Robot system distributed formation control method and device based on U-K theory

Abstract

The invention provides a robot system distributed formation control method and device based on a U-K theory, and the method comprises the steps: building a dynamic model of a networked robot system through employing a Newton-Euler mechanics method according to system parameters in the networked robot system moving in a two-dimensional space; according to a preset algebraic graph theory strategy, a communication relation between robots is established, a communication topological graph of a directed weighted graph with a directed spanning tree is set, and an expected formation control target is converted into a constraint equation. And combining the kinetic model with a U-K equation to calculate servo control force required by the robot system under the incomplete constraint to complete an expected formation control target, and designing a distributed formation controller under the condition of no leader by adopting a preset distributed formation control algorithm based on the servo control force. According to the technical scheme, the technical problem of lack of universality in related technologies is solved, the application range is expanded, generality and universality are achieved, and formation control stability is guaranteed on the basis of simplifying operation of control force.

Description

Technical Field

[0001] The present invention relates to the technical field of intelligent robots, and in particular to a distributed formation control method and device for a robot system based on UK (Udwadia-Kalaba). Background Art

[0002] In recent years, the cooperative control problem of networked mobile robot systems has attracted extensive attention. Compared with a single robot, a networked mobile robot system can demonstrate stronger capabilities in tasks such as cooperative search and cooperative handling. However, mobile robots are usually a type of system subject to non-holonomic constraints, and their lateral motion is subject to certain restrictions, which makes the formation control of mobile robots a hot research issue.

[0003] In the related art, most of the research on the formation control problem of networked mobile robot systems is based on the kinematic model of the robot. For example, the Chinese patent "CN116954221A" proposes a distributed inherent time formation control method, and the Chinese patent "CN115729239A" proposes a predetermined time consistency control method. These methods mainly establish a nonlinear kinematic model of the robot, and then use the linearization method to convert the nonlinear model into a linear model. However, this controller design based on the kinematic model is difficult to reflect the actual dynamic characteristics of the robot system. In actual applications, the robot uses a servo mechanism to generate a driving torque to achieve movement, so the control strategy based solely on the kinematic model has limitations in some scenarios.

[0004] To overcome this problem, some researchers have tried to design formation control strategies based on dynamic models. For example, the Chinese patent "CN111596690A" uses the Newton-Euler method to establish a dynamic model of a quadrotor flying robot, and performs formation control on this basis. However, this type of method usually requires the introduction of multiple auxiliary variables, which increases the computational complexity and the interpretability of the auxiliary variables is poor. In this regard, the UK equation proposed by Udwadia and Kalaba can effectively simplify the calculation process when solving the control force of a system with complete constraints and incomplete constraints, and the obtained control force is the minimum control force.

[0005] In addition, most existing formation control methods are based on undirected and unweighted communication topology graphs. Although this topology graph is simple, its application has certain limitations. For example, the limited time competition formation control method proposed by the Chinese patent "CN116276964A" adopts an undirected and unweighted graph. However, the undirected and unweighted graph is a special communication topology graph and cannot be extended to a more complex directed weighted graph. In addition, the Baumgarte correction form used in the research based on the UK method is only applicable to the case of undirected graphs, so it is insufficient under more complex topological structures. Therefore, in order to study the communication topological relationship based on directed weighted graphs, the Baumgarte correction form used also needs to be innovated. And because directed weighted graphs can more widely describe communication networks in practical applications, the formation control method designed based on directed weighted graphs has stronger universality and versatility.

[0006] In general, the existing technologies have the following deficiencies: (1) Control methods based on kinematic models are difficult to reflect the dynamic characteristics of robot systems and it is difficult to obtain good control effects in practical applications; (2) The introduction of auxiliary variables increases the computational complexity, and these variables are difficult to interpret; (3) Existing methods are mostly based on the communication topology of undirected unweighted graphs and lack universality. (4) Existing Baumgarte correction forms are mostly based on the communication topology of undirected unweighted graphs and cannot be extended to the communication topology of directed weighted graphs. The solution to the above problems requires further technological innovation. Summary of the invention

[0007] The main purpose of the present invention is to propose a distributed formation control method and device for a robot system based on UK theory, so as to at least solve the technical problems of lack of universality and innovation in related technologies.

[0008] A first aspect of the present invention provides a distributed formation control method for a robot system based on UK theory, comprising the following steps:

[0009] Step S1, establishing a dynamic model of the networked robot system using the Newton-Euler mechanics method according to system parameters in the networked robot system moving in two-dimensional space; wherein the networked robot system includes n robots, where n is a positive integer;

[0010] Step S2, establishing a communication relationship between the robots according to a preset algebraic graph theory strategy, and setting a communication topology graph corresponding to the communication relationship; wherein the communication topology graph includes a directed weighted graph having a directed spanning tree;

[0011] Step S3, converting the expected formation control target into a constraint equation according to the communication topology diagram, and combining the dynamic model with the UK equation to calculate the servo control force required for the robot system subject to non-holonomic constraints to achieve the expected formation control target;

[0012] Step S4, based on the servo control force, using a preset distributed formation control algorithm to design a distributed formation controller without a leader; wherein the distributed formation controller is used to perform formation control on the networked robot system;

[0013] Step S5, performing stability analysis and simulation verification on the networked robot system according to the distributed formation controller.

