Non-cooperative game driven unmanned aerial vehicle cooperative obstacle avoidance and path optimization method

Abstract

The invention discloses a non-cooperative game driven unmanned aerial vehicle cooperative obstacle avoidance and path optimization method, which comprises the following steps: acquiring sensing data of an unmanned aerial vehicle, and predicting and simulating according to the sensing data to obtain an unmanned aerial vehicle flight path set; constructing an unmanned aerial vehicle flight strategy model, wherein the unmanned aerial vehicle flight strategy model takes the lowest cost of the unmanned aerial vehicle flight path as a target; according to the flight strategy model of the unmanned aerial vehicle, constructing a Karush-Kuhn-Tucker condition; and carrying out equivalence transformation through the substitution function to obtain an equivalence condition, and solving the unmanned aerial vehicle flight path set according to the equivalence condition to obtain an optimal flight strategy of the unmanned aerial vehicle. According to the method, the Nash equilibrium concept in the game theory is utilized to construct the multi-unmanned aerial vehicle collaborative obstacle avoidance model. According to the model, through a self-adaptive decision-making mode, the unmanned aerial vehicle is prevented from colliding with obstacles or other unmanned aerial vehicles in the flight process, meanwhile, the flight path is optimized, and the dynamic change and complexity of the flight environment can be coped with.

Description

Technical Field

[0001] The present invention belongs to the technical field of UAV path optimization, and particularly relates to a method for collaborative obstacle avoidance and path optimization of UAVs driven by non - cooperative games. Background Technique

[0002] With the rapid development of modern unmanned aerial vehicle (UAV) technology, UAV swarms face significant challenges in effectively avoiding obstacles when performing various complex tasks. During flight, UAVs must confront static or dynamic obstacles (such as buildings, trees, other aircraft, etc.). Especially in dynamic environments, multiple UAVs must coordinate their flight paths to avoid collisions while ensuring the efficient execution of tasks. To avoid collisions and ensure flight safety, UAVs need to make real - time decisions about their flight paths. In multi - UAV flight scenarios, the obstacle - avoidance decisions of each UAV are affected not only by its own flight state but also by the behaviors of other UAVs. Current obstacle - avoidance methods usually rely on centralized control systems. However, centralized methods have limitations such as poor scalability, heavy computational burden, and strong dependence on communication. Especially in large - scale UAV swarms, the centralized control method is difficult to meet the requirements of real - time performance and efficiency. Therefore, it is very necessary to explore a UAV collaborative obstacle - avoidance method based on distributed decision - making, aiming to reduce the dependence on centralized control and improve the flexibility and scalability of the system.

[0003] Non - cooperative games provide an effective framework for distributed decision - making. In a multi - UAV system, each UAV can be regarded as an independent game player and makes decisions based on its own goals (such as obstacle avoidance success rate, shortest flight time, least energy consumption, etc.). Non - cooperative games enable each UAV to choose its flight path according to its own observations of the environment and speculation about the behaviors of other UAVs, without considering the overall interests of other UAVs. The decisions are local and independent. In game theory, the Nash equilibrium is an important concept, which means that in a non - cooperative game, the strategies of all players have adapted to each other. That is, each player cannot obtain a better result by unilaterally changing its own strategy when knowing the strategies of others. Applied to the UAV obstacle avoidance problem, the Nash equilibrium means that each UAV adjusts its flight path through the game in the interaction with other UAVs and finally reaches a stable obstacle avoidance state. However, in the actual application of multi - UAV cooperative flight, the selection of flight paths often shows non - linear characteristics, involving factors such as the relative positions, speeds of UAVs, and obstacles in the flight environment. The path selections among different UAVs are interdependent, and there are risks of path overlap and collision, which makes it impossible to directly apply traditional game models. Therefore, in view of this characteristic, non - convex games are proposed as a solution. In non - convex games, the structure of the strategy space is no longer a simple convex shape, but a multi - dimensional and complex space. The mutual dependence between strategies makes the solution of the multi - UAV obstacle avoidance problem more complex and unable to be effectively solved, but it can also more realistically reflect the actual challenges in multi - UAV obstacle avoidance. Summary of the Invention

[0004] To solve the above - mentioned technical problems, the present invention proposes a non - cooperative game - driven UAV cooperative obstacle avoidance and path optimization method to solve the problems existing in the above - mentioned prior art.

