Data-based predefined time heterogeneous multi-agent formation collision avoidance method

Abstract

The invention discloses a data-based predefined time heterogeneous multi-agent formation collision avoidance method. The method comprises the following steps: establishing a nonlinear heterogeneous multi-agent system; designing a bimodal artificial potential field function to perform dynamic obstacle avoidance and prevent regional escape; establishing a self-adaptive robust controller used for generating an obstacle avoidance safety motion trail of the root leader; designing a self-adaptive formation zooming mechanism of the leader, and constructing a predefined time affine observer of the follower based on the self-adaptive formation zooming mechanism; designing a unified obstacle function; constructing a virtual control law for processing tracking errors based on the unified obstacle function; designing a neural network estimator; designing controllers of the leader and the follower according to the virtual control law; and forming a collision avoidance decision of the heterogeneous multi-agent formation based on a self-adaptive robust controller, a predefined time affine observer, a neural network estimator and controllers of the leader and the follower. According to the method, safe, efficient and robust cooperative control of the formation in a complex environment is realized, and the safety and task execution efficiency of the heterogeneous multi-agent formation in a limited and unknown environment are remarkably improved.

Description

Technical Field

[0001] This invention relates to the field of multi-agent system control technology, and in particular to a data-based predefined time heterogeneous multi-agent formation collision avoidance method. Background Technology

[0002] The demand for multi-agent system formation control technology is increasingly urgent in collaborative operations, especially in complex and constrained environments (such as collaborative exploration and inspection by multiple underwater robots). However, existing technologies still face the following significant challenges when handling such scenarios: (1) Insufficient adaptability and safety in restricted environments: Existing formation control strategies struggle to simultaneously achieve high-precision trajectory tracking, dynamic obstacle avoidance, and prevention of area escape in restricted areas (with obstacles, narrow passages, and safety boundaries). Formation scaling strategies based on preset time (such as formation compression / restoration) lack flexibility and cannot adjust autonomously and smoothly according to real-time environmental changes, thus weakening the adaptability of multi-agent systems to dynamic and complex terrains. Traditional artificial potential field methods are prone to causing severe jitter in agents when used for obstacle avoidance, disrupting formation stability. (2) Limited ability to handle full-state constraints and uncertainties: In applications where the states of the agent (such as position and velocity) are strictly limited, existing methods have obvious shortcomings: traditional obstacle Lyapunov functions and preset performance controls impose strict constraints on the design of virtual control laws. Although general obstacle functions can handle dynamic constraints, they often impose too many restrictions on boundary functions, introducing unnecessary conservatism and affecting control performance. At the same time, the model uncertainties (such as unmodeled dynamics and parameter perturbations) that are common in multi-agent systems, as well as the heterogeneous characteristics among agents, lack effective online compensation mechanisms, which can easily lead to problems such as decreased tracking accuracy and insufficient robustness. (3) State estimation efficiency and hardware dependency issues: Fast and accurate estimation of follower states (especially velocity information that cannot be directly measured) is crucial for ensuring formation coordination. Commonly used methods, such as high-gain observers, suffer from uncertain convergence times and susceptibility to noise in estimation accuracy, making it difficult to meet the requirement of accurate state reconstruction within a finite time. In addition, existing solutions typically require all agents to be equipped with expensive environmental perception sensors (such as sonar and vision), which significantly increases system costs and limits the potential for large-scale applications. Summary of the Invention

[0003] This invention provides a data-based, predefined time-based heterogeneous multi-agent formation collision avoidance method to overcome the aforementioned technical problems.

[0004] To achieve the above objectives, the technical solution of the present invention is as follows: A data-driven, predefined temporal heterogeneous multi-agent formation collision avoidance method includes the following steps: S1. Divide several agents into root leader, leader and follower according to the set rules, and establish a nonlinear heterogeneous multi-agent system; S2. The root leader is configured to collect sensing data in real time through sensors, and design a bimodal artificial potential field function based on the sensing data and the nonlinear heterogeneous multi-agent system to perform dynamic obstacle avoidance and prevent regional escape; the sensing data includes information on the boundary of the restricted area and the spatial distribution of obstacles; A data-driven neural network is constructed for online estimation of the uncertainties of the nonlinear heterogeneous multi-agent system and real-time compensation. An adaptive robust controller for generating the obstacle avoidance safe movement trajectory of the root leader is established based on the aforementioned dual-modal artificial potential field function and data-driven neural network. S3. Design an adaptive formation scaling mechanism for the leader, and construct a predefined time affine observer for the followers based on the adaptive formation scaling mechanism to estimate the pose state of the followers in real time and ensure that the followers complete the formation state convergence within a preset time. S4. Design a unified barrier function for handling constrained states in nonlinear heterogeneous multi-agent systems; A virtual control law for handling tracking errors is constructed based on the unified barrier function; Design a neural network estimator to estimate the output of the data-driven neural network to compensate for uncertainties in nonlinear heterogeneous multi-agent systems; S5. Design controllers for leaders and followers based on the virtual control law; S6. Collision avoidance decisions are formed for heterogeneous multi-agent formations based on the adaptive robust controller, predefined time affine observer, neural network estimator, and the controllers for leaders and followers.

[0005] Furthermore, in S1, several agents are divided into root leader, leader, and follower groups according to the set rules, including: Based on the differences in the tracking capabilities of the agents, all agents are divided into high-level agents and low-level agents. The high-level agents are designated as root leaders, which have the ability to perceive the boundaries of the restricted area and obstacles. The low-level agents are designated as leaders and followers. The established expression for the nonlinear heterogeneous multi-agent system is as follows: (1) In the formula: and It is a non-zero gain term. and For unknown parameter variables, and For nonlinear function vectors, and They represent the first j The control inputs and outputs of an intelligent agent Indicates the first j The position vectors of each agent. Indicates the first j The velocity vector of each agent. and This indicates modeling uncertainty; Furthermore, the nonlinear heterogeneous multi-agent system satisfies the following full-state dynamic constraints: (2) In the formula: and These represent the time-varying upper and lower constraint boundaries of the state of a nonlinear heterogeneous multi-agent system, respectively. ; , as well as These represent the state information of the root leader, leader, and followers, respectively.