[0014] A second aspect of the present invention provides a distributed formation control device for a robot system based on UK theory, comprising:

[0015] A dynamic model module, used to establish a dynamic model of a networked robot system using a Newton-Euler mechanics method according to system parameters in the networked robot system moving in two-dimensional space; wherein the networked robot system includes n robots, where n is a positive integer;

[0016] A communication topology graph module, used to establish a communication relationship between the robots according to a preset algebraic graph theory strategy, and set a communication topology graph corresponding to the communication relationship; wherein the communication topology graph includes a directed weighted graph with a directed spanning tree;

[0017] A servo control force module is used to convert the expected formation control target into a constraint equation according to the communication topology diagram, and to calculate the servo control force required by the robot system subject to non-holonomic constraints to achieve the expected formation control target by combining the dynamic model with the UK equation;

[0018] A formation control module is used to design a distributed formation controller in the absence of a leader based on the servo control force and using a preset distributed formation control algorithm; wherein the distributed formation controller is used to perform formation control on the networked robot system.

[0019] A third aspect of the present invention provides an electronic device, including a memory, a processor and a bus;

[0020] The bus is used to realize the connection and communication between the memory and the processor;

[0021] The processor is used to execute the computer program stored in the memory;

[0022] When the processor executes the computer program, the steps in the distributed formation control method of the robot system based on UK theory provided in the first aspect are implemented.

[0023] A fourth aspect of the present invention provides a computer-readable storage medium having a computer program stored thereon, characterized in that when the computer program is executed by a processor, the steps of the distributed formation control method for a robot system based on UK theory provided in the first aspect are implemented.

[0024] The robot system distributed formation control method and device based on UK theory of the present invention have the following beneficial effects:

[0025] (1) Not only does it use the dynamic model of the mobile robot and reflect the dynamic characteristics of the robot, but it is also based on a directed weighted graph with a directed spanning tree. Since the directed weighted graph is the most common communication topology graph, the formation control method of the present invention can be extended to a formation control scheme based on any communication topology graph, thereby solving the problem of lack of universality in related technologies, avoiding the phenomenon of lack of universality, expanding the scope of application, and being more general and universal.

[0026] (2) The present invention uses the UK method and the innovative Baumgarte correction form to establish a formation controller for a networked mobile robot system. The control force obtained is still the minimum control force, which simplifies the calculation of the control force and calculates a better control force.

[0027] (3) The formation controller established by the present invention is a distributed controller that only requires the neighbor information of each robot in the communication network, rather than the information of all robots. This greatly reduces the communication burden while improving communication efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0029] Figure 1 This is a schematic diagram of the steps of a distributed formation control method for a robot system based on UK theory provided in one embodiment of the present application;

[0030] Figure 2 It is a schematic diagram of the geometric model of the mobile robot;

[0031] Figure 3 is a communication topology graph having a directed spanning tree;

[0032] Figure 4 This is the motion trajectory diagram of the robot in the first set of experiments;

[0033] Figure 5 is the velocity diagram of the robot in the x direction in the first set of experiments;

[0034] Figure 6 This is the velocity diagram of the robot in the y direction in the first set of experiments;

[0035] Figure 7 This is the error convergence diagram in the first set of experiments;

[0036] Figure 8 This is the motion trajectory diagram of the robot in the second group of experiments;

[0037] Fig. 9 is the velocity diagram of the robot in the x direction in the second set of experiments;

[0038] Fig.10 is the velocity diagram of the robot in the y direction in the second set of experiments;

[0039] Fig.11 This is the error convergence diagram in the second set of experiments;

[0040] Fig.12 A schematic diagram of module connections of a UK-based distributed formation device for a robot system provided in an embodiment of the present application;

[0041] Fig.13 A schematic diagram of the structure of an electronic device provided in an embodiment of the present application.

[0042] The functions, features and advantages of the present invention will be further described in conjunction with the embodiments and with reference to the accompanying drawings. Figure 4 To Attachment Fig.11 A variety of different colors are used to indicate. DETAILED DESCRIPTION

[0043] It should be understood that the specific embodiments described herein are only used to explain the present invention, and are not used to limit the present invention.

[0044] It should be noted that related terms such as "first", "second", etc. can be used to describe various components, but these terms do not limit the components. These terms are only used to distinguish one component from another component. For example, without departing from the scope of the present invention, the first component can be referred to as the second component, and the second component can also be referred to as the first component similarly. The term "and / or" refers to any one or more combinations of related items and description items. In addition, in order to better illustrate the present invention, numerous specific details are given in the specific embodiments below. Those skilled in the art will understand that the present invention can also be implemented without these specific details. In some other examples, the well-known structures and components are not described in detail to highlight the main purpose of the present invention. In addition, the following embodiments "*" all represent multiplication operations, and the end "." in the calculation formula represents a period ".". It should also be noted that the Udwadia-Kalaba theory (Udwadia-Kalaba Equation) is a method for solving the constraint force of a system subject to a complete constraint and a non-complete constraint. This method was proposed by Udwadia and Kalaba in 1992, and can directly obtain an explicit solution of a constrained dynamic system without introducing Lagrange multipliers. The Udwadia-Kalaba equation provides a concise and efficient tool for studying systems with non-holonomic constraints or complex constraints.