[0005] To achieve the above object, the present invention provides a non - cooperative game - driven UAV cooperative obstacle avoidance and path optimization method, including:

[0006] Obtain the sensing data of the UAVs, and predict and simulate to obtain a set of UAV flight paths according to the sensing data;

[0007] Construct a UAV flight strategy model, where the UAV flight strategy model aims to minimize the cost of the UAV flight path;

[0008] Construct the Karush - Kuhn - Tucker conditions according to the UAV flight strategy model;

[0009] Equivalently transform the Karush-Kuhn-Tucker conditions through a substitution function to obtain equivalent conditions, and solve the set of UAV flight paths according to the equivalent conditions to obtain the optimal UAV flight strategy.

[0010] Optionally, the sensing data includes radar data, positioning data, speed data, acceleration data, and power data.

[0011] Optionally, the UAV flight strategy model is:

[0012]

[0013] x i ∈Ω i , i = 1, 2, …, N.

[0014] where x i is the flight path selection result of the i-th UAV, x -i represents the flight paths of other UAVs, J i (x i , x -i ) is the cost function of the i-th UAV, where the cost function is the weighted sum of the obstacle avoidance cost and the flight efficiency cost, g i (x i , x -i ) is the inequality constraint during the flight of the i-th UAV, h i (x i , x -i ) is the equality constraint during the flight of the i-th UAV, Ω i is the strategy space of the i-th UAV, which contains the predicted flight paths of each UAV, and N represents the total number of UAVs.

[0015] Optionally, the Karush-Kuhn-Tucker conditions are:

[0016]

[0017] x i ∈Ω i ,

[0018] where λ i and μ i are the Lagrange multipliers related to the inequality constraint and the equality constraint respectively, represents the gradient operator, represents taking the gradient with respect to the flight path x i .

[0019] Optionally, the substitution function satisfies the following transformation conditions:

[0020]

[0021] Among them, p i is the auxiliary variable vector, representing the virtual flight path of the i-th unmanned aerial vehicle (UAV), represents the rate of change of the cost function when the i-th UAV selects or adjusts its path, δ u represents the minimum eigenvalue of the matrix u, where represents the surrogate function z i with respect to the sensitivity of the virtual path selection p i to changes, p = col[p 1 , …, p N , x = col[x 1 , …, x N , represents the sensitivity of the inequality constraint to changes in the virtual path selection p i to changes, represents the sensitivity of the equality constraint to changes in the virtual flight path selection p i to changes. The superscript * represents the parameters corresponding to the optimal strategy.

[0022] Optionally, the surrogate function is:

[0023]

[0024] The coefficients α i and β i represent the weights corresponding to the comprehensive differences.

[0025] Optionally, the equivalent condition of the Karush - Kuhn - Tucker condition is:

[0026]

[0027] Optionally, the process of solving the UAV flight path set includes:

[0028] Construct a solution model according to the equivalent condition, and perform iterative solution on the solution model until the rate of change converges to obtain the optimal flight strategy of the UAV; where the solution model is:

[0029]

[0030] Among them, y ij represents the estimation of the flight path selection of the j-th UAV by the i-th UAV. represents the rate of change of the estimation of the path selection of the j-th UAV by the i-th UAV. y irepresents the estimation of the flight paths of all UAVs in the UAV swarm by the $i$-th UAV. $y$ -i represents the estimation of the flight paths of other UAVs in the UAV swarm except itself by the $i$-th UAV.

[0031] Compared with the prior art, the present invention has the following advantages and technical effects:

[0032] The present invention aims to propose a multi-UAV obstacle avoidance strategy based on non-cooperative non-convex games. By using the concept of Nash equilibrium in game theory, this method constructs a multi-UAV cooperative obstacle avoidance model. Through an adaptive decision-making method, the UAVs can avoid collisions with obstacles or other UAVs during flight, and at the same time optimize the flight paths, being able to cope with the dynamic changes and complexities of the flight environment.

[0033] Through this technical solution, multiple UAVs can achieve adaptive obstacle avoidance in a complex flight environment without relying on centralized control or external instructions. Each UAV makes independent decisions through the game theory model and selects the optimal path, thus achieving cooperative obstacle avoidance in the group. Compared with traditional methods, the obstacle avoidance strategy based on non-cooperative non-convex games has the following advantages:

[0034] 1. Distributed decision-making: Without central control, each UAV makes independent decisions through local information and game strategies, with strong adaptability;

[0035] 2. Efficient obstacle avoidance: By dynamically adjusting the path, it ensures that the UAVs avoid collisions with obstacles and other UAVs, and at the same time maximizes the task execution efficiency;

