A multi-aquatic robot distributed data-driven consistency control method and system

Abstract

The application discloses a kind of multi-underwater robot distributed data driven consistency control method and system, it is related to underwater unmanned system control technical field, based on the discretization state space model of multi-underwater robot system and the distributed optimal performance index function with communication topology coupling, select the communication subgraph of maximum degree node and build temporary full connection learning structure, two core gain matrix of controller are solved iteratively by recursive least square method;Based on the discretization state space model and two core gain matrix, the strategy iteration method of subgraph cooperative learning is used Robust stability margin theory, design distributed data driven consistency controller;According to the eigenvalue range of controller gain and the dynamic updating rule of stability margin, the condition that multi-underwater robot system is globally stable and state asymptotically consistent is obtained.The complexity of calculation and communication is reduced, and the robustness and collaborative control accuracy of the system in complex underwater environment are improved.

Description

Technical Field

[0001] This invention relates to the field of underwater unmanned system control technology, and in particular to a distributed data-driven consistency control method and system for multiple underwater robots. Background Technology

[0002] The statements in this section are merely background information relating to this disclosure and do not necessarily constitute prior art.

[0003] Autonomous underwater vehicles (AUVs), as core equipment of underwater unmanned systems, have broad application prospects in underwater exploration, seabed resource development, underwater search and rescue, and marine environmental monitoring. With increasing mission complexity, single AUVs, due to limitations in payload, endurance, and operating range, are unable to meet actual operational needs. Multi-AUV collaborative operations have become an important direction for the development of underwater unmanned systems.

[0004] The core of cooperative control in multi-AUV systems is to achieve state consistency among the AUVs, meaning that the positions, velocities, attitudes, and other states of all AUVs tend to be consistent, thereby enabling tasks such as cooperative formation and joint detection. However, the underwater environment is characterized by strong interference, limited communication bandwidth, and dynamic topology changes, which brings many challenges to the consistency control of multi-AUVs: existing centralized control methods require global state information, and the computational and communication complexity increases quadratically with the number of AUVs, making it difficult to adapt to large-scale multi-AUV systems; traditional distributed control methods rely on accurate system models, but the uncertainties of the underwater environment (such as wind, waves, and current interference) and the time-varying nature of AUV parameters make it difficult to establish accurate models, severely affecting control accuracy and robustness; in addition, existing data-driven control methods in multi-AUV cooperative scenarios suffer from low learning efficiency and poor policy scalability, making it difficult to balance learning accuracy and system stability. Summary of the Invention

[0005] To address the problems of strong model dependence, large communication topology constraints, high computational complexity, and weak anti-interference capability in existing multi-AUV cooperative control, this invention provides a distributed data-driven consistency control method and system for multiple underwater robots. It does not rely on an accurate system model and achieves online estimation and optimization of controller parameters through data-driven methods, reducing computational and communication complexity and improving the robustness and cooperative control accuracy of the system in complex underwater environments.

[0006] To achieve the above objectives, one or more embodiments of the present invention provide the following technical solutions: In a first aspect, the present invention provides a distributed data-driven consistency control method for multiple underwater robots, comprising: The kinematic and dynamic models of the multi-underwater robot system are linearized and discretized to obtain the discretized state-space model of the multi-underwater robot system. We construct a distributed optimal performance index function coupled with communication topology, and combine communication graph theory to characterize the adjacency interaction cost and self-state cost of a multi-underwater robot system, thus establishing a distributed optimal control problem constrained by communication topology. Based on the discretized state-space model and the distributed optimal performance index function, a communication subgraph containing the maximum degree node is selected and a temporary fully connected learning structure is constructed. The cost matrix of the subgraph is identified by the recursive least squares method, and the two core gain matrices of the controller are solved iteratively by combining the Lyapunov equation. Based on a discretized state-space model and two core gain matrices, a distributed data-driven consistency controller is designed using a subgraph collaborative learning strategy iteration method and robust stability margin theory. According to the eigenvalue range of the controller gain and the dynamic update rule of the stability margin, the conditions for global stability and asymptotic consistency of the multi-underwater robot system are obtained.

[0007] A further technical solution involves linearizing and discretizing the kinematic and dynamic models of the multi-underwater robot system to obtain a discretized state-space model of the multi-underwater robot system, specifically including: The motion of multiple underwater robot systems in the horizontal plane is simplified into a dynamic model of swaying, rolling, and pitching, while ignoring heave, roll, and pitching motions. Based on the state variables of a multi-underwater robot system, a Taylor expansion is used at the nominal operating point to ignore higher-order nonlinear terms. The system parameters are embedded into the linearized state matrix and control matrix, and then the sampling time is introduced through the forward Euler discretization method to obtain a discretized state-space model.

[0008] A further technical solution defines a communication topology graph to describe the communication topology of a multi-underwater robot system. Specifically, this includes: constructing an algebraic graph with each participating underwater robot as a node and the communication channels between underwater robots as edges; defining the communication relationship between nodes as an adjacency matrix; characterizing the connection characteristics between nodes through a Laplace matrix; and clarifying the rule that underwater robot nodes only interact with their neighboring nodes.

[0009] A further technical solution is that the distributed optimal performance index function with communication topology coupling is expressed by the following formula:

[0010] in, For performance index functions, for time, This represents the global state vector of a multi-underwater robot system. For transpose, This is the global control input vector. , For the global penalty matrix, For a custom positive definite state penalty matrix, For a custom positive semidefinite state penalty matrix, For Kronecker product, For Laplace matrix, for 3D identity matrix The input penalty matrix is ​​a custom positive definite control.

[0011] A further technical solution involves solving the two core gain matrices of the controller. Specifically, this includes: calculating the degree of each node based on a discretized state-space model and a distributed optimal performance index function, combined with a communication topology graph; selecting a subgraph containing the node with the maximum degree; adding a temporary communication link to this subgraph to construct a fully connected learning structure; injecting Gaussian noise signals that satisfy continuous excitation conditions into the fully connected learning structure; collecting the state and control input data of the underwater robot within the subgraph; identifying the cost matrix of the subgraph using a recursive least squares method; and extracting the matrix block elements. Finally, combining the Lyapunov equation, iteratively updating the two core gain matrices through policy iteration until the gain matrices converge.