[0006] Furthermore, in S2, the specific steps for designing the dual-modal artificial potential field function based on the perceived data and the nonlinear heterogeneous multi-agent system include: S21. Definition For the first The position vectors of each agent. For the first The velocity vector of each agent. , Then, the nonlinear heterogeneous multi-agent system is converted into a standard nonlinear heterogeneous multi-agent system, expressed as: (3) In the formula: To concentrate uncertainties, , Indicates the control gain term. ; S22. Construct a sliding mode surface based on a standard nonlinear heterogeneous multi-agent system, denoted as: (4) In the formula: J The first in the root leader formation J A root leader, Here is the diagonal coefficient matrix of the sliding surface. and The error information of the position and derivative of the virtual boundary function of the root leader is represented as follows: (5) Will and Converted to matrix form, it can be represented as: (6) In the formula: and These are the virtual boundary function of the restricted region and its first-order time derivative, respectively. , , Indicates the Kronecker product. Adjacency matrix The Middle J Line number j Column elements, It is a virtual Laplace matrix; S23. Design a bimodal artificial potential field function, including a boundary escape avoidance potential function and an obstacle collision avoidance potential function: Boundary escape potential function: (7) In the formula: Time-related terms for achieving smooth obstacle avoidance in multi-agent formations. ,definition , and These represent the potential energy information at the upper and lower boundaries, respectively. , The Euclidean distance between the vertical coordinates of the upper and lower boundaries of the restricted region. Let be the perpendicular distance from the virtual boundary function of the restricted region to the center of the restricted region. , The width of the defined safety boundary, The Euclidean distance between the root leader and the center coordinates of the obstacle. The distance between the root leader and the center line of the restricted area. ; The collision avoidance potential functions of obstacles and root leader, leader, and followers: (8) In the formula: , This represents the Euclidean distance between the root leader and obstacles, leaders, or followers. , For the first The coordinates of the center of each obstacle , and They represent the first An obstacle x and y Axis coordinate information, For the first The location coordinates of a leader For the first The position coordinates of each follower , , and These represent the minimum and maximum safe distances used to ensure that a collision does not occur, respectively. For time-related items in the design, , and This indicates the positive scalar that needs to be designed. Indicates the root leader is in K The time spent in the potential field; This represents distance information between the multi-agent formation and surrounding obstacles, as well as the nearest low-level agent. when At that time, a repulsive force is generated pointing towards the interior of the restricted area. The net repulsive force acting on the root leader is: (9) In the formula: It is the number of obstacles. Represents potential field exist gradient of direction, Represents potential field exist Gradient of direction; It is represented as an adjustable positive scalar.

[0007] Furthermore, the specific steps for constructing a data-driven neural network for online estimation and real-time compensation of uncertainties in nonlinear heterogeneous multi-agent systems include: Design a real-time changing queue To store historical data The input of the data-driven neural network comes from arrive Discrete data elements; A data-driven neural network is constructed based on a historical data queue. The expression of the data-driven neural network is: (10) In the formula: For ideal weights, , To estimate the error, satisfy the following conditions: , It is a bounded constant; It is an activation function, and:

[0008] (11) In the formula: The first data-driven neural network One input, It is a positive integer. , The number of neurons in a data-driven neural network. and These are the first in the data-driven neural network. The center and width of each neuron; The form is , For the first A set of historical data stored in a continuous time series, the length of which satisfies , The queue length is time-varying. For the runtime of a nonlinear heterogeneous multi-agent system; The data-driven neural network estimates the uncertainty of each agent model in the following form: (12) In the formula: To estimate the weight vector.

[0009] Furthermore, the adaptive robust controller for generating the obstacle avoidance safe motion trajectory of the root leader, based on a bimodal artificial potential field function and a data-driven neural network, is expressed as follows: (13) In the formula: Indicates the number of rows. unit column vector, , and These are the exponent values ​​of the predefined time exponent terms, and they satisfy... , The predefined convergence time is set. This represents the activation function used to fit uncertain data-driven neural networks. This represents the weight estimate of the adaptive robust controller. This represents the gain estimate of the adaptive robust controller. , ; Describes a positive definite parametric diagonal matrix. , This represents a column vector whose elements are all positive scalars. ; Design the weight estimates for the adaptive robust controller respectively and gain estimate The adaptive update law is: (14) In the formula: For the design of the positive parameter vector, , This is an estimate of the gain of the adaptive robust controller. , The expression form is ,in This indicates the root leader's ability to detect the virtual upper and lower boundaries of the restricted region; For terms related to data-driven neural networks, For the first J The activation function for each state. For the first The root leader neural network's historical input data is stored in a continuous time series. For the design of the positive definite parameter diagonal matrix, yes Historical data.

[0010] Furthermore, the specific steps for designing an adaptive formation scaling mechanism include: In a two-dimensional plane, the first L The expected trajectory vector of a leader is defined as follows: , and The root leader is in x and y The desired trajectory vector formed along the axial direction; definition For the first J The planar coordinate vectors of the root leaders, ,in, and The first J Individual leaders x and y The adaptive formation scaling mechanism for the leader formation, based on the coordinates along the axis, takes the following form: (15) In the formula: The first L A leader in x and y Coordinates along the axis and They represent the first L The predefined formation information of each leader relative to the root leader and the corresponding time-varying offset function. , Indicates the first L The non-zero gain of the leader, They represent the first L The initial configuration of each leader corresponds to x and y Coordinate information along the axis. This indicates the maximum width of the formation in the vertical direction of the preset formation. The minimum width required for the formation to operate safely within a confined area. Represented as the root leader and the first The Euclidean distance of each obstacle ,in, The form is: (16) In the formula: It is based on design parameters Variables and parameters that are updated in real time The range of values ​​is , This represents the relative distance between the root leader and the current boundary. Furthermore, the predefined temporal affine observer for followers, constructed based on an adaptive formation scaling mechanism, is expressed as: (17) In the formula: and They are followers and The estimated value, Indicates the number of rows. unit column vector, and They represent the estimated first and second halves of the series. f The position and speed information of each follower. and These represent the position and velocity observation errors, respectively, and their expressions are as follows: (18) In the formula: Let be the in-degree matrix, denoted as the th The communication between a follower and a leader.

[0011] Furthermore, a unified obstacle function is designed to handle constrained states, namely velocity and position, in nonlinear heterogeneous multi-agent systems. The specific steps for constructing a virtual control law based on this unified obstacle function to handle tracking errors include: S41. To achieve state constraints within a confined region, a unified obstacle function is designed to transform the constrained state. The designed unified obstacle function is expressed as follows: (19) In the formula: For the positive scalar parameters that need to be designed, Representing the Status information of a leader or follower lf For the total number of leaders and followers, when Time indicates pose information. Time indicates speed information. and Let represent the upper and lower boundaries of the constraint state, respectively, and satisfy . ; right Differentiation yields: (20) In the formula: , The second-order nonlinear intelligent agent system described in S1 is transformed into the following form: (twenty one) In the formula: , and , and They represent the first I The constrained and actual expected trajectory of an intelligent agent, where, The expression is: (twenty two) In the formula: Indicates the first The constrained state of an intelligent agent; Using the transformed second-order nonlinear agent system, the following error transformation formula is constructed: (twenty three) In the formula: For the virtual control law to be designed, This represents the state of the transformed second-order nonlinear intelligent agent system. , and These represent the transformed position and velocity errors, respectively. right Taking the first differential, we get: (twenty four) In the formula: , This represents an uncertain structure approximated using a data-driven neural network. (25) In the formula: Let the expected weight variables be ideal and have an upper bound, satisfying , , This represents the activation function. As input to the data-driven neural network, , The estimation error is the data-driven neural network approximation, and ; S42. Construct a virtual control law based on the error transformation formula, the expression of which is: (26) In the formula: For the design parameters of the virtual control law, This represents the estimated data that drives the neural network weights; in, The adaptive law is: (27) In the formula: and The design of the first I Gain parameter for a leader or follower For terms related to data-driven neural networks, the expression is: (28).