[0036] 3. Strong scalability: As the number of UAVs increases, the scalability of the system is stronger, and it can handle large-scale UAV cooperative flight problems;

[0037] 4. Robustness: The system can cope with complex environments and emergencies, and has strong fault tolerance. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] The drawings constituting a part of this application are used to provide a further understanding of this application. The schematic embodiments of this application and their descriptions are used to explain this application and do not constitute an improper limitation to this application. In the drawings:

[0039] Figure 1 is a schematic flowchart of the method according to an embodiment of the present invention;

[0040] Figure 2 is a two-dimensional schematic diagram of the aggregation of UAV paths in an example according to an embodiment of the present invention;

[0041] Figure 3 is a three-dimensional schematic diagram of the aggregation of UAV paths in an example according to an embodiment of the present invention. Detailed implementation manners

[0042] It should be noted that, without conflict, the embodiments in the present application and the features in the embodiments can be combined with each other. The present application will be described in detail below with reference to the drawings and in combination with the embodiments.

[0043] It should be noted that the steps shown in the flowchart of the drawings can be executed in a computer system such as a set of computer-executable instructions, and although the logical order is shown in the flowchart, in some cases, the steps shown or described can be executed in a different order than here.

[0044] As Figure 1 shown, in this embodiment, a method for collaborative obstacle avoidance and path optimization of unmanned aerial vehicles driven by non-cooperative games is provided, including:

[0045] The core idea of the present invention is: regarding multiple unmanned aerial vehicles as participants in the game, each unmanned aerial vehicle selects an optimal flight path according to its own state and environmental information to avoid collisions with obstacles or other unmanned aerial vehicles. In a multi-unmanned aerial vehicle system, the path selection of each unmanned aerial vehicle not only depends on its own decision, but is also affected by the behaviors of other unmanned aerial vehicles. Therefore, the present invention constructs a non-cooperative non-convex game model and proposes a distributed decision-making method based on Nash equilibrium, so that each unmanned aerial vehicle can avoid conflicts with other unmanned aerial vehicles while avoiding obstacles and maximize the flight efficiency.

[0046] The technical solutions therein include the following contents:

[0047] S1. First, obtain the relevant sensing data of the unmanned aerial vehicle, and preprocess the relevant sensing data to provide a data basis for the unmanned aerial vehicle flight strategy model used for unmanned aerial vehicle decision-making for subsequent decision-making. Based on the preprocessed data, different simulated flight paths can be generated through existing flight path simulation software.

[0048] S2. Construct an unmanned aerial vehicle flight strategy model, where the unmanned aerial vehicle flight strategy model includes an objective function and constraint conditions with the lowest flight path cost as the goal.

[0049] S3. Construct the Karush-Kuhn-Tucker conditions of the unmanned aerial vehicle flight strategy model. Among them, the parameter point that satisfies the Karush-Kuhn-Tucker conditions is the game KKT point of the above-mentioned unmanned aerial vehicle flight strategy model, that is, the optimal strategy, where the optimal strategy includes the flight path with the lowest flight cost that meets the constraint conditions;

[0050] S4. To facilitate the efficient analysis of the UAV flight strategy model, the Karush-Kuhn-Tucker conditions are equivalently transformed and solved by introducing a surrogate function to obtain the optimal strategy.

[0051] A detailed description of the above technical solution is as follows:

[0052] In some embodiments, step S1 specifically includes the following content:

[0053] During the UAV obstacle avoidance and path optimization process, data acquisition and preprocessing are important prerequisites for model construction. First, flight environment data is collected in real time through various sensors (such as lidar, radar, vision sensors, ultrasonic sensors, etc.). These sensors can provide information about the position, size, dynamic changes of obstacles, and the state of the aircraft itself, such as GPS positioning, speed, acceleration, and battery power. In addition, the communication network also plays a key role, allowing multiple UAVs to share their position information, speed, and other state data, enhancing the ability of collaborative operations. The communication relationship between the above UAVs constitutes an undirected graph communication network structure.

[0054] After obtaining these raw data, data cleaning is performed to remove outliers and noise to ensure data accuracy; at the same time, the data format is unified and time synchronization is carried out so that all data has consistency at the same moment. In addition, the data from multiple sensors needs to be integrated through fusion technology. Common technologies include Kalman filtering, aiming to improve the positioning accuracy and the reliability of obstacle perception. To further improve the performance of the model, feature extraction of data is particularly important. Obstacle features are extracted through image processing or point cloud analysis, and dynamic information such as speed and acceleration is extracted from flight data. After data preprocessing is completed, path prediction and simulation can be carried out to obtain the prediction and simulation path set x=(x 1 ,…,x N ) of each UAV, providing a necessary basis for subsequent model construction and path optimization. Finally, these processed data will be used to construct a non-convex non-cooperative game model, that is, the UAV flight strategy model, to help the UAV achieve obstacle avoidance and optimal path planning.

