Robot system distributed formation control method and device based on u-k theory

Abstract

The application provides a robot system distributed formation control method and device based on U-K theory, which comprises the following steps: establishing a dynamic model of a networked robot system by adopting a Newton-Euler mechanical method according to system parameters in the networked robot system moving in a two-dimensional space, establishing a communication relationship between robots according to a preset algebraic graph theory strategy, setting a communication topological graph of a directed weighted graph with a directed spanning tree, converting an expected formation control target into a constraint equation, combining the dynamic model with a U-K equation to calculate a servo control force required by a non-complete constraint robot system to complete the expected formation control target, and designing a distributed formation controller in a leaderless case based on the servo control force by adopting a preset distributed formation control algorithm. The technical scheme solves the technical problem of lack of universality in the related art, expands the application range, is more general and universal, and guarantees the formation control stability on the basis of simplifying the calculation of the control force.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of intelligent robots, and particularly relates to a robot system distributed formation control method and device based on U-K (Udwadia-Kalaba). BACKGROUND

[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 exhibit stronger capabilities in cooperative search, cooperative transportation and other tasks. However, mobile robots are usually a kind of nonholonomic systems, and their lateral movement is subject to certain restrictions, which makes the formation control of mobile robots a hot research topic.

[0003] In related technologies, 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, Chinese patent "CN116954221A" proposes a distributed intrinsic time formation control method, and Chinese patent "CN115729239A" proposes a predetermined time consensus control method. These methods mainly establish a nonlinear kinematic model of the robot, and then convert the nonlinear model into a linear model by means of linearization. However, this controller design based on the kinematic model is difficult to reflect the actual dynamics of the robot system. In practical applications, the robot is driven by 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 attempted to design formation control strategies based on the dynamics model. For example, Chinese patent "CN111596690A" uses the Newton-Euler method to establish a dynamics model of a quadrotor flying robot, and conducts formation control based on this. However, this kind of method usually needs to introduce multiple auxiliary variables, which increases the computational complexity and the explanatory power of the auxiliary variables is poor. In this regard, the U-K equation proposed by Udwadia and Kalaba can effectively simplify the calculation process when solving the control force of a system with complete constraints and nonholonomic constraints, and the control force obtained is the minimum control force.

[0005] In addition, the existing formation control method is mostly based on a communication topology graph without direction and weight. Such a topology graph is simple, but its application has certain limitations. For example, the finite-time competitive formation control method proposed in the Chinese patent CN116276964A adopts a graph without direction and weight. However, the graph without direction and weight is a special communication topology graph, and cannot be extended to a more complex directed and weighted graph. In addition, the Baumgarte modification form adopted in the research based on the U-K method is only applicable to the case of a graph without direction, and thus has deficiencies in a more complex topology structure. Therefore, in order to study the communication topology relationship based on a directed and weighted graph, the Baumgarte modification form to be adopted also needs to be innovated. Since the directed and weighted graph can more widely describe the communication network in actual applications, the formation control method designed based on the directed and weighted graph has stronger universality and generality.

[0006] In general, the prior art has the following deficiencies: (1) the control method based on the kinematic model is difficult to reflect the dynamic characteristics of the robot system, and it is difficult to obtain good control effect in actual applications; (2) the calculation complexity is increased by introducing auxiliary variables, and these variables are difficult to explain; (3) the existing methods are mostly based on the communication topology of a graph without direction and weight, and lack of universality; (4) the existing Baumgarte modification form is mostly based on the communication topology of a graph without direction and weight, and cannot be extended to the communication topology of a directed and weighted graph. That is, the above problems need to be solved by further technical innovation. SUMMARY

[0007] The main purpose of the present application is to provide a robot system distributed formation control method and device based on U-K theory, to at least solve the technical problems of lack of universality and innovation in the related art.

[0008] In a first aspect, the present application provides a robot system distributed formation control method based on U-K theory, comprising the following steps:

[0009] Step S1: a dynamics model of a networked robot system in two-dimensional space motion is established by using a Newton-Euler mechanics method according to system parameters in the networked robot system; wherein the networked robot system comprises n robots, and n is a positive integer;

[0010] Step S2: a communication relationship between the robots is established according to a preset algebraic graph theory strategy, and a communication topology graph corresponding to the communication relationship is set; wherein the communication topology graph comprises a directed and weighted graph with a directed spanning tree;

[0011] Step S3, converting the expected formation control target into a constraint equation according to the communication topology graph, and calculating the servo control force required for the non-holonomic constrained robot system to complete the desired formation control target by combining the dynamic model with the U-K equation;

