A multi-arm robot system distributed optimal control method and system

Abstract

The application discloses a multi-single-arm manipulator system distributed optimal control method and system, and belongs to the field of industrial control. For the three-difficult problem that the speed dynamics is completely unknown, the communication needs to be kept connected, and the input exists saturation constraint, the RNN is adopted to identify the unknown speed dynamics on line; the communication barrier function is designed to transform the consistency error to maintain the communication connection; the augmented system and the zero-sum game optimal control framework are constructed based on the barrier error and the speed consistency error; the adaptive dynamic programming is introduced to design the execution evaluation network update law and the approximate optimal controller; and the network weight is updated on line to realize the approximate optimal control. The application is suitable for the model unknown scene, and can meet the cooperative control, the communication keeping and the input saturation constraint simultaneously.

Description

Technical Field

[0001] This invention relates to the field of industrial process control technology, and in particular to a distributed optimal control method and system for a multi-single-arm robotic arm system. Background Technology

[0002] Multi-arm robotic systems can achieve higher operational efficiency and greater workspace coverage through distributed collaborative control. However, in actual industrial environments, robotic dynamics are often affected by complex factors such as friction, load changes, and unmodeled dynamics, making it difficult to obtain accurate system models or even completely unknown, which may result in deficiencies in control performance.

[0003] Besides the unknown model, multi-arm robotic systems face the dual challenges of maintaining communication and addressing input constraints during collaborative operations. On one hand, stable communication connections need to be maintained between the robotic arms to ensure information exchange and collaborative control. However, existing distributed control methods often assume that the communication topology remains connected at all times, failing to fully consider the impact of communication distance constraints on system performance. On the other hand, the physical amplitude characteristics of the actuators determine that there are inherent saturation constraints on the control input.

[0004] Therefore, in multi-arm manipulator systems, the velocity dynamics are completely unknown, the communication topology needs to be kept connected, and the actuators have input saturation limitations. These three factors are coupled with each other, which brings significant difficulties to the design of distributed optimal control. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides a distributed optimal control method and system for multi-arm manipulator systems with communication maintenance and input constraints; On the one hand, a distributed optimal control method for a multi-single-arm manipulator system is provided, including: A state-dynamic model of a multi-single-arm manipulator is constructed. An RNN system is used to identify the model and approximate the unknown velocity-dynamics online to obtain the RNN-estimated state. The RNN is used to estimate the state and define the velocity consistency error; a communication barrier function is designed based on the communication maintenance constraint to transform the relative position consistency error of the multi-arm manipulator and obtain the communication barrier error. Based on the communication barrier error and speed consistency error, an augmented state system is constructed, and a zero-sum game optimal control framework is established. Based on the zero-sum game optimal control framework, an adaptive dynamic programming algorithm is introduced to construct a three-network system consisting of Critic, u-Action, and w-Action. The weight update law for each network is designed to obtain an approximate optimal controller. Approximate optimal control is achieved by updating the weights of the three networks online and executing the approximate optimal controller based on the updated network output.

[0006] On the other hand, a distributed optimal control system for a multi-single-arm robotic arm system is provided, including: Modeling module: Used to construct state dynamics models of multiple single-arm manipulators. The model is identified by an RNN system, and the unknown velocity dynamics are approximated online using input-output data to obtain the RNN estimated state. Communication barrier module: used to estimate the state definition speed consistency error using the RNN, design the communication barrier function according to the communication maintenance constraint, transform the consistency error of the multi-arm manipulator, and obtain the transformed communication barrier error; Augmented System Construction Module: Used to construct an optimal control framework for augmented systems and zero-sum games based on communication barrier error and velocity consistency error; Adaptive Dynamic Programming Control Module: Based on the zero-sum game optimal control framework, it introduces an adaptive dynamic programming algorithm, designs a three-network structure, designs the execution-evaluation network update law, and designs an approximate optimal controller. Online update control module: used to achieve near-optimal control by updating the weights of the three networks online based on the near-optimal controller.

[0007] Furthermore, an electronic device is also provided, including: A memory for non-transitory storage of computer-readable instructions; and a processor for executing the computer-readable instructions. When the computer-readable instructions are executed by the processor, they perform the method described in the first aspect above.

[0008] In another aspect, a storage medium is also provided for non-transitory storage of computer-readable instructions, wherein when the non-transitory computer-readable instructions are executed by a computer, the method described in the first aspect is performed.

[0009] A computer program product is also provided, comprising a computer program that, when run on one or more processors, is used to implement the method described in the first aspect above.