[0055] Among them, the above path set can be used as the initial value for subsequent model solving, and iterative adjustment is performed to generate the optimal path. Or the above path set is a random value, and through iterative solving of the model, the path set is iteratively adjusted to generate the optimal path.

[0056] Each predicted and simulated path of each UAV includes the position, speed, acceleration, and endurance information of the UAV under that path.

[0057] In some embodiments, step S2 specifically includes the following content:

[0058] Among them, the UAV flight strategy model is as follows:

[0059]

[0060] x i ∈Ω i , i = 1, 2, …, N,

[0061] The strategy space Ω of each UAV i is composed of its possible flight paths, and each path corresponds to a cost function J i (x i , x -i ). The cost function usually includes factors such as flight time, energy consumption, and collision risk. Specifically, the cost function J i (x i , x -i ) consists of two parts:

[0062] 1. Obstacle avoidance cost: If a UAV collides with an obstacle or another UAV, the obstacle avoidance cost will increase; among them, the obstacle avoidance cost is predicted and simulated based on the position, speed, and acceleration in the path predicted by each UAV simulation and the moving trajectory of the obstacle to calculate whether a collision will occur.

[0063] 2. Flight efficiency cost: The time and energy consumption that each UAV may face on the flight path, and the flight efficiency cost is calculated based on the information of time and energy consumption.

[0064] Among them, the cost function J i (x i , x -i ) is the weighted sum of the obstacle avoidance cost and the flight efficiency cost. Among them, the weight set for the obstacle avoidance cost is larger than the weight of the flight efficiency cost. A weight value of more than 5 times or even more of the flight efficiency can be selected. The weight of the obstacle avoidance cost increases, indicating that the obstacle avoidance cost has more influence and tries to avoid the occurrence of collision situations.

[0065] Among them, represents the flight path selection of the i-th UAV. Among them, the flight path selection contains different dimensions, and each dimension represents a different flight parameter (such as position, speed, acceleration, etc. in the UAV path decision), represents the flight paths of other UAVs. Since the path selection of each UAV will be affected by the strategies of other UAVs, the final cost function is a non-convex function, resulting in a more complex solution to the game problem.

[0066] The inequality constraint g i (x i , x -iIndicates some restrictive conditions that must be satisfied during flight, which ensure the safety, efficiency, and feasibility of the UAV flight. It mainly includes the safety distance for obstacle avoidance, speed limit, energy consumption, etc. The subscript 0 represents the corresponding parameter m i and q i Dimensional constraint, m i Indicates the dimension of the inequality constraint, q i Indicates the dimension of the equality constraint.

[0067] Equality constraint h i (x i ,x -i ) Represents some precise requirements that must be satisfied to ensure that the flight trajectory of the UAV meets the physical constraints while fulfilling the mission requirements. For example, the flight path must be continuous from the starting point to the ending point without sudden changes and must be within the specified flight area.

[0068] As some embodiments, step S3 specifically includes the following content:

[0069] The Karush-Kuhn-Tucker (KKT) conditions are:

[0070]

[0071] x i ∈Ω i ,

[0072] Among them, and are the Lagrange multipliers related to the inequality constraint and the equality constraint respectively. Further define, and Among them, The solution col[x i ,x -i ,λ i ,μ i that satisfies the above Karush-Kuhn-Tucker conditions is called the KKT point of the game, where i represents the serial number of the UAV, and col[] represents the function that converts the parameters into a column vector.

[0073] Specifically, Represents the rate of change of the cost function when the i-th UAV selects or adjusts its path, that is, the impact of path selection on the optimization objective of the UAV. and Indicate whether the inequality or equality constraint is satisfied or the trend of violating the constraint as the flight path x i of the UAV changes. The gradient tells the UAV how to adjust its path during flight to avoid collisions, where represents the gradient operator.

[0074] In a game problem with convexity, the KKT conditions are necessary and sufficient conditions for identifying the Generalized Nash Equilibrium (GNE). In non-convex non-cooperative games, the KKT conditions are necessary conditions for identifying the local GNE. Using these conditions to find the KKT points can significantly simplify the search for the local GNE. This method not only simplifies the local analysis but also provides a scheme for discovering the global GNE, and global optimality can be deduced from the local conditions.

