Unmanned aerial vehicle differentiated search path planning method based on probability partitioning

Abstract

The invention relates to an unmanned aerial vehicle differentiated search path planning method based on probability partitioning, and belongs to the technical field of unmanned aerial vehicle autonomous navigation. The method comprises the following steps: firstly, generating a probability grid map according to target existence probability distribution data; then, dividing the map into a high-probability concentrated area and a low-probability dispersed area by adopting a weighted K-means clustering algorithm; for a high-probability concentrated area, a bow-shaped scanning path is used for realizing full coverage; for the low-probability dispersion region, dynamically selecting nodes by adopting a gain-first greedy strategy; then optimizing the path by using a 2-opt algorithm, and eliminating redundancy; and finally, through Clothoid curve smoothing processing, generating a flying trajectory which is continuous in curvature and conforms to the maneuvering constraint of the unmanned aerial vehicle. The method can effectively improve the search coverage rate and path efficiency, reduces redundant flight, and is suitable for tasks such as maritime search and rescue and area monitoring.

Description

Technical Field

[0001] This invention relates to the field of autonomous navigation and path planning technology for unmanned aerial vehicles (UAVs), and in particular to a UAV differentiated search path planning method based on probability partitioning. Background Technology

[0002] Due to their high mobility, flexible deployment, and low cost, drones have been widely used in various mission scenarios such as regional monitoring, search and rescue, disaster assessment, agricultural and forestry inspection, and border patrol. In these applications, efficient searching is often required in environments where the target's location is uncertain, in order to quickly locate the target or obtain regional information. The success of a search mission largely depends on the rationality and adaptability of the path planning.

[0003] Traditional UAV search path planning methods mainly include full-coverage path planning and probabilistic graph-based path planning. Full-coverage path planning methods (such as zigzag scanning) typically assume that targets are uniformly distributed within the task area, thus generating regular scanning paths. However, in practical applications, target distribution often exhibits significant spatial heterogeneity. This method does not consider probability differences, leading to unreasonable allocation of search resources, failure to prioritize the coverage of high-probability areas, and overall low search efficiency.

[0004] While probabilistic graphical path planning methods incorporate the probability of target existence, most fail to divide the probability distribution into regions, treating the entire region as a single entity. When the probability distribution exhibits a pattern of high-probability concentration and low-probability dispersion, the paths generated by these methods often contain numerous ineffective cross-regional transfers, resulting in long journeys, high time consumption, and difficulty in maximizing search performance under limited time and energy constraints.

[0005] Furthermore, existing methods, in the path geometry optimization stage, mostly focus only on shortening the path length, neglecting the physical and dynamic constraints of the UAV itself, such as minimum turning radius, maximum curvature, and rate of curvature change. The generated polyline path has discontinuous curvature at the nodes, which does not meet the smooth flight requirements of fixed-wing UAVs and other types of UAVs. In actual tracking, this can easily lead to problems such as control instability and large tracking errors, affecting mission safety and execution effectiveness.

[0006] Therefore, there is an urgent need in this field for a differentiated search path planning method that can adapt to the target probability distribution, rationally allocate search resources, and generate smooth trajectories that conform to the maneuver constraints of UAVs, so as to improve search efficiency and path flyability in uncertain environments. Summary of the Invention

[0007] Purpose of the invention: This invention aims to solve the problems of low search efficiency and unflyable paths in the prior art. By differentiating high and low probability areas and generating smooth trajectories that conform to the maneuver constraints of UAVs, it maximizes search efficiency within a limited time and range.

[0008] Technical solution: The present invention provides a method for differentiated search path planning for unmanned aerial vehicles based on probability partitioning, comprising the following steps:

[0009] S1. Search Space Probability Modeling and Discretization: Based on the target existence probability distribution data, a continuous probability field is generated through kernel density estimation and then rasterized to construct a probability raster map. The raster probability values ​​are normalized, and a probability threshold is set based on the cumulative distribution function to determine the effective probability region (i.e., the target probability region TPA).

