A method and system for elastic consistency control of a multi-aquatic robot system

Abstract

The present application relates to underwater robot cooperative control technical field, provide a kind of elasticity consistency control method and system of multi underwater robot system.The elasticity consistency control method of multi underwater robot system includes, by carrying out discretization and linearization processing to multi-AUV system, introduce performance index to depict the influence of communication topology on system dynamic behavior, based on the centralized optimal control method and robust stability theory of local decoupling system, elasticity consistency controller is designed and controller gain is obtained by solving local algebraic Riccati equation, the consistency control of multi-AUV system state is realized.According to the sparse mode matrix spectrum of distributed controller, the system stability condition is given, to ensure the efficient cooperation and stable operation of multi-AUV system in complex underwater environment.The method significantly reduces the complexity of calculation and communication, suitable for multi-AUV cooperative working environment, provides a new technical solution for underwater unmanned system cooperative control.

Description

Technical Field

[0001] This invention relates to the field of underwater robot cooperative control technology, and in particular to a flexible consistency control method and system for multiple underwater robot systems. Background Technology

[0002] The statements in this section are merely background information related to the present invention and do not necessarily constitute prior art.

[0003] Underwater robots, as an important type of marine robot, can independently perform tasks such as underwater target tracking, seabed exploration, and marine sampling. With the increasing complexity of underwater operations, the operational efficiency of a single underwater robot is no longer sufficient to meet the demands of large-scale, high-precision marine exploration. Therefore, collaborative operations among multiple underwater robots have become an effective way to solve this problem. Multi-underwater robot collaborative systems possess flexible spatial scheduling capabilities, and underwater robots with different functions can significantly improve the efficiency of underwater target search and detection through collaboration. Their collaborative control technology has become a research hotspot in the field of marine robotics.

[0004] The core objective of multi-underwater robot cooperative control is to achieve the system's overall pre-defined task by coordinating the actions of multiple underwater robots. Existing cooperative control methods include adaptive control, PID control, and optimal control, and some progress has been made in areas such as formation tracking, consistency control, and swarm control. Among these, consistency control is the core of distributed cooperative control, aiming to design control protocols that enable the states of multiple underwater robots to gradually converge over time through shared interaction information.

[0005] However, existing multi-underwater robot consistency control technologies have the following key problems:

[0006] 1. High complexity of centralized control: Traditional centralized control relies on a central node to process the status information of all underwater robots. When the number of underwater robots increases (system scale expands), the amount of computation and communication increases exponentially, making it difficult to adapt to large-scale multi-underwater robot systems.

[0007] 2. Insufficient stability and topology adaptability: Some distributed control methods do not fully consider the impact of communication topology on the dynamic behavior of the system, or the stability conditions depend on complex global matrix operations, making it difficult to deploy efficiently in actual underwater scenarios. Summary of the Invention

[0008] To address the problems of high complexity in centralized control, heavy computational burden in distributed control, and insufficient stability and topology adaptability in existing multi-underwater robot collaborative control technologies, this invention provides a flexible consistency control method and system for multi-underwater robot systems. While ensuring system stability and state consistency, it significantly reduces computational and communication complexity and improves the real-time performance and reliability of multi-underwater robot collaborative operations.

[0009] To achieve the above objectives, the present invention adopts the following technical solution:

[0010] The first aspect of the present invention provides a method for elastic consistency control of a multi-underwater robot system.

[0011] A method for resilient consistency control of a multi-underwater robot system includes:

[0012] Discretize and linearize the multi-underwater robot system to obtain a discrete dynamic model;

[0013] Construct a performance index function and combine it with the coupled dynamic behavior between multiple underwater robot systems to characterize the dynamic behavior of multiple underwater robot systems affected by the communication topology graph;

[0014] Based on the discrete dynamics model and performance index function, combined with the centralized optimal control method of the locally decoupled system, the gain matrix of the elastic consistency controller is obtained by solving two local algebraic Riccati equations and combining intermediate parameters.

[0015] Based on the discrete dynamics model and the two gain matrices of the elastic consistency controller, and combined with the robust stability theory of the local controller, an elastic consistency controller is designed; according to the elastic consistency controller matrix spectrum representing the desired sparse mode, the stability conditions of the multi-underwater robot system are obtained.

[0016] Furthermore, the multi-underwater robot system is discretized and linearized to obtain a discrete dynamic model; the methods include:

[0017] The motion of multiple underwater robot systems in the horizontal plane is simplified to a dynamic model of forward movement, lateral movement, and yaw, ignoring lateral, longitudinal, and vertical oscillations;

[0018] Based on the state variables of the multi-underwater robot system, including displacement and velocity, the dynamic model is discretized using the forward Euler discretization method, and a nonlinear perturbation term is introduced to characterize the linearization error and external disturbances, resulting in a discrete dynamic model.

[0019] Furthermore, the communication topology is constructed as follows: with participating robots as nodes, communication channels between robots as edges, the communication relationships between nodes are defined as an adjacency matrix, the information interaction rules between robot nodes are clarified, and the communication topology is constructed.

[0020] Furthermore, the performance index function is expressed by the following formula:

[0021]

[0022] in, Represents a performance metric function; Represents identical and decoupled robots; For the first Status information of the underwater robot. A custom positive definite penalty matrix is ​​used to constrain the state fluctuations of a single robot; This represents the combined effect of the control input and disturbance of a single robot. , for the first The control input for the robot A custom positive definite penalty matrix is ​​used to limit and control energy consumption; This represents the penalty for state differences between robots. A custom positive semidefinite penalty matrix is ​​used to drive the states of multiple robots to converge. For the first The robot is affected by ocean disturbances caused by wind, waves, and currents.