[0075] As some embodiments, step S4 specifically includes the following:

[0076] Perform equivalent transformation on the above Karush-Kuhn-Tucker conditions according to the surrogate function:

[0077] Construct the surrogate function z i (p i , x i , x -i ), aiming to help identify the KKT points described in the Karush-Kuhn-Tucker conditions. The surrogate function is crucial for solving the problem of finding the GNE in non-cooperative games, where the surrogate function is constructed in a way that satisfies the following transformation conditions:

[0078]

[0079] where, represents the vector of auxiliary variables, z i : is the surrogate function of the cost function J i applicable to each unmanned aerial vehicle i = 1, 2,..., N. In addition, d represents a constant value related to the flight strategy model of the unmanned aerial vehicle, and δ u represents the minimum eigenvalue of the matrix u, defined as represents the sensitivity of the surrogate function z i to the change in the virtual path selection p i , where p = col[p 1 , …, p N , x = col[x 1 , …, x N , represents the sensitivity of the inequality constraint to the change in the virtual path selection p i , represents the sensitivity of the equality constraint to the change in the virtual flight path selection p i , and the superscript * represents the parameters corresponding to the optimal strategy.

[0080] Denote the surrogate function z i For the virtual path selection p i The sensitivity of change, which helps the UAV optimize the path and minimize the combination of cost and other objectives and constraints as much as possible. If the second derivative of a certain dimension is large, it indicates that the change of the virtual path in that dimension has a relatively strong impact on the surrogate function, which may lead to a larger cost change. δ z Denote the minimum sensitivity of the virtual path selection to the change of the surrogate function.

[0081] Denote that this inequality constraint changes in the direction of the virtual flight path p i The sensitivity of change. If the second derivative is large, it indicates that a small change in the path selection will significantly change the degree of constraint satisfaction, that is, if the UAV path changes slightly, the safety distance will change greatly, and the flight path needs to be carefully adjusted to avoid violating this constraint. δ g Denote the minimum sensitivity of the virtual path selection to the change of the inequality constraint.

[0082] Similarly, Denote the sensitivity of the equality constraint to the change in the direction of the virtual flight path p i The sensitivity of change. If the second derivative is large, it indicates that a small change in the path selection will significantly change the degree of constraint satisfaction. δ h Denote the minimum sensitivity of the virtual path selection to the change of the equality constraint.

[0083] Some specific surrogate functions z i (p i ,x i ,x -i ) are applicable to finding the KKT points of the UAV flight strategy model as follows:

[0084]

[0085] Among them, for the conversion condition ①, the first function and the second function are naturally satisfied. For the conversion condition ②, it is necessary to satisfy α≥d - δ J -δ g -δ h and β≥d - δ g -δ h , where δ J Denote the minimum sensitivity of the virtual path selection to the change of the cost function, that is The minimum eigenvalue of; among them, Denote the cost function J i The sensitivity of change to the virtual path selection p i Helping the UAV optimize the path and minimize the cost as much as possible, where

[0086] ||p i -x i || 2 is the comprehensive difference metric of the flight path selection of the i-th UAV and its virtual flight path in dimensions of state variables such as position, speed, and acceleration. Coefficient α i and β i represent the weights of this comprehensive difference. α = min{α 1 ,…,α N}, β = min{β 1 ,…,β N} represents the minimum weight.

[0087] By substituting the function z i (p i ,x i ,x -i ), equivalent conditions related to the KKT conditions of the UAV flight strategy model are introduced.

[0088] Where when satisfies the following equivalent conditions:

[0089]

[0090] Then is the KKT point of the UAV flight strategy model. Conversely, if is the KKT point of the UAV flight strategy model, then there exists such that satisfies the above conditions. According to the above equivalent conditions, points that meet the above equivalent conditions are screened out among the predicted and simulated flight paths.

[0091] After finding the points that satisfy the above equivalent conditions, the KKT points of the UAV flight strategy model can be effectively identified. This method simplifies the solution process by centrally processing a subset of feasible points that satisfy the KKT conditions.

