Unmanned aerial vehicle cluster formation control method suitable for heterogeneous multiplicative noise disturbance environment

Abstract

The application relates to the field of control and information technology, and particularly discloses a UAV cluster formation control method suitable for a heterogeneous multiplicative noise disturbance environment, which comprises the following steps: constructing a UAV dynamics model containing heterogeneous multiplicative noise; adopting an undirected connected graph to describe the communication relationship among UAVs, and constructing a Laplacian matrix of the undirected connected graph; constructing a total objective function; constructing an optimal value function of the total objective function; constructing a Hamilton function of the optimization problem; utilizing a random dynamic programming theory to solve a parameter algebraic Riccati equation, so as to obtain a distributed optimal control law; setting a running time, an initial state of the UAV and a target formation state, and utilizing the distributed optimal control law to perform UAV cluster formation control. The application enables each UAV to realize global optimal formation under the condition of only relying on neighbor information, and provides a feasible solution for UAV cluster cooperation in a heterogeneous disturbance environment.

Description

Technical Field

[0001] This invention relates to the fields of control and information technology, and in particular to a method for controlling unmanned aerial vehicle (UAV) swarm formations in environments with heterogeneous multiplicative noise disturbances. Background Technology

[0002] With the rapid development of drone technology, drone swarms have been widely applied in several key areas such as urban emergency search and rescue, border patrol, agricultural plant protection, and logistics transportation. Compared to single drones, swarm systems have significant advantages such as high task parallelism, strong fault tolerance, and wide coverage, making them capable of collaborative operations in complex environments. To achieve efficient collaboration, distributed control architecture has gradually become the mainstream choice. This architecture eliminates the need for a central node; each drone only needs to utilize neighbor information to make decisions, significantly reducing system communication load and the risk of single points of failure. It also possesses stronger scalability and environmental adaptability, making it particularly suitable for large-scale, highly dynamic, and communication-constrained mission scenarios.

[0003] However, in actual deployments, communication links between UAVs are highly susceptible to environmental interference, such as building obstruction, electromagnetic interference, and sensor nonlinear errors. This causes the received signal strength to dynamically change with the relative state of the UAVs, manifesting as multiplicative noise. Especially due to differences in hardware configuration and deployment location among UAVs, the noise disturbance intensity experienced by each communication link is inconsistent, exhibiting heterogeneous multiplicative noise characteristics. This noise not only disrupts information consistency but also amplifies error propagation through state coupling, severely weakening the convergence performance and stability of formation control. Heterogeneous multiplicative noise not only transforms the system model into stochastic differential equations but also directly causes the traditional optimal control framework based on deterministic models to fail: 1. Noise intensity is coupled with state, requiring the Hamiltonian function to simultaneously handle first-order and second-order costate vectors, greatly increasing the solution complexity; 2. The eigenvalues ​​of the Laplace matrix are introduced with random terms, making it impossible for the standard network cost function to guarantee distributed implementation; 3. The overall system performance is determined by the weakest link, and heterogeneity leads to significant differences in the convergence rate among the UAVs. However, existing research mostly focuses on additive noise or homogeneous multiplicative noise, and there is no effective solution for optimal distributed control under heterogeneous multiplicative noise. Summary of the Invention

[0004] This invention aims to address the negative impact of heterogeneous multiplicative noise on formation convergence speed and stability, and the inability of traditional optimal control methods to achieve distributed implementation. To this end, this invention provides a UAV swarm formation control method suitable for environments with heterogeneous multiplicative noise disturbances. It constructs a stochastic dynamic model incorporating heterogeneous noise intensity, designs an optimized cost function that integrates energy, formation error, and network cost, ensuring the existence and feasibility of a distributed optimal control algorithm in such stochastic environments, and derives a distributed optimal control law based on stochastic dynamic programming theory. This invention enables each UAV to achieve globally optimal formation by adaptively adjusting gain based on noise intensity, relying solely on neighbor information, providing a feasible solution for UAV swarm collaboration in heterogeneous disturbance environments. This invention is applicable to UAV swarm formation control in real-world scenarios such as complex electromagnetic environments, urban canyons, and disaster sites.

[0005] This invention provides a method for controlling UAV swarm formations in environments with heterogeneous multiplicative noise disturbances. The technical solution adopted is as follows: It includes the following steps:

[0006] S1: Construct a dynamic model of the UAV that includes heterogeneous multiplicative noise;

[0007] S2: Use an undirected connected graph to describe the communication relationships between UAVs and construct the Laplace matrix of the undirected connected graph;

[0008] S3: Based on the Laplace matrix, construct the overall objective function, which includes an energy cost function, a formation cost function, and a network cost function; the network cost function is designed to handle heterogeneous multiplicative noise.