[0010] S2. Adaptive Probability Region Partitioning Based on Weighted K-means: Using node spatial coordinates as clustering features and probability weights as weights, a weighted distance metric-based K-means clustering algorithm is employed to partition the region. The optimal number of clusters is adaptively determined using the silhouette coefficient method, dividing the search space into a high-probability concentrated region and several low-probability dispersed regions.

[0011] S3, Differentiated Path Generation:

[0012] For high-probability concentrated areas, a bow-shaped full-coverage scanning path is used to ensure no repeated traversal;

[0013] For low-probability dispersed areas, a gain-first greedy search strategy is adopted. The benefit-cost ratio of nodes is dynamically evaluated through the gain function, and high-gain nodes are iteratively selected for insertion into the path (the path initially includes the sub-region entry point and exit point).

[0014] S4. Path optimization and smoothing:

[0015] The 2-opt algorithm is used for local path optimization to eliminate path intersections and redundant segments; based on this, a Clothoid curve is used for smoothing to realize path inflection points. Continuous transition ensures that both the trajectory curvature and the rate of change of curvature meet the UAV maneuver constraints.

[0016] Beneficial effects: This invention is applicable to mission scenarios that require efficient searching of areas where the target location is uncertain, such as maritime search and rescue, regional monitoring, and disaster assessment. It can adaptively generate optimized search paths that meet the maneuver constraints of the UAV, such as the minimum turning radius and maximum curvature, based on the target probability distribution.

[0017] It has the following significant effects: 1. Improved search efficiency: By using probability partitioning and differentiated strategies, search resources are rationally allocated, increasing the probability of target discovery; 2. High path quality: 2-opt optimization shortens the flight distance, and Clothoid smoothing ensures the flightability of the path, enhancing tracking accuracy and safety; 3. Strong adaptability: Based on data-driven region partitioning, it adapts to different probability distribution patterns and has good versatility; 4. Great engineering application value: It provides a complete technical link from probability map to flightable trajectory, which is easy to implement. Attached Figure Description

[0018] Figure 1 is a flowchart of the overall process of the method of the present invention;

[0019] Figure 2 is a schematic diagram of the original probability grid distribution of the target presence in the search area;

[0020] Figure 3 is a schematic diagram of the cumulative probability curve after the search area is sorted by grid probability.

[0021] Figure 4 is a schematic diagram of the boundary of the Probability Region for Search Target (TPA);

[0022] Figure 5 is a flowchart of the probability region adaptive partitioning algorithm based on weighted K-means;

[0023] Figure 6 shows the number of clusters. With average profile coefficient A schematic diagram of the relationship curve;

[0024] Figure 7 is a schematic diagram of the high / low probability sub-region clustering results based on weighted K-means;

[0025] Figure 8 is a schematic diagram of a single-step node selection decision in the gain-first greedy search strategy.

[0026] Figure 9 is a schematic diagram comparing the path shape and total length before and after optimization by the 2-opt algorithm;

[0027] Figure 10 is a schematic diagram of the smooth transition of inflection points based on the three-segment Clothoid curve;

[0028] Figure 11 is a schematic diagram of the relationship between the curvature and arc length of the search path after Clothoid smoothing;

[0029] Figure 12 shows a simulation comparison of various search path planning algorithms (traditional full-area bow-shaped algorithm / low-probability grid bow-shaped algorithm / probability partitioning differentiation method).

[0030] Figure 13 shows the simulation comparison curves of the number of nodes covered by each search path planning algorithm and the cumulative flight length.

[0031] Figure 14 shows the relationship between the curvature of the UAV differentiated search path and the cumulative flight length based on probability partitioning;

[0032] Figure 15 shows the relationship between the rate of change of curvature of the UAV differentiated search path and the cumulative flight length based on probability partitioning. Detailed Implementation

[0033] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. These embodiments are implemented based on the technical solution of the present invention, but the scope of protection of the present invention is not limited to the following embodiments.

[0034] The implementation of this invention relies on a device with computing capabilities, such as a ground control station for an unmanned aerial vehicle (UAV) or a high-performance airborne computer. This device includes at least a processor, a memory, and a computer program stored in the memory. When the program is executed by the processor, it implements the various steps of the method described below. The core flow of this method is shown in Figure 1.

