Distributed optimization control method, device and medium for nonlinear multi-manipulator system

Abstract

The present application discloses a distributed optimization control method, device and medium for a nonlinear multi-manipulator system. The method comprises: determining a target control function based on a state space equation of the nonlinear multi-manipulator system; wherein the state space equation includes unknown nonlinear terms; obtaining a global optimal estimate of the target control function based on a distributed proportional integral optimization algorithm; inputting the global optimal estimate into a pre-filter for reconstruction to obtain an optimal control signal without any global information; constructing an error transformation equation based on the optimal control signal; constructing a fixed time controller of a radial basis neural control network using a backstepping method based on a preset function and the error change equation; and quickly tracking the optimal control signal based on the fixed time controller so that the nonlinear multi-manipulator system reaches an optimal consensus. Thus, the present application achieves rapid convergence of the system that is independent of the initial state.

Description

Technical Field

[0001] The present application relates to the field of robot arm control, and in particular to a distributed optimization control method, device and storage medium for a nonlinear multi-robot arm system. Background Art

[0002] The collaboration of multiple manipulators is one of the hot topics in the current research field of manipulators. The emergence of collaborative multi-manipulator systems overcomes the working limits of single manipulator systems by providing a larger workspace, stronger working ability, more flexible system structure and greater load capacity than single manipulators, thereby completing many difficult tasks that single manipulators cannot complete, such as collaborative handling and welding. Although multi-manipulator collaboration has many advantages over single manipulators, it also introduces many control problems. Compared with a single manipulator, the collaborative multi-manipulator system has a more complex organizational structure, and it is not a simple combination of multiple manipulators. It needs to solve the uncertainty of environmental interaction, feasible control methods and optimization coordination planning. Therefore, studying the coordination control method of nonlinear multi-manipulator systems is one of the difficult problems in the field of robotics. With the rapid development of technologies such as the Internet of Things, 5G, artificial intelligence, and big data, complexity, networking and large data volume have become the characteristics of the times. With the rapid development of big data and networking, distributed optimization theory, technology and related applications have received more and more attention. Distributed optimization problem refers to distributing large-scale and complex optimization problems to multiple intelligent agents for distributed computing. Each intelligent agent performs its own optimization and decision-making through certain pre-defined coordination rules, and continuously exchanges information through communication networks to ultimately obtain the optimal solution to the global objective function. Its flexibility and convenience make distributed optimization have important application prospects in many industrial and technological fields, such as smart grids, sensor networks, machine learning, and information-physical systems.

[0003] In distributed algorithms, in order to get rid of the constraints of the initial state of the system and further improve the convergence performance of the closed-loop system in a finite time, fixed-time stability has been developed in recent years based on finite-time stability, which can give a uniform and fixed convergence time that is independent of the initial value of the system. However, for nonlinear multi-manipulator systems, there are still very few results on fixed-time distributed optimization, which needs to be solved urgently.

[0004] Application Contents

[0005] The main purpose of this application is to provide a distributed optimization control method, device and medium for a nonlinear multi-manipulator system, aiming to solve the technical problem that it is difficult for existing nonlinear multi-manipulator systems to achieve a uniform and fixed convergence time that is independent of the system initial value.

[0006] To achieve the above objectives, the present application provides a distributed optimization control method for a nonlinear multi-manipulator system, the method comprising:

[0007] Determining a target control function of the nonlinear multi-manipulator system based on a state-space equation of the nonlinear multi-manipulator system; wherein the state-space equation includes an unknown nonlinear term;

[0008] Based on a distributed proportional-integral optimization algorithm, a global optimal estimate of the objective control function is obtained;

[0009] Inputting the global optimal estimation value into a pre-filter for reconstruction to obtain an optimal control signal without any global information;

[0010] Based on the optimal control signal, construct an error transformation equation of the nonlinear multi-manipulator system;

[0011] Based on the preset Lyapunov function and the error variation equation, a fixed time controller of the radial basis neural control network is constructed by backstepping method;

[0012] Based on the fixed time controller, the optimal control signal is quickly tracked, and during the tracking process, the control input torque value of each robot in the nonlinear multi-robot system is adjusted based on the radial basis function neural control network, so that the nonlinear multi-robot system reaches the optimal consensus.

[0013] In a possible embodiment of the present application, the error transformation equation includes a tracking error transformation equation and an error surface transformation equation, and the fixed time controller includes a fixed time sub-virtual controller and a fixed time actual controller;

[0014] The fixed time controller of the radial basis neural control network is constructed by backstepping method based on the preset Lyapunov function and the error variation equation, including:

[0015] Based on the first preset Lyapunov function and the tracking error transformation equation, generating a fixed-time sub-virtual controller and a corresponding first neural network update law;

[0016] Based on the second preset Lyapunov function and the error surface transformation equation, a fixed-time actual controller and a corresponding second neural network update law are generated.