[0012] Furthermore, the specific steps for designing a neural network estimator to estimate the output of a data-driven neural network to compensate for uncertainties in a nonlinear heterogeneous multi-agent system include: Design a neural network estimator to estimate the output of a data-driven neural network. The expression for the neural network estimator is: (29) In the formula: To estimate the error, , It is a positive definite matrix.

[0013] Furthermore, in S5, the expression for the leader and follower controllers designed according to the virtual control law is as follows: (30) In the formula: and These are the estimated weights of the data-driven neural network and the estimated gains of the leader and follower controllers, respectively. Build and The adaptive law is expressed as: (31) In the formula: , , as well as For the parameters that need to be designed, For terms related to data-driven neural networks.

[0014] Beneficial Effects: This invention divides several agents into a root leader, leaders, and followers, and establishes a nonlinear heterogeneous multi-agent system with second-order nonlinear dynamics, optimizing system resource allocation and reducing dependence on high-cost hardware. The nonlinear heterogeneous multi-agent system can actively avoid obstacles and prevent escape from the operational area by utilizing the root leader's real-time environmental perception and bimodal artificial potential field function; the leader dynamically adjusts its formation to adapt to complex terrain based on an adaptive formation scaling mechanism; the pose state of all followers is quickly and accurately estimated through a predefined time-state observer, ensuring state convergence within a user-defined time; combining data-driven neural network online approximation and compensation for system uncertainties and heterogeneous agent characteristics, and using a unified obstacle function to strictly constrain the full-state trajectories of all agents, navigation safety is ensured; this invention integrates environmental perception, trajectory planning, state observation, and adaptive robust tracking control to form a collaborative control system with autonomous obstacle avoidance, dynamic reconstruction, and strong anti-disturbance capabilities, achieving safe, efficient, and robust collaborative control of the formation in complex environments, significantly improving the safety and task execution efficiency of heterogeneous multi-agent formations in constrained and unknown environments. Attached Figure Description

[0015] To more clearly illustrate the technical solutions in the embodiments of the present 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 the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0016] Figure 1 This is a flowchart of a data-based predefined time heterogeneous multi-agent formation collision avoidance method according to the present invention; Figure 2 This is a schematic diagram illustrating the unmanned vessel navigation-following formation tracking control principle in an embodiment of the present invention; Figure 3 This is a flowchart of the control design method for a multi-underwater robot system in an embodiment of the present invention; Figure 4 This is a schematic diagram of the topology of the control design method for a multi-underwater robot system in an embodiment of the present invention; Figure 5 This is a two-dimensional trajectory diagram of the control design method for a multi-underwater robot system in an embodiment of the present invention; Figure 6This is a schematic diagram of the constraints in the X direction of the control design method for a multi-underwater robot system in an embodiment of the present invention; Figure 7 This is a comparison diagram of the affine transformation error of the control design method for the multi-underwater robot system in this embodiment of the invention; Figure 8 This is a comparison diagram of leader formation affine errors in the control design method for a multi-underwater robot system in this embodiment of the invention. Figure 9 This is a schematic diagram of the velocity trajectories of the leader and follower underwater robot formations under constraints in the multi-underwater robot system control design method of this invention. Figure 10 This is a schematic diagram illustrating the control inputs for assembling all levels of underwater robots in the multi-underwater robot system control design method of this invention. Figure 11 This is a schematic diagram showing the estimated control gain and error of the multi-underwater robot system control design method in an embodiment of the present invention; Figure 12 This is a schematic diagram comparing the obstacle avoidance performance of the potential function in the control design method of the multi-underwater robot system in an embodiment of the present invention. Detailed Implementation

[0017] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0018] This embodiment provides a data-based, predefined temporal heterogeneous multi-agent formation collision avoidance method, such as... Figure 1 and Figure 2 As shown, the specific steps include: S1. Divide several agents into root leader, leader and follower according to the set rules, and establish a nonlinear heterogeneous multi-agent system with second-order nonlinear dynamic characteristics; at the same time, establish a directed graph communication topology of the nonlinear heterogeneous multi-agent system. In a specific embodiment, in S1, dividing several agents into root leader, leader, and followers according to a set rule includes: Based on the differences in the tracking capabilities of the agents, all agents are divided into high-level agents and low-level agents. The high-level agents are designated as root leaders, which have the ability to perceive the boundaries of the restricted area and obstacles. The low-level agents are designated as leaders and followers. The established expression for the nonlinear heterogeneous multi-agent system is as follows: (1) In the formula: and It is a non-zero gain term. and For unknown parameter variables, and For nonlinear function vectors, and They represent the first j The control inputs and outputs of an intelligent agent Indicates the first j The position / velocity vector of an agent , Indicates the first j The position vectors of each agent. Indicates the first j The velocity vector of each agent. and This indicates modeling uncertainty; Furthermore, the nonlinear heterogeneous multi-agent system satisfies the following full-state dynamic constraints: (2) In the formula: and These represent the time-varying upper and lower constraint boundaries of the state of a nonlinear heterogeneous multi-agent system, respectively. ; , as well as These represent the state information of the root leader, leader, and followers, respectively.

[0019] In a specific embodiment, the specific steps for establishing the directed graph communication topology of a nonlinear heterogeneous multi-agent system include: Since the entire multi-agent formation communicates and exchanges data with each other through a communication topology, a directed graph can be used. To describe a group of entities within the constraint boundary, consisting of the root leader, leaders, and followers, with... Communication networks for individual agent formations For a set of nodes, , For edge set, These represent the number of the root leader, leaders, and followers, respectively. N The number of nodes; It is an adjacency matrix and is a non-singular matrix. ; Assuming the communication topology under consideration is fixed, when the... The first agent and the second When there is a communication connection between intelligent agents ,otherwise, Let the in-degree matrix of each agent in the directed graph be defined as follows: When the first i The leader has a direction towards the first j The root leader or the first i The followers have a direction towards the first j When a leader establishes a communication connection, If the communication direction is opposite, then If there is no communication, then The stress matrix characterizes the information interaction relationships between agents. The stress matrix is ​​expressed as: (3) In the formula: , , , and These represent the communication relationships between root leaders, between root leaders and leaders, between leaders and followers, and among followers, respectively. , , , , ; and It is a non-negative matrix and the sum of the elements in each row is 1.

