A multi-robot system scheduled time tracking control method based on double-layer communication

Abstract

The application relates to the technical field of multi-agent system cooperative control, in particular to a multi-robot system predetermined time tracking control method based on a double-layer communication, which comprises the following steps: a double-layer communication framework containing a leader planning layer and a follower execution layer is constructed; a distributed virtual controller and an actual controller are designed for the leader planning layer, a parameter self-adaptive updating mechanism is constructed, a leader layer predetermined time consistency control scheme is formed; a distributed virtual controller and an actual controller are designed for the follower execution layer, a parameter self-adaptive updating mechanism is constructed, a follower layer cooperative tracking control scheme is formed; the stability of a double-layer closed-loop system is analyzed based on Lyapunov stability theory, a time sequence cooperation mechanism is constructed, and each agent is driven to realize stable and consistent tracking within a predetermined time. The application effectively reduces the system communication complexity in a multi-leader scene, overcomes model parameter uncertainty, and realizes the convergence of global tracking error within a preset time.

Description

Technical Field

[0001] This invention relates to the field of cooperative control technology for multi-agent systems, specifically a predetermined time tracking control method for multi-robot systems based on two-layer communication. Background Technology

[0002] Cooperative control of multi-agent systems has become a research focus in fields such as intelligent manufacturing, low-altitude economy, and unmanned systems. As a typical representative of multi-agent systems in the physical world, multi-robot systems have received widespread attention, and their ability to cooperate in complex environments directly affects the efficiency and safety of practical engineering tasks.

[0003] To meet the demands of rapid response in multi-agent systems in practical engineering, predetermined time control theory exhibits significant technical advantages. Compared to finite-time control, where convergence time depends on the initial state, and fixed-time control, whose upper bound estimation is conservative and difficult to adjust, predetermined time control allows for the direct pre-setting of the system's convergence time upper bound, independent of the initial state, based on task requirements. This greatly enhances the flexibility and reliability of practical engineering applications. However, existing predetermined time control collaborative schemes are mainly limited to single-leader or leaderless scenarios. In practical engineering, multi-robot systems often face multi-leader scenarios, such as multi-robot cluster collaborative operations. Complex dynamic coupling exists between multiple reference signals, and the communication topology between robots is complex and heterogeneous, posing significant challenges to the design of distributed consensus controllers.

[0004] Furthermore, existing communication architectures in multi-leader scenarios often employ global interconnection, requiring each node to interact with numerous other nodes, resulting in heavy communication burdens and poor scalability. Simultaneously, robot systems inherently suffer from model parameter uncertainties and external environmental interference, making it difficult for traditional control methods to simultaneously guarantee convergence speed and robustness. Therefore, designing a multi-robot cooperative control method that effectively reduces communication complexity, overcomes model uncertainties, and achieves convergence within a predetermined timeframe has become a pressing technical challenge in this field. Summary of the Invention

[0005] The purpose of this invention is to provide a predetermined time tracking control method for a multi-robot system based on two-layer communication, so as to solve the problems mentioned in the background art.

[0006] To achieve the above objectives, the present invention provides the following technical solution.

[0007] A pre-time tracking control method for a multi-robot system based on two-layer communication includes the following steps: S1: Constructing a two-layer communication framework that includes a leader planning layer and a follower execution layer.

[0008] S2: For the leader planning layer, a leader distributed virtual controller is designed based on the relative position and state information between nodes and the predetermined time control theory.

[0009] S3: Combine the aforementioned leader distributed virtual controller to design the leader actual controller, and construct a parameter adaptive update mechanism based on power terms to form a leader layer predetermined time consistency control scheme.

[0010] S4: For the follower execution layer, combine the adjacency interaction information within the follower layer with the cross-layer connection information to design a follower distributed virtual controller.

[0011] S5: Combine the aforementioned follower distributed virtual controller to design the follower actual controller and construct a corresponding parameter adaptive update mechanism to form a follower-layer collaborative tracking control scheme.

