An unmanned aerial vehicle autonomous inspection route planning method and system

Abstract

The application provides a kind of unmanned aerial vehicle autonomous inspection route planning method and system, including collecting inspection area boundary, obstacle distribution, inspection point and unmanned aerial vehicle movement, safety spacing parameter, constructs three-dimensional planning space;Based on the accessibility of inspection point and the piecewise weighted sampling of obstacle distribution to generate candidate points, determine the extension direction of tree node, combine obstacle distance, corner constraint and path cost to construct extension criterion, under the condition of meeting turning radius, climbing gradient and safety constraint, variable step extension generates initial search tree, and the initial route covering all inspection points is obtained by parent node optimization reconnection;According to the node corner change and the traffic allowance, the route is divided into smooth area and sensitive area, the nodes in the smooth area are thinned, the sensitive area is reconstructed according to the continuous constraint of safety spacing and curvature, and the unmanned aerial vehicle inspection route meeting the inspection order, obstacle avoidance and movement constraint is output after discretization, redundant point elimination and feasibility check.

Description

Technical Field

[0001] This application belongs to the field of flight path planning, and in particular relates to a method and system for autonomous inspection flight path planning by unmanned aerial vehicles (UAVs). Background Technology

[0002] Flight path planning, as a core technology of autonomous UAV inspection systems, determines mission efficiency and flight safety. However, real-world 3D inspection environments often feature undulating terrain, randomly and densely distributed obstacles, and require visiting multiple designated inspection points per mission. Faced with this environment, flight path planning methods struggle to cover multiple inspection points while ensuring obstacle avoidance, and they often overlook the UAV's own flight limitations, resulting in planned flight paths that frequently exhibit spatially broken line characteristics. The Fast Random Tree (RRT) algorithm possesses strong spatial exploration capabilities when handling high-dimensional space search and obstacle avoidance constraints; furthermore, to improve the flight quality of the initial path, a specific path smoothing mechanism is typically incorporated after RRT planning to optimize the trajectory.

[0003] However, the node sampling and expansion process of the RRT algorithm is blind, lacking a comprehensive guidance mechanism for local obstacle distribution, the cost of unvisited inspection points, and UAV motion constraints. This results in low search efficiency and high tree structure redundancy in multi-point inspection tasks, and the generated initial routes are prone to violating UAV turning angle and climb gradient constraints. The path smoothing mechanism adopts a globally uniform processing approach, failing to differentiate operations based on the local characteristics of the route. Due to the omission of differences in node turning angle and passage margin, this global smoothing retains unnecessary redundant nodes in smooth passage areas, while in obstacle-dense, turning-sensitive areas, it is prone to violating safety distance constraints or curvature continuity requirements due to excessive smoothing. The output route cannot simultaneously take into account safe obstacle avoidance, strict motion constraints, and the order requirements of multi-point inspections, reducing the engineering practicality of the UAV autonomous inspection system. Summary of the Invention

[0004] To address the problems in existing technologies, such as lack of guidance in search, low efficiency, easy violation of motion constraints, and poor route quality due to the inability of global smoothing to distinguish local features of the route.

[0005] In the first aspect, the present invention provides the following technical solution: a method for autonomous inspection route planning of unmanned aerial vehicles (UAVs), comprising: Acquire the boundary data of the inspection area, obstacle distribution information, inspection point set, UAV motion constraint parameters and environmental safety distance parameters, and construct a three-dimensional planning space including the UAV's starting point, ending point and all inspection points; Based on the reachability relationships between inspection points and the distribution of obstacles, the 3D planning space is segmented and weighted to generate candidate sampling points. The expansion direction of the tree node is determined based on the direction of the line connecting the current node and the candidate sampling points. An expansion criterion is constructed by combining the distance of the candidate sampling point to the neighboring obstacles, the current node's turning angle constraint, and the path cost from the node to the unvisited inspection point. Variable step size expansion is performed while satisfying the constraints of the UAV's minimum turning radius, maximum climb gradient, and safe distance to generate an initial search tree. Neighboring parent node selection and reconnection operations are performed on the newly generated nodes to obtain an initial flight path covering all inspection points. The initial route is divided into a smooth passage zone and a turning-sensitive zone based on the turning angle change and passage margin of each node. The smooth passage zone is processed by node sparsification, and the turning-sensitive zone is reconstructed into a segmented curve based on the modified safety distance and curvature continuity constraints. The reconstructed route is discretized, redundant points are deleted, and feasibility is checked to output an autonomous inspection route of the UAV that meets the inspection sequence, obstacle avoidance constraints, and motion constraints.

[0006] In a second aspect, the present invention provides the following technical solution: an autonomous unmanned aerial vehicle (UAV) inspection route planning system, comprising the following modules: The module is used to acquire boundary data of the inspection area, obstacle distribution information, inspection point set, UAV motion constraint parameters and environmental safety distance parameters, and construct a three-dimensional planning space including the UAV's starting point, ending point and all inspection points; The reconnection module is used to perform segmented weighted sampling of the 3D planning space based on the reachability relationships between inspection points and the distribution of obstacles, generate candidate sampling points, and determine the tree node expansion direction based on the direction of the line connecting the current node and the candidate sampling points. Combining the distance of the candidate sampling point to the neighboring obstacles, the current node's turning angle constraint, and the path cost from the node to the unvisited inspection point, the module constructs an expansion criterion. Under the constraints of the UAV's minimum turning radius, maximum climb gradient, and safe distance, the module performs variable step-size expansion to generate an initial search tree. The module then performs neighboring parent node optimization and reconnection operations on the newly generated nodes to obtain an initial flight path covering all inspection points. The output module is used to divide the initial route into a smooth passage zone and a turning sensitive zone based on the turning angle change and passage margin corresponding to each node of the initial route; it performs node sparsification processing on the smooth passage zone and reconstructs the segmented curves of the turning sensitive zone according to the modified safety distance and curvature continuity constraints; it discretizes the reconstructed route, deletes redundant points and verifies its feasibility, and outputs an autonomous inspection route of the UAV that meets the inspection sequence, obstacle avoidance constraints and motion constraints.