[0017] In a possible embodiment of the present application, determining the target control function of the nonlinear multi-manipulator system based on the state space equation of the nonlinear multi-manipulator system includes:

[0018] Construct the dynamic equation of the i-th robot in the nonlinear multi-robot system; wherein the dynamic equation is: ;

[0019] The dynamic equation is converted into the state space equation; wherein the state space equation is:

[0020] ;

[0021] Based on the state space equation, the target control function of the nonlinear multi-manipulator system is determined; wherein the target control function is:

[0022] ;

[0023] Define the global objective function And R is a real number domain, then the target control function is simplified to:

[0024] ;

[0025] The objective control function is converted to find the optimal Make each robot arm meet ;

[0026] in, is the angular position of the manipulator joint in the i-th manipulator, is the angular velocity of the manipulator joint in the i-th manipulator, is the angular acceleration of the manipulator joint in the i-th manipulator, is the symmetric positive definite moment of inertia of the i-th robotic arm, is the centripetal force of the i-th robotic arm, is the gravitational torque of the i-th robotic arm, is the control input torque of the i-th robotic arm, , , is the output state, , is the local objective function of the i-th robotic arm.

[0027] In a possible embodiment of the present application, obtaining the global optimal estimate of the objective control function based on the distributed proportional integral optimization algorithm includes:

[0028] According to the communication relationship between the various mechanical arms in the nonlinear multi-manipulator system, a communication topology structure of the nonlinear multi-manipulator system is generated; wherein the communication topology structure is expressed as ; is a vertex set, represented by ; is an edge set, represented by ; is the adjacency matrix, expressed as ;

[0029] In the communication topology, when the i-th robot arm among the N robot arms can receive the information of the k-th robot arm, it is expressed as , the neighbor set of the i-th robot Expressed as ; Among them, if , then the corresponding >0, if If not established, =0; according to The specific value of ,like , then the communication topology is an undirected topology;

[0030] Based on the distributed proportional-integral optimization algorithm and the communication topology, construct a virtual system model of the nonlinear multi-manipulator system;

[0031] Based on the virtual system model, obtaining a global optimal estimate of the objective control function;

[0032] Wherein, the virtual system model is:

[0033] ;

[0034] ;

[0035] in, and are control parameters, is the global optimal estimate, is the status of the virtual system.

[0036] In a possible embodiment of the present application, the pre-filter is:

[0037] ;

[0038] in, is the optimal control signal, is the order of the highest-order derivative of the optimal control signal, is a positive constant, and satisfy: Construct the Hurwitz polynomial.

[0039] In a possible embodiment of the present application, the tracking error transformation equation is: ; wherein said is the tracking error, = ;

[0040] The error surface transformation equation is: ;in, is the error surface, It is a fixed-time sub-virtual controller.

[0041] In a possible embodiment of the present application, before determining the target control function of the nonlinear multi-manipulator system based on the state space equation of the nonlinear multi-manipulator system, the method further includes:

[0042] The unknown nonlinear term is approximated by the radial basis neural control network to obtain the unknown nonlinear term; the unknown nonlinear term is:

[0043] ;

[0044] ;

[0045] in, and are the unknown nonlinear terms, and are ideal weights, and are basis functions, and are all approximation errors, satisfying and , and is an arbitrarily small positive constant, For fixed time sub virtual controller The derivative of .

[0046] In a possible embodiment of the present application, the first preset Lyapunov function is: ;

[0047] The fixed time sub-virtual controller is:

[0048] ,in,

[0049] ;

[0050] The first neural network update law is:

[0051] ;in, , , , , , are the design parameters of the i-th robotic arm; The ideal weight An estimated value of

[0052] The second preset Lyapunov function is: ;

[0053] The fixed time actual controller is:

[0054] ,in,

[0055] ;

[0056] The update law of the second neural network is:

[0057] ;in, , , , , , are the design parameters of the i-th robotic arm; The ideal weight The estimated value of .

[0058] In the second aspect, the present application also provides a distributed optimization control device for a nonlinear multi-robotic arm system, comprising: a processor, a memory, and a distributed optimization control program for the nonlinear multi-robotic arm system stored in the memory, wherein the distributed optimization control program for the nonlinear multi-robotic arm system implements the steps of the distributed optimization control method for the nonlinear multi-robotic arm system as described above when executed by the processor.

