Unmanned aerial vehicle three-dimensional path planning method based on double-probability prediction double-direction tree optimization

Abstract

The application relates to the technical field of three-dimensional path planning, and discloses a three-dimensional path planning method for unmanned aerial vehicles based on double-probability prediction bidirectional tree optimization, which comprises the following steps: S1, establishing a three-dimensional space path evaluation space; S2, constructing a double-probability prediction evaluation mechanism; S3, generating a deterministic connected guiding path and performing bidirectional tree batch search; S4, implementing multi-stage path structure reconstruction; and S5, performing voxel-level continuous verification and determining a final path. The application aims to provide the three-dimensional path planning method for unmanned aerial vehicles based on double-probability prediction bidirectional tree optimization, form a three-dimensional path planning method for unmanned aerial vehicles which takes into account forward risk perception, bidirectional global search, local fine optimization and whole-process feasibility control, and finally obtain a three-dimensional path which is stably connected between a starting point and an ending point, has relatively low comprehensive risk, has reasonable path length, has stable turning change and has actual flight executability.

Description

Technical Field

[0001] This invention relates to the field of three-dimensional path planning technology, and more specifically, to a three-dimensional path planning method for unmanned aerial vehicles (UAVs) based on bidirectional tree optimization with dual-probability prediction. Background Technology

[0002] With the continued application of drones in low-altitude logistics, emergency inspection, facility monitoring, and aerial operations, their operating space is gradually shifting from open, regular, and simple environments to three-dimensional airspaces with complex structures, uneven risk distribution, and varied connectivity. Three-dimensional airspace maps can uniformly describe spatial location, obstacle distribution, traffic conditions, risk information, and altitude layer characteristics, serving as a crucial data foundation for drone three-dimensional path planning.

[0003] The goal of UAV 3D path planning is to generate a flight path that satisfies spatial constraints and has superior overall performance, given a known starting point, ending point, and 3D airspace map. Compared to 2D path planning, 3D path planning adds a height dimension, significantly expands the search state scale, and makes the connections between nodes more complex. During the planning process, the UAV not only needs to perform horizontal position transfers but also needs to adjust its ascent, descent, and heading based on the airspace structure and risk distribution. Therefore, under conditions where narrow passages, complex boundaries, partially enclosed areas, and high-risk clusters coexist, path search is prone to problems such as an increase in invalid extensions, local search stagnation, difficulties in connecting the starting and ending points, and unstable path quality.

[0004] Existing UAV path planning methods mainly include graph search-based path planning, sampling-based path planning, and intelligent optimization-based path planning. Graph search-based methods typically expand stepwise based on the adjacency relationships between discrete nodes, featuring a clear search process and stable results. However, in large-scale 3D airspace maps, they require maintaining a large amount of node information, resulting in high computational and storage requirements. Sampling-based methods generate random nodes in the search space and establish tree-like connections to construct paths, reducing the dependence on complete spatial traversal. However, their search performance is significantly affected by the sampling location, expansion direction, and inter-tree connection method. Intelligent optimization-based methods typically treat path nodes as variables to be optimized, adjusting the path structure through group iteration or random search. They possess strong nonlinear optimization capabilities, but the initial path quality, constraint handling methods, and parameter settings directly affect the convergence speed and final results.

[0005] In risk-guided path planning research, existing methods mainly focus on path evaluation based on obstacle threats, ground exposure risks, meteorological disturbances, and single risk maps, and incorporate relevant risk information as node costs, edge costs, or heuristic information into the search. Existing publicly available solutions have not yet formed a complete technical system that models static and dynamic risk probabilities separately and jointly guides bidirectional tree expansion through a forward-looking mechanism. Especially in the selection of candidate expansion directions, existing methods typically emphasize the immediate evaluation of the current node, candidate nodes, and local neighborhoods, lacking joint analysis of risk change trends in continuous areas ahead of the candidate direction. This makes the search process susceptible to the influence of local low-cost areas, making it difficult to identify high-risk clusters, narrow enclosed areas, and low-connectivity areas in advance.

[0006] In path post-processing, existing methods typically employ node deletion, shortcut connections, curve fitting, and control point adjustments to reduce path redundancy and improve geometry. However, path post-processing alters the original node positions and connections, potentially leading to newly generated line segments entering impassable areas. Some methods only validate the optimized path nodes, failing to continuously detect the complete space traversed by connecting line segments between nodes. This results in planning results that satisfy constraints at the discrete node level, but still may traverse obstacle boundaries and restricted areas at the line segment level.

[0007] Therefore, existing technologies still lack a unified technical connection between risk forward perception, global path construction, local path reconstruction and full-process constraint maintenance, making it difficult to simultaneously achieve high search efficiency, strong risk avoidance capability and stable path executability in complex 3D spatial maps.

[0008] Existing UAV 3D path planning technologies mainly revolve around spatial geometric obstacle avoidance, target-oriented search, and individual performance improvements. Their technical focus is usually on whether the path can reach the target location. A technical system has not yet been established that uses multi-source risk forward representation as the search driver and integrates the optimization of global path configuration and local path quality.

[0009] Existing solutions typically generate paths step-by-step based on pre-defined adjacency relationships, random sample distributions, and target distance information during path search. Their search decisions primarily depend on the current search state. Even when risk information is incorporated, it is mostly used as a path evaluation result or additional cost in the calculation, without directly affecting the growth direction of the search tree, candidate node selection, or end-to-end connection decisions. Therefore, the resulting path generation process is essentially still a geometrically reachable-driven search model, making it difficult to proactively predict the changing trends of static and dynamic risks in the foreground space, and also difficult to adjust search resources and path connection strategies in a timely manner based on risk distribution.

[0010] Existing UAV 3D path planning methods still have significant limitations in the application of complex 3D airspace maps. First, existing search strategies mostly determine the expansion direction based on the current node position, target distance, and local cost, lacking a joint assessment of changes in static and dynamic risks ahead of candidate directions. When the risk distribution exhibits significant clustering, abrupt changes, and non-uniformity, the search tree is easily misled by local low-cost areas, entering high-risk areas, low-connectivity areas, and narrow, closed areas, resulting in an increase in invalid nodes, repeated adjustments to the search direction, and wasted computational resources.

[0011] Secondly, traditional unidirectional search, uniform sampling, and fixed heuristic expansion methods do not adequately utilize the structural information of the three-dimensional spatial domain. In complex boundaries, narrow passages, and areas with dense obstacles, candidate nodes are prone to imbalanced distribution, resulting in a low effective expansion ratio. Establishing connections between the start and end points relies on numerous repeated attempts, leading to slow initial path discovery. The planning results are significantly affected by random sampling, making it difficult to balance search efficiency and solution stability.

[0012] Furthermore, the initial paths generated by existing methods often contain redundant nodes, local reversals, abrupt turns, and unnecessary altitude changes. Conventional node removal and curve smoothing methods primarily aim to shorten the path length, but they do not adequately consider path risks, obstacle proximity, turning variations, and the passability of connecting segments. The new segments formed after path adjustment may traverse impassable areas, improving the geometry of the optimized result, but failing to meet actual flight requirements.