[0023] Furthermore, the method based on the discrete dynamics model and performance index function, combined with the centralized optimal control method for locally decoupled systems, obtains the gain matrix of the elastic consistency controller by solving two local algebraic Riccati equations and combining intermediate parameters. Based on the discrete dynamics model and the two gain matrices of the elastic consistency controller, the elastic consistency controller is designed using the robust stability theory of local controllers. The method includes: calculating the neighbor set and degree of nodes based on the discrete dynamics model and performance index function, combined with the communication topology graph, constructing the degree matrix and Laplace matrix, solving and outputting the eigenvalues ​​of the Laplace matrix; solving two local algebraic Riccati equations based on the discrete dynamics model to obtain the correlation matrix, calculating intermediate parameters and the gain matrix; determining the range of values ​​for the gain margin adjustment parameter by calculating the singular values ​​of the cost matrix and the correlation matrix, and outputting the elastic consistency controller of the target robot.

[0024] Furthermore, the stability conditions of the multi-underwater robot system are obtained based on the spectrum of the elastic consistency controller matrix representing the desired sparse mode. The method includes: constructing a Lyapunov function by analyzing the sparse mode matrix spectrum of the elastic consistency controller, proving the asymptotic stability of the closed-loop system under given conditions, ensuring the consistency of the state of the multi-underwater robot system, and obtaining the stability conditions of the multi-underwater robot system.

[0025] A second aspect of the present invention provides a resilient consistency control system for a multi-underwater robot system.

[0026] A resilient consistency control system for a multi-underwater robot system, comprising:

[0027] The discrete dynamics model construction module is configured to discretize and linearize the multi-underwater robot system to obtain a discrete dynamics model.

[0028] The communication topology and performance index construction module is configured to: construct performance index functions, combine the coupled dynamic behavior between multiple underwater robot systems, and characterize the dynamic behavior of multiple underwater robot systems affected by the communication topology graph.

[0029] The controller gain matrix solving module is configured to: based on the discrete dynamics model and performance index function, combined with the centralized optimal control method of the locally decoupled system, obtain the gain matrix of the elastic and consistent controller by solving two local algebraic Riccati equations and combining intermediate parameters;

[0030] The controller design module is configured to: design an elastic and consistent controller based on the discrete dynamics model and the two gain matrices of the elastic and consistent controller, using the centralized optimal control method of the locally decoupled system and the robust stability theory of the local controller; and obtain the stability conditions of the multi-underwater robot system based on the elastic and consistent controller matrix spectrum representing the desired sparse mode.

[0031] A third aspect of the present invention provides a computer device comprising:

[0032] A processor, adapted to execute computer programs;

[0033] A computer-readable storage medium storing a computer program, which, when executed by a processor, implements the steps in the resilient consistency control method for a multi-underwater robot system as described in the first aspect above.

[0034] A fourth aspect of the present invention provides a computer-readable storage medium storing a computer program adapted to be loaded by a processor and to execute steps in the resilient consistency control method for a multi-underwater robot system as described in the first aspect above.

[0035] The fifth aspect of the present invention provides a computer program product or computer program.

[0036] This invention provides a computer program product or computer program comprising computer instructions stored in a computer-readable storage medium. A processor of a computer device reads the computer instructions from the computer-readable storage medium and executes the computer instructions, causing the computer device to perform the steps in the resilient consistency control method for a multi-underwater robot system as described in the first aspect above.

[0037] Compared with the prior art, the beneficial effects of the present invention are:

[0038] (1) This invention accurately constructs a discrete linearized model of multiple underwater robots by discretizing and linearizing the underwater robot system. At the same time, it introduces the performance index of the associated communication topology to fully characterize the influence of the communication topology on the dynamic behavior of multiple underwater robots. Based on the centralized optimal control method of the local decoupled system and the robust stability theory of the local controller, an elastic consistency controller is designed. The controller gain is obtained by solving two local algebraic Riccati equations with the same dimension as a single underwater robot. There is no need to deal with large-scale centralized matrix operations, which significantly reduces the computational complexity and ensures the efficient realization of system state consistency control. It is suitable for the collaborative operation scenario of multiple underwater robots and provides a stable and reliable control scheme for underwater tasks.

[0039] (2) The present invention uses a connected undirected graph to describe the communication topology of multiple underwater robots. The designed elastic consistency controller is a distributed structure. Each robot only relies on its own state and the state information of its neighboring nodes to realize the control input calculation, without the need for global state information interaction. While ensuring the asymptotic stability of the system, the amount of communication data increases linearly with the number of robots, effectively reducing the transmission burden and interaction overhead of the underwater acoustic communication network, and improving the communication efficiency and real-time response capability of the multi-underwater robot collaborative system.

[0040] (3) Considering unknown disturbances such as ocean wind, waves and currents, the present invention reduces the consumption of computing and communication resources and improves the stability, robustness and environmental adaptability of multi-underwater robot collaborative control, making it suitable for complex long-term underwater operations such as seabed exploration and underwater target tracking. Attached Figure Description

[0041] 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.

[0042] Figure 1This is a flowchart illustrating the elastic consistency control method for a multi-underwater robot system according to an embodiment of the present invention;

[0043] Figure 2 This is a schematic diagram illustrating a multi-underwater robot system and its information interaction, as shown in an embodiment of the present invention.

[0044] Figure 3 This is a diagram illustrating the convergence of positions of multiple AUVs in the x-axis direction, as shown in an embodiment of the present invention.

[0045] Figure 4 This is a diagram illustrating the convergence of positions of multiple AUVs in the y-axis direction, as shown in an embodiment of the present invention.

