Distributed multi-agent security control method based on non-smooth graph barrier function

Abstract

The application relates to the technical field of dynamic system obstacle avoidance, in particular to a distributed multi-agent safety control method based on a non-smooth graph barrier function. The method comprises the following steps: defining a node set, constructing a communication graph topology and a neighbor interaction relationship according to the node set; giving boundary conditions required for constructing a non-smooth graph barrier function, and constructing the non-smooth graph barrier function according to the boundary conditions; formulating a multi-agent system dynamics equation with an uncertainty parameter according to the non-smooth graph barrier function; designing a reference model and an adaptive law according to the multi-agent system dynamics equation, and constructing a stable reference trajectory; constructing and improving a filter according to the reference trajectory; and inputting unmanned aerial vehicle (UAV) group motion data into the filter to obtain a motion control result of the UAV. By introducing an absolute continuity modeling tool, the application directly supports the description of non-smooth safety regions such as polygonal obstacles, and breaks through the dependence of traditional methods on differentiable boundaries.

Description

Technical Field

[0001] This invention relates to the field of obstacle avoidance technology for dynamic systems, and in particular to a distributed multi-agent safety control method based on a non-smooth graph barrier function. Background Technology

[0002] With the rapid development of technologies such as autonomous drones and collaborative robots, multi-agent systems have demonstrated significant advantages in performing complex tasks. However, ensuring the safety of these systems in real-world dynamic environments faces severe and unique challenges. The core of this challenge lies in the fact that obstacles in real-world operating environments are often not ideal smooth surfaces or spheres, but rather non-smooth geometric features with sharp edges or flat surfaces. These non-smooth boundaries contain non-differentiable points at their vertices or edges, causing analysis and control design methods based on traditional differential tools to fail at such points.

[0003] Traditional safety control methods based on control barrier functions are an important framework for ensuring system safety. However, their effectiveness relies heavily on the assumption that the safety function and the boundary of its defined safety set are everywhere smooth and differentiable. This smoothness requirement encounters fundamental difficulties at non-smooth boundaries: gradient-based Lie derivative calculations become undefined or invalid at these non-differentiable points, making it impossible to accurately describe the dynamic evolution of safety constraints and thus failing to guarantee the system's safety when avoiding such obstacles. Furthermore, in the case of combined constraints of multiple smooth obstacles, non-differentiable points are generated at the intersection of their constraint boundaries, and traditional barrier function methods also struggle to effectively handle this non-smoothness caused by combined constraints. Therefore, traditional methods have significant deficiencies in their safety assurance capabilities when facing the prevalent non-smooth geometric constraints in real-world environments. Summary of the Invention

[0004] This invention aims to at least solve one of the technical problems existing in related technologies. To this end, this invention provides a distributed multi-agent safety control method based on a non-smooth graph barrier function, which directly supports the description of non-smooth safety regions such as polygonal obstacles, breaking through the dependence of traditional methods on differentiable boundaries.

[0005] This invention provides a distributed multi-agent security control method based on a non-smooth graph barrier function, comprising:

[0006] S1: Define a node set, and construct a communication graph topology and neighbor interaction relationships based on the node set;

[0007] S2: Provide the boundary conditions required to construct the non-smooth graph barrier function, and construct the non-smooth graph barrier function according to the boundary conditions;

[0008] S3: Form the dynamic equations of a multi-agent system with uncertain parameters based on the non-smooth graph barrier function;

[0009] S4: Based on the dynamic equations of the multi-agent system, design a reference model and adaptive law to construct a stable reference trajectory;

[0010] S5: Construct and improve the QP-NGBF filter based on the reference trajectory;

[0011] S6: Input the UAV group motion data into the QP-NGBF filter to obtain the motion control results of the UAV.

[0012] According to the present invention, a distributed multi-agent security control method based on a non-smooth graph barrier function is provided, wherein step S1 includes:

[0013] S11: Define the communication diagram , ;

[0014] in, For a set of nodes, ,in, The node ordinal number. This represents the total number of nodes, with each node corresponding to one agent.

[0015] For edge set, , For Kronecker product;

[0016] Among them, if ,but and They are neighbors. For the first intelligent agent and As a second intelligent agent;

[0017] S12: Define the neighbor set:

[0018]

[0019] in, for The set of neighbors.