[0020] S2. The root leader is configured to collect sensing data in real time through sensors, and design a bimodal artificial potential field function based on the sensing data and the nonlinear heterogeneous multi-agent system to perform dynamic obstacle avoidance and prevent regional escape; the sensing data includes information on the boundary of the restricted area and the spatial distribution of obstacles; Construct a data-driven neural network for online estimation and real-time compensation of uncertainties in nonlinear heterogeneous multi-agent systems; An adaptive robust controller for generating obstacle avoidance safe motion trajectories for the root leader is established based on a dual-modal artificial potential field function and a data-driven neural network. In a specific embodiment, S2, the specific steps for designing the dual-modal artificial potential field function based on the perceived data and the nonlinear heterogeneous multi-agent system include: S21. Definition For the first The position vectors of each agent. For the first The velocity vector of each agent. , Then, the nonlinear heterogeneous multi-agent system is converted into a standard nonlinear heterogeneous multi-agent system, expressed as: (4) In the formula: To concentrate uncertainties, , Indicates the control gain term. .

[0021] S22. Construct a sliding mode surface based on a standard nonlinear heterogeneous multi-agent system, denoted as: (5) In the formula: J The first in the root leader formation J A root leader, Here is the diagonal coefficient matrix of the sliding surface. and The error information of the position and derivative of the virtual boundary function of the root leader is represented as follows: (6) Will and Converted to matrix form, it can be represented as: (7) In the formula: and These are the virtual boundary function of the restricted region and its first-order time derivative, respectively. , , Indicates the Kronecker product. Adjacency matrix The Middle J Line number j Column elements, It is a virtual Laplace matrix used to represent that each root leader has the ability to detect boundary distances. Each element in the array is equal to -1; S23. For example Figure 2 As shown, the red dashed line represents the security boundary, the blue solid line with a star represents the root leader's trajectory, the green solid line with a triangle represents the leader, and the orange solid line with a circle represents the follower. Represented as the first The maximum obstacle avoidance radius of each obstacle. For the first The minimum obstacle avoidance radius for each obstacle. Let be the center coordinates of the obstacle. To achieve the obstacle avoidance and collision avoidance functions, a bimodal artificial potential field function is designed, including a boundary escape avoidance potential function and an obstacle collision avoidance potential function: Boundary escape potential function: (8) In the formula: Time-related terms for achieving smooth obstacle avoidance in multi-agent formations. ,definition , and These represent the potential energy information at the upper and lower boundaries, respectively. , The Euclidean distance between the vertical coordinates of the upper and lower boundaries of the restricted region. Let be the perpendicular distance from the virtual boundary function of the restricted region to the center of the restricted region. , The width of the defined safety boundary, The Euclidean distance between the root leader and the center coordinates of the obstacle. The distance between the root leader and the center line of the restricted area. ; Specifically, when the distance satisfies the inequality At that time, the repulsive force is activated, and when the root leader is running above the center line, The intelligent agent only considers The effect, conversely, when At that time, the agent only considers The effect, that is, the repulsive force on the intelligent agent at the same time. or Its function; The collision avoidance potential functions of obstacles and root leader, leader, and followers: (9) In the formula: , This represents the Euclidean distance between the root leader and obstacles, leaders, or followers. , For the first The coordinates of the center of each obstacle , and They represent the first An obstacle x and y Axis coordinate information, For the first The location coordinates of a leader For the first The position coordinates of each follower , , and These represent the minimum and maximum safe distances, set based on the size of the intelligent agent, to ensure that no collision occurs. The time-dependent terms are designed to achieve smooth obstacle avoidance. , and This indicates the positive scalar that needs to be designed. Indicates the root leader is in K The time spent in an individual potential field (obstacle potential field or other intelligent agent potential field); This represents the distance information between the multi-agent formation and surrounding obstacles as well as the nearest low-level agent. This information is used to ensure that after the formation scales and avoids obstacles, the root leader will detect the minimum distance between all obstacles and each low-level agent in real time. When the minimum distance is detected to be greater than the safe distance, it means that the formation has entered the safe zone, and at this time the formation begins to smoothly recover to the initial configuration. when At that time, a repulsive force is generated pointing towards the interior of the restricted area. The net repulsive force acting on the root leader is: (10) In the formula: It is the number of obstacles. Represents potential field exist gradient of direction, Represents potential field exist Gradient of direction; It is represented as an adjustable positive scalar.

[0022] In a specific embodiment, the specific steps for constructing a data-driven neural network for online estimation and real-time compensation of uncertainties in a nonlinear heterogeneous multi-agent system include: To fit uncertainty using only the historical input data of a data-driven neural network, a real-time changing queue is designed. To store historical data The input of the data-driven neural network comes from arrive Discrete data elements; A data-driven neural network is constructed based on a historical data queue. The expression of the data-driven neural network is: (11) In the formula: For ideal weights, , To estimate the error, satisfy the following conditions: , It is a bounded constant; It is an activation function, and: , (12) In the formula: The first data-driven neural network One input, It is a positive integer. , The number of neurons in a data-driven neural network. and These are the first in the data-driven neural network. The center and width of each neuron; The form is , For the first A set of historical data stored in a continuous time series, the length of which satisfies , The queue length is time-varying. For the runtime of a nonlinear heterogeneous multi-agent system; The data-driven neural network estimates the uncertainty of each agent model in the following form: (13) In the formula: To estimate the weight vector.

[0023] In a specific embodiment, the adaptive robust controller for generating the obstacle avoidance safety trajectory of the root leader, based on a dual-modal artificial potential field function and a data-driven neural network, is represented as follows: (14) In the formula: Indicates the number of rows. unit column vector, , and These are the exponent values ​​of the predefined time exponent terms, and they satisfy... , The predefined convergence time is set. This represents the activation function used to fit uncertain data-driven neural networks. This represents the weight estimate of the adaptive robust controller. This represents the gain estimate of the adaptive robust controller. , ; Describes a positive definite parametric diagonal matrix. , This represents a column vector whose elements are all positive scalars. ; Among them, the weight estimates of the adaptive robust controller are designed respectively. and gain estimate The adaptive update law is: (15) In the formula: For the design of the positive parameter vector, , This is an estimate of the gain of the adaptive robust controller. , The expression form is ,in This indicates the root leader's ability to detect the virtual upper and lower boundaries of the restricted region; it should be noted that all the root leaders mentioned have the ability to detect the virtual upper and lower boundaries of the restricted region, therefore ; For terms related to data-driven neural networks, , The expression is , For the first J The activation function for each state. For the first The root leader neural network's historical input data is stored in a continuous time series. For the design of the positive definite parameter diagonal matrix, yes Historical data.