[0046] Figure 5 This is a diagram illustrating the convergence effect of yaw angle deviations among multiple AUVs as shown in an embodiment of the present invention;

[0047] Figure 6 This is a diagram illustrating the velocity convergence effect in the x-axis direction as shown in an embodiment of the present invention;

[0048] Figure 7 This is a diagram illustrating the velocity convergence effect in the y-axis direction as shown in an embodiment of the present invention;

[0049] Figure 8 This is a diagram illustrating the convergence effect of angular velocities as shown in an embodiment of the present invention;

[0050] Figure 9 This is a structural diagram of the elastic consistency control system of a multi-underwater robot system shown in an embodiment of the present invention;

[0051] Figure 10 This is a structural diagram of a computer device shown in an embodiment of the present invention. Detailed Implementation

[0052] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0053] It should be noted that the following detailed description is illustrative and intended to provide further explanation 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.

[0054] 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.

[0055] As described in the background section, in collaborative operation scenarios involving multiple underwater robots, underwater acoustic communication networks suffer from limited bandwidth and fluctuating transmission delays. Traditional centralized control requires real-time aggregation of all robot status information, which not only exacerbates the communication load but also leads to a decrease in real-time performance due to the exponential increase in computational load with the number of robots. While existing distributed control reduces reliance on global information, it still needs to handle complex multi-node coordination and information synchronization, placing a heavy computational burden on local controllers and making it difficult to adapt to dynamic changes in the communication topology. Furthermore, unknown disturbances in the underwater environment, such as wind, waves, and currents, can also affect the stability of robot state consistency.

[0056] To address this, the present invention provides a resilient consistency control method and system for multiple underwater robot systems. This method utilizes discretized modeling to adapt to digital control, a distributed structure to reduce communication and computation costs, and robust stability analysis to resist disturbances, ensuring efficient state consistency for multiple unmanned underwater robots in complex underwater environments. The following detailed description of the invention's solution is provided through several embodiments.

[0057] Figure 1 This is a flowchart illustrating the elastic consistency control method for a multi-underwater robot system according to an embodiment of the present invention; see also... Figure 1 The method includes:

[0058] Discretize and linearize the multi-underwater robot system to obtain a discrete dynamic model;

[0059] Construct a performance index function and combine it with the coupled dynamic behavior between multiple underwater robot systems to characterize the dynamic behavior of multiple underwater robot systems affected by the communication topology graph;

[0060] Based on the discrete dynamics model and performance index function, combined with the centralized optimal control method of the locally decoupled system, the gain matrix of the elastic consistency controller is obtained by solving two local algebraic Riccati equations and combining intermediate parameters.

[0061] Based on the discrete dynamics model and the two gain matrices of the elastic consistency controller, an elastic consistency controller is designed using the centralized optimal control method for locally decoupled systems and the robust stability theory of local controllers. The stability conditions of the multi-underwater robot system are obtained based on the elastic consistency controller matrix spectrum representing the desired sparse mode.

[0062] The following is a detailed description of the specific implementation process of the elastic consistency control method for the multi-underwater robot system described in this embodiment, including the following steps:

[0063] In step 1, the kinematic and dynamic models of the target robot are established, and the model is discretized using the properties of derivatives.

[0064] (1) Establishing the kinematic model of AUV

[0065] like Figure 2 As shown, assuming multiple underwater robots move in a horizontal plane, with oscillations such as roll, pitch, and heave approaching zero, their motion can be described by wave, sway, and yaw dynamics. A state-space model of a single robot is then established:

[0066] 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. A volume coordinate system is 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:

[0067]

[0068] 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.

[0069] Here is the transformation matrix used to convert linear velocity in body coordinates to volume coordinates:

[0070]

[0071] (2) Establish an AUV dynamic model

[0072] According to the Lagrange mechanics method, the dynamic model of the target AUV can be established in the following form:

[0073]

[0074] 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. This is the quality matrix; The matrix represents the Coriolis matrix and the centripetal force matrix. Here is the damping matrix; In order to control the input amount; in addition, it is also subject to unknown disturbances caused by ocean winds, waves, and currents. . and The following represents an uncertain system:

[0075] , =

[0076] in, and It is nominal. and This is an unknown term. Based on the above kinematic and dynamic models, the system model can be obtained as follows:

[0077]

[0078] Based on the formulas of the system model, the following transformations can be obtained:

[0079]

[0080] in, express The corresponding second derivative, i.e., the acceleration of position and attitude; The inverse matrix of the transformation matrix; This indicates taking the derivative with respect to each element of the transformation matrix; This indicates that the system is at a certain speed. Below, the sum of all forces related to inertia and damping.

[0081] make This represents the position and attitude vector of the underwater robot at time t; Indicates the change in pose over time; This describes the forces generated by external disturbances and internal inertia and damping within the system. After inverse inertial transformation and pose-velocity mapping, the system pose is determined. The equivalent impact produced; Given the description of the robot's posture and velocity information at time t, the following state-space form can be obtained from the transformed system model formula:

[0082]

[0083] in, This indicates the robot's speed and acceleration information; This represents the state transition matrix, which describes the natural evolution of pose and velocity states without external input. This represents the input matrix, describing how external inputs affect the pose and velocity states; Indicates control input, describing the active force applied by the controller to counteract disturbances and internal dynamic effects, and to drive the system to track the desired trajectory; Represents a 3x3 identity matrix; as well as It is bounded.

[0084] To facilitate system analysis and design and improve system performance, the system is discretized. Time in the continuous state is represented by t, and to distinguish the discretized time states, this invention uses k to represent the discretized time states. The system model after forward Euler discretization is as follows:

[0085]

[0086] in, This represents the robot's velocity and acceleration information at time k; , , represents the discretized model parameter matrix. I represents the sampling time, and I represents the identity matrix with the same dimension as matrix A. This represents the force generated at time k by external disturbance and the system's internal inertia, damping, etc. Indicates control input, describing the active force applied by the controller to counteract disturbances and internal dynamic effects, and to drive the system to track the desired trajectory; It represents the combined effect of control input and disturbance.