[0012] A further technical solution involves designing a distributed data-driven consensus controller, specifically including: based on a discretized state-space model and two core gain matrices, determining the adjustment range of the controller gain according to the stability margin dynamically updated during the subgraph learning process, combined with robust stability theory; removing the temporary communication links of the subgraph, extending the subgraph controller to the entire network, and obtaining a distributed data-driven consensus controller.

[0013] A further technical solution is to provide distributed control input as follows:

[0014] in, For the first The control inputs of the underwater robot , For the first The controller gain of step iteration, For the size of the subgraph, For stability margin, Gather for the neighbors, For the first The state vector of the underwater robot. For the first The state vector of the underwater robot.

[0015] In a second aspect, the present invention provides a distributed data-driven consistency control system for multiple underwater robots, comprising: The discrete dynamics model construction module is configured to linearize and discretize the kinematic and dynamic models of the multi-underwater robot system to obtain a discretized state-space model of the multi-underwater robot system. The communication topology and performance index construction module is configured to: construct a distributed optimal performance index function coupled with communication topology, combine communication graph theory to characterize the adjacency interaction cost and self-state cost of a multi-underwater robot system, and establish a distributed optimal control problem constrained by communication topology. The controller gain matrix solving module is configured to: select a communication subgraph containing the maximum degree node and construct a temporary fully connected learning structure based on a discretized state-space model and a distributed optimal performance index function; identify the subgraph cost matrix through a recursive least squares method; and iteratively solve the two core gain matrices of the controller by combining the Lyapunov equation. The controller design module is configured to: design a distributed data-driven consistency controller based on a discretized state-space model and two core gain matrices, using a strategy iteration method of subgraph collaborative learning and robust stability margin theory; and obtain the conditions for global stability and asymptotic consistency of the multi-underwater robot system according to the eigenvalue range of the controller gain and the dynamic update rules of the stability margin.

[0016] Thirdly, the present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of a distributed data-driven consistency control method for multiple underwater robots as described in the first aspect.

[0017] Fourthly, the present invention provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the steps of a distributed data-driven consistency control method for multiple underwater robots as described in the first aspect.

[0018] The above one or more technical solutions have the following beneficial effects: This invention significantly reduces computational complexity (independent of network size, relying only on the maximum communication network), eliminates dependence on precise system model parameters, and improves the stability, robustness, and consistent control accuracy of multi-AUV systems in complex underwater environments. It effectively solves the challenges of collaborative control under model uncertainty and communication constraints, providing reliable technical support for multi-AUV collaborative operation scenarios such as deep-sea resource exploration and marine environmental monitoring, and promoting the development of underwater multi-agent data-driven control technology.

[0019] Advantages of additional aspects of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0020] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0021] Figure 1 This is a flowchart of a distributed data-driven consistency control method for multiple underwater robots according to an embodiment of the present invention; Figure 2 This is a schematic diagram of a multi-underwater robot system and information interaction according to an embodiment of the present invention; Figure 3 This is a convergence trajectory diagram of the algorithm under 20 sets of random parameters in Embodiment 2 of the present invention; Figure 4 This is a diagram showing the position error variation of multiple AUVs according to an embodiment of the present invention, wherein (a) is a position error diagram in the x direction, (b) is a position error diagram in the y direction, and (c) is a yaw angle error diagram. Figure 5 These are velocity error variation diagrams of multiple AUVs according to embodiments of the present invention, wherein (a) is a velocity error diagram in the x-direction, (b) is a velocity error diagram in the y-direction, and (c) is an angular velocity error diagram. Detailed Implementation

[0022] It should be noted that the following detailed descriptions are exemplary and intended to provide further illustration of the invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0023] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the scope of exemplary embodiments according to the invention. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0024] Where there is no conflict, the embodiments and features in the embodiments of the present invention can be combined with each other.

[0025] Example 1 like Figure 1 As shown in the figure, this embodiment discloses a distributed data-driven consistency control method for multiple underwater robots, which includes the following steps: S1: Linearize and discretize the kinematic and dynamic models of the multi-underwater robot system to obtain the discretized state-space model of the multi-underwater robot system; In this embodiment, the kinematic and dynamic models of the multi-underwater robot system (multi-AUV system) are linearized and discretized to obtain a discretized state-space model of the multi-underwater robot system. This includes: simplifying the motion of the multi-underwater robot in the horizontal plane into a dynamic model of heave, sway, and yaw, ignoring heave, yaw, and pitch motions; based on the state variables of the multi-underwater robot system (including x / y axis displacement, yaw angle, and corresponding velocity / angular velocity), Taylor expansion is used at the nominal operating point to ignore higher-order nonlinear terms, the system parameters are embedded into the linearized state matrix and control matrix, and then sampling time is introduced through the forward Euler discretization method to obtain a discretized state-space model, which satisfies the controllability condition.

[0026] Establish the kinematic and dynamic models of the target robot, and discretize the models using the properties of partial derivatives.

[0027] (1) Establishing the kinematic model of AUV like Figure 2 As shown, assuming a multi-underwater robot system moves in a horizontal plane, with oscillations such as roll, pitch, and heave approaching zero, its motion can be described by wave, sway, and yaw dynamics. A state-space model of a single robot is then established: In the inertial coordinate system, the robot's position is represented by ( ) represent longitudinal and lateral displacements, respectively; attitude is represented by This represents the bow angle (heading angle). A volume coordinate system is also defined, with its origin at the robot's center of gravity and its coordinate axes coinciding with the robot's geometric symmetry axes. In the volume coordinate system, linear velocity is expressed as... This indicates that the coordinates are along the body coordinate system. Axis (direction of travel) and Velocity along the axis (perpendicular to the direction of travel); angular velocity is... This indicates that the coordinate system is around the body. The bow angular velocity along the axis (perpendicular to the horizontal plane). Based on the principles of rigid body motion, kinematic equations are established to describe the relationship between position, attitude, and velocity:

[0028] in, This represents the velocity in the x-direction, the velocity in the y-direction, and the rate of change of the heading angle; This represents the position and attitude vector of the underwater robot, where x and y are the position coordinates. It is the heading angle; This represents the linear and angular velocity vectors of the underwater robot in the body coordinate system, where u is the linear velocity along the x-axis, w is the linear velocity along the y-axis, and r is the angular velocity.