[0007] This invention generates candidate points through segmented weighted sampling during path search, constructs expansion criteria by combining obstacle distance, turning angle constraints, and path cost, and performs variable step-size expansion and node optimization and reconnection under the conditions of satisfying minimum turning radius and maximum climb gradient constraints. This improves search efficiency and ensures the safety of the initial flight path. Based on local environmental characteristics, the initial flight path is divided into a smooth passage zone and a turning-sensitive zone, and node sparsification and curvature-continuous segmented curve reconstruction are implemented respectively, supplemented by redundancy removal and feasibility verification. This mechanism reduces computational burden, improves path smoothness, and the output flight path not only takes into account multi-point inspection sequence and obstacle avoidance requirements, but also deeply matches the actual kinematic characteristics of the UAV, improving the stability and safety of actual inspection flights. Attached Figure Description

[0008] Figure 1 A flowchart of the first embodiment; Figure 2 This is a schematic diagram of the variable step size expansion and safe obstacle avoidance mechanism based on obstacle distance; Figure 3 This is a comparison chart of the experiments. Detailed Implementation

[0009] The exemplary embodiments of this disclosure are described below with reference to the accompanying drawings, including various details of the embodiments to aid understanding, and should be considered merely exemplary. Therefore, those skilled in the art will recognize that various changes and modifications can be made to the embodiments described herein without departing from the scope of this disclosure. Similarly, for clarity and brevity, descriptions of well-known functions and structures are omitted in the following description.

[0010] In the first embodiment, the present invention proposes a method for autonomous inspection route planning for unmanned aerial vehicles (UAVs), such as... Figure 1 As shown, it includes:

[0011] S1 acquires the boundary data of the inspection area, obstacle distribution information, inspection point set, UAV motion constraint parameters and environmental safety distance parameters, and constructs a three-dimensional planning space including the UAV's starting point, ending point and all inspection points.

[0012] The point cloud processing library PCL is called to read the point cloud data scanned by the LiDAR and perform voxel filtering preprocessing. An octree mapping algorithm is used to convert the processed point cloud data into a 3D raster map, representing obstacle distribution information and inspection area boundary data. The origin and destination coordinates of the UAV and the latitude, longitude, and elevation information of the inspection point set are received through a global positioning system, and the information is uniformly converted to the global world coordinate system of the 3D raster map using a geodetic coordinate system conversion algorithm. The geodetic coordinate system conversion algorithm, such as the ENU algorithm, is a method for converting position and longitude in a global reference system. ,latitude Elevation A mathematical method for converting to a local rectangular coordinate system with a fixed ground point as the origin.

[0013] The minimum turning radius, maximum climb gradient motion constraint parameters, and environmental safety distance parameters based on the UAV's geometry are read from the configuration file. Using the free grid in the global world coordinate system as the state space, and combining the aforementioned coordinate points and parameters, a planning environment object is instantiated to complete the construction of the three-dimensional planning space.

[0014] In an optional embodiment, the construction of a three-dimensional planning space including the drone's starting point, ending point, and all inspection points includes: The input 3D terrain data is divided into a cuboid cell array according to a preset step size to construct a 3D rectangular grid map environment model. Extract the minimum physical collision distance of the obstacle and add a preset safety margin to the distance as the environmental safety distance parameter; Extract the maximum permissible yaw rate of the UAV as the motion constraint parameter of the UAV; Extract the three-dimensional coordinates of the first takeoff position as the starting point of the UAV, and extract the three-dimensional coordinates of the landing position as the ending point.

[0015] The system receives digital elevation model (DEM) or lidar 3D point cloud data of the inspection area and sets the grid division step size within a preferred range of 0.5m to 2.0m, for example, 1.0m. Based on this step size, the entire inspection airspace and terrain are divided into an array of rectangular block units with equal length, width, and height dimensions. For example, a planned space with a volume of 500m×500m×100m is divided into a 500×500×100 three-dimensional grid matrix, thereby establishing a 3D rectangular grid map environment model. The data structure of each grid includes a status label: free (value 0) or occupied (value 1).

[0016] When constructing environmental safety constraint boundaries, the minimum circumscribed sphere radius of the bounding box is calculated using the 3D CAD model of the current operating UAV as the minimum physical collision boundary distance. For example, for a certain type of multi-rotor UAV, the calculated circumscribed sphere radius is 0.6m. To resist crosswind disturbances and GPS positioning drift, a preset safety margin ranging from 0.5m to 1.5m is superimposed on this, for example, set to 0.8m, thus obtaining an environmental safety distance parameter of 1.4m. A no-fly zone will be constructed by expanding obstacles by 1.4m in the global grid map. Simultaneously, the UAV flight control system's underlying configuration protocol is retrieved to extract the maximum permissible yaw rate during UAV flight. For example, the extreme value of the turning yaw rate is set to 45° per second as a motion constraint parameter.

[0017] The latitude, longitude, and elevation data of the first takeoff and landing positions are parsed from the manually input inspection task sheet. A coordinate transformation algorithm is used to convert the coordinates from WGS84 to ECEF (Earth-centered rectangular coordinate system) and then to ENU (Earth-centered coordinate system) to a local northeast-northeast coordinate system with the takeoff point as the origin, resulting in three-dimensional spatial coordinates. For example, the starting point coordinates are mapped to [0.0, 0.0, 0.0] and the ending point coordinates to [350.0, 420.5, 50.0]. Combining the coordinates of all target inspection points in the inspection sheet, a three-dimensional planning space topology base with complete Euclidean metrics, obstacle avoidance envelope, and physical motion boundary constraints is constructed in memory.

[0018] S2: Based on the reachability relationships between inspection points and the distribution of obstacles, the three-dimensional planning space is segmented and weighted to generate candidate sampling points. The expansion direction of the tree node is determined based on the direction of the line connecting the current node and the candidate sampling points. The expansion criteria are constructed by combining the distance of the candidate sampling point to the neighboring obstacles, the current node's turning angle constraint, and the path cost from the node to the unvisited inspection point. Variable step size expansion is performed when the minimum turning radius, maximum climb gradient, and safety distance constraints of the UAV are met to generate the initial search tree. The newly generated nodes are then subjected to neighboring parent node optimization and reconnection operations to obtain the initial flight path covering all inspection points.

[0019] Based on the improved Fast Random Tree Algorithm (RRT) framework, a heuristic bias sampling strategy is adopted to calculate the Euclidean distance between the currently unvisited inspection point and the current search tree node. The distance value is used as a weight to adjust the random sampling function to generate candidate sampling points in the free grid. The expansion direction of the tree node is determined by calculating the normalized result of the three-dimensional vector from the current tree node to the candidate sampling point.

