A bidirectional path planning method and system fusing feedback-driven sampling and hierarchical delay scheduling

Abstract

A bidirectional path planning method and system fusing feedback-driven sampling and hierarchical delay scheduling, the system comprising: an initialization module for obtaining environment information and initializing a bidirectional random tree with a start point and a target point as root nodes; a multi-stage hierarchical scheduling module for sequentially attempting to execute strategy one, strategy two and strategy three according to priority to generate new nodes; wherein strategy one is a self-repairing greedy target expansion, strategy two is a feedback-driven hierarchical sampling expansion, and strategy three is a global compensation sampling expansion; a tree updating module for adding the successfully generated new nodes to the corresponding random tree and executing local rerouting optimization; a intersection detection module for judging whether the new nodes are connected with another random tree, and if connected, outputting an initial feasible path, and if not connected, alternating the double-tree growth order and driving the multi-stage hierarchical scheduling module to continue iteration. The present application can quickly generate an initial feasible path with high safety and high smoothness.

Description

Technical Field

[0001] This invention relates to the field of robot path planning technology, specifically to a bidirectional path planning method and system that integrates feedback-driven sampling and hierarchical delay scheduling. Background Technology

[0002] Path planning, as a core technology for autonomous navigation of mobile robots, directly affects the robot's efficiency and safety in complex environments. In recent years, with the widespread application of robots in scenarios such as autonomous driving and disaster relief, path planning not only needs to meet accessibility requirements but also needs to consider path length, smoothness, and safety.

[0003] Among existing sampling-based path planning algorithms, the asymptotically optimal fast expanding random tree (RRT*) possesses strong spatial exploration capabilities and asymptotic optimality. However, traditional RRT-like algorithms still have many shortcomings in complex environments: First, some algorithms (such as GB-RRT*) employ a fixed target bias strategy, which significantly increases the expansion failure rate when the connection between the start and end points is severely obstructed by obstacles. Second, some bidirectional search algorithms (such as BI-RRT*) expand the two trees independently, resulting in suboptimal paths at the intersections, and blind sampling in narrow channels severely limits expansion efficiency. Third, some algorithms that introduce geometric inspiration (such as BAI-RRT* elliptic sampling) or artificial potential fields (such as BI-APF-RRT*) are prone to sampling region mismatch or getting stuck in local minima when the real feasible space deviates from the principal axis of the start and end points, or when facing trap topologies, leading to planning stagnation.

[0004] Therefore, how to quickly generate a high-quality initial feasible path with both high security and high smoothness in complex, narrow and trap environments is a technical problem that urgently needs to be solved in this field. Summary of the Invention

[0005] To address the problems of existing algorithms blindly exploring in complex environments, easily getting stuck in local stagnation, and having poor initial path quality, this invention provides a bidirectional path planning method and system that integrates feedback-driven sampling and hierarchical delayed scheduling. This achieves hierarchical collaboration from rapid local advancement to global backoff exploration, significantly improving the planning efficiency, success rate, and path safety margin of the algorithm in narrow passages and complex obstacle environments.

[0006] The technical solution adopted in this invention is as follows: A bidirectional path planning method integrating feedback-driven sampling and hierarchical delay scheduling includes the following steps: S1: Obtain the starting point, target point, and environmental obstacle information of the mobile robot, and initialize the starting point tree with the starting point as the root node and the ending point tree with the target point as the root node. S2: Execute strategy one: Select a node from the currently expanding random tree, perform self-repairing greedy target expansion along the target guidance direction, and attempt to generate new nodes; S3: Determine if Strategy 1 has failed. If so, execute Strategy 2: trigger feedback-driven hierarchical sampling expansion and attempt to generate new nodes. If not, jump directly to S6. S4: Determine if Strategy 2 has failed. If yes, execute Strategy 3: trigger global compensation sampling expansion to generate new nodes; otherwise, skip directly to S6. S5: Determine whether a new node was successfully generated using strategy one, strategy two, or strategy three. If so, proceed to S6. S6: Add the newly generated node to the currently expanding random tree and perform local rewiring optimization; S7: Perform a two-tree intersection detection to determine whether the new node and another random tree satisfy the collision-free connectivity condition. If so, output the initial feasible path connecting the starting point and the target point. If not, swap the growth order of the two random trees and return to S2 for iteration until the maximum number of iterations is reached.