[0029] Here is the transformation matrix used to convert linear velocity in body coordinates to volume coordinates:

[0030] (2) Establish an AUV dynamic model According to the Lagrange mechanics method, the dynamic model of the target AUV can be established in the following form:

[0031] in, It is a velocity vector The derivative of the derivative characterizes the rate of change of the linear velocity and angular velocity of the underwater robot in the body coordinate system, and quantifies how fast the motion state of the AUV changes over time. For the quality matrix, For quality parameters; The matrix represents the Coriolis matrix and the centripetal force matrix. It is a linear damping matrix. For damping parameters; To control the input amount, It is a diagonal matrix. and These represent the forward and backward thrust and yaw moment, respectively.

[0032] make This represents the position and attitude vectors of the underwater robot, as well as the changes in velocity in the x-direction, velocity in the y-direction, and heading angle. Controller: After Taylor expansion, the AUV system can be linearized as follows:

[0033]

[0034]

[0035] in, It is a composite parameter composed of the parameters of pitch, sway, and yaw inertia. , used to simplify The element representation of the matrix essentially reflects the coupling relationship of the inertial characteristics of the AUV in the horizontal plane; It is a composite parameter composed of the damping / inertia ratio of the longitudinal and transverse sway. ,simplify Matrix operations essentially reflect the difference in damping-inertia characteristics between the sway and roll motions of an AUV, and are a key quantity for characterizing the damping coupling of motion in the horizontal plane. The diagonal elements of the mass and additional mass matrix of the AUV correspond to the total mass in the sway (x-axis), y-axis, and pitch (about z-axis) directions of motion, respectively. The diagonal elements of the linear damping matrix of the AUV are the linear damping coefficients for sway, roll, and pitch motion, respectively, reflecting the viscous drag characteristics of the water on the AUV's motion in different directions. The greater the damping, the faster the speed of the AUV decays during motion. It represents the resultant velocity of the AUV along the x and y axes in equilibrium state. It is the velocity characteristic of the AUV at the nominal operating point and serves as the reference velocity parameter for the linearization process. This represents the forward and backward thrust of an AUV when it is in a constant equilibrium state. It is the AUV maintaining balance speed The core control input parameters are directly related to the output of the AUV's propulsion system; It is the state Jacobian matrix obtained by Taylor expansion of the AUV nonlinear dynamic model at the nominal operating point (equilibrium state), which describes the inherent evolution characteristics of the AUV state variables; It is the control Jacobian matrix obtained by Taylor expansion of the AUV nonlinear dynamic model at the nominal operating point, which describes the characteristics of the effect of the control input on the state variables; Indicates forward and backward thrust The coefficient of action on sway acceleration reflects the force and acceleration gain of the sway direction control input; Indicates the bow roll torque The coefficient of action on the bow roll angular acceleration reflects the torque and angular acceleration gain of the bow roll direction control input.

[0036] To facilitate system analysis and design and improve system performance, the system is now discretized. The system model after forward Euler discretization is as follows:

[0037] in, express Real-time robot speed and acceleration information; express Real-time robot speed and acceleration information; , These represent the linearly discretized state matrix and control matrix, respectively. , , represents the discretized model parameter matrix; Indicates the sampling time; Representation and matrix Identity matrices with consistent dimensions This represents the system's input vector.

[0038] The above technical solution simplifies the motion of a multi-AUV system in the horizontal plane into a dynamic model of forward, lateral, and yaw movements, ignoring lateral, longitudinal, and vertical oscillations, as well as small pitch and roll angles. Based on the state variables of the multi-AUV system, including displacement, velocity, and attitude angles, the dynamic model is linearized using Taylor expansion, clarifying the embedding form of system parameters in the state and control matrices. The linearized model is discretized using the forward Euler discretization method, and the sampling time is set. Thus, a discrete dynamic model is obtained.

[0039] S2: Construct a distributed optimal performance index function with communication topology coupling, combine communication graph theory to characterize the adjacency interaction cost and self-state cost of a multi-underwater robot system, and establish a distributed optimal control problem constrained by communication topology. In this embodiment, this step focuses on the information interaction rules and optimization objectives of multi-underwater robot collaborative control, and combines underwater communication characteristics and system control requirements to complete communication topology modeling and performance index definition.

[0040] A communication topology graph and performance index function are constructed, and the coupled dynamic behavior between multiple AUV systems is combined to characterize the data-driven collaborative learning characteristics constrained by the communication topology. A fixed-connected undirected graph is used to describe the multi-AUV communication topology, clarifying the information interaction relationships between nodes. The specific modeling process is as follows: Define the communication topology. Node set ,in The number of robots participating in the collaboration; edge set If an edge exists Belongs to matrix , indicating the first The machine can supply the first The machine sends status information; because underwater communication is bidirectional, therefore... belong Equivalent to belong Adjacency matrix It is an N-dimensional real matrix used to quantify the communication relationships between nodes, and the matrix elements satisfy... (The machine does not communicate with itself) (like belong Robot With machines (Communication connection exists) (like Not belonging to (i.e., no communication connection); neighbor set , indicating the first The set of other machines from which this machine can directly obtain information reflects the local information interaction range of the machines; degree matrix. It is an N-dimensional diagonal matrix with diagonal elements of 1. ,in For the first The number of adjacencies of the robots is represented by a matrix where only the diagonal has non-zero elements, and the rest are 0; this is a Laplace matrix. , representing the difference between the degree matrix D and the adjacency matrix This is used to characterize the overall connectivity properties of a communication topology, and its elements satisfy the following condition: the main diagonal elements satisfy... Off-diagonal elements satisfy ( ), This indicates the position of an element in the matrix.