[0020] According to the present invention, a distributed multi-agent security control method based on a non-smooth graph barrier function is provided, wherein step S2 includes:

[0021] S21: Based on the nonsmooth graph barrier function Absolutely continuous, This makes the following equation true:

[0022]

[0023]

[0024] in, for Along the system vector field Li Daoshu, for Along the input vector field Li Daoshu, For Neighbor Intelligent Agent Distributed control law, For Neighbor Intelligent Agent Extended K-class functions, For Neighbor Intelligent Agent Non-smooth graph barrier function, To extend the K-class functions, This indicates that it exists. Indicates any, It means almost everywhere;

[0025] S22: Based on the nonsmooth graph barrier function Absolutely continuous, This makes the following equation true:

[0026]

[0027]

[0028]

[0029] in, for The first derivative, for Non-smooth graph barrier function, for Extended K-class functions.

[0030] According to the present invention, a distributed multi-agent security control method based on a non-smooth graph barrier function is provided, wherein step S3 includes:

[0031] Constructing the first intelligent agent Multi-agent system dynamic equations:

[0032]

[0033] in, for The first derivative, for The state vector, For the system matrix, Given the input matrix, For the control gain matrix, To control the input vector, The unknown perturbation coupling matrix, The nonlinear perturbation term is known.

[0034] According to the present invention, a distributed multi-agent security control method based on a non-smooth graph barrier function is provided, wherein the dynamic equations of the multi-agent system include:

[0035] There is an upper realm. It is a full-rank matrix and all eigenvalues ​​have non-zero real parts;

[0036] There exists a constant matrix , so that:

[0037]

[0038] in, The Hurwitz matrix is ​​known.

[0039] According to the present invention, a distributed multi-agent security control method based on a non-smooth graph barrier function is provided, wherein step S4 includes:

[0040]

[0041]

[0042] in, for The reference model state, for The reference model state, for The first derivative, Given the Hurwitz matrix, For distributed control input, For a constant control gain matrix, This represents the target's relative state offset.

[0043] According to the present invention, a distributed multi-agent security control method based on a non-smooth graph barrier function is provided. For real-world systems with uncertainties, the distributed control input is designed as follows:

[0044]

[0045]

[0046]

[0047]

[0048] in, for The first estimated parameter, for The second estimated parameter, for The third estimated parameter, for The actual state, for The actual state, This is the first adaptive gain matrix. Design a matrix for the adaptive law. Indicates matrix transpose. This is the second adaptive gain matrix. This is the third adaptive gain matrix.

[0049] According to the present invention, a distributed multi-agent security control method based on a non-smooth graph barrier function is provided, wherein step S5 includes:

[0050] S51: Design control gain:

[0051]

[0052]

[0053] in, For gain parameters, This is a solution to the Lyapunov equation. It is the second smallest eigenvalue of the Laplace matrix. Indicates matrix transpose;

[0054] S52: Generate reference input:

[0055]

[0056]

[0057] in, for and The relative state of the target for The relative state of the target for The relative state of the target.

[0058] According to the present invention, a distributed multi-agent security control method based on a non-smooth graph barrier function is provided to apply stability constraints to the QP-NGBF filter:

[0059]

[0060]

[0061] in, To find the minimum value function, It is a quadratic norm. For ideal formation offset, Indicates constraints. The safety gain constant, As a safety buffer, for The non-smooth graph barrier function value of the reference model state.

[0062] According to the present invention, a distributed multi-agent security control method based on a non-smooth graph barrier function is provided to apply stability and security constraints to a QP-NGBF filter:

[0063]

[0064]

[0065] in, As the upper bound of transient safety, For steady-state safety boundary, It is a time constant. At the initial moment, For time.

[0066] The above-described one or more technical solutions in the embodiments of the present invention have at least one of the following technical effects:

[0067] The distributed multi-agent safety control method based on non-smooth graph barrier functions provided by this invention is particularly suitable for distributed safety assurance in non-smooth obstacle environments in dynamic systems such as UAV swarms and collaborative robots, and has the following advantages:

[0068] 1. Non-smooth compatibility: Introduces an absolute continuity modeling tool that directly supports the description of non-smooth safe regions such as polygonal obstacles, breaking through the dependence of traditional methods on differentiable boundaries;

[0069] 2. Distributed Adaptability: Based on the graph topology structure, a local neighbor state interaction mechanism is designed, which can dynamically update the security state with only local communication, eliminating global communication overhead and significantly improving the scalability of large-scale systems;

[0070] 3. Optimized architecture: Combining quadratic programming filtering and adaptive control, precise obstacle avoidance of polyhedral obstacles is achieved through convex optimization, reducing conservatism and compatibility with parameter uncertainty models.