[0035] S1. Probabilistic Modeling and Discretization of the Search Space

[0036] The purpose of this step is to transform the prior probability distribution data of the target into a discretized search probability grid map that can be processed by a computer, providing input for subsequent path planning.

[0037] S11. Probability field modeling and normalization:

[0038] Data Input: Obtain the prior probability distribution data of the target's existence. This data can be the output of any model or observation that reflects the uncertainty distribution of the target in space.

[0039] Continuous probability field generation: If the input data is a discrete point set, a Gaussian kernel function is used to estimate the kernel density in order to reconstruct a smooth continuous probability density function. The Gaussian kernel function is... ,in To standardize the distance, Let be the spatial location vector of the probability to be estimated. For the discrete point set, the first The position vector of each point This is the smoothing coefficient. Kernel density estimation can transform a discrete point distribution into a spatially smooth, continuous probability distribution.

[0040] Rasterization and normalization: Dividing the region of interest for the task into sections with a side length of... A regular square grid. Grid side length. Based on the effective coverage radius of the drone's sensors To ensure coverage efficiency, the preferred settings are... Calculate each grid cell. Normalized probability weights This ensures that the sum of the probability weights of all grid cells is 1. A schematic diagram of the generated original probability distribution is shown in Figure 2.

[0041] S12. Determining the target probability region:

[0042] To focus search efforts, a probability threshold is determined based on the cumulative distribution function. This is to extract high-probability effective search regions. The specific steps are as follows:

[0043] S121. All grid cells are assigned their probability weights. Sort by size from largest to smallest.

[0044] S122, after sequential cumulative sorting Until the cumulative level accumulates and first reaches or exceeds the preset confidence level. Based on the requirements of the search task, it is usually taken (High-risk tasks such as personnel search and rescue may be set up) Low-risk tasks such as regional monitoring can be set up The cumulative probability curve corresponding to this process is shown in Figure 3.

[0045] S123, Find the smallest value in the current cumulative sequence. Let it be denoted as probability threshold. .

[0046] S124. Filter out all that meet the requirements. The grid, whose set constitutes the target probability region (TPA), is then used to determine the center point coordinates of these effective grids. and its probability weights (Right now ) form a valid set of nodes This serves as the input for subsequent path planning. A schematic diagram of the TPA boundary extraction results is shown in Figure 4.

[0047] S2. Adaptive partitioning of probability regions based on weighted K-means

[0048] This step aims to compile a set of valid nodes. The algorithm is divided into several spatially compact sub-regions with consistent probabilities to reduce the complexity of subsequent path planning. The overall flowchart of the algorithm is shown in Figure 5.

[0049] S21, Optimal Cluster Number Adaptive determination:

[0050] Adaptive determination of the optimal number of clusters using the silhouette coefficient method .

[0051] Profile coefficient calculation: for nodes ,remember Let it be the average distance to all other nodes in the same cluster. It is the average distance to all nodes in the nearest heterogeneous cluster. contour coefficient Defined as:

[0052]

[0053] Mean silhouette coefficient: for a given number of clusters Calculate the average silhouette coefficient of all nodes to obtain the average silhouette coefficient of the clustering result. .

[0054] Optimal Value selection: within the preset range Inside (usually) , (The specific amount can be adjusted according to the area of ​​the search region) for each candidate Perform a full weighted K-means clustering operation on the value and compute the corresponding... The final choice made Reaching the maximum value As the optimal number of clusters. and The relationship curve is shown in Figure 6.

[0055] S22, Weighted K-means clustering process:

[0056] Initialization: Initialization is performed using the K-means++ algorithm. Cluster centers are used to improve convergence and solution quality.

[0057] Node allocation: For each node Calculate its distance to all cluster centers Weighted distance :

[0058]

[0059] in, This is the weight adjustment coefficient, used to balance the influence of spatial distance and probability weights, and is usually taken as... . Node Assign it to the cluster center with the smallest weighted distance.