[0041] Based on the above definition, the optimal performance index function for a distributed system with communication topology coupling is expressed by the following formula:

[0042] in, Represents a performance metric function; This represents the global state vector of a multi-AUV system. For the first The state vector of the AUV; This is the global control input vector. For the first Control inputs for the AUV; , Represents the global penalty matrix; for An identity matrix of dimensionality; A custom positive definite state penalty matrix is ​​used to constrain the state fluctuations of a single robot, and the weights are determined by the robot's motion accuracy requirements. A custom positive definite control input penalty matrix is ​​used to limit control energy consumption, such as avoiding excessive output of the thrusters. The weights are determined by the robot's energy capacity. A custom semi-positive definite state penalty matrix is ​​used to promote the convergence of states of multiple robots. The smaller the difference, the smaller the penalty term. The weight is determined by the cooperative positioning accuracy requirements. For Kronecker product.

[0043] visible, For custom positive definite state penalty matrix; The custom positive definite control input penalty matrix is ​​used to constrain the control output amplitude. Both are positive definite matrices and can be set independently according to the actual working conditions.

[0044] Based on this, a distributed optimal control problem is established: in the communication topology graph Solve for a distributed feedback controller that satisfies the topology under sparse constraints where fixed connectivity is maintained and each AUV interacts with its neighbor nodes only. This makes the multi-AUV system globally asymptotically stable and its state asymptotically consistent, and minimizes the infinite time-domain distributed optimal performance index, forming a distributed linear quadratic optimal control problem constrained by the communication topology.

[0045] S3: Based on a discretized state-space model and a distributed optimal performance index function, a communication subgraph containing the node with the maximum degree is selected and a temporary fully connected learning structure is constructed. The cost matrix of the subgraph is identified using a recursive least squares method, and the two core gain matrices of the controller (the core gain matrices of the distributed consensus controller) are iteratively solved using the Lyapunov equation. Specifically, this includes: calculating the degree of each node based on a discretized state-space model and a distributed optimal performance index function, combined with the communication topology graph, and selecting a subgraph containing the node with the maximum degree. And add temporary communication links to the subgraph to build a fully connected learning structure. ;Towards Gaussian noise signals satisfying the continuous excitation (PE) condition are injected to collect the state and control input data of AUVs within the subgraph; the subgraph cost matrix is ​​identified using the recursive least squares (RLS) method. Extract the elements of the matrix blocks; combine the Lyapunov equations, and update the two core gain matrices iteratively through policy. and until the gain matrix converges.

[0046] In this embodiment, during the learning phase, based on the communication topology graph Calculate the degree of all nodes to obtain the maximum degree. Set the subgraph size: From the original image Select the node that contains at least one maximum degree node and in A connected subgraph is denoted as This subgraph This is the core local structure used for learning. The algorithm needs to be applied to the subgraph. Temporary communication links are added to the subgraph to make it a cluster. The dynamic representation of the subgraph is as follows:

[0047] in, , This describes the collective state evolution characteristics of all AUVs within the subgraph and the effect of control inputs on the collective state. It is the core of the linear dynamics model at the subgraph level. express 3D identity matrix; , Depend on The concatenation of the state and control signals in the system forms a representation of the state in the system. The collective state vector and collective control input vector at time t are composed of the states and control inputs of all AUVs within the subgraph, representing the overall state and control at the subgraph level. From the Bellman equations, Cost matrix Related to one-step linear quadratic cost:

[0048] in, The single-step instantaneous cost function of the subgraph system has the physical meaning of: The penalty cost incurred due to deviation from the expected state at any given moment, as well as the penalty cost incurred due to the application of control inputs (energy consumption / actuator losses), are quantitative indicators of the performance loss in a linear quadratic problem at one step. satisfy , It is the iteration number The controller gain matrix of the next-time subgraph is the core iterative object of data-driven collaborative learning. , For subgraph The state cost matrix and control cost matrix of the linear quadratic optimal problem:

[0049]

[0050] in, For a custom positive definite penalty matrix, This is used to constrain the state fluctuations of a single robot, and the weights are determined by the robot's motion accuracy requirements. For a custom positive definite penalty matrix, It is used to limit and control energy consumption, such as to avoid excessive output of the thrusters, and the weight is determined by the robot's energy capacity; A custom positive semidefinite penalty matrix is ​​used to promote the consistency of the states of multiple robots. The smaller the difference, the smaller the penalty term. The weight is determined by the cooperative positioning accuracy requirements. The size and number of AUVs in the subgraph.

[0051] In each iteration of the dynamic programming method for solving linear quadratic programming problems, a subsystem is proposed. Feedback format .Will Rearranged, we get:

[0052] in, express Transpose of a vector This represents the joint vector formed by concatenating the state of the AUV and the control input within the subgraph. , ; The joint cost matrix for the k-th iteration is the core matrix of this invention's data-driven learning. The physical meaning of each block matrix is ​​as follows: Representing state-related blocks, derived from the state cost matrix. It consists of the cost coupling terms of the system state matrix, which characterize the optimal cost contribution brought about by the state evolution itself; , The optimal cost contribution resulting from the interaction between the state and control inputs is the core part reflecting the state-control coupling characteristics of the system. It represents the contribution of the optimal cost (energy consumption / actuator loss) brought about by applying the control input itself.

[0053] Below, a distributed data-driven algorithm is used to... The system learns and iteratively solves for the two core gain matrices of the controller. The specific steps are as follows: (1) Initialization settings Select the subgraph containing the node with the maximum degree Subgraph size ( For communication topology (maximum degree), for subgraph Temporarily add communication links to build a fully connected learning structure . Initialize the state adjustment cost matrix Neighbor difference cost matrix Initial state (6-dimensional random vector), initial matrix Set the least squares parameters ,in, To ensure Positive definite constants ( ,make sure (Positive definiteness), initialize controller parameters , To ensure system stability; construct subgraphs. Temporary fully connected links form a unified structure for the learning phase. Initialization stability margin This ensures the initial controller stabilizes the multi-AUV system.