[0045] See also Figure 1 The embodiment of the present invention provides a distributed formation control method for a robot system based on UK theory, which at least includes the following steps:

[0046] Step S1, according to the system parameters of the networked robot system moving in two-dimensional space, a dynamic model of the networked robot system is established by using the Newton-Euler mechanics method.

[0047] The networked robot system includes n robots, where n is a positive integer. In step S1, a dynamic model of the networked robot system is established by the Newton-Euler mechanics method. Based on the Newton-Euler method, combined with Newton's second law and the Euler equation, it is used to analyze the system parameters of the networked robot system in two-dimensional space motion, such as system parameters that can reflect the position, velocity, acceleration and other motion states of each robot, determine the force conditions of the robot in two-dimensional space, and thus construct a dynamic model of the networked robot system.

[0048] Step S2, establishing a communication relationship between robots according to a preset algebraic graph theory strategy, and setting a communication topology graph corresponding to the communication relationship.

[0049] Wherein, the communication topology diagram includes a directed weighted graph with a directed spanning tree. In step S2, the communication relationship between the robots is established through an algebraic graph theory strategy. In a networked robot system, the communication relationship between each robot is very important. In order to better realize formation control, the method of algebraic graph theory is used to describe and establish these communication relationships. Optionally, the communication topology diagram can be represented in the form of a directed weighted graph, which includes a directed spanning tree, which can ensure that there are effective communication links between all robots. In the communication topology diagram, the weight of each edge represents the communication strength or control weight between the robots. Through this directed weighted graph structure, effective communication between multiple robots can be achieved.

[0050] Step S3, converting the expected formation control target into a constraint equation according to the communication topology diagram, and combining the dynamic model with the UK equation to calculate the servo control force required for the robot system subject to non-holonomic constraints to achieve the expected formation control target.

[0051] Specifically, in step S3, the communication topology diagram is used as a basis to convert the expected formation control target into a constraint equation. Combined with the UK equation, the servo control force required by the robot system to achieve the formation control target under non-holonomic constraints is further calculated. The UK equation is a commonly used analysis method combining kinematics and dynamics, which is used to describe and solve robot control problems under constrained conditions. By combining the dynamic model with the UK equation, the servo control force required for each robot to achieve the target can be accurately calculated, thereby providing a basis for controller design.

[0052] Step S4, based on the servo control force, a preset distributed formation control algorithm is used to design a distributed formation controller in the absence of a leader.

[0053] Among them, the distributed formation controller is used to perform formation control on the networked robot system. In step S4, based on the servo control force calculated above, a distributed formation control algorithm is used to design a distributed formation controller. Compared with the traditional centralized formation controller, the distributed formation controller only needs to obtain the information of neighbors, which greatly reduces the communication burden and improves the communication efficiency. At the same time, compared with the centralized formation controller, the distributed formation controller improves the robustness and flexibility of the formation controller.

[0054] Combining the above steps S1 to S4, the present invention establishes a dynamic model of the robot based on the Newton-Euler method. Compared with the kinematic model of the robot, the formation controller designed based on the dynamic model can not only better reflect the dynamic characteristics of the robot, but also better achieve the control goal, and obtain a wider range of practical applications. Secondly, the present invention establishes a communication topological relationship between robots based on a directed weighted graph with a directed spanning tree. The undirected unweighted graph is a special form of a directed weighted graph. Compared with the communication topology based on the undirected unweighted graph, the present invention is more general and universal. Finally, the present invention uses the UK method and the innovative Baumgarte correction form to design a distributed formation controller for a networked robot system, and verifies the effectiveness of the formation controller through stability proof and numerical simulation experiments.

[0055] See also Figure 2 The embodiment of the present invention further provides a robot system distributed formation control method based on UK theory. Compared with the previous embodiment, after step S4, it further includes:

[0056] Step S5, performing stability analysis and simulation verification on the networked robot system according to the distributed formation controller.

[0057] In this embodiment, after step S1 to step S4, the networked robot system is subjected to stability analysis and simulation verification according to the distributed formation controller. The effectiveness and reliability of the distributed formation controller can be further verified, that is, the system is subjected to stability analysis and simulation verification. The specific implementation methods for stability analysis and simulation verification will be described in subsequent embodiments and will not be repeated here.

[0058] In some optional implementations of this embodiment, with respect to step S1, step S1 specifically includes:

[0059] Obtain system parameters in the networked robot system; the system parameters include the robot's center of mass coordinate x-axis component x, the robot's center of mass coordinate y-axis component y, the angle θ between the robot's velocity direction and the positive direction of the x-axis, the robot's mass m, the robot's moment of inertia J around the center of mass, the lateral distance l between the robot's center of mass and the wheel center, the wheel radius d, the robot's speed v, and the driving torque u of the motor acting on the right rear wheel r , the driving torque u of the motor acting on the left rear wheel l , the driving force generated by the robot's right rear wheel f r and the driving force f generated by the robot's left rear wheel l .

[0060] Specifically, the system parameters of a networked robot system involve multiple physical quantities and kinematic parameters, which are usually used to represent the robot's position in the environment, its motion state, and the torque and driving force associated with the drive wheels. Understanding and accurately obtaining these parameters is crucial to controlling the stability, navigation capability, and operational performance of a networked robot system. System parameters can help accurately control and model the robot.

[0061] It should also be noted that a networked robot system refers to a robot system in which multiple robots or robots and a control center are connected and coordinated through a network to achieve information sharing and collaborative work. They can transmit control instructions, status information, environmental perception data, and task information through wired networks, wireless networks, cloud computing platforms, etc., to complete complex tasks.

