Unmanned aerial vehicle penetration trajectory online planning method based on adaptive Hybrid-A*

Abstract

The invention relates to the technical field of flight path autonomous planning, in particular to an unmanned aerial vehicle low-altitude penetration trajectory online planning method based on adaptive Hybrid-A *, which comprises the following steps: determining a starting point and a target point of a path in a gridded task area, and determining joint detection probability distribution of detection probabilities of a plurality of radars in the task area; establishing a discretized unmanned aerial vehicle motion model; based on the joint detection probability distribution, the path length from the starting point to the to-be-selected planning point and the path length from the to-be-selected planning point to the target point, path planning is carried out based on an extension point given by a discretization unmanned aerial vehicle motion model, and a low-altitude penetration trajectory is obtained; evaluating the low-altitude penetration trajectory: calculating an average detected probability of the low-altitude penetration trajectory based on the joint detection probability distribution; according to the invention, the flight path planning efficiency and stability can be improved.

Description

Technical Field

[0001] This invention relates to the field of autonomous trajectory planning technology, specifically to an online trajectory planning method for low-altitude penetration of unmanned aerial vehicles (UAVs) based on adaptive Hybrid-A*. Background Technology

[0002] The core principle of low-altitude penetration technology lies in using the concealment effect of terrain to break through the detection and interception lines of the enemy's air defense system. At that time, with the continuous advancement of radar technology, the survival probability of traditional high-altitude flight methods was greatly reduced under the enemy's strict radar surveillance. In stark contrast, in the low-altitude environment, radar beams are affected by both terrain reflection and attenuation, thus creating a large number of detection blind spots for aircraft to carry out low-altitude penetration.

[0003] In the context of increasingly complex modern battlefield environments, unmanned aerial vehicles (UAVs) have gained wider application compared to manned aircraft due to their significant advantages such as low cost, operational flexibility, versatility, and strong battlefield survivability. Their suitability is particularly prominent when performing dangerous missions in harsh environments. Driven by the demands of battlefield operations, the low-altitude penetration capability of UAVs has gradually become an indispensable key capability in the development of weaponry worldwide.

[0004] Autonomous trajectory planning and task allocation together constitute the UAV mission planning system, with autonomous trajectory planning being the core technology for enhancing the autonomous combat capability of UAV formations. In modern warfare, the combat environment is extremely harsh, and countries are placing increasing emphasis on the rapid response capabilities of their weapons and equipment. This undoubtedly places more stringent demands on the real-time performance and stability of planning algorithms. For UAVs, improving the planning efficiency and stability of algorithms is of great significance, directly affecting the survival probability of the UAVs and the success or failure of combat missions.

[0005] In practical applications of autonomous flight path planning for unmanned aerial vehicles (UAVs), UAVs typically require onboard mission planning computers to plan feasible flight paths. However, this process often faces numerous challenges. First, traditional manual path calibration methods are no longer sufficient for actual combat needs. Second, during the planning process, the UAV is constantly in motion, and the onboard computer's computing power is limited, making it difficult to quickly derive feasible paths using complex trajectory planning methods. This results in low efficiency, lengthy planning times, and poor real-time performance. Third, the planned path results often fail to meet the maneuverability constraints of the UAV, making it difficult to implement the planned paths in complex environments and effectively engage targets.

[0006] Therefore, improving the efficiency and reliability of flight path planning, and quickly planning feasible flight paths for UAV formations in the ever-changing battlefield environment, plays a crucial role in the success or failure of combat missions and the survival of UAVs.

[0007] In recent years, the A* algorithm has been widely recognized as one of the most efficient pathfinding algorithms due to its superior performance, theoretically achieving time optimization. This algorithm, through careful design of the cost function, prioritizes the node with the smallest cost function value as the next node to expand when searching waypoints, thus ensuring the shortest path is ultimately found. The A* algorithm not only has a wide range of applications but also strong scalability, and the algorithm itself is very mature, enabling efficient planning. Summary of the Invention

[0008] In view of the above problems, the present invention provides an online trajectory planning method for low-altitude penetration of UAVs based on adaptive Hybrid-A*, which solves the technical problem that the trajectory planning efficiency and stability of the prior art are not high enough.