[0059] In a third aspect, the present application also provides a computer-readable storage medium, on which a distributed optimization control program for a nonlinear multi-robotic arm system is stored. When the distributed optimization control program for a nonlinear multi-robotic arm system is executed by a processor, the distributed optimization control method for a nonlinear multi-robotic arm system as described above is implemented.

[0060] A distributed optimization control method for a nonlinear multi-manipulator system is proposed in an embodiment of the present application. The method includes: determining a target control function of the nonlinear multi-manipulator system based on a state-space equation of the nonlinear multi-manipulator system; wherein the state-space equation includes an unknown nonlinear term; obtaining a global optimal estimate of the target control function based on a distributed proportional-integral optimization algorithm; inputting the global optimal estimate into a pre-filter for reconstruction to obtain an optimal control signal without any global information; constructing an error transformation equation for the nonlinear multi-manipulator system based on the optimal control signal; constructing a fixed-time controller of a radial basis function neural control network using a backstepping method based on a preset Lyapunov function and the error change equation; based on the fixed-time controller, quickly tracking the optimal control signal, and adjusting the control input torque value of each manipulator in the nonlinear multi-manipulator system based on the radial basis function neural control network during the tracking process, so that the nonlinear multi-manipulator system reaches an optimal consensus.

[0061] In this application, the distributed optimization control problem of a multi-manipulator system with unknown nonlinearities is considered, and the distributed optimization problem is cleverly converted into a consistent optimal control problem through a pre-filter. In addition, this application adopts a fixed-time controller, and thus provides a fixed-time distributed optimization method based on the fixed-time convergence theoretical method, which can give a more accurate upper bound of the optimization time estimate, and the upper bound is independent of the initial state of the system. Therefore, this application achieves rapid convergence of the system that is independent of the initial state. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] Figure 1 A schematic diagram of the structure of a distributed optimization control device for a nonlinear multi-manipulator system in a hardware operating environment involved in an embodiment of the present application;

[0063] Figure 2 This is a flow chart of the first embodiment of the distributed optimization control method for a nonlinear multi-manipulator system of the present application process;

[0064] Figure 3 It is a non-directional communication topology structure of a nonlinear multi-manipulator system in an example of the present application;

[0065] Figure 4 is the change curve of the rotation angle of the four robotic arms;

[0066] Figure 5 is the variation curve of the rotation angular velocity of the four robotic arms;

[0067] Figure 6 is the transformation curve of the weight norm of the radial basis neural control network;

[0068] Figure 7The change curve of the control input torque value of the four robotic arms.

[0069] The realization of the purpose, functional features and advantages of this application will be further explained in conjunction with embodiments and with reference to the accompanying drawings. DETAILED DESCRIPTION

[0070] It should be understood that the specific embodiments described herein are only used to explain the present application and are not used to limit the present application.

[0071] The present application provides a solution, taking into account the distributed optimization control problem of a multi-manipulator system with unknown nonlinearities, and cleverly converts the distributed optimization problem into a consistent optimal control problem through a pre-filter. The present application adopts a fixed-time controller, and thus provides a fixed-time distributed optimization method based on a fixed-time convergence theoretical method, which can give a relatively accurate upper bound of the optimization time estimate, and the upper bound is independent of the initial state of the system. Therefore, the present application achieves rapid convergence of the system that is independent of the initial state.

[0072] The inventive concept of the present application is further described below in conjunction with some specific embodiments.

[0073] Reference Figure 1 , Figure 1 This is a schematic diagram of the structure of a distributed optimization control device for a nonlinear multi-manipulator system in the hardware operating environment involved in an embodiment of the present application.

[0074] like Figure 1 As shown, the playback terminal may include: a processor 1001, such as a central processing unit (CPU), a communication bus 1002, a user interface 1003, a network interface 1004, and a memory 1005. Among them, the communication bus 1002 is used to realize the connection and communication between these components. The user interface 1003 may include a display screen (Display), an input unit such as a keyboard (Keyboard), and the optional user interface 1003 may also include a standard wired interface and a wireless interface. The network interface 1004 may optionally include a standard wired interface and a wireless interface (such as a wireless fidelity (WIreless-FIdelity, WI-FI) interface). The memory 1005 may be a high-speed random access memory (Random Access Memory, RAM) memory, or a stable non-volatile memory (Non-Volatile Memory, NVM), such as a disk memory. The memory 1005 may also be a storage device independent of the aforementioned processor 1001.

[0075] Those skilled in the art will understand that Figure 1The structure shown in does not constitute a limitation on the distributed optimization control device of the nonlinear multi-manipulator system, and may include more or less components than shown in the figure, or a combination of certain components, or a different arrangement of components.