[0020] The KDTree data structure is used to quickly query the nearest obstacle distance in the vicinity of a candidate sampling point. A comprehensive cost function, including distance penalty, angle change penalty, and heuristic Manhattan distance cost, is established as the expansion criterion. The expected turning radius and expected ascent gradient formed by the current node and the expansion direction vector are calculated. When the expected turning radius is greater than the minimum turning radius, the expected ascent gradient is less than the maximum ascent gradient, and the nearest obstacle distance is greater than the environmental safety distance parameter, the expansion step size is adjusted according to the nearest obstacle distance, node generation is performed, and the newly generated node is added to the initial search tree.

[0021] Within the search radius set by KDTree, find all potential parent nodes of the newly generated node. Calculate the cumulative cost of reaching the newly generated node via potential parent nodes, and select the node with the smallest cumulative cost as the optimal parent node for connection. Traverse other nodes in the neighborhood. If the cumulative cost of reaching the node via the newly generated node decreases, and no collision occurs when the connection is detected using a straight-line intersection algorithm, disconnect the original parent node and reconnect the newly generated node as the new parent node. Repeat the above process until the search tree expands to all inspection points and the endpoint. Backtrack the node pointers to extract the initial route connecting the starting point, endpoint, and all inspection points.

[0022] In an optional embodiment, the step of segmenting and weighting the three-dimensional planning space based on the reachability relationships between inspection points and the distribution of obstacles to generate candidate sampling points includes: Divide the spherical search field of view at the current drone node into multiple three-dimensional view partitions to construct an exploration space set; Count the number of obstacle grids contained in each stereoscopic view zone; Add a preset constant to the number of obstacle grids and take the reciprocal to obtain the unobstructed passage rate of each stereoscopic view zone; Using the unobstructed passage rate as the sampling weight, a weighted random sampling strategy is used to extract three-dimensional coordinate points in each stereoscopic view partition to generate candidate sampling points.

[0023] When planning to any current UAV node, a spherical search field of view with a radius of 10.0m to 30.0m is set with the spatial coordinates of that node as the origin. For example, the field of view exploration radius is set to 20.0m. According to the dimensions of horizontal azimuth and vertical pitch angle, the spherical search space is divided into equal angles, preferably with an angle interval of 30° or 45°. For example, it is divided into 45° intervals horizontally and 45° intervals vertically. This constructs an exploration space set containing 32 stereoscopic view partitions, each partition corresponding to a three-dimensional cone-shaped search subset.

[0024] The previously constructed dilated raster map data is used, and a spatial ray casting traversal algorithm is employed to scan and count the actual number of obstacle grids within each stereoscopic viewpoint partition. To prevent overflow errors (denominator equal to zero) and to achieve a smooth probability distribution, a preset constant between 1 and 5 is added to the counted number of obstacle grids in each partition; for example, the preset smoothing constant is set to 2. The reciprocal of this sum is calculated to obtain the unobstructed passage rate for each stereoscopic viewpoint partition. For example, if 18 obstacle grids are counted in a forward partition, the unobstructed passage rate is 0.05; if another lateral partition is completely unobstructed (i.e., the number of grids is 0), the passage rate is 0.50.

[0025] After calculating the absolute unobstructed passage rate for all 32 partitions, the floating-point values ​​are globally normalized to a sum of 1, resulting in the standard probability quality function (PMF) used as the sampling weight for each partition. The engine employs a weighted random sampling strategy using a roulette wheel selection method, randomly throwing probability pointers based on the generated weight intervals. Since the weights are proportional to the passage rate, a pseudo-random number generator is activated within open and unobstructed view partitions, extracting random floating-point numbers in the X, Y, and Z dimensions as three-dimensional coordinate points, thereby generating a set of candidate sampling points with inherent obstacle avoidance advantages.

[0026] In an optional embodiment, the expansion criterion, which combines the distance to obstacles in the neighborhood of candidate sampling points, the current node's turning angle constraint, and the path cost from the node to unvisited inspection points, is used to perform variable step-size expansion to generate an initial search tree while satisfying the constraints of the UAV's minimum turning radius, maximum climb gradient, and safe distance. Calculate the straight-line distance from the candidate sampling point to the nearest obstacle boundary; Calculate the comprehensive evaluation cost of each candidate sampling point. The comprehensive evaluation cost is obtained by weighted summation of the reciprocal of the straight-line distance, the current node's corner constraint cost, and the heuristic path cost to the unvisited inspection point after normalization. The direction of the candidate sampling point with the lowest comprehensive evaluation cost is selected as the direction of tree node expansion. The expansion step size is calculated based on the preset initial baseline step size and the straight-line distance. A new node is generated along the expansion direction of the tree node with the expansion step size, and the new node is added to the initial search tree.

[0027] Using a KD-tree spatial index data structure, the expanded map is quickly retrieved for each candidate sampling point generated in the previous step. The absolute straight-line distance from each candidate point to the outer boundary of the nearest obstacle is calculated using the three-dimensional Euclidean distance formula. For example, the calculated distance for a candidate sampling point is 4.5m. The comprehensive evaluation cost J is calculated based on three core evaluation indicators: the first is the reciprocal of the straight-line distance to the obstacle, which constitutes the collision risk penalty; the second is the turning angle constraint cost of the line connecting the current node and the candidate sampling point relative to the previous flight segment, i.e., the absolute value of the yaw angle difference is calculated, and the cost increases if the turning angle reaches 30°; the third is the heuristic path cost from the current candidate point to the next unvisited target inspection point, using the straight-line Euclidean distance.

[0028] After obtaining the above three values, the Min-Max normalization method is used to map them to the interval [0,1], and preset weight factors of, for example, 0.3, 0.3, and 0.4 are assigned, as shown in the formula. A weighted summation calculation is performed. By traversing all candidate sampling points, the spatial orientation of the point with the smallest comprehensive evaluation cost J value is selected as the optimal tree node expansion direction for this random tree.