[0010] The above technical solution has the following advantages or beneficial effects: This invention utilizes an RNN system identification model to approximate unknown velocity dynamics online using input-output data, eliminating the need for precise system dynamic parameters. This allows the resulting controller to be applicable to real-world industrial scenarios where the model is completely unknown, resulting in stronger robustness and better control performance. By designing a communication barrier function based on communication maintenance constraints, the communication constraints are incorporated as part of the control objective, ensuring that the distance between manipulators remains within the communication radius. This guarantees that multiple single-arm manipulators can effectively track given signals and maintain distributed communication connectivity. Furthermore, this method has wider applicability and does not require additional requirements for the initial communication topology. By introducing an adaptive dynamic programming algorithm into a zero-sum game optimal control framework, employing a three-network structure of Critic, u-Action, and w-Action, the invention simplifies control design while ensuring system optimality and disturbance suppression performance, achieving a trade-off between control effectiveness and control cost. Attached Figure Description

[0011] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0012] Figure 1 This is a flowchart of the method in Example 1; Figure 2 This is a communication topology diagram between single-arm robotic arms; Figure 3 The diagram shows the formation control performance of the simulation test; where (a) is the position tracking curve of the manipulator, (b) is the position tracking error, (c) is the speed tracking curve of the manipulator, and (d) is the speed consistency error. Figure 4 Here is a convergence curve of the RNN estimation error in the simulation experiment; where (a) is the position estimation error and (b) is the velocity estimation error. Figure 5 The simulation test communication maintenance verification diagram includes (a) the distance curve between the manipulators and (b) the communication barrier error curve. Figure 6 The input constraint verification diagram is used for the simulation experiment; where (a) is the actual control input curve and (b) is the auxiliary variable curve. Figure 7 The figure shows the convergence curve of the ADP three-network weights in the simulation experiment; where (a) is the weight of the Critic network, (b) is the weight of the u-Action network, and (c) is the weight of the w-Action network. Detailed Implementation

[0013] Example 1 This embodiment provides a distributed optimal control method for a multi-single-arm robotic system, such as... Figure 1 As shown; S1. Construct a state dynamics model for multiple single-arm manipulators.

[0014] Specifically, the construction of the state-dynamic model of the multi-arm manipulator includes: S101. Construct the standard dynamic equations for a single-arm robotic arm that follows the robotic arm; The standard dynamic equation for the i-th single-arm robotic arm that follows the robotic arm is:

[0015] In the formula, , , These represent the position, velocity, and acceleration of the robotic arm, respectively. Represents the moment of inertia. Indicates the damping coefficient. Indicates the magnitude of gravity. To control the torque input, The external disturbance is N, and the number of following robotic arms is N.

[0016] S102. Establish a graph theory description of the communication topology between multiple single-arm robotic arms; We introduce algebraic graph theory to describe the communication relationships between robotic arms, and adopt... Let represent a directed communication topology in graph theory, where For vertex set, For edge set, It is an adjacency matrix; Indicates the first The robotic arm system can transmit information to the first... A robotic arm, when hour, In other cases If the leader can transmit information to the robotic arm ,but ,otherwise .

[0017] S103. Construct state-space equations containing unknown velocity dynamics and bounded perturbations.

[0018] Define state variables , For complex working conditions where the velocity dynamics are completely unknown, the motion model of the multi-arm manipulator is transformed into a state-space equation:

[0019] In the formula, Let be an unknown smooth nonlinear function, representing the unknown velocity-dynamic characteristics of the robotic arm. To control the torque input, Describes a bounded external disturbance that satisfies .

[0020] S104. Construct an ideal RNN model to achieve theoretical reconstruction of the unknown velocity dynamics of the robot.

[0021] Construct an ideal recurrent neural network (RNN) model and use the system's true state and ideal weights to approximate and reconstruct the unknown velocity dynamics:

[0022] In the formula, This represents the actual state of the system. , , , Given an unknown ideal weight matrix and vector, the activation function is... For a given Lipschitz continuous function, satisfying , For finite approximation errors, satisfying .

[0023] S105. Based on the ideal RNN model, construct an actual RNN estimation model.

[0024] Build a data-driven, real-world estimation model that can run online based on an ideal RNN model:

[0025] In the formula, Estimate the state for the RNN. Indicates the first The actual estimated value of the system's position and state at each moment. Indicates the first The actual estimated value of the system velocity state at each moment; and These are the position estimation error and the velocity estimation error, respectively. and Inject the gain matrix into the error. , , , and For online weight estimation, Let χ be the activation function, and let it be its Lipschitz constant. Represents the smallest eigenvalue of the matrix. satisfy , satisfy .

