Multi-unmanned aerial vehicle flight parameter collaborative optimization method for three-dimensional stealth path design

Abstract

The invention discloses a multi-unmanned aerial vehicle flight parameter collaborative optimization method for three-dimensional stealth path design, and the method comprises the steps: building a three-dimensional environment model which comprises a terrain environment model and an enemy radar detection model; based on a multi-unmanned aerial vehicle endurance energy consumption function, a radio frequency stealth performance evaluation function, a path smoothing evaluation function, a dynamic energy consumption function and an aggregation density evaluation function, performing weighted summation on each function to construct a multi-unmanned aerial vehicle path planning performance evaluation function; establishing a multi-unmanned aerial vehicle flight parameter collaborative optimization model for three-dimensional stealth path design by taking minimization of a multi-unmanned aerial vehicle path planning performance evaluation function as an optimization target and taking meeting of path feasibility judgment and unmanned aerial vehicle dynamics limitation as constraint conditions; and carrying out two-step solution on the optimization model by adopting a three-dimensional improved A * algorithm. According to the method, the calculation complexity is reduced while the radio frequency stealth performance of the multiple unmanned aerial vehicles is improved.

Description

Technical Field

[0001] The present invention belongs to the field of UAV path planning, and specifically relates to a collaborative optimization method for multi-UAV flight parameters for three-dimensional stealth path design. Background Art

[0002] Modern battlefield environments are characterized by three-dimensional features and highly real-time situational changes. Traditional path planning methods based on two-dimensional static models have significant limitations and are unable to adapt to the demands of dynamic combat. Against this backdrop, studying path planning for drone swarms in three-dimensional dynamic environments is of vital practical significance. In recent years, scholars at home and abroad have conducted in-depth research on the problem of collaborative path optimization for multiple drones in three-dimensional dynamic space. Current research focuses on shifting from single-path optimization to the integration of multi-dimensional constraints, incorporating collaborative metrics such as mission time synchronization and communication link stability into cost functions. Furthermore, various improvement strategies have been developed to address the common problem of traditional algorithms that often fall into local optimality.

[0003] However, research on drone path planning in 3D environments often fails to consider the drone's own RCS, focuses on a single scenario, or considers only the path planning of a single drone, without considering the path planning of a swarm of drones or the dynamic interaction with radar. In summary, there is no existing method for collaboratively optimizing flight parameters of multiple drones for 3D stealth path design. Summary of the Invention

[0004] Purpose of the invention: The purpose of the present invention is to provide a collaborative optimization method for multi-UAV flight parameters for three-dimensional stealth path design, so as to achieve the purpose of improving the radio frequency stealth performance of multiple UAVs in a three-dimensional environment.

[0005] Technical solution: The collaborative optimization method for multi-UAV flight parameters for three-dimensional stealth path design described in the present invention includes the following steps:

[0006] Establish a three-dimensional environmental model, including terrain environment model and enemy radar detection model;

[0007] Based on the multi-UAV endurance energy consumption function, radio frequency stealth performance evaluation function, path smoothness evaluation function, kinetic energy consumption function and clustering density evaluation function, a multi-UAV path planning performance evaluation function is constructed by weighted summation of each function.

[0008] Taking minimizing the performance evaluation function of multi-UAV path planning as the optimization goal and satisfying the path feasibility determination and the UAV's own dynamic limitations as the constraints, a multi-UAV flight parameter collaborative optimization model for three-dimensional stealth path design is established.

[0009] The three-dimensional improved A* algorithm is used to solve the optimization model in two steps, including: using the three-dimensional improved A* algorithm to perform reverse path planning for the drone cluster and storing the path planning results; the drone cluster first flies according to the global planned path stored in PATH, and when encountering sudden threats, it immediately performs local replanning.

[0010] Furthermore, the terrain environment model is expressed as:

[0011] z=H(x,y)

[0012] Where z represents the altitude of the terrain; H(i) is the function corresponding to the terrain environment; (x, y) represents the horizontal coordinates;

[0013] The enemy radar detection model is expressed as:

[0014]

[0015] in, is the detection probability of the target by the networked radar at time t, P i t represents the probability of detecting a UAV by the i-th radar at time t, and N is the number of networked radars on the ground.