[0007] S2 includes the following steps: S2.1: Using the preset target bias probability, the target point is used as the guiding sampling point, and in the node set of the currently expanding random tree, the node with the closest Euclidean distance to the target point is found as the expansion starting point; ; In the formula, As the starting point for expansion; This is the set of nodes in the currently expanding random tree; For set Candidate nodes in; For the target point; The second norm of a vector; This represents the value of the variable that minimizes the objective function.

[0008] S2.2: Calculate the unit direction vector pointing from the expansion starting point to the target point, and perform direct expansion along this line with a fixed step size; the formula for calculating the unit direction vector is: ; In the formula, This is the unit direction vector pointing towards the target point; S2.3: If a collision occurs between directly extended connections, a local sector repair mechanism is triggered: using a unit vector along the connection direction... Construct a local search sector for the centerline and discretize it into a set of multiple candidate deflection angles symmetrical about the centerline. ; The preset angle resolution, This represents the maximum number of unfolded layers. Calculate the candidate direction vectors after deflection sequentially. : ; In the formula,

[0009] Then, candidate nodes are calculated and generated. : ; In the formula, To deflect along the candidate direction vector Candidate nodes generated after angle adjustment To extend the step size.

[0010] Subsequently, the candidate directions on both sides are symmetrically scanned in order of increasing deflection amplitude, and the first candidate point that passes the collision-free detection is taken as the new node after repair.

[0011] S3 includes the following steps: S3.1: Divide the search area into a hierarchical space of multiple concentric rings centered on the target point; First, define the maximum search radius. : ; In the formula, This is the search margin scaling factor; As the starting point; and These are the width and height of the configuration space, respectively; Indicates the width of the configuration space. and high The maximum value in.

[0012] Furthermore, the division into the first Layered regions : ; In the formula, Collision-free free space Any spatial node within, It is a free space without collisions; The total number of floors set; For floor number; S3.2: Maintain the sampling probability weights of each layer space, select the target layer according to the sampling probability weights, and generate candidate sampling points within it; In the In-layer generated sampling radius The formula is: ; In the formula, A uniformly distributed random number within the interval (0,1). The first The inner and outer diameters of the layer; The formula for calculating the coordinates of candidate sampling points is: ; In the formula, Coordinates of the candidate sampling points; for Uniformly distributed random angles within the interval; Indicates vector transpose; S3.3: When a newly generated node effectively advances the currently expanding random tree toward the target point, a positive reward is applied to the sampling probability weights of the hierarchical space where the new node is located and its adjacent inner layers, and the sampling probability distribution of each layer is dynamically updated. If the new node advances effectively, it will affect the layer it belongs to. and inner layer Apply reward factors This makes the updated unnormalized probability The global probability distribution is then normalized and updated. ; In the formula, The first [item] after applying the reward factor but before normalization. Layer sampling probability, For the first time before the update Sampling probability of layer This represents the normalized probability of the new sample. The unnormalized probabilities of each layer after applying the reward; S3.4: Select the best source node from the candidate sampling points and perform expansion to generate new nodes. Specifically, this includes: A multi-factor evaluation mechanism is used to comprehensively score candidate nodes within the neighborhood. The comprehensive score is obtained by weighted summation of the following three factors: Path guiding factor Used to quantify the degree of deviation of a node from the ideal axis connecting the starting point and the target point; ; In the formula, This represents the vertical deviation distance from the candidate node to the ideal connection. For guiding bandwidth coefficient; Target approach factor Used to evaluate the remaining distance between a node and the target point; ; In the formula, Let be the Euclidean distance from the node to the target point. This is the distance attenuation coefficient; Safety margin factor Used to evaluate the safe distance penalty of a node relative to surrounding obstacles; ; In the formula, Let Euclidean distance be the distance from the candidate node to the nearest obstacle. This is the distance sensitivity coefficient; The three factors are linearly weighted to obtain the total score formula: ; In the formula, , , These are the non-negative weights of the corresponding factors; The node with the highest overall score and that meets the geometric connection cost requirement is selected as the optimal expansion source node. : ; In the formula, This represents a random sampling point in the current iteration; To prevent the positive minimum constant with a denominator of zero, This is the set of nodes in the current random tree; For set Candidate nodes in.