[0092] Based on the above equivalent conditions, a subsequent solution model is constructed. When the rate in the solution model no longer changes, or in other words, when the rate parameters are all 0, the obtained results can ensure that they satisfy the above equivalent conditions. And the points that satisfy the equivalent conditions are also the solutions when the rate parameters of the solution model are all 0. The solution model is:

[0093]

[0094] represents the flight path of the i-th UAV, represents the dynamic behavior of the i-th UAV on the flight path, specifically the rate of change of the position of this UAV on the path. represents the virtual flight path of the i-th drone, represents the rate of change of the position of the virtual flight path of the i-th drone; where the virtual flight path p of the drone i corresponds to the virtual predicted flight path decision, x i corresponds to the actual flight path decision of the drone, and the virtual flight path p of the drone i is an intermediate variable for solving the actual flight path decision. Based on the above formula, the ultimate goal is p i = x i , that is, when the virtual predicted path decision is the same as the actual flight path decision, the calculated x i is equivalent to the above KKT point.

[0095] Ω i represents the strategy space; represents the vector x i projected onto the set Ω i is defined as follows: where y i represents the vector in the set Ω i and is interpreted as the feasible flight path in the strategy space that is closest to the flight path x i .

[0096] represents the estimate of the j-th drone's flight path selection by the i-th drone. represents the rate of change of the estimate of the j-th drone's path selection by the i-th drone. represents the estimate of the flight paths of all drones in the drone swarm by the i-th drone. represents the estimate of the flight paths of other drones in the drone swarm except itself by the i-th drone.

[0097] represents the importance of the i-th drone needing to satisfy the inequality constraint g i (x i , x -i ) during its decision-making process. For example, when two drones are approaching each other, the importance of the safety, efficiency, etc. of the drone flight ensured by the inequality constraint increases, will increase accordingly. At this time, reflects the rate of this increase in importance, indicating that more adjustments are needed to meet requirements such as safety.

[0098] Similarly, reflects the i-th drone's satisfaction of the equality constraint h i (x i , x -i) The importance of this prompts the UAV to adjust its flight path or speed to avoid violating the constraints. Describes the rate of change of the importance of the equality constraint. When the equality constraint (such as the specified flight area limit) approaches its boundary, it will increase, indicating that the i-th UAV needs to pay more attention to this constraint and make corresponding adjustments.

[0099] The surrogate function z i : Represents the combination of the cost function J i with other objectives, constraints, or rewards, used to comprehensively consider multiple factors (such as the shortest path, least energy). Represents the rate of change of the surrogate function when the i-th UAV selects or adjusts its path, that is, the impact of path selection on the optimization objective of this UAV. If a ij is greater than 0, it means there is information interaction between the i-th UAV and the j-th UAV. If a ij = 0, it means there is no information interaction. and Indicate whether the inequality or equality constraint is satisfied as the virtual UAV path p i changes, or the trend of violating the constraint. The gradient tells the UAV how to adjust its path during flight to avoid collisions.

[0100] Based on the above solution model, iterative solution of the solution model is performed, where according to the rate of change of the UAV's position on the path The rate of change of the position of the UAV's virtual flight path The rate of change of different importance parameters and the estimated rate of change are used as evaluation values to guide the adjustment of [p i , x i , x -i , λ i , μ i in the direction and position where the evaluation value is equal to 0. By performing iterative solution on the above model, when the above solution model converges to the equilibrium point, its equilibrium point is equivalent to the above KKT point, and the final result can be used as the final KKT point.

[0101] The iterative solution process for the above solution model is as follows:

[0102] First, determine the number of UAVs in the above UAV system, i.e., the number of agents, the adjacency matrix, i.e., whether there is communication, the convergence threshold, the maximum number of iterations, and the integration step size dt to determine the initial parameters for iterative solution;

[0103] For p i , x i , λi , μ i , y ij are initialized, and at the same time, the iteration counter t is initialized, where p i , x i , λ i , μ i , y ij During initialization, random values are assigned.

[0104] When the iteration counter t has not reached the maximum number of iterations and the above result does not converge, the calculation of the above solution model is performed, and the corresponding parameters are updated according to the change rates of different parameters in the solution model to provide a numerical basis for the next iteration process;

[0105]

[0106] Among them,

[0107]

[0108] After the update, the convergence is checked,

[0109] Among them, the primal residual primal_error = max(||x i - p i ||, ||y ij - p j ||)

[0110] Dual residual

[0111] Complementary slackness

[0112] If the above primal residual, dual residual, and complementary slackness are less than the set threshold, it means the corresponding convergence, and then the current p i , x i , λ i , μ i , y ij are projected into the feasible set to obtain the final result [p i , x i , x -i , λ i , μ i .