[0054] (2) Iterative optimization of controller parameters Set iteration parameters , Determine controller parameters , Whether it has converged (the convergence condition is that the difference in parameters between two iterations is less than 1) If convergence is not achieved, perform the following operations: 1) Control input calculation: For those not belonging to the subgraph The node, ,in, Indicates stability margin, Indicates the size of the subgraph; for items belonging to the subgraph The node, ,in For nodes The set of neighbors.

[0055] 2) Cost Matrix Update: Call the matrix update algorithm and input the communication topology graph. Learning Structure Estimated control input Previous round cost matrix and least squares parameters Output the updated cost matrix Among them, Gaussian noise obey Distribution ensures that the incentive conditions are met continuously.

[0056] 3) Key Submatrix Extraction: From the cost matrix Extract key submatrices from them. , representing the extraction matrix For rows 1-6 and columns 1-6, the following operations are similar; ; , It is the largest subgraph; ; ; ; ; .

[0057] 4) Controller parameter update: Calculate the intermediate matrix , , , ,renew , .in, It represents the state cost coupling difference of a single AUV within the subgraph, reflecting the difference between the AUV's own state evolution cost and the neighbor's state interaction cost, and is the core state item for the controller's state gain update; It represents the interaction difference of state-control coupling terms within a subgraph, reflecting the difference in cross-coupling costs between the state and the control input, and is used to construct the state-control correlation terms of the controller gain; It represents the coupling difference of the control input cost within the subgraph, reflects the difference in control energy consumption cost between itself and its neighbors, and is the inverse matrix term of the control cost for solving the controller gain; This represents the interaction difference of control-state coupling terms within a subgraph, reflecting the difference in the cost of the control input's effect on state evolution, and is directly used to calculate the controller's core gain. .

[0058] 5) Stability margin update: Calculation , , , .in, The smallest eigenvalue of the cost matrix of the closed-loop system is represented, which is the lower bound of the system stability. This represents the largest eigenvalue of the system's dynamic coupling matrix and serves as the upper bound for the perturbation. The stability coefficient represents the ratio of the lower bound of stability to the upper bound of disturbance. It represents the robustness margin of the system, used to ensure global stability during the learning process; Represents the smallest eigenvalue of the matrix; This represents the largest eigenvalue of the matrix.

[0059] 6) Iterative Update: Settings Return to the step of determining whether the controller parameters have converged, until the controller parameters converge.

[0060] Furthermore, the matrix update algorithm includes the following steps: (1) Input communication topology diagram Learning Structure , Previous round cost matrix and least squares parameters ,judge Check if the connection has converged. If not, perform the following operations.

[0061] (2) Towards learning structure Inject an input signal that satisfies the continuous excitation condition, i.e., superimposed Gaussian noise. The mean is covariance is Collect the first subgraph within the subgraph Iterative wheel controller and The status and input interaction data of the AUV at any time Obtain the learning structure The state in and control input Gaussian noise was selected. ( (Noise variance matrix), update control input This ensures that the continuous incentive (PE) conditions are met, guarantees data diversity, and avoids local optimization.

[0062] (3) In the updated control input Running learning structure under the action Collect the state of all nodes in the next time step. and control input .

[0063] (4) Settings ,calculate and ,in This is a matrix vectorization operation; 1 represents a vector consisting entirely of 1s. For Kronecker product, for Learning Structure Joint state difference vector at previous and next time steps, for Learning Structure Internal multi-AUV local aggregation state vector, for Learning Structure Internal multi-AUV local aggregation control input vector, It is obtained by semi-vectorization of the outer product of difference vectors. Time-regression feature vector.

[0064] (5) Settings Update least squares parameters Update parameters This achieves recursive optimization of the parameters. Among them, Cost matrix The semi-vectorized form is used to transform the quadratic cost problem in matrix form into a linear regression problem; The recursive least squares covariance matrix is ​​used to characterize the uncertainty of parameter estimation. It is dynamically updated during the iteration process to control the parameter update step size and prevent overfitting. for The time-step feature regression vector is obtained by semi-vectorizing the state difference matrix and serves as the input feature quantity for iterative updates.

[0065] (6) Through Operation will Convert to matrix ,renew = ,set up Return judgment Whether the convergence step is reached, up to the cost matrix. convergence.

[0066] Furthermore, the state dimension of each AUV in a multi-AUV system Input dimension System parameters (including) (etc.) through normal distribution Obtained through random sampling to ensure system controllability. State cost matrix. Neighbor state penalty matrix Control input cost matrix ,in It is an identity matrix.

[0067] S4: Based on a discretized state-space model and two core gain matrices, a distributed data-driven consistency controller is designed using a subgraph collaborative learning strategy iteration method and robust stability margin theory. Based on the eigenvalue range of the controller gain and the dynamic update rule of the stability margin, the conditions for global stability and asymptotically consistent state of the multi-underwater robot system are obtained. Specifically, this includes: based on the discretized state-space model and the converged core gain matrix... The stability margin is dynamically updated during the subgraph learning process. Based on robust stability theory, the adjustment range of the controller gain is determined; subgraphs are removed. The temporary communication link extends the subgraph controller to the entire network, resulting in a distributed data-driven consistency controller that ensures that each AUV achieves state coordination only through local neighbor information exchange.

[0068] In this embodiment, by dynamically adjusting the stability margin, the asymptotic stability and state consistency of the multi-AUV system during the learning process and actual operation are ensured, including: Based on the controller gain matrix and the global cost matrix Calculate the stability margin:

[0069]

[0070] in, Indicates the first The system's stability coefficients in the next iteration are used to update the robust stability margin. ; , Let represent the minimum and maximum eigenvalues ​​of the matrix, respectively. For the cost matrix related terms of the subgraph system, For the size of the subgraph, For a custom penalty matrix, , For the first The controller gain of step iteration, , The system parameter matrix is ​​obtained through the global cost matrix. The obtained parameters.