[0013] Furthermore, some methods only perform collision detection on path nodes, without continuously detecting the complete voxel sequence traversed between adjacent nodes. Even if all path nodes are located in passable areas, the connecting lines between nodes may still overlap with obstacle boundaries or confined spaces, resulting in a lack of reliable spatial accessibility guarantees for the generated path. Summary of the Invention

[0014] The technical problem to be solved by this invention is to provide a UAV 3D path planning method based on bidirectional tree optimization with dual probability prediction, forming a UAV 3D path planning method that takes into account forward risk perception, bidirectional global search, local fine optimization and full-process feasibility control, and finally obtains a 3D path with stable connection between the start and end points, low overall risk, reasonable path length, smooth turning changes and actual flight feasibility.

[0015] The present invention achieves its objective by employing the following technical solution: The UAV 3D path planning method based on bidirectional tree optimization with dual-probability prediction includes the following steps: S1: Establish a three-dimensional spatial path evaluation space; S2: Construct a dual-probability prediction and evaluation mechanism; S3: Generate deterministic connectivity guidance paths and perform bidirectional tree batch search; S4: Implement multi-stage path structure restructuring; S5: Perform voxel-level continuous verification and determine the final path.

[0016] This method is designed for 3D airspace maps with complex connectivity structures and non-uniform risk distributions. It integrates static risk perception, dynamic risk perception, deterministic connectivity guidance, bidirectional batch tree search, multi-scale path reconstruction, and constrained stochastic optimization into a unified technical process, achieving high-quality generation of UAV 3D paths while maintaining consistency in spatial constraints.

[0017] This invention uses a 3D airspace map, a static risk probability field, a dynamic risk probability field, spatial traffic conditions, and the mission start and end points as basic inputs. The algorithm first analyzes the spatial connectivity and risk distribution characteristics in the 3D airspace, then constructs a dual-probability predictive evaluation mechanism, and performs a bidirectional tree batch search based on a deterministic connectivity-guided path. After obtaining the main path structure, it further implements strict shortcut compression, third-order voxel neighborhood corridor reconnection, and constrained path integral correction, finally outputting a UAV 3D path that meets the planning requirements through continuous voxel-level detection.

[0018] As a further limitation of this technical solution, the specific steps of S1 are as follows: S11: Extract the allowed path search area based on the spatial access status, and calculate the proximity relationship between each spatial location and the boundary of the restricted area to characterize the spatial safety redundancy of the candidate path near the complex boundary. S12: Incorporate path physical length, static and dynamic fusion risk, boundary proximity, height change and turning change into a unified evaluation system; For a candidate path P consisting of the task start point and the task end point, its comprehensive evaluation function is expressed as:

[0019]

[0020]

[0021] in: This represents a candidate path from the start point of the task to the end point of the task; Indicate candidate path The overall evaluation value; Represents the normalized path length cost of the candidate path; This represents the risk cost of normalized static-dynamic fusion of candidate paths; Represents the normalized boundary proximity cost of the candidate path; This represents the normalized cumulative height variation cost of the candidate path; Represents the normalized turning change cost of the candidate path; , , , and These represent the weights of the evaluation indicators.

[0022] As a further limitation of this technical solution, the specific steps of S2 are as follows: For the current search node and candidate expansion direction Multiple forward observation positions are set along this direction, and attenuation weights are configured according to the distance between the observation position and the current node. The static risk prediction value, dynamic risk prediction value, and biprobability comprehensive prediction value of the candidate direction are expressed as follows:

[0023] in: Indicates along the candidate direction The first One forward observation voxel; Represents the observation position mapping operator; Indicates the current search node Physical coordinates; This indicates the total number of observation positions set in front of the candidate direction; Indicates the forward observation position number; Indicates the physical interval between adjacent forward observation positions;

[0024] in: Indicates the first Distance attenuation weights for each forward observation position; This indicates the distance decay rate control parameter; This indicates the summation number in the attenuation weight normalization calculation;

[0025] in: Indicate candidate direction The static risk prediction value; Indicates the first k Distance attenuation weights for each forward observation position; and This represents the normalized static risk value;

[0026] in: Representing candidate directions Dynamic risk prediction value; This represents the normalized dynamic risk value;

[0027]

[0028] in: Indicate candidate direction The combined predictive value of the two probabilities; and These represent the combined weights of static risk and dynamic risk, respectively.

[0029] Multiple forward observation positions are set along the candidate expansion direction to obtain static and dynamic risk probabilities, respectively. Attenuation weights are configured based on the observation distance to form static risk prediction values, dynamic risk prediction values, and a combined prediction value based on both probabilities. The prediction results based on both probabilities directly participate in candidate node selection, expansion direction ranking, parent node selection, and edge evaluation. This transforms risk information from a post-path generation evaluation indicator into an active decision-making basis during the search process, thereby proactively avoiding high-risk clustering areas, areas of sudden risk changes, and areas with low connectivity.

[0030] As a further limitation of this technical solution, the specific steps of S3 are as follows: S31: First, analyze the voxel connectivity in the three-dimensional spatial domain, and then simultaneously perform deterministic connectivity expansion from the starting point and the ending point; S32: After the two ends of the connected wavefront establish a connection relationship, a connected guiding path that meets the spatial passage conditions is generated by backtracking. S33: Build a forward search tree and a backward search tree with the task start point and task end point as root nodes respectively; the algorithm adopts a batch candidate node generation mechanism; For each candidate node In its neighboring set of parent nodes, a multi-parent node competition is performed, and the node with the minimum overall expansion cost is selected as the optimal parent node of the candidate node, that is:

[0031] in: Indicates the candidate nodes to be connected; Indicates candidate nodes The set of candidate parent nodes within the neighborhood that satisfy the connection distance requirement and the continuous space constraint; Represents a set Any candidate parent node in; This represents the optimal parent node that minimizes the overall expansion cost. This indicates the search tree from the root node to the candidate parent node. The cumulative path cost; Indicates the connection node With candidate nodes The total cost of line segments; Indicates that by node Pointing to candidate nodes The direction of unit expansion; This represents the adjustment coefficient for the biprobability prediction term; Represents a node The parent node in the current search tree; Represents a node ,node With candidate nodes The resulting penalty for turning changes; The adjustment coefficient representing the penalty for changes in direction during turns; S34: The forward search tree and reverse search tree are expanded alternately in batches, and the size of candidate nodes and the range of inter-tree connections are dynamically adjusted according to the current connection status. The node pair with the lowest overall connection cost is selected to establish a dual-tree connection, that is:

[0032] in: This represents a forward search tree built with the task's starting point as the root node; This represents a reverse search tree built with the task endpoint as the root node; Represents a forward search tree Candidate successor nodes in; Represents a reverse search tree Candidate successor nodes in; and These represent the forward optimal succession node and the reverse optimal succession node determined when the overall succession cost is minimized, respectively. and Representing nodes respectively and nodes Physical coordinates; Indicates the physical distance between two candidate successor nodes; This indicates the maximum allowed connection distance for establishing a two-tree connection; Represents a node With nodes The set of finite voxels covered by the connecting line segments; This represents the voxel space that is allowed to pass through; This indicates that all voxels covered by the candidate continuation segment belong to the allowed passage space; This indicates the node reached from the starting point of the task along the forward search tree. The cumulative path cost; Represents a node The cumulative path cost to reach the task endpoint along the reverse search tree; This represents the comprehensive edge cost of the candidate continuation segment; This indicates the penalty for directional changes between the candidate continuation segment and the end segment of the forward tree and the end segment of the reverse tree, respectively. This represents the adjustment coefficient for the penalty term indicating a change in the direction of continuation.