[0062] Combining the Newton-Euler mechanics method, a dynamic model of the networked robot system is established; wherein the dynamic model includes dynamic equations.

[0063] Among them, the combination of Newton-Euler mechanics methods includes:

[0064] See also Figure 2 , define the generalized coordinates of the mobile robot q = (x, y, θ) T , where (x, y) is the position coordinate of the center of mass of the mobile robot, and θ represents the attitude angle of the mobile robot in the inertial coordinate system.

[0065] The system parameters are shown in Table 1 (geometric model of mobile robot), where u r and u l The direction in which the mobile robot moves forward is positive.

[0066] Table 1

[0067]

[0068] In the robot's forward direction, Newton's laws of motion give:

[0069]

[0070] Which meets

[0071] The speed of the robot is expressed as:

[0072]

[0073] Taking the derivative of the robot's velocity with respect to time, we get:

[0074]

[0075] Substituting equation (1.3) into (1.1) we get:

[0076]

[0077] The robot has nonholonomic constraints, which can be expressed as:

[0078]

[0079] Taking the first-order differential of equation (1.5) with respect to time, we can obtain:

[0080]

[0081] From the angular momentum theorem we can get:

[0082]

[0083] Right now

[0084]

[0085] Writing equations (1.4), (1.6), and (1.8) in matrix form yields:

[0086]

[0087] The dynamic equation of the networked robot system is expressed as:

[0088]

[0089] in,

[0090]

[0091] Among them, the Chinese meaning and explanation of each element of the dynamic equation are as follows:

[0092] M(q, t) represents the mass matrix. M is a matrix that represents the inertia or mass characteristics of the system, which is usually related to the generalized coordinates q of the robot and time t. It represents the change of mass or inertia in different postures or states of the robot system. The mass matrix reflects the mass distribution and inertial characteristics of each component of the robot system. q represents the generalized coordinates, which are used to describe the position information of the system. The generalized coordinates can include the position, angle, relative position between the links, etc. of the robot in two-dimensional or three-dimensional space. It represents the second-order derivative of the generalized coordinate q with respect to time, that is, the generalized acceleration, which represents the acceleration change of each generalized coordinate (such as position or angle) in the robot system over time. In addition, is the generalized coordinate q, the generalized velocity And the generalized force or control force term related to time t. It refers to the constraint force generated when the system is subject to constraints. This constraint force is to ensure that the generalized coordinate q of the system meets the predetermined constraint conditions. For example, in a robot formation, in order to maintain the relative position between robots, a certain constraint force may be generated to limit the free movement of the robots.

[0093] In addition, the Chinese meanings and explanations of the elements involved in formulas 1.1 to 1.10 are as follows: represents the velocity component along the x direction, represents the velocity component along the y direction, represents the acceleration component in the x direction, represents the acceleration component in the y direction, represents the rate of change of angle θ with time, Represents the angular acceleration of the object.

[0094] Combining the above formulas 1.1 to 1.10, the dynamic model of the robot is established through Newton-Euler mechanics, which can not only reflect the dynamic characteristics of the robot, but also has the non-holonomic characteristics of full integration. Compared with the kinematic model of the robot, the formation controller designed based on the dynamic model can not only better reflect the dynamic characteristics of the robot, but also better achieve the control objectives, and has been widely used in practice.

[0095] In some optional implementations of this embodiment, with respect to step S2, in step S2, an algebraic graph theory strategy is a method for representing and analyzing a multi-agent system using a graph structure. In this technical field, robots are regarded as nodes of a graph, and communication links are regarded as edges of a graph. Through algebraic graph theory, the communication relationship between robots and the influence of the topological structure on the propagation and control of global information can be easily defined and described. A typical communication topology graph should have connectivity and effective information propagation capabilities.

[0096] In this embodiment, the communication topology graph is in the form of a directed weighted graph, in which each node represents a robot and each directed edge represents a communication link between robots. The construction of a directed weighted graph should meet the following conditions: there is at least one directed spanning tree in the graph. This ensures that the communication links between all robots are connected and that information can be transmitted from any robot to all other robots. The weight of the edge is used to represent the communication strength or importance between robots. This can be set according to the actual communication distance, signal quality or control weight. Component function: The main components of the communication topology graph include nodes and edges. Node: represents each robot in the networked robot system. Edge: represents the information transmission channel between robots, which has directionality and weight properties.

[0097] Assume that the communication topology between robots in a networked robot system is composed of a directed graph Represents, where Ω = {1, 2, ..., n} represents the set of mobile robot nodes in the network, represents the set of edges between mobile robot nodes in the network, is the adjacency matrix;

[0098] If (i, j)∈Θ, it means that nodes i and j are neighbors, and node j can obtain the status information of node i;

[0099] a ij is an element in the adjacency matrix. If (j, i)∈Θ, then a ij > 0, otherwise a ij =0;

[0100] Degree Matrix The elements in If i≠j, then d ij = 0, the Laplace matrix associated with the communication topology graph g is defined as in, satisfy

[0101] Furthermore, through the corresponding lemma we can get:

[0102] picture The corresponding Laplace matrix The rank of is N-1, that is If and only if the graph With spanning tree.