[0087] Considering that the robot does not rely on direct velocity measurement, three-dimensional position is used as the core state vector to replace the traditional state definition that includes velocity. At the same time, taking into account the uncertainties in the underwater environment such as wind, waves, and currents, process noise interference terms are introduced into the model to quantify the impact of environmental disturbances on the robot's motion state. Finally, a discrete dynamic model that can completely describe the robot's motion trajectory and state change laws is formed, providing an accurate motion basis for subsequent state estimation and consistent control.

[0088] In step 2, the communication topology and performance indicators of multiple underwater robots are constructed.

[0089] This step focuses on the information interaction rules and optimization objectives for collaborative control of multiple underwater robots. Combining underwater communication characteristics and system control requirements, it completes the communication topology modeling and performance index definition. Considering the limited bandwidth of underwater acoustic communication and the need to avoid redundant transmission in multi-node information interaction, 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:

[0090] Define the communication topology. Node set ,in The number of robots participating in the collaboration; edge set If an edge exists Belonging to matrix E, indicating the first The machine can supply the first The machine sends status information; because underwater communication is bidirectional, therefore... Belonging to E is equivalent to Belongs to E; 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 Belongs to E, i.e., robot With machines (Communication connection exists) (like Not belonging to E, 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... Non-diagonal elements satisfy ( ), This indicates the position of an element in the matrix.

[0091] Based on the above definitions, in order to balance the state consistency, control energy consumption, and dynamic response characteristics of multiple underwater robots, we first introduce... Performance metrics of the associated communication topology of identical and decoupled robots The dynamic behavior and control costs of multiple underwater robots are quantified, and are specifically defined as follows:

[0092]

[0093] State penalty for a single underwater robot: For the first Status information of the underwater robot. A custom positive definite penalty matrix is ​​used to constrain the state fluctuations of a single robot, such as avoiding excessive position deviations and sudden changes in posture. The weights are determined by the robot's motion accuracy requirements. This represents the combined effect of control inputs and disturbances on a single robot. Control input penalty term: , for the first The control input for the robot A custom positive definite penalty matrix is ​​used to limit control energy consumption, such as preventing excessive thruster output. The weights are determined by the robot's energy capacity. Inter-robot state difference penalty term: , A custom positive semidefinite penalty matrix is ​​used to promote consistency in the states of multiple robots. The smaller the difference, the smaller the penalty term. The weights are determined by the cooperative localization accuracy requirements. Disturbance compensation term: For the first Incorporating ocean disturbances caused by wind, waves, and currents into the performance indicators of the robot can enhance the robustness of the controller to disturbances.

[0094] Cost function After calculation, it can be represented in the following compact form:

[0095]

[0096] Among them, the penalty matrix and Special structures defined as follows:

[0097]

[0098]

[0099] in, express The state vector of each robot [ ]; express The combined effect vector of the robot's control input and disturbance ; and All of these are penalty matrices that are custom-defined based on the robot's state; Represents the Cartesian product of matrices.

[0100] By using a penalty term for state differences among multiple underwater robots, when the robot With robots When a communication connection exists, the difference in state between the two will be severely penalized, driving the consistency of the state of the information interaction nodes; conversely, the penalty weight for the difference between robots without a communication connection is weaker, which is consistent with the characteristics of distributed control and avoids the introduction of redundant calculations.

[0101] By using graph theory modeling, the scope of information interaction among multiple underwater robots is clarified. The eigenvalues ​​of the Laplace matrix provide key parameters for subsequent controller stability analysis, ensuring the locality of distributed control adapted to underwater communication.

[0102] Step 3: Based on Step 1 and Step 2, obtain the core gain matrix of the controller by solving the local algebraic Riccati equation;

[0103] This step is based on the performance metrics of the discretized model and associated topology of multiple underwater robots. By decomposing the centralized optimal control problem and solving the low-dimensional local algebraic Riccati equation (ARE), the controller gain matrix is ​​efficiently obtained, fundamentally avoiding the large-scale matrix operation burden of traditional centralized control. The specific process is as follows:

[0104] (1) Centralized problem decomposition and localization transformation

[0105] Because the traditional centralized optimal control gain matrix is:

[0106]

[0107] In optimal control theory, control gain This is used to determine the proportional relationship between control inputs and system states, so that the system minimizes a quadratic performance index. , For matrix The inverse matrix, This is the control weight matrix, which reflects the cost of the control input. In practical control, it is undesirable for the control input to be too large, as this may lead to damage to actuators, excessive energy consumption, and other problems. This is used to quantify the cost of controlling the size of the input. It is its inverse matrix, which plays an important role in calculating optimal control gain, etc. The control input matrix describes how control inputs affect the state of each subsystem in a multi-AUV system. , For matrix The transpose of describes the dynamic characteristics of the multi-AUV system itself. An ARE that satisfies the following condition is associated with both state weights. System dynamics and control weight :

[0108]

[0109] and, , .

[0110] Because multi-AUV systems exhibit symmetry—for example, all AUVs have identical dynamics and control weights—submatrices at different locations will be repeated. The self-coupling term corresponding to the state of a single AUV. Inter-coupling terms corresponding to different states of AUV. It is a block identity matrix, corresponding to the dimension of the entire multi-AUV system. This indicates the collective impact of control inputs on the status of each AUV in the entire multi-AUV system after being distributed through the network.