[0012] Step S4, based on the servo control force, a distributed formation controller in a leaderless case is designed by using a preset distributed formation control algorithm; wherein the distributed formation controller is used for formation control of the networked robot system;

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

[0014] The second aspect of the application provides a robot system distributed formation control device based on U-K theory, comprising:

[0015] A dynamic model module is configured to establish a dynamic model of the networked robot system by using a Newton-Euler mechanical method according to system parameters in the networked robot system in a two-dimensional space motion; wherein the networked robot system comprises n robots, and n is a positive integer;

[0016] A communication topology graph module is configured 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 comprises a directed weighted graph with a directed spanning tree;

[0017] A servo control force module is configured to convert the expected formation control target into a constraint equation according to the communication topology graph, and calculate the servo control force required for the non-holonomic constrained robot system to complete the desired formation control target by combining the dynamic model with the U-K equation;

[0018] A formation control module is configured to design a distributed formation controller in a leaderless case by using a preset distributed formation control algorithm based on the servo control force; wherein the distributed formation controller is used for formation control of the networked robot system.

[0019] The third aspect of the application provides an electronic device comprising 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] The processor implements the steps in the U-K theory-based distributed formation control method of a robot system when executing the computer program.

[0023] The fourth aspect of the present application provides a computer readable storage medium, which stores a computer program, and the computer program is characterized in that the processor implements the steps in the U-K theory-based distributed formation control method of a robot system when executing the computer program.

[0024] The U-K theory-based distributed formation control method and device of a robot system have the following beneficial effects:

[0025] (1) Not only the dynamics model of the mobile robot is used, but also the dynamics characteristics of the robot are embodied; and the formation control method can be extended to the formation control scheme based on any communication topology graph because the directed weighted graph with a directed spanning tree is the most common communication topology graph, thereby solving the lack of universality in the related art, avoiding the lack of universality, expanding the application range, and being more general and universal.

[0026] (2) The U-K method and the innovative Baumgarte modified form are used to establish the formation controller of the networked mobile robot system, and the obtained control force is the minimum control force, thereby simplifying the operation of the control force and calculating the control force with better effect.

[0027] (3) The established formation controller is a distributed controller, and only the neighbor information of each robot in the communication network is required, and the information of all the robots is not required, thereby greatly reducing the communication burden on the basis of improving the communication efficiency. BRIEF DESCRIPTION OF DRAWINGS

[0028] In order to more clearly illustrate the technical solutions in the embodiments or the prior art, the following will briefly introduce the drawings needed to be used in the embodiments or the prior art description. Obviously, the drawings in the following description only some embodiments described in the present application, and for those skilled in the art, without creative labor, can also obtain other drawings according to these drawings.

[0029] Figure 1 The step flowchart of the U-K theory-based distributed formation control method of a robot system provided in an embodiment of the present application is shown in the figure.

[0030] Figure 2 The geometric model of the mobile robot is shown in the figure.

[0031] Figure 3 The communication topology graph with a directed spanning tree is shown in the figure.

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

[0033] Figure 5 This is a velocity diagram of the robot in the x-direction during the first group of experiments;

[0034] Figure 6 This is a velocity diagram of the robot in the y-direction during the first group of experiments;

[0035] Figure 7 This is the error convergence plot for the first group of experiments;

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

[0037] Figure 9 This is a velocity diagram of the robot in the x-direction in the second set of experiments;

[0038] Figure 10 This is a velocity diagram of the robot in the y-direction during the second set of experiments;

[0039] Figure 11 This is the error convergence plot for the second group of experiments;

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

[0041] Figure 13 This is a schematic diagram of the structure of the electronic device provided in the embodiments of this application.

[0042] The achievable functions, features, and advantages of this invention will be further explained in conjunction with the embodiments and with reference to the accompanying drawings; to better illustrate and explain the differences in experimental data comparison between different robots in the experiment, the accompanying drawings... Figure 4 To be continued Figure 11 The text uses multiple different colors to indicate different meanings. Detailed Implementation

[0043] It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.