[0103] Directed Graph has a directed spanning tree if and only if At least one node has a directed path to all other nodes. In this paper, we assume that the directed graph A directed weighted graph with a directed spanning tree, the communication topology diagram established is as follows Figure 3 As shown (the communication topology diagram is a directed weighted graph with a directed spanning tree).

[0104] The corresponding Laplace matrix is:

[0105]

[0106] The Laplace matrix is ​​generated based on the structure of the communication topology graph. It contains the degree of each node in the graph and the connectivity relationship between adjacent nodes. In an undirected or directed graph, the Laplace matrix can characterize the direct connection relationship between nodes and the connectivity of the overall topology. The eigenvalues ​​and eigenvectors of the Laplace matrix can reflect certain properties of the topology graph, such as whether the graph is connected. In other words, the role of the Laplace matrix in the communication topology graph is mainly reflected in representing the topology structure and connectivity, measuring consistency, stability analysis, describing information flow, and detecting faults.

[0107] In summary, in a multi-robot system, each robot exchanges information through the set communication topology. The communication topology can meet the connectivity requirements in algebraic graph theory to ensure that global information can be effectively transmitted. Through this topology, all robots can receive the status information of other robots and make decisions and controls based on this information, thereby realizing global formation or collaborative tasks. Through the above method, the established communication topology can effectively describe and regulate the communication relationship between robots, providing a solid foundation for subsequent control algorithms.

[0108] In some optional implementations of this embodiment, with respect to step S3, in step S3, specifically including:

[0109] Acquire a formation control task; wherein the formation control task is described as making the robots in the multi-wheeled robot system form a desired formation shape and keep a fixed distance between each other;

[0110] Consider a networked multi-robot system with n identical wheeled robots, which are numbered from 1 to n. The directed communication topology of the robot system is given by It means that Ω={1,2,…,n}, The corresponding Laplace matrix is

[0111] Let q i =(x i ,y i ,θ i ) T represents the generalized coordinates of the i-th wheeled robot in the system, and the dynamic model of the system is expressed as:

[0112]

[0113] in,

[0114] M=diag{M1,…,M n},

[0115] make represents the desired formation of the system. The formation control problem is to enable multiple robots to form the desired formation shape under the action of the controller. The control objective is expressed as:

[0116]

[0117] Rewrite (1.12) as:

[0118]

[0119] Among them, a ij Is the communication topology diagram The corresponding adjacency matrix The elements in .

[0120] The control objective is further expressed as a constraint equation:

[0121]

[0122] For the constrained equation For a mechanical system, the control force obtained by solving the UK equation requires that the initial conditions must satisfy the constraint equation. However, in actual situations, the initial conditions of the robot system are difficult to satisfy the constraint equation. For this reason, Baumgarte proposed a constraint correction method to convert the constraint equation Rewrite as Among them, α>0, β>0 are coupling strength parameters.

[0123] For undirected unweighted graphs, the Baumgarte correction form can be used directly; however, for directed weighted graphs, the error system is difficult to converge to 0 when the original Baumgarte correction form is used directly in the subsequent stability derivation process. Therefore, in order to realize the formation control of the robot system based on the directed weighted graph, an improved innovative Baumgarte correction form is proposed. Through the improved innovative Baumgarte correction form, the constraint equation can be rewritten as:

[0124]

[0125] Substituting into the UK equation, the expression for the constraint force is:

[0126]

[0127] Usually N=M, then the expression of constraint force can be rewritten as:

[0128]

[0129] Combining the above calculation formulas 1.11 to 1.17, according to the relationship between each robot in the communication topology, the constraint equation is used to express the formation goal, and these constraints are combined with the dynamic model of the robot system and the innovative Baumgarte correction form. Since the original Baumgarte correction form is only applicable to undirected and unweighted graphs, when used in directed and weighted communication topologies, it cannot satisfy the stability of the formation controller, so an innovative Baumgarte correction form is proposed.

[0130] The innovative Baumgarte correction form can be improved in terms of adaptive parameter adjustment, introduction of nonlinear correction terms, observer-based disturbance compensation, and dynamic target correction, thereby enhancing the flexibility and robustness of the correction method and making it more suitable for complex multi-robot systems, especially in formation control or high dynamic environments. These improved methods not only solve the shortcomings of traditional correction forms, but also better adapt to the nonlinearity and uncertainty of complex multi-robot systems. In practical applications, all robots exchange data in the communication topology graph. After each robot receives the status information of its neighboring robots, it calculates the constraint force, that is, the servo control force it needs to apply, according to the set formation goal and constraint equation. The design of the servo control force is based on the feedback control algorithm to ensure that each robot can achieve the global formation goal based on local information. In this way, the networked robot system can achieve stable and efficient formation control under non-holonomic constraints.

[0131] In some optional implementations of this embodiment, with respect to step S4, in step S4, the expression of the constraint force is further rewritten as:

[0132]

[0133] Definition η=(η1, η2,…, η n ) T satisfy According to the properties of the Laplace matrix, we know that:

[0134]

[0135] in,

[0136] Combining (1.19) with (1.18), we get:

[0137]

[0138] So the distributed formation controller is:

[0139]

[0140] Among them, the formula elements in the distributed formation controller are as follows:

[0141]

[0142] Combining the above formulas 1.18 to 1.21, based on the calculated servo control force, a distributed formation controller of a networked robot system without a leader is designed. The formation controller can be a control calculation formula, through which the networked robot system can be controlled in formation. In addition, the core goal of the leaderless distributed formation controller is to achieve the global formation goal of the networked robot system through a distributed control algorithm without a central control node (leader). Each robot independently calculates its control force only by communicating with adjacent robots, thereby completing the overall formation task. That is, each robot can achieve global coordination based on local information, and at the same time, the robustness and dynamic adaptability of the system are enhanced through adaptive strategies. This distributed formation controller is very suitable for multi-robot collaboration and task execution in a dynamic environment.