[0009] This invention provides an online trajectory planning method for low-altitude penetration of unmanned aerial vehicles (UAVs) based on adaptive Hybrid-A*, comprising the following steps:

[0010] Step S1: Determine the gridded mission area, determine the starting point and target point of the route, and determine the joint detection probability distribution of the detection area and blind zone of multiple radars in the mission area;

[0011] Step S2: Establish a discrete UAV motion model, which is used to determine the change in the motion state of the UAV from the current moment to the next moment;

[0012] Step S3: Based on the joint detection probability distribution, the path length from the starting point to the candidate planning point and the path length from the candidate planning point to the target point, and based on the extension points given by the discretized UAV motion model, perform path planning to obtain the low-altitude penetration trajectory.

[0013] Step S4: Evaluate the low-altitude penetration trajectory, including: calculating the average probability of detection of the low-altitude penetration trajectory based on the joint detection probability distribution.

[0014] Preferably, step S1 specifically includes:

[0015] Step S1-1: Divide the area where the UAV will perform its mission into an evenly distributed grid of square grid cells;

[0016] Step S1-2: Determine the grid where the starting point and target point of the route are located, and determine the heading angle of the UAV at the starting point and target point;

[0017] Steps S1-3: Mark the elevation information of each grid cell to obtain a grid elevation map. Determine the joint detection probability distribution of the detection area and blind zone of multiple radars based on the multiple radar locations and the grid elevation map.

[0018] Preferably, steps S1-3 specifically include:

[0019] Step S1-3-1: For each radar, the line-of-sight occlusion relationship from the radar to each grid cell obtained from the elevation map is used to determine the radar's detection area and blind zone. Within the detection area, the detection probability value of the grid cell is determined by the distance between the grid cell and the radar, thus obtaining the detection probability distribution of each radar.

[0020] Step S1-3-2: Fuse the detection probability distributions of each radar to obtain a joint detection probability distribution.

[0021] Preferably, step S2 specifically includes:

[0022] Step S2-1: Determine the discretized model of the UAV's planar motion, the expression of which is:

[0023]

[0024] Where, x k ,y k and x k+1 ,y k+1 The x and y coordinates of the UAV at time k and time k+1 are respectively, θ k and θ k+1 Δt represents the heading angles at time k and k+1, respectively, and Δt is the time step.

[0025] Step S2-2: Determine the heading angle interval Δθ between the candidate planning points obtained by the UAV from time k to time k+1, expressed as:

[0026]

[0027] Where N is the total number of candidate planning points, ω max This represents the rate of change of the maximum heading angle.

[0028] Preferably, step S3 specifically includes:

[0029] Step S3-1: Based on the joint detection probability distribution, the path length from the starting point to the candidate planning point, and the path length from the candidate planning point to the target point, establish the adaptive cost function of Hybrid-A*;

[0030] Step S3-2: Create and initialize the OPEN and CLOSED sets;

[0031] Step S3-3: Determine if the OPEN set is empty. If it is not empty, select the grid point with the smallest cost function value from the OPEN set as the current candidate planning point, move it from the OPEN set to the CLOSED set, and mark the current candidate planning point as Best.

[0032] Step S3-4: Determine whether the current candidate planning point has reached the target point. If it has not reached the target point, obtain multiple candidate planning points of the current candidate planning point, calculate the cost function value of each candidate planning point, select the planning point with the minimum cost, mark it as Best and move it into the OPEN set, and return to step S3-3.

[0033] If the target node has been reached, the current candidate planning point is moved into the CLOSED set, and the nodes generated in each step of the CLOSED set are traced back in turn to generate a low-altitude penetration trajectory.

[0034] Preferably, in step S3-1, the adaptive cost function is:

[0035]

[0036] Where f represents the adaptive cost function, κ1 and κ2 are adaptive weight coefficients, P is the joint detection probability distribution at the candidate planning point, G is the path length cost from the starting point to the candidate planning point, and H is the estimated path length cost from the candidate planning point to the target point. is the floor operator, and e is the cost function adjustment factor.

[0037] Preferably, in step S3-4, the criterion for determining whether the current candidate planning point has reached the target point is:

[0038]

[0039] Where |·| represents calculating the absolute value, θ f x is the heading angle that the drone is required to reach when arriving at the target point. f ,y f These are the coordinates of the target point.