[0111] Traditional centralized control requires consideration of the joint state of all underwater robots (dimension 1). , Build a global ARE for the number of robots, when The time matrix dimension has reached 18, and the computational cost increases accordingly. It grows quadratically. This invention, by analyzing the symmetry and topological correlation of multi-AUV systems, decomposes the global optimal control problem into multiple local problems consistent with the single-AUV dimension:

[0112] By utilizing the consistency of multiple underwater robot models, the global state matrix is ​​decomposed into a superposition of local performance indices through the Kronecker integral solution, which is ultimately transformed into solving two 6th-order local AREs.

[0113] First, define the key auxiliary matrix, and input the weight matrix:

[0114]

[0115] The association weights between the control inputs and state changes of a single robot are represented, and their dimensions are consistent with the state matrix of a single robot. Local synthesis penalty matrix of identical and decoupled robots :

[0116]

[0117] The single state constraint and the difference constraint between multiple robots are integrated as a penalty term for the second local ARE.

[0118] (2) Solve the two local algebraic Riccati equations (ARE).

[0119]

[0120]

[0121] In the formula, It is a symmetric positive definite solution matrix of the equation, representing the state-optimal weights of a single underwater robot, and its elements reflect the degree of influence of different states on stability; It is a state penalty matrix for a single underwater robot, and its positive definiteness ensures that state fluctuations are effectively suppressed. The formula integrates state difference constraints among multiple underwater robots, ensuring that individual robots converge to a unified state of the group during the collaborative process. It is a symmetric positive definite solution, representing the optimal weight of a single robot in a collaborative scenario. Its elements simultaneously consider both its own stability and the consistency of the group. This represents the local comprehensive penalty matrix, which integrates the penalties for individual robot states. Differential penalties between multiple robots This ensures that state differences are suppressed during the collaborative process.

[0122] Step 4: Based on the optimal solutions of the two local AREs in Step 3, the two core gain matrices of the controller are obtained, thereby designing a distributed resilient consistency controller and determining the value range of key adjustment parameters.

[0123] This step uses the optimal solutions to the two local algebraic Riccati equations (ARE) obtained in step 3. , Using [the controller] as the core, the controller gain matrix is ​​derived through algebraic operations, a distributed resilient consistency controller is constructed, and the value range of key adjustment parameters is determined by combining communication topology characteristics and robust stability requirements. The specific content is as follows:

[0124] (1) Calculation of the core gain matrix of the controller

[0125] Based on the two local ARE optimal solutions obtained in step 3, the feedforward gain matrix of the controller is finally obtained by decomposing the multi-AUV state coupling relationship and introducing intermediate parameters. With feedback gain matrix The entire process involves only 6th-order matrix operations (consistent with single AUV dimension).

[0126] Focusing on the steady-state regulation of a single AUV, based on the optimal solution of the first ARE. With single AUV state penalty matrix The calculation yielded: Where R is the control input penalty matrix, used to limit the energy consumption of actuators such as AUV thrusters; It reflects the deviation between the optimal weight of a single AUV state and the basic penalty, ensuring It can effectively suppress fluctuations in its own state. That is... It is a core parameter for single-AUV stability in multi-AUV controllers. Its calculation integrates three layers of logic: optimal state expectation, state deviation penalty, and actuator energy consumption limit, ultimately achieving the goal of making the state of a single AUV as stable as possible with minimal energy consumption.

[0127] Focusing on state consistency adjustment among multiple AUVs, based on intermediate parameters Difference penalty matrix between AUVs The calculation formula is as follows: ,in Indicates to Find the inverse matrix. For matrix The transpose of . The negative sign ensures that when the difference between the AUV and its neighboring states increases, the control input will be adjusted in the opposite direction to reduce the difference; Since the matrix is ​​positive semi-definite, the larger the weights, the faster the AUV converges to a unified state. It is the core parameter for the differences in state between multiple AUVs in a multi-AUV controller. Its calculation integrates three layers of logic: group state correlation, state difference penalty, and adjustment intensity coefficient. Ultimately, it achieves the goal of quickly aligning the states between AUVs using control input, enabling the entire group to coordinate efficiently. The negative sign design further endows it with the intelligent characteristic that the greater the difference, the stronger the reverse adjustment, ensuring that the multi-AUV system can reach consistency within a finite time.

[0128] Combining the basic gain matrices yields the two core gain matrices of the controller, used for subsequent controller architecture design: the feedforward gain matrix. = It integrates the individual AUV's own state adjustment and group cooperative adjustment for the controller's feedforward control term, ensuring that the AUV can maintain basic stable motion even without neighbor information; feedback gain matrix = The group collaborative adjustment part is extracted separately and used for the neighbor feedback control term of the controller to realize state coordination among multiple AUVs.

[0129] (2) Distributed elastic consistency controller architecture design

[0130] Taking advantage of the distributed information interaction characteristics of multiple AUVs, a controller structure is designed to ensure that the control input of each AUV is calculated only from local information, without the need for global state interaction. Specifically, the structure is as follows:

[0131]

[0132] in:

[0133]

[0134]

[0135] in, This indicates finding the minimum eigenvalue of a matrix; This represents finding the largest eigenvalue of a matrix. It is based on finding the largest eigenvalue of the Laplace matrix in the communication topology from step 2. This is combined with indicators reflecting the degree of matching between the system's own stability reserve and feedback adjustment capability. An index that reflects the upper limit of the maximum potential disturbance that the control input will cause to the system. Adjust parameters It can be dynamically adjusted according to task requirements, giving the controller flexible adaptability. The ocean disturbances encountered (defined by the discretized model in step 1, including disturbances caused by wind, waves, and currents) are compensated in reverse to ensure that the disturbances do not disrupt the state consistency of the multiple AUVs, thereby improving the robustness of the controller.