[0009] S4: Construct the optimal value function of the overall objective function;

[0010] S5: Construct the Hamiltonian function for the optimization problem based on the optimal value function and the UAV dynamics model;

[0011] S6: Based on the Hamiltonian function, the parametric algebraic Riccati equation is solved using stochastic dynamic programming theory to obtain the distributed optimal control law;

[0012] S7: Set the running time, initial state of the UAVs and target formation state, and use distributed optimal control law to control the UAV swarm formation.

[0013] Furthermore, in step S1, the UAV dynamics model including heterogeneous multiplicative noise is as follows:

[0014]

[0015] in, Indicates the first The status of the drone Indicates the first Control input for the drone Represents standard one-dimensional Brownian motion. Indicates the first The heterogeneous noise intensity of the drone, where t represents time.

[0016] Furthermore, in step S2, the nodes of the undirected connected graph represent drones, and the edges between nodes represent the communication relationships between drones.

[0017] Furthermore, in step S3, the overall objective function is the sum of the energy cost function, the formation cost function, and the network cost function.

[0018] Furthermore, in step S3,

[0019] Network cost function Represented as:

[0020]

[0021] in, Represents the mathematical expectation. Indicates the status of all drones. This indicates the target status of all drones. Represents a positive semidefinite matrix. t represents time. This indicates the matrix transpose.

[0022] Furthermore, in step S3,

[0023] Energy cost function Represented as:

[0024]

[0025] in, Represents the mathematical expectation. This represents the control input for all drones, where t represents time. Indicates matrix transpose;

[0026] Formation cost function Represented as:

[0027]

[0028] in, Indicates the status of all drones. This indicates the target status of all drones. Let represent the Laplacian matrix of an undirected connected graph.

[0029] Furthermore, in step S3, the distributed optimal control problem is defined as: designing the optimal control input that minimizes the overall objective function for the system based solely on local information interaction between UAVs, while ensuring that the system can achieve the required formation in the mean square sense.

[0030] Furthermore, in step S4, the optimal value function of the overall objective function is... Represented as:

[0031]

[0032] in, Denotes the first Laplace matrix 1 eigenvalue, Indicates the first Control parameters of the drone State vector representing state transitions The There are 1 element, where n is the number of drones.

[0033] Furthermore, in step S5,

[0034] Hamiltonian function Represented as:

[0035]

[0036] in, The first state vector representing the transition state of the control input One element, Denotes the first Laplace matrix 1 eigenvalue, Represents a positive semidefinite matrix The 1 eigenvalue, The state vector representing the state transition. One element, Indicates the first Control parameters of the drone Indicates the first The heterogeneous noise intensity of the drone.

[0037] Furthermore, in step S6, based on the principle of stochastic dynamic programming, stability conditions are applied. The optimal control expression for the transformation is obtained, and then the parametric algebraic Riccati equation is obtained. The optimal control parameters are solved, and the optimal control parameters are substituted back into the optimal control expression for the transformation. Then, the optimal distributed formation control law is obtained by performing an inverse transformation:

[0038]

[0039] in, For the first system parameter, For the second system parameter, The number of drones, This represents the element in the i-th row and j-th column of the adjacency matrix. Indicates the first The optimal control input for a drone. Indicates correspondence The optimal state, Indicates correspondence The optimal state, This represents the optimal control input for the j-th UAV. Represents a node and nodes The relative state of the targets between them.

[0040] The above-described one or more technical solutions in the embodiments of the present invention have at least one of the following technical effects:

[0041] (1) First time to address heterogeneous multiplicative noise: Most existing studies on optimal distributed formation control focus on additive noise or homogeneous multiplicative noise, without considering the impact of noise intensity differences among UAVs on system performance. This invention is designed for heterogeneous multiplicative noise scenarios, filling a research gap in this field.

[0042] (2) Distributed optimality guarantee: By designing a network cost function for heterogeneous multiplicative noise, the problem of non-distributed implementation caused by the need for global information in traditional optimal control is avoided. This ensures that each UAV can achieve global optimality by relying only on the state of its neighbors, which not only reduces the communication cost of UAV clusters, but also significantly improves computational efficiency.