[0143] In some optional implementations of this embodiment, with respect to step S5, in step S5, stability analysis and simulation verification are performed on the networked robot system according to the distributed formation controller.

[0144] Substituting (1.21) into (1.11) we can see that:

[0145]

[0146] Multiply both sides of (1.22) by Then we can get

[0147]

[0148] The formation error is defined as

[0149]

[0150] The formation error can be rewritten as:

[0151]

[0152] Substituting into (1.22), we can see:

[0153]

[0154] Rewrite (1.26) into matrix form:

[0155]

[0156] The characteristic equation of (1.27) is:

[0157]

[0158] Solving the characteristic equation (1.28), we can get the characteristic root:

[0159]

[0160] It can be verified. A directed graph has a directed spanning tree if and only if the following holds

[0161]

[0162] Combining the above formulas 1.22 to 1.30, it can be seen from the above analysis that the formation error can converge to 0, which proves that under the control of the formation controller (1.21), the networked robot system is stable, that is, it passes the stability analysis.

[0163] The first set of numerical simulation experiments is carried out below:

[0164] Experiment 1:

[0165] Set the desired formation shape to a square, with the following details:

[0166]

[0167] Set the initial state of the networked robot system as shown in Table 2:

[0168] Table 2 Initial state of the networked robot

[0169]

[0170] Write a control program and conduct numerical simulation experiments. The following are the results of the numerical simulation experiments:

[0171] See also Figures 4 to 7 , Figure 4 The solid dots of different colors in the figure represent the initial positions of different robots. Their starting positions are on the same vertical line with equal vertical distances. The solid lines of different colors represent the motion trajectories of different robots, and the black solid and dotted lines represent the formation shapes formed. It can be seen that the networked robot system finally forms a square formation shape and the motion trajectory is a straight line motion. Figure 5 and Figure 6 It can be seen that the speeds of the four robots in the x and y directions finally reached the same level, indicating that the robot system moved together after achieving the desired formation. Figure 7 It can be seen that the formation errors of the four robots quickly converge to 0, proving that the robot system is stable.

[0172] The second set of numerical simulation experiments is carried out below:

[0173] Experiment 2:

[0174] Set the desired formation shape to a square, with the following details:

[0175]

[0176] Set the initial state of the networked robot system as shown in Table 3:

[0177] Table 3 Initial state of the networked robot system

[0178]

[0179] Write a control program and conduct numerical simulation experiments. The following are the results of the numerical simulation experiments:

[0180] See also Figures 8 to 11 , Figure 8 The solid dots of different colors in the figure represent the initial positions of different robots. Their starting positions are on the same vertical line with equal vertical distances. The solid lines of different colors represent the motion trajectories of different robots, and the black solid and dotted lines represent the formation shapes formed. It can be seen that the networked robot system finally forms a square formation shape and the motion trajectory is a circular motion. Fig. 9 and Fig.10 It can be seen that the speeds of the four robots in the x and y directions finally reached the same level, indicating that the robot system achieved the desired formation and then performed circular motion together. Fig.11 It can be seen that the formation errors of the four robots quickly converge to 0, proving that the robot system is stable.

[0181] Combining the above stability analysis and the numerical simulation experiments of the two groups of experiments, the distributed formation controller obtained by steps S1 to S4 can verify the effectiveness of the formation controller. The technical key point of the present invention is that based on the dynamic model of the robot and the directed weighted graph with a directed spanning tree, the UK method and the innovative Baumgarte correction form are used to realize the formation control problem of the networked robot system. First, the present invention establishes the dynamic model of the robot based on the Newton-Euler method. Compared with the kinematic model of the robot, the formation controller designed based on the dynamic model can not only better reflect the dynamic characteristics of the robot, but also better achieve the control target, and obtain a wider range of practical applications. Secondly, the present invention establishes the communication topological relationship between robots based on the directed weighted graph with a directed spanning tree. The undirected unweighted graph is a special form of the directed weighted graph. Compared with the communication topology based on the undirected unweighted graph, the present invention is more general and universal. Finally, the present invention uses the UK method and the innovative Baumgarte correction form to design a distributed formation controller for the networked robot system, and verifies the effectiveness of the formation controller through stability proof and numerical simulation experiments.

[0182] See also Fig.12 , Fig.12 A distributed formation control device for a robot system based on UK theory provided in an embodiment of the present application is shown, comprising the following modules:

[0183] A dynamic model module, used to establish a dynamic model of the networked robot system using Newton-Euler mechanics method according to system parameters in the networked robot system moving in two-dimensional space; wherein the networked robot system includes n robots, where n is a positive integer;

[0184] A communication topology graph module, used to establish a communication relationship between the robots according to a preset algebraic graph theory strategy, and set a communication topology graph corresponding to the communication relationship; wherein the communication topology graph includes a directed weighted graph with a directed spanning tree;

[0185] A servo control force module is used to convert the expected formation control target into a constraint equation according to the communication topology diagram, and to calculate the servo control force required by the robot system subject to non-holonomic constraints to achieve the expected formation control target by combining the dynamic model with the UK equation;

[0186] A formation control module is used to design a distributed formation controller in the absence of a leader based on the servo control force and using a preset distributed formation control algorithm; wherein the distributed formation controller is used to perform formation control on the networked robot system.

