Unmanned aerial vehicle search planning method and system based on Minimax strategy

Abstract

The invention discloses an unmanned aerial vehicle search planning method and system based on a Minimax strategy, which considers the influence of variable terrains on the detection capability, divides targets into static targets and dynamic targets, respectively performs strategy calculation, constructs a mini-max planning model for the static targets, introduces a zero-sum game model, fully simulates the rational and dynamic characteristics of the targets, and improves the accuracy of the unmanned aerial vehicle search planning. Therefore, the unmanned aerial vehicle can make an optimal search decision for the maneuvering behavior of the target, the search efficiency is improved, optimal strategy distribution between the unmanned aerial vehicle and the target is solved through convex programming for the dynamic target, reasonable scheduling of unmanned aerial vehicle search resources is realized, and the detection probability of the target is maximized. According to the method, the search path is optimized by combining actual terrain data, the search efficiency of the unmanned aerial vehicle in a complex environment is improved, meanwhile, the tracking capability of a high-maneuvering target is enhanced, the method disclosed by the invention can cope with maneuvering, transferring and mixing strategies of the target in continuous multiple stages, and the tracking capability is better.

Description

Technical Field

[0001] The present invention belongs to the technical field of unmanned aerial vehicle (UAV) search, and relates to a UAV search planning method and system based on Minimax strategy. Background Art

[0002] In reconnaissance and situational awareness, unmanned aerial vehicles (UAVs), with their low cost and high maneuverability, have become an important means of performing target search and surveillance missions. Typical UAV target search planning research is often based on the following assumptions: UAVs have a basic understanding of the mission area's geographic or environmental information, can detect potential targets through onboard sensors, and rationally allocate search resources to maximize the probability of target discovery. However, in complex real-world environments, the following impacts and challenges must also be considered:

[0003] Drone operating environments often feature highly variable terrain. Valleys, plateaus, hills, and plains, among other landforms, can block or attenuate detection methods like radar waves and optical sensors to varying degrees. Existing technologies for planning drone search paths often only consider geometric line-of-sight or simple detection models, failing to fully integrate complex factors like terrain attenuation and ambient noise. This results in inefficient target search in these changing terrains, making it difficult to develop effective drone search strategies.

[0004] Traditional methods and techniques often assume that targets are "stationary" or "passive," meaning they won't autonomously change their positions or adopt countermeasures in response to the drone's search behavior. Such research often directly plans search paths or allocates search volume for drones by determining a priori distribution of targets within a region. However, in real-world non-cooperative scenarios, targets often possess a degree of rationality and maneuverability, exploiting terrain advantages or adopting evasive routes to reduce their probability of detection. While some existing research has incorporated game theory into search models, most scenarios offer relatively simplistic descriptions of target behavior or simply consider the target's optimal static position, failing to address the target's maneuvering, relocation, and mixed strategies across multiple stages. Summary of the Invention

[0005] The purpose of the present invention is to solve the problem that most scenarios in the existing technology have relatively simple characterizations of target behavior, only consider the selection of the optimal static position of the target, cannot cope with the maneuvering, transfer and hybrid strategies of the target in continuous multiple stages, and have limitations in rational dynamic target search. A drone search planning method and system based on the Minimax strategy are provided.

[0006] In order to achieve the above object, the present invention adopts the following technical solutions:

[0007] A UAV search planning method based on Minimax strategy includes the following steps:

[0008] Get task parameters;

[0009] Determine the type of target to be searched:

[0010] If the target type is a static target, a minimax planning model is constructed based on the obtained task parameters, and the minimax planning model is solved to obtain the search allocation strategy for the static target;

[0011] If the target type is a dynamic target, a dynamic game convex programming model is constructed based on the obtained task parameters, and the dynamic game convex programming model is solved to obtain the search allocation strategy for the dynamic target.

[0012] A further improvement of the present invention is:

[0013] The acquisition mission parameters include the sub-region area, the sensor radius, the scanning width of the UAV and the gain coefficient of the UAV.