[0040] Preferably, in step S3-4, the step of obtaining multiple candidate planning points for the current candidate planning point specifically includes:

[0041] Centered on the current candidate planning point, with the distance the UAV can fly at the time step Δt as the radius, and based on the current flight direction of the UAV, multiple candidate planning points are generated according to the heading angle interval Δθ, and candidate planning points that overlap with obstacles are discarded.

[0042] Preferably, in step S3-3, when the OPEN set is empty, the path planning is determined to have failed, the adaptive weight coefficients κ1 and κ2 are adjusted, the cost function adjustment factor e is adjusted, and the process returns to step S3-2.

[0043] Preferably, step S4 specifically includes:

[0044] The average probability of detection is obtained by calculating the arithmetic mean or weighted average of the joint detection probability values ​​of the low-altitude penetration trajectory in the corresponding grid cells of the mission area.

[0045] Compared with the prior art, the present invention has at least the following beneficial effects:

[0046] (1) The online planning method for low-altitude penetration trajectory of UAVs based on adaptive Hybrid-A* provided in this invention achieves effective avoidance of high-risk areas by clearly defining the gridded task area, fusing the joint detection probabilities of multiple radars in real time, and combining the UAV motion discretization model. By dynamically adjusting the path cost function using adaptive weights, the method can effectively optimize the flight path while minimizing the enemy radar detection probability. This planning method greatly improves the survival probability of UAVs in complex and high-threat environments, while taking into account the flight time and mission efficiency of penetration.

[0047] (2) This invention employs a Hybrid-A* online planning algorithm based on graph search principles, which has high computational and execution efficiency. By performing real-time gridding of the mission area, it can quickly generate optimal penetration trajectories that meet terrain and radar distribution constraints, efficiently completing real-time online planning of penetration trajectories, meeting the needs of rapid response in actual combat, and possessing good engineering feasibility and application promotion value.

[0048] (3) This invention, through the fusion analysis of distributed multi-radar and terrain elevation information, can fully utilize terrain-concealed areas in a densely covered radar monitoring network to plan a penetration path with a low probability of detection. This avoids the inefficient traditional method of flying around restricted areas over a large area, and achieves flexible and rapid penetration in highly contested environments, effectively improving the battlefield adaptability and penetration success rate of UAVs. Attached Figure Description

[0049] The accompanying drawings are for illustrative purposes only and are not intended to limit the scope of the invention.

[0050] Figure 1 The flowchart shows the online trajectory planning method for low-altitude penetration of UAVs based on adaptive Hybrid-A* provided by this invention.

[0051] Figure 2 A detailed flowchart of the online trajectory planning method for low-altitude penetration of UAVs based on adaptive Hybrid-A* provided by this invention.

[0052] Figure 3 The image provided by this invention is a joint detection probability distribution map of multiple radar detection areas and their blind spots, obtained from a grid elevation map within the mission area in the early stages.

[0053] Figure 4 This is a schematic diagram of point expansion when the number of expansion points is 5, as provided by the present invention.

[0054] Figure 5 A comparison chart of the trajectory of the UAV low-altitude penetration trajectory planning provided by the present invention and the conventional UAV low-altitude penetration trajectory with the shortest penetration time.

[0055] Figure 6 A comparison chart showing the probability of detection of the UAV low-altitude penetration trajectory planned by this invention and the conventional UAV low-altitude penetration trajectory with the shortest time cost. Detailed Implementation

[0056] To better understand the above-described objectives, features, and advantages of the present invention, the invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be noted that, unless otherwise specified, the embodiments of the present invention and the features thereof can be combined with each other. Furthermore, the present invention can be implemented in other ways different from those described herein; therefore, the scope of protection of the present invention is not limited to the specific embodiments disclosed below.