[0071] This framework establishes a theoretical unification of nonsmooth safe sets and graph interactions, resolving the key contradiction in distributed systems where nonsmooth geometric constraints and real-time adaptability are difficult to balance. Simulation results demonstrate that in multi-UAV formation scenarios with square obstacles, this invention can ensure that all agents stably converge to the target configuration while avoiding nonsmooth obstacles.

[0072] Compared with the prior art, the present invention has the following outstanding advantages:

[0073] 1) Directly supports modeling of non-smooth obstacles such as polygons, significantly improving applicability to complex environments;

[0074] 2) A distributed architecture based on local neighbor states avoids global communication load and supports large-scale multi-agent systems;

[0075] 3) By dynamically adjusting the safety boundary through the QP-NGBF filter, the constraints caused by the conservatism of traditional methods are effectively reduced;

[0076] 4) It can guarantee the safety and convergence of the system under parameter uncertainty.

[0077] 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

[0078] 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.

[0079] Figure 1 This is a flowchart illustrating the distributed multi-agent security control method based on a non-smooth graph barrier function provided by the present invention.

[0080] Figure 2 This is a communication topology diagram of a drone according to an embodiment of the present invention.

[0081] Figure 3 This is a simulation result diagram of an embodiment of the present invention. Detailed Implementation

[0082] 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. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. Based on the embodiments of this invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this invention. The following embodiments are used to illustrate this invention but cannot be used to limit the scope of this invention.

[0083] 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, materials, 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, materials, 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.

[0084] The following is combined Figures 1 to 3 This invention is described.

[0085] Example

[0086] like Figure 1 As shown, this invention provides a distributed multi-agent security control method based on a non-smooth graph barrier function, comprising the following steps:

[0087] S1: Define a node set, and construct a communication graph topology and neighbor interaction relationships based on the node set;

[0088] S2: Provide the boundary conditions required to construct the non-smooth graph barrier function, and construct the non-smooth graph barrier function based on the boundary conditions. ;

[0089] S3: Form the dynamic equations of a multi-agent system with uncertain parameters based on the non-smooth graph barrier function;

[0090] S4: Based on the dynamic equations of the multi-agent system, design a reference model and adaptive law to construct a stable reference trajectory;

[0091] S5: Construct and improve the QP-NGBF filter based on the reference trajectory;

[0092] S6: Input the UAV group motion data into the QP-NGBF filter to obtain the motion control results of the UAV.

[0093] Specifically, step S1 includes:

[0094] S11: Define the communication diagram , ;

[0095] in, For a set of nodes, ,in, The node ordinal number. This represents the total number of nodes, with each node corresponding to one agent.

[0096] For edge set, , For Kronecker product;

[0097] Among them, if ,but and They are neighbors. For the first intelligent agent and It is the second intelligent agent.

[0098] The Thulaplac matrix The definition of is:

[0099]

[0100] in, For degree matrix, It is an adjacency matrix.

[0101] S12: Define the neighbor set:

[0102]

[0103] in, for The set of neighbors.

[0104] In step S2, the theoretical preconditions required for constructing the non-smooth graph barrier function are given. Non-smooth graph barrier function It has the following three characteristics:

[0105] 1. Absolutely continuous.

[0106] 2. Due to the existence Differential includes, It must satisfy local boundedness and upper semi-continuity.

[0107] 3. The generalized gradient is non-empty, compact, and convex.

[0108] Specifically, the non-smooth graph barrier function is formally defined, and its security guarantee step S2 is established through property 1-2, including:

[0109] Based on characteristic 1, the existence of distributed security conditions is mainly explained.

[0110] S21: Based on the nonsmooth graph barrier function Absolutely continuous, This makes the following equation true:

[0111]

[0112]

[0113] in, for Along the system vector field Li Daoshu, for Along the input vector field Li Daoshu, For Neighbor Intelligent Agent Distributed control law, For Neighbor Intelligent Agent Extended K-class functions, For Neighbor Intelligent Agent Non-smooth graph barrier function, To extend the K-class functions, This indicates that it exists. Indicates any, It means almost everywhere.

[0114] Based on property 2, the forward invariance of the safe set is mainly explained.

[0115] S22: Based on the nonsmooth graph barrier function Absolutely continuous, This makes the following equation true:

[0116]

[0117]

[0118]

[0119] in, for The first derivative, for Non-smooth graph barrier function, for Extended K-class functions.