[0026] Define state estimation error , .

[0027] S106. Design an adaptive weight update law for RNNs to ensure that the estimation error is consistent and eventually bounded.

[0028]

[0029] In the formula, The normal learning rate is preset; this update law can guarantee the accuracy of position state estimation. Velocity state estimation error Both the weight estimation error matrix and the weight estimation error matrix are uniformly bounded (UUB).

[0030] S2. Design a communication barrier function based on the communication maintenance constraint, transform the consistency error of the multi-arm manipulator, and obtain the transformed communication barrier error.

[0031] Specifically, S2 includes: S201. Combining graph theory communication topology and system model, define the relative position error between robotic arms and introduce the desired position offset.

[0032] Define the consistency error as:

[0033] In the formula, For the first The position of the robotic arm For the first The position of the robotic arm; set up For the first Each robotic arm is offset relative to the leader's desired position, with the desired relative position being... .

[0034] S202. Construct a communication barrier function that satisfies the communication maintenance constraint.

[0035] The communication barrier function is:

[0036] in, For robotic arms Communication radius, and The actual relative position and the expected relative position are respectively the first Dimensional components.

[0037] The barrier function has the following properties: when the relative position is close to the communication boundary, the barrier function value increases and produces a repulsion effect; when it is in a safe area, the barrier function approaches zero.

[0038] S203. Define the speed consistency error and aggregate the barrier functions of each link to obtain the unified communication barrier error.

[0039] The speed consistency error is:

[0040] in, and These are the adjacency weights and leader connection weights mentioned above. , Let RNNs estimate the velocities of the i-th and j-th robotic arms, respectively. For the leader's speed.

[0041] The unified communication barrier error is:

[0042] in, Let i be the communication barrier function between the i-th robotic arm and the leader in the k-th direction.

[0043] S3. Based on communication barrier error, construct an optimal control framework for augmented systems and zero-sum games.

[0044] Specifically, the construction of the augmented system and zero-sum game optimal control framework based on communication barrier error includes: S301. Combine the communication barrier error vector and the speed consistency error vector to construct the augmented state vector of the i-th manipulator:

[0045] In the formula, This is the communication barrier error vector. This is the speed consistency error vector.

[0046] S302. Reconstruct the velocity dynamics based on the RNN estimation results, and construct the augmented system for the i-th manipulator:

[0047] In the formula, For system drift term, For the control gain matrix, The perturbation gain matrix is... The combined perturbation vector, including barrier error, reconstruction error, and RNN model estimation error, satisfies... , It is a positive number; in, For the velocity estimation error term, its first... Dimensional components are defined as follows

[0048] In the formula, express The One portion, ; in, The comprehensive estimation error is defined as follows:

[0049] In the formula, , , , , For weight estimation error, For state estimation error, Estimate the error for the activation function; because and All are finite sets, and based on the convergence of RNN identification, both the weight estimation error and the state estimation error are uniformly bounded (UUB), therefore, there exists a positive constant. This makes the overall estimation error bounded: .

[0050] S303, Comprehensive disturbances in augmented systems As the system control input, the augmented system control problem with disturbance is transformed into a two-person zero-sum optimal control problem between the controller and the disturbance, and an infinite time-domain performance index function is defined.

[0051] The performance index function is:

[0052] In the formula, As a discount factor, Let be the state penalty matrix. This is the disturbance attenuation coefficient. For the perturbation penalty matrix, The input penalty function is used to control the integration variable, τ.

[0053] S304. Design a non-quadratic control input penalty function that adapts to actuator input saturation constraints.

[0054] The non-quadratic control input penalty function is:

[0055] In the formula, To control the input saturation limit, for The One portion, For the control input number The integration variable introduced when integrating each component. To control the weight matrix, Represents the hyperbolic tangent function The inverse function of .

[0056] S305. Combining the dynamic equations and performance index functions of the augmented system, construct the corresponding Hamiltonian function.

[0057]

[0058] S306. Based on the Bellman optimization principle, the analytical solutions of the HJI equation and the game equilibrium are obtained.

[0059] Based on Bellman's optimization principle, the optimal control pair in a zero-sum game... Satisfying the Hamilton-Jacobi-Isaacs (HJI) equation The analytical solution is:

[0060] in, and These are the optimal control input and the worst-case disturbance, respectively. This is the gradient of the optimal performance index function.