[0076] like Figure 1 As shown, the memory 1005 as a storage medium may include an operating system, a data storage module, a network communication module, a user interface module, and a distributed optimization control program for a nonlinear multi-manipulator system.

[0077] exist Figure 1 In the distributed optimization control device of the nonlinear multi-robotic arm system shown, the network interface 1004 is mainly used for data communication with the network server; the user interface 1003 is mainly used for data interaction with the user; the processor 1001 and the memory 1005 in the distributed optimization control device of the nonlinear multi-robotic arm system of the present application can be set in the distributed optimization control device of the nonlinear multi-robotic arm system, and the distributed optimization control device of the nonlinear multi-robotic arm system calls the distributed optimization control program of the nonlinear multi-robotic arm system stored in the memory 1005 through the processor 1001, and executes the distributed optimization control method of the nonlinear multi-robotic arm system provided in the embodiment of the present application.

[0078] Based on the above hardware structure but not limited to the above hardware structure, the present application provides a first embodiment of a distributed optimization control method for a nonlinear multi-manipulator system. Figure 2 , Figure 2 A flow chart of the first embodiment of the distributed optimization control of a nonlinear multi-manipulator system is shown.

[0079] It should be noted that although a logical order is shown in the flowchart, in some cases, the steps shown or described may be performed in an order different from that shown here.

[0080] In this embodiment, the method includes:

[0081] Step S100: determining a target control function of the nonlinear multi-manipulator system based on a state-space equation of the nonlinear multi-manipulator system; wherein the state-space equation includes unknown nonlinear terms.

[0082] Among them, firstly, the dynamic equation of the i-th robot in the nonlinear multi-robot system is constructed. The dynamic equation is: ;

[0083] in, is the angular position of the manipulator joint in the i-th manipulator, is the angular velocity of the manipulator joint in the i-th manipulator, is the angular acceleration of the manipulator joint in the i-th manipulator, is the symmetric positive definite moment of inertia of the i-th robotic arm, is the centripetal force of the i-th robotic arm, is the gravitational torque of the i-th robotic arm, is the control input torque of the i-th robotic arm.

[0084] Considering that the multi-manipulator system in a complex environment is affected by unknown nonlinearity, let , , convert the dynamic equation of the i-th robot into the state space equation; ;

[0085] is the output state, that is, the angular velocity of the robot arm, where and are the unknown nonlinear terms. In one embodiment, , .

[0086] Determining the target control function of the nonlinear multi-manipulator system based on the state space equations of all the manipulators;

[0087] ;

[0088] in, , R is the real number domain, and N is the total number of manipulators in the nonlinear multi-manipulator system.

[0089] That is, in this embodiment, by constructing a global objective function, the global objective function is also the consistency optimal control problem to be solved by this application. is the local objective function of the i-th robot arm. It can be understood that in the distributed control algorithm, each robot arm has a local objective function known only to itself. .

[0090] Therefore, in this embodiment, the goal is to design a fixed-time controller with a configured control rate so that the nonlinear multi-manipulator system can solve the target control function.

[0091] Furthermore, the global objective function can be defined ,and is a real number domain, then the above target control function can be simplified as:

[0092] ;

[0093] That is, the goal of this application is to find the optimal , so that each robotic arm system satisfies .

[0094] Step S200: obtaining a global optimal estimate of the objective control function based on a distributed proportional integral optimization algorithm.

[0095] Specifically, in this embodiment, a virtual system is established for each robotic arm system, and a distributed proportional integral optimization algorithm is used based on the virtual system to estimate the global optimal solution online, that is, to find the optimal , so that each robotic arm system satisfies .

[0096] Specifically, step S200 specifically includes:

[0097] Step S201: Generate a communication topology structure of the nonlinear multi-manipulator system according to the communication relationship between the manipulators in the nonlinear multi-manipulator system.

[0098] Wherein, the communication topology is expressed as ; is a vertex set, represented by ; is an edge set, represented by ; is the adjacency matrix, expressed as ;

[0099] Step S202: constructing a virtual system model of the nonlinear multi-manipulator system based on a distributed proportional-integral optimization algorithm and the communication topology structure.

[0100] Step S203: obtaining a global optimal estimation value of the target control function based on the virtual system model.

[0101] In this embodiment, an undirected topological graph describing the communication relationship between nonlinear multi-manipulator systems is first established. Specifically, the communication relationship between nonlinear multi-manipulator systems, that is, the communication topological structure, can be described by graph theory G. Since in this embodiment, the nonlinear multi-manipulator system has N manipulators. Therefore, it can be used represents a directed communication topology in graph theory, where is the vertex set in the nonlinear multi-manipulator system, expressed as ; is the edge set of the nonlinear multi-manipulator system, expressed as ; is the adjacency matrix, expressed as .