[0060] Central update: For each cluster Update its cluster centers according to the following formula. :

[0061]

[0062] This updated formula causes the cluster centers to shift towards areas with high probability of node density.

[0063] Iteration and Convergence: Repeat the node assignment and center update steps until the root mean square (RMS) of the position changes of all cluster centers is less than the preset convergence threshold. Or it may reach the maximum number of iterations.

[0064] Post-processing: The clustering results are smoothed at the boundaries and outliers are removed to ensure geographical continuity of each sub-region. Final output. Clusters The cluster with the highest average probability weight is identified as a high-probability concentrated region, while the rest are low-probability dispersed regions. A schematic diagram of the final clustering results is shown in Figure 7.

[0065] S3, Heuristic Path Generation and Local Optimization

[0066] Based on the characteristics of the sub-regions, different strategies are used to generate initial paths, which are then optimized.

[0067] S31. Generation of Differentiated Initial Paths:

[0068] High-probability concentrated areas: A bow-shaped full-coverage scanning path is adopted. Since the search space has been discretized into regular grids according to the coverage radius of the UAV sensor, this method directly connects the center points of each grid in the area sequentially. During connection, parallel straight line segments are generated along the direction of the grid rows (or columns), and the segments are connected end to end in a bow-shaped reciprocating sequence to form a continuous, non-repeating scanning path that can completely cover all grids in the area.

[0069] Low-probability dispersed areas: A gain-first greedy search strategy is adopted.

[0070] S311, Path Initialization: Path Initially, only the entry point of this sub-region is included. (The point on the sub-region boundary closest to the drone's starting point) and the exit point (The point at the boundary of the sub-region that is closest to the next sub-region to be searched).

[0071] S312. Definition of gain function: For candidate nodes and current path Define its gain function for:

[0072]

[0073] in, It is a tiny positive number set to avoid division by zero.

[0074] S313, Iterative Path Construction:

[0075] For each unvisited candidate node Calculate and insert it into the current path The increment of the total path length after all possible positions (between every two adjacent nodes) and find the way The smallest insertion position.

[0076] Calculate each candidate node Gain at the optimal insertion position .

[0077] Select the node with the highest gain. and insert it into such that The smallest path location.

[0078] Repeat the above steps until all nodes are inserted into the path. A diagram illustrating a single-step decision-making process is shown in Figure 8.

[0079] S32, Local Path Optimization (2-opt Algorithm):

[0080] The initially generated path is locally optimized to shorten the total flight distance.

[0081] Algorithm steps:

[0082] S321. Set the current path and its length .

[0083] S322, Traverse each pair of non-adjacent edges in the path. and ,in .

[0084] S323. Calculate the result if these two edges are swapped (disconnected and reconnected). and ), and simultaneously reverse the sub-path segments The new path obtained and its length .

[0085] S324, if If so, then accept the exchange, and , .

[0086] S325. Repeat steps S322 to S324, traversing all possible edge pairs until no swaps that shorten the path length are found in a single complete traversal. To reduce computation, a neighborhood constraint strategy can be used. The path comparison before and after optimization is shown in Figure 9.

[0087] S4. Track smoothing processing to meet flight constraints

[0088] S41. Calculation of mobility constraints:

[0089] Calculate the minimum turning radius based on the drone's performance parameters. and maximum permissible curvature .

[0090]

[0091] in, For the drone's flight speed, It is the acceleration due to gravity. This is the maximum roll angle.

[0092] At the same time, the maximum rate of change of curvature must be considered. Constraints, which are related to the maximum roll rate of the drone. Related: .

[0093] S42, Based on Clothoid Curve Continuous smoothing:

[0094] The optimized polygonal path is transformed into a smooth trajectory with continuous curvature. The curvature of the Clothoid curve (Euler spiral) is... With curve arc length Linear change: ,in is the constant rate of change of curvature.

[0095] Smoothing process: For each inflection point (node) in the original path, a three-segment Clothoid curve is used for smooth transition to achieve... Continuous (position, tangent direction, and curvature are all continuous). As shown in Figure 10.