[0029] After determining the optimal expansion direction, a variable step size mechanism is used to set the initial baseline expansion step size to 1.0m to 5.0m, for example, a preferred baseline step size of 2.0m. An adjustment coefficient is constructed based on the previously calculated straight-line distance to the nearest obstacle in that direction. The adjustment formula is set as follows: when the nearest obstacle distance is greater than 5.0m, the step size is increased to 1.5 times the baseline step size, i.e., 3.0m, to accelerate crossing open areas; when the obstacle distance is reduced to within 3.0m, the expansion step size is reduced to 0.5 times the baseline step size, i.e., 1.0m. A new node coordinate is generated by extrapolating the calculated expansion step size along the optimal direction. During this process, the flight control equations are verified to ensure that the expanded connection does not exceed the minimum turning radius, such as 1.5m, and the maximum climb gradient, such as 0.3 (i.e., the ratio of altitude change to horizontal distance does not exceed the limit of 0.3) and the entire line is greater than the safe distance. After successful verification, the new node is added to the memory of the currently growing initial search tree. Figure 2 As shown, when in open airspace, the search convergence is accelerated by large step-size scaling; when approaching an obstacle entity, it switches to small step-size sensitive mode and follows the extended environmental redundancy no-fly safety virtual boundary contour to ensure safe obstacle avoidance under the premise of meeting the environmental safety distance parameters.

[0030] In an optional embodiment, the step of performing neighboring parent node selection and reconnection operations on the newly generated node to obtain an initial route covering all inspection points includes: Construct a neighborhood search space with the newly generated node as the center and the preset search radius as the radius; Nodes that already exist in the initial search tree within the neighborhood search space are selected to form a set of candidate parent nodes; Calculate the total path cost from the current segment starting point through each candidate parent node to the newly generated node; Select the candidate parent node with the minimum total path cost as the optimal parent node of the newly generated node, delete the original parent node connection of the newly generated node, and establish a connection between the newly generated node and the optimal parent node. Following the inspection sequence, the starting point of the UAV and each inspection point are taken as the starting point of the current segment. The above expansion and reconnection steps are repeated until the search tree reaches the next target point. The continuous node sequence between each segment starting point and the next target point is extracted and spliced ​​to obtain the initial flight path.

[0031] Each time the initial search tree completes the generation and mounting of a new node, a local path rewiring optimization mechanism is initiated. Using the 3D coordinates of the newly generated node as the center, a preset search radius between 5.0m and 15.0m is calculated and set. Preferably, this radius is determined according to... The optimal formula is calculated, where Here, N is the preset coefficient, and N is the current number of nodes. This represents the total number of nodes. If the current number of nodes is N, a radius of 12.0m is used to construct a spherical neighborhood search space in three-dimensional space. The system iterates through all existing historical nodes already included in the initial search tree within this spherical neighborhood and pulls them all into the candidate parent node set. For example, if nodes A, B, and C are all within a 12.0m radius, the search will find them.

[0032] The algorithm backtracks along the tree topology, using a distance accumulation algorithm to calculate the cumulative total spatial path cost from the segment starting point of the current planning task, through hierarchical paths in the tree, and via direct connections to each candidate parent node to the newly generated node. For example, the total distance to the new node via the original parent node is calculated to be 68.5m, while the total distance via the neighboring node B is reduced to 64.2m. Based on conditional judgment, the candidate node with the smallest absolute total path cost, i.e., node B with the aforementioned total cost of 64.2m, is selected as the optimal parent node of the newly generated node. The underlying pointer data is modified, removing the rigid connection topology between the newly generated node and the original parent node from the memory table, and instead establishing a directed tree connection between the new node and node B, thus straightening the local path.

[0033] Based on a manually set inspection log sequence list, the UAV's global takeoff point is used as the starting point of the first segment, with the target being the first inspection point. The first inspection point is then used as the starting point of the second segment, with the target being the second inspection point, and so on. Within each segment, the aforementioned directional expansion, neighborhood optimization, and reconnection steps are triggered in a high-speed loop until the spatial tolerance between the newly generated node of the search tree and the target point of the next stage is less than a preset convergence threshold, such as 0.5m, indicating that the current segment pathfinding is successful. Using Depth-First Search (DFS), the tree nodes are backtracked to extract a series of ordered and coherent 3D coordinate sequences connecting the beginning and end of each segment. These sequences are then concatenated in order to output a global initial polyline path that can pass through all necessary inspection points.

[0034] S3 divides the initial route into a smooth passage zone and a turning-sensitive zone based on the turning angle change and passage margin of each node. Node sparsification is performed on the smooth passage zone, and piecewise curve reconstruction is performed on the turning-sensitive zone based on the modified safety distance and curvature continuity constraints. The reconstructed route is discretized, redundant points are deleted, and feasibility is checked, outputting an autonomous UAV inspection route that satisfies the inspection sequence, obstacle avoidance constraints, and motion constraints.

[0035] The initial route is traversed to extract the three-dimensional coordinates of each node. The angle between adjacent line segments is calculated using the vector dot product inverse trigonometric function as the turning angle change. The distance to the nearest obstacle is subtracted from the environmental safety distance parameter to obtain the passage margin.

[0036] An angle threshold and a margin threshold are set. Based on these thresholds, the node and its immediate and adjacent nodes are classified into either a smooth passage zone or a transition sensitive zone. For the smooth passage zone, the Douglas-Pokal algorithm is used to remove collinear or nearly collinear intermediate nodes, achieving node sparsity. The Douglas-Pokal algorithm is a classic algorithm for simplifying curves or polylines. Its idea is to reduce the amount of data by removing redundant vertices while maintaining the overall shape. For the transition sensitive zone, a control vertex optimization model is used. Under the constraint of curvature continuity (greater than the corrected safety margin and continuous second derivative), a cubic B-spline curve interpolation algorithm is employed to generate a smooth transition three-dimensional spatial curve for piecewise curve reconstruction. Discrete trajectory points are extracted from the reconstructed B-spline flight path using the equal time step interpolation method. A greedy algorithm is called to delete redundant trajectory points on the curve whose Euclidean distance is less than the set minimum tolerance. The bounding box collision detection algorithm AABB is used to perform secondary interference checks and kinematic derivative calculations on all trajectory points and line segments to ensure that the yaw rate and acceleration do not exceed the limits and complete the feasibility verification. The three-dimensional coordinate sequence is output to the flight control system as the UAV's autonomous inspection flight path.

[0037] In an optional embodiment, dividing the initial route into a smooth traffic zone and a turning-sensitive zone based on the angle change and traffic margin corresponding to each node of the initial route includes: Three adjacent nodes in the initial route are selected sequentially to form two continuous route segments, and the included angle between the two continuous route segments is calculated as the change in turning angle. Calculate the straight-line distance from the current node to the nearest obstacle, and use the difference between the straight-line distance and the environmental safety distance parameter as the passage margin; Determine whether the change in the turning angle is greater than a preset angle threshold and whether the passage margin is less than a preset distance threshold; If so, the route segment formed by the current node and its adjacent nodes will be designated as a turning sensitive area. If not, the corresponding route segment will be designated as a smooth passage zone.