[0016] Furthermore, the energy consumption function of multiple UAVs is the product of the total flight time of multiple UAVs and the average flight altitude, which can be expressed as:

[0017]

[0018] Among them, Γ1 is the energy consumption evaluation of the cluster, ζ m represents the flight time of the mth UAV; K 3D,m represents the number of path segments of the mth UAV; H0 represents the expected flight altitude of the UAV cluster; the i-th path point of the mth UAV is It represents the ordinate of the mth UAV at the i-th path point, and M is the number of UAVs in the cluster.

[0019] Furthermore, considering that the enemy deploys networked radars in the flight area, the evaluation function of the multi-UAV RF stealth performance is expressed as:

[0020]

[0021] Among them, Γ2 is the RF stealth performance evaluation function of UAV stealth, M is the number of UAVs in the cluster, ζ m represents the flight time of the mth UAV, is the probability that the mth UAV is detected by the networked radar at time t.

[0022] Furthermore, the evaluation function expression of multi-UAV path smoothness is:

[0023]

[0024] Among them, Γ3 is the multi-UAV path smoothing evaluation function, M is the number of UAVs in the cluster, K 3D,m represents the number of path segments of the mth UAV, Indicates the heading angle of the i+1th path point of the mth UAV; is the heading angle of the i-th path point of the m-th UAV; φ i+1,m represents the pitch angle of the i+1th path point of the mth UAV; φ i,m represents the pitch angle of the i-th path point of the m-th UAV; represents the expected change in heading angle; φ0 represents the expected change in pitch angle.

[0025] Furthermore, based on the amplitude of the heading angle and pitch angle changes of each UAV at each path point, a multi-UAV dynamic energy consumption function is constructed, which is expressed as:

[0026]

[0027] Among them, Γ4 is the multi-UAV dynamic energy consumption function, M is the number of UAVs in the cluster, K 3D,m represents the number of path segments of the mth UAV, Indicates the heading angle of the i+1th path point of the mth UAV; is the heading angle of the i-th path point of the m-th UAV; φ i+1,m represents the pitch angle of the i+1th path point of the mth UAV; φ i,m Represents the pitch angle of the i-th path point of the m-th UAV.

[0028] Furthermore, the multi-UAV aggregation density evaluation function is expressed as:

[0029]

[0030] Among them, Γ5 is the density of multiple drones, M is the number of drones in the cluster, K 3D,max =max(K 3D,m ,K 3D,n ), K 3D,m represents the number of path segments of the mth UAV, K 3D,n represents the number of path segments of the nth UAV; ||·|| represents the modulus of the vector; Represents the coordinates of the i-th path point of the m-th UAV; Represents the coordinates of the i-th path point of the n-th drone.

[0031] Furthermore, a collaborative optimization model of multi-UAV flight parameters for three-dimensional stealth path design is established, which is expressed as:

[0032]

[0033] in, is the probability that the mth UAV is detected by the network radar at time t; P c represents the detection threshold of the networked radar; dist(i) represents the distance between two points in three-dimensional space; represents the spatial position of the mth UAV at time t; obstacle represents the no-fly zone; Robstacle represents the range of the no-fly zone; is the spatial position of the jth UAV at time t; d safe For safe distance; represents the flight distance of the mth UAV in the kth path segment; L max Indicates the maximum range that the drone can fly; Indicates the heading angle of the i+1th path point of the mth UAV; is the heading angle of the i-th path point of the m-th UAV; represents the maximum turning angle of the mth UAV; φ i+1,m represents the pitch angle of the i+1th path point of the mth UAV; φ i,m represents the pitch angle of the i-th path point of the m-th UAV; △φ max is the maximum value of the pitch angle change of the drone; is the spatial position of the i-th path point of the m-th UAV; H(i) is the function corresponding to the terrain environment.