[0057] The present invention provides an online trajectory planning method for low-altitude penetration of unmanned aerial vehicles (UAVs) based on adaptive Hybrid-A*. First, it describes and models the scenario and problem to be planned, establishing a motion model for the UAV and a terrain model for the mission area. It also establishes a detection probability model considering multi-radar joint surveillance under terrain-concealed blind spots. Based on the traditional Hybrid-A* algorithm, the multi-radar joint detection probability is introduced into the cost function, and the weights of each component are dynamically adjusted, achieving an adaptive trade-off between radar avoidance and shortest path during UAV path planning. Simultaneously, the algorithm combines the UAV's kinematic constraints with the actual mission requirements, generating safe and efficient trajectories that meet low-altitude penetration requirements, thus improving the autonomous passage capability in complex surveillance environments.

[0058] like Figure 1 As shown, this invention discloses an online planning method for low-altitude penetration trajectory of unmanned aerial vehicles (UAVs) based on adaptive Hybrid-A*, comprising the following steps:

[0059] Step S1: Determine the gridded mission area, determine the starting point and target point of the route, and determine the joint detection probability distribution of the detection areas and blind zones of multiple radars in the mission area.

[0060] This invention divides the area where the UAV performs its mission into a grid, dividing the mission area into an average grid of square regions.

[0061] In some embodiments, the side length of the gridded square region can be determined based on the actual length of the task area.

[0062] Determining the starting and target points of the route includes determining the positions and heading angles of the starting and target points. Specifically, the grid containing the starting and target points of the UAV's mission route is selected in the mission area grid, and the heading angles of the UAV at the starting and target points are determined.

[0063] Within the gridded mission area, input the joint detection probability distribution of multiple radar detection areas and blind zones, obtained previously based on the gridded elevation map within the mission area, such as... Figure 3 As shown.

[0064] In some embodiments, the elevation information of each grid cell is first labeled according to a gridded map of the mission area to obtain a grid elevation map. For each radar deployed in the mission area, based on its installation location, height, orientation, beam parameters (such as elevation angle, azimuth angle, maximum detection range, etc.) and the grid elevation map, the probability of each grid cell being directly detected by the radar is calculated using a spatial geometric projection method, taking into account blind spots caused by terrain obstruction, buildings, and other obstacles. Specifically, ray projection analysis can be used to determine the obstruction of each line-of-sight path from the radar to each grid cell based on the grid elevation map and radar parameters, thereby determining whether the grid cell belongs to the radar detection area or blind spot, and assigning a corresponding detection probability value (e.g., 1 for the detection area, 0 for the blind spot, and a value between 0 and 1 for partial obstruction).

[0065] In some embodiments, after obtaining the detection probability distribution of each radar for each grid cell in the mission area, the detection probability distributions of all radars can be fused. Specifically, a joint probability method can be used, such as weighted summation, taking the maximum value, or Bayesian inference of the detection probability of each grid cell, to generate the joint detection probability distribution of that grid cell under the multi-radar system. The joint detection probability distribution can accurately reflect the coverage of each grid cell in the mission area under multi-radar cooperation, including complex scenarios such as multi-radar detection overlap enhancement and shared blind spots due to elevation obstacles.

[0066] Through the above methods, this invention establishes a gridded radar joint detection probability distribution for subsequent UAV path planning.

[0067] Step S2: Establish a discrete UAV motion model, which is used to determine the change in the motion state of the UAV from the current moment to the next moment;

[0068] In this step, the planar motion model of the UAV is first established, and its expression is:

[0069]

[0070] in, Here, V represents the velocity components of the UAV's horizontal and vertical axes, respectively, where V is the flight speed and θ is the heading angle. ω is the rate of change of the heading angle.

[0071] Using Δt as the step size, the planar motion model of the UAV in the step is discretized, and the discretized expression is:

[0072]

[0073] Where, x k ,y k and x k+1 ,y k+1 The x and y coordinates of the UAV at time k and time k+1 are respectively, θ k and θ k+1 Δt represents the heading angles at time k and k+1, respectively, and Δt is the time step.

[0074] From time k to time k+1, the discrete coordinates of the location of the UAV of this invention can be expanded to obtain N candidate planning points at time k+1, as shown in Figure 4. The heading angle interval Δθ between adjacent candidate planning points is:

[0075]

[0076] Where N is the total number of candidate planning points, ω max This represents the maximum rate of change of heading angle, which corresponds to the maximum turning capability of the UAV.

[0077] Based on the above discretized UAV motion model, this invention determines the position change and heading angle change of the UAV from the current moment to the next moment during the execution of the mission, and determines that the candidate planning point for the next moment requires that the adjacent candidate planning points meet the heading angle interval.