[0044] It is to 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 application, a first component can be referred to as a second component, and a second component can similarly be referred to as a first component. The term "and / or" refers to a combination of the relevant items and the described items. In addition, in order to better illustrate the present application, numerous specific details are given in the following specific embodiments. Those skilled in the art will understand that the present application can also be implemented without these specific details. In some examples, well-known structures and components are not described in detail in order to highlight the main idea of the present application. In addition, the following examples "*" all represent multiplication operations, and the end of the calculation formula "." represents the 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 with complete constraints and non-complete constraints. This method was proposed by Udwadia and Kalaba in 1992, which can directly obtain the explicit solution of a constrained dynamic system without introducing the Lagrange multiplier. The Udwadia-Kalaba equation provides a simple and efficient tool for studying systems with non-holonomic constraints or complex constraint conditions.

[0045] Referring to Figure 1 The embodiment of the present application provides a robot system distributed formation control method based on U-K theory, which at least includes the following steps:

[0046] Step S1, according to the system parameters of the networked robot system in two-dimensional space motion, the Newton-Euler mechanics method is used to establish the dynamic model of the networked robot system.

[0047] Among them, the networked robot system includes n robots, and n is a positive integer. In step S1, the 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 Euler's equation, the system parameters of the networked robot system in two-dimensional space motion are analyzed, such as the system parameters reflecting the motion state of each robot, such as position, velocity and acceleration, the force condition of the robot in two-dimensional space is determined, and the dynamic model of the networked robot system is constructed.

[0048] Step S2, according to the preset algebraic graph theory strategy, the communication relationship between the robots is established, and the communication topological graph corresponding to the communication relationship is set.

[0049] The communication topology graph includes a directed weighted graph with a directed spanning tree. In step S2, the communication relationship between the robots is established by an algebraic graph theory strategy. In a networked robot system, the communication relationship between the robots is very important. In order to better achieve formation control, an algebraic graph theory method is used to describe and establish the communication relationship. Alternatively, the communication topology graph can be represented in the form of a directed weighted graph, which includes a directed spanning tree, and can ensure that there is an effective communication link between all the robots. In the communication topology graph, 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] In step S3, the expected formation control target is converted into a constraint equation based on the communication topology graph, and the dynamics model is combined with the U-K equation to calculate the servo control force required by the non-holonomic constrained robot system to complete the desired formation control target.

[0051] Specifically, in step S3, the communication topology graph is used as a basis to convert the expected formation control target into a constraint equation. In combination with the U-K equation, the servo control force required by the robot system under non-holonomic constraints to achieve the formation control target is further calculated. The U-K equation is a commonly used kinematics and dynamics combined analysis method for describing and solving robot control problems under restricted conditions. By combining the dynamics model with the U-K equation, the servo control force required by each robot to achieve the target can be accurately calculated, thereby providing a basis for controller design.

[0052] In step S4, based on the servo control force, a distributed formation controller in a leaderless situation is designed using a preset distributed formation control algorithm.

[0053] The distributed formation controller is used for formation control of 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, greatly reducing the communication burden and improving 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] Based on the above steps S1 to S4, the application 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 target and obtain more extensive practical application. Secondly, the application establishes the communication topological relationship between the robots based on the directed weighted graph with a directed spanning tree. The undirected and unweighted graph is a special form of the directed weighted graph. Compared with the communication topologies based on the undirected and unweighted graph, the application is more general and universal. Finally, the application designs a distributed formation controller of the networked robot system by using the U-K method and the innovative Baumgarte modification form, and the effectiveness of the formation controller is verified through stability proof and numerical simulation experiment.

[0055] Please refer to Figure 2 The embodiment of the application also provides a distributed formation control method of a robot system based on U-K theory. Compared with the previous embodiment, after step S4, the method further comprises:

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

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

[0058] In some optional embodiments of the embodiment, for step S1, the step S1 specifically comprises:

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

[0060] Specifically, the system parameters of the networked robot system relate to a plurality of physical quantities and kinematic parameters, which are generally used to represent the position, motion state of the robot in the environment, and the torque and driving force related to the driving wheel. Understanding and accurately obtaining these parameters is crucial for the stability, navigation ability and operation performance of the networked robot system, and through the system parameters, the robot can be precisely controlled and modeled.

[0061] It should also be noted that the networked robot system refers to a plurality of robots or robots connected and coordinated with the control center through the network to realize information sharing and collaborative work. They can transmit control instructions, state information, environmental perception data and task information through wired networks, wireless networks, cloud computing platforms, etc., so as to complete complex tasks.

[0062] In combination with the Newton-Euler mechanical method, a dynamic model of the networked robot system is established, wherein the dynamic model includes a dynamic equation.

[0063] In combination with the Newton-Euler mechanical method, a dynamic model of the networked robot system is established, wherein the dynamic model includes a dynamic equation.