[0043] (3) Robustness and convergence are unified: the control gain is adaptively adjusted according to the noise intensity, and the cooperative strength is automatically increased when the noise increases, avoiding the problem of instability of traditional fixed gain controllers under strong noise.

[0044] Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0045] To more clearly illustrate the technical solutions in this invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0046] Figure 1 This is a flowchart of the method provided by the present invention.

[0047] Figure 2 This is a drone cluster communication topology diagram provided by the present invention.

[0048] Figure 3 This is a simulation result diagram of the drone swarm operation trajectory and final formation provided by the present invention. Detailed Implementation

[0049] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention. The following embodiments are used to illustrate this invention but should not be used to limit the scope of this invention.

[0050] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., refer to specific features, structures, or characteristics described in connection with that embodiment or example, which are included in at least one embodiment or example of the present invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of different embodiments or examples.

[0051] The following is combined Figures 1 to 3 The present invention will be further described in detail below, providing a method for controlling UAV swarm formations in environments with heterogeneous multiplicative noise disturbances:

[0052] In this embodiment, as Figure 1 As shown, a method for controlling UAV swarm formations suitable for heterogeneous multiplicative noise disturbance environments is provided, including the following steps:

[0053] S1: Construct a dynamic model of the UAV that includes heterogeneous multiplicative noise.

[0054] A first-order dynamic model of the UAV considering heterogeneous multiplicative noise is constructed, expressed as:

[0055] ,

[0056] in, Indicates the first The status of the drone Indicates the first The initial state of the drone. Indicates the first Control input for the drone , , , For the set of real numbers, Represents standard one-dimensional Brownian motion. Indicates the first The heterogeneous noise intensity of the drone t represents time.

[0057] S2: Use an undirected connected graph to describe the communication relationships between UAVs and construct the Laplace matrix of the undirected connected graph.

[0058] Assuming a drone swarm consists of n drones, the communication topology between the drones can be represented as an undirected connected graph. , ,in, Represents a set of nodes. , Indicates the first 1 node Describe the set of edges. , satisfy This means that communication between nodes is bidirectional. Different nodes represent different drones, and the edges between nodes represent the communication relationships between the drones. Represents the adjacency matrix of an undirected connected graph. , This represents the element in the i-th row and j-th column of the adjacency matrix. When the element in the adjacency matrix... When, it indicates a node and nodes There is a connection between them, allowing communication; conversely, if... , then it represents a node and nodes There are no edges connecting them, and no communication exists. The degree matrix of this network... It can be represented as The i-th element in the degree matrix for .

[0059] Construct an undirected connected graph Laplace matrix , , Let represent the element in the i-th row and j-th column of the Laplace matrix, which has symmetric positive semi-definite properties, where ,when hour, The Laplace matrix can be diagonalized as follows: ,in, The matrix representing the orthogonal eigenvectors of the Laplacian matrix. , Indicates the first 3 orthogonal eigenvectors; The eigenvalue matrix represents the Laplacian matrix. and , This represents the first element of the Laplace matrix; This indicates the matrix transpose.

[0060] S3: Based on the Laplace matrix, construct the overall objective function, which includes the energy cost function, the formation cost function, and the network cost function.

[0061] This embodiment first defines the energy cost function, the formation cost function, and the network cost function.

[0062] Define the energy cost function to be optimized. :

[0063]

[0064] in, Represents the mathematical expectation. This represents all control inputs for the drone. , , This represents the control input for the first drone, and t represents time.

[0065] Define the formation cost function to be optimized. :

[0066]

[0067] in, Indicates the status of all drones. , , This indicates the status of the first drone. This indicates the target status of all drones. , , This indicates the target status of the first drone.

[0068] Design a network cost function that ensures the coexistence of optimal control and distributed structure. :

[0069]

[0070] in, Represents a positive semidefinite matrix. This will be designed in subsequent steps.

[0071] The network cost function is designed to address heterogeneous multiplicative noise: a mathematical expectation is introduced into the network cost function to suppress the random perturbation of heterogeneous multiplicative noise; heterogeneous multiplicative noise has different effects on different dimensions of UAV state perturbation and needs to be specifically suppressed, and the network cost function achieves this through... Its positive semidefinite property ensures that the function is non-negative and suppresses noise-sensitive dimensions.

[0072] Construct the overall objective function that needs to be optimized. :

[0073]

[0074] The overall objective function includes the energy cost function, the formation cost function, and the network cost function, and its value is the sum of the three.