[0034] Furthermore, the three-dimensional improved A* algorithm is used to solve the optimization model in two steps, specifically:

[0035] (1) Use the three-dimensional improved A* algorithm to perform reverse path planning for the UAV cluster and store the path planning results;

[0036] (i) Assuming that a certain point in space is O, the actual evaluation g(O) of the mth UAV starting from the end point and reaching point O is expressed as:

[0037]

[0038] Among them, K O,m represents the number of path segments of the mth UAV from the end point to point O;

[0039] The heuristic function value f(O) of the mth UAV from the end point through point O to the starting point is expressed as:

[0040]

[0041] Where ω is the weighting factor; h(O) is the estimated function from point O to the starting point;

[0042] (ii) The UAV expands spatially in a three-dimensional sector shape. Assume that the current path point is A. 3D,0 , current path point A 3D,0 The next path point to be extended is A 3D,1 ;

[0043] (iii) Calculate the heuristic function for all possible next path points that meet the constraints;

[0044] (iv) Finally, select the next possible path point A with the smallest heuristic function value 3D,1 As the next waypoint of the current waypoint, waypoint A 3D,1 Become the new current path point and continue to the next step of optimization and expansion;

[0045] (v) By continuously searching for the optimal path, an optimal path from the end point to the starting point is eventually found. When the reverse path planning of the mth UAV is completed, the reverse path planning of the next UAV is continued until all the cluster paths are planned, and the planned paths are stored in PATH;

[0046] (2) The drone cluster first flies according to the global planning path stored in PATH. When encountering sudden threats, it performs local replanning. When the drone senses that the environment has changed, it uses the current path point as the starting point for local replanning and the path point in the global planning path that is closest to the end point and meets the platform safety as the end point for local replanning. The improved three-dimensional A* algorithm is used for local replanning. After the local replanning is completed, the drone continues to fly along the global planning path.

[0047] The multi-UAV flight parameter collaborative optimization system for three-dimensional stealth path design of the present invention includes:

[0048] A three-dimensional environment model building unit, used to build a three-dimensional environment model, including a terrain environment model and an enemy radar detection model;

[0049] An evaluation function construction unit is used to construct a multi-UAV path planning performance evaluation function based on a multi-UAV endurance energy consumption function, a radio frequency stealth performance evaluation function, a path smoothness evaluation function, a kinetic energy consumption function, and an aggregation density evaluation function by performing a weighted summation of each function;

[0050] The optimization model construction unit is used to establish a multi-UAV flight parameter collaborative optimization model for three-dimensional stealth path design, with the optimization goal of minimizing the multi-UAV path planning performance evaluation function and satisfying the path feasibility determination and the UAV's own dynamic limitations as constraints;

[0051] The model solving unit is used to use the three-dimensional improved A* algorithm to perform a two-step solution to the optimization model, including: using the three-dimensional improved A* algorithm to perform reverse path planning for the drone cluster and storing the path planning results; the drone cluster first flies according to the global planned path stored in PATH, and when encountering sudden threats, it immediately performs local replanning.

[0052] Beneficial effects: Compared with the existing technology, the significant technical effects of the present invention are: guided by the detection probability of networked radars for drone clusters, by constructing a multi-UAV path planning performance evaluation function, the energy consumption of multiple UAVs and the risk of radar detection are combined together, thereby meeting the radio frequency stealth requirements of multiple UAVs; on this basis, considering the constraints of path feasibility and UAV dynamics limitations, a multi-UAV flight parameter collaborative optimization model based on three-dimensional stealth path design is established, and the flight parameters of multiple UAVs are adaptively optimized; and for the optimization model, a two-step solution method based on the three-dimensional improved A* algorithm is proposed, which not only effectively improves the radio frequency stealth performance of multiple UAVs, but also reduces the computational complexity. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 Flow chart of the method of the present invention;

[0054] Figure 2 3D graph of multi-UAV path planning simulation results;

[0055] Figure 3 A top view of the multi-UAV path planning simulation results;

[0056] Figure 4 The heading angle change diagrams of multiple UAVs are shown in Figure 1, where (a) is the heading angle change diagram of UAV1, (b) is the heading angle change diagram of UAV2, (c) is the heading angle change diagram of UAV3, (d) is the heading angle change diagram of UAV1, (e) is the heading angle change diagram of UAV4, and (f) is the heading angle change diagram of UAV5.

[0057] Figure 5 Figure 1 is a graph showing the pitch angle changes of multiple drones, where (a) is the pitch angle change graph of drone UAV1, (b) is the pitch angle change graph of drone UAV2, (c) is the pitch angle change graph of drone UAV3, (d) is the pitch angle change graph of drone UAV4, (e) is the pitch angle change graph of drone UAV5, and (f) is the pitch angle change graph of drone UAV6.