[0096] First paragraph (entrance paragraph) The curvature increases linearly from 0 to .

[0097] Second paragraph (middle section) ): Curvature from Linear change to .

[0098] The third section (exit section) ): Curvature from It decreases linearly to 0.

[0099] Rate of change of curvature of the three curve segments Keep it constant. This is achieved by adjusting the arc length of each segment. and curvature boundary value ( This ensures that the smoothed curve and the straight line segment of the original path are connected at the point of intersection. Continuous, and the absolute value of curvature along the entire path is always less than [value missing]. The rate of change of curvature does not exceed Figure 11 shows a schematic diagram of the relationship between the curvature and arc length of the smoothed path.

[0100] Example 1:

[0101] To verify the effectiveness of this invention, in maritime search and rescue scenarios where target locations are uncertain and personnel survival time is limited, it is necessary to prioritize early search efficiency to improve the probability of survival while also considering overall coverage. The method of this invention is compared with two types of bow-shaped search schemes, defined as follows: 1. Traditional full-area bow-shaped search: No probability preprocessing is performed; a single bow-shaped scanning path is used for the entire task area, with no resource allocation optimization. 2. Full-area bow-shaped search by removing grids with lower weights: Low-probability grids are removed based on probability thresholds; for the remaining effective area, no probability partitioning is performed, and a single bow-shaped scan is directly used across the entire area. 3. The method of this invention: First, the effective area is divided into high-probability concentrated areas and low-probability dispersed areas using weighted K-means; high-probability areas are fully covered using a bow-shaped pattern, while low-probability areas use a gain-priority greedy strategy; then, redundancy is eliminated through 2-opt optimization, and the Clothoid curve ensures curvature continuity.

[0102] Search efficiency analysis:

[0103] Based on the measured data in Figure 12: the coverage rate of the traditional scheme is 58.1%, the scheme excluding low-probability cases is 88.1%, and the coverage rate of this method is 87.8%. Comparing this with the curves of the number of covered nodes and cumulative flight length in Figure 13, the following comparative analysis is performed from two dimensions: early-stage timeliness and overall growth rate.

[0104] 1. Traditional full-area bow-shaped search: The efficiency is lagging behind in all aspects; it does not consider the probability distribution of the target, and wastes a lot of resources in low-probability areas, resulting in slow coverage in the early stage and low coverage in the end; when the cumulative flight is 20km, the number of covered nodes is only 22, accounting for 6% of this method; and the final coverage rate is only 58.1%, which is far lower than the other two types of schemes, and does not meet the timeliness and coverage requirements of maritime search and rescue.

[0105] 2. Bow-shaped search excluding low-weight grids: Excellent coverage but insufficient efficiency in the early stages; By excluding low-probability grids, resource waste is avoided, and the final coverage rate is increased to 88.1%, which is 51.6% higher than the traditional solution, solving the resource waste problem of full-area scanning; However, only low-probability and non-probability partitions are excluded, and all retained areas are still scanned in a single bow-shaped pattern without priority differences, resulting in untimely coverage of high-value areas in the early stages; In the first 20km of flight, the number of nodes covered by this method is 374, while the other solution only covers 104 (the growth rate of this method in the early stages is 259.6% higher than that of the other solution).

[0106] 3. The method of this invention: prioritizing timeliness while considering overall coverage; although the final coverage rate of 87.8% is 0.3 percentage points lower than the low-probability elimination scheme, the initial coverage speed is significantly faster, and there is no plateau in the later growth period, which fully meets the core requirement of prioritizing timeliness in maritime search and rescue; In the early stage: after probability partitioning, high-probability concentrated areas are covered by a bow-shaped pattern to ensure no omissions, while low-probability scattered areas are covered by a gain-priority greedy strategy, prioritizing nodes with high probability weights and close to the current path (based on the gain function). (Filtering) to avoid invalid flights; during the first 40km of flight, this method has covered more than 60% of the nodes in the high-probability area; in the later stage: the 2-opt algorithm eliminates path intersections and redundancy, and after flying to 80km, this method still maintains a coverage node growth rate of 4 / km.