[0033] Before performing a bidirectional tree search, the connectivity relationships in the 3D voxel space are simultaneously resolved from both the task start and end points. A deterministic connected skeleton satisfying spatial accessibility conditions is then generated backtrackingly to verify the spatial reachability between the start and end points and to provide a path structure reference for subsequent searches. Based on this, a forward search tree and a backward search tree are established with the task start and end points as root nodes, respectively. In each round, local expansion samples, connected skeleton neighborhood samples, quality bias samples, and spatial coverage samples are generated in batches. The optimal connection relationship of candidate nodes is determined through competition among multiple parent nodes. As the two search trees gradually approach each other, among candidate node pairs satisfying the continuity constraints of the connection distance and connecting segments, the optimal connection node pair is determined by comprehensively considering the cumulative cost on the start side, the cost of the connecting segments, the cumulative cost on the end side, and the change in the connection direction. This improves the effective expansion ratio in complex 3D space, the ability to traverse narrow passages, and the connection efficiency between the start and end points.

[0034] As a further limitation of this technical solution, the specific steps of S4 are as follows: S41: Perform cross-node connectivity analysis on non-adjacent nodes in the main path. S42: Construct a third-order voxel neighborhood corridor centered on the compressed path, and establish a third-order voxel neighborhood centered on the reference voxel node in the compressed path. The candidate displacement vector set, candidate reconnection nodes, and path reconnection acceptance conditions of the third-order voxel neighborhood are expressed as follows:

[0035] in: This represents the set of candidate voxel displacement vectors in the neighborhood of a third-order voxel. Represents a three-dimensional integer displacement vector in units of voxels; Represents a three-dimensional integer coordinate space; Represents the displacement vector The maximum value among the absolute values ​​of the three coordinate components; This indicates that the candidate displacement does not exceed three voxels along any of the three coordinate directions; This excludes zero displacement vectors that do not produce a change in position.

[0036] in: Indicates the number of candidate voxel shift vectors;

[0037] in: This represents the reference voxel node in the path segment to be optimized; Indicates the reference voxel node According to the candidate displacement vector The generated candidate reconnected voxel nodes;

[0038] in: and Indicates the endpoint numbers of a local path segment, and satisfies ; and These represent the beginning and end points of the original local path segment, respectively. This indicates that the original path contains nodes. To node The local path segment formed; Indicates that by node Candidate reconnection nodes and nodes The candidate reconnection path segments formed;

[0039] in: and Let each represent a finite set of voxels covered by one of the two candidate connecting segments; and These represent the comprehensive evaluation values ​​of the local path segments before and after reconnection; S42: Using intermediate nodes of the path as adjustable control points, multiple sets of random disturbance trajectories are generated within a limited space. Each set of candidate trajectories is comprehensively evaluated. Based on the relative performance between candidate trajectories, exponential weights are constructed to update the control point positions in a weighted manner. No. The current control point in the wheel path integral correction is Multiple sets of candidate control points are generated through random perturbation, and exponential weights are calculated from candidate trajectories that satisfy continuous spatial constraints. The relationship between candidate control point generation and weighted update is expressed as follows:

[0040]

[0041] in: This indicates the total number of control points contained in the current path. and They represent the first The starting and ending points of the task path; Indicates the internal control point number; This represents the total number of candidate trajectories generated in each round; Indicates the candidate trajectory number; Indicates the first The control point applies the first control point. Candidate control points generated after a group of random perturbations; Indicates the first The action of the wheel on the first The first control point A set of random perturbation vectors; This indicates that the mean vector is zero and the covariance matrix is... The multivariate normal distribution; Indicates the first The covariance matrix of the random perturbation; Represents a locally effective location mapping operator;

[0042] in: Indicates the first Wheel by the first The candidate trajectory is formed by a group of candidate control points and a fixed task start and end point; and Let represent the task start point and task end point of the path in the r-th round, respectively, and keep them fixed during the path integral correction process;

[0043] in: Representing candidate trajectories The results of the continuous feasibility assessment; Indicates the first The set of valid candidate trajectory numbers that pass continuous feasibility testing at the voxel level during the round;

[0044] in: This represents the minimum comprehensive evaluation value among the valid candidate trajectories in the r-th round; This represents the k-th valid candidate trajectory in the r-th round. The overall evaluation value;

[0045] in: Indicates the first The path integral temperature parameter of the wheel; Indicates the first Normalized exponential weights of the valid candidate trajectories; This represents the candidate trajectory summation number in the exponentially weighted normalized denominator; Indicates the first r Round l Valid candidate trajectories The overall evaluation value;

[0046]

[0047] in: This represents the weighted calculation based on all valid candidate control points. Update control points in rounds.

[0048] The main path generated by the bidirectional tree search is sequentially subjected to strict shortcut compression, third-order voxel neighborhood corridor reconnection, and constrained path integral correction. Strict shortcut compression is used to remove intermediate redundant nodes; the third-order voxel neighborhood uses 342 candidate voxel displacement vectors to generate candidate reconnection nodes to correct local detours, backtracking structures, and unnecessary height changes; constrained path integral correction updates the control point positions through random perturbation, effective candidate trajectory screening, and exponential weighting. Each stage is updated only when the candidate path satisfies the continuous passage constraint and the overall evaluation is improved, thus achieving a progressive optimization from path topology compression and local discrete reconstruction to fine-tuning of control points.

[0049] As a further limitation of this technical solution, the specific steps of S5 are as follows: The path to be verified is , Indicates the total number of nodes contained in the path; Indicates the first in the path The voxel-level continuity feasibility determination function for path nodes and complete connecting line segments between nodes is expressed as:

[0050]

[0051] in: Represents any voxel to be determined; Indicates the allowed voxel space Indicator function, when voxel belong The value is 1 when the voxel is... Not belonging to The value is 0 at that time;

[0052] in: Indicates adjacent path nodes and The set of finite voxels successively covered by the connecting line segments; Represents a set Any covering voxel in; Indicates the path to be verified The results of the voxel-level continuous feasibility assessment; when When the path to be verified is deemed to meet the voxel-level continuous feasibility requirement; when If the path to be verified does not meet the voxel-level continuous feasibility requirement, it is determined that the path to be verified does not meet the requirement.