[0058] Figure 6 This is a graph showing the detection probability changes of multiple UAVs by the networked radar using the method described in the present invention;

[0059] Figure 7 This is a graph showing the detection probability changes of multiple UAVs by networked radars under the particle swarm optimization algorithm. DETAILED DESCRIPTION

[0060] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0061] Starting from actual combat scenarios and considering the requirements of radio frequency stealth, the present invention conducts collaborative optimization design of the flight parameters of multiple UAVs in a three-dimensional environment, and proposes a collaborative optimization method for the flight parameters of multiple UAVs for three-dimensional stealth path design. First, a three-dimensional dynamic environment model is established that takes into account radar and no-fly zones. Then, a multi-UAV path planning performance evaluation function is constructed based on the detection probability, energy consumption, path smoothness, and cluster density of multiple UAVs. On this basis, with minimizing the multi-UAV path planning performance evaluation function as the optimization goal, and with the path feasibility determination and UAV cluster dynamics restrictions in a three-dimensional environment as constraints, a multi-UAV flight parameter collaborative optimization model for three-dimensional stealth path design is established. Finally, a two-step decomposition algorithm based on the three-dimensional improved A* algorithm is used to solve the above optimization model and adaptively optimize the flight parameters of multiple UAVs to achieve the purpose of improving the radio frequency stealth performance of multiple UAVs in a three-dimensional environment.

[0062] like Figure 1 As shown, the method of the present invention comprises the following steps:

[0063] S1. Establish a three-dimensional environmental model, including a terrain environment model and an enemy radar detection model;

[0064] (1) Construct a terrain environment model; assuming that the coordinates of any point in the terrain are (x, y, z), the terrain environment can be expressed as:

[0065] z=H(x,y) (1)

[0066] Where z represents the altitude of the terrain; H(i) is the function corresponding to the terrain environment; (x, y) represents the horizontal plane coordinates, that is, the plane parallel to the ground and with an altitude of 0.

[0067] (2) Construct an enemy radar detection model. Assuming that there are N networked radars on the ground, the probability of the networked radar detecting the target at time t can be expressed as:

[0068]

[0069] in, is the detection probability of the target by the networked radar at time t, P i t represents the probability of detecting the UAV by the i-th radar at time t.

[0070] S2. Construct a multi-UAV path planning performance evaluation function:

[0071] (1) Construct a multi-UAV endurance energy consumption function; assuming that there are M UAVs forming a cluster, the cluster endurance energy consumption evaluation Γ1 takes into account the flight time and flight altitude of each UAV, and is specifically expressed as the product of the total flight time of multiple UAVs and the average flight altitude, that is:

[0072]

[0073] Among them, m represents the flight time of the mth UAV; K 3D,m represents the number of path segments of the mth UAV; H0 represents the expected flight altitude of the UAV cluster; the i-th path point of the mth UAV is Represents the ordinate of the mth UAV at the i-th path point.

[0074] (2) Construct a multi-UAV RF stealth performance evaluation function; considering that the enemy deploys networked radars in the flight area, the RF stealth performance evaluation function Γ2 of the UAV stealth is:

[0075]

[0076] in, is the probability that the mth UAV is detected by the networked radar at time t.

[0077] (3) Construct the multi-UAV path smoothness evaluation function Γ3, which is expressed as:

[0078]

[0079] in, Indicates the heading angle of the i+1th path point of the mth UAV; is the heading angle of the i-th path point of the m-th UAV; φ i+1,m represents the pitch angle of the i+1th path point of the mth UAV; φ i,m represents the pitch angle of the i-th path point of the m-th UAV; represents the expected change in heading angle; φ0 represents the expected change in pitch angle.

[0080] (4) Construct the multi-UAV dynamic energy consumption function Γ4; it is related to the amplitude of the heading angle and pitch angle changes of each UAV at each path point, that is:

[0081]

[0082] Among them, it is considered that the drone consumes more energy when climbing.

[0083] (5) Construct a multi-UAV cluster density evaluation function; in order to reduce the probability of UAV clusters being discovered and the possibility of collisions between platforms, the multi-UAV cluster density Γ5 is expressed as follows:

[0084]

[0085] Among them, K 3D,max =max(K 3D,m ,K 3D,n ), K 3D,n represents the number of path segments of the nth UAV; ||·|| represents the modulus of the vector; Represents the coordinates of the i-th path point of the m-th UAV; Represents the coordinates of the i-th path point of the n-th drone.