[0136] The specific implementation process of the resilient consistency control scheme for the multi-AUV system described in this invention was completed using the simulation tool Matlab, and its control effect can be further verified and illustrated through the following experimental simulations. In this embodiment, a ring topology communication network composed of four isomorphic AUVs was constructed. This topology has the following characteristics: each AUV adopts the same dynamic structure and sensor configuration; and ring information interaction is achieved through bidirectional communication links. First, based on the discretized dynamic model constructed in step 1 and the connected undirected communication topology defined in step 2, a distributed resilient consensus controller is directly designed by using the pose and velocity sensing data collected by each AUV and solving the optimal solution of the local algebraic Riccati equation obtained in step 3. This controller relies on the optimal feedback gain matrix to dynamically suppress the impact of underwater communication topology fluctuations and ocean wind and wave surge interference on the system's collaborative control accuracy, ensuring that each AUV can still achieve asymptotic consistency with its neighboring nodes even when relying solely on local neighbor information interaction. Second, based on the error dynamic characteristics derived from the error system stability analysis in step 4, the weight allocation strategy of each AUV in the consensus control protocol is dynamically adjusted, assigning higher fusion weights to nodes with stable communication links and less disturbance, thereby improving the overall collaborative control accuracy of the multi-AUV system. Finally, the local state information and neighbor information of each AUV are fused according to the consensus control protocol and used as the input of the distributed resilient consensus controller designed in step 4 to drive the actuators of each UUV to adjust their actions, achieving precise execution of formation or collaborative tasks.

[0137] In this embodiment, a ring topology of 7 AUVs is considered. It is assumed that the 7 underwater robots have the same structure, and their parameters are set as follows: This embodiment only considers the planar motion of the target AUV, so heave motion is ignored. Considering the good static stability of the AUV, it will only generate very small pitch and roll angles during motion, therefore roll and pitch angles are ignored and set to zero. Penalty matrix: , .

[0138] Figure 3 This demonstrates the convergence of positions of multiple AUVs along the x-axis. Figure 4 This shows the positional convergence effect of AUVs in the y-axis direction. Figure 5 This demonstrates the convergence effect of AUV yaw angles. Figure 6 , Figure 7 as well as Figure 8The simulation results demonstrate the convergence effects of velocity and angular velocity in the x-axis and y-axis directions, respectively. Simulation results show that the distributed elastic controller design algorithm proposed in this invention meets the requirements of precise cooperative control. The convergence process is smooth, with no obvious overshoot or oscillation, ensuring the stability and safety of the AUV formation. It exhibits fast convergence characteristics, good robustness, and an efficient distributed computing architecture. This algorithm provides a reliable control solution for the cooperative operation of multiple AUV systems, and is particularly suitable for applications such as underwater exploration, search and rescue, and monitoring.

[0139] Existing technologies for the cooperative control of multi-AUV systems face challenges such as dynamic changes in communication topology, limited information interaction, and uncertainties in environmental interference. Traditional centralized control methods suffer from high computational and communication complexity, making it difficult to meet the requirements of real-time cooperative and high-precision consistent control for multi-AUV systems. This invention proposes a design method for a resilient consistency controller for multi-AUV systems. By discretizing and linearizing the AUV system model, performance indicators characterizing the impact of communication topology are introduced. Combining the centralized optimal control method for locally decoupled systems and the robust stability theory of local controllers, a distributed resilient consistency controller based on two local algebraic Riccati equations is constructed. The controller gain is solved to achieve consistent control of the system state. Simultaneously, by analyzing the matrix spectrum of the desired sparse structure of the distributed controller, the system stability conditions are given. Compared with traditional centralized control algorithms, this invention significantly reduces computational and communication complexity, improves the accuracy and robustness of cooperative control of multi-AUV systems in complex underwater environments, effectively solves the consistency control problem caused by communication limitations and model uncertainties in existing technologies, provides an efficient and reliable solution for underwater multi-robot cooperative operations, and promotes the development and application of underwater unmanned system control technology.

[0140] The above combination Figure 1 The elastic consistency control method for a multi-underwater robot system provided in the embodiments of the present invention has been described in detail. Next, the elastic consistency control system for a multi-underwater robot system provided in the embodiments of the present invention will be described in conjunction with the accompanying drawings.

[0141] Figure 9 This is a schematic diagram of the structure of the elastic consistency control system of a multi-underwater robot system shown in an embodiment of the present invention, with reference to... Figure 9 The system described in this invention includes:

[0142] The discrete dynamics model construction module is configured to discretize and linearize the multi-underwater robot system to obtain a discrete dynamics model.

[0143] The communication topology and performance index construction module is configured to: construct performance index functions, combine the coupled dynamic behavior between multiple underwater robot systems, and characterize the dynamic behavior of multiple underwater robot systems affected by the communication topology graph.

[0144] The controller gain matrix solving module is configured to: based on the discrete dynamics model and performance index function, combined with the centralized optimal control method of the locally decoupled system, obtain the gain matrix of the elastic and consistent controller by solving two local algebraic Riccati equations and combining intermediate parameters;

[0145] The controller design module is configured to: design an elastic and consistent controller based on the discrete dynamics model and the two gain matrices of the elastic and consistent controller, using the centralized optimal control method of the locally decoupled system and the robust stability theory of the local controller; and obtain the stability conditions of the multi-underwater robot system based on the elastic and consistent controller matrix spectrum representing the desired sparse mode.

[0146] In some embodiments, the multi-underwater robot system is discretized and linearized to obtain a discrete dynamic model; this includes: simplifying the motion of the multi-underwater robot system in the horizontal plane into a dynamic model of forward movement, lateral movement, and yaw, ignoring lateral, longitudinal, and vertical oscillations; based on the state variables of the multi-underwater robot system, including displacement and velocity, the dynamic model is discretized using the forward Euler discretization method, and a nonlinear perturbation term is introduced to characterize the linearization error and external disturbances, thus obtaining a discrete dynamic model.