[0024] S3: Design an adaptive formation scaling mechanism for the leader to ensure that formation compression is triggered when the multi-agent formation enters a restricted area and the initial configuration is automatically restored after entering a safe area; and build a predefined time affine observer for the followers based on the adaptive formation scaling mechanism to estimate the pose state of the followers in real time and ensure that the followers complete the formation state convergence within a preset time.

[0025] In a specific embodiment, formation compression is triggered when entering a restricted area (narrow area or area with obstacles), and the initial configuration is automatically restored after entering a safe area. To ensure that the formation can safely pass through the restricted area while maintaining its basic shape, an adaptive formation scaling mechanism is designed. When the root leader detects that the boundary is too narrow or that there is an obstacle in front, the formation scaling mechanism is triggered. When the formation moves away from the obstacle or the boundary area is not smaller than a set value, the formation is restored to its initial state. The specific steps for designing the adaptive formation scaling mechanism include: In a two-dimensional plane, the first L The expected trajectory vector of a leader is defined as follows: , and The root leader is in x and y The desired trajectory vector formed along the axial direction; definition For the first J The planar coordinate vectors of the root leaders, ,in, and The first J Individual leaders x and y The adaptive formation scaling mechanism for the leader formation, based on the coordinates along the axis, takes the following form: (16) In the formula: The first L A leader in x and y Coordinates along the axis and They represent the first L The predefined formation information of each leader relative to the root leader and the corresponding time-varying offset function. , Indicates the first L The non-zero gain of the leader, They represent the first L The initial configuration of each leader corresponds to x and y Coordinate information along the axis. This indicates the maximum width of the formation in the vertical direction of the preset formation. The minimum width required for the formation to operate safely within a confined area. Represented as the root leader and the first The Euclidean distance of each obstacle ,in, The form is: (17) In the formula: It is based on design parameters Variables and parameters that are updated in real time The range of values ​​is , This represents the relative distance between the root leader and the current boundary, satisfying the inequality before formation scaling. After formation scaling, the inequality is satisfied. , This represents the vertical safety distance between the upper safety boundary and the virtual upper boundary function of the confined region. , This represents the vertical safety distance between the lower safety boundary and the virtual lower boundary function of the confined region. . In a specific embodiment, the predefined time-affine observer for followers, constructed based on an adaptive formation scaling mechanism, is expressed as: (18) In the formula: and They are followers and The estimated value, Indicates the number of rows. unit column vector, and They represent the estimated first and second halves of the series. f The position and speed information of each follower. and These represent the position and velocity observation errors, respectively, and their expressions are as follows: (19) In the formula: Let be the in-degree matrix, denoted as the th By designing appropriate parameters, the convergence of a predefined time affine observer can be ensured by analyzing the communication between a follower and a leader.

[0026] S4: Design a unified obstacle function for handling constrained states (velocity and position) in nonlinear heterogeneous multi-agent systems, and construct a virtual control law based on the unified obstacle function to handle tracking errors; Design a neural network estimator to estimate the output of a data-driven neural network to compensate for uncertainties in nonlinear heterogeneous multi-agent systems.

[0027] In a specific embodiment, the specific steps for designing a virtual control law based on a unified obstacle function to handle the constrained state in a nonlinear heterogeneous multi-agent system include: S41. To achieve state constraints within a confined region, a unified obstacle function is designed to transform the constrained state. The designed unified obstacle function is expressed as follows: (20) In the formula: For the positive scalar parameters that need to be designed, Representing the Status information of a leader or follower lf For the total number of leaders and followers, when Time indicates pose information. Time indicates speed information. and Let represent the upper and lower boundaries of the constraint state, respectively, and satisfy . ; right Differentiation yields: (twenty one) In the formula: , The second-order nonlinear intelligent agent system described in S1 is transformed into the following form: (twenty two) In the formula: , and , and They represent the first I The constrained and actual expected trajectory of an intelligent agent, where, The expression is: (twenty three) In the formula: Indicates the first The constrained state of an intelligent agent; Using the transformed second-order nonlinear agent system, the following error transformation formula is constructed: (twenty four) In the formula: For the virtual control law to be designed, This represents the state of the transformed second-order nonlinear intelligent agent system. , and These represent the transformed position and velocity errors, respectively. right Taking the first differential, we get: (25) In the formula: , This represents an uncertain structure approximated using a data-driven neural network. (26) In the formula: Let the expected weight variables be ideal and have an upper bound, satisfying , , This represents the activation function. As input to the data-driven neural network, , The estimation error is the data-driven neural network approximation, and ; S42. Construct a virtual control law based on the error transformation formula, the expression of which is: (27) In the formula: For the design parameters of the virtual control law, This represents the estimated data that drives the neural network weights; in, The adaptive law is: (28) In the formula: and The design of the first I Gain parameter for a leader or follower For terms related to data-driven neural networks, the expression is: (29) In a specific embodiment, the specific steps for designing a neural network estimator to estimate the output of a data-driven neural network to compensate for uncertainties in a nonlinear heterogeneous multi-agent system include: Design a neural network estimator to estimate the output of a data-driven neural network. The expression for the neural network estimator is: (30) In the formula: The estimation error of the neural network estimator. , It is a positive definite matrix; right Differentiation yields: (31) In the formula: For the uncertainty term, its ideal estimation expression is: (32) in, , This represents the input to the data-driven neural network, and .

[0028] S5: Design controllers for leaders and followers based on the virtual control law.

[0029] In a specific embodiment, in S5, the expression for the leader and follower controllers designed according to the virtual control law is as follows: (33) In the formula: and These are the estimated weights of the data-driven neural network and the estimated gains of the leader and follower controllers, respectively. Build and The adaptive law is expressed as: (34) In the formula: , , as well as For the parameters that need to be designed, For terms related to data-driven neural networks, the expression is: (35) In the formula: ; This indicates an adjustable positive scalar parameter.

[0030] S6. Collision avoidance decisions are formed for heterogeneous multi-agent formations based on the adaptive robust controller, predefined time affine observer, neural network estimator, and the controllers for leaders and followers.

[0031] Example 1: The method proposed in this invention is applicable to collaborative operation scenarios of heterogeneous multi-underwater robot systems: two types of underwater robots are configured: the leader is equipped with sonar / visual sensors and is responsible for environmental reconnaissance, while the leader and followers act as formation execution units; a three-degree-of-freedom dynamic model (planar position + yaw angle) is established. The root leader controller integrates perception data to generate obstacle avoidance trajectories, the follower predefined time observer ensures state estimation in complex environments, and the formation tracking controller embeds full-state constraints to ensure safe navigation.