[0064] Please refer to Figure 2 , the generalized coordinates of the mobile robot are defined as q = (x, y, θ) T , wherein (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 (mobile robot geometric model), wherein u r and u l The direction of forward movement of the mobile robot is positive.

[0066] Table 1

[0067]

[0068] In the forward direction of the robot, the Newton's law of motion can be obtained as:

[0069]

[0070] wherein satisfies

[0071] The velocity of the robot is represented as:

[0072]

[0073] The derivative of the velocity of the robot with respect to time can be obtained as:

[0074]

[0075] Substituting equation (1.3) into equation (1.1) gives:

[0076]

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

[0078]

[0079] Taking the first-order derivative of equation (1.5) with respect to time gives:

[0080]

[0081] From the angular momentum theorem, we have:

[0082]

[0083] That is,

[0084]

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

[0086]

[0087] The dynamics equation of the networked robot system is represented as:

[0088]

[0089] where,

[0090]

[0091] The Chinese meanings and explanations of the elements of the dynamics equation are as follows:

[0092] M(q, t) represents the mass matrix, M is a matrix representing the inertia or mass characteristics of the system, usually related to the generalized coordinates q of the robot and time t. It represents the changes in mass or inertia at different poses or states of the robot system. The mass matrix reflects the mass distribution and inertia characteristics of each component of the robot system. q represents the generalized coordinates, which describe the position information of the system. The generalized coordinates can include the position, angle, relative position between links, etc. of the robot in two or three-dimensional space. represents the second-order derivative of the generalized coordinates q with respect to time, i.e. the generalized acceleration, which represents the acceleration change of each generalized coordinate (such as position or angle) in the robot system with respect to time. In addition, is the generalized force or control force term related to the generalized coordinates q, the generalized velocity and the time t. is referred to as the constraint force generated when the system is subjected to constraint conditions. This constraint force is to ensure that the generalized coordinates q of the system meet the predetermined constraint conditions. For example, in a robot formation, in order to maintain the relative positions 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 include the following: 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 respect to time, represents the angular acceleration of the object.

[0094] By integrating the above Formulas 1.1 to 1.10, the dynamics model of the robot is established by Newton-Euler mechanics, which not only embodies the dynamic characteristics of the robot, but also has the complete integrated nonholonomic characteristics. Compared with the kinematics model of the robot, the formation controller designed based on the dynamics model not only better embodies the dynamic characteristics of the robot, but also better achieves the control goal and is more widely used in practice.

[0095] In some optional embodiments of the present embodiment, for step S2, in step S2, the algebraic graph theory strategy is a method of using graph structure to represent and analyze multi-agent systems. In this technical field, robots are regarded as nodes of the graph, and communication links are regarded as edges of the graph. Through algebraic graph theory, the communication relationship between robots and the influence of topological structure on the propagation and control of global information can be conveniently defined and described. A typical communication topology graph should have connectivity and effective information propagation capability.

[0096] In this embodiment, the communication topology graph adopts the form of a directed weighted graph, where each node represents a robot and each directed edge represents a communication link between robots. The construction of the directed weighted graph should satisfy the following condition: there exists at least one directed spanning tree in the graph. In this way, the communication links between all robots are guaranteed to be connected, ensuring that information can be propagated from any one 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 functions: 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, with directionality and weight attributes.

[0097] Assuming that the communication topology graph between robots in the networked robot system is a directed graph denotes a set of edges between mobile robot nodes in the network, denotes a set of edges between mobile robot nodes in the network, is an adjacency matrix;

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

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

[0100] an element in the degree matrix satisfies if i≠j, d ij = 0, the Laplacian matrix associated with the communication topology graph g is defined as where, satisfies

[0101] Further, by the corresponding lemma can be obtained:

[0102] the graph the rank of the corresponding Laplacian matrix is N-1, i.e. if and only if the graph has a spanning tree.

[0103] the 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, it is assumed that the directed weighted graph has a directed spanning tree, the established communication topology graph is as shown in Figure 3 (the communication topology graph is a directed weighted graph with a directed spanning tree).

[0104] the corresponding Laplacian matrix is:

[0105]

[0106] The Laplacian matrix is generated according to the structure of the communication topology graph, and contains the degree of each node in the graph and the connection relationship between adjacent nodes. In an undirected graph or a directed graph, the Laplacian matrix can represent the direct connection relationship between nodes and the connectivity of the overall topology. The eigenvalues and eigenvectors of the Laplacian matrix can reflect some properties of the topology graph, such as whether the graph is connected. That is, the role of the Laplacian matrix in the communication topology graph mainly reflects in representing the topology structure and connectivity, measuring consistency, stability analysis, describing information flow, detecting faults, etc.