[0078] Step S3: Based on the joint detection probability distribution, the path length from the starting point to the candidate planning point and the path length from the candidate planning point to the target point, and based on the extension points given by the discretized UAV motion model, perform path planning to obtain the low-altitude penetration trajectory.

[0079] In this step, the invention introduces the probability distribution of multi-radar joint detection into the cost function, determines the adaptive cost function of the adaptive Hybrid-A* algorithm, and combines the kinematic constraints such as the UAV's turning radius and heading angular velocity to finally complete the trajectory planning, as described in detail below.

[0080] Step S3-1: Establish the adaptive cost function for the Hybrid-A* algorithm.

[0081] The adaptive cost function for the Hybrid-A* algorithm is established as follows:

[0082] f = κ1P + κ2(G + H)

[0083]

[0084] Where f represents the adaptive cost function, κ1 and κ2 are adaptive weight coefficients, P is the joint detection probability distribution at the candidate planning point, G is the path length cost from the starting point to the candidate planning point, and H is the estimated path length cost from the candidate planning point to the target point. The estimated path length cost can be calculated based on the straight-line distance from the candidate planning point to the target point, ignoring obstacles. The integer part is the rounding operator, and e is the cost function adjustment factor, which can be set to a positive integer.

[0085] Step S3-2: Create and initialize the OPEN and CLOSED sets.

[0086] Create an OPEN set and a CLOSED set. The OPEN set stores nodes that have been generated but not yet expanded, while the CLOSED set stores nodes that have been expanded. During initialization, the trajectory starting point is loaded into the OPEN set, and the CLOSED set is cleared. The expansion refers to the ability of the discrete coordinates of the UAV's location from time k to time k+1 to expand into N candidate planning points at time k+1.

[0087] Step S3-3: Determine if the OPEN set is empty. If it is not empty, select the node with the lowest replacement value from the OPEN set as the current candidate planning point and move it from the OPEN set to the CLOSED set. Mark the current candidate planning point as Best.

[0088] Step S3-4: Determine whether the current candidate planning point has reached the target point. The criteria for determining whether the target point has been reached are as follows:

[0089]

[0090] Where |·| represents calculating the absolute value, θ f x is the heading angle that the drone is required to reach when arriving at the target point. f,y f These are the coordinates of the target point.

[0091] If the target node has not yet been reached, then using the current candidate planning point as the center, with the distance the UAV can fly at the time step Δt as the radius, and with the current flight direction of the UAV as the reference, expand according to the heading angle interval Δθ to generate N=5 candidate planning points, such as... Figure 4 As shown, if a node collides with an obstacle, discard that node. Calculate the cost function value for each candidate planning point, select the planning point with the minimum cost, mark it as Best, and move it into the OPEN set. Return to step S3-3.

[0092] If the target node has been reached, the current candidate planning point is moved into the CLOSED set, and the nodes generated in each step of the CLOSED set are traced back in turn to generate a low-altitude penetration trajectory.

[0093] In some embodiments, in step S3-3, when the OPEN set is empty, the path planning is determined to have failed. At this time, the adaptive weight coefficients κ1 and κ2, the cost function adjustment factor e, etc. can be adjusted, and then the process returns to step S3-2 to replan the path.

[0094] Step S4: Evaluate the low-altitude penetration trajectory, including: calculating the average probability of detection of the low-altitude penetration trajectory based on the joint detection probability distribution.

[0095] In this step, the low-altitude penetration trajectory is composed of a series of consecutive or adjacent grid cells in a grid map. Based on the path of the low-altitude penetration trajectory, the index set of all grid cells traversed by the trajectory is first determined. Subsequently, the detection probability value corresponding to each grid cell traversed by the trajectory is extracted from the joint detection probability distribution. Specifically, the average detection probability of the low-altitude penetration trajectory can be obtained by calculating the arithmetic mean of the joint detection probability values ​​of all traversed grid cells.

[0096] In some embodiments, the joint detection probability of each grid on the trajectory can be weighted and averaged. For example, the weights can be adjusted based on the trajectory's dwell time, speed, or mission requirements within each grid. If the trajectory spends a longer time in certain grid areas, the weight of the joint detection probability of that grid is increased accordingly.