[0102] In this graph theory, the i-th robot among N robots can receive information from the k-th robot, which can be expressed as At this time, the neighbor set of the i-th robot It can be expressed as . Thus, if , then the corresponding >0, otherwise, if If not established, =0. Therefore, according to The specific value of .

[0103] It is worth mentioning that if, . Then the graph G is considered to be an undirected topology.

[0104] Then, the virtual system model is constructed based on the distributed proportional integral algorithm and communication topology as follows:

[0105] ;

[0106] ;

[0107] in, and are all positive control parameters, and Both indicate the status of the virtual system. Represents the local objective function gradient.

[0108] Then, based on the virtual system model, the global optimal estimated value of the target control function is obtained by online estimation. .

[0109] Step S300: input the global optimal estimation value into a pre-filter for reconstruction to obtain an optimal control signal without any global information.

[0110] Specifically, the global optimal estimate generated The input to the pre-filter reconstructs a new optimization reference signal, which is the optimal control information of this embodiment. Thus, the distributed optimization problem is cleverly converted into a consistent optimal control problem through the pre-filtering technology. That is, the distributed optimization method in this embodiment is completely distributed and does not require any global information, such as the information of neighboring mechanical arms, etc., avoiding the problems of poor robustness of single point failure, poor confidentiality, poor timeliness, etc., which can further reduce the computational complexity and communication loss of the multi-manipulator system and improve the rapid convergence performance of the system.

[0111] It can be understood that in this embodiment, the optimal control signal is the output angular velocity of each robotic arm. After obtaining the optimal control signal, the output parameters of the radial basis neural control network can be adjusted so that the actual angular velocity of each robotic arm meets the optimal control signal.

[0112] Specifically, in one embodiment, the pre-filter is:

[0113] ;

[0114] in, is the optimal control signal, is the order of the highest-order derivative of the optimal control signal, is a positive constant, and satisfy: Constitute the Hurwitz polynomial. It is understandable that are all normal numbers, Construct the Hurwitz polynomial.

[0115] Step S400: constructing an error transformation equation of the nonlinear multi-manipulator system based on the optimal control signal.

[0116] Specifically, the optimal control signal That is, the tracking reference signal. In actual control, the radial basis neural control network tracks the signal. However, it is inevitable that a tracking error will occur during the tracking. Therefore, this step sets the error transformation system corresponding to the tracking reference signal, which is the aforementioned error transformation equation.

[0117] Specifically, in the tracking process, the error includes tracking error and error surface. In one embodiment, the tracking error transformation equation is:

[0118] ; wherein said is the tracking error, = ;

[0119] The error surface transformation equation is:

[0120] ;in, is the error surface. It is a fixed-time sub-virtual controller.

[0121] It can be understood that the error transformation system is established here to facilitate the subsequent design of the fixed-time controller, that is, based on the Lyapunov stability theory, the backstepping method is used as the framework, and the final fixed-time controller is gradually obtained through the recursive method.

[0122] Step S500: Based on a preset Lyapunov function and the error variation equation, a fixed-time controller of a radial basis function neural control network is constructed using a backstepping method.

[0123] In this embodiment, the preset Lyapunov function includes:

[0124] The first preset Lyapunov function: ;

[0125] The second preset Lyapunov function: .

[0126] Specifically, step S500 includes:

[0127] Step S501: Based on a first preset Lyapunov function and the tracking error transformation equation, generate a fixed-time sub-virtual controller and a corresponding first neural network update law.

[0128] Therefore, based on , the tracking error transformation equation The fixed-time sub-virtual controller can be obtained by taking the derivative for:

[0129] ,in,

[0130] ;

[0131] The corresponding first neural network update law for:

[0132] ;in, , , , , , are all positive design parameters of the i-th robot arm; The ideal weight An estimated value of

[0133] Step S502: Generate a fixed-time actual controller and a corresponding second neural network update law based on a second preset Lyapunov function and the error surface transformation equation.

[0134] based on Error surface transformation equation By taking the derivative, we can get the fixed time actual controller as:

[0135] ,in,

[0136] ;

[0137] The corresponding second neural network update law for:

[0138] ;in, , , , , , are all positive design parameters of the i-th robot arm; The ideal weight The estimated value of .

[0139] Step S600: Based on the fixed time controller, the optimal control signal is quickly tracked. During the tracking process, the control input torque value of each robot in the nonlinear multi-robot system is adjusted based on the radial basis function neural control network, so that the nonlinear multi-robot system reaches an optimal consensus.