[0053] Compared with related technologies, the UAV 3D path planning method based on bidirectional tree optimization with dual-probability prediction provided by this invention has the following beneficial effects: (1) The bidirectional tree optimization algorithm proposed in this invention uses the joint prediction of static risk probability and dynamic risk probability to comprehensively evaluate the risk changes of candidate expansion directions and their front regions, guiding the search process to avoid high-risk and low-connectivity regions; it improves the path connection efficiency and global search capability in complex three-dimensional space through bidirectional expansion of the starting tree and the ending tree; it reduces path redundancy and improves local geometry and turning characteristics through path compression, voxel neighborhood reconnection and constrained path integral correction; and it performs unified voxel-level feasibility detection on path nodes and connecting line segments between nodes during path expansion, tree connection and local optimization to prevent the optimized path from crossing impassable areas.

[0054] (2) Advantages of proactive risk avoidance through dual-probability forward perception: Existing methods typically determine the search direction based on the immediate risks of the current node, candidate nodes, or local neighborhood, making it difficult to identify risk concentration areas and risk mutation areas ahead of the candidate direction in advance. This invention evaluates the continuous risk changes of candidate directions before path node expansion by independently representing static and dynamic risk probabilities and jointly forward predicting them. The dual-probability prediction results are directly used for node screening, parent node selection, and edge evaluation, transforming risk information from a passive evaluation basis after path generation into proactive decision-making information during the search process. This helps reduce the probability of the search tree entering high-risk and low-connectivity areas.

[0055] (3) Advantages of efficient and stable search with enhanced connectivity priors: Existing unidirectional search or uniform random sampling methods do not make sufficient use of the connectivity structure and existing path information in the three-dimensional spatial domain, and are prone to generating a large number of invalid samples in narrow channels, complex boundaries and areas with dense obstacles. This invention first generates a deterministic connectivity skeleton to provide reachability verification and path structure reference for bidirectional tree search; then, by combining the generation of multiple types of batch candidate nodes, competition among multiple parent nodes and determination of comprehensive succession cost, path connections are collaboratively established from the starting point and the ending point of the task, thereby improving the utilization rate of effective candidate nodes, the probability of bi-tree succession and the ability to traverse complex channels, and reducing the dependence of initial path discovery on random sampling results.

[0056] (4) Advantages of multi-scale progressive optimization for improving path quality: Existing path post-processing methods mainly aim to reduce the number of nodes or shorten the path length, easily ignoring path risks, boundary proximity, altitude changes, and the passability of connecting segments. This invention employs strict shortcut compression, third-order voxel neighborhood corridor reconnection, and constrained path integral correction in sequence to progressively optimize the path topology, local configuration, and control point positions, and simultaneously verifies the complete voxel sequence covered by path nodes and connecting segments between nodes at each stage. Only when the candidate path meets the continuous passability constraint and the overall evaluation is improved is it accepted for updating, thereby reducing path redundancy, local detours, abrupt turns, and unnecessary altitude changes, and preventing optimized connecting segments from crossing impassable areas, ensuring that the final path has good continuous feasibility and actual flight execution conditions. Attached Figure Description

[0057] Figure 1 This is a schematic diagram of the method flow of the present invention. Detailed Implementation

[0058] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0059] The UAV 3D path planning method based on bidirectional tree optimization with dual probability prediction constructs a dual probability prediction mechanism using static risk probability and dynamic risk probability. Before node expansion, the risk distribution ahead of the candidate direction is jointly evaluated, enabling the search tree to avoid high-risk clustering areas and low connectivity areas in advance, reducing ineffective expansion caused by insufficient local information.

[0060] This method employs a bidirectional growth search structure with both a starting tree and an ending tree, combined with deterministic connectivity guidance and a batch candidate node screening mechanism, to improve the utilization rate of effective samples and the probability of inter-tree connections. Compared to traditional methods that rely on uniform random sampling, this method can more fully utilize the connectivity structure and risk distribution information in the three-dimensional spatial domain, shorten the initial path establishment process, and enhance the search stability in complex spaces.

[0061] After path generation, strict path compression, voxel neighborhood reconnection, and constrained path integral correction are sequentially applied to address redundant nodes, local reversals, and abrupt turns in stages. Each stage uses path length, risk level, obstacle proximity, and turning changes as evaluation criteria to improve path geometry while preventing path adjustments from deviating from the allowable passage space.

[0062] Furthermore, voxel-level continuous detection is performed on the complete connecting segments between path nodes and adjacent nodes, and this detection mechanism is embedded in key processes such as node expansion, inter-tree connection, path reconnection, and path correction, thereby effectively preventing newly generated segments from crossing impassable areas.

[0063] A UAV 3D path planning method is developed, which has forward risk prediction capability, bidirectional efficient connection capability, phased path reconstruction capability and continuous spatial detection capability. Ultimately, a 3D path with low overall risk, reasonable path length, smooth turning changes, appropriate obstacle spacing and actual flight feasibility is obtained.

[0064] This invention includes the following steps: S1: Establish a three-dimensional spatial path evaluation space.

[0065] The specific steps of S1 are as follows: Read the three-dimensional airspace map and its corresponding static risk probability field, dynamic risk probability field and spatial passage status to determine the starting point and ending point of the UAV mission, and establish the correspondence between the three-dimensional airspace location, risk attributes and passage attributes.

[0066] S11: Extract the allowed path search area based on the spatial access status, and calculate the proximity relationship between each spatial location and the boundary of the restricted area to characterize the spatial safety redundancy of the candidate path near the complex boundary. S12: Incorporate path physical length, static and dynamic fusion risk, boundary proximity, height change and turning change into a unified evaluation system; For a candidate path P consisting of the task start point and the task end point, its comprehensive evaluation function is expressed as:

[0067]

[0068]

[0069] in: This represents a candidate path from the start point of the task to the end point of the task; Indicate candidate path The overall evaluation value; Represents the normalized path length cost of the candidate path; This represents the risk cost of normalized static-dynamic fusion of candidate paths; Represents the normalized boundary proximity cost of the candidate path; This represents the normalized cumulative height variation cost of the candidate path; Represents the normalized turning change cost of the candidate path; , , , and These represent the weights of the evaluation indicators; each evaluation item has been dimensionless, and each weight is a non-negative number with a sum of 1. The smaller the value, the better the overall evaluation result of the candidate path.

[0070] This evaluation system runs through the candidate node selection, tree edge connection, double tree continuation, path reconnection and path correction processes, so that each stage uses consistent performance criteria and avoids using mutually exclusive optimization objectives in different processing links.

[0071] This step is not simply about reading map data, but about transforming the geometric structure, risk attributes, and connectivity attributes of the three-dimensional spatial domain into a structured evaluation space that can directly drive path search, providing a unified and high-resolution decision-making basis for subsequent algorithms.

[0072] S2: Construct a dual-probability prediction and evaluation mechanism.