[0014] If the target type is a static target, a minimax planning model is constructed based on the obtained task parameters, and the minimax planning model is solved to obtain a search allocation strategy for the static target, including:

[0015] Construct the target's policy set and the drone's policy set separately;

[0016] Calculate the probability of the target not being detected based on the target's policy set and the drone's policy set;

[0017] Calculate the probability of the target being detected based on the probability of the target not being detected;

[0018] Construct a minimax planning model based on the probability of the target not being detected and the probability of the target being detected;

[0019] Set the constraints for solving the minimax programming model;

[0020] Combined with the constraints, the minimax programming model is solved to obtain the search allocation strategy for the static target.

[0021] Solving the minimax programming model to obtain a search allocation strategy for a static target includes:

[0022] Construct a minimax planning model:

[0023]

[0024] Given any strategy s, the constraints for selecting the optimal strategy are:

[0025]

[0026] Define the optimal response region of strategy s:

[0027] I * ≡{i∈N|α i s i =v≡min j∈N α j s j}

[0028] The optimal strategy for the drone is:

[0029]

[0030] And the value v of the game strategy used by both parties is:

[0031]

[0032] Among them, α i represents the gain per unit search amount in region i; α j represents the gain per unit search volume in region j; N represents the sub-region; and Z represents the total search volume.

[0033] If the target type is a dynamic target, a dynamic game convex programming model is constructed based on the obtained task parameters, and the dynamic game convex programming model is solved to obtain a search allocation strategy for the dynamic target, including:

[0034] Divide the task area into multiple discrete stages and set relevant parameters based on the divided task areas;

[0035] Based on the set relevant parameters, a hybrid strategy set of the target and a strategy set of the drone are constructed;

[0036] Calculate the probability of the target not being detected based on the target's hybrid strategy set and the drone's strategy set;

[0037] Calculate the probability of the target being detected based on the probability of the target not being detected;

[0038] A state game convex programming model is constructed based on the probability of the target not being detected and the probability of the target being detected;

[0039] The Gurobi solver is introduced to solve the game convex programming model to obtain the target trajectory and the search volume allocation results of the drone.

[0040] The task area is divided into a plurality of discrete stages, and relevant parameters are set based on the divided task areas, including:

[0041] The task area is set as multiple discrete stages K = {1, ..., K}, each stage is set to have an equal time interval δ, the condition for the end of the game is to reach stage K, the set of all paths is Ω, and a path is selected from Ω as ω∈Ω, then the position of the target at stage k∈K is ω(k)∈N;

[0042] Assuming that the UAV action lags behind the target, the UAV starts searching after stage τ∈K. The stage when the UAV starts searching is The total search volume that the drone has at stage k is Z(k).

[0043] The step of obtaining the target trajectory and the search volume distribution result of the drone includes:

[0044] Obtain the probability Q(π,s) that the target is not detected and the probability R(π,s) that the target is detected, and use Q(π,s) and R(π,s) as the profit functions of the target and the UAV respectively;

[0045] Given the drone’s strategy s, R(π,s) is a convex combination of R(ω,s), then min π R(π,s)=min ω R(ω,s), optimal response π * For any R(ω,s)>v=min ω′ The path ω of R(ω′,s) satisfies: π * (ω) = 0;

[0046] Then the Nash equilibrium solution of the game satisfies:

[0047]

[0048] in, is the benefit of taking the avoidance strategy for the target, and the above formula is transformed into a convex programming problem:

[0049]

[0050] Among them, Z(k) represents the total search volume of the drone in stage k, which means the sum of the search volumes that can be allocated to each region in stage k; s(i,k) represents the search volume invested by the drone in region i in stage k.