[0075] Due to the presence of noise, the long-term behavior of the system must be characterized probabilistically. Therefore, this implementation defines formation reachability in the mean-square sense. The distributed optimal control problem is defined as: designing a system that minimizes the overall objective function based solely on local information interactions between UAVs. Optimal control input At the same time, it ensures that the system can achieve the required formation in the mean-square sense, that is

[0076]

[0077] in, Represents a node and nodes The relative states of the targets between them, and the nodes and nodes For neighbors, , This represents the upper limit as time approaches infinity. This represents the square of the Euclidean norm.

[0078] S4: Construct the optimal value function of the overall objective function.

[0079] Define the optimal value function of the overall objective function. :

[0080]

[0081] in, Denotes the first Laplace matrix 1 eigenvalue, Indicates the first Control parameters of the drone , State vector representing state transitions The One element, .

[0082] S5: Based on the optimal value function and the UAV dynamics model, construct the Hamiltonian function for the optimization problem.

[0083] Define a Hamiltonian function that includes the optimal value function. :

[0084]

[0085] in, The transition state vector representing the control input The One element, , express The Each feature value.

[0086] According to the optimal value function in step S4, it can be known that

[0087] , .

[0088] Then, Hamiltonian function It can be written as:

[0089] .

[0090] S6: Based on the Hamiltonian function, the parametric algebraic Riccati equation is solved using stochastic dynamic programming theory to obtain the distributed optimal control law.

[0091] Based on the principles of stochastic dynamic programming, and applying stability conditions... To obtain the optimal control for the transformation The expression:

[0092]

[0093] in, This represents the optimal state of the optimal control during the transition. This represents the optimal control parameters for the optimal control during the transition.

[0094] Furthermore, the parametric algebraic Riccati equation can be obtained:

[0095]

[0096] in, , For the first system parameter, For the second system parameter, satisfying , The two parameter constraints can guarantee the positive semidefiniteness of the cost function.

[0097] Solving this equation yields the optimal control parameters:

[0098] .

[0099] Substituting the optimal control parameters back into the transformed optimal control expression and performing the inverse transformation, we obtain the optimal distributed formation control law as follows:

[0100]

[0101] in, This represents the optimal control input for the i-th UAV. Indicates correspondence The optimal state, Indicates correspondence The optimal state, Let represent the optimal control input for the j-th UAV.

[0102] S7: Set the running time, initial state of the UAVs and target formation state, and use distributed optimal control law to control the UAV swarm formation.

[0103] Set the runtime and target formation state. The target formation state is the formation configuration that the UAVs need to achieve at the end of the runtime. Obtain the initial state of the UAVs, i.e., the initial position of each UAV. Calculate the system parameters based on the eigenvalues ​​of the Laplace matrix. and Then, the formation trajectory under optimal control is calculated using a distributed optimal control law. After the operation is completed, the final target formation state can be obtained.

[0104] This embodiment enables all drones to fly to the target formation state through distributed communication and with minimal energy consumption.

[0105] This invention focuses on ensuring optimal formation control and a distributed communication architecture in complex environments considering heterogeneous multiplicative noise. The core method is to introduce a network cost framework to design control algorithms for heterogeneous multiplicative noise systems. By designing a network cost function specifically for heterogeneous multiplicative noise, this invention avoids the non-distributable implementation problem caused by the need for global information in traditional optimal control. It ensures that each UAV can achieve global optimum by relying only on the states of its neighbors, reducing the communication cost of the UAV swarm and significantly improving computational efficiency. The distributed communication method employed in this invention gives the UAV swarm's communication network higher robustness, stability, and reliability. Furthermore, it maintains good anti-interference capabilities even in the presence of heterogeneous noise disturbances, preventing divergence due to heterogeneous noise and ensuring that all UAVs eventually converge to the expected formation state.

[0106] This embodiment verifies the effectiveness of the method through simulation experiments, as detailed below:

[0107] First, given a number of 10 drones, set the Laplace matrix for drone swarm communication, and the corresponding communication topology is as follows. Figure 2 As shown. Setting parameters =0.6826, =4.991. The initial state of the UAV is random. The running time is 2 minutes. The target formation is a spiral shape with a height of 25m, a radius of 5m, and 1.5 rotations. The simulation results are as follows. Figure 3 As shown, Figure 3 In the diagram, "*" represents the initial position of the drone, "·" represents the final position, the solid black line represents the trajectory of a single drone, and the dashed blue line depicts the final shape of the drone swarm. Simulation results show that, using this method, a multi-drone system with heterogeneous noise can asymptotically converge to the expected spiral queue.