[0097] By combining the joint detection probability distribution with the spatial distribution of low-altitude penetration trajectories, the detectability of selected trajectories under multi-radar coverage can be effectively quantitatively evaluated.

[0098] To illustrate the effectiveness of the method proposed in this invention, the following detailed description of the above technical solution of this invention is provided through a specific embodiment.

[0099] Example 1

[0100] In this embodiment, the UAV flies at a speed of 0.8 Mach and has a minimum turning radius of 10 km. The cost function is an adaptive minimum cost that balances joint detection probability and penetration time; the comparative case has the shortest penetration time. For example... Figure 2 As shown in this embodiment, a method for planning low-altitude penetration trajectory of UAVs based on the adaptive Hybrid-A* algorithm is disclosed, which includes the following steps:

[0101] Step 1: Select a randomly generated canyon terrain as the task area and enter the task information.

[0102] Step 1.1: Select the task area as a rectangle, with a size of 200x200km. 2 Then, the map of the task area is gridded, with each grid being a square grid of 200x200m. 2 .

[0103] Step 1.2: Input the starting point and target point of the plan and their heading angle constraints. The starting point is (0km, 140km), and the initial heading angle is 0°; the target point is (190km, 0km), and the target heading angle is 0°.

[0104] Step 2: On the drone's penetration altitude plane, input the joint detection probability distribution results of multiple radar detection areas and their blind spots, obtained in the early stage based on the grid elevation map of the mission area, such as... Figure 3 As shown in Table 1, there are three radars within the mission area, and their location coordinates, detection radius, and altitude are as follows.

[0105] Table 1

[0106] Radar number coordinate Detection radius Radar altitude 1 (160,160)km 100km 0.05km 2 (80,40)km 70km 0.02km 3 (40,100)km 50km 0.03km

[0107] Step 3: On the plane of the UAV's penetration altitude, establish a planar motion model of the UAV's low-altitude penetration and discretize it.

[0108] Step 3.1: Establish a planar motion model of the UAV.

[0109]

[0110] Step 3.2: Discretize the UAV planar motion model from Step 3.1 with a step size of Δt = 0.1s. The discretized model can be written as:

[0111]

[0112] From the current time to the next time, each discrete point can be expanded to obtain N candidate discrete points, and the heading angle interval Δθ between adjacent candidate discrete points is:

[0113]

[0114] Step 4: Use the adaptive Hybrid-A* algorithm to plan the low-altitude penetration trajectory of the UAV in the multi-radar joint surveillance area.

[0115] The specific implementation method for step 4 is as follows:

[0116] Step 4.1: Design the adaptive cost function for the Hybrid-A* algorithm.

[0117] f = κ1P + κ2(G + H)

[0118] κ1 and κ2 are the adaptive weighting coefficients of the design, which can be written as

[0119]

[0120] Step 4.2: Create the OPEN set and the CLOSED set. The OPEN set is used to store nodes that have been generated but not expanded, and the CLOSED set is used to store nodes that have been expanded.

[0121] During initialization, the trajectory starting point is loaded into the OPEN set, and the CLOSED set is cleared. Initially, the OPEN set contains only the starting point (0,0) and the CLOSED set is empty, containing no node information.

[0122] Step 4.3: If the OPEN set is empty, the planning fails and ends. If the OPEN set is not empty, select the node with the lowest replacement value from the OPEN set as the current node and move it from the OPEN set to the CLOSED set. Mark the node with the lowest replacement value as Best.

[0123] At the start of the planning process, taking the result of step 4.2 as an example, when executing step 4.3, the OPEN set is not empty. The node with the lowest value in the OPEN table is taken as the current Best node, i.e., node (0,0), and this node is placed into the CLOSED set. When step 4.3 ends, the OPEN set is empty, and the CLOSED set contains node (0,0), and so on.

[0124] Step 4.4: Determine whether the target point has been reached. The criteria for determining whether the target point has been reached are as follows:

[0125]

[0126] If the target node is reached, the target node is added to the CLOSED set. The nodes generated in each step are traced back in sequence to generate a low-altitude penetration trajectory, and step 4.4 is executed. If the target node has not yet been reached, step 4.5 is executed.