[0051] Through KKT condition analysis and solution, the Lagrangian function of P(s) is:

[0052]

[0053] Among them, λ(k),γ(ω),μ(i,k) are the corresponding Lagrange multipliers;

[0054] The KKT conditions for P(s) are as follows:

[0055]

[0056] Based on the above KKT conditions, the optimal Lagrange multiplier γ * (ω) satisfies:∑ ω∈Ω γ * (ω)=1, and for any path ω∈Ω, when R(ω,s)>v=min ω′ R(ω′,s),γ * (ω)=0, then the optimal Lagrange multiplier γ * (ω) and the optimal mixed strategy π * (ω) is consistent, through the KKT point (γ * ,s * ), a mixed strategy γ that can obtain the target * and drone strategies * .

[0057] A UAV search planning system based on Minimax strategy, including:

[0058] Parameter acquisition module, used to obtain task parameters;

[0059] A judgment module, used to judge the type of target to be searched;

[0060] A static target allocation strategy acquisition module is used to construct a minimax planning model based on the obtained task parameters if the target type is a static target, solve the minimax planning model, and obtain a search allocation strategy for the static target;

[0061] The dynamic and static target allocation strategy acquisition module is used to construct a dynamic game convex programming model based on the obtained task parameters if the target type is a dynamic target, solve the dynamic game convex programming model, and obtain the search allocation strategy for the dynamic target.

[0062] A terminal device comprises a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the steps of any one of the methods of the present invention when executing the computer program.

[0063] A computer-readable storage medium stores a computer program, wherein the computer program, when executed by a processor, implements the steps of any method described in the present invention.

[0064] Compared with the prior art, the present invention has the following beneficial effects:

[0065] The present invention discloses a drone search planning method based on the Minimax strategy. This method considers the impact of variable terrain on detection capabilities, divides targets into static targets and dynamic targets, and performs strategy calculations on them separately. For static targets, a Minimax planning model is constructed, and a zero-sum game model is introduced to fully simulate the rational and dynamic characteristics of the target, enabling the drone to make optimal search decisions based on the target's maneuvering behavior, thereby improving search efficiency. For dynamic targets, the optimal strategy allocation between the drone and the target is solved through convex programming, achieving reasonable scheduling of drone search resources, thereby maximizing the probability of target detection. By combining actual terrain data to optimize the search path, the present invention not only improves the drone's search efficiency in complex environments, but also enhances its tracking capability for highly maneuverable targets. The method disclosed in this invention can cope with the maneuvering, transfer, and mixed strategies of targets in multiple consecutive stages, and has better tracking capabilities. BRIEF DESCRIPTION OF THE DRAWINGS

[0066] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for use in the embodiments. It should be understood that the following drawings only illustrate certain embodiments of the present invention and therefore should not be regarded as limiting the scope. For ordinary technicians in this field, other relevant drawings can be obtained based on these drawings without paying any creative work.

[0067] Figure 1 is a flow chart of the present invention; DETAILED DESCRIPTION

[0068] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions of the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Generally, the components of the embodiments of the present invention described and shown in the drawings herein can be arranged and designed in various different configurations.

[0069] Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the invention as claimed, but rather merely represents selected embodiments of the present invention. All other embodiments derived by persons of ordinary skill in the art based on the embodiments of the present invention without creative effort are intended to fall within the scope of protection of the present invention.

[0070] It should be noted that similar reference numerals and letters denote similar items in the following drawings, and therefore, once an item is defined in one drawing, it does not need to be further defined or explained in subsequent drawings.

[0071] In the description of the embodiments of the present invention, it should be noted that if the terms "upper," "lower," "horizontal," "inner," etc. appear, the orientation or positional relationship indicated is based on the orientation or positional relationship shown in the accompanying drawings, or the orientation or positional relationship in which the inventive product is typically placed when in use. These terms are merely for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or component referred to must have a specific orientation, be constructed, or operate in a specific orientation. Therefore, they should not be construed as limitations on the present invention. In addition, the terms "first," "second," etc. are used only to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0072] In addition, if the term "horizontal" appears, it does not mean that the component must be absolutely horizontal, but can be slightly tilted. For example, "horizontal" only means that its direction is more horizontal than "vertical", and does not mean that the structure must be completely horizontal, but can be slightly tilted.