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

[0108] In some optional embodiments of the present embodiment, for step S3, in step S3, specifically comprising:

[0109] An formation control task is obtained; 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 from each other;

[0110] Consider a networked multi-robot system containing n identical wheeled robots, the robots are labeled as serial numbers 1 to n. The directed communication topology of the robot system is represented by , satisfying Ω={1, 2, …, n}, The corresponding Laplacian matrix is

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

[0112]

[0113] wherein,

[0114] M=diag{M1, …, M n},

[0115] Let The formation control problem is to make multiple robots form a desired formation shape under the action of a controller, and the control objective can be expressed as:

[0116]

[0117] Rewrite (1.12) as:

[0118]

[0119] where a ij is the element in the adjacency matrix corresponding to the communication topology .

[0120] The control objective can be further expressed in the form of constraint equation as:

[0121]

[0122] For a mechanical system subject to the constraint equation , the control force obtained by solving the U-K equation requires that the initial condition satisfies the constraint equation, but in actual situations, it is difficult for the initial condition of the robot system to satisfy the constraint equation. Therefore, Baumgarte proposed a constraint correction method, which rewrites the constraint equation as where α>0, β>0 are coupling strength parameters.

[0123] For an undirected and unweighted graph, the Baumgarte correction form can be used directly; however, for a directed and weighted graph, directly using the original form of the Baumgarte correction may cause the error system to be difficult to converge to 0 in the subsequent stability derivation process. Therefore, in order to realize the formation control of the robot system based on the directed and 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 the U-K equation, the expression of the constraint force is:

[0126]

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

[0128]

[0129] Based on the above calculation formula 1.11 to 1.17, according to the relationship of each robot in the communication topology graph, the formation target is expressed by using constraint equation, and the constraints are combined with the dynamics model of the robot system and the innovative Baumgarte modified form. Since the original Baumgarte modified form can only be applied to the undirected and unweighted graph, when applied to the directed and weighted communication topology, the formation controller cannot be stable, and thus the innovative Baumgarte modified form is proposed.

[0130] The innovative Baumgarte modified form can be improved from the aspects of adaptive parameter adjustment, nonlinear correction term introduction, disturbance compensation based on observer, and dynamic target correction, so as to improve the flexibility and robustness of the modified method, and make it more suitable for complex multi-robot systems, especially in formation control or high dynamic environment. These improvement methods not only solve the shortcomings of the traditional modified form, but also better adapt to the nonlinearity and uncertainty of complex multi-robot systems. In actual application, all robots exchange data in the communication topology graph, and each robot receives the state information of the neighbor robots, and calculates the constraint force, i.e. the servo control force to be applied by itself, according to the set formation target and constraint equation. The design of servo control force is based on feedback control algorithm, which ensures that each robot can realize the global formation target according to local information. Through this method, the networked robot system can realize stable and efficient formation control under nonholonomic constraint conditions.

[0131] In some optional embodiments of the present embodiment, for step S4, in step S4, the expression of the constraint force is further rewritten as:

[0132]

[0133] Let η=(η1,η2,…,η n ) T Satisfy According to the properties of Laplacian matrix, it can be known that:

[0134]

[0135] Wherein,

[0136] Combining (1.19) and (1.18), we have:

[0137]

[0138] Therefore, the distributed formation controller is:

[0139]

[0140] Wherein, for each formula element in the distributed formation controller is as follows:

[0141]

[0142] Based on the calculated servo control force, the distributed formation controller for the networked robot system in the leaderless case is designed according to the above formulas 1.18 to 1.21, which can be a control calculation formula by 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 through communication with adjacent robots, thereby completing the overall formation task. That is, each robot can achieve global collaboration based on local information, and at the same time, the system's robustness and dynamic adaptability are enhanced through adaptive strategies. Such a distributed formation controller is very suitable for multi-robot cooperation and task execution in dynamic environments.

[0143] In some optional embodiments of the present embodiment, for step S5, in step S5, the networked robot system is analyzed for stability and simulated and verified according to the distributed formation controller.