[0013] S4 includes the following steps: S4.1: Real-time statistics of the effective expansion count and total number of attempts of Strategy 2 in the current stage, and calculation of the activation probability of Strategy 2. : ; In the formula, The preset minimum activation threshold, This represents the effective number of times strategy 2 can generate collision-free nodes in the current stage. This represents the total number of attempts for Strategy 2 in the current phase.

[0014] S4.2: When the activation probability is lower than the preset minimum activation threshold, the advancement capability of Strategy 2 is determined to be reduced and ineffective, triggering the execution of global compensation sampling expansion; S4.3: The global compensation sampling extension adopts a hybrid scheduling mechanism: Generate a uniformly distributed random number. and the set hybrid scheduling probability threshold Compare and alternate between one of the following two sampling strategies: ①: If Then, Halton low-difference sequences are used for global uniform sampling, and their first... sampling points The formula for generating it is: ; In the formula, and These are the basis inversion functions with the prime numbers 2 and 3 as their bases, respectively. ; Represents element-wise multiplication (Hadamard product); Configure the scale mapping vector of the environment space; ②: If Then, the Bridge test is used to extract local guide points in narrow passages inside the obstacle for sampling: First, randomly sample the first test point inside the obstacle area. The second test point is generated by Gaussian perturbation. : ; In the formula, To conform to a mean of 0 and a standard deviation of The Gaussian distribution perturbation vector; It is a two-dimensional identity matrix; Then calculate the midpoint between the two. : ; Then, the generated points are structurally determined. If the following conditions are met: ; That is, the first test point Second test point All are located in obstacle space Inside, and its midpoint Located in free space If it is inside, then the midpoint is accepted. As a local guide point for compensation sampling.

[0015] S6 includes the following steps: S6.1: Within the neighborhood of the given search radius, obtain the new nodes successfully generated in this iteration. potential parent node set ; Calculate the values ​​via the set of potential parent nodes respectively Different potential nodes reach new nodes The cumulative cost of the path is calculated, and the node with the minimum total cost and whose connection satisfies the collision-free condition is selected as the new node. final parent node : ; And it satisfies the constraints: Node With new nodes The lines connecting them are free from obstacles and collisions. In the formula, Set of potential parent nodes Candidate nodes in; To reach a node from the root node of the current tree along the tree structure The accumulated path cost; The cost of connecting the two points using the Euclidean distance; S6.2: Utilizing new nodes For neighborhood set Perform rewiring tests on other nodes within the system: For any neighboring node in the set If via a new node Reaching this neighboring node If the new cumulative path has a lower cost and the connection between the two points has no collision, then the neighboring node is disconnected. The existing parent-child connection is updated by changing its parent node to the new node. ; The formula for determining rewiring is: ; In the formula, The final parent node newly determined in S6.1 Reaching a new node The actual cumulative path cost; For the neighboring nodes before the update The original cumulative path cost; This represents the Euclidean distance cost from the new node to the neighboring nodes.

[0016] S7 includes the following steps: S7.1: When generating a new node After completing the local rewiring, find the distance to the new node in the node set of another random tree that has not yet been expanded. The node with the closest Euclidean distance is denoted as the opposite nearest node. ; S7.2: Determine the new node Nearest node on the opposite side Does it meet the collision-free connectivity condition? The collision-free connectivity condition includes: ; And the constraint condition is: node With nodes The connecting lines did not collide with environmental obstacles; In the formula, This is the preset threshold for the intersection distance between two trees; S7.3: If the collision-free connectivity condition is met, the two trees are determined to have successfully intersected. Backtrack the parent-child connection relationships of the nodes in the two random trees and output the initial feasible path connecting the starting point and the target point. If the no-collision connectivity condition is not met, the intersection is determined to have failed. At this time, the growth order of the two random trees is swapped: the current starting tree is used as the target tree for the next round, and the current target tree is used as the starting tree for the next round. Then, the process returns to step S2 to continue the next round of iteration until the maximum number of iterations is reached.