[0073] In the description of the embodiments of the present invention, it should be noted that, unless otherwise expressly specified or limited, the terms "disposed," "installed," "connected," and "connected" should be understood in a broad sense. For example, they can refer to fixed connections, detachable connections, or integral connections; they can refer to mechanical connections or electrical connections; they can refer to direct connections or indirect connections through an intermediate medium; and they can refer to internal connections between two components. Those skilled in the art will understand the specific meanings of the above terms in the present invention based on specific circumstances.

[0074] The present invention is described in further detail below with reference to the accompanying drawings:

[0075] See also Figure 1 The present invention discloses an approach to optimizing drone search strategies for dynamic, rational targets through a zero-sum game model, thereby increasing the probability of target detection. This approach combines geographic elevation data to calculate the detection coverage of each sub-region, enabling drone search planning to adapt to varying terrain characteristics, thereby improving search accuracy and effectiveness.

[0076] This embodiment of the present invention establishes a game model between the target and the drone, deriving the optimal maneuvering path for the target and the optimal search allocation strategy for the drone. It then solves the Nash equilibrium using convex optimization methods, ensuring that the drone can efficiently search for targets in complex environments. Furthermore, by considering the target's mobility characteristics and energy constraints, the proposed trajectory is optimized, enabling the drone to develop a more precise search plan.

[0077] Furthermore, the present invention utilizes convex optimization modeling and optimization to find the optimal solution for the search strategy, and combines it with terrain data to visualize the search planning results, thereby improving the efficiency of drone search resource allocation and the probability of target discovery. This method can be widely applied in fields such as security monitoring and emergency rescue, enhancing drone search capabilities in complex environments.

[0078] Specifically, the following steps are included:

[0079] Step 1: Based on geographic elevation data (such as SRTM), select the mission area and divide it into several grid-shaped sub-areas with a unified area of ​​A. Simulate the radar equation and propagation loss based on numerical calculations or MATLAB radar toolbox, calculate the radar coverage at any position in the grid, and thus estimate the average coverage radius R in each sub-area i∈N i .

[0080] The specific steps include:

[0081] The mission area is divided into several sub-regions N = {1, 2, ..., N} of the grid, and the area of ​​each sub-region is A. Before performing the search mission, the UAV only knows the terrain information of the mission area and the initial location distribution of the target. Through the search, the uncertainty about the target location is continuously reduced.

[0082] When the UAV searches in area i∈N, the average effective radius of the sensor in the area is R i , when the target is within the detection radius of the sensor, the sensor will successfully detect the target with a probability of 1. Define the scanning width W of the drone i =2R i . Drones take Figure 1 In the parallel search mode shown in the figure, the length of the route or the search amount invested in the parallel search route is z. Assuming that the probability of the drone detecting the target with the search amount z in the area i∈N is P i (z), the probability of not detecting the target within the search volume z is Q i (z) = 1-P i (z), when the search amount Δz is increased, the probability of finding the target within Δz is:

[0083]

[0084] thus:

[0085]

[0086] Furthermore, the solution of formula (2) is obtained as P i (z) = 1-cexp(-α i z), where α i =W i / A, represents the gain per unit search amount in region i, and is represented by P i (0)=0 can determine that c=1.

[0087] Step 2: If it is a static target, use the zero-sum game model of static search to solve it, and set A and Ri Substituting the same parameters into equations (13) and (14) directly gives the result and ends. If it is a dynamic target, proceed to step 3.

[0088] The specific steps include:

[0089] The gains gained from investing search effort in different sub-areas vary. Therefore, the drone needs to rationally distribute its limited search effort across sub-areas to maximize gains. This example focuses on the decision-making question of which sub-areas the drone should search and how much search effort to invest in each sub-area.