[0187] See also Fig.13 , Fig.13 An electronic device provided in an embodiment of the present invention is shown, and the electronic device can be used to implement the robot system distributed formation control method based on UK theory in any of the above embodiments. The electronic device includes:

[0188] Memory 401, processor 402, bus 403, and a computer program stored in memory 401 and executable on processor 402, memory 401 and processor 402 are connected via bus 403. When processor 402 executes the computer program, the robot system distributed formation control method based on UK theory in the aforementioned embodiment is implemented. The number of processors may be one or more.

[0189] The memory 401 may be a high-speed random access memory (RAM) memory, or a non-volatile memory, such as a disk memory. The memory 401 is used to store executable program codes, and the processor 402 is coupled to the memory 401 .

[0190] Furthermore, an embodiment of the present application also provides a computer-readable storage medium, which may be disposed in the electronic device in each of the above embodiments, and the computer-readable storage medium may be a memory.

[0191] The computer readable storage medium stores a computer program, and when the program is executed by the processor, the operating method of the tooling software in the aforementioned embodiment is implemented. Furthermore, the computer storable medium can also be a U disk, a mobile hard disk, a read-only memory (ROM), a RAM, a magnetic disk or an optical disk, and other media that can store program codes.

[0192] In the several embodiments provided in the present application, it should be understood that the disclosed devices and methods can be implemented in other ways. For example, the device embodiments described above are only schematic. For example, the division of modules is only a logical function division. There may be other division methods in actual implementation, such as multiple modules or components can be combined or integrated into another system, or some features can be ignored or not executed. Another point is that the mutual coupling or direct coupling or communication connection shown or discussed can be through some interfaces, indirect coupling or communication connection of devices or modules, which can be electrical, mechanical or other forms.

[0193] The modules described as separate components may or may not be physically separated, and the components shown as modules may or may not be physical modules, that is, they may be located in one place or distributed on multiple network modules. Some or all of the modules may be selected according to actual needs to achieve the purpose of the solution of this embodiment.

[0194] In addition, each functional module in each embodiment of the present application can be integrated into a processing module, or each module can exist physically separately, or two or more modules can be integrated into one module. The above integrated modules can be implemented in the form of hardware or software functional modules.

[0195] If the integrated module is implemented in the form of a software function module and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present application, or the part that contributes to the prior art, or all or part of the technical solution can be embodied in the form of a software product, which is stored in a readable storage medium, including several instructions for a computer device (which can be a personal computer, a server, or a network device, etc.) to perform all or part of the steps of the various embodiments of the present application. The aforementioned readable storage medium includes: various media that can store program codes, such as USB flash drives, mobile hard drives, ROM, RAM, magnetic disks, or optical disks.

[0196] It should be noted that, for the above-mentioned method embodiments, for the sake of simplicity of description, they are all expressed as a series of action combinations, but those skilled in the art should be aware that the present application is not limited by the described action sequence, because according to the present application, certain steps can be performed in other sequences or simultaneously. Secondly, those skilled in the art should also be aware that the embodiments described in the specification are all preferred embodiments, and the actions and modules involved are not necessarily required by the present application.

[0197] In the above embodiments, the description of each embodiment has its own emphasis. For parts that are not described in detail in a certain embodiment, reference can be made to the relevant descriptions of other embodiments.

[0198] The above are only preferred embodiments of the present invention, and are not intended to limit the patent scope of the present invention. Any equivalent structure or equivalent process transformation made using the contents of the present invention specification and drawings, or directly or indirectly applied in other related technical fields, are also included in the patent protection scope of the present invention.

Claims

1. A distributed formation control method for a robot system based on UK theory, characterized in that: The robot system distributed formation control method based on UK theory comprises the following steps: Step S1, establishing a dynamic model of the networked robot system using the Newton-Euler mechanics method according to system parameters in the networked robot system moving in two-dimensional space; wherein the networked robot system includes n robots, where n is a positive integer; Step S2, establishing a communication relationship between the robots according to a preset algebraic graph theory strategy, and setting a communication topology graph corresponding to the communication relationship; wherein the communication topology graph includes a directed weighted graph having a directed spanning tree; Step S3, converting the expected formation control target into a constraint equation according to the communication topology diagram, and combining the dynamic model with the UK equation to calculate the servo control force required for the robot system subject to non-holonomic constraints to achieve the expected formation control target; Step S4, based on the servo control force, a preset distributed formation control algorithm is used to design a distributed formation controller in the absence of a leader; wherein the distributed formation controller is used to perform formation control on the networked robot system.

2. The distributed formation control method of robot system based on UK theory according to claim 1 is characterized in that: After step S4, the method further includes: Step S5, performing stability analysis and simulation verification on the networked robot system according to the distributed formation controller.