[0017] A path planning system integrating feedback-driven and hierarchical scheduling, the system comprising: The initialization module is used to obtain environmental information and initialize a bidirectional random tree with the starting point and the target point as the root nodes; The multi-level hierarchical scheduling module is used to attempt to execute strategy one, strategy two, and strategy three in order of priority to generate new nodes. Among them, strategy one is a self-healing greedy target extension, strategy two is a feedback-driven hierarchical sampling extension, and strategy three is a global compensation sampling extension. The next level strategy is only triggered when the previous level strategy fails or is blocked. The tree update module is used to add successfully generated new nodes to the corresponding random tree and perform local rewiring optimization. The intersection detection module is used to determine whether a new node is connected to another random tree. If it is connected, it outputs the initial feasible path. If it is not connected, it alternates the growth order of the two trees and drives the multi-level hierarchical scheduling module to continue iterating.

[0018] This invention provides a bidirectional path planning method and system that integrates feedback-driven sampling and hierarchical delay scheduling, with the following technical advantages: 1) Planning efficiency has been significantly improved: This invention constructs a three-level expansion mechanism triggered on demand. Most iterations are completed within a low-overhead, locally fast first-level expansion (self-healing greedy expansion), effectively avoiding unnecessary complex computational overhead. Compared with traditional algorithms, the initial feasible path generation time of this method can be reduced by 20.21%–67.77%.

[0019] 2) Strong adaptability to complex environments: Faced with narrow passages and trap environments, this invention introduces historical feedback-driven hierarchical sampling in the second stage to dynamically concentrate computing power in the effective area; in the third stage of extreme constraints, it introduces Halton-Bridge global compensation hybrid sampling to completely break local stagnation and maintain an extremely high planning success rate in various extreme test environments.

[0020] 3) Excellent initial path quality: The multi-factor node optimization mechanism of this invention comprehensively considers path guidance, target approach and safety margin, so that the generated initial path not only significantly reduces redundant polylines and shortens the path length by 5.56%~10.96%, but also effectively pushes away obstacles, improves the average safety margin, and greatly reduces the computational burden of subsequent trajectory smoothing optimization. Attached Figure Description

[0021] The present invention will be further described below with reference to the accompanying drawings and examples; Figure 1 A flowchart illustrating a path planning method that integrates feedback-driven and hierarchical scheduling, as provided in an embodiment of the present invention.

[0022] Figure 2 This is a schematic diagram illustrating the principle of the local fan-shaped repair mechanism provided in an embodiment of the present invention.

[0023] Figure 3 The hierarchical sampling and probability update diagram provided in the embodiments of the present invention.

[0024] Figure 4 The multi-factor evaluation mechanism and adaptive hierarchical sampling principle diagram provided for the embodiments of the present invention.

[0025] Figure 5 A schematic diagram of the hardware structure of a computer device provided in an embodiment of the present invention. Detailed Implementation

[0026] A path planning method integrating feedback-driven and hierarchical scheduling is proposed. Under the framework of bidirectional fast-expanding random trees, a three-level delayed scheduling mechanism is constructed on demand: low-overhead self-healing greedy target expansion is prioritized to achieve local fast advancement; when expansion is blocked, feedback-driven hierarchical sampling is triggered, and the sampling probability is dynamically adjusted and multi-factor node selection is performed based on historical effective expansion results; when the advancement capability decreases, a global compensation sampling mechanism is triggered to break the trap stagnation; finally, the bidirectional tree intersection is detected and the path is output.

[0027] Example 1: like Figure 1 As shown, this invention provides a path planning method that integrates feedback-driven and hierarchical scheduling. This method is based on a Bidirectional Rapidly Expanding Random Tree (Bidirectional RRT*) framework and is implemented through a three-level delayed scheduling mechanism triggered on demand. Specifically, it includes the following steps: Step S1. Initialization: Obtain the starting point and target point of the mobile robot, and initialize the starting point tree rooted at the starting point and the target point tree rooted at the target point in free space. Set basic parameters such as the maximum number of iterations and the step size.