[0090] Assume that the UAV only knows the position distribution of the target as π=(π1,π2,…,π N ),π i It represents the probability that the target is in sub-area i, and the specific location of the target needs to be determined by searching. The strategy of the drone is s i Indicates that s i represents the amount of search the drone has invested in sub-area i, and the total amount of search the drone has is Z. The drone's strategy set is:

[0091]

[0092] To maximize the detection probability, the optimal strategy of the drone can be determined by the following planning problem:

[0093]

[0094] Furthermore, for p i > 0, the above planning problem has a unique solution:

[0095]

[0096] Where c is a normalization constant, defined as follows:

[0097]

[0098] Equation (5) determines the optimal strategy for a known target location distribution. However, the exact location distribution is not easy to obtain. In addition, targets with a certain degree of rationality and intelligence will adopt strategies to counter the drone's search, similar to a game of hide-and-seek, where targets will choose favorable terrain to reduce the probability of being discovered.

[0099] Consider the target to adopt a mixed strategy π=(π1,π2,…,π N ), where π i represents the probability that the target chooses to hide in the subregion i∈N. The target randomly selects its own position according to the probability distribution π. The target's strategy set is:

[0100]

[0101] Furthermore, the drone’s strategy set is:

[0102]

[0103] Furthermore, when the target adopts strategy π and the drone adopts strategy s∈S, the probability that the target is not detected is:

[0104]

[0105] Furthermore, the probability of the target not being detected is taken as the utility function of the target, and the probability of the target being successfully detected P(π,s)=1-Q(π,s) is taken as the utility function of the drone.

[0106] The goal is to maximize the undetected probability Q(π,s) by selecting a strategy π∈Π, while the drone maximizes the detection probability or minimizes the undetected probability Q(π,s) by selecting a strategy s∈S. This game is a zero-sum game, and the equilibrium solution can be expressed as the following minimax problem:

[0107]

[0108] Given any strategy s, the optimal strategy for target selection satisfies the following conditions:

[0109]

[0110] Define the optimal response region for strategy s:

[0111] I * ≡{i∈N|α i s i =v≡min j∈N α j s j} (12)

[0112] From formula (11), we can know that the optimal response of the target is * ∈Π satisfies the following conditions: when hour, When i∈I * hour, Take any value. In other words, in order to maximize the value of the game, the optimal response of the goal is to concentrate the probability on those areas with the highest payoff.

[0113] if Or α i s i >min j∈N α j s j , according to the optimal response of the target, we can get π i= 0, at this time, in order to maximize its own benefits, the drone should not waste its search volume at location i, that is, This is consistent with the assumption Contradiction, therefore, Both have α i s i =v (v is a constant), combined with formula (11), the optimal strategy of the UAV can be given as:

[0114]

[0115] in:

[0116]

[0117] The above describes a single-stage game strategy for a rational target. In practice, for example, in a hide-and-seek game, players can continuously move their positions to achieve better hiding effects. The target can also be maneuverable. While the drone searches each sub-area, the target also slowly maneuvers between sub-areas. In this case, the target's strategy expands from selecting the optimal position to selecting the optimal path.

[0118] Step 3: Use Gurobi to solve the convex programming problem (see Equation (22)). Obtain the target trajectory and the search volume distribution results of the drones, and visualize them on the terrain. For the target, draw the route with the highest target probability. For the drones, design parallel search trajectories for the drones in each sub-area based on the search volume. The larger the search volume, the denser the search trajectories in that sub-area.

[0119] Assume multiple discrete stages K = {1,…,K}, each with an equal time interval δ, and the game ends when reaching stage K. Denote all paths as a set Ω, and the target selects a path ω∈Ω from Ω. Then the target's position at stage k∈K is ω(k)∈N. The target evades the drone's search by selecting a path in advance.

[0120] Assuming that the UAV action lags behind the target, the UAV can start searching after stage τ∈K. The stage when the UAV starts searching is The total search volume of the drone at stage k is Z(k), which mainly depends on the number of drones available at each stage.