[0086] (6) Construct the multi-UAV path planning performance evaluation function Θ, which is expressed as:

[0087]

[0088] Among them, α1, α2, α3, α4, and α5 are the weight coefficients of each performance evaluation, and α1+α2+α3+α4+α5=1. At the same time, α1, α2, α3, α4, and α5 are all between [0,1].

[0089] S3. Establish a collaborative optimization model for multi-UAV flight parameters for three-dimensional stealth path design;

[0090] Taking minimizing the multi-UAV path planning performance evaluation function as the optimization goal and satisfying the path feasibility judgment and the UAV's own dynamic limitations as the constraints, a multi-UAV flight parameter collaborative optimization model for three-dimensional stealth path design is established, which is expressed as follows:

[0091]

[0092] in, is the probability that the mth UAV is detected by the network radar at time t; P c represents the detection threshold of the networked radar; dist(i) represents the distance between two points in three-dimensional space; represents the spatial position of the mth UAV at time t; obstacle represents the no-fly zone; Robstacle represents the range of the no-fly zone; is the spatial position of the jth UAV at time t; d safe For safe distance; represents the flight distance of the mth UAV in the kth path segment; L max Indicates the maximum range that the drone can fly; Indicates the heading angle of the i+1th path point of the mth UAV; is the heading angle of the i-th path point of the m-th UAV; represents the maximum turning angle of the mth UAV; φ i+1,m represents the pitch angle of the i+1th path point of the mth UAV; φ i,m represents the pitch angle of the i-th path point of the m-th UAV; △φ max is the maximum value of the pitch angle change of the drone; is the spatial position of the i-th path point of the m-th UAV; H(i) is the function corresponding to the terrain environment.

[0093] S4. For the optimization model (9), a two-step solution is performed using the three-dimensional improved A* algorithm. The specific steps are as follows:

[0094] Step 1: Use the three-dimensional improved A* algorithm to perform reverse path planning for the UAV cluster and store the path planning results.

[0095] (i) Taking the mth UAV as an example, assuming that a certain point in space is O, the actual evaluation g(O) of the mth UAV starting from the end point and reaching point O can be expressed as:

[0096]

[0097] Among them, K O,m Represents the number of path segments that the mth UAV takes to reach point O from the end point.

[0098] Then, the heuristic function value f(O) of the mth UAV from the end point through point O to the starting point can be expressed as:

[0099]

[0100] Among them, ω is the weighting factor; h(O) is the estimated function from point O to the starting point, represented by the Manhattan distance.

[0101] (ii) The UAV expands spatially in a three-dimensional sector shape. Assume that the current path point is A. 3D,0 , current path point A 3D,0 The next path point to be extended is A 3D,1 ;

[0102] (iii) Based on formula (11), the heuristic function is calculated for all possible next path points that meet the constraints;

[0103] (iv) Finally, select the next possible path point A with the smallest heuristic function value 3D,1 As the next waypoint of the current waypoint, waypoint A 3D,1Become the new current path point and continue to the next step of optimization and expansion;

[0104] (v) By continuously optimizing, an optimal path from the end point to the starting point is eventually found. When the reverse path planning of the mth UAV is completed, the reverse path planning of the next UAV is continued until all cluster paths are planned and the planned paths are stored in PATH.

[0105] Step 2: The drone swarm first flies along the globally planned path stored in PATH. When encountering unexpected threats, it performs local replanning. When a drone senses a change in the environment, it uses the current pathpoint as the starting point for local replanning and the pathpoint closest to the endpoint in the globally planned path that meets platform safety requirements as the endpoint. Local replanning is performed using an improved 3D A* algorithm. After local replanning is complete, the drone continues to fly along the globally planned path.

[0106] Simulation results:

[0107] Assume that the drone swarm consists of 6 drones, and the starting and ending points of each drone are set as follows: drone 1 starts at (30, 40, 2.75) km and ends at (490, 470, 2.8) km; drone 2 starts at (20, 120, 2.7) km and ends at (160, 460, 2.75) km; drone 3 starts at (50, 130, 2.75) km and ends at (340, 470, 2.8) km; drone 4 starts at (30, 30, 2.92) km and ends at (490, 300, 2.88) km; drone 5 starts at (30, 60, 2.8) km and ends at (490, 225, 2.79) km; drone 6 starts at (20, 20, 2.93) km and ends at (490, 450, 2.8) km.