[0108] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for controlling UAV swarm formations in environments with heterogeneous multiplicative noise disturbances, characterized in that, Includes the following steps: S1: Construct a dynamic model of the UAV that includes heterogeneous multiplicative noise; S2: Use an undirected connected graph to describe the communication relationships between UAVs and construct the Laplace matrix of the undirected connected graph; S3: Based on the Laplace matrix, construct the overall objective function, which includes an energy cost function, a formation cost function, and a network cost function; the network cost function is designed to handle heterogeneous multiplicative noise. S4: Construct the optimal value function of the overall objective function; S5: Construct the Hamiltonian function for the optimization problem based on the optimal value function and the UAV dynamics model; In step S5, the Hamiltonian function Represented as: in, The first state vector representing the transition state of the control input One element, Denotes the first Laplace matrix 1 eigenvalue, Represents a positive semidefinite matrix The 1 eigenvalue, The state vector representing the state transition. One element, Indicates the first Control parameters of the drone Indicates the first The intensity of heterogeneous noise from the drone; S6: Based on the Hamiltonian function, the parametric algebraic Riccati equation is solved using stochastic dynamic programming theory to obtain the distributed optimal control law; In step S6, the stability condition is applied according to the principle of stochastic dynamic programming. The optimal control expression for the transformation is obtained, and then the parametric algebraic Riccati equation is obtained. The optimal control parameters are solved, and the optimal control parameters are substituted back into the optimal control expression for the transformation. Then, the optimal distributed formation control law is obtained by performing an inverse transformation: in, For the first system parameter, Here is the second system parameter, where n is the number of drones. This represents the element in the i-th row and j-th column of the adjacency matrix. Indicates the first The optimal control input for a drone. Indicates correspondence The optimal state, Indicates correspondence The optimal state, This represents the optimal control input for the j-th UAV. Represents a node and nodes The relative state of the targets between them; S7: Set the running time, initial state of the UAVs and target formation state, and use distributed optimal control law to control the UAV swarm formation.

2. The UAV swarm formation control method applicable to heterogeneous multiplicative noise disturbance environments as described in claim 1, characterized in that, In step S1, the UAV dynamics model including heterogeneous multiplicative noise is as follows: in, Indicates the first The status of the drone Indicates the first Control input for the drone Represents standard one-dimensional Brownian motion. Indicates the first The heterogeneous noise intensity of the drone, where t represents time.

3. The UAV swarm formation control method applicable to heterogeneous multiplicative noise disturbance environments as described in claim 1, characterized in that, In step S2, the nodes of the undirected connected graph represent drones, and the edges between nodes represent the communication relationships between drones.

4. The UAV swarm formation control method applicable to heterogeneous multiplicative noise disturbance environments as described in claim 1, characterized in that, In step S3, the overall objective function is the sum of the energy cost function, the formation cost function, and the network cost function.

5. A method for controlling UAV swarm formations in heterogeneous multiplicative noise disturbance environments as described in claim 1 or 4, characterized in that, In step S3, Network cost function Represented as: in, Represents the mathematical expectation. Indicates the status of all drones. This indicates the target status of all drones. Represents a positive semidefinite matrix. t represents time. This indicates the matrix transpose.

6. A method for controlling UAV swarm formations in heterogeneous multiplicative noise disturbance environments as described in claim 1 or 4, characterized in that, In step S3, Energy cost function Represented as: in, Represents the mathematical expectation. This represents the control input for all drones, where t represents time. Indicates matrix transpose; Formation cost function Represented as: in, Indicates the status of all drones. This indicates the target status of all drones. Let represent the Laplacian matrix of an undirected connected graph.

7. The UAV swarm formation control method applicable to heterogeneous multiplicative noise disturbance environments as described in claim 1, characterized in that, In step S3, the distributed optimal control problem is defined as: designing the optimal control input that minimizes the overall objective function for the system based solely on local information interaction between UAVs, while ensuring that the system can achieve the required formation in the mean square sense.

8. The UAV swarm formation control method applicable to heterogeneous multiplicative noise disturbance environments as described in claim 1, characterized in that, In step S4, the optimal value function of the overall objective function is... Represented as: in, Denotes the first Laplace matrix 1 eigenvalue, Indicates the first Control parameters of the drone State vector representing state transitions The There are 1 element, where n is the number of drones.

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