[0073] The specific steps of S2 are as follows: To address the issue of insufficient response to changes in forward risks in traditional node expansion mechanisms, this invention extracts both static and dynamic risk probabilities to establish a dual-probability predictive evaluation mechanism. For the current search node... and candidate expansion direction Multiple forward observation positions are set along this direction, and attenuation weights are configured according to the distance between the observation position and the current node. The static risk prediction value, dynamic risk prediction value, and biprobability comprehensive prediction value of the candidate direction are expressed as follows:

[0074] in: Indicates along the candidate direction The first One forward observation voxel; Represents the observation position mapping operator; Indicates the current search node Physical coordinates; This indicates the total number of observation positions set in front of the candidate direction; Indicates the forward observation position number; Indicates the physical interval between adjacent forward observation positions;

[0075] in: Indicates the first Distance attenuation weights for each forward observation position; This indicates the distance decay rate control parameter; This indicates the summation number in the attenuation weight normalization calculation;

[0076] in: Indicate candidate direction The static risk prediction value; Indicates the firstk Distance attenuation weights for each forward observation position; and This represents the normalized static risk value;

[0077] in: Representing candidate directions Dynamic risk prediction value; This represents the normalized dynamic risk value;

[0078]

[0079] in: Indicate candidate direction The combined predictive value of the two probabilities; and These represent the fusion weights for static and dynamic risks, respectively. Both are non-negative and their sum is 1. When a forward observation position exceeds the path search area or cannot be mapped to a valid voxel, the corresponding candidate expansion direction is determined as an invalid direction and will not participate in subsequent node selection.

[0080] Static risk reflects the persistent risk formed by fixed spatial elements, while dynamic risk reflects the time-varying risk that changes with operational status. The two types of risk are characterized independently and jointly analyzed during the candidate expansion decision-making stage.

[0081] The algorithm assigns differentiated priorities to different expansion directions based on the risk level, risk gradient, and continuous risk distribution characteristics ahead of the candidate directions. When a candidate direction points to a risk concentration area, a risk increase area, or a region with weak connectivity, the retention probability of the corresponding candidate node is reduced; when a candidate direction has a low risk level, sufficient spatial redundancy, and better target approach characteristics, the search priority of the corresponding expansion direction is increased.

[0082] The biprobabilistic prediction results directly participate in candidate node generation, parent node selection, edge evaluation, and dual-tree continuation determination, transforming risk information from traditional post-hoc path evaluation parameters into proactive decision-making information during the search process. This enables risk direction identification before the path structure is formed, significantly reducing the scale of ineffective searches in high-risk areas and improving direction selection accuracy in complex risk fields.

[0083] S3: Generate deterministic connectivity bootstrap paths and perform bidirectional tree batch search.

[0084] The specific steps of S3 are as follows: S31: Before formally executing the bidirectional tree search, the present invention first parses the voxel connectivity in the three-dimensional spatial domain and simultaneously carries out deterministic connectivity expansion from the starting end and the ending end. S32: After the two ends of the connected wavefront establish a connection relationship, a connected guiding path that meets the spatial passage conditions is generated by backtracking. This connectivity guidance path is used to verify the spatial reachability between the task start and end points and to provide a prior path skeleton for subsequent bidirectional tree search. Its purpose is not to directly replace the final optimized path, but rather to provide a stable connectivity reference for random search, reducing the uncertainty arising from relying entirely on random samples to find initial solutions in complex and narrow spaces.

[0085] S33: Build a forward search tree and a backward search tree with the task start point and task end point as root nodes respectively; the algorithm adopts a batch candidate node generation mechanism, and in each round, it simultaneously constructs local expansion samples, guiding path neighborhood samples, quality bias samples and spatial coverage samples; Local expansion samples are used to enhance the fine search around the current dominant tree branch; guide path neighborhood samples are used to maintain the consistency between the search direction and the known connectivity structure; quality bias samples are preferentially distributed in spatial regions with lower risk, larger boundary spacing and better overall evaluation; spatial coverage samples are used to maintain the search domain exploration capability and prevent the search process from prematurely focusing on a single local region.

[0086] For each candidate node In its neighboring set of parent nodes, a multi-parent node competition is performed. Taking into account the cumulative path cost from the current search tree root node to the candidate parent node, the candidate connection edge cost, the biprobability prediction value of the candidate direction, and the continuity of path turns, the node with the minimum comprehensive expansion cost is selected as the optimal parent node of the candidate node.

[0087] in: Indicates the candidate nodes to be connected; Indicates candidate nodes The set of candidate parent nodes within the neighborhood that satisfy the connection distance requirement and the continuous space constraint; Represents a set Any candidate parent node in; This represents the optimal parent node that minimizes the overall expansion cost. This indicates the search tree from the root node to the candidate parent node. The cumulative path cost; Indicates the connection node With candidate nodes The line segment comprehensive cost is calculated based on path length, static and dynamic fusion risk, boundary proximity, and height variation. Indicates that by node Pointing to candidate nodes The direction of unit expansion; This represents the adjustment coefficient for the biprobability prediction term; Represents a node The parent node in the current search tree; Represents a node ,node With candidate nodes The resulting penalty for turning changes; The adjustment coefficient representing the penalty for changes in direction during turns; The connecting line segment between the candidate node and the parent node must pass the continuous space test and be included in the search tree only after meeting the conditions.

[0088] S34: The forward search tree and reverse search tree expand alternately in batches, and the size of candidate nodes and the range of inter-tree connections are dynamically adjusted according to the current connection state. As the forward search tree and the reverse search tree gradually approach each other, the algorithm, among the candidate node pairs that satisfy the continuity distance constraint and the complete connection segment passage constraint, comprehensively considers the cumulative cost at the starting point, the cost of the candidate continuity segment, the cumulative cost at the ending point, and the directional change of the continuity position, and selects the node pair with the minimum comprehensive continuity cost to establish a dual-tree continuity, that is:

[0089] in: This represents a forward search tree built with the task's starting point as the root node; This represents a reverse search tree built with the task endpoint as the root node; Represents a forward search tree Candidate successor nodes in; Represents a reverse search tree Candidate successor nodes in; and These represent the forward optimal succession node and the reverse optimal succession node determined when the overall succession cost is minimized, respectively. and Representing nodes respectively and nodes Physical coordinates; Indicates the physical distance between two candidate successor nodes; This indicates the maximum allowed connection distance for establishing a two-tree connection; Represents a node With nodes The set of finite voxels covered by the connecting line segments; This represents the voxel space that is allowed to pass through; This indicates that all voxels covered by the candidate continuation segment belong to the allowed passage space; This indicates the node reached from the starting point of the task along the forward search tree. The cumulative path cost; Represents a node The cumulative path cost to reach the task endpoint along the reverse search tree; This represents the comprehensive edge cost of the candidate continuation segment; This indicates the penalty for directional changes between the candidate continuation segment and the end segment of the forward tree and the end segment of the reverse tree, respectively. This represents the adjustment coefficient for the penalty term indicating a change in the direction of succession. When the optimal succession node pair satisfies the continuous space constraint, the algorithm completes the dual-tree succession and backtracks the forward search tree and the reverse search tree respectively to generate a succession tree starting from the task origin. , The main path to the end of the mission.

[0090] This search structure combines deterministic connectivity priors with probabilistic sampling search, significantly enhancing effective sample utilization, bi-tree continuation probability, and the ability to traverse complex pathways while retaining full-space exploration capabilities. For narrow connected regions and irregular boundary regions, this mechanism maintains strong search stability and reduces the sensitivity of initial path discovery to random sampling results.

[0091] S4: Implement multi-stage path structure reconstruction.