[0121] The target mixed strategy can be expressed as π = {π(ω), ω∈Ω}, where π(ω) represents the probability of selecting the path ω∈Ω. The target mixed strategy set is:

[0122]

[0123] The drone’s strategy can be represented by s(i,k), which means the amount of search the drone invests in region i at stage k. The drone’s strategy set is:

[0124]

[0125] When the target adopts the pure strategy ω and the drone adopts the strategy s∈S, the probability of non-detection is:

[0126]

[0127] The probability of the target not being detected in K stages is R(ω,s) = , 1-Q(ω,s) is a concave function of s. When the target adopts the mixed strategy π, the probability of the target not being detected by the drone is:

[0128]

[0129] The probability of a target being successfully detected by the drone is:

[0130]

[0131] Furthermore, we can denote Q(π,s) and R(π,s) as the payoff functions of the target and the drone, respectively. The target maximizes Q(π,s) by selecting a strategy π∈Π, while the drone maximizes R(π,s) by selecting a strategy s∈S, which minimizes Q(π,s). This game is a zero-sum game.

[0132] Given the drone’s strategy s, R(π,s) is a convex combination of R(ω,s), so min π R(π,s)=min ω R(ω,s), optimal response π * For any R(ω,s)>v=min ω′ The path ω, π of R(ω′,s) * (ω) = 0. The optimal response of the target is to concentrate the probability on those areas that bring the highest benefits to itself.

[0133] The Nash equilibrium solution of the game satisfies:

[0134]

[0135] Formula (21) corresponds to the following convex programming problem:

[0136]

[0137] The above convex programming problem can be analyzed and solved by KKT conditions. The Lagrangian function of P(s) is:

[0138]

[0139] The KKT conditions for P(s) are as follows:

[0140]

[0141] According to the above KKT conditions, the optimal Lagrange multiplier γ * (ω) satisfies:∑ ω∈Ω γ * (ω)=1, and for any path ω∈Ω, when R(ω,s)>v=min ω′ R(ω′,s),γ * (ω)=0. So the optimal Lagrange multiplier γ * (ω) and the optimal mixed strategy π * (ω) is consistent, through the KKT point (γ * ,s * ), we can determine the target mixed strategy γ * and drone strategies * , thus ensuring that the game has a Nash equilibrium. This proof only requires ensuring that R(π,s) is a concave function of s, since R C (π,s) is also a concave function of s, so the game also has at least one Nash equilibrium.

[0142] The method disclosed in the present invention can effectively overcome the limitations of traditional methods in complex environments. Compared with the existing technology, the present invention fully considers the impact of variable terrain on detection capabilities, calculates the detection coverage of each area through geographic elevation data and radar equations, and improves the accuracy of search planning. At the same time, the present invention innovatively introduces a zero-sum game model to fully simulate the rationality and dynamic characteristics of the target, so that the UAV can make optimal search decisions based on the maneuvering behavior of the target, thereby improving search efficiency. In addition, the present invention solves the optimal strategy allocation between the UAV and the target through convex programming, realizes the reasonable scheduling of UAV search resources, and thus maximizes the detection probability of the target. By combining actual terrain data to optimize the search path, the present invention not only improves the search efficiency of the UAV in complex environments, but also enhances the tracking capability of highly maneuverable targets.

[0143] This embodiment also discloses a drone search planning system based on the Minimax strategy, including:

[0144] Parameter acquisition module, used to obtain task parameters;

[0145] A judgment module, used to judge the type of target to be searched;

[0146] A static target allocation strategy acquisition module is used to construct a minimax planning model based on the obtained task parameters if the target type is a static target, solve the minimax planning model, and obtain a search allocation strategy for the static target;

[0147] The dynamic and static target allocation strategy acquisition module is used to construct a dynamic game convex programming model based on the obtained task parameters if the target type is a dynamic target, solve the dynamic game convex programming model, and obtain the search allocation strategy for the dynamic target.