[0032] In this embodiment, a multi-sensor underwater robot is used as the root leader to conduct terrain exploration in a confined area. The remaining low-function underwater robots are divided into two groups: a leader and followers. All underwater robot models are selected as three-degree-of-freedom (x, y, and yaw angle) underwater robots, specifically, such as... Figure 3 As shown, consider a heterogeneous formation system consisting of a highly intelligent underwater robot as the root leader, four leaders, and four followers (a total of eight less intelligent underwater robots). Its directed communication topology is as follows: Figure 4 As shown, the highly intelligent underwater robot is marked with a five-pointed star "0", and the four leader and four follower underwater robots are marked with triangles and circles "1", "2", "3" and "4" respectively.

[0033] The expression for the second-order model of the three-degree-of-freedom dynamics model of the underwater robot is as follows: (36) In the formula: Defined as the first jThe rotation matrix of an underwater robot, where... , Representing the j The pose information of an underwater robot in a fixed Earth coordinate system. , express x , y Axial plane position coordinates, , Let yaw angle be the yaw angle of the underwater robot in a two-dimensional plane. Indicates the first j The velocity information of an underwater robot in its own coordinate system , This represents the corresponding planar velocity vector. This represents the sum of information related to Coriolis, damping, and gravity. For control input; The gain of each underwater robot controller; Design a root leader controller. Based on the adaptive robust controller design method for the root leader described in S2, the designed adaptive robust controller for the root leader model is as follows: (37) In the formula: This represents the estimated adaptive robust controller gain. To estimate the weights, based on the adaptive robust controller gain and the online adaptive weight update method, the relevant adaptive law of the root leader underwater robot is designed as follows: (38) In the formula: J Representing the J The status information of each root leader , , as well as These are the parameters that need to be designed.

[0034] Based on the S3 design, a predefined time-affine observer for the follower is expressed as follows: (39) In the formula: as well as These represent the position and velocity information observed by the predefined time affine observer, respectively. Indicates the first f A rotation matrix for underwater robot followers. as well as These represent the affine position error and the affine velocity error, respectively, and their corresponding expressions are:

[0035] (40) In the formula: the parameters provided are designed using the same method as the corresponding parameters in S3.

[0036] To design the controllers for the leader and followers, firstly, construct the virtual control laws for the underwater robot leader and followers based on S4, with the following expression: (41) In the formula: This refers to the number of leaders or followers, as indicated by the letters shown in S4. I The meaning is the same, and the design method for the other provided parameters is the same as that for the parameters described in S4. The expression for the adaptive law is: (42) In the formula: The gain parameter is to be designed; the other parameters and variables are the same as those in S4 in terms of design method and meaning.

[0037] According to S5, the controller design for the leader and follower in a heterogeneous multi-underwater robot system is as follows: (43) In the formula: For the positive parametric diagonal matrix that needs to be designed, For activation functions; and These are the estimated values ​​of the weights and the estimated value of the gain of the data-driven neural network, respectively. As described in S5, they are updated by constructing the following adaptive law, the expression of which is: (44) In the formula: the parameters and variables provided are designed in the same way as the relevant parameters in S4 and S5.

[0038] Specifically Figure 5 The demonstration showed that the root leader successfully led other low-intelligence underwater robots to achieve a predefined formation, in which CB Represented as the midpoint of the vertical virtual boundary function, the root leader underwater robot ( rootleader The actual trajectory of the underwater robot formation is represented by a blue dashed line with an asterisk in the diagram. leaders The actual trajectory of the underwater robot formation is represented by a green dashed line with a triangle in the diagram. followersThe actual trajectory of the formation is represented by an orange dashed line with circles. When approaching narrow areas, the entire formation can smoothly expand the area or obstacle. As can be seen in the enlarged view, the leader and followers achieve a pre-defined hexagonal formation. Simultaneously, the root leader guides the entire formation, thus successfully avoiding obstacles.

[0039] like Figure 6 As shown, where , and These respectively represent the results of applying a traditional fixed-time control scheme with a signed function, a traditional fixed-time control scheme without a signed function, and a predefined time control scheme designed in this embodiment, all while keeping other parameters constant. x Tracking performance in the axial direction. Simulation results show that the unified barrier function proposed in this embodiment does not have strict requirements on the positive or negative sign of the boundary function. In the comparison of leader tracking performance in the X direction, the transient performance of the unified barrier function proposed in this embodiment is better than other methods.

[0040] from Figure 7 As can be seen from the magnified view, the method proposed in this embodiment has a faster convergence speed and a smaller stability error. They represent Tracking error in three degrees of freedom, This indicates that, with other parameters remaining constant, under the traditional fixed-time control scheme using unsigned functions, the leader ( ) and followers ( Tracking error in three degrees of freedom, This indicates the leader (or leader) under the predefined time control scheme proposed in this embodiment. ) and followers ( The tracking error is shown in the figure, which illustrates the smaller overshoot and stability error of the controller presented in this embodiment.

[0041] from Figure 8 As can be seen, the observation error can converge within the preset time of 2 seconds, and compared with the other two, the predefined time affine observer has a smaller stability error. This indicates that the method proposed in this embodiment was used to obtain the data. Affine error in two degrees of freedom ( This further demonstrates that the controller proposed in this embodiment has excellent robustness.

[0042] Figure 9 and Figure 10The velocities of the leader and followers in the X and Y axes under constrained conditions are given, along with the controller inputs for all levels of the underwater robot. and These represent the virtual upper and lower boundaries in the velocity direction, respectively. This indicates that the method proposed in this embodiment is used in... Examining the velocity constraint errors across the three degrees of freedom, it's easy to see that the leader and follower controllers exhibit smoother control inputs. Aside from momentary overshoot during obstacle avoidance, both the leader and follower controllers demonstrate better transient performance. express Control inputs in three degrees of freedom. These represent the three control inputs of the root leader.

[0043] Figure 11 This demonstrates that the method proposed in this embodiment can quickly and accurately approximate the control gain, wherein... This represents the three controller gain estimates for the root leader. They represent Controller gain estimates under three degrees of freedom They represent the leaders respectively. Controller gain estimates under three degrees of freedom Indicates the leader Controller gain estimation error under three degrees of freedom; Indicates follower Controller gain estimates under three degrees of freedom Indicates follower Controller gain estimation error under three degrees of freedom. Impact on steering obstacle avoidance Figure 12 This demonstrates that the method proposed in this embodiment can ensure that the entire formation avoids obstacles. The introduction of the potential function not only enables the entire formation to avoid obstacles but also allows for smoother obstacle avoidance. This indicates that the application of the potential function proposed in this embodiment plays a crucial role in obstacle avoidance, where the vertical axis represents the distance between the leader or follower and the obstacle. and These represent the obstacle avoidance performance exhibited by the leader and the follower in this embodiment, respectively. and These represent the obstacle avoidance performance of the leader and followers under the traditional predefined time control method, respectively.