[0038] Following the coordinate sequence list of the generated global initial route, a sliding window with a span of 3 is set to extract any three adjacent discrete spatial nodes in sequence, and label them as follows. , , By performing vector subtraction, the inflow to the current node is constructed. spatial line segment vector ,Depend on point to and outflow nodes spatial line segment vector ,Depend on point to The inverse cosine formula is obtained by dividing the inner product of three-dimensional vectors by the product of their magnitudes. The actual geometric angle between two consecutive flight path segments in three-dimensional space is calculated, and this angle is used as the intermediate node. The current angle change parameter, for example, the calculated heading angle change is 28.5°.

[0039] At the same time, for intermediate nodes The spatial indexing module is invoked again to probe the surrounding area and calculate the shortest absolute straight-line distance from the 3D center point to the nearest obstacle grid boundary. For example, the distance measurement yields a value of 3.2m. The environmental safety distance parameter that has been frozen in the previous step is retrieved, for example, a fixed value of 1.4m. The calculated straight-line distance to the nearest obstacle is subtracted from this environmental safety distance to obtain the passage margin variable value representing the lateral drift tolerance of the flight path. For example, the calculated margin at this time is 1.8m.

[0040] After parameter extraction, a set of binary Boolean logic is set, where the preset angle threshold is optimized within a range of 15° to 30° (e.g., a preferred threshold of 20°), and the preset distance threshold is optimized within a range of 1.0m to 3.0m (e.g., a preferred threshold of 2.0m). An AND gate logic checks whether the current node's angle change is greater than 20° and whether the calculated clearance margin is less than 2.0. If both conditions return true, it indicates that the airspace requires aircraft to turn and there is a collision risk of being too close to the outer edge of an obstacle, and the node will be immediately... , and The local route segment defined by the three points is sliced ​​into data and labeled with the turning sensitive area attribute. Conversely, if any one condition is not met, the risk of the route is considered controllable, and the corresponding route segment is then classified as a smooth passage zone, thereby achieving decoupling and classification of the risk of the entire long inspection route.

[0041] In an optional embodiment, the node sparsification process performed on the smooth passage area includes: Within the smooth traffic zone, extract five consecutive adjacent nodes in sequence, and connect the first node and the last node to generate a benchmark verification line. Calculate the vertical distances from the three middle nodes to the reference verification line; Determine whether the vertical distances are all less than a preset straightness deviation threshold; If so, delete the three middle nodes, retain the connection route between the first and last nodes, and complete the node sparsification process in the smooth passage area.

[0042] For dense waypoint sequences labeled with transitive stable zones in the data structure, a dimensionality reduction and compression mechanism is employed. A slider queue of size 5 is used to continuously capture 5 adjacent 3D nodes along the temporal direction, and these nodes are labeled sequentially. , , , , This constitutes a local processing unit. Intermediate transition points are removed, and the first and second nodes of the queue are extracted. 3D coordinate data and last node The three-dimensional coordinate data is used to generate a reference line running from beginning to end, i.e., the benchmark verification line, in the three-dimensional virtual planning space through the equation connecting two points.

[0043] Using the formula for calculating the modulus of the three-dimensional distance vector from a point to a line in spatial geometry, the three middle nodes that are retained in the queue can be calculated. , , The distance from the aforementioned reference line to the spatial normal perpendicular projection. For example, after calculation, The perpendicular distance from the verification line is 0.12m. The perpendicular distance from the verification line is 0.15m. The vertical deviation from the calibration line is 0.08m. Prior to this, the operator will pre-program a straightness deviation threshold parameter representing the extreme value of tolerance for small oscillations into the configuration items. The reasonable value range is limited to the interval between 0.1m and 0.5m, for example, a threshold of 0.2m can be selected.

[0044] After distance calculation, concurrent judgment logic is implemented to compare whether the vertical distances obtained from the three intermediate nodes are all and uniformly less than the preset straightness deviation threshold of 0.2m. When the verification result is true, such as the example above where 0.12m, 0.15m, and 0.08m are all qualified, it proves that the local flight trajectory composed of 5 coordinates actually exhibits high spatial collinearity, which is a redundant fluctuation caused by the random tree growth process. In order to minimize the overhead of storing and issuing control commands on the UAV flight control motherboard, the underlying route list memory will be stored in... , , The three intermediate nodes execute the erase command, leaving only the starting point. Straight to the destination Long-span direct-connection flight line segments. As the sliding window advances point by point and is repeatedly cleaned and reorganized, it is possible to achieve large-scale sparse extraction of nodes within a large-scale stable airspace.

[0045] In an optional embodiment, the piecewise curve reconstruction of the inflection-sensitive region based on the modified safety spacing and curvature continuity constraint includes: On the intersecting line segments on both sides of the turning node within the turning sensitive area, points at positions a preset length from the turning node are respectively selected as curve control points. The corrected safety distance is obtained by adding a preset safety margin to the original environmental safety distance parameters; Using the curve control points and the corrected safety clearance as constraints, a third-order B-spline curve is used to perform continuous and smooth fitting calculations on the flight segment of the turning sensitive area. Replace the original broken line segment with the fitted third-order B-spline curve to complete the piecewise curve reconstruction.

[0046] For rigid corner segments in the data sequence that are identified as turning sensitive areas, the sharp central vertex that causes the large angle is identified as the turning node. On the three-dimensional straight segment entering and exiting the turning point, from... Begin reverse projection ranging towards both ends, selecting a segment of coordinates that meets a preset length threshold of 1.5m to 3.5m at each end, for example, selecting a position coordinate point with a cut-off length of 2.5m. Mark these two coordinate points as the first and second curve control points for initiating the flexible fitting equation. , and the control point of the last curve This isolates the acute-angled bend corner area from the air.

[0047] To address the potential risks of dynamic sideslip and trajectory divergence that may occur when drones traverse sharp turns at high speeds, a dedicated preset safety margin of 0.2m to 0.6m is added to the existing 1.4m environmental safety distance parameter. For example, an additional 0.4m is added to the preset safety margin. Through numerical accumulation, a corrected safety distance red line that meets the 1.8m collision avoidance standard is calculated, and a collision penalty circle of 1.8m is temporarily updated in the environmental matrix for local obstacles near the turning point.