3. The distributed formation control method of robot system based on UK theory according to claim 1 is characterized in that: The step S1 specifically includes: Obtain system parameters in the networked robot system; wherein the system parameters include the robot mass center coordinate x-axis component x, the robot mass center coordinate y-axis component y, the angle θ between the robot speed direction and the positive direction of the x-axis, the robot mass m, the robot's moment of inertia J around the mass center, the lateral distance l between the robot mass center and the wheel center, the wheel radius d, the robot's speed v, and the driving torque u of the motor acting on the right rear wheel r , the driving torque u of the motor acting on the left rear wheel l , the driving force generated by the robot's right rear wheel f r and the driving force f generated by the robot's left rear wheel l ; In combination with the Newton-Euler mechanics method, a dynamic model of the networked robot system is established; wherein the dynamic model includes a dynamic equation; Among them, the combination of Newton-Euler mechanics methods includes: Define the generalized coordinates of the mobile robot q = (x, y, θ) T , where (x, y) is the position coordinate of the center of mass of the mobile robot, θ represents the attitude angle of the mobile robot in the inertial coordinate system, and u r and u l The direction that drives the vehicle forward is positive. In the robot's forward direction, Newton's laws of motion give: Which meets The speed of the robot is expressed as: Taking the derivative of the robot's velocity with respect to time, we get: Through the above calculation formula, we can get: The robot has nonholonomic constraints, which can be expressed as: Taking the first-order differential of time gives: From the angular momentum theorem we can get: Right now Written in matrix form: Then the dynamic equation of the networked robot system is expressed as: in, 4. The distributed formation control method of robot system based on UK theory according to claim 3 is characterized in that: In step S2, the communication topology graph between robots in the networked robot system is composed of a directed graph Represents, where Ω = {1, 2, ..., n} represents the set of mobile robot nodes in the network, represents the set of edges between mobile robot nodes in the network, is the adjacency matrix; If (i, j)∈Θ, it means that nodes i and j are neighbors, and node j can obtain the status information of node i; a ij is an element in the adjacency matrix. If (j, i)∈Θ, then a ij > 0, otherwise a ij =0; Degree Matrix The elements in If i≠j, then d ij =0, and the communication topology diagram The associated Laplacian matrix is ​​defined as in, l ij =-a ij , i≠j, satisfying 5. The robot system distributed formation control method based on UK theory according to claim 4 is characterized in that: The step S3 specifically includes: Acquire a formation control task; wherein the formation control task is described as making the robots in the multi-wheeled robot system form a desired formation shape and keep a fixed distance between each other; Consider a networked multi-robot system with n identical wheeled robots, where the robots are numbered from 1 to n. The directed communication topology of the robot system is given by express, satisfy The corresponding Laplace matrix is Let q i =(x i ,y i ,θ i ) T represents the generalized coordinates of the i-th wheeled robot in the system, and the dynamic model of the networked multi-robot system is expressed as: in, make represents the desired formation of the system, and the control objective is expressed as: Rewritten as: Among them, a ij Is the communication topology diagram The corresponding adjacency matrix Elements in The control objective is expressed as a constraint equation in the form of: By using the improved Baumgarte correction form, the constraint equation is rewritten as: Substituting into the UK equation, the expression for solving the constraint force is: Usually N=M -2 , then the constraint expression can be rewritten as:

6. The distributed formation control method of robot system based on UK theory according to claim 5 is characterized in that: In step S4, the expression of the constraint force is rewritten as: Definition η=(η1, η2,…, η n ) T satisfy According to the properties of the Laplace matrix, we know that: in, Combining the above formulas, we get: The distributed formation controller is obtained as: in, 7. The distributed formation control method of robot system based on UK theory according to claim 2 is characterized in that: In step S5, through the formation controller, it can be obtained: Multiply both sides by Then we can get: The formation error is defined as: The formation error can be rewritten as: It can be seen that: Rewritten in matrix form: The characteristic equation is: Solving the characteristic equation, we can get the characteristic root: It can be verified. A directed graph has a directed spanning tree if and only if the following holds From the above analysis, it can be seen that the formation error can converge to 0, which proves that the networked robot system is stable under the control of the formation controller.

8. A distributed formation control device for a robot system based on UK theory, characterized in that: include: A dynamic model module, used to establish a dynamic model of a networked robot system using a Newton-Euler mechanics method according to system parameters in the networked robot system moving in two-dimensional space; wherein the networked robot system includes n robots, where n is a positive integer; A communication topology graph module, used to establish a communication relationship between the robots according to a preset algebraic graph theory strategy, and set a communication topology graph corresponding to the communication relationship; wherein the communication topology graph includes a directed weighted graph with a directed spanning tree; A servo control force module is used to convert the expected formation control target into a constraint equation according to the communication topology diagram, and to calculate the servo control force required by the robot system subject to non-holonomic constraints to achieve the expected formation control target by combining the dynamic model with the UK equation; A formation control module is used to design a distributed formation controller in the absence of a leader based on the servo control force and using a preset distributed formation control algorithm; wherein the distributed formation controller is used to perform formation control on the networked robot system.

9. An electronic device, characterized in that: Includes memory, processor and bus; The bus is used to realize the connection and communication between the memory and the processor; The processor is used to execute the computer program stored in the memory; When the processor executes the computer program, the steps of the distributed formation control method of a robot system based on UK theory described in any one of claims 1 to 7 are implemented.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps in the distributed formation control method of a robot system based on UK theory as described in any one of claims 1 to 7 are implemented.

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