[0012] S6: Based on Lyapunov stability theory, the practical predetermined time stability of a two-layer closed-loop system is analyzed. A timing coordination mechanism is constructed with the constraint that the predetermined convergence time of the leader layer is less than that of the predetermined convergence time of the follower layer. The corresponding intelligent agent is driven according to the control torque command output by the actual controller of each layer, so as to realize the practical predetermined time stability and consistency tracking of the two-layer multi-agent system.

[0013] As a further aspect of the present invention, step S1 specifically includes: S11: Introducing the concept of hierarchical control to construct a two-layer communication framework that includes a leader planning layer and a follower execution layer.

[0014] S12: Use a directed graph to describe the multi-leader communication network structure, construct a leader planning layer communication topology containing at least one directed spanning tree, and define the corresponding Laplace matrix.

[0015] S13: Use a directed graph to describe the multi-follower communication network structure, construct the follower execution layer communication topology, and define its Laplace matrix.

[0016] S14: The planning layer and the execution layer adopt a top-down one-way communication and define an inter-layer connection matrix. Under the two-layer communication framework, only some followers in the execution layer need to directly receive the leader's instructions, while the remaining followers achieve indirect tracking through the collaborative interaction within the execution layer.

[0017] S15: For any first... in the two-layer communication framework For each intelligent agent, establish its system dynamics equations: In the formula, , , These are joint position, velocity, and acceleration, respectively. It is a symmetric positive definite inertial matrix; The matrix represents the Coriolis force and the centrifugal force. It is the gravity vector; For a bounded external unknown disturbance, it satisfies ,in ; To control the input torque.

[0018] S16: Introduce state variables and convert the dynamic equations into state-space form to obtain the state-space dynamic model of each agent.

[0019] As a further aspect of the present invention: step S2 specifically includes: S21: establishing a mathematical evaluation criterion for cooperative tracking targets, that is, for a certain dynamic system and any initial state If a pre-set time constant exists and boundary constants This makes the system state Satisfy: When hour, If the condition is always true, then the system is determined to be practically stable over a predetermined time.

[0020] S22: Based on the communication topology information within the leader planning layer, define the leader's position consistency error and design the leader's virtual control law.

[0021] As a further aspect of the present invention: step S3 specifically includes: introducing the leader's velocity tracking error, differentiating it and using a radial basis function neural network to approximate the unknown nonlinear dynamics of the system online, designing the leader's actual control torque in combination with predetermined time control theory, and constructing a parameter adaptive update law based on power terms.

[0022] As a further aspect of the present invention, step S4 specifically includes: defining the positional collaborative tracking error of the follower based on the communication topology information within the follower execution layer and the inter-layer communication information with the leader planning layer, and designing the follower distributed virtual control law.

[0023] As a further aspect of the present invention: step S5 specifically includes: introducing the velocity tracking error of the follower, differentiating it and using a radial basis function neural network to approximate the unknown nonlinear dynamics of the system online, designing the actual control torque of the follower in combination with the predetermined time control theory, and constructing a parameter adaptive update law based on the power term.

[0024] As a further aspect of the present invention: step S6 specifically includes: S61: by constructing a leader layer Lyapunov function containing an inertia term, it is proven that the leader layer achieves practical predetermined time stability.

[0025] S62: By constructing a follower layer Lyapunov function containing an inertia term, we prove that the follower layer achieves practical time-stability.

[0026] S63: Define the position tracking error of the follower relative to its corresponding leader, and prove that the global tracking error converges within a predetermined time based on matrix invertibility; set the time-series constraints of the two-layer communication framework so that the leader layer achieves consistency first, thereby ensuring that the follower layer achieves tracking stability.

[0027] Compared with the prior art, the beneficial effects of the present invention are: 1. Reduced communication complexity: The hierarchical architecture of upper-layer multi-leader planning reference trajectory and lower-layer follower collaborative tracking effectively solves the communication problems caused by multiple reference signal coupling and complex topology, and significantly improves the collaborative efficiency of large-scale heterogeneous systems.

[0028] 2. Absolute time performance guarantee: Unlike traditional asymptotic stability control, this method ensures that the global tracking error of the system converges to the neighborhood of the equilibrium point within a preset time, and the upper limit of the convergence time is completely independent of the initial state of the system.