[0140] In this step, the Lyapunov stability theory is used to perform stability analysis during the control process to ensure that the entire system can coordinate control and work stably within a fixed time.

[0141] Specifically, in this embodiment, based on the fixed time sub-virtual controller constructed above , control rate , fixed time actual controller and control rate , which is the adaptive control algorithm of the radial basis function neural control network, quickly tracks the optimal control signal, combines the tracking error of each robot arm during the tracking process, and automatically adjusts the radial basis function neural control network parameters and dynamic model parameters during the movement of the robot, that is, the control input torque value of each robot arm, so that the nonlinear multi-robot system reaches the optimal consensus to ensure that the entire system can be coordinated and controlled and work stably within a fixed time.

[0142] As an embodiment, it is worth mentioning that the method further includes:

[0143] Step S700: Approximate the unknown nonlinear term by using the radial basis neural control network to obtain the unknown nonlinear term.

[0144] The unknown nonlinear term is:

[0145] ;

[0146] ;

[0147] in, and are the unknown nonlinear terms of the i-th robotic arm, and are ideal weights, and are basis functions, and are all approximation errors, satisfying and , and is an arbitrarily small positive constant, For fixed-time sub-virtual controllers The derivative of .

[0148] It should be noted that, in this embodiment, the radial basis neural control network online identifies the unknown nonlinear terms existing in each robot arm. Therefore, the specific execution order of step S700 in the method is not limited. For example, step S700 can be executed together with step S600, and can also be performed before step S500. In this embodiment, online identification of unknown nonlinear terms existing in each robot arm based on the radial basis neural control network can improve the control accuracy of the nonlinear multi-robot system.

[0149] It is worth mentioning that the unknown nonlinear term can be obtained by approximating the unknown nonlinear term using the radial basis neural control network.

[0150] Based on the above explanation, it can be seen that in this embodiment, the distributed optimization control problem of a multi-robot system with unknown nonlinearities is considered, and the distributed optimization problem is cleverly converted into a consistent optimal control problem through a pre-filter. In addition, the present application adopts a fixed-time controller, thereby providing a fixed-time distributed optimization method based on a fixed-time convergence theoretical method, which can give a more accurate upper bound of the optimization time estimate, and the upper bound is independent of the initial state of the system. Therefore, the present application achieves rapid convergence of the system that is independent of the initial state.

[0151] In addition, in this embodiment, the fixed-time sub-virtual controller is designed , control rate , Fixed time actual controller and control rate There is no need to use any global information, such as the information of neighboring robotic arms, etc., thus avoiding problems such as poor robustness of single point failure, poor confidentiality, and poor timeliness. It can further reduce the computational complexity and communication loss of the multi-robotic arm system and improve the rapid convergence performance of the system.

[0152] In order to enable those skilled in the art to better understand the scope of protection of the claims of this application, the following is an explanation of the technical solutions recorded in the claims of this application through specific implementation examples in specific application scenarios. It can be understood that the following examples are only used to explain this application, and are not used to limit the scope of protection of the claims of this application.

[0153] In one example, the nonlinear multi-manipulator system includes a robot 1, a robot 2, a robot 3, and a robot 4. Among them, the robot 1, the robot 2, the robot 3, and the robot 4 are all single robots. Figure 3 , the undirected communication topology of the nonlinear multi-manipulator system.

[0154] In the nonlinear multi-manipulator collaborative lifting work, initial alignment is very important, which can be achieved by making the angular position of the link of each manipulator reach a consistent value with the minimum sum of the square of the angular movement distance. In this example, the initial calibration will be implemented as the control target.

[0155] First, let , .in, is the acceleration due to gravity, is the distance from the connecting rod to the center of gravity of the i-th robot arm, Represents the drag coefficient. The system parameters in the nonlinear multi-manipulator system are configured as: , , .

[0156] Secondly, the initial state of the nonlinear multi-manipulator system can be expressed as:

[0157] , , , , at this time, the rest of the initial states are set to 0.

[0158] Then, the control parameters and design parameters of the nonlinear multi-manipulator system are: , , , , , , , , .

[0159] In this example, the objective function designed based on the initial calibration control goal is: .

[0160] As can be understood, in this example, i=1,2,3,4.