[0071] When controller parameters , Upon convergence, remove the subgraph. The temporary link extends the control strategy to the entire multi-AUV network, and the distributed control input is designed as follows:

[0072] in, , For the first The controller gain of step iteration, For the size of the subgraph, For stability margin; neighbor set , indicating the first The set of other machines that this machine can directly obtain information from reflects the local information interaction range of the machines; For the first The state vector of the AUV.

[0073] This distributed control input achieves system performance through two parts: Self-feedback item Suppress individual machine state deviations and ensure stable individual machine control; Neighbor interaction items By exchanging information with its neighbors, the state of each AUV is driven to become consistent.

[0074] This invention uses a data-driven iterative algorithm to automatically ensure that the system meets the conditions of global stability and asymptotic consistency when the controller parameters converge, without requiring additional complex calculations.

[0075] The above technical solution, based on the discrete dynamics model and core gain matrix, combined with robust stability theory, designs a distributed data-driven controller. By dynamically adjusting the stability margin, it ensures the asymptotic stability and state consistency of the multi-AUV system during the learning process and actual operation.

[0076] Therefore, addressing the problems of strong model dependence, large communication topology constraints, high computational complexity, and weak anti-interference capability in existing multi-AUV cooperative control systems, this invention embeds nonlinear system parameters into the linearized state and control matrices through Taylor expansion. A temporary fully connected learning structure is constructed using a subgraph containing the maximum degree node, and online estimation of controller parameters is achieved using recursive least squares. After learning, the original network structure is restored, and the controller gain matrix is ​​obtained by solving a local optimization problem. A distributed controller is then designed to achieve state consistency control of the multi-AUV system. This invention does not rely on an accurate system model, reducing computational and communication complexity and improving the system's robustness and cooperative control accuracy in complex underwater environments. It is suitable for multi-AUV cooperative operation scenarios such as underwater exploration, search and rescue, and monitoring.

[0077] In summary, the beneficial effects of this invention are as follows: No need to rely on an accurate system model: By embedding nonlinear system parameters into the linearized state and control matrices through Taylor expansion, and combining the data-driven RLS algorithm, online estimation of controller parameters is achieved, which effectively alleviates the dependence of traditional control methods on accurate models and adapts to the uncertainty of the underwater environment and the time-varying nature of AUV parameters.

[0078] Low computational and communication complexity: Local learning is performed through a subgraph containing the node with the maximum degree. The controller parameter update only involves matrix operations related to the subgraph dimension. The algorithm iteration complexity is independent of the number of AUVs N. It is suitable for large-scale multi-AUV network structures with a large number of nodes and a small maximum degree, solving the problem of high complexity in traditional centralized control.

[0079] High robustness: By injecting Gaussian noise to meet the continuous excitation conditions, data diversity is ensured and local optimization is avoided; the introduction of a dynamic adjustment control strategy for stability margin improves the system's resistance to underwater wind, wave and current disturbances, ensuring stable operation of the system in complex environments.

[0080] Good policy scalability: During the learning phase, a temporary fully connected subgraph is constructed to improve learning efficiency. After learning is completed, the original network structure is restored, and the optimized control policy is extended to the entire network, balancing learning accuracy and long-term system stability. It is suitable for multi-AUV systems with different communication topologies.

[0081] The specific implementation process of the distributed data-driven consistency control scheme of the multi-AUV system of this invention was completed with the help of the simulation tool Matlab, and its control effect can be further verified and illustrated by the following experimental simulation.

[0082] In this embodiment, a ring topology communication network consisting of six homogeneous AUVs was constructed. This topology has the following characteristics: each AUV adopts the same dynamic structure and sensor configuration; and ring information exchange is achieved through bidirectional communication links.

[0083] First, based on the discretized state-space model of the multi-submarine robot constructed by S1 and the distributed optimal performance index with communication topology coupling defined by S2, a distributed data-driven consistency controller is directly designed by using the motion state and control input data collected by each AUV and solving the iterative optimal solution of the Lyapunov equation in S3. This controller relies on two core gain matrices to dynamically offset the control deviation caused by unknown underwater environmental parameters and communication topology constraints, ensuring that each AUV can still achieve asymptotic consistency with the global node under the condition of relying only on local neighbor information interaction.

[0084] Secondly, based on the controller gain characteristic value range and stability margin dynamic update rules derived in S4, the state interaction coefficients of each AUV in the consensus control protocol are dynamically adjusted, and nodes with high communication connectivity and large stability margin are given higher state fusion weights, thereby improving the global cooperative control robustness of the multi-AUV system in unknown underwater environments.

[0085] Finally, the local state information of each AUV and the state information of its neighbors are weighted and fused according to the consensus control protocol, and used as the input of the distributed data-driven consensus controller designed by S4 to drive the propulsion and steering actuators of each AUV to adjust their actions, so as to achieve precise execution of tasks such as multi-underwater robot formation maintenance and cooperative exploration.

[0086] In this embodiment, a circular topology of six AUVs is considered, assuming that the six underwater robots have identical structures. This embodiment only considers the planar motion of the target AUV, so heave motion is ignored. Considering the good static stability of AUVs, which only generate very small pitch and roll angles during motion, roll and pitch angles are ignored and set to zero. Penalty matrix: , .

[0087] Figure 2 The topology of a communication network consisting of 6 AUVs is shown. Nodes represent AUVs and edges represent communication links between AUVs, forming a ring communication topology. The node with the highest degree is AUV1. Figure 3 The graph shows the convergence trajectory of the algorithm under 20 sets of random parameters. The horizontal axis represents the number of iterations, and the vertical axis represents the relative error of the cost matrix. It can be seen that the error of the algorithm tends to stabilize after about 5 iterations, which verifies the convergence of the algorithm. Figure 4 (a), (b), and (c) are graphs showing the position error variation of the multi-AUV system. The horizontal axis represents time, and the vertical axis represents position error. It can be seen that the position error quickly approaches zero, achieving position consistency. Figure 5Figures (a), (b), and (c) show the velocity error variation of the multi-AUV system. The horizontal axis represents time, and the vertical axis represents velocity error. It can be seen that the velocity error quickly approaches zero, achieving velocity consistency.