[0092] The specific steps of S4 are as follows: The main path generated by bidirectional tree search has established an effective connection between the start and end points, but its node distribution is still affected by the sampling process. To further improve the quality of the path structure, this invention sequentially implements strict shortcut compression, third-order voxel neighborhood corridor reconnection, and constrained path integral correction.

[0093] S41: Perform cross-node connection analysis on non-adjacent nodes in the main path, use a strict shortcut compression method to extract the complete spatial location covered by candidate direct connection segments, verify their traffic status, and compare the comprehensive path evaluation before and after direct connection. When a candidate direct connection can reduce path redundancy without reducing spatial safety redundancy, delete intermediate redundant nodes to form a more compact path skeleton.

[0094] S42: Construct a third-order voxel neighborhood corridor centered on the compressed path. This neighborhood forms 342 candidate voxel displacement vectors in 3D space, which can break through the directional limitations of traditional local adjustments of adjacent voxels, providing more sufficient spatial reconstruction degrees of freedom for path segments. The third-order voxel neighborhood is established centered on the reference voxel node in the compressed path. The set of candidate displacement vectors, candidate reconnection nodes, and path reconnection acceptance conditions of the third-order voxel neighborhood are expressed as follows:

[0095] in: This represents the set of candidate voxel displacement vectors in the neighborhood of a third-order voxel. Represents a three-dimensional integer displacement vector in units of voxels; Represents a three-dimensional integer coordinate space; Represents the displacement vector The maximum value among the absolute values ​​of the three coordinate components; This indicates that the candidate displacement does not exceed three voxels along any of the three coordinate directions; This excludes zero displacement vectors that do not produce a change in position.

[0096] in: This indicates the number of candidate voxel displacement vectors. After excluding zero vectors, a total of 342 candidate voxel displacement vectors are obtained.

[0097] in: This represents a reference voxel node in the path segment to be optimized, and its coordinates are represented using voxel index coordinates. Indicates the reference voxel node According to the candidate displacement vector The generated candidate reconnected voxel nodes;

[0098] in: and Indicates the endpoint numbers of a local path segment, and satisfies ; and These represent the beginning and end points of the original local path segment, respectively. This indicates that the original path contains nodes. To node The local path segment formed; Indicates that by node Candidate reconnection nodes and nodes The candidate reconnection path segments formed;

[0099] in: and Let each represent a finite set of voxels covered by one of the two candidate connecting segments; and These represent the comprehensive evaluation values ​​of the local path segments before and after reconnection; The path reconnection will only be accepted if both candidate connection segments are located within the allowed passage space and the overall evaluation value after reconnection is lower than the overall evaluation value of the original local path segment.

[0100] The described third-order voxel neighborhood corridor reconnection method generates multiple candidate reconnection structures for each segment to be optimized, and evaluates the path length, risk accumulation, boundary proximity, height change, and turning change of each candidate structure. A candidate reconnection structure is only accepted when the complete connecting segment meets the passage requirements and the overall evaluation shows substantial improvement. Through multi-directional corridor reconnection, local detours, foldback structures, abrupt turns, and unnecessary height changes in bidirectional tree paths can be corrected, and the path's adaptability to complex three-dimensional channel morphologies can be enhanced.

[0101] S42: After completing the discrete path structure reconstruction, the constrained path integral correction method is used to further optimize the path. Using intermediate nodes of the path as adjustable control points, multiple sets of random disturbance trajectories are generated within a confined space. Each set of candidate trajectories is comprehensively evaluated, and exponential weights are constructed based on the relative performance of the candidate trajectories to implement weighted updates of the control point positions. Let the first The current control point in the wheel path integral correction is Multiple sets of candidate control points are generated through random perturbation, and exponential weights are calculated from candidate trajectories that satisfy continuous spatial constraints. The relationship between candidate control point generation and weighted update is expressed as follows:

[0102]

[0103] in: This indicates the total number of control points contained in the current path. and They represent the first The starting and ending points of the task path remain fixed during the calibration process; Indicates the internal control point number; This represents the total number of candidate trajectories generated in each round; Indicates the candidate trajectory number; Indicates the first The control point applies the first control point. Candidate control points generated after a group of random perturbations; Indicates the first The action of the wheel on the first The first control point A set of random perturbation vectors; This indicates that the mean vector is zero and the covariance matrix is... The multivariate normal distribution; Indicates the first The covariance matrix of the random perturbation; This represents a local effective position mapping operator, used to map disturbed control points to nearby permitted passage positions;

[0104] in: Indicates the first Wheel by the first The candidate trajectory is formed by a group of candidate control points and a fixed task start and end point; and Let represent the task start point and task end point of the path in the r-th round, respectively, and keep them fixed during the path integral correction process;

[0105] in: Representing candidate trajectories The results of the continuous feasibility assessment; Indicates the first The set of valid candidate trajectory numbers that pass continuous feasibility testing at the voxel level during the round;

[0106] in: This represents the minimum comprehensive evaluation value among the valid candidate trajectories; This represents the k-th valid candidate trajectory in the r-th round. The overall evaluation value;

[0107] in: Indicates the first The path integral temperature parameter of the wheel, and satisfies ; Indicates the first Normalized exponential weights of the valid candidate trajectories; This represents the candidate trajectory summation number in the exponentially weighted normalized denominator; Indicates the first r Round l Valid candidate trajectories The overall evaluation value;

[0108]

[0109] in: This represents the weighted calculation based on all valid candidate control points. Round-robin update of control points; The path integral correction employs a progressively shrinking perturbation scale, enabling strong spatial exploration capabilities in the early stages of the search, while later updates gradually shift towards fine-tuning. Each round of candidate trajectories undergoes spatial constraint testing; only updates with superior overall performance and meeting connectivity requirements are allowed to proceed to the next iteration. This mechanism can further improve the path's risk distribution, spatial redundancy, turning continuity, and altitude variation characteristics while preserving the main path topology.

[0110] By employing rigorous shortcut compression, third-order voxel neighborhood corridor reconnection, and constrained path integral correction, this invention establishes a progressive processing system from path topology compression and discrete structure reconstruction to stochastic weighted refinement. Different stages address path redundancy, local structural defects, and fine-grained control point deviations, resulting in a final path that achieves higher levels of structural compactness, spatial adaptability, and flight quality.

[0111] S5: Perform voxel-level continuous verification and determine the final path.

[0112] The specific steps of S5 are as follows: After the path structure reconstruction is completed, voxel-level continuous verification is performed on the candidate paths. The verification process includes path node verification and inter-node connection segment verification.

[0113] Path node verification checks the spatial state of all path nodes; inter-node connection segment verification extracts the complete voxel sequence covered by the segments between adjacent nodes and performs continuous determination on all traversed positions. Let the path to be verified be... , Indicates the total number of nodes contained in the path; Indicates the first in the path The voxel-level continuity feasibility determination function for path nodes and complete connecting line segments between nodes is expressed as:

[0114]

[0115] in: Represents any voxel to be determined; Indicates the allowed voxel space Indicator function, when voxel belong The value is 1 when the voxel is... Not belonging to The value is 0 at that time;

[0116] in: Indicates adjacent path nodes and The set of finite voxels successively covered by the connecting line segments; Represents a set Any covering voxel in; Indicates the path to be verified The results of the voxel-level continuous feasibility assessment; when When the path to be verified is deemed to meet the voxel-level continuous feasibility requirement; when If the path to be verified does not meet the voxel-level continuous feasibility requirement, it is determined that the path to be verified does not meet the requirement.