[0148] A schematic diagram of a terminal device provided in one embodiment of the present invention. The terminal device in this embodiment includes: a processor, a memory, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, the steps of each of the aforementioned method embodiments are implemented. Alternatively, when the processor executes the computer program, the functions of each module / unit in each of the aforementioned device embodiments are implemented.

[0149] The computer program may be divided into one or more modules / units, which are stored in the memory and executed by the processor to accomplish the present invention.

[0150] The terminal device may be a computing device such as a desktop computer, a notebook computer, a PDA, a cloud server, etc. The terminal device may include, but is not limited to, a processor and a memory.

[0151] The processor can be a central processing unit (CPU), or other general-purpose processors, digital signal processors (DSP), application-specific integrated circuits (ASIC), field-programmable gate arrays (FPGA) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc.

[0152] The memory may be used to store the computer programs and / or modules, and the processor implements various functions of the terminal device by running or executing the computer programs and / or modules stored in the memory and calling the data stored in the memory.

[0153] If the module / unit integrated in the terminal device is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the present invention implements all or part of the process in the above-mentioned embodiment method, and can also be completed by instructing the relevant hardware through a computer program. The computer program can be stored in a computer-readable storage medium. When the computer program is executed by a processor, it can implement the steps of each of the above-mentioned method embodiments. The computer program includes computer program code, which can be in source code form, object code form, executable file or some intermediate form. The computer-readable medium may include: any entity or device capable of carrying the computer program code, recording medium, USB flash drive, mobile hard disk, magnetic disk, optical disk, computer memory, read-only memory (ROM), random access memory (RAM), electric carrier signal, telecommunication signal and software distribution medium. It should be noted that the content contained in the computer-readable medium can be appropriately increased or decreased according to the requirements of legislation and patent practice in the jurisdiction. For example, in some jurisdictions, according to legislation and patent practice, computer-readable media do not include electric carrier signals and telecommunication signals.

[0154] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Those skilled in the art will readily appreciate that various modifications and variations of the present invention are possible. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention shall be included within the scope of protection of the present invention.

Claims

1. A UAV search planning method based on Minimax strategy, characterized in that: The following steps are involved: Get task parameters; Determine the type of target to be searched: If the target type is a static target, a minimax planning model is constructed based on the obtained task parameters, and the minimax planning model is solved to obtain the search allocation strategy for the static target; If the target type is a dynamic target, a dynamic game convex programming model is constructed based on the obtained task parameters, and the dynamic game convex programming model is solved to obtain the search allocation strategy for the dynamic target.

2. The UAV search planning method based on Minimax strategy according to claim 1 is characterized in that: The acquisition mission parameters include the sub-region area, the sensor radius, the scanning width of the UAV and the gain coefficient of the UAV.

3. The UAV search planning method based on Minimax strategy according to claim 1 is characterized in that: If the target type is a static target, a minimax planning model is constructed based on the obtained task parameters, and the minimax planning model is solved to obtain a search allocation strategy for the static target, including: Construct the target's policy set and the drone's policy set separately; Calculate the probability of the target not being detected based on the target's policy set and the drone's policy set; Calculate the probability of the target being detected based on the probability of the target not being detected; Construct a minimax planning model based on the probability of the target not being detected and the probability of the target being detected; Set the constraints for solving the minimax programming model; Combined with the constraints, the minimax programming model is solved to obtain the search allocation strategy for the static target.

4. The UAV search planning method based on Minimax strategy according to claim 3 is characterized in that: Solving the minimax programming model to obtain a search allocation strategy for a static target includes: Construct a minimax planning model: stπ i ≥0,i∈N s i v0,i∈N Given any strategy s, the constraints for selecting the optimal strategy are: Define the optimal response region of strategy s: I * ≡{i∈N|α i s i ≡v≡min j∈N a j s j } The optimal strategy for the drone is: And the value v of the game strategy used by both parties is: Among them, α i represents the gain per unit search amount in region i; α j represents the gain per unit search volume in region j; N represents the sub-region; and Z represents the total search volume.