[0127] Step 4.5: Using the node Best from Step 4.3 as the center, generate N = 5 candidate discrete points according to equation (3), such as... Figure 4 As shown, if a node collides with an obstacle, discard that node. Calculate the cost of each candidate discrete point, select the Best point with the lowest cost, add it to the OPEN set, and continue with step 4.3.

[0128] For example, when the formation of UAVs extends from (0,0) towards the target node, five nodes to be extended are created, starting from (0,0) and constrained by the turning radius and the rate of change of heading angle. The cost value of each node to be extended is calculated. The cost value is calculated according to equation (10). The node to be extended with the smallest cost value is loaded into the OPEN set, and step 4.2 is continued.

[0129] This embodiment is implemented using C++ simulation, and the simulation results are shown in the figure below. Figure 5 and Figure 6 As shown in Table 2, the average probability of being detected and the planning time are as follows.

[0130] Table 2

[0131] Planning that minimizes the time required to penetrate defenses This embodiment Average probability of being detected 0.217 0.00482 Flight path planning time / s 0.75s 1.06s

[0132] The calculation results from this embodiment show that the proposed planning method can quickly plan low-altitude penetration trajectories. Both this embodiment and the comparative case can achieve planning within seconds. However, the probability of detection for the planning method that prioritizes minimizing penetration time is 45 times higher than that of this embodiment. The planning time of this embodiment is slightly longer than that of the planning method that prioritizes minimizing penetration time because it requires processing the detection probability information.

[0133] The UAV low-altitude penetration trajectory planning method based on the adaptive Hybrid-A* algorithm disclosed in this example can quickly obtain the UAV's low-altitude penetration trajectory under the dense distribution and joint surveillance of multiple radars, and has high planning efficiency. It can effectively reduce the probability of UAV low-altitude penetration being detected, which meets the needs of combat applications, has a high penetration success rate and real-time performance, is easy to implement in engineering, and has broad prospects for combat applications.

[0134] While the specific embodiments of the present invention depict actions or steps in a particular order, this should be understood as requiring such actions or steps to be performed in the specific order shown or in sequential order, or requiring all illustrated actions or steps to be performed to achieve the desired result. In certain environments, multitasking and parallel processing may be advantageous. Similarly, although several specific implementation details are included in the above discussion, these should not be construed as limiting the scope of this disclosure. Certain features described in the context of individual embodiments may also be implemented in combination in a single implementation. Conversely, various features described in the context of a single implementation may also be implemented individually or in any suitable sub-combination in multiple implementations.

[0135] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. An online planning method for low-altitude penetration trajectory of UAVs based on adaptive Hybrid-A*, comprising the following steps: Step S1: Determine the gridded mission area, determine the starting point and target point of the route, and determine the joint detection probability distribution of the detection area and blind zone of multiple radars in the mission area; Step S2: Establish a discrete UAV motion model, which is used to determine the change in the motion state of the UAV from the current moment to the next moment; Step S3: Based on the joint detection probability distribution, the path length from the starting point to the candidate planning point and the path length from the candidate planning point to the target point, and based on the extension points given by the discretized UAV motion model, perform path planning to obtain the low-altitude penetration trajectory. Step S4: Evaluate the low-altitude penetration trajectory, including: calculating the average probability of detection of the low-altitude penetration trajectory based on the joint detection probability distribution.

2. The method for online planning of low-altitude penetration trajectory of UAVs based on adaptive Hybrid-A* as described in claim 1, characterized in that, Step S1 specifically includes: Step S1-1: Divide the area where the UAV will perform its mission into an evenly distributed grid of square grid cells; Step S1-2: Determine the grid where the starting point and target point of the route are located, and determine the heading angle of the UAV at the starting point and target point; Steps S1-3: Mark the elevation information of each grid cell to obtain a grid elevation map. Determine the joint detection probability distribution of the detection area and blind zone of multiple radars based on the multiple radar locations and the grid elevation map.