[0028] Step S2. Execute Strategy 1 (Level 1 Expansion): Self-healing greedy target expansion: In this embodiment, to accelerate path generation in open spaces, low-overhead exploration along the target direction with a higher target offset probability is prioritized. Specifically: The system expands directly along the node connection direction with a fixed step size; if a collision occurs along the connection, a local sector repair mechanism is immediately triggered, such as... Figure 2 As shown.

[0029] Preferably, the principal direction is set as a vector. The system is based on Construct a local search sector centered on the center and discretize it into a set of candidate angles. The algorithm scans symmetrically in ascending order of deflection magnitude, and the first node to pass collision detection is used as the new node after repair. This mechanism greatly improves the success rate of a single expansion.

[0030] Step S3. Execute Strategy Two (Secondary Extension): Feedback-driven hierarchical sampling extension.

[0031] Determine whether Strategy 1 has failed (i.e., failed to generate a new collision-free node). If yes, it indicates that there is a local obstacle occlusion, and the algorithm triggers a second-level expansion; otherwise, skip directly to step S6.

[0032] In the second-level extension, this invention proposes a feedback-based online probability adjustment mechanism, the principle of which is as follows: Figure 3 As shown. Preferably, it specifically includes: (1) Divide the search area into sections centered on the target point. A concentric ring layer.

[0033] (2) During sampling, the target layer is selected and candidate sampling points are generated based on the discrete probability vector. When a new node makes effective progress, that is, it is closer to the target than the parent node, a positive reward is applied to the layer where the node is located and its adjacent inner layers to increase the sampling probability. This allows the layers that can continuously make effective progress to obtain higher sampling weights, thereby concentrating computing power in the locally feasible channels.

[0034] (3) Multi-factor expansion source node optimization mechanism, such as Figure 4 As shown: To improve the compactness and security of the branches, this embodiment uses a comprehensive scoring function. The starting point for screening, and the scoring factors include: Path guiding factor The Gaussian decay model constrains the nodes to approach the ideal axis at the start and end points. The calculation formula is as follows: ; In the formula, This represents the vertical deviation distance from the candidate node to the ideal connection. This is the bandwidth factor.

[0035] Target approach factor The convergence trend towards the target is enhanced by an exponential decay function, the calculation formula of which is: ; In the formula, Let be the Euclidean distance from the node to the target point. This is the distance attenuation coefficient.

[0036] Safety margin factor A logarithmic model is used to penalize dangerous areas, causing nodes to actively push away obstacles. The calculation formula is as follows: ; In the formula, Let Euclidean distance be the distance from the candidate node to the nearest obstacle. This is the distance sensitivity coefficient.

[0037] Finally, the three factors are normalized and linearly weighted, and the node with the highest comprehensive score and no collision is selected as the starting point for expansion.

[0038] Step S4. Execute Strategy Three (Level Three Extension): Halton-Bridge Global Compensation Sampling: Determine whether Strategy 2 has failed. If yes, it means the algorithm has fallen into a complex trap or dead end, triggering a third-level expansion; if no, proceed to step S6.

[0039] Preferably, the system uses the ratio of the effective expansion count to the total number of attempts as the activation probability. .when When the threshold is lower than the minimum activation threshold, the global compensation module is triggered.

[0040] In this stage, this embodiment designs a hybrid scheduling model: based on a set probability threshold, Halton low-dispersion sequences and bridging tests are used alternately. Halton low-dispersion sequences improve global spatial coverage uniformity and avoid clustered holes from pseudo-random sampling. Bridging tests sample inside obstacles and take the midpoint, enhancing penetration through narrow passages. Step S5. Connectivity determination mechanism: Determine whether a new node has been successfully generated using any of the above strategies. If yes, proceed to step S6; otherwise (in extreme exceptional cases), skip this iteration.

[0041] Step S6. Tree Update and Local Rerouting: Add the new node to the current random tree. Then, perform the standard RRT* parent reselection and rewire operations within the neighborhood of the given radius. By comparing the cumulative cost of the paths, optimize the local tree structure and reduce path redundancy.