[0029] 3. Strong robustness and anti-interference capability: To address the nonlinear characteristics of the physical system, an RBF neural network is used for online approximation, and a power-law driving term is introduced to effectively compensate for the effects of external environmental interference and the uncertainty of its own parameters. Attached Figure Description

[0030] Figure 1 This is a flowchart of the present invention.

[0031] Figure 2 This is a schematic diagram of the two-layer collaborative framework of the present invention.

[0032] Figure 3 This is a communication topology diagram of the leader layer and the follower layer in an embodiment of the present invention.

[0033] Figure 4 This is the hierarchical cooperative error convergence curve of the two-layer multi-agent system in an embodiment of the present invention.

[0034] Figure 5 The actual physical tracking error curves of each agent in the follower layer in this embodiment of the invention are shown. Detailed Implementation

[0035] The technical solution of this application will be further described in detail below with reference to specific embodiments.

[0036] The embodiments of this application are described in detail below. Examples of these embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain this application, and should not be construed as limiting this application.

[0037] like Figure 1 As shown, this invention proposes a two-layer communication method for multi-robot predetermined time tracking control, comprising the following steps: S1: For robot systems in multi-leader scenarios, construct a system including... Figure 2 The two-layer communication framework of leader planning layer and follower execution layer is shown; step S1 is as follows: S11: For robot systems in multi-leader scenarios, the hierarchical control concept is introduced to construct a two-layer communication framework including leader planning layer and follower execution layer, and the large-scale communication complexity of the system is reduced by decomposing tasks.

[0038] S12: Use a directed graph to describe the multi-leader communication network structure, and construct a leader planning layer communication topology containing at least one directed spanning tree. And define the corresponding Laplace matrix. ,in Let be the in-degree matrix. It is an adjacency matrix.

[0039] S13: Use a directed graph to describe the multi-follower communication network structure and construct the follower execution layer communication topology. And define its Laplace matrix. .

[0040] S14: The planning layer and the execution layer use top-down unidirectional communication, defining an inter-layer connection matrix. If followers in the execution layer can directly obtain information about the corresponding leader in the planning layer, then the weight... ,otherwise In the aforementioned two-layer communication framework, only some followers in the execution layer need to directly receive instructions from the leader, while the remaining followers indirectly track the leader through collaborative interactions within the execution layer. This results in the global construction of an extended communication topology containing a directed spanning tree with the leader layer as the root node.

[0041] S15: For any first... in the two-layer communication framework For each intelligent agent, establish its system dynamics equations: (1); where, , , These are joint position, velocity, and acceleration, respectively. It is a symmetric positive definite inertial matrix; The matrix represents the Coriolis force and the centrifugal force. It is the gravity vector; For a bounded external unknown disturbance, it satisfies ,in ; To control the input torque.

[0042] S16: Introducing State Variables and The dynamic equations are then converted into state-space form to obtain the state-space dynamic models of each agent: (2).

[0043] S2: For the leader planning layer, based on the relative position and state information between nodes and the predetermined time control theory, a leader distributed virtual controller is designed. Step S2 is as follows: S21: First, establish the mathematical evaluation criteria for the collaborative tracking target of this invention: for a certain dynamic system and any initial state If there exists a pre-defined time constant and boundary constants This makes the system state Satisfy: When hour, If the condition is always true, then the system is considered to be stable over a predetermined time. Under this definition, the upper bound of the system's convergence time is... It must be a parameter that can be freely set by the user and is completely independent of the system's initial state.

[0044] To satisfy the above practical requirement of stable convergence at predetermined time, a relevant stability lemma is introduced: Consider system (1), if there exists a continuously positive definite Lyapunov function satisfy: (3); among which, , , It is a positive number, and Then system (1) is stable for practical scheduled time.

[0045] Introducing constant parameters The system convergence time satisfies: . The set time. Furthermore, the system state eventually converges and remains within the following bounded region. Inside: .