[0120] Specifically, step S3 includes:

[0121] Constructing the first intelligent agent Multi-agent system dynamic equations:

[0122]

[0123] in, for The first derivative, for The state vector, For the system matrix, Given the input matrix, For the control gain matrix, To control the input vector, The unknown perturbation coupling matrix, The nonlinear perturbation term is known.

[0124] in, There is an upper realm. It is a full-rank matrix and all eigenvalues ​​have non-zero real parts;

[0125] There exists a constant matrix , so that:

[0126]

[0127] in, The Hurwitz matrix is ​​known.

[0128] Specifically, step S4 includes:

[0129]

[0130]

[0131] in, for The reference model state, for The reference model state, for The first derivative, Given the Hurwitz matrix, For distributed control input, For a constant control gain matrix, This represents the target's relative state offset.

[0132] For real-world systems with uncertainties, the distributed control input is designed as follows:

[0133]

[0134]

[0135]

[0136]

[0137] in, for The first estimated parameter, for The second estimated parameter, for The third estimated parameter, for The actual state, for The actual state, This is the first adaptive gain matrix. Design a matrix for the adaptive law. Indicates matrix transpose. This is the second adaptive gain matrix. This is the third adaptive gain matrix.

[0138] Specifically, step S5 includes:

[0139] S51: Design control gain:

[0140]

[0141]

[0142] in, For gain parameters, This is a solution to the Lyapunov equation. It is the second smallest eigenvalue of the Laplace matrix;

[0143] in, The solution to the equation:

[0144]

[0145] in, Let be any given positive definite matrix.

[0146] S52: Generate reference input:

[0147]

[0148]

[0149] in, for and The relative state of the target for The relative state of the target for The relative state of the target.

[0150] Stability constraints are applied to the QP-NGBF filter:

[0151]

[0152]

[0153] in, To find the minimum value function, It is a quadratic norm. For ideal formation offset, Indicates constraints. The safety gain constant, This is a safety buffer.

[0154] Apply stability and security constraints to the QP-NGBF filter:

[0155]

[0156]

[0157] in, As the upper bound of transient safety, For steady-state safety boundary, It is a time constant. At the initial moment, For time.

[0158] like Figure 2 As shown, Figure 2 This invention provides a UAV communication topology configuration for an embodiment of the UAV. The embodiments of the invention also configure the parameters of the agent system. Considering a multi-agent system with four agents, the state dimension is configured. Number of intelligent agents Simulation step size Total simulation time Total number of iterations Its communication topology is as follows: Figure 2 As shown, the adjacency matrix is ​​defined as follows:

[0159]

[0160] It was observed that, , , , .in, For the neighbor set of the drone; For the neighbor set of drone 2; For the drone's three neighbor set; For the drone's neighbor set.

[0161] This invention assumes that the first The dynamic equations of an agent are:

[0162]

[0163] The dynamic parameters are set as follows:

[0164]

[0165]

[0166] The initial position is set as follows:

[0167]

[0168]

[0169] in, The initial position of the first drone; The initial position of UAV 2; The initial position of the third drone; The initial position of the fourth drone.

[0170] Target location Set to:

[0171]

[0172] This invention constructs a non-smooth graph barrier function. First, the obstacles are modeled, with their centers located at... and A square obstacle with a side length of , Among them, safety conditions This indicates that the agent is outside the obstacle. Define the barrier function:

[0173]

[0174] Among them, the security parameters are set to This is the function for finding the maximum value.

[0175] In step 3, the present invention configures various parameters. The reference model matrix is ​​set to... Its eigenvalues ​​all have negative real parts, ensuring system stability. Assume... Here is a solution to the following Lyapunov equation:

[0176]

[0177] Solving Then, the control gain matrix can be further calculated. .

[0178] Assuming reference input The adaptive gain matrix is ​​selected as ,matrix ,parameter , , The initial value is 0. It is a second-order identity matrix.

[0179] like Figure 3 As shown. Figure 3 In the diagram, the red squares represent obstacles, the black octagons represent the initial positions of the drones, the purple dashed lines represent the trajectory of drone one, the yellow dashed lines represent the trajectory of drone two, the red dashed lines represent the trajectory of drone three, and the blue dashed lines represent the trajectory of drone four. Simulation experiments show that, under the controller-driven system, the system output trajectory satisfies the following:

[0180] 1. Precise obstacle avoidance: All agents can avoid square obstacles ( (Ever established).

[0181] 2. Formation convergence: All agents eventually reach the target location.