3. The online planning method for low-altitude penetration trajectory of UAVs based on adaptive Hybrid-A* as described in claim 2, characterized in that, Steps S1-3 specifically include: Step S1-3-1: For each radar, the line-of-sight occlusion relationship from the radar to each grid cell obtained from the elevation map is used to determine the radar's detection area and blind zone. Within the detection area, the detection probability value of the grid cell is determined by the distance between the grid cell and the radar, thus obtaining the detection probability distribution of each radar. Step S1-3-2: Fuse the detection probability distributions of each radar to obtain a joint detection probability distribution.

4. The online planning method for low-altitude penetration trajectory of UAVs based on adaptive Hybrid-A* as described in claim 3, characterized in that, Step S2 specifically includes: Step S2-1: Determine the discretized model of the UAV's planar motion, the expression of which is: Where, x k ,y k and x k+1 ,y k+1 The x and y coordinates of the UAV at time k and time k+1 are respectively, θ k and θ k+1 Δt represents the heading angles at time k and k+1, respectively, and Δt is the time step. Step S2-2: Determine the heading angle interval Δθ between the candidate planning points obtained by the UAV from time k to time k+1, expressed as: Where N is the total number of candidate planning points, ω max This represents the rate of change of the maximum heading angle.

5. The online planning method for low-altitude penetration trajectory of UAVs based on adaptive Hybrid-A* as described in claim 4, characterized in that, Step S3 specifically includes: Step S3-1: Based on the joint detection probability distribution, the path length from the starting point to the candidate planning point, and the path length from the candidate planning point to the target point, establish the adaptive cost function of the Hybrid-A* algorithm; Step S3-2: Create and initialize the OPEN and CLOSED sets; Step S3-3: Determine if the OPEN set is empty. If it is not empty, select the grid point with the smallest cost function value from the OPEN set as the current candidate planning point, move it from the OPEN set to the CLOSED set, and mark the current candidate planning point as Best. Step S3-4: Determine whether the current candidate planning point has reached the target point. If it has not reached the target point, obtain multiple candidate planning points of the current candidate planning point, calculate the cost function value of each candidate planning point, select the planning point with the minimum cost, mark it as Best and move it into the OPEN set, and return to step S3-3. If the target node has been reached, the current candidate planning point is moved into the CLOSED set, and the nodes generated in each step of the CLOSED set are traced back in turn to generate a low-altitude penetration trajectory.

6. The online planning method for low-altitude penetration trajectory of UAVs based on adaptive Hybrid-A* as described in claim 5, characterized in that, In step S3-1, the adaptive cost function is: f = κ1P + κ2(G + H) Where f represents the adaptive cost function, κ1 and κ2 are adaptive weight coefficients, P is the joint detection probability distribution at the candidate planning point, G is the path length cost from the starting point to the candidate planning point, and H is the estimated path length cost from the candidate planning point to the target point. is the floor operator, and e is the cost function adjustment factor.

7. The online planning method for low-altitude penetration trajectory of UAVs based on adaptive Hybrid-A* as described in claim 6, characterized in that, In step S3-4, the criterion for determining whether the current candidate planning point has reached the target point is: Where |·| represents calculating the absolute value, θ f x is the heading angle that the drone is required to reach when arriving at the target point. f ,y f These are the coordinates of the target point.

8. The online planning method for low-altitude penetration trajectory of UAVs based on adaptive Hybrid-A* as described in claim 7, characterized in that, In steps S3-4, the step of obtaining multiple candidate planning points for the current candidate planning point specifically includes: Centered on the current candidate planning point, with the distance the UAV can fly at the time step Δt as the radius, and based on the current flight direction of the UAV, multiple candidate planning points are generated according to the heading angle interval Δθ, and candidate planning points that overlap with obstacles are discarded.

9. The online planning method for low-altitude penetration trajectory of UAVs based on adaptive Hybrid-A* as described in claim 8, characterized in that, In step S3-3, when the OPEN set is empty, the path planning is determined to have failed. The adaptive weight coefficients κ1 and κ2 are adjusted, the cost function adjustment factor e is adjusted, and the process returns to step S3-2.

10. The online planning method for low-altitude penetration trajectory of UAVs based on adaptive Hybrid-A* as described in claim 9, characterized in that, Step S4 specifically includes: The average probability of detection is obtained by calculating the arithmetic mean or weighted average of the joint detection probability values ​​of the low-altitude penetration trajectory in the corresponding grid cells of the mission area.

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