[0088] Existing technologies for consensus control in multi-AUV systems are limited by the unknown model parameters, communication topology constraints, and high computational complexity in underwater environments. Traditional model-driven methods are prone to model mismatch, while existing data-driven methods lack stable theoretical support and are difficult to adapt to distributed scenarios, making it difficult to achieve efficient and stable collaborative consensus control. This invention proposes a distributed data-driven consensus control method for multi-AUV systems. By linearizing and discretizing the AUV kinematics and dynamics model, a distributed optimal performance index function with communication topology coupling is constructed. A communication subgraph containing the maximum degree node is selected and a temporary fully connected learning structure is constructed. The controller's core gain matrix is ​​iteratively solved using a recursive least squares method. A distributed data-driven consensus controller is designed, and a dynamic update rule based on the controller gain eigenvalue range and stability margin ensures global system stability and asymptotic state consistency. Compared with existing technologies, this invention significantly reduces computational complexity (independent of network size, relying only on the maximum communication network), eliminates dependence on precise system model parameters, improves the stability, robustness, and consistent control accuracy of multi-AUV systems in complex underwater environments, effectively solves the collaborative control problem under model uncertainty and communication constraints, provides reliable technical support for multi-AUV collaborative operation scenarios such as deep-sea resource exploration and marine environmental monitoring, and promotes the development of underwater multi-agent data-driven control technology.

[0089] Example 2 This embodiment discloses a distributed data-driven consistency control system for multiple underwater robots, including: The discrete dynamics model construction module is configured to linearize and discretize the kinematic and dynamic models of the multi-underwater robot system to obtain a discretized state-space model of the multi-underwater robot system. The communication topology and performance index construction module is configured to: construct a distributed optimal performance index function coupled with communication topology, combine communication graph theory to characterize the adjacency interaction cost and self-state cost of a multi-underwater robot system, and establish a distributed optimal control problem constrained by communication topology. The controller gain matrix solving module is configured to: select a communication subgraph containing the maximum degree node and construct a temporary fully connected learning structure based on a discretized state-space model and a distributed optimal performance index function; identify the subgraph cost matrix through a recursive least squares method; and iteratively solve the two core gain matrices of the controller by combining the Lyapunov equation. The controller design module is configured to: design a distributed data-driven consistency controller based on a discretized state-space model and two core gain matrices, using a strategy iteration method of subgraph collaborative learning and robust stability margin theory; and obtain the conditions for global stability and asymptotic consistency of the multi-underwater robot system according to the eigenvalue range of the controller gain and the dynamic update rules of the stability margin.

[0090] In this embodiment, the communication topology is constructed as follows: an algebraic graph is built with each participating AUV as a node and the communication channels between AUVs as edges. The communication relationships between nodes are defined as an adjacency matrix. Through the Laplace matrix Characterize the connectivity between nodes, clarify the rules that AUV nodes only interact with their neighboring nodes, and ensure that the communication topology is a known, fixed, and connected structure.

[0091] In this embodiment, a subgraph containing the maximum degree node is selected and a temporary fully connected learning structure is constructed. Based on the discrete dynamics model and performance index function, and combined with the recursive least squares (RLS) method, the core gain matrix of the distributed consensus controller is obtained by iteratively updating the cost matrix and intermediate parameters. Based on the discrete dynamics model and the core gain matrix, and combined with robust stability theory, a distributed data-driven controller is designed, specifically including: Select the subgraph containing the node with the maximum degree Subgraph size ( For communication topology (maximum degree), for subgraph Temporarily add communication links to build a fully connected learning structure Initialize least squares parameters ,in, To ensure Positive definite constants, controller initial parameters and stability margin To ensure the initial controller is stable in a multi-AUV system; to learn the structure Inject an input signal that satisfies the continuous excitation condition, i.e., superimposed Gaussian noise. The mean is covariance is Collect the state and input interaction data of AUVs within the subgraph. .

[0092] Update the global cost matrix based on the least squares algorithm. This represents the number of times the update iteration parameters are performed, and the difference data vector is calculated. Vectorization operations are performed using MATLAB toolboxes. and Updated via least squares iteration and through MATLAB functions The updated cost matrix is ​​obtained by restoration. ; and from Extract the key submatrix.

[0093] Repeat the above steps until the controller parameters converge, then remove the subgraph. The temporary communication link is restored to the original communication topology, and the core gain matrix of the final distributed consensus controller is output. , .

[0094] Example 3 The purpose of this embodiment is to provide a computing device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the steps of the method of Embodiment 1.

[0095] Example 4 The purpose of this embodiment is to provide a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, performs the steps of the method of Embodiment 1.

[0096] The steps and methods involved in the apparatuses of Embodiments 3 and 4 above correspond to those in Embodiment 1. For specific implementation details, please refer to the relevant description section of Embodiment 1. The term "computer-readable storage medium" should be understood as a single medium or multiple media including one or more instruction sets; it should also be understood as including any medium capable of storing, encoding, or carrying an instruction set for execution by a processor and enabling the processor to perform any of the methods in this invention.

[0097] Those skilled in the art will understand that the modules or steps of the present invention described above can be implemented using general-purpose computer devices. Optionally, they can be implemented using computer-executable program code, thereby allowing them to be stored in a storage device for execution by a computer device, or they can be fabricated as separate integrated circuit modules, or multiple modules or steps can be fabricated as a single integrated circuit module. The present invention is not limited to any particular combination of hardware and software.

[0098] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

[0099] While the specific embodiments of the present invention have been described above in conjunction with the accompanying drawings, this is not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art without creative effort based on the technical solutions of the present invention are still within the scope of protection of the present invention.

