations (9) to (14); the cost function is defined using equations (15) to (22); and the constraints are defined using equations (23) to (28), thus obtaining the trajectory planning model in the corner environment.

9. The trajectory planning method for an unmanned power line inspection machine according to claim 1, characterized in that: In the finite difference method of S3, the value of the subgradient is estimated by calculating the rate of change of the objective function under small perturbations: The Nesterov multi-step accelerated neighboring beam method, combined with the finite difference method and the NAG method based on interpolated momentum estimation, improves the solution speed. Based on this accelerated algorithm, parameters are adjusted step by step to reduce oscillation. The following are specific strategies for this problem: using the momentum term to predict the next position, calculating the gradient at this position and updating the momentum; and using the interpolated momentum estimation strategy, selecting an interpolated point between the current point and the predicted point to calculate the momentum.

10. A trajectory planning system for an unmanned power line inspection machine, characterized in that: The system comprises: The candidate trajectory generation module is used to transform the platform coordinate system, calculate the parameters related to the power lines near the corners, and generate candidate trajectories based on the circular interpolation method. Based on the UAV motion characteristics information and the lidar working characteristics information, the initial candidate trajectory space is generated through circular interpolation, and the discrete candidate trajectory space is obtained through processing; a cost function definition module, configured to define a multi-index cost function, use the multi-index cost function as an optimization target, and select an optimal trajectory from the discrete subsequent trajectory space; the cost function definition module is connected to the candidate trajectory generation module; A function solving module is used to combine Nesterov acceleration technology with adaptive parameter adjustment, tune the neighboring beam method, and solve the function. Specifically, based on the multi-index cost function, the cost function problem is analyzed, and a convex optimization method is introduced in non-smooth scenarios. The tuning direction is updated according to historical information. The neighboring beam method based on multi-step acceleration is executed in combination with the finite difference method to approximately calculate the subgradient. The function solving module is connected to the cost function definition module.

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