[0144] Substituting (1.21) into (1.11) gives:

[0145]

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

[0147]

[0148] Define the formation error as

[0149]

[0150] The formation error can be rewritten as:

[0151]

[0152] Substituting (1.26) into (1.22) gives:

[0153]

[0154] Rewrite (1.26) as a matrix:

[0155]

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

[0157]

[0158] Solving the characteristic equation (1.28), the characteristic roots are

[0159]

[0160] It can be proved that iff the directed graph has a directed spanning tree and the following equation holds

[0161]

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

[0163] The first set of numerical simulation experiments is as follows:

[0164] Experiment 1:

[0165] The desired formation shape is set to be a square, and the specific information is as follows:

[0166]

[0167] The initial state of the networked robot system is set as shown in Table 2 below:

[0168] Table 2 Initial state of the networked robot

[0169]

[0170] The control program is written, and the numerical simulation experiment results are as follows:

[0171] Please refer to Figures 4 to 7 , Figure 4 The solid circles of different colors in the figure represent the initial positions of different robots, and their starting positions are on the same vertical line with equal vertical distance intervals. The solid lines of different colors represent the motion trajectories of different robots, and the black solid and dashed line represents the formation shape formed. It can be seen that the networked robot system finally forms a square formation shape and the motion trajectory is a straight line. Figure 5 and Figure 6 It can be seen that the x-direction and y-direction velocities of the four robots finally reach a consensus, indicating that the robot system moves together after achieving the desired formation. Figure 7 It can be seen from 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 as follows:

[0173] Experiment 2:

[0174] The desired formation shape is set to be square, and the detailed information is as follows

[0175]

[0176] The initial state of the networked robot system is set as follows: Table 3

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

[0178]

[0179] The control program is written, and the numerical simulation experiment is carried out. The numerical simulation experiment results are as follows:

[0180] Please refer to Figures 8 to 11 , Figure 8 The solid dots of different colors in represent the initial positions of different robots, and their starting positions are on the same vertical line with equal vertical distance intervals. The solid lines of different colors represent the motion trajectories of different robots, and the black solid and dashed lines represent the formation shape formed. It can be seen that the networked robot system finally forms a square formation shape and the motion trajectory is circular motion. Figure 9 and Figure 10 It can be seen that the x-direction and y-direction velocities of the four robots finally reach consistency, indicating that the robot system realizes the desired formation and moves together in circular motion. Figure 11 It can be seen from that the formation errors of the four robots quickly converge to 0, proving that the robot system is stable.

[0181] Based on the above stability analysis and the numerical simulation experiment of the two groups, the distributed formation controller obtained by steps S1 to S4 can verify the effectiveness of the formation controller. The technical key point of the application is to realize the formation control problem of the networked robot system based on the dynamics model of the robot and the directed weighted graph with a directed spanning tree, using the U-K method and the innovative Baumgarte modification form. First, the application establishes the dynamics model of the robot based on the Newton-Euler method. Compared with the kinematics model of the robot, the design of the formation controller based on the dynamics model not only better reflects the dynamics characteristics of the robot, but also better achieves the control target and is widely used in practice. Second, the application establishes the communication topology relationship between the robots based on the directed weighted graph with a directed spanning tree. The undirected and unweighted graph is a special form of the directed weighted graph. Compared with the communication topology based on the undirected and unweighted graph, the application is more general and universal. Finally, the application uses the U-K method and the innovative Baumgarte modification form to design the distributed formation controller of the networked robot system. The effectiveness of the formation controller is verified by stability proof and numerical simulation experiment.

[0182] Referring to Figure 12 , Figure 12 The application provides a kind of distributed formation control device of robot system based on U-K theory provided by the embodiment of the application, comprising the following modules:

[0183] The dynamics model module is used to establish the dynamics model of the networked robot system according to the system parameters in the two-dimensional space motion networked robot system using the Newton-Euler mechanics method;Wherein, the networked robot system includes n robots, and n is a positive integer;

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

[0185] The servo control force module is used to convert the expected formation control target into a constraint equation according to the communication topology graph, and calculate the servo control force required for the non-complete constrained robot system to complete the desired formation control target by combining the dynamics model with the U-K equation;

[0186] The formation control module is used to design a distributed formation controller in a leaderless situation based on the servo control force using a preset distributed formation control algorithm;Wherein, the distributed formation controller is used to control the formation of the networked robot system.