Claims

1. A distributed data-driven consistency control method for multiple underwater robots, characterized in that, include: The kinematic and dynamic models of the multi-underwater robot system are linearized and discretized to obtain the discretized state-space model of the multi-underwater robot system. We construct a distributed optimal performance index function coupled with communication topology, and combine communication graph theory to characterize the adjacency interaction cost and self-state cost of a multi-underwater robot system, thus establishing a distributed optimal control problem constrained by communication topology. Based on the discretized state-space model and the distributed optimal performance index function, a communication subgraph containing the maximum degree node is selected and a temporary fully connected learning structure is constructed. The cost matrix of the subgraph is identified by the recursive least squares method, and the two core gain matrices of the controller are solved iteratively by combining the Lyapunov equation. Solving for the two core gain matrices of the controller involves: calculating the degree of each node based on a discretized state-space model and a distributed optimal performance index function, combined with the communication topology graph, and selecting the subgraph containing the node with the maximum degree. A temporary communication link is added to the subgraph to construct a fully connected learning structure; Gaussian noise signals that meet the continuous excitation conditions are injected into the fully connected learning structure to collect the state and control input data of the underwater robot in the subgraph; the cost matrix of the subgraph is identified by the recursive least squares method, and the matrix block elements are extracted; combined with the Lyapunov equation, the two core gain matrices are updated through policy iteration until the gain matrices converge. Based on a discretized state-space model and two core gain matrices, a distributed data-driven consistency controller is designed using a subgraph collaborative learning strategy iteration method and robust stability margin theory. According to the eigenvalue range of the controller gain and the dynamic update rule of the stability margin, the conditions for global stability and asymptotic consistency of the multi-underwater robot system are obtained.

2. The distributed data-driven consistency control method for multiple underwater robots as described in claim 1, characterized in that, The kinematic and dynamic models of the multi-underwater robot system are linearized and discretized to obtain a discretized state-space model of the multi-underwater robot system, specifically including: The motion of multiple underwater robot systems in the horizontal plane is simplified into a dynamic model of swaying, rolling, and pitching, while ignoring heave, roll, and pitching motions. Based on the state variables of a multi-underwater robot system, a Taylor expansion is used at the nominal operating point to ignore higher-order nonlinear terms. The system parameters are embedded into the linearized state matrix and control matrix, and then the sampling time is introduced through the forward Euler discretization method to obtain a discretized state-space model.

3. The distributed data-driven consistency control method for multiple underwater robots as described in claim 1, characterized in that, The communication topology graph is defined to describe the communication topology of a multi-underwater robot system. Specifically, it includes: constructing an algebraic graph with each underwater robot participating in the collaboration as a node and the communication channels between underwater robots as edges; defining the communication relationship between nodes as an adjacency matrix; characterizing the connection characteristics between nodes through a Laplace matrix; and clarifying the rule that underwater robot nodes only interact with their neighboring nodes.

4. The distributed data-driven consistency control method for multiple underwater robots as described in claim 1, characterized in that, The distributed optimal performance index function with communication topology coupling is expressed by the following formula: in, For performance index functions, for time, This represents the global state vector of a multi-underwater robot system. For transpose, This is the global control input vector. , For the global penalty matrix, For a custom positive definite state penalty matrix, For a custom positive semidefinite state penalty matrix, For Kronecker product, For Laplace matrix, for 3D identity matrix The input penalty matrix is ​​a custom positive definite control.

5. The distributed data-driven consistency control method for multiple underwater robots as described in claim 1, characterized in that, The design of a distributed data-driven consensus controller includes: based on a discretized state-space model and two core gain matrices, determining the adjustment range of the controller gain according to the stability margin dynamically updated during the subgraph learning process and in conjunction with robust stability theory; removing the temporary communication links of the subgraph and extending the subgraph controller to the entire network to obtain a distributed data-driven consensus controller.

6. The distributed data-driven consistency control method for multiple underwater robots as described in claim 1, characterized in that, Distributed control inputs are: in, For the first Control inputs for the underwater robot , For the first The controller gain of step iteration, For the size of the subgraph, For stability margin, Gather for the neighbors, For the first The state vector of the underwater robot. For the first The state vector of the underwater robot.

7. A distributed data-driven consistency control system for multiple underwater robots, characterized in that, include: The discrete dynamics model construction module is configured to linearize and discretize the kinematic and dynamic models of the multi-underwater robot system to obtain a discretized state-space model of the multi-underwater robot system. The communication topology and performance index construction module is configured to: construct a distributed optimal performance index function coupled with communication topology, combine communication graph theory to characterize the adjacency interaction cost and self-state cost of a multi-underwater robot system, and establish a distributed optimal control problem constrained by communication topology. The controller gain matrix solving module is configured to: select a communication subgraph containing the maximum degree node and construct a temporary fully connected learning structure based on a discretized state-space model and a distributed optimal performance index function; identify the subgraph cost matrix through a recursive least squares method; and iteratively solve the two core gain matrices of the controller by combining the Lyapunov equation. Solving for the two core gain matrices of the controller involves: calculating the degree of each node based on a discretized state-space model and a distributed optimal performance index function, combined with the communication topology graph, and selecting the subgraph containing the node with the maximum degree. A temporary communication link is added to the subgraph to construct a fully connected learning structure; Gaussian noise signals that meet the continuous excitation conditions are injected into the fully connected learning structure to collect the state and control input data of the underwater robot in the subgraph; the cost matrix of the subgraph is identified by the recursive least squares method, and the matrix block elements are extracted; combined with the Lyapunov equation, the two core gain matrices are updated through policy iteration until the gain matrices converge. The controller design module is configured to: design a distributed data-driven consistency controller based on a discretized state-space model and two core gain matrices, using a strategy iteration method of subgraph collaborative learning and robust stability margin theory; and obtain the conditions for global stability and asymptotic consistency of the multi-underwater robot system according to the eigenvalue range of the controller gain and the dynamic update rules of the stability margin.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the steps in the distributed data-driven consistency control method for multiple underwater robots as described in any one of claims 1-6.

9. A computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the steps in the distributed data-driven consistency control method for multiple underwater robots as described in any one of claims 1-6.

Images