[0147] In some embodiments, the communication topology is constructed by defining the communication relationships between nodes as adjacency matrices, taking the robots participating in the collaboration as nodes, the communication channels between robots as edges, clarifying the information interaction rules between robot nodes, and constructing the communication topology.

[0148] In some embodiments, the performance metric function is expressed by the following formula:

[0149]

[0150] in, Represents a performance metric function; Represents identical and decoupled robots; For the first Status information of the underwater robot. A custom positive definite penalty matrix is ​​used to constrain the state fluctuations of a single robot; This represents the combined effect of the control input and disturbance of a single robot. , for the first The control input for the robot A custom positive definite penalty matrix is ​​used to limit and control energy consumption; This represents the penalty for state differences between robots. A custom positive semidefinite penalty matrix is ​​used to drive the states of multiple robots to converge. For the first The robot is affected by ocean disturbances caused by wind, waves, and currents.

[0151] In some embodiments, the method based on a discrete dynamics model and performance index function, combined with a centralized optimal control method for locally decoupled systems, obtains the gain matrix of the resilient consistency controller by solving two local algebraic Riccati equations and incorporating intermediate parameters. Based on the discrete dynamics model and the two gain matrices of the resilient consistency controller, and employing a centralized optimal control method for locally decoupled systems and the robust stability theory of local controllers, the resilient consistency controller is designed. This includes: calculating the neighbor set and degree of nodes based on the discrete dynamics model and performance index function, combined with the communication topology graph, constructing the degree matrix and Laplace matrix, solving and outputting the eigenvalues ​​of the Laplace matrix; solving two local algebraic Riccati equations based on the discrete dynamics model to obtain the correlation matrix, calculating intermediate parameters and the gain matrix; determining the range of values ​​for the gain margin adjustment parameter by calculating the singular values ​​of the cost matrix and the correlation matrix, and outputting the resilient consistency controller for the target robot.

[0152] In some embodiments, obtaining the stability conditions of the multi-underwater robot system based on the spectrum of the elastic consistency controller matrix representing the desired sparse modes includes: constructing a Lyapunov function by analyzing the sparse mode matrix spectrum of the elastic consistency controller, proving the asymptotic stability of the closed-loop system under given conditions, ensuring the consistency of the state of the multi-underwater robot system, and obtaining the stability conditions of the multi-underwater robot system.

[0153] According to embodiments of the present invention, the resilient consistency control system of a multi-underwater robot system can correspond to the execution of the methods described in the embodiments of the present invention, and the above and other operations and / or functions of each module of the resilient consistency control system of the multi-underwater robot system are respectively for implementing Figure 1 For the sake of brevity, the corresponding processes of each method in the code will not be elaborated here.

[0154] See Figure 10The diagram shows the structure of a computer device, which includes a processor, a communication interface, and a computer-readable storage medium. The processor, communication interface, and computer-readable storage medium are connected via a bus or other means. The communication interface is used to receive and send data. The computer-readable storage medium can be stored in the computer device's memory. The computer-readable storage medium stores computer programs, including program instructions, and the processor executes the program instructions stored in the computer-readable storage medium. The processor (or CPU, Central Processing Unit) is the computing and control core of the computer device, adapted to implement one or more instructions, specifically adapted to load and execute one or more instructions to achieve the corresponding steps in the embodiment of the resilient consistency control method for a multi-underwater robot system.

[0155] This embodiment provides a computer-readable storage medium (Memory), which is a memory device in a computer device used to store programs and data. It is understood that the computer-readable storage medium here can include both the built-in storage medium in the computer device and extended storage media supported by the computer device. The computer-readable storage medium provides storage space that stores the processing system of the computer device.

[0156] Furthermore, this storage space also contains one or more instructions suitable for loading and execution by the processor. These instructions can be one or more computer programs (including program code). It should be noted that the computer-readable storage medium here can be high-speed RAM memory or non-volatile memory, such as at least one disk storage device; optionally, it can also be at least one computer-readable storage medium located remotely from the aforementioned processor.

[0157] In one embodiment, the computer-readable storage medium stores one or more instructions; the processor loads and executes one or more instructions stored in the computer-readable storage medium to implement the corresponding steps in the above-described embodiment of the resilient consistency control method for a multi-underwater robot system.

[0158] This embodiment provides a computer program product or computer program that includes computer instructions stored in a computer-readable storage medium. A processor of a computer device reads the computer instructions from the computer-readable storage medium and executes the computer instructions, causing the computer device to perform the corresponding steps in the above-described embodiment of the resilient consistency control method for a multi-underwater robot system.

[0159] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of hardware embodiments, software embodiments, or embodiments combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage and optical storage) containing computer-usable program code.

[0160] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0161] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0162] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0163] Those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware. The program can be stored in a computer-readable storage medium, and when executed, it can include the processes of the embodiments of the above methods. The storage medium can be a magnetic disk, optical disk, read-only memory (ROM), or random access memory (RAM), etc.

[0164] 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.