[0117] The first product term verifies whether all path nodes belong to the allowed passage space; the second product term verifies whether the voxels covered by the connecting segments between all adjacent path nodes belong to the allowed passage space. When all indicator function values ​​are 1... Candidate paths are determined to be continuous and feasible; as long as any path node or any connecting segment covering voxel does not belong to the allowed passage space, there is... The corresponding candidate path was rejected.

[0118] If the path integral correction result does not meet the continuous verification requirements, the corresponding update is rejected, and the path result that has already passed verification at the previous level is retained. Through the hierarchical result retention mechanism, it is ensured that no subsequent optimization stage will overwrite the established valid path structure.

[0119] The final output path has the following technical characteristics: 1. Risk-oriented proactive search capability. Static and dynamic risk probabilities directly participate in the decision-making of candidate expansion directions and connection structures, enabling path search to have forward identification capabilities for non-uniform risk fields.

[0120] 2. Integration of deterministic priors and probabilistic search capabilities. Connectivity-guided paths provide stable spatial priors for bidirectional trees, while batch quality sampling maintains path optimization capabilities, effectively mitigating the blindness of search in high-dimensional 3D space.

[0121] 3. Highly efficient connection capability under complex conditions. The forward tree and reverse tree grow synchronously, combined with dynamic batch node generation and multi-parent node competition, improving the probability of effective connection under narrow channels and irregular boundary conditions.

[0122] 4. Multi-scale path structure shaping capability. Strict shortcut compression, neighborhood reconnection based on 342 candidate voxel displacement vectors, and constrained path integral correction are applied to the path topology, local configuration, and control point position, respectively, forming a multi-scale progressive path optimization structure.

[0123] 5. Unified evaluation of driving capabilities. Path length, dual-probability risk, spatial safety redundancy, altitude changes, and turning changes all affect the search, connection, and reconstruction processes, ensuring consistent performance across different path generation stages.

[0124] 6. High-reliability spatial output capability. The complete voxel sequences between path nodes are included in the continuous detection range, and the spatial validity and task adaptability of the output path are guaranteed through a hierarchical result retention mechanism.

[0125] In summary, this invention establishes a UAV 3D path planning technology system comprising biprobabilistic forward risk characterization, deterministic connectivity guidance, bidirectional batch tree search, third-order voxel neighborhood path structure reconstruction, constrained path integral correction, and voxel-level continuous verification. This system can deeply utilize risk, connectivity, and geometric information from 3D airspace maps, maintaining high search efficiency and path optimization capabilities under complex spatial structures and non-uniform risk distribution conditions, providing a solution with significant technical depth and engineering value for highly reliable 3D path generation for UAVs.

[0126] This invention uses the forward joint representation of static and dynamic risk probabilities as the core driving information for path search, constructs a dual-probability prediction mechanism, and embeds it into the node generation, direction selection, connection determination, and path evaluation processes of a bidirectional tree. Based on this, a complete path optimization process is formed through connectivity structure guidance, batch candidate node screening, path configuration reconstruction, and constraint correction, enabling global path search and local structure adjustment to proceed continuously under a unified evaluation mechanism.

[0127] This invention uses a joint forward representation of static and dynamic risk probabilities as the basis for search decisions. It establishes a global connection between the origin and destination through bidirectional tree collaborative expansion, and optimizes the generated path step-by-step using path structure reconstruction and continuous constraint verification. Its path search is no longer limited to the local geometric information of the current node, but actively adjusts the expansion direction and connection strategy based on the evolving trend of the risk ahead, thus forming an integrated path generation mechanism that runs through the entire process of global search, local optimization, and feasibility maintenance.

[0128] The above description is merely an embodiment of the present invention and does not limit the patent scope of the present invention. Any equivalent structural or procedural transformations made based on the content of the present invention specification and drawings, or direct or indirect applications in other related technical fields, are similarly included within the patent protection scope of the present invention.

Claims

1. A UAV 3D path planning method based on bidirectional tree optimization with dual-probability prediction, characterized by: Includes the following steps: S1: Establish a three-dimensional spatial path evaluation space; S2: Construct a dual-probability prediction and evaluation mechanism; S3: Generate deterministic connectivity guidance paths and perform bidirectional tree batch search; S4: Implement multi-stage path structure restructuring; S5: Perform voxel-level continuous verification and determine the final path.

2. The UAV 3D path planning method based on bidirectional tree optimization with dual-probability prediction as described in claim 1, characterized in that: The specific steps of S1 are as follows: S11: Extract the allowed path search area based on the spatial access status, and calculate the proximity relationship between each spatial location and the boundary of the restricted area to characterize the spatial safety redundancy of the candidate path near the complex boundary. S12: Incorporate path physical length, static and dynamic fusion risk, boundary proximity, height change and turning change into a unified evaluation system; For a candidate path P consisting of the task start point and the task end point, its comprehensive evaluation function is expressed as: ； ； ； in: This represents a candidate path from the start point of the task to the end point of the task; Indicate candidate path The overall evaluation value; Represents the normalized path length cost of the candidate path; This represents the risk cost of normalized static-dynamic fusion of candidate paths; Represents the normalized boundary proximity cost of the candidate path; This represents the normalized cumulative height variation cost of the candidate path; Represents the normalized turning change cost of the candidate path; , , , and These represent the weights of the evaluation indicators.

3. The UAV 3D path planning method based on bidirectional tree optimization with dual-probability prediction as described in claim 1, characterized in that: The specific steps of S2 are as follows: For the current search node and candidate expansion direction Multiple forward observation positions are set along this direction, and attenuation weights are configured according to the distance between the observation position and the current node. The static risk prediction value, dynamic risk prediction value, and biprobability comprehensive prediction value of the candidate direction are expressed as follows: ； in: Indicates along the candidate direction The first One forward observation voxel; Represents the observation position mapping operator; Indicates the current search node Physical coordinates; This indicates the total number of observation positions set in front of the candidate direction; Indicates the forward observation position number; Indicates the physical interval between adjacent forward observation positions; ； in: Indicates the first Distance attenuation weights for each forward observation position; This indicates the distance decay rate control parameter; This indicates the summation number in the attenuation weight normalization calculation; ； in: Indicate candidate direction The static risk prediction value; Indicates the first k Distance attenuation weights for each forward observation position; and This represents the normalized static risk value; ； in: Representing candidate directions Dynamic risk prediction value; This represents the normalized dynamic risk value; ； ； in: Indicate candidate direction The combined predictive value of the two probabilities; and These represent the combined weights of static risk and dynamic risk, respectively.