[0042] Step S7. Dual-tree intersection and loop control: Check if the new node and a node in another tree satisfy the collision-free connectivity condition and the distance is less than a threshold. If they satisfy the condition, it means that the two trees have successfully intersected, and the path is extracted and smoothed before outputting the initial feasible path; if they do not satisfy the condition, the starting tree and the ending tree are swapped (Swap operation), and the process returns to step S2 for the next round of iterations until the maximum number of iterations is reached.

[0043] Example 2: A path planning system integrating feedback-driven and hierarchical scheduling, the system comprising: The initialization module is used to obtain environmental information and initialize a bidirectional random tree with the starting point and the target point as the root nodes; The multi-level hierarchical scheduling module is used to attempt to execute strategy one, strategy two, and strategy three in order of priority to generate new nodes. Among them, strategy one is a self-healing greedy target extension, strategy two is a feedback-driven hierarchical sampling extension, and strategy three is a global compensation sampling extension. The next level strategy is only triggered when the previous level strategy fails or is blocked. The tree update module is used to add successfully generated new nodes to the corresponding random tree and perform local rewiring optimization. The intersection detection module is used to determine whether a new node is connected to another random tree. If it is connected, it outputs an initial feasible path. If it is not connected, it alternates the growth order of the two trees and drives the multi-level hierarchical scheduling module to continue iterating.

Claims

1. A bidirectional path planning method integrating feedback-driven sampling and hierarchical delay scheduling, characterized in that... Includes the following steps: S1: Obtain the starting point, target point, and environmental obstacle information of the mobile robot, and initialize the starting point tree with the starting point as the root node and the ending point tree with the target point as the root node. S2: Execute strategy one: Select a node from the currently expanding random tree, perform self-repairing greedy target expansion along the target guidance direction, and attempt to generate new nodes; S3: Determine if Strategy 1 has failed. If so, execute Strategy 2: trigger feedback-driven hierarchical sampling expansion and attempt to generate new nodes. If not, jump directly to S6. S4: Determine if Strategy 2 has failed. If yes, execute Strategy 3: trigger global compensation sampling expansion to generate new nodes; otherwise, skip directly to S6. S5: Determine whether a new node was successfully generated using strategy one, strategy two, or strategy three. If so, proceed to S6. S6: Add the newly generated node to the currently expanding random tree and perform local rewiring optimization; S7: Perform a two-tree intersection detection to determine whether the new node and another random tree satisfy the collision-free connectivity condition. If so, output the initial feasible path connecting the starting point and the target point. If not, swap the growth order of the two random trees and return to S2 for iteration until the maximum number of iterations is reached.

2. The bidirectional path planning method integrating feedback-driven sampling and hierarchical delay scheduling according to claim 1, characterized in that: S2 includes the following steps: S2.1: Using the preset target bias probability, the target point is used as the guiding sampling point, and in the node set of the currently expanding random tree, the node with the closest Euclidean distance to the target point is found as the expansion starting point; ； In the formula, As the starting point for expansion; This is the set of nodes in the currently expanding random tree; For set Candidate nodes in; For the target point; The second norm of a vector; This represents the value of the variable that minimizes the objective function. S2.2: Calculate the unit direction vector pointing from the expansion starting point to the target point, and perform direct expansion along this line with a fixed step size; the formula for calculating the unit direction vector is: ； In the formula, This is the unit direction vector pointing towards the target point; S2.3: If a collision occurs between directly extended connections, a local sector repair mechanism is triggered.

3. The bidirectional path planning method integrating feedback-driven sampling and hierarchical delay scheduling according to claim 2, characterized in that: The specific mechanism of local fan-shaped repair is as follows: unit vector in the direction of the line Construct a local search sector for the centerline and discretize it into a set of multiple candidate deflection angles symmetrical about the centerline. ; The preset angle resolution, This represents the maximum number of unfolded layers. Calculate the candidate direction vectors after deflection sequentially. : ； In the formula, Then, candidate nodes are calculated and generated. : ； In the formula, To deflect along the candidate direction vector Candidate nodes generated after angle adjustment To extend the step size; Subsequently, the candidate directions on both sides are symmetrically scanned in order of increasing deflection amplitude, and the first candidate point that passes the collision-free detection is taken as the new node after repair.