[0187] Referring to Figure 13 ,Figure 13 An electronic device provided in an embodiment of the present application is shown, which can be used to implement the U-K theory based distributed formation control method of a robot system in any of the foregoing embodiments. The electronic device comprises:

[0188] The memory 401, the processor 402, the bus 403, and the computer program stored in the memory 401 and executable on the processor 402 are connected through the bus 403. When the processor 402 executes the computer program, the U-K theory based distributed formation control method of a robot system in the foregoing embodiments is implemented. The number of processors can be one or more.

[0189] The memory 401 can be a high-speed random access memory (RAM) 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 with the memory 401.

[0190] Further, the present application also provides a computer readable storage medium, which can be arranged in the electronic device in the foregoing embodiments, and the computer readable storage medium can be a memory.

[0191] The computer readable storage medium stores a computer program, which is executed by the processor to implement the operation method of the tooling software in the foregoing embodiments. Further, the computer readable storage 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 various media that can store program codes.

[0192] In several embodiments provided in the present application, it should be understood that the disclosed apparatus and method can be implemented in other manners. For example, the apparatus embodiments described above are merely schematic; the division of the modules is merely a logical function division; other division manners can be adopted during actual implementation; for example, a plurality of modules or components can be combined or integrated into another system, or some features can be ignored or not executed. In addition, the displayed or discussed mutual couplings or direct couplings or communication connections can be indirect couplings or communication connections through some interfaces, devices or modules, and can be electrical, mechanical or in other forms.

[0193] The modules described as separate components may or may not be physically separate, and the components shown as modules may or may not be physical modules, i.e., may be located in one place, or may be distributed to multiple network modules. Part or all of the modules can be selected according to actual needs to achieve the purpose of the embodiment.

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

[0195] If the integrated module is realized in the form of a software functional 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 solutions of the present application essentially or the part that contributes to the prior art or the whole or part of the technical solutions can be embodied in the form of a software product. The computer software product is stored in a readable storage medium, including a plurality of instructions for causing a computer device (which can be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the embodiments of the present application. The aforementioned readable storage medium includes: U disk, mobile hard disk, ROM, RAM, magnetic disk or optical disk, and various program code storage media.

[0196] It should be noted that, for the foregoing method embodiments, in order to facilitate description, they are all described as a combination of a series of actions, but those skilled in the art should know that the present application is not limited by the order of the actions described, because according to the present application, certain steps can be performed in other orders or simultaneously. Secondly, those skilled in the art should know that the embodiments described in the specification all belong to preferred embodiments, and the actions and modules involved are not necessarily essential to the present application.

[0197] In the above embodiments, the description of each embodiment has its own emphasis, and the parts not described in detail in a certain embodiment can be referred to the related description of other embodiments.

[0198] The above is only the preferred embodiment of the present application, and does not limit the patent scope of the present application, and any equivalent structure or equivalent process transformation using the content of the present application specification and drawings, or direct or indirect application in other related technical fields, are also included in the patent protection scope of the present application.