[0048] Entering the mathematical fitting stage, based on the extracted first and last spatial control points... and As the clamping jaws for the start and end of the curve, and with the straight-line distance from any point on the fitted trajectory to surrounding obstacles not less than 1.8m as an insurmountable penalty inequality constraint. Substituting the above input quantities together into the condition... The curve is of the third order (k=3) with continuous curvature and no abrupt changes in order. It is defined in the B-spline basis function matrix iterative equation. A spatially smooth, differentiable 3D spline curve data set is generated using a basis function control point weighted mixing algorithm. The curve is then stripped from the initial global trajectory matrix, removing components containing... The coordinate group of the rigid triangular polyline segment is written into the new flexible coordinate set generated by high-density interpolation of third-order B-splines, thereby eliminating the control divergence caused by the UAV's kinematic over-limit in the sharp curve section and achieving smooth piecewise curve reconstruction.

[0049] This ablation experiment used a terrain region with a length, width, and height of 500m and 100m, randomly distributed with a dense grid of obstacles. The starting point coordinates were set as [0,0,0], and the ending point coordinates as [350,420.5,50]. The minimum physical outer radius of the UAV was 0.6m, the global environmental safety distance was maintained at 1.4m, and the maximum yaw rate was limited to 45° per second. The experiment was divided into three groups: a traditional 3D random tree baseline group without any optimization; a first variant group using only piecewise weighted sampling and variable step-size expansion strategies; a second variant group that added node sparsification to the smooth passage region based on the first variant group; and the complete scheme presented in this paper, which includes a third-order B-spline reconstruction strategy for the turning sensitive region. Each group underwent 100 pathfinding tests, and the average values ​​of various indicators were taken. The comparison results are as follows: Figure 3 As shown. The segmented weighted sampling and variable step-size expansion strategy proposed in this invention can reduce planning time by more than 50%; the node sparsification strategy in the stable passage area reduces the number of redundant trajectory nodes by more than 70% without increasing the computational load; the complete solution achieves smooth trajectory reconstruction while maintaining low computational load and low number of nodes, fully verifying the effectiveness and synergistic gains of each optimization module.

[0050] The baseline group had an average planning time of 11.6s, an average path length of 475.4m, and a total of 142 retained nodes, with abrupt changes in the trajectory. The first variant group reduced the planning time to 5.3s, shortened the path length to 438.5m, and reduced the number of nodes to 110. The second variant group, with a planning time of 5.4s, achieved a path length of 437.2m and reduced the number of retained nodes to 34. The complete solution group presented in this paper achieved a planning time of 5.8s, optimized the average total path length to 431.5m, stabilized the number of retained nodes at around 36, and smoothed out large turns greater than 20° in the flight segment, achieving smooth and continuous curvature throughout the entire flight segment while meeting the 1.8m corrected collision avoidance safety distance throughout. Segmented weighted sampling combined with a variable step size mechanism avoided high-density obstacle areas, improving planning efficiency by more than 54%. The node sparsity processing strategy in the smooth passage area reduced the UAV flight control waypoint storage load by approximately 69% without significantly affecting the total path length, thus reducing the latency of underlying command communication. Although the segmented curve smoothing reconstruction strategy for sensitive turning areas increases the time spent on mathematical fitting calculations by a very small amount, it eliminates the risk of dynamic overshoot caused by traditional rigid corners, avoids the sideslip and altitude loss problems that occur when the aircraft makes sharp turns at large angles, and improves the high-speed smoothness and obstacle avoidance operation safety factor of long-distance routes.

[0051] In the second embodiment, the present invention also proposes an autonomous unmanned aerial vehicle (UAV) inspection route planning system, comprising the following modules: The module is used to acquire boundary data of the inspection area, obstacle distribution information, inspection point set, UAV motion constraint parameters and environmental safety distance parameters, and construct a three-dimensional planning space including the UAV's starting point, ending point and all inspection points; The reconnection module is used to perform segmented weighted sampling of the 3D planning space based on the reachability relationships between inspection points and the distribution of obstacles, generate candidate sampling points, and determine the tree node expansion direction based on the direction of the line connecting the current node and the candidate sampling points. Combining the distance of the candidate sampling point to the neighboring obstacles, the current node's turning angle constraint, and the path cost from the node to the unvisited inspection point, the module constructs an expansion criterion. Under the constraints of the UAV's minimum turning radius, maximum climb gradient, and safe distance, the module performs variable step-size expansion to generate an initial search tree. The module then performs neighboring parent node optimization and reconnection operations on the newly generated nodes to obtain an initial flight path covering all inspection points. The output module is used to divide the initial route into a smooth passage zone and a turning sensitive zone based on the turning angle change and passage margin corresponding to each node of the initial route; it performs node sparsification processing on the smooth passage zone and reconstructs the segmented curves of the turning sensitive zone according to the modified safety distance and curvature continuity constraints; it discretizes the reconstructed route, deletes redundant points and verifies its feasibility, and outputs an autonomous inspection route of the UAV that meets the inspection sequence, obstacle avoidance constraints and motion constraints.

[0052] In an optional embodiment, the construction of a three-dimensional planning space including the drone's starting point, ending point, and all inspection points includes: The input 3D terrain data is divided into a cuboid cell array according to a preset step size to construct a 3D rectangular grid map environment model. Extract the minimum physical collision distance of the obstacle and add a preset safety margin to the distance as the environmental safety distance parameter; Extract the maximum permissible yaw rate of the UAV as the motion constraint parameter of the UAV; Extract the three-dimensional coordinates of the first takeoff position as the starting point of the UAV, and extract the three-dimensional coordinates of the landing position as the ending point.

[0053] In an optional embodiment, the step of segmenting and weighting the three-dimensional planning space based on the reachability relationships between inspection points and the distribution of obstacles to generate candidate sampling points includes: Divide the spherical search field of view at the current drone node into multiple three-dimensional view partitions to construct an exploration space set; Count the number of obstacle grids contained in each stereoscopic view zone; Add a preset constant to the number of obstacle grids and take the reciprocal to obtain the unobstructed passage rate of each stereoscopic view zone; Using the unobstructed passage rate as the sampling weight, a weighted random sampling strategy is used to extract three-dimensional coordinate points in each stereoscopic view partition to generate candidate sampling points.