[0107] Path quality and flyability:

[0108] After smoothing with a Clothoid curve, the final trajectory generated by this method has continuous curvature, and both its curvature and rate of change of curvature strictly satisfy the UAV maneuver constraints, as shown in Figures 14 and 15. The curvature of the entire path is... rate of change of curvature It can be directly used in actual flight, avoiding the risk of control instability.

[0109] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for differentiated search path planning for unmanned aerial vehicles (UAVs) based on probability partitioning, characterized in that, Includes the following steps: S1. Based on the probability distribution data of the target existence, generate a probability grid map. Each grid cell in the probability grid map is assigned a normalized probability weight. Grid cells with probability weights greater than a set probability threshold are found to form valid nodes. S2. The weighted K-means clustering algorithm is used to adaptively divide the probabilistic raster map into regions, dividing the search space into a high-probability concentrated region and multiple low-probability dispersed regions. S3. For high-probability concentrated areas, a bow-shaped full-coverage scanning path is used for traversal; for the low-probability dispersed areas, an access path is generated based on a gain-first greedy search strategy. S4. Use the 2-opt algorithm to locally optimize the access path generated in step S3 to obtain the optimized path, eliminate path intersections and redundant segments, and shorten the total flight distance. S5. Smooth the optimized path using the Clothoid curve to generate a flyable trajectory with continuous curvature that satisfies the drone's maneuvering constraints.

2. The method as described in claim 1, characterized in that, The generation of the probabilistic raster map in step S1 includes: A continuous probability density function is generated from the probability distribution data of the target through kernel density estimation; the continuous probability field is discretized into a regular grid with fixed side lengths, and the normalized probability weights in each grid are statistically analyzed. The sum of the probability weights of all grids is 1.

3. The method as described in claim 1, characterized in that, The generation of the probabilistic raster map in step S1 further includes: A probability threshold is determined based on the cumulative distribution function, and grids with probability weights greater than the threshold are selected as valid search areas, wherein the probability threshold corresponds to a preset confidence level.

4. The method as described in claim 1, characterized in that, The weighted K-means clustering algorithm mentioned in step S2 includes: Using the spatial coordinates of nodes as clustering features and the probability weights of nodes as clustering features. As a weight, nodes are assigned using a weighted distance metric, where the weighted distance is calculated using the following formula: ； in, For node coordinates, The coordinates of the cluster centers This is the weight adjustment coefficient.

5. The method as described in claim 2, characterized in that, The region division in step S2 also includes: The optimal number of clusters is determined adaptively based on the silhouette coefficient, where the number of clusters is selected from a preset range by maximizing the average silhouette coefficient.

6. The method as described in claim 1, characterized in that, The bow-shaped full-coverage scanning path described in step S3 is generated using a reciprocating scanning method to ensure that high-probability concentrated areas are not traversed repeatedly.

7. The method as described in claim 1, characterized in that, The gain-first greedy search strategy described in step S3 includes: The gain function is defined as follows: ； in, The set of nodes on the current path. represents the probability weights of the candidate nodes. For the current path node, It is a small constant; during the path generation process, the node that maximizes the gain function is iteratively selected for insertion into the path.

8. The method as described in claim 1, characterized in that, The 2-opt algorithm described in step S4 includes: Traverse the edge pairs in the path. If swapping two edges can shorten the total path length, then perform the edge swapping operation and reduce computational complexity through a neighborhood restriction strategy.

9. The method as described in claim 1, characterized in that, The Clothoid curve smoothing process described in step S5 includes: The path inflection point is achieved by splicing three Clothoid curve segments. A continuous transition is achieved, where the curvature changes linearly with the arc length, ensuring that the curvature of the entire path does not exceed the maximum permissible curvature of the UAV, and that the rate of change of curvature does not exceed the maximum permissible rate of change of curvature of the UAV.

10. The method as described in claim 1, characterized in that, The UAV maneuver constraints mentioned in step S5 include the minimum turning radius and the maximum curvature. The minimum turning radius is calculated based on the UAV's flight speed, maximum roll angle, and gravitational acceleration, using the following formula: .

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