[0044] In summary, the beneficial effects of this invention include: (1) Safe autonomous obstacle avoidance and escape prevention capability: The leader can avoid dynamic obstacles in real time based on the dual-modal artificial potential field and strictly constrain the operation boundary; (2) Dynamic formation reconstruction adaptability: By triggering an adaptive formation scaling mechanism in narrow areas, smooth formation transformation is achieved, which significantly improves the passability of complex terrain; (3) Strong robust finite-time convergence: The predefined time observer only needs the leader's position information to reconstruct the follower's full state (including unmeasurable velocity) with high accuracy within a set time. The data-driven neural network online compensates for the uncertainty and heterogeneity of the system, ensuring that the tracking error strictly meets the preset transient and steady-state performance boundaries. (4) Safety assurance under full-state constraints: A unified obstacle function is used to handle the trajectory constraints of the intelligent agent, and virtual control law and adaptive gain adjustment work together to ensure navigation safety; (5) Resource optimization and cost control: Hierarchical design (only the root leader is equipped with high-end sensors) reduces hardware dependence, and predefined time mechanisms reduce communication load.

[0045] 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 or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A data-based, predefined temporal heterogeneous multi-agent formation collision avoidance method, characterized in that, The specific steps include: S1. Divide several agents into root leader, leader and follower according to the set rules, and establish a nonlinear heterogeneous multi-agent system; S2. The root leader is configured to collect sensing data in real time through sensors, and design a bimodal artificial potential field function based on the sensing data and the nonlinear heterogeneous multi-agent system to perform dynamic obstacle avoidance and prevent regional escape; the sensing data includes information on the boundary of the restricted area and the spatial distribution of obstacles; A data-driven neural network is constructed for online estimation of the uncertainties of the nonlinear heterogeneous multi-agent system and real-time compensation. An adaptive robust controller for generating the obstacle avoidance safe movement trajectory of the root leader is established based on the aforementioned dual-modal artificial potential field function and data-driven neural network. S3. Design an adaptive formation scaling mechanism for the leader, and construct a predefined time affine observer for the followers based on the adaptive formation scaling mechanism to estimate the pose state of the followers in real time and ensure that the followers complete the formation state convergence within a preset time. S4. Design a unified barrier function for handling constrained states in nonlinear heterogeneous multi-agent systems; A virtual control law for handling tracking errors is constructed based on the unified barrier function; Design a neural network estimator to estimate the output of the data-driven neural network to compensate for uncertainties in nonlinear heterogeneous multi-agent systems; S5. Design controllers for leaders and followers based on the virtual control law; S6. Collision avoidance decisions are formed for heterogeneous multi-agent formations based on the adaptive robust controller, predefined time affine observer, neural network estimator, and the controllers for leaders and followers.

2. The data-based predefined time heterogeneous multi-agent formation collision avoidance method according to claim 1, characterized in that, In S1, several agents are divided into root leader, leader, and follower groups according to the set rules, including: Based on the differences in the tracking capabilities of the agents, all agents are divided into high-level agents and low-level agents. The high-level agents are designated as root leaders, which have the ability to perceive the boundaries of the restricted area and obstacles. The low-level agents are designated as leaders and followers. The established expression for the nonlinear heterogeneous multi-agent system is as follows: (1) In the formula: and It is a non-zero gain term. and For unknown parameter variables, and For nonlinear function vectors, and They represent the first j The control inputs and outputs of an intelligent agent Indicates the first j The position vectors of each agent. Indicates the first j The velocity vector of each agent. and This indicates modeling uncertainty; Furthermore, the nonlinear heterogeneous multi-agent system satisfies the following full-state dynamic constraints: (2) In the formula: and These represent the time-varying upper and lower constraint boundaries of the state of a nonlinear heterogeneous multi-agent system, respectively. ; , as well as These represent the state information of the root leader, leader, and followers, respectively.

3. The data-based predefined time heterogeneous multi-agent formation collision avoidance method according to claim 2, characterized in that, In S2, the specific steps for designing the dual-modal artificial potential field function based on the perceived data and the nonlinear heterogeneous multi-agent system include: S21. Definition For the first The position vectors of each agent. For the first The velocity vector of each agent. , Then, the nonlinear heterogeneous multi-agent system is converted into a standard nonlinear heterogeneous multi-agent system, expressed as: (3) In the formula: To concentrate uncertainties, , Indicates the control gain term. ; S22. Construct a sliding mode surface based on a standard nonlinear heterogeneous multi-agent system, denoted as: (4) In the formula: J The first in the root leader formation J A root leader, Here is the diagonal coefficient matrix of the sliding surface. and The error information of the position and derivative of the virtual boundary function of the root leader is represented as follows: (5) Will and Converted to matrix form, it can be represented as: (6) In the formula: and These are the virtual boundary function of the restricted region and its first-order time derivative, respectively. , , Indicates the Kronecker product. Adjacency matrix The Middle J Line number j Column elements, It is a virtual Laplace matrix; S23. Design a bimodal artificial potential field function, including a boundary escape avoidance potential function and an obstacle collision avoidance potential function: Boundary escape potential function: (7) In the formula: For time-related terms in achieving smooth obstacle avoidance in multi-agent formations, ,definition , and These represent the potential energy information at the upper and lower boundaries, respectively. , The Euclidean distance between the vertical coordinates of the upper and lower boundaries of the restricted region. Let be the perpendicular distance from the virtual boundary function of the restricted region to the center of the restricted region. , The width of the defined safety boundary, The Euclidean distance between the root leader and the center coordinates of the obstacle. The distance between the root leader and the center line of the restricted area. ; The collision avoidance potential functions of obstacles and root leader, leader, and followers: (8) In the formula: , This represents the Euclidean distance between the root leader and obstacles, leaders, or followers. , For the first The coordinates of the center of each obstacle , and They represent the first An obstacle x and y Axis coordinate information, For the first The location coordinates of a leader For the first The position coordinates of each follower , , and These represent the minimum and maximum safe distances used to ensure that a collision does not occur, respectively. For time-related items in the design, , and This indicates the positive scalar that needs to be designed. Indicates the root leader is in K The time spent in the potential field; This represents distance information between the multi-agent formation and surrounding obstacles, as well as the nearest low-level agent. when At that time, a repulsive force is generated pointing towards the interior of the restricted area. The net repulsive force acting on the root leader is: (9) In the formula: It is the number of obstacles. Represents potential field exist gradient of direction, Represents potential field exist Gradient of direction; It is represented as an adjustable positive scalar.