[0054] In an optional embodiment, the expansion criterion, which combines the distance to obstacles in the neighborhood of candidate sampling points, the current node's turning angle constraint, and the path cost from the node to unvisited inspection points, is used to perform variable step-size expansion to generate an initial search tree while satisfying the constraints of the UAV's minimum turning radius, maximum climb gradient, and safe distance. Calculate the straight-line distance from the candidate sampling point to the nearest obstacle boundary; Calculate the comprehensive evaluation cost of each candidate sampling point. The comprehensive evaluation cost is obtained by weighted summation of the reciprocal of the straight-line distance, the current node's corner constraint cost, and the heuristic path cost to the unvisited inspection point after normalization. The direction of the candidate sampling point with the lowest comprehensive evaluation cost is selected as the direction of tree node expansion. The expansion step size is calculated based on the preset initial baseline step size and the straight-line distance. A new node is generated along the expansion direction of the tree node with the expansion step size, and the new node is added to the initial search tree.

[0055] In an optional embodiment, the step of performing neighboring parent node selection and reconnection operations on the newly generated node to obtain an initial route covering all inspection points includes: Construct a neighborhood search space with the newly generated node as the center and the preset search radius as the radius; Nodes that already exist in the initial search tree within the neighborhood search space are selected to form a set of candidate parent nodes; Calculate the total path cost from the current segment starting point through each candidate parent node to the newly generated node; Select the candidate parent node with the minimum total path cost as the optimal parent node of the newly generated node, delete the original parent node connection of the newly generated node, and establish a connection between the newly generated node and the optimal parent node. Following the inspection sequence, the starting point of the UAV and each inspection point are taken as the starting point of the current segment. The above expansion and reconnection steps are repeated until the search tree reaches the next target point. The continuous node sequence between each segment starting point and the next target point is extracted and spliced ​​to obtain the initial flight path.

[0056] In an optional embodiment, dividing the initial route into a smooth traffic zone and a turning-sensitive zone based on the angle change and traffic margin corresponding to each node of the initial route includes: Three adjacent nodes in the initial route are selected sequentially to form two continuous route segments, and the included angle between the two continuous route segments is calculated as the change in turning angle. Calculate the straight-line distance from the current node to the nearest obstacle, and use the difference between the straight-line distance and the environmental safety distance parameter as the passage margin; Determine whether the change in the turning angle is greater than a preset angle threshold and whether the passage margin is less than a preset distance threshold; If so, the route segment formed by the current node and its adjacent nodes will be designated as a turning sensitive area. If not, the corresponding route segment will be designated as a smooth passage zone.

[0057] In an optional embodiment, the node sparsification process performed on the smooth passage area includes: Within the smooth traffic zone, extract five consecutive adjacent nodes in sequence, and connect the first node and the last node to generate a benchmark verification line. Calculate the vertical distances from the three middle nodes to the reference verification line; Determine whether the vertical distances are all less than a preset straightness deviation threshold; If so, delete the three middle nodes, retain the connection route between the first and last nodes, and complete the node sparsification process in the smooth passage area.

[0058] In an optional embodiment, the piecewise curve reconstruction of the inflection-sensitive region based on the modified safety spacing and curvature continuity constraint includes: On the intersecting line segments on both sides of the turning node within the turning sensitive area, points at positions a preset length from the turning node are respectively selected as curve control points. The corrected safety distance is obtained by adding a preset safety margin to the original environmental safety distance parameters; Using the curve control points and the corrected safety clearance as constraints, a third-order B-spline curve is used to perform continuous and smooth fitting calculations on the flight segment of the turning sensitive area. Replace the original broken line segment with the fitted third-order B-spline curve to complete the piecewise curve reconstruction.

[0059] It should be understood that the various forms of processes shown above can be used to rearrange, add, or delete steps. For example, the steps described in this disclosure can be executed in parallel, sequentially, or in different orders, as long as the desired result of the technical solution disclosed in this disclosure can be achieved, and this is not limited herein.

[0060] The specific embodiments described above do not constitute a limitation on the scope of protection of this disclosure. Those skilled in the art should understand that various modifications, combinations, sub-combinations, and substitutions can be made according to design requirements and other factors. Any modifications, equivalent substitutions, and improvements made within the principles of this disclosure should be included within the scope of protection of this disclosure.

Claims

1. A method for autonomous inspection route planning by unmanned aerial vehicles (UAVs), characterized in that, include: Acquire the boundary data of the inspection area, obstacle distribution information, inspection point set, UAV motion constraint parameters and environmental safety distance parameters, and construct a three-dimensional planning space including the UAV's starting point, ending point and all inspection points; Based on the reachability between inspection points and the distribution of obstacles, the three-dimensional planning space is segmented and weighted for sampling to generate candidate sampling points. The expansion direction of the tree node is determined based on the direction of the line connecting the current node and the candidate sampling points. An expansion criterion is constructed by combining the distance of neighboring obstacles of candidate sampling points, the current node's turning angle constraint, and the path cost from the node to the unvisited inspection point. Variable step size expansion is performed while satisfying the constraints of the UAV's minimum turning radius, maximum climb gradient, and safe distance to generate an initial search tree. Neighboring parent node optimization and reconnection operations are performed on the newly generated nodes to obtain an initial flight path covering all inspection points. The initial route is divided into a smooth passage zone and a turning-sensitive zone based on the turning angle change and passage margin of each node. The smooth passage zone is processed by node sparsification, and the turning-sensitive zone is reconstructed into a segmented curve based on the modified safety distance and curvature continuity constraints. The reconstructed route is discretized, redundant points are deleted, and feasibility is checked to output an autonomous inspection route of the UAV that meets the inspection sequence, obstacle avoidance constraints, and motion constraints.

2. The method according to claim 1, characterized in that, The construction of the three-dimensional planning space includes the drone's starting point, ending point, and all inspection points, including: The input 3D terrain data is divided into a cuboid cell array according to a preset step size to construct a 3D rectangular grid map environment model. Extract the minimum physical collision distance of the obstacle and add a preset safety margin to the distance as the environmental safety distance parameter; Extract the maximum permissible yaw rate of the UAV as the motion constraint parameter of the UAV; Extract the three-dimensional coordinates of the first takeoff position as the starting point of the UAV, and extract the three-dimensional coordinates of the landing position as the ending point.