[0108] The detection probability threshold P of the networked radar to the UAV c = 0.3; the maximum horizontal turning angle of the UAV is 2π / 3; the maximum pitch angle change of the UAV is π / 2; there are five radars and one no-fly zone in the three-dimensional terrain environment, and their positions are as follows Figure 2 As shown in .

[0109] Figure 2 A three-dimensional diagram of the multi-UAV path planning simulation results is given. Figure 3A top-down view of the multi-UAV path planning simulation results is provided. As can be seen from the figure, the method described in the present invention can effectively plan multi-UAV flight paths in a three-dimensional environment while meeting platform safety and dynamic constraints, validating the effectiveness of the algorithm described in the present invention in global planning. Under the optimization method described in the present invention, each UAV's path from the starting point to the end point is relatively smooth and avoids no-fly zones. Furthermore, during flight, each UAV stays as far away from the radar detection area as possible to reduce the probability of detection by the networked radar.

[0110] Figure 4 (a) to (f) and Figure 5 Figures (a) through (f) show the horizontal heading and pitch angle variations of multiple drones, respectively. Observe that the heading and pitch angle variations of each drone during flight meet the specified constraints. Furthermore, the range of heading and pitch angle variations is small, minimizing flight costs and meeting expectations.

[0111] In order to verify the superiority of the method of the present invention, the method of the present invention is compared with the particle swarm optimization algorithm. Figure 6 The graph of the detection probability variation of the networked radar to multiple UAVs under the method of the present invention is given. Figure 7 A graph showing the detection probability of multiple drones by a networked radar using a particle swarm optimization algorithm is presented. As can be seen, using the optimization method described in this invention, the probability of multiple drones being detected by the networked radar remains below the set threshold of 0.3 throughout their flight, effectively improving the drones' RF stealth performance. However, using the particle swarm optimization algorithm, the detection probability of multiple drones is significantly higher than the set threshold. Simulations show that using the optimization method described in this invention, the path planning performance of the multiple drones is evaluated at 113.92, and the algorithm runtime is 38.12 seconds. The performance and runtime achieved using the particle swarm optimization algorithm are 142.98 and 255.89 seconds, respectively, both significantly superior to the proposed method. Clearly, the method described in this invention is capable of planning drone flight paths that achieve superior performance in a three-dimensional environment, meet dynamic constraints, and maintain platform safety, while also ensuring a shorter runtime, validating the superiority of the proposed method.

[0112] Working principle and working process of the present invention:

[0113] Considering the requirements of radio frequency stealth, the flight parameters of multiple UAVs in a three-dimensional environment are collaboratively optimized, and the stealth path of UAV clusters in a three-dimensional environment is designed. First, the impact of flight paths on the probability of networked radar detection is considered and analyzed, and a three-dimensional dynamic environment model considering radar and no-fly zones is established. Then, guided by radio frequency stealth performance and flight cost, a multi-UAV path planning performance evaluation function is constructed based on multi-UAV energy consumption, detection probability, path smoothness, and cluster density. On this basis, with minimizing the multi-UAV path planning performance evaluation function as the optimization goal, considering conditions such as UAV maneuver constraints, cluster density, energy consumption, path smoothness, and path feasibility determination and UAV dynamics constraints as constraints, a multi-UAV flight parameter collaborative optimization model for three-dimensional stealth path design is established. Finally, a two-step solution method based on an improved three-dimensional A* algorithm is used to solve the above optimization model, thereby improving the radio frequency stealth performance of multiple UAVs in a three-dimensional environment. The multi-UAV flight parameter collaborative optimization model constructed by the present invention is a nonlinear optimization with many constraints. It is based on a two-step solution method based on an improved three-dimensional A* algorithm to reduce the complexity of the calculation. The simulation results show that the proposed method can plan a multi-UAV collaborative flight path with better performance evaluation and guaranteed platform safety. It can improve the three-dimensional radio frequency stealth performance of multiple UAVs while achieving a shorter operating time, verifying the effectiveness and superiority of the proposed method.