[0046] S22: Based on the communication topology information within the leader planning layer, define the first... Consistency error in the position of each leader: (4); among which For the first The set of neighbor nodes of a leader. The adjacency matrix weights of the leader communication topology. and Leaders and The position and state vector.

[0047] To ensure the positional consistency error To converge within a predetermined time and provide a smooth reference trajectory for the velocity subsystem, design a leader virtual control law: (5); where is the first The in-degree of each leader node. For a vector mapping of a sign function with exponentiation, for any dimensional vector and constants The mapping is defined as follows: ; The preset power constant parameter, , , The control gain parameters to be designed are given; and unified parameters for the planning layer are introduced. The control gain parameter is set to satisfy an algebraic relationship. , , In the formula Let be the dimension of the state space of the multi-agent system.

[0048] S3: For the leader planning layer, design the actual leader controller in conjunction with the leader distributed virtual controller, and construct a parameter adaptive update mechanism based on power terms to form a leader layer predetermined time consistency control scheme; Step S3 is as follows: Introduce the first... Speed ​​tracking error of the leader: (6); Taking its derivative, combined with equation (2), we can obtain: (7).

[0049] For the unknown nonlinear dynamics of the system in the equation, it is defined as For this nonlinear function, the functional approximation property of the radial basis function neural network is used for online approximation, and the Gaussian function is selected as the radial basis function: ;in, The neural network joint input vector consists of the system state and the virtual control signal. and Let be the center vector and width of the Gaussian function, respectively; the nonlinear function is equivalently approximated as... ,in For the ideal weight matrix, For radial basis function vectors, To minimize the approximation error, and .

[0050] Define adaptive scalar parameters In the formula For the ideal weight matrix, Let be the Frobenius norm of the matrix, and let be... Let this be an estimated value of the parameter; let the upper bound of the eigenvalues ​​of the system's inertia matrix be... Using the oblique symmetry property of the dynamic model Design the leader's actual control torque by combining predefined time control theory: (8); among which As an adjustment constant, Given a radial basis function vector; simultaneously construct an adaptive parameter update law based on power terms: (9); among which For adaptive gain, , , For correction parameters, For a scalar mapping of a sign function with exponentiation, for any dimensional vector and constants The mapping is defined as Based on this, a unified gain parameter for the planning layer is introduced. The above parameters are set to satisfy the algebraic relationship. , , , , , .

[0051] S4: For the follower execution layer, combining the adjacency interaction information within the follower layer and the cross-layer connection information, design a follower distributed virtual controller; step S4 is as follows: Based on the communication topology information within the follower execution layer and the inter-layer communication information with the leader planning layer, define the first... The positional tracking error of each follower: (10); among which For the first in the execution layer The set of neighboring nodes of a follower The adjacency matrix weights of the follower communication topology. The weights of the inter-layer connectivity matrix are... and Followers and The position state vector, For the corresponding leader The position and state vector.

[0052] To counteract the effects of coupling terms in the dynamics of the follower's position error, a distributed virtual control law for the follower is designed: (11); among which To achieve comprehensive communication weight, Introducing a unified gain parameter for the execution layer The control gain parameter is set to satisfy an algebraic relationship. , , .

[0053] S5: For the follower execution layer, design the follower actual controller in conjunction with the follower distributed virtual controller, and construct a corresponding parameter adaptive update mechanism to form a follower layer collaborative tracking control scheme; Step S5 is as follows: Introduce the first Speed ​​tracking error of each follower: (12); Taking its derivative, combined with equation (2), we can obtain: (13).

[0054] For the unknown nonlinear dynamics of the system in the equation, it is defined as For this nonlinear function, the functional approximation property of the radial basis function neural network is used for online approximation, and the Gaussian function is selected as the radial basis function: ;in, The neural network joint input vector consists of the system state and the virtual control signal. and Let be the center vector and width of the Gaussian function, respectively; the nonlinear function is equivalently approximated as... ,in For the ideal weight matrix, For radial basis function vectors, To minimize the approximation error, and .