Claims

1. A method for elastic consistency control of a multi-underwater robot system, characterized in that, include: Discretize and linearize the multi-underwater robot system to obtain a discrete dynamic model; Construct a performance index function and combine it with the coupled dynamic behavior between multiple underwater robot systems to characterize the dynamic behavior of multiple underwater robot systems affected by the communication topology graph; Based on the discrete dynamics model and performance index function, combined with the centralized optimal control method of the locally decoupled system, the gain matrix of the elastic consistency controller is obtained by solving two local algebraic Riccati equations and combining intermediate parameters. Based on the discrete dynamics model and the two gain matrices of the elastic consensus controller, an elastic consensus controller is designed using the centralized optimal control method for locally decoupled systems and the robust stability theory of local controllers. The stability conditions of the multi-underwater robot system are obtained based on the elastic consensus controller matrix spectrum representing the desired sparse mode. Based on the discrete dynamics model and performance index function, combined with the communication topology graph, the neighbor set and degree of the node are calculated, the degree matrix and Laplace matrix are constructed, and the eigenvalues ​​of the Laplace matrix are solved and output. By combining the discrete dynamics model, the correlation matrix is ​​obtained by solving two local algebraic Riccati equations, and the intermediate parameters and gain matrix are calculated. By calculating the singular values ​​of the cost matrix and the correlation matrix, the range of values ​​for the gain margin adjustment parameter is determined, and the elastic consistency controller of the target robot is output. Taking advantage of the distributed information interaction characteristics of multiple AUVs, a controller structure is designed to ensure that the control input of each AUV is calculated only from local information, without the need for global state interaction. Specifically, the structure is as follows: in: in, This indicates finding the minimum eigenvalue of a matrix; This indicates finding the largest eigenvalue of a matrix.

2. The elastic consistency control method for a multi-underwater robot system according to claim 1, characterized in that, Discretization and linearization are performed on a multi-underwater robot system to obtain a discrete dynamic model; the methods include: The motion of multiple underwater robot systems in the horizontal plane is simplified to a dynamic model of forward movement, lateral movement, and yaw, ignoring lateral, longitudinal, and vertical oscillations; Based on the state variables of the multi-underwater robot system, including displacement and velocity, the dynamic model is discretized using the forward Euler discretization method, and a nonlinear perturbation term is introduced to characterize the linearization error and external disturbances, resulting in a discrete dynamic model.

3. The elastic consistency control method for a multi-underwater robot system according to claim 1, characterized in that, The communication topology is as follows: with participating robots as nodes, communication channels between robots as edges, the communication relationships between nodes are defined as an adjacency matrix, the information interaction rules between robot nodes are clarified, and the communication topology is constructed.

4. The elastic consistency control method for a multi-underwater robot system according to claim 1, characterized in that, The performance index function is expressed by the following formula: in, Represents a performance metric function; Represents identical and decoupled robots; For the first Status information of the underwater robot. A custom positive definite penalty matrix is ​​used to constrain the state fluctuations of a single robot; This represents the combined effect of the control input and disturbance of a single robot. , for the first The control input for the robot A custom positive definite penalty matrix is ​​used to limit and control energy consumption; This represents the penalty for state differences between robots. A custom positive semidefinite penalty matrix is ​​used to drive the states of multiple robots to converge. For the first The robot is affected by ocean disturbances caused by wind, waves, and currents.

5. The elastic consistency control method for a multi-underwater robot system according to claim 1, characterized in that, The method involves obtaining the stability conditions of a multi-underwater robot system based on the spectrum of the elastic consistency controller matrix representing the desired sparse modes. The method includes: constructing a Lyapunov function by analyzing the sparse mode matrix spectrum of the elastic consistency controller, proving the asymptotic stability of the closed-loop system under given conditions, ensuring the consistency of the state of the multi-underwater robot system, and obtaining the stability conditions of the multi-underwater robot system.

6. A resilient consistency control system for a multi-underwater robot system, characterized in that, include: The discrete dynamics model construction module is configured to discretize and linearize the multi-underwater robot system to obtain a discrete dynamics model. The communication topology and performance index construction module is configured to: construct performance index functions, combine the coupled dynamic behavior between multiple underwater robot systems, and characterize the dynamic behavior of multiple underwater robot systems affected by the communication topology graph. The controller gain matrix solving module is configured to: based on the discrete dynamics model and performance index function, combined with the centralized optimal control method of the locally decoupled system, obtain the gain matrix of the elastic and consistent controller by solving two local algebraic Riccati equations and combining intermediate parameters; The controller design module is configured to: design an elastic and consistent controller based on the discrete dynamics model and the two gain matrices of the elastic and consistent controller, using the centralized optimal control method for locally decoupled systems and the robust stability theory of local controllers; and obtain the stability conditions of the multi-underwater robot system based on the elastic and consistent controller matrix spectrum representing the desired sparse mode. Based on the discrete dynamics model and performance index function, combined with the communication topology graph, the neighbor set and degree of the node are calculated, the degree matrix and Laplace matrix are constructed, and the eigenvalues ​​of the Laplace matrix are solved and output. By combining the discrete dynamics model, the correlation matrix is ​​obtained by solving two local algebraic Riccati equations, and the intermediate parameters and gain matrix are calculated. By calculating the singular values ​​of the cost matrix and the correlation matrix, the range of values ​​for the gain margin adjustment parameter is determined, and the elastic consistency controller of the target robot is output. Taking advantage of the distributed information interaction characteristics of multiple AUVs, a controller structure is designed to ensure that the control input of each AUV is calculated only from local information, without the need for global state interaction. Specifically, the structure is as follows: in: in, This indicates finding the minimum eigenvalue of a matrix; This indicates finding the largest eigenvalue of a matrix.

7. A computer device, characterized in that, A processor, adapted to execute computer programs; A computer-readable storage medium storing a computer program, which, when executed by the processor, implements the steps of the resilient consistency control method for a multi-underwater robot system as described in any one of claims 1-5.

8. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program adapted to be loaded by a processor and execute the steps of the resilient consistency control method for a multi-underwater robot system as described in any one of claims 1-5.

9. A computer program product, characterized in that, The computer program product includes a computer program that, when executed by a processor, implements the steps in the resilient consistency control method for a multi-underwater robot system as described in any one of claims 1-5.

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