4. The bidirectional path planning method integrating feedback-driven sampling and hierarchical delay scheduling according to claim 3, characterized in that: S3 includes the following steps: S3.1: Divide the search area into a hierarchical space of multiple concentric rings centered on the target point; First, define the maximum search radius. : ； In the formula, This is the search margin scaling factor; As the starting point; and These are the width and height of the configuration space, respectively; Indicates the width of the configuration space. and high The maximum value in; Furthermore, the division into the first Layered regions : ； In the formula, Collision-free free space Any spatial node within, It is a free space without collisions; The total number of floors set; For floor number; S3.2: Maintain the sampling probability weights of each layer space, select the target layer according to the sampling probability weights, and generate candidate sampling points within it; In the In-layer generated sampling radius The formula is: ； In the formula, A uniformly distributed random number within the interval (0,1). The first The inner and outer diameters of the layer; The formula for calculating the coordinates of candidate sampling points is: ； In the formula, Coordinates of the candidate sampling points; for Uniformly distributed random angles within the interval; Indicates vector transpose; S3.3: When a newly generated node effectively advances the currently expanding random tree toward the target point, a positive reward is applied to the sampling probability weights of the hierarchical space where the new node is located and its adjacent inner layers, and the sampling probability distribution of each layer is dynamically updated. If the new node advances effectively, it will affect the layer it belongs to. and inner layer Apply reward factors This makes the updated unnormalized probability Then, the global probability distribution is normalized and updated: ； In the formula, The first [item] after applying the reward factor but before normalization. Layer sampling probability, For the first time before the update Sampling probability of layer This represents the normalized probability of the new sample. The unnormalized probabilities of each layer after applying the reward; S3.4: Select the best source node from the candidate sampling points and perform the expansion to generate a new node.

5. The bidirectional path planning method integrating feedback-driven sampling and hierarchical delay scheduling according to claim 4, characterized in that: S3.4 specifically includes: A multi-factor evaluation mechanism is used to comprehensively score candidate nodes within the neighborhood. The comprehensive score is obtained by weighted summation of the following three factors: Path guiding factor Used to quantify the degree of deviation of a node from the ideal axis connecting the starting point and the target point; ； In the formula, This represents the vertical deviation distance from the candidate node to the ideal connection. For guiding bandwidth coefficient; Target approach factor Used to evaluate the remaining distance between a node and the target point; ； In the formula, Let be the Euclidean distance from the node to the target point. This is the distance attenuation coefficient; Safety margin factor Used to evaluate the safe distance penalty of a node relative to surrounding obstacles; ； In the formula, Let Euclidean distance be the distance from the candidate node to the nearest obstacle. This is the distance sensitivity coefficient; The three factors are linearly weighted to obtain the total score formula: ； In the formula, , , These are the non-negative weights of the corresponding factors; The node with the highest overall score and that meets the geometric connection cost requirement is selected as the optimal expansion source node. : ； In the formula, This represents a random sampling point in the current iteration; To prevent the positive minimum constant with a denominator of zero, This is the set of nodes in the current random tree; For set Candidate nodes in.

6. The bidirectional path planning method integrating feedback-driven sampling and hierarchical delay scheduling according to claim 5, characterized in that: S4 includes the following steps: S4.1: Real-time statistics of the effective expansion count and total number of attempts of Strategy 2 in the current stage, and calculation of the activation probability of Strategy 2. : ； In the formula, The preset minimum activation threshold, This represents the effective number of times strategy 2 can generate collision-free nodes in the current stage. This represents the total number of attempts for Strategy 2 in the current phase. S4.2: When the activation probability is lower than the preset minimum activation threshold, the advancement capability of Strategy 2 is determined to be reduced and ineffective, triggering the execution of global compensation sampling expansion; S4.3: The global compensation sampling extension adopts a hybrid scheduling mechanism.