[0113] Code related to the model iteration solution algorithm: It should be noted that the subscript i is represented as [i], and the change rate punctuation is represented as dot[i].

[0114] Input: N: number of agents, a[i,j]: adjacency matrix, tol: convergence threshold, max_iter: maximum number of iterations, dt: integration step size;

[0115] Initialize: x[i] ← random values / / decision variable; p[i] ← random values / / auxiliary variable; λ[i] ← random values / / Lagrange multiplier; μ[i] ← random values / / Lagrange multiplier; y[i,j] ← random values / / consensus variable; t ← 0 / / iteration counter; where random values represent random numbers.

[0116] Main Loop: while t < max_iter and not converged do / / when t is less than the maximum number of iterations and not converged; for i = 1 to N do in parallel / /

[0117] / / 1. Update x_i: x_dot[i] = p[i] - x[i]; x[i] = x[i] + dt * x_dot[i];

[0118] / / 2. Update p_i:

[0119] / / 3. Update λ_i: λ_dot[i] = -λ[i] + (λ[i] + g_i(p[i], y[-i]))^+; λ[i] = λ[i] + dt * λ_dot[i];

[0120] / / 4. Update μ_i: μ_dot[i] = h_i(p[i], y[-i]); μ[i] = μ[i] + dt * μ_dot[i];

[0121] / / 5. Update y_ij: for j = 1 to N do; sum = 0; for k = 1 to N do; sum += a[i,k] * (y[i,j] - y[k,j]); y_dot[i,j] = -(sum + a[i,j] * (y[i,j] - p[j])); y[i,j] = y[i,j] + dt * y_dot[i,j]; endfor; endfor;

[0122] / / Check convergence: if Check_Convergence() then; converged = true; endif; t = t + 1; endwhile;

[0123] FunctionCheck_Convergence():

[0124] / / Calculate the primal residual: primal_error = max(║x[i] - p[i]║, ║y[i,j] - p[j]║);

[0125] / / Calculate the dual residual: dual_error = max(║λ_dot[i]║, ║μ_dot[i]║);

[0126] / / Calculate the complementary slackness: complementarity = max(|λ[i]^T * g_i(p[i], y[-i])|);

[0127] return (primal_error < tol) && (dual_error < tol) && (complementarity < tol)

[0128] FunctionP_Ωi(p):

[0129] / / Project onto the feasible set Ωi: return projection_of_p_onto_Ωi;

[0130] Output: x[i]; p[i]; λ[i]; μ[i]; y[i,j].

[0131] By solving the above formulas, the optimal strategy can be obtained as the combination of the left and right strategies for each UAV, and the other parameters are only variables to assist in finding the optimal strategy.

[0132] Describe the above content with an actual model:

[0133] Among them, the optimal aggregation model for UAV flight is:

[0134]

[0135] κ i ∈[-0.5, 2]×[-0.5, 2], i = 1, …, 20,

[0136] For the parameters in the cost function : Among them, κ i represents the path selection of the i-th UAV, R iis a positive definite matrix, usually representing the "cost" of path selection or state, or some form of constraint, such as the deviation from the target state, or certain optimization objectives during flight (such as flight time, energy consumption, or path smoothness). This quadratic form is usually used to penalize large deviations in path or state selection, making path optimization tend towards an ideal solution.

[0137] where b i is a vector, usually representing external factors related to path optimization (such as target points, offsets, etc.). This term is the linear cost, usually penalizing deviations in certain path selections. The inner product between it and the path selection of the i-th UAV usually represents the influence of some linear constraints, such as flight time, target direction, etc. c i is a constant term, independent of the flight path κ i , and may include certain fixed costs of the system, such as initial costs, fixed operation costs, etc. It does not affect the optimal path selection, but will affect the constant value of the final minimization result. represents the difference between the path selection of the i-th UAV and the path selections of 20 UAVs including itself. Here, ||κ i -κ j || 2 represents the square of the Euclidean distance between the path selection of the i-th UAV and the path selection of the j-th UAV. Minimizing this term means that the path selection of the UAV will tend to be close to the path selections of other UAVs, thus achieving a certain degree of cooperation or synchronized flight. It is used to achieve path coordination, such as avoiding collisions between UAVs or optimizing the flight efficiency of the UAV swarm.