[0161] The distributed optimization control method of the nonlinear multi-manipulator system provided in this embodiment is used to control it. Please refer to FIG. Figure 4-Figure 7 This is a simulation effect diagram of distributed optimization control of a multi-manipulator system based on fixed time control. Specifically, Figure 4 is the change curve of the rotation angle of the four robotic arms; Figure 5 is the variation curve of the rotation angular velocity of the four robotic arms; Figure 6 is the transformation curve of the weight norm of the radial basis neural control network; Figure 7 The curves of the control input torque values ​​of the four manipulators are shown in Figure 2. From the above simulation results, it can be seen that under the proposed distributed fixed-time optimization algorithm, the rotation angles of all manipulator systems can quickly converge to the minimum optimal value within a fixed time, and the rotation angular velocity converges to the control target of zero within a fixed time, ensuring the stable operation of the entire system.

[0162] It can be seen that, thanks to the pre-filter technology and fixed-time control, the distributed fixed-time optimization algorithm adopted by the present invention is completely distributed under the undirected topology, has lower computing and communication costs, and can ensure that the system reaches the optimal consensus quickly and accurately. The simulation results in the above examples further demonstrate the effectiveness of the method of the present application.

[0163] In addition, an embodiment of the present application further proposes a computer storage medium, on which a distributed optimization control method program for a nonlinear multi-robotic arm system is stored. When the distributed optimization control method program for a nonlinear multi-robotic arm system is executed by a processor, the steps of the distributed optimization control method for a nonlinear multi-robotic arm system described above are implemented. Therefore, no further description will be given here. In addition, the description of the beneficial effects of adopting the same method will not be repeated. For technical details not disclosed in the computer-readable storage medium embodiment involved in the present application, please refer to the description of the method embodiment of the present application. As an example, program instructions may be deployed to be executed on one computing device, or on multiple computing devices located at one location, or on multiple computing devices distributed at multiple locations and interconnected by a communication network.

[0164] Those skilled in the art can understand that all or part of the processes in the above-mentioned embodiments can be implemented by instructing the relevant hardware through a computer program, and the above-mentioned program can be stored in a computer-readable storage medium, and when the program is executed, it can include the processes of the embodiments of the above-mentioned methods. Among them, the above-mentioned storage medium can be a disk, an optical disk, a read-only memory (ROM) or a random access memory (RAM), etc.

[0165] It should also be noted that the device embodiments described above are merely schematic, wherein the units described as separate components may or may not be physically separated, and the components displayed as units may or may not be physical units, that is, they may be located in one place, or they may be distributed on multiple network units. Some or all of the modules may be selected according to actual needs to achieve the purpose of the scheme of this embodiment. In addition, in the accompanying drawings of the device embodiments provided by the present application, the connection relationship between the modules indicates that there is a communication connection between them, which may be specifically implemented as one or more communication buses or signal lines. A person of ordinary skill in the art may understand and implement it without paying any creative effort.

[0166] Through the description of the above implementation mode, the technicians in the field can clearly understand that the present application can be implemented by means of software plus necessary general hardware, and of course, it can also be implemented by special hardware including special integrated circuits, special CPUs, special memories, special components, etc. In general, all functions completed by computer programs can be easily implemented by corresponding hardware, and the specific hardware structure used to implement the same function can also be various, such as analog circuits, digital circuits or special circuits. However, for the present application, software program implementation is a better implementation mode in more cases. Based on such an understanding, the technical solution of the present application is essentially or the part that contributes to the prior art can be embodied in the form of a software product, which is stored in a readable storage medium, such as a computer floppy disk, a U disk, a mobile hard disk, a read-only memory (ROM, Read-Only Memory), a random access memory (RAM, Random Access Memory), a disk or an optical disk, etc., including a number of instructions to enable a computer device (which can be a personal computer, a server, or a network device, etc.) to execute the method of each embodiment of the present application.

[0167] The above are only preferred embodiments of the present application, and are not intended to limit the patent scope of the present application. Any equivalent structure or equivalent process transformation made using the contents of the present application specification and drawings, or directly or indirectly applied in other related technical fields, are also included in the patent protection scope of the present application.