7. The bidirectional path planning method integrating feedback-driven sampling and hierarchical delay scheduling according to claim 6, characterized in that: S4.3 specifically includes: Generate a uniformly distributed random number. and the set hybrid scheduling probability threshold Compare and alternate between one of the following two sampling strategies: ①: If Then, Halton low-difference sequences are used for global uniform sampling, and its first... sampling points The formula for generating it is: ； In the formula, and These are the basis inversion functions with the prime numbers 2 and 3 as bases, respectively. Represents element-wise multiplication; Configure the scale mapping vector of the environment space; ②: If Then, the Bridge test is used to extract local guide points in narrow passages inside the obstacle for sampling: First, randomly sample the first test point inside the obstacle area. The second test point is generated by Gaussian perturbation. : ； In the formula, To conform to a mean of 0 and a standard deviation of The Gaussian distribution perturbation vector; It is a two-dimensional identity matrix; Then calculate the midpoint between the two. : ； Then, the generated points are structurally determined. If the following conditions are met: ； That is, the first test point Second test point All are located in obstacle space Inside, and its midpoint Located in free space If it is inside, then the midpoint is accepted. As a local guide point for compensation sampling.

8. The bidirectional path planning method integrating feedback-driven sampling and hierarchical delay scheduling according to claim 7, characterized in that: S6 includes the following steps: S6.1: Within the neighborhood of the given search radius, obtain the new nodes successfully generated in this iteration. potential parent node set ; Calculate the values ​​via the set of potential parent nodes respectively Different potential nodes reach new nodes The cumulative cost of the path is calculated, and the node with the minimum total cost and whose connection satisfies the collision-free condition is selected as the new node. final parent node : ； And it satisfies the constraints: Node With new nodes The lines connecting them are free from obstacles and collisions. In the formula, Set of potential parent nodes Candidate nodes in; To reach a node from the root node of the current tree along the tree structure The accumulated path cost; The cost of connecting the two points using the Euclidean distance; S6.2: Utilizing new nodes For neighborhood set Perform rewiring tests on other nodes within the system: For any neighboring node in the set If via a new node Reaching this neighboring node If the new cumulative path has a lower cost and the connection between the two points has no collision, then the neighboring node is disconnected. The existing parent-child connection is updated by changing its parent node to the new node. ; The formula for determining rewiring is: ； In the formula, The final parent node newly determined in S6.1 Reaching a new node The actual cumulative path cost; For the neighboring nodes before the update The original cumulative path cost; This represents the Euclidean distance cost from the new node to the neighboring nodes.

9. The bidirectional path planning method integrating feedback-driven sampling and hierarchical delay scheduling according to claim 8, characterized in that: S7 includes the following steps: S7.1: When generating a new node After completing the local rewiring, find the distance to the new node in the node set of another random tree that has not yet been expanded. The node with the closest Euclidean distance is denoted as the opposite nearest node. ; S7.2: Determine the new node Nearest node on the opposite side Does it meet the collision-free connectivity condition? The collision-free connectivity condition includes: ； And the constraint condition is: node With nodes The connecting lines did not collide with environmental obstacles; In the formula, This is the preset threshold for the intersection distance between two trees; S7.3: If the collision-free connectivity condition is met, the two trees are determined to have successfully intersected. Backtrack the parent-child connection relationships of the nodes in the two random trees and output the initial feasible path connecting the starting point and the target point. If the collision-free connectivity condition is not met, the intersection is determined to have failed. At this time, the growth order of the two random trees is swapped: the current starting tree is used as the target tree for the next round, and the current target tree is used as the starting tree for the next round. Then, the process returns to step S2 to continue the next round of iteration until the maximum number of iterations is reached.

10. A path planning system integrating feedback-driven and hierarchical scheduling, characterized in that... The system includes: The initialization module is used to obtain environmental information and initialize a bidirectional random tree with the starting point and the target point as the root nodes; The multi-level hierarchical scheduling module is used to attempt to execute strategy one, strategy two, and strategy three in order of priority to generate new nodes. Among them, strategy one is a self-healing greedy target extension, strategy two is a feedback-driven hierarchical sampling extension, and strategy three is a global compensation sampling extension. The next level strategy is only triggered when the previous level strategy fails or is blocked. The tree update module is used to add successfully generated new nodes to the corresponding random tree and perform local rewiring optimization. The intersection detection module is used to determine whether a new node is connected to another random tree. If it is connected, it outputs the initial feasible path. If it is not connected, it alternates the growth order of the two trees and drives the multi-level hierarchical scheduling module to continue iterating.

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