Claims

1. A collaborative optimization method for multi-UAV flight parameters for three-dimensional stealth path design, characterized by: The following steps are involved: Establish a three-dimensional environmental model, including terrain environment model and enemy radar detection model; Based on the multi-UAV endurance energy consumption function, radio frequency stealth performance evaluation function, path smoothness evaluation function, kinetic energy consumption function and clustering density evaluation function, a multi-UAV path planning performance evaluation function is constructed by weighted summation of each function. Taking minimizing the performance evaluation function of multi-UAV path planning as the optimization goal and satisfying the path feasibility determination and the UAV's own dynamic limitations as the constraints, a multi-UAV flight parameter collaborative optimization model for three-dimensional stealth path design is established. The optimization model is solved in two steps using the three-dimensional improved A* algorithm, including: using the three-dimensional improved A* algorithm to perform reverse path planning for the UAV cluster and storing the path planning results; The drone swarm first flies according to the global planned path stored in PATH, and then performs local replanning when encountering sudden threats.

2. The collaborative optimization method for multi-UAV flight parameters for three-dimensional stealth path design according to claim 1 is characterized in that: The terrain environment model is expressed as: z=H(x,y) Where z represents the altitude of the terrain; H(·) is the function corresponding to the terrain environment; (x, y) represents the horizontal coordinates; The enemy radar detection model is expressed as: in, is the detection probability of the target by the networked radar at time t, P i t represents the probability of detecting a UAV by the i-th radar at time t, and N is the number of networked radars on the ground.

3. The collaborative optimization method for multi-UAV flight parameters for three-dimensional stealth path design according to claim 1 is characterized in that: The energy consumption function of multiple UAVs is the product of the total flight time of multiple UAVs and the average flight altitude, which can be expressed as: Among them, Γ1 is the energy consumption evaluation of the cluster, ζ m represents the flight time of the mth UAV; K 3D,m represents the number of path segments of the mth UAV; H0 represents the expected flight altitude of the UAV cluster; the i-th path point of the mth UAV is It represents the ordinate of the mth UAV at the i-th path point, and M is the number of UAVs in the cluster.

4. The collaborative optimization method for multi-UAV flight parameters for three-dimensional stealth path design according to claim 1 is characterized in that: Considering that the enemy deploys networked radars in the flight area, the evaluation function of multi-UAV RF stealth performance is expressed as: Among them, Γ2 is the RF stealth performance evaluation function of UAV stealth, M is the number of UAVs in the cluster, ζ m represents the flight time of the mth UAV, is the probability that the mth UAV is detected by the networked radar at time t.

5. The collaborative optimization method for multi-UAV flight parameters for three-dimensional stealth path design according to claim 1 is characterized in that: The expression of the multi-UAV path smoothness evaluation function is: Among them, Γ3 is the multi-UAV path smoothing evaluation function, M is the number of UAVs in the cluster, K 3D,m represents the number of path segments of the mth UAV, Indicates the heading angle of the i+1th path point of the mth UAV; is the heading angle of the i-th path point of the m-th UAV; φ i+1,m represents the pitch angle of the i+1th path point of the mth UAV; φ i,m represents the pitch angle of the i-th path point of the m-th UAV; represents the expected change in heading angle; φ0 represents the expected change in pitch angle.

6. The collaborative optimization method for multi-UAV flight parameters for three-dimensional stealth path design according to claim 1 is characterized in that: According to the amplitude of the heading angle and pitch angle changes of each UAV at each path point, the multi-UAV dynamic energy consumption function is constructed, which is expressed as follows: Among them, Γ4 is the multi-UAV dynamic energy consumption function, M is the number of UAVs in the cluster, K 3D,m represents the number of path segments of the mth UAV, Indicates the heading angle of the i+1th path point of the mth UAV; is the heading angle of the i-th path point of the m-th UAV; φ i+1,m represents the pitch angle of the i+1th path point of the mth UAV; φ i,m Represents the pitch angle of the i-th path point of the m-th UAV.

7. The collaborative optimization method for multi-UAV flight parameters for three-dimensional stealth path design according to claim 1 is characterized in that: The evaluation function of multi-UAV aggregation density is expressed as: Among them, Γ5 is the density of multiple drones, M is the number of drones in the cluster, K 3D,max =max(K 3D,m ,K 3D,n ), K 3D,m represents the number of path segments of the mth UAV, K 3D,n represents the number of path segments of the nth UAV; ||·|| represents the modulus of the vector; Represents the coordinates of the i-th path point of the m-th UAV; Represents the coordinates of the i-th path point of the n-th drone.