4. The UAV 3D path planning method based on bidirectional tree optimization with dual-probability prediction as described in claim 3, characterized in that: The specific steps of S3 are as follows: S31: First, analyze the voxel connectivity in the three-dimensional spatial domain, and then simultaneously perform deterministic connectivity expansion from the starting point and the ending point; S32: After the two ends of the connected wavefront establish a connection relationship, a connected guiding path that meets the spatial passage conditions is generated by backtracking. S33: Build a forward search tree and a backward search tree with the task start point and task end point as root nodes respectively; The algorithm employs a batch candidate node generation mechanism; For each candidate node In its neighboring set of parent nodes, a multi-parent node competition is performed, and the node with the minimum overall expansion cost is selected as the optimal parent node of the candidate node, that is: ； in: Indicates the candidate nodes to be connected; Indicates candidate nodes The set of candidate parent nodes within the neighborhood that satisfy the connection distance requirement and the continuous space constraint; Represents a set Any candidate parent node in; This represents the optimal parent node that minimizes the overall expansion cost. This indicates the search tree from the root node to the candidate parent node. The cumulative path cost; Indicates the connection node With candidate nodes The total cost of line segments; Indicates that by node Pointing to candidate nodes The direction of unit expansion; This represents the adjustment coefficient for the biprobability prediction term; Represents a node The parent node in the current search tree; Represents a node ,node With candidate nodes The resulting penalty for turning changes; The adjustment coefficient representing the penalty for changes in direction during turns; S34: The forward search tree and reverse search tree are expanded alternately in batches, and the size of candidate nodes and the range of inter-tree connections are dynamically adjusted according to the current connection status. The node pair with the lowest overall connection cost is selected to establish a dual-tree connection, that is: ； in: This represents a forward search tree built with the task's starting point as the root node; This represents a reverse search tree built with the task endpoint as the root node; Represents a forward search tree Candidate successor nodes in; Represents a reverse search tree Candidate successor nodes in; and These represent the forward optimal succession node and the reverse optimal succession node determined when the overall succession cost is minimized, respectively. and Representing nodes respectively and nodes Physical coordinates; Indicates the physical distance between two candidate successor nodes; This indicates the maximum allowed connection distance for establishing a two-tree connection; Represents a node With nodes The set of finite voxels covered by the connecting line segments; This represents the voxel space that is allowed to pass through; This indicates that all voxels covered by the candidate continuation segment belong to the allowed passage space; This indicates the node reached from the starting point of the task along the forward search tree. The cumulative path cost; Represents a node The cumulative path cost to reach the task endpoint along the reverse search tree; This represents the comprehensive edge cost of the candidate continuation segment; This indicates the penalty for directional changes between the candidate continuation segment and the end segment of the forward tree and the end segment of the reverse tree, respectively. This represents the adjustment coefficient for the penalty term indicating a change in the direction of continuation.

5. The UAV 3D path planning method based on bidirectional tree optimization with dual-probability prediction as described in claim 4, characterized in that: The specific steps of S4 are as follows: S41: Perform cross-node connectivity analysis on non-adjacent nodes in the main path. S42: Construct a third-order voxel neighborhood corridor centered on the compressed path, and establish a third-order voxel neighborhood centered on the reference voxel node in the compressed path. The candidate displacement vector set, candidate reconnection nodes, and path reconnection acceptance conditions of the third-order voxel neighborhood are expressed as follows: ； in: This represents the set of candidate voxel displacement vectors in the neighborhood of a third-order voxel. Represents a three-dimensional integer displacement vector in units of voxels; Represents a three-dimensional integer coordinate space; Represents the displacement vector The maximum value among the absolute values ​​of the three coordinate components; This indicates that the candidate displacement does not exceed three voxels along any of the three coordinate directions; This excludes zero displacement vectors that do not produce a change in position. ； in: Indicates the number of candidate voxel shift vectors; ； in: This represents the reference voxel node in the path segment to be optimized; Indicates the reference voxel node According to the candidate displacement vector The generated candidate reconnected voxel nodes; ； in: and Indicates the endpoint numbers of a local path segment, and satisfies ; and These represent the beginning and end points of the original local path segment, respectively. This indicates that the original path contains nodes. To node The local path segment formed; Indicates that by node Candidate reconnection nodes and nodes The candidate reconnection path segments formed; ； in: and Let each represent a finite set of voxels covered by one of the two candidate connecting segments; and These represent the comprehensive evaluation values ​​of the local path segments before and after reconnection; S42: Using intermediate nodes of the path as adjustable control points, multiple sets of random disturbance trajectories are generated within a limited space. Each set of candidate trajectories is comprehensively evaluated. Based on the relative performance between candidate trajectories, exponential weights are constructed to update the control point positions in a weighted manner. No. The current control point in the wheel path integral correction is Multiple sets of candidate control points are generated through random perturbation, and exponential weights are calculated from candidate trajectories that satisfy continuous spatial constraints. The relationship between candidate control point generation and weighted update is expressed as follows: ； ； in: This indicates the total number of control points contained in the current path. and They represent the first The starting and ending points of the task path; Indicates the internal control point number; This represents the total number of candidate trajectories generated in each round; Indicates the candidate trajectory number; Indicates the first The control point applies the first control point. Candidate control points generated after a group of random perturbations; Indicates the first The action of the wheel on the first The first control point A set of random perturbation vectors; This indicates that the mean vector is zero and the covariance matrix is... The multivariate normal distribution; Indicates the first The covariance matrix of the random perturbation; Represents a locally effective location mapping operator; ； in: Indicates the first Wheel by the first The candidate trajectory is formed by a group of candidate control points and a fixed task start and end point; and Let represent the task start point and task end point of the path in the r-th round, respectively, and keep them fixed during the path integral correction process; ； in: Representing candidate trajectories The results of the continuous feasibility assessment; Indicates the first The set of valid candidate trajectory numbers that pass continuous feasibility testing at the voxel level during the round; ； in: This represents the minimum comprehensive evaluation value among the valid candidate trajectories in the r-th round; This represents the k-th valid candidate trajectory in the r-th round. The overall evaluation value; ； in: Indicates the first The path integral temperature parameter of the wheel; Indicates the first Normalized exponential weights of the valid candidate trajectories; This represents the candidate trajectory summation number in the exponentially weighted normalized denominator; Indicates the first r Round l Valid candidate trajectories The overall evaluation value; ； ； in: This represents the weighted calculation based on all valid candidate control points. Update control points in rounds.

6. The UAV 3D path planning method based on bidirectional tree optimization with dual-probability prediction as described in claim 5, characterized in that: The specific steps of S5 are as follows: The path to be verified is , Indicates the total number of nodes contained in the path; Indicates the first in the path The voxel-level continuity feasibility determination function for path nodes and complete connecting line segments between nodes is expressed as: ； ； in: Represents any voxel to be determined; Indicates the allowed voxel space Indicator function, when voxel belong The value is 1 when the voxel is... Not belonging to The value is 0 at that time; ； in: Indicates adjacent path nodes and The set of finite voxels successively covered by the connecting line segments; Represents a set Any covering voxel in; Indicates the path to be verified The results of the voxel-level continuous feasibility assessment; when When the path to be verified is deemed to meet the voxel-level continuous feasibility requirement; when If the path to be verified does not meet the voxel-level continuous feasibility requirement, it is determined that the path to be verified does not meet the requirement.

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