[0055] Define adaptive scalar parameters In the formula For the ideal weight matrix of the follower layer, Let Frobenius norm be the matrix norm, and let... Let this be an estimated value of the parameter; let the upper bound of the eigenvalues ​​of the system's inertia matrix be... Using the oblique symmetry property of the dynamic model The actual control torque of the follower is designed by combining the predetermined time control theory: (14); among which As an adjustment constant, Given the radial basis function vectors of the follower layer, we simultaneously construct an adaptive parameter update law based on power terms: (15); among which For follower adaptive gain, , , For the correction parameters; based on this, a unified gain parameter for the execution layer velocity subsystem is introduced. The above parameters are set to satisfy the algebraic relationship. , , , , , .

[0056] S6: Based on Lyapunov stability theory, the practical predetermined time stability of the two-layer closed-loop system is analyzed. A timing coordination mechanism is constructed with the predetermined convergence time of the leader layer being less than that of the predetermined convergence time of the follower layer as a constraint. The corresponding intelligent agent is driven according to the control torque command output by the actual controller of each layer, so as to realize the practical predetermined time stability and consistency tracking of the two-layer multi-agent system. The specific steps of S6 are as follows.

[0057] S61: Stability Analysis of Practical Pre-determined Time for the Leadership Layer: Introducing the System Inertia Matrix Design a leader layer Lyapunov function that includes an inertia term: (16).

[0058] in For parameter estimation error, i.e. .

[0059] For the Lyapunov function at position Substituting equations (4) and (5), we can deduce: (17).

[0060] Subsequently, for the leader layer velocity Lyapunov function including the inertia term: Differentiate, and consider the oblique symmetry property of the dynamic model. Eliminate inclusion From the nonlinear term, we can obtain: (18).

[0061] Further processing of the above items easily leads to the conclusion that: (19); (20); (twenty one); (22); among which .

[0062] Substituting equation (8) and equations (19)-(22) into equation (18), we get: (23); among which .

[0063] Set the predetermined convergence time constant for the leader layer. Introducing a unified gain parameter for the leader layer Easy to obtain: (24); This proves that the leader layer achieves practical scheduled time stability, and the synchronization error signal of the leader layer. , and adaptive parameter estimation error In the setting Internal consistency is eventually bounded.

[0064] S62: Practical Pre-determined Time Stability Analysis of Follower Layer: Introducing the System Inertia Matrix Design a follower layer Lyapunov function that includes an inertia term: (25); among which For parameter estimation error, i.e. .

[0065] For the Lyapunov function at position Substituting equations (10) and (11), we get: (26).

[0066] Subsequently, for the follower layer velocity Lyapunov function containing the inertial term... Differentiate, and consider the oblique symmetry property of the dynamic model. Eliminate inclusion The nonlinear term can be derived through an analysis process similar to equations (18)-(22): (27); among which , Set a predetermined convergence time constant for the follower layer. Introducing a unified gain parameter for the follower layer ,have: (28); This proves that the follower layer achieves practical time-stability stability, and the synchronization error of the follower layer is... , and adaptive parameter estimation error In the setting Internal consistency is eventually bounded.

[0067] S63: Temporal Coordination Mechanism and Global Error Convergence Analysis.

[0068] Definition of the first The position tracking error of a follower relative to its corresponding leader is: Substituting it into equation (10), we get: (29).

[0069] Define the follower tracking error vector and synchronization error vector Equation (29) can be written as: ;in For the Laplace matrix of the follower layer, This is the inter-layer connectivity matrix. .

[0070] Due to the matrix Invertible, the global tracking error norm bound satisfies: .

[0071] From steps S61 and S62, it can be seen that... and Bounded, therefore, followers can successfully track their corresponding leaders, and the global tracking error is... The convergence occurs within a predetermined time; the timing constraints of the two-layer communication framework are set as follows: This enabled the leadership to take the lead in Internal consistency is achieved and makes Prioritize convergence, thereby ensuring that the follower layer achieves the set convergence. Internal tracking stability is achieved, driving the entire system to a global upper bound. Internally implements practical consistency collaborative tracking.