8. The collaborative optimization method for multi-UAV flight parameters for three-dimensional stealth path design according to claim 1 is characterized in that: The established multi-UAV flight parameter collaborative optimization model for three-dimensional stealth path design is expressed as: in, is the probability that the mth UAV is detected by the network radar at time t; P c represents the detection threshold of the networked radar; dist(·) represents the distance between two points in three-dimensional space; represents the spatial position of the mth UAV at time t; obstacle represents the no-fly zone; Robstacle represents the range of the no-fly zone; is the spatial position of the jth UAV at time t; d safe For safe distance; represents the flight distance of the mth UAV in the kth path segment; L max Indicates the maximum range that the drone can fly; Indicates the heading angle of the i+1th path point of the mth UAV; is the heading angle of the i-th path point of the m-th UAV; represents the maximum turning angle of the mth UAV; φ i+1,m represents the pitch angle of the i+1th path point of the mth UAV; φ i,m represents the pitch angle of the i-th path point of the m-th UAV; △φ max is the maximum value of the pitch angle change of the drone; is the spatial position of the i-th path point of the m-th UAV; H(·) is the function corresponding to the terrain environment.

9. The collaborative optimization method for multi-UAV flight parameters for three-dimensional stealth path design according to claim 1 is characterized in that: The three-dimensional improved A* algorithm is used to solve the optimization model in two steps, specifically: (1) Use the three-dimensional improved A* algorithm to perform reverse path planning for the UAV cluster and store the path planning results; (i) Assuming that a certain point in space is O, the actual evaluation g(O) of the mth UAV starting from the end point and reaching point O is expressed as: Among them, K O,m represents the number of path segments of the mth UAV from the end point to point O; The heuristic function value f(O) of the mth UAV from the end point through point O to the starting point is expressed as: Where ω is the weighting factor; h(O) is the estimated function from point O to the starting point; (ii) The UAV expands spatially in a three-dimensional sector shape. Assume that the current path point is A. 3D,0 , current path point A 3D,0 The next path point to be extended is A 3D,1 ; (iii) Calculate the heuristic function for all possible next path points that meet the constraints; (iv) Finally, select the next possible path point A with the smallest heuristic function value 3D,1 As the next waypoint of the current waypoint, waypoint A 3D,1 Become the new current path point and continue to the next step of optimization and expansion; (v) By continuously searching for the optimal path, an optimal path from the end point to the starting point is eventually found. When the reverse path planning of the mth UAV is completed, the reverse path planning of the next UAV is continued until all the cluster paths are planned, and the planned paths are stored in PATH; (2) The drone cluster first flies according to the global planning path stored in PATH. When encountering sudden threats, it performs local replanning. When the drone senses that the environment has changed, it uses the current path point as the starting point for local replanning and the path point in the global planning path that is closest to the end point and meets the platform safety as the end point for local replanning. The improved three-dimensional A* algorithm is used for local replanning. After the local replanning is completed, the drone continues to fly along the global planning path.

10. A multi-UAV flight parameter collaborative optimization system for three-dimensional stealth path design, characterized by: include: A three-dimensional environment model building unit, used to build a three-dimensional environment model, including a terrain environment model and an enemy radar detection model; An evaluation function construction unit is used to construct a multi-UAV path planning performance evaluation function based on a multi-UAV endurance energy consumption function, a radio frequency stealth performance evaluation function, a path smoothness evaluation function, a kinetic energy consumption function, and an aggregation density evaluation function by performing a weighted summation of each function; The optimization model construction unit is used to establish a multi-UAV flight parameter collaborative optimization model for three-dimensional stealth path design, with the optimization goal of minimizing the multi-UAV path planning performance evaluation function and satisfying the path feasibility determination and the UAV's own dynamic limitations as constraints; A model solving unit is used to use a three-dimensional improved A* algorithm to perform a two-step solution to the optimization model, including: using the three-dimensional improved A* algorithm to perform reverse path planning for the UAV cluster and storing the path planning results; The drone swarm first flies according to the global planned path stored in PATH, and then performs local replanning when encountering sudden threats.

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