[0182] Furthermore, although the operation of the methods of this disclosure is described in a specific order in the accompanying drawings, this does not require or imply that these operations must be performed in that specific order, or that all the operations shown must be performed to achieve the desired result. Rather, the steps depicted in the flowcharts may be performed in a different order. Additionally or alternatively, certain steps may be omitted, multiple steps may be combined into one step, and / or one step may be broken down into multiple steps. It should also be noted that the features and functions of two or more devices according to this disclosure may be embodied in one device. Conversely, the features and functions of one device described above may be further divided and embodied by multiple devices.

[0183] While this disclosure has been described with reference to several specific embodiments, it should be understood that this disclosure is not limited to the specific embodiments disclosed. This disclosure is intended to cover various modifications and equivalent arrangements included within the spirit and scope of the appended claims.

Claims

1. A distributed multi-agent security control method based on a non-smooth graph barrier function, characterized in that, Includes the following steps: S1: Define a node set, and construct a communication graph topology and neighbor interaction relationships based on the node set; S2: Provide the boundary conditions required to construct the non-smooth graph barrier function, and construct the non-smooth graph barrier function according to the boundary conditions; S3: Formulate the dynamic equations of a multi-agent system with uncertain parameters based on the non-smooth graph barrier function, including: Constructing the first intelligent agent Multi-agent system dynamic equations: in, for The first derivative, for The state vector, For the system matrix, For the control gain matrix, To control the input vector, The unknown perturbation coupling matrix, Given the nonlinear perturbation term; S4: Based on the dynamic equations of the multi-agent system, design a reference model and adaptive law, and construct a stable reference trajectory, including: in, for The reference model state, for The reference model state, for The first derivative, Given the Hurwitz matrix, For distributed control inputs, and considering real-world systems with uncertainties, the distributed control inputs are designed as follows: in, for The first estimated parameter, for The second estimated parameter, for The third estimated parameter, for The actual state, for The actual state, This is the first adaptive gain matrix. Design a matrix for the adaptive law. Indicates matrix transpose. This is the second adaptive gain matrix. The third adaptive gain matrix S5: Construct and improve the QP-NGBF filter based on the reference trajectory. Step S5 includes: S51: Design control gain: in, For a constant control gain matrix, For gain parameters, Given the input matrix, This is a solution to the Lyapunov equation. It is the second smallest eigenvalue of the Laplace matrix. Indicates matrix transpose; S52: Generate reference input: in, This represents the target's relative state offset. for The neighborhood group, As the first intelligent agent, for and The relative state of the target for The relative state of the target for The relative state of the target For neighboring intelligent agents; S6: Input the UAV group motion data into the QP-NGBF filter to obtain the motion control results of the UAV.

2. The distributed multi-agent security control method based on a non-smooth graph barrier function according to claim 1, characterized in that, Step S1 includes: S11: Define the communication diagram , ; in, For a set of nodes, ,in, The node ordinal number. This represents the total number of nodes, with each node corresponding to one agent. For edge set, , For Kronecker product; Among them, if ,but and They are neighbors. As a second intelligent agent; S12: Define the neighbor set: 。 3. The distributed multi-agent security control method based on a non-smooth graph barrier function according to claim 2, characterized in that, Step S2 includes: S21: Based on the nonsmooth graph barrier function Absolutely continuous, This makes the following equation true: in, for Along the system vector field Li Daoshu, for Along the input vector field Li Daoshu, for Distributed control law, for Extended K-class functions, for Non-smooth graph barrier function, To extend the K-class functions, This indicates that it exists. Indicates any, It means almost everywhere; S22: Based on the nonsmooth graph barrier function Absolutely continuous, This makes the following equation true: in, for The first derivative, for Non-smooth graph barrier function, for Extended K-class functions.

4. The distributed multi-agent security control method based on a non-smooth graph barrier function according to claim 1, characterized in that, The dynamic equations of a multi-agent system include: There is an upper realm. It is a full-rank matrix and all eigenvalues ​​have non-zero real parts; There exists a constant matrix , so that: in, The Hurwitz matrix is ​​known.

5. The distributed multi-agent security control method based on a non-smooth graph barrier function according to claim 1, characterized in that, Stability constraints are applied to the QP-NGBF filter: in, To find the minimum value function, It is a quadratic norm. For ideal formation offset, Indicates constraints. The safety gain constant, As a safety buffer, for The non-smooth graph barrier function value of the reference model state.

6. The distributed multi-agent security control method based on a non-smooth graph barrier function according to claim 5, characterized in that, Apply stability and security constraints to the QP-NGBF filter: in, As the upper bound of transient safety, For steady-state safety boundary, It is a time constant. At the initial moment, For time.

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