[0072] To verify the effectiveness of the control method described in this invention, this embodiment constructs a system composed of... One leader and A two-layer multi-agent system consisting of several followers was simulated and verified. The communication topology is shown in the figure below. Figure 3 As shown. In this embodiment, a multi-robot system consisting of 12 heterogeneous two-degree-of-freedom (2-DOF) planar manipulators is selected as the simulation object, and its dynamic behavior is described by step (1) in S1. For the first An agent, whose state vector Represents joint angles. Inertia matrix. Coriolis and centrifugal force matrix and gravity vector Specifically, it is expressed as follows: Among them, the gravitational acceleration is taken as a conventional value. ,vector This represents the lumped physical parameters of the robotic arm.

[0073] The specific conversion relationship is as follows: .

[0074] In the specific implementation process, each intelligent agent ( The physical parameters are set as shown in Table 1. The initial states of the leader and followers are initialized within the intervals [0.5, 1.3] and [-2.0, -1.2], respectively. The controller parameters are designed as follows: the basic control gain parameters in the control laws of the leader and followers are uniformly configured as follows. Based on the timing coordination mechanism requirements of the layered architecture, the predetermined convergence time for the leader layer's consistency is set to... The tracking convergence time of the follower layer is set to... Furthermore, to simulate complex scenarios in real industrial environments, time-varying periodic external disturbances are introduced. .

[0075] Table 1. Parameter settings for each agent

[0076]

[0077] Figure 4 This is the hierarchical cooperative error convergence curve of the two-layer multi-agent system in an embodiment of the present invention. For example... Figure 4 As shown, Figures (a) and (c) record the evolution trajectories of the positional consistency error of the leader layer at joints 1 and 2, respectively; Figures (b) and (d) record the evolution trajectories of the positional cooperative tracking error of the follower layer at joints 1 and 2, respectively. The simulation results show that the cooperative error of the leader layer, within a pre-set range... The trajectory accurately converges to the neighborhood of the origin, achieving planning and consistency of the upper-level reference trajectory; subsequently, the cooperative error of the follower layer is within the set range. The convergence was completed within the timeframe.

[0078] Figure 5 This shows the actual physical tracking error curves of each agent in the follower layer at two-degree-of-freedom joints in an embodiment of the present invention. Figure 5 As shown, Figures (a) and (b) respectively characterize the actual position tracking error of the follower at joint 1. With speed tracking error The convergence trajectory; Figures (c) and (d) respectively characterize the actual position tracking error of the follower at joint 2. With speed tracking error The convergence trajectory is shown. Simulation results indicate that the tracking error of the node converges to a minimal neighborhood near the equilibrium point earlier than the predetermined time.

[0079] This pre-time tracking control method for multi-robot systems based on two-layer communication employs a hierarchical architecture with multiple leaders planning reference trajectories at the upper layer and followers cooperating in tracking at the lower layer. This effectively solves the communication challenges caused by the coupling of multiple reference signals and complex topologies, significantly improving the collaborative efficiency of large-scale heterogeneous systems. Unlike traditional asymptotically stable control, this method ensures that the system's global tracking error converges to the neighborhood of the equilibrium point within a preset time, and this upper limit of convergence time is completely independent of the system's initial state. Addressing the nonlinear characteristics of the physical system, an RBF neural network is used for online approximation, and a power-law driving term is introduced to effectively compensate for the effects of external environmental disturbances and uncertainties in the system's own parameters.

[0080] The above are merely preferred embodiments of the present invention. It should be noted that those skilled in the art can make several modifications and improvements without departing from the concept of the present invention, and these should also be considered within the scope of protection of the present invention. These will not affect the effectiveness of the implementation of the present invention or the practicality of the patent.