Claims

1. A distributed optimization control method for a nonlinear multi-manipulator system, characterized in that: The method comprises: Determining a target control function of the nonlinear multi-manipulator system based on a state-space equation of the nonlinear multi-manipulator system; wherein the state-space equation includes an unknown nonlinear term; Based on a distributed proportional-integral optimization algorithm, a global optimal estimate of the objective control function is obtained; Inputting the global optimal estimation value into a pre-filter for reconstruction to obtain an optimal control signal without any global information; Based on the optimal control signal, construct an error transformation method for the nonlinear multi-manipulator system; Based on the preset Lyapunov function and the error transformation method, a fixed-time controller of the radial basis neural control network is constructed by backstepping method; Based on the fixed time controller, the optimal control signal is quickly tracked, and during the tracking process, the control input torque value of each manipulator in the nonlinear multi-manipulator system is adjusted based on the radial basis neural control network, so that the nonlinear multi-manipulator system reaches an optimal consensus; The method of obtaining the global optimal estimate of the objective control function based on the distributed proportional integral optimization algorithm includes: According to the communication relationship between the various mechanical arms in the nonlinear multi-manipulator system, a communication topology structure of the nonlinear multi-manipulator system is generated; wherein the communication topology structure is expressed as ; is a vertex set, represented by ; is an edge set, represented by ; is the adjacency matrix, expressed as ; In the communication topology, when the i-th robot among the N robot arms can receive the information of the k-th robot arm, it is expressed as , the neighbor set of the i-th robot Expressed as ; Among them, if , then the corresponding >0, if If not established, =0; according to The specific value of ,like , then the communication topology is an undirected topology; Determining the target control function of the nonlinear multi-manipulator system based on the state space equation of the nonlinear multi-manipulator system includes: Construct the dynamic equation of the i-th robot in the nonlinear multi-robot system; wherein the dynamic equation is: ; The dynamic equation is converted into the state space equation; wherein the state space equation is: ； Based on the state space equation, the target control function of the nonlinear multi-manipulator system is determined; wherein the target control function is: ； Define the global objective function And R is a real number domain, then the target control function is simplified to: ； The objective control function is converted to find the optimal Make each robot arm meet ; in, is the angular position of the manipulator joint in the i-th manipulator, is the angular velocity of the manipulator joint in the i-th manipulator, is the angular acceleration of the manipulator joint in the i-th manipulator, is the symmetric positive definite moment of inertia of the i-th robotic arm, is the centripetal force of the i-th robotic arm, is the gravitational torque of the i-th robotic arm, is the control input torque of the i-th robotic arm, , , is the output state, , is the local objective function of the i-th robotic arm, and are all the unknown nonlinear terms, and N is the total number of robotic arms in the nonlinear multi-robotic arm system.

2. The distributed optimization control method of a nonlinear multi-manipulator system according to claim 1, characterized in that: The error transformation method includes a tracking error transformation equation and an error surface transformation equation, and the fixed time controller includes a fixed time sub-virtual controller and a fixed time actual controller; The fixed time controller of the radial basis neural control network is constructed by backstepping method based on the preset Lyapunov function and the error transformation method, including: Based on the first preset Lyapunov function and the tracking error transformation equation, generating a fixed-time sub-virtual controller and a corresponding first neural network update law; Based on the second preset Lyapunov function and the error surface transformation equation, a fixed-time actual controller and a corresponding second neural network update law are generated.

3. The distributed optimization control method of a nonlinear multi-manipulator system according to claim 2, characterized in that: The method of obtaining the global optimal estimate of the objective control function based on the distributed proportional integral optimization algorithm includes: Based on the distributed proportional-integral optimization algorithm and the communication topology, construct a virtual system model of the nonlinear multi-manipulator system; Based on the virtual system model, obtaining a global optimal estimate of the objective control function; Wherein, the virtual system model is: ； ； in, and are control parameters, is the global optimal estimate, and Both indicate the status of the virtual system. Represents the local objective function gradient.

4. The distributed optimization control method of a nonlinear multi-manipulator system according to claim 3, characterized in that: The tracking error transformation equation is: ; wherein said is the tracking error, = ; The error surface transformation equation is: ;in, is the error surface, It is a fixed-time sub-virtual controller.

5. The distributed optimization control method of a nonlinear multi-manipulator system according to claim 4, characterized in that: The method further comprises: The unknown nonlinear term is approximated by the radial basis neural control network to obtain the unknown nonlinear term; the unknown nonlinear term is: ； ； in, and are the unknown nonlinear terms of the i-th robotic arm, and are ideal weights, and are basis functions, and are all approximation errors, satisfying and , and is an arbitrarily small positive constant, For fixed-time sub-virtual controllers The derivative of .

6. A distributed optimization control device for a nonlinear multi-manipulator system, characterized in that: include: A processor, a memory, and a distributed optimization control program for a nonlinear multi-robotic arm system stored in the memory. When the distributed optimization control program for the nonlinear multi-robotic arm system is executed by the processor, the steps of the distributed optimization control method for a nonlinear multi-robotic arm system as described in any one of claims 1 to 5 are implemented.

7. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a distributed optimization control program for a nonlinear multi-robotic arm system, and when the distributed optimization control program for a nonlinear multi-robotic arm system is executed by a processor, the distributed optimization control method for a nonlinear multi-robotic arm system as described in any one of claims 1 to 5 is implemented.

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