4. The data-based predefined time heterogeneous multi-agent formation collision avoidance method according to claim 3, characterized in that, The specific steps for constructing a data-driven neural network for online estimation and real-time compensation of uncertainties in nonlinear heterogeneous multi-agent systems include: Design a real-time changing queue To store historical data The input of the data-driven neural network comes from arrive Discrete data elements; A data-driven neural network is constructed based on a historical data queue. The expression of the data-driven neural network is: (10) In the formula: For ideal weights, , To estimate the error, satisfy the following conditions: , It is a bounded constant; It is an activation function, and: (11) In the formula: The first data-driven neural network One input, It is a positive integer. , The number of neurons in a data-driven neural network. and These are the first in the data-driven neural network. The center and width of each neuron; The form is , For the first A set of historical data stored in a continuous time series, the length of which satisfies , The queue length is time-varying. For the runtime of a nonlinear heterogeneous multi-agent system; The data-driven neural network estimates the uncertainty of each agent model in the following form: (12) In the formula: To estimate the weight vector.

5. The data-based predefined time heterogeneous multi-agent formation collision avoidance method according to claim 4, characterized in that, An adaptive robust controller for generating the obstacle avoidance safety trajectory of the root leader, based on a dual-modal artificial potential field function and a data-driven neural network, is represented as follows: (13) In the formula: Indicates the number of rows. unit column vector, , and These are the exponent values ​​of the predefined time exponent terms, and they satisfy... , The predefined convergence time is set. This represents the activation function used to fit uncertain data-driven neural networks. This represents the weight estimate of the adaptive robust controller. This represents the gain estimate of the adaptive robust controller. , ; Describes a positive definite parametric diagonal matrix. , This represents a column vector whose elements are all positive scalars. ; Design the weight estimates for the adaptive robust controller respectively and gain estimate The adaptive update law is: (14) In the formula: For the design of the positive parameter vector, , This is an estimate of the gain of the adaptive robust controller. , The expression form is ,in This indicates the root leader's ability to detect the virtual upper and lower boundaries of the restricted region; For terms related to data-driven neural networks, For the first J The activation function for each state. For the first The root leader neural network's historical input data is stored in a continuous time series. For the design of the positive definite parameter diagonal matrix, yes Historical data.

6. The data-based predefined time heterogeneous multi-agent formation collision avoidance method according to claim 5, characterized in that, The specific steps for designing an adaptive formation scaling mechanism include: In a two-dimensional plane, the first L The expected trajectory vector of a leader is defined as follows: , and The root leader is in x and y The desired trajectory vector formed along the axial direction; definition For the first J The planar coordinate vectors of the root leaders, ,in, and The first J Individual leaders x and y The adaptive formation scaling mechanism for the leader formation, based on the coordinates along the axis, takes the following form: (15) In the formula: The first L A leader in x and y Coordinates along the axis and They represent the first L The predefined formation information of each leader relative to the root leader and the corresponding time-varying offset function. , Indicates the first L The non-zero gain of the leader, They represent the first L The initial configuration of each leader corresponds to x and y Coordinate information along the axis. This indicates the maximum width of the formation in the vertical direction of the preset formation. The minimum width required for the formation to operate safely within a confined area. Represented as the root leader and the first The Euclidean distance of each obstacle ,in, The form is: (16) In the formula: It is based on design parameters Variables and parameters that are updated in real time The range of values ​​is , This represents the relative distance between the root leader and the current boundary.

7. The data-based predefined time heterogeneous multi-agent formation collision avoidance method according to claim 6, characterized in that, A predefined time-based affine observer for followers, built based on an adaptive formation scaling mechanism, is expressed as follows: (17) In the formula: and They are followers and The estimated value, Indicates the number of rows. unit column vector, and They represent the estimated first and second halves of the series. f The position and speed information of each follower. and These represent the position and velocity observation errors, respectively, and their expressions are as follows: (18) In the formula: Let be the in-degree matrix, denoted as the th The communication between a follower and a leader.

8. The data-based predefined temporal heterogeneous multi-agent formation collision avoidance method according to claim 7, characterized in that, The design of a unified obstacle function for handling constrained states, i.e., velocity and position, in nonlinear heterogeneous multi-agent systems, and the specific steps for constructing a virtual control law to handle tracking errors based on the unified obstacle function include: S41. To achieve state constraints within a confined region, a unified obstacle function is designed to transform the constrained state. The designed unified obstacle function is expressed as follows: (19) In the formula: For the positive scalar parameters that need to be designed, Representing the Status information of a leader or follower lf For the total number of leaders and followers, when Time indicates pose information. Time indicates speed information. and Let represent the upper and lower boundaries of the constraint state, respectively, and satisfy . ; right Differentiation yields: (20) In the formula: , The second-order nonlinear intelligent agent system described in S1 is transformed into the following form: (21) In the formula: , and , and They represent the first I The constrained and actual expected trajectory of an intelligent agent, where, The expression is: (22) In the formula: Indicates the first The constrained state of an intelligent agent; Using the transformed second-order nonlinear agent system, the following error transformation formula is constructed: (23) In the formula: For the virtual control law to be designed, This represents the state of the transformed second-order nonlinear intelligent agent system. , and These represent the transformed position and velocity errors, respectively. right Finding the first differential yields: (24) In the formula: , This represents an uncertain structure approximated using a data-driven neural network. (25) In the formula: Let the expected weight variables be ideal and have an upper bound, satisfying , , This represents the activation function. As input to the data-driven neural network, , The estimation error is the data-driven neural network approximation, and ; S42. Construct a virtual control law based on the error transformation formula, the expression of which is: (26) In the formula: For the design parameters of the virtual control law, This represents the estimated data that drives the neural network weights; in, The adaptive law is: (27) In the formula: and The design of the first I Gain parameter for a leader or follower For terms related to data-driven neural networks, the expression is: (28)。 9. The data-based predefined temporal heterogeneous multi-agent formation collision avoidance method according to claim 8, characterized in that, The specific steps involved in designing a neural network estimator to estimate the output of a data-driven neural network to compensate for uncertainties in a nonlinear heterogeneous multi-agent system include: Design a neural network estimator to estimate the output of a data-driven neural network. The expression for the neural network estimator is: (29) In the formula: To estimate the error, , It is a positive definite matrix.

10. The data-based predefined temporal heterogeneous multi-agent formation collision avoidance method according to claim 9, characterized in that, In S5, the expressions for the leader and follower controllers designed according to the virtual control law are as follows: (30) In the formula: and These are the estimated weights of the data-driven neural network and the estimated gains of the leader and follower controllers, respectively. Build and The adaptive law is expressed as: (31) In the formula: , , as well as For the parameters that need to be designed, For terms related to data-driven neural networks.

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