Claims

1. A method for distributed formation control of a robot system based on U-K theory, characterized in that, The robot system distributed formation control method based on U-K theory comprises the following steps: Step S1, a dynamic model of a networked robot system is established according to system parameters in the networked robot system moving in a two-dimensional space by using a Newton-Euler mechanical method; wherein the networked robot system comprises n robots, and n is a positive integer; Step S2, a communication relationship between the robots is established according to a preset algebraic graph theory strategy, and a communication topology graph corresponding to the communication relationship is set; wherein the communication topology graph comprises a directed weighted graph having a directed spanning tree; Step S3, an expected formation control target is converted into a constraint equation according to the communication topology graph, and a servo control force required for the robot system under nonholonomic constraint to complete the expected formation control target is calculated by combining the dynamic model with a U-K equation; Step S4, a distributed formation controller in a no-leader case is designed by using a preset distributed formation control algorithm based on the servo control force; wherein the distributed formation controller is used for formation control of the networked robot system; After the step S4, the following steps are further included: Step S5, stability analysis and simulation verification of the networked robot system are performed according to the distributed formation controller; The step S1 specifically comprises: obtaining system parameters in the networked robot system; wherein the system parameters include robot centroid coordinate x-axis component x, robot centroid coordinate y-axis component y, robot speed direction and x-axis positive direction included angle θ, mass of the robot m, rotation inertia of the robot around the centroid J, lateral distance of the robot centroid and the wheel center l, wheel radius d, speed of the robot v, driving torque of the motor acting on the right rear wheel u r , driving torque of the motor acting on the left rear wheel u l , driving force f r generated by the right rear wheel of the robot, and driving force f l generated by the left rear wheel of the robot; The dynamic model of the networked robot system is established by combining the Newton-Euler mechanical method; wherein the dynamic model comprises a dynamic equation; Wherein combining the Newton-Euler mechanical method comprises: Define the generalized coordinates of the mobile robot q = (x, y, θ) T , where (x, y) are the position coordinates of the mobile robot's center of mass, and θ represents the orientation angle of the mobile robot in the inertial coordinate frame, u r and u l are positive in the direction that drives the vehicle to move forward. In the advancing direction of the robot, the Newton's law of motion can be obtained as follows: wherein satisfies The velocity of the robot is expressed as: The velocity of the robot is differentiated with respect to time to obtain: By the above calculation formula, we can get: The robot has nonholonomic constraint, which can be expressed as: The first-order time differentiation is performed to obtain: According to the angular momentum theorem, the following equation can be obtained: That is Written in matrix form, the following equation can be obtained: Therefore, the dynamic equation of the networked robot system is expressed as: Wherein, 2. The robot system distributed formation control method based on U-K theory according to claim 1, wherein, In the step S2, the communication topology graph between robots in the networked robotic system is represented by a directed graph 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 an adjacency matrix; If (i, j) ∈ Θ, it means that node i and node j are neighbors, and node j can obtain the state information of node i; a ij is an element in the adjacency matrix, a ij > 0 if (j, i) e Θ, otherwise a ij = 0. Degree matrix The elements in satisfy If i ≠ j, then d ij =0, and the communication topology diagram The associated Laplace matrix is ​​defined as in, satisfy 3. The method of claim 2, wherein, The step S3 specifically comprises: An formation control task is obtained; wherein the formation control task describes that the robots in the multi-wheeled robot system form a desired formation shape and keep a fixed distance from each other; Consider a networked multi-robot system with n identical wheeled robots, denoted as 1 to n; the directed communication topology of the robot system is denoted as , satisfying The corresponding Laplacian matrix is Let q i = (x i , y i , θ i ) T denote the generalized coordinates of the ith wheeled robot in the system, the dynamic model of the networked multi-robot system is represented as: Wherein, Let The desired formation of the system is represented, the control objective is expressed as: Rewritten as: wherein a ij is an element in a corresponding adjacency matrix of a communication topology graph ​ The control target is expressed in the form of a constraint equation as: By using the improved Baumgarte correction form, the constraint equation is rewritten as: Substituting the U-K equation, the expression of the constraint force is solved as: Often N = M -2 The expression for the constraint force then becomes 4. The robot system distributed formation control method based on U-K theory according to claim 3, wherein, In the 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: wherein, By combining the above formula, the following equation is obtained: The distributed formation controller is obtained as: Wherein, 5. The method of claim 1, wherein, In the step S5, by using the formation controller, the following equation can be obtained: Both sides are multiplied simultaneously Then we have: The formation error is defined as: The formation error can be rewritten as: It can be known that: Rewritten in matrix form as: The characteristic equation is: By solving the characteristic equation, the characteristic roots are obtained as: It can be proved that iff the digraph has a directed spanning tree and the following equation holds From the above analysis, the formation error can converge to 0, which proves that the networked robot system is stable under the control of the formation controller.

6. A device for distributed formation control of a U-K theory based robot system, for implementing the method for distributed formation control of a U-K theory based robot system according to any one of claims 1 to 5, characterized in that, The method comprises the following steps: A dynamics model module is configured to establish a dynamics model of the networked robot system according to system parameters in the networked robot system in two-dimensional space motion by using a Newton-Euler mechanical method; wherein the networked robot system comprises n robots, and n is a positive integer; A communication topology graph module is configured 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 comprises a directed weighted graph having a directed spanning tree; A servo control force module is configured to convert an expected formation control target into a constraint equation according to the communication topology graph, and calculate a servo control force required by the robot system under non-complete constraint to complete the expected formation control target by combining the dynamics model with a U-K equation; A formation control module is configured to design a distributed formation controller in a no-leader case by using a preset distributed formation control algorithm based on the servo control force; wherein the distributed formation controller is configured to perform formation control on the networked robot system.

7. An electronic device, comprising: The computer program is executed by the processor, and the steps in the robot system distributed formation control method based on the U-K theory in any one of claims 1 to 5 are implemented. The computer program is executed by the processor, and the steps in the robot system distributed formation control method based on the U-K theory in any one of claims 1 to 5 are implemented. ​ ​ 8. A computer-readable storage medium having stored thereon a computer program, characterized in that, ​

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