Claims

1. A method for time-based tracking control of a multi-robot system based on two-layer communication, characterized in that, Includes the following steps: S1: Construct a two-layer communication framework that includes a leader planning layer and a follower execution layer; S2: For the leader planning layer, a leader distributed virtual controller is designed based on the relative position and state information between nodes and the predetermined time control theory; S3: Combine the aforementioned leader distributed virtual controller to design the leader actual controller, and construct a parameter adaptive update mechanism based on power terms to form a leader layer predetermined time consistency control scheme; S4: For the follower execution layer, combine the adjacency interaction information within the follower layer with the cross-layer connection information to design a follower distributed virtual controller; S5: Combine the aforementioned follower distributed virtual controller to design the follower actual controller, and construct a corresponding parameter adaptive update mechanism to form a follower-layer collaborative tracking control scheme; S6: Based on Lyapunov stability theory, analyze the practical predetermined time stability of a two-layer closed-loop system, construct a timing coordination mechanism with the constraint that the predetermined convergence time of the leader layer is less than that of the predetermined convergence time of the follower layer, drive the corresponding intelligent agent according to the control torque command output by the actual controller of each layer, and realize the practical predetermined time stability and consistency tracking of the two-layer multi-agent system. Step S1 specifically includes: S11: Introducing the concept of hierarchical control, constructing a two-layer communication framework that includes a leader planning layer and a follower execution layer; S12: Use a directed graph to describe the multi-leader communication network structure, construct a leader planning layer communication topology containing at least one directed spanning tree, and define the corresponding Laplace matrix; S13: Use a directed graph to describe the multi-follower communication network structure, construct the follower execution layer communication topology, and define its Laplace matrix; S14: The leader planning layer and the follower execution layer adopt a top-down one-way communication and define an inter-layer connection matrix. Under the two-layer communication framework, only some followers in the execution layer need to directly receive the leader's instructions, while the remaining followers achieve indirect tracking through the collaborative interaction within the execution layer. S15: For any first... in the two-layer communication framework For each intelligent agent, establish its system dynamics equations: ； In the formula, , , These are joint position, velocity, and acceleration, respectively. It is a symmetric positive definite inertial matrix; The matrix represents the Coriolis force and the centrifugal force. It is the gravity vector; For a bounded external unknown disturbance, it satisfies ,in ; To control the input torque; S16: Introduce state variables and convert the dynamic equations into state-space form to obtain the state-space dynamic model of each agent; Step S5 specifically includes: introducing the velocity tracking error of the follower, differentiating it and using a radial basis function neural network to approximate the unknown nonlinear dynamics of the system online, designing the actual control torque of the follower in combination with the predetermined time control theory, and constructing a parameter adaptive update law based on power terms; Step S6 specifically includes: S61: By constructing a leader layer Lyapunov function containing an inertia term, we prove that the leader layer achieves practical time-stability stability. S62: By constructing a follower layer Lyapunov function containing an inertia term, we prove that the follower layer achieves practical time-stability stability. S63: Define the position tracking error of the follower relative to its corresponding leader, and prove that the global tracking error converges within a predetermined time based on matrix invertibility; set the time sequence constraints of the two-layer communication architecture so that the leader layer achieves consistency first, thereby ensuring that the follower layer achieves tracking stability.

2. The multi-robot system predetermined time tracking control method based on two-layer communication according to claim 1, characterized in that, Step S2 specifically includes: S21: Establish mathematical evaluation criteria for cooperative tracking targets, that is, for a certain dynamic system and any initial state. If a pre-set time constant exists and boundary constants This makes the system state Satisfy: When hour, If the condition is always met, then the system is determined to be stable for a given time. S22: Based on the communication topology information within the leader planning layer, define the leader's position consistency error and design the leader's virtual control law.

3. The multi-robot system time-tracking control method based on two-layer communication according to claim 2, characterized in that, Step S3 specifically includes: introducing the leader's velocity tracking error, differentiating it and using a radial basis function neural network to approximate the unknown nonlinear dynamics of the system online, designing the leader's actual control torque in combination with predetermined time control theory, and constructing a parameter adaptive update law based on power terms.

4. The pre-time tracking control method for a multi-robot system based on two-layer communication according to claim 1, characterized in that, Step S4 specifically includes: defining the follower's position collaborative tracking error based on the communication topology information within the follower execution layer and the inter-layer communication information with the leader planning layer, and designing the follower's distributed virtual control law.

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