3. The method according to claim 1, characterized in that, The step of segmenting and weighting the three-dimensional planning space based on the reachability relationships between inspection points and the distribution of obstacles to generate candidate sampling points includes: Divide the spherical search field of view at the current drone node into multiple three-dimensional view partitions to construct an exploration space set; Count the number of obstacle grids contained in each stereoscopic view zone; Add a preset constant to the number of obstacle grids and take the reciprocal to obtain the unobstructed passage rate of each stereoscopic view zone; Using the unobstructed passage rate as the sampling weight, a weighted random sampling strategy is used to extract three-dimensional coordinate points in each stereoscopic view partition to generate candidate sampling points.

4. The method according to claim 2, characterized in that, The expansion criterion is constructed by combining the distance to obstacles in the neighborhood of candidate sampling points, the current node's turning angle constraint, and the path cost from the node to unvisited inspection points. Variable step size expansion is performed while satisfying the constraints of the UAV's minimum turning radius, maximum climb gradient, and safe distance, generating an initial search tree, including: Calculate the straight-line distance from the candidate sampling point to the nearest obstacle boundary; Calculate the comprehensive evaluation cost of each candidate sampling point. The comprehensive evaluation cost is obtained by weighted summation of the reciprocal of the straight-line distance, the current node's corner constraint cost, and the heuristic path cost to the unvisited inspection point after normalization. The direction of the candidate sampling point with the lowest comprehensive evaluation cost is selected as the direction of tree node expansion. The expansion step size is calculated based on the preset initial baseline step size and the straight-line distance. A new node is generated along the expansion direction of the tree node with the expansion step size, and the new node is added to the initial search tree.

5. The method according to claim 1, characterized in that, The process of selecting and reconnecting neighboring parent nodes for newly generated nodes to obtain an initial route covering all inspection points includes: Construct a neighborhood search space with the newly generated node as the center and the preset search radius as the radius; Nodes that already exist in the initial search tree within the neighborhood search space are selected to form a set of candidate parent nodes; Calculate the total path cost from the current segment starting point through each candidate parent node to the newly generated node; Select the candidate parent node with the minimum total path cost as the optimal parent node of the newly generated node, delete the original parent node connection of the newly generated node, and establish a connection between the newly generated node and the optimal parent node. Following the inspection sequence, the starting point of the UAV and each inspection point are taken as the starting point of the current segment. The above expansion and reconnection steps are repeated until the search tree reaches the next target point. The continuous node sequence between each segment starting point and the next target point is extracted and spliced ​​to obtain the initial flight path.

6. The method according to claim 1, characterized in that, The initial route is divided into a smooth traffic zone and a turning-sensitive zone based on the angle change and traffic margin corresponding to each node of the initial route, including: Three adjacent nodes in the initial route are selected sequentially to form two continuous route segments, and the included angle between the two continuous route segments is calculated as the change in turning angle. Calculate the straight-line distance from the current node to the nearest obstacle, and use the difference between the straight-line distance and the environmental safety distance parameter as the passage margin; Determine whether the change in the turning angle is greater than a preset angle threshold and whether the passage margin is less than a preset distance threshold; If so, the route segment formed by the current node and its adjacent nodes will be designated as a turning sensitive area. If not, the corresponding route segment will be designated as a smooth passage zone.

7. The method according to claim 1, characterized in that, The node sparsification process performed on the smooth traffic area includes: Within the smooth traffic zone, extract five consecutive adjacent nodes in sequence, and connect the first node and the last node to generate a benchmark verification line. Calculate the vertical distances from the three middle nodes to the reference verification line; Determine whether the vertical distances are all less than a preset straightness deviation threshold; If so, delete the three middle nodes, retain the connection route between the first and last nodes, and complete the node sparsification process in the smooth passage area.

8. The method according to claim 6, characterized in that, The segmented curve reconstruction of the transition sensitive area based on the modified safety distance and curvature continuity constraint includes: On the intersecting line segments on both sides of the turning node within the turning sensitive area, points at positions a preset length from the turning node are respectively selected as curve control points. The corrected safety distance is obtained by adding a preset safety margin to the original environmental safety distance parameters; Using the curve control points and the corrected safety clearance as constraints, a third-order B-spline curve is used to perform continuous and smooth fitting calculations on the flight segment of the turning sensitive area. Replace the original broken line segment with the fitted third-order B-spline curve to complete the piecewise curve reconstruction.

9. A drone autonomous inspection route planning system, characterized in that, Includes the following modules: The module is used to acquire boundary data of the inspection area, obstacle distribution information, inspection point set, UAV motion constraint parameters and environmental safety distance parameters, and construct a three-dimensional planning space including the UAV's starting point, ending point and all inspection points; The reconnection module is used to perform segmented weighted sampling of the 3D planning space based on the reachability relationship between inspection points and the distribution of obstacles, generate candidate sampling points, and determine the tree node expansion direction based on the direction of the connection between the current node and the candidate sampling points. An expansion criterion is constructed by combining the distance of neighboring obstacles of candidate sampling points, the current node's turning angle constraint, and the path cost from the node to the unvisited inspection point. Variable step size expansion is performed while satisfying the constraints of the UAV's minimum turning radius, maximum climb gradient, and safe distance to generate an initial search tree. Neighboring parent node optimization and reconnection operations are performed on the newly generated nodes to obtain an initial flight path covering all inspection points. The output module is used to divide the initial route into a smooth passage zone and a turning sensitive zone based on the turning angle change and passage margin corresponding to each node of the initial route; it performs node sparsification processing on the smooth passage zone and reconstructs the segmented curves of the turning sensitive zone according to the modified safety distance and curvature continuity constraints; it discretizes the reconstructed route, deletes redundant points and verifies its feasibility, and outputs an autonomous inspection route of the UAV that meets the inspection sequence, obstacle avoidance constraints and motion constraints.

10. The system according to claim 9, characterized in that, The construction of the three-dimensional planning space includes the drone's starting point, ending point, and all inspection points, including: The input 3D terrain data is divided into a cuboid cell array according to a preset step size to construct a 3D rectangular grid map environment model. Extract the minimum physical collision distance of the obstacle and add a preset safety margin to the distance as the environmental safety distance parameter; Extract the maximum permissible yaw rate of the UAV as the motion constraint parameter of the UAV; Extract the three-dimensional coordinates of the first takeoff position as the starting point of the UAV, and extract the three-dimensional coordinates of the landing position as the ending point.

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