5. The UAV search planning method based on Minimax strategy according to claim 1 is characterized in that: If the target type is a dynamic target, a dynamic game convex programming model is constructed based on the obtained task parameters, and the dynamic game convex programming model is solved to obtain a search allocation strategy for the dynamic target, including: Divide the task area into multiple discrete stages and set relevant parameters based on the divided task areas; Based on the set relevant parameters, a hybrid strategy set of the target and a strategy set of the drone are constructed; Calculate the probability of the target not being detected based on the target's hybrid strategy set and the drone's strategy set; Calculate the probability of the target being detected based on the probability of the target not being detected; A state game convex programming model is constructed based on the probability of the target not being detected and the probability of the target being detected; The Gurobi solver is introduced to solve the game convex programming model to obtain the target trajectory and the search volume allocation results of the drone.

6. The UAV search planning method based on Minimax strategy according to claim 5 is characterized in that: The task area is divided into a plurality of discrete stages, and relevant parameters are set based on the divided task areas, including: The task area is set as multiple discrete stages K = {1, ..., K}, each stage is set to have an equal time interval δ, the condition for the end of the game is to reach stage K, the set of all paths is Ω, and a path is selected from Ω as ω∈Ω, then the position of the target at stage k∈K is ω(k)∈N; Assuming that the UAV action lags behind the target, the UAV starts searching after stage τ∈K. The stage when the UAV starts searching is The total search volume that the drone has at stage k is Z(k).

7. The UAV search planning method based on Minimax strategy according to claim 6, characterized in that: The step of obtaining the target trajectory and the search volume distribution result of the drone includes: Obtain the probability Q(π,s) that the target is not detected and the probability R(π,s) that the target is detected, and use Q(π,s) and R(π,s) as the profit functions of the target and the UAV respectively; Given the drone’s strategy s, R(π,s) is a convex combination of R(ω,s), then min π R(π,s)=min ω R(ω,s), optimal response π * For any R(ω,s)>v=min ω′ The path ω of R(ω′,s) satisfies: π * (ω) = 0; Then the Nash equilibrium solution of the game satisfies: in, is the benefit of taking the avoidance strategy for the target, and the above formula is transformed into a convex programming problem: stv≤R(ω,s),ω∈Ω, Among them, Z(k) represents the total search volume of the UAV in stage k, which means the sum of the search volume that can be allocated to each area in stage k; s(i,k) represents the search volume invested by the UAV in area i in stage k; Through KKT condition analysis and solution, the Lagrangian function of P(s) is: Among them, λ(k),γ(ω),μ(i,k) are the corresponding Lagrange multipliers; The KKT conditions for P(s) are as follows: γ(ω)(vR(ω,s))=0,γ(ω)≥0,R(ω,s)≥v ω∈Ω Based on the above KKT conditions, the optimal Lagrange multiplier γ * (ω) satisfies:∑ ω∈Ω γ * (ω)=1, and for any path ω∈Ω, when R(ω,s)>v=min ω′ R(ω′,s),γ * (ω)=0, then the optimal Lagrange multiplier γ * (ω) and the optimal mixed strategy π * (ω) is consistent, through the KKT point (γ * ,s * ), a mixed strategy γ that can obtain the target * and drone strategies * .

8. A UAV search planning system based on Minimax strategy, characterized by: include: Parameter acquisition module, used to obtain task parameters; A judgment module, used to judge the type of target to be searched; A static target allocation strategy acquisition module is used to construct a minimax planning model based on the obtained task parameters if the target type is a static target, solve the minimax planning model, and obtain a search allocation strategy for the static target; The dynamic and static target allocation strategy acquisition module is used to construct a dynamic game convex programming model based on the obtained task parameters if the target type is a dynamic target, solve the dynamic game convex programming model, and obtain the search allocation strategy for the dynamic target.

9. A terminal device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the computer program, the steps of the method according to any one of claims 1 to 7 are implemented.

10. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 7 are implemented.

Images