[0138] such as Figures 2 - 3 shown, where, Figures 2 - 3 the x-axis coordinate in represents the position on the x-axis, the y-axis coordinate is representing the position on the y-axis, Figure 3 the third coordinate Time in i represents time, and different line segments represent the flight path planning results of different UAVs. The inequality constraint g(κ i ) means that the flight area is outside the circle with a radius of square root of 2 centered at (-1, -1). The bounded constraint κ Figures 2 - 3 ∈[-0.5,2]×[-0.5,2] represents the rectangular constraint on the UAV flight area, that is, the x-axis coordinate and the y-axis coordinate

[0139] The result shows that, Figures 2 - 3Here are the two-dimensional and three-dimensional path images of 20 drones implemented according to the proposed strategy, where the black dots represent the optimal aggregation points sought. Under the proposed method, the 20 drones can reach the optimal aggregation point under constraints and stabilize at this point.

[0140] The UAV and obstacle avoidance strategy based on non-cooperative non-convex game proposed by the present invention provides an efficient solution for the adaptive obstacle avoidance of multi-UAV systems in complex environments. By introducing the Nash equilibrium method in game theory, the problems of poor scalability and heavy computational burden existing in traditional centralized control methods are solved, and it has a wide range of application prospects, especially suitable for multiple fields such as military, disaster response, and logistics distribution.

[0141] The above is only a preferred specific embodiment of the present application, but the protection scope of the present application is not limited thereto. Any changes or substitutions that can be easily thought of by those skilled in the art within the technical scope disclosed in the present application should be covered within the protection scope of the present application. Therefore, the protection scope of the present application should be subject to the protection scope of the claims.

Claims

1. A non-cooperative game-driven UAV collaborative obstacle avoidance and path optimization method, characterized in that: include: Acquire sensor data of the UAV, and obtain a set of UAV flight paths through prediction and simulation based on the sensor data; Constructing a UAV flight strategy model, wherein the UAV flight strategy model aims to minimize the cost of the UAV flight path; According to the UAV flight strategy model, the Karush-Kuhn-Tucker condition is constructed; The Karush-Kuhn-Tucker condition is equivalently transformed by a substitution function to obtain an equivalent condition, and the UAV flight path set is solved according to the equivalent condition to obtain the optimal flight strategy of the UAV.

2. The method according to claim 1, characterized in that The sensor data includes radar data, positioning data, speed data, acceleration data and power data.

3. The method according to claim 1, characterized in that The UAV flight strategy model is: Among them, x i The flight path selection result for the i-th UAV, x -i represents the flight path of other UAVs, J i (x i ,x -i ) is the cost function of the ith UAV, where the cost function is the weighted sum of obstacle avoidance cost and flight efficiency cost, g i (x i ,x -i ) is the inequality constraint during the flight of the i-th UAV, h i (x i ,x -i ) is the equality constraint during the flight of the i-th UAV, Ω i is the strategy space of the i-th UAV, including the predicted flight path of each UAV, and N represents the total number of UAVs.

4. The method according to claim 3, characterized in that The Karush-Kuhn-Tucker condition is: Among them, λ i and μ i are the Lagrange multipliers associated with the inequality constraints and equality constraints, respectively. represents the gradient operator, For the flight path x i Find the gradient.

5. The method according to claim 1, characterized in that The substitution function satisfies the following conversion conditions: Among them, p i is an auxiliary variable vector, representing the virtual flight path of the i-th UAV, represents the rate of change of the cost function of the i-th UAV when selecting or adjusting its path, δ u represents the smallest eigenvalue of matrix u, represents the substitution function z i Select p for the virtual path i The sensitivity of the changes p=col[p1,…,p N ],x=col[x1,…,x N ], Indicates the inequality constraint on the virtual path selection p i The sensitivity of the changes, Represents the equality constraint on the virtual flight path selection p i The sensitivity of the change, the superscript * indicates the parameter corresponding to the optimal strategy.

6. The method according to claim 5, characterized in that The substitution function is: Coefficient α i and β i Represents the weight of the corresponding comprehensive difference.

7. The method according to claim 6, characterized in that The equivalent conditions are:

8. The method according to claim 1, characterized in that The process of solving the set of UAV flight paths includes: According to the equivalent conditions, a solution model is constructed and iteratively solved until the change rate converges to the optimal flight strategy of the UAV; the solution model is: Among them, y ij represents the estimation of the flight path selected by the i-th UAV for the j-th UAV, represents the rate of change of the path selection estimate of the jth UAV by the i-th UAV, y i represents the estimation of the flight paths of all drones in the drone swarm by the i-th drone, y -i It represents the estimation of the flight paths of other drones in the drone swarm except itself by the i-th drone.

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