[0061] S4. Based on the zero-sum game optimal control framework, we introduce an adaptive dynamic programming algorithm and design a three-network structure, design the execution-evaluation network update law, and an approximate optimal controller.

[0062] Specifically, the process of introducing an adaptive dynamic programming algorithm and designing a three-network structure based on the zero-sum game optimal control framework, as well as designing the execution-evaluation network update law and an approximate optimal controller, includes: S401, a three-layer neural network approximation architecture.

[0063] To address the difficulty of directly solving HJI partial differential equations analytically, an adaptive dynamic programming algorithm is introduced, employing a three-network structure to achieve distributed online learning. Three single-layer neural networks (SLNNs) are used to approximate the optimal performance index function. Control channel auxiliary variables and optimal perturbation law The network adopts a network architecture with randomly fixed hidden layer weights and online updates only to the output layer weights, reducing the computational complexity of online learning.

[0064] S402. Design the Critic evaluation network and its weight update law to approximate the optimal performance index function.

[0065] Using the Critic network to study the optimal performance index function under the zero-sum game framework To approximate the ideal network output expression, we have:

[0066] in, For ideal Critic weights, The Critic network basis function vector. This represents the network approximation error.

[0067] The actual output of the Critic network is

[0068] in, The Critic output layer weights are updated online.

[0069] Design the weight adaptive update law for the Critic network:

[0070] In the formula, For learning rate, Define instantaneous cost term .

[0071] S403. Design the u-Action network, handle actuator input saturation constraints, and configure the weight update law.

[0072] Construct u Action controls the execution network and introduces auxiliary variable methods to handle input constraints; Define auxiliary variables:

[0073] in, For the u-Action network basis function vectors, The output layer weights are updated online.

[0074] The actual control input is obtained through tanh transformation:

[0075] This mapping ensures that the control input meets the amplitude constraint. .

[0076] Configure the u-Action network weight update law:

[0077] in, is the learning rate of the u-Action network.

[0078] S404, Design w The Action perturbation executes the network to approximate the worst-case optimal perturbation law, and configures the corresponding weight update law.

[0079] Build w The Action perturbation execution network is used to approximate the worst perturbation strategy in zero-sum games. The actual output of the network is...

[0080] in Update the output layer weights of the w-Action network online. is the basis function vector of the w-Action network.

[0081] Design w Action Network Weight Update Law:

[0082] in, is the learning rate for the w-Action network.

[0083] S405. Construct a distributed near-optimal controller.

[0084] In the process of three-network collaborative online learning, the Critic network, u Action Network, w The Action network iterates synchronously according to its respective weight update law; The output of the Action network is transformed to obtain an approximately optimal control torque that satisfies the input saturation constraint. This torque is then used as the control input for the i-th manipulator, enabling distributed online optimal control of the multi-single-arm manipulator system.

[0085] S5. Based on the distributed near-optimal controller, near-optimal control is achieved by updating the weights of the three networks online.

[0086] Specifically, the step of achieving near-optimal control based on a distributed near-optimal controller by updating the weights of the three networks online includes: S501. Obtain the actual control input by applying a hyperbolic tangent transform to the auxiliary variables output by the u-Action network:

[0087] The control input directly acts on the velocity-dynamic system of the i-arm manipulators, strictly satisfying the input saturation constraint. .

[0088] S502, Input actual control data Substitute the actual RNN estimation model into the equation and update the RNN estimation state:

[0089] S503. Based on the updated estimated state, recalculate the communication barrier error. and speed consistency error Update augmentation status .

[0090] S504, Update the augmentation status Input the Critic network and calculate the approximate Hamiltonian residual. Update the Critic network weights .

[0091] S505, based on the updated Critic network weights Recalculate the target auxiliary variables of the u-Action network. The target perturbation of the w-Action network ;

[0092]

[0093] S506. Repeat steps S501-S505 to achieve online collaborative updates of the three networks at each sampling time until the weights of the Critic, u-Action, and w-Action networks converge to steady-state values.

[0094] Furthermore, in a simulation experiment of this embodiment: The control objective of the simulation experiment is to control the angular position of the robotic arm. Tracking the leader's trajectory signals Considering the influence of external disturbances, the disturbance signal is a decaying sinusoidal interference superimposed on the velocity channel, in the form of... Amplitude not exceeding In connection with the actual system, the system parameters are designed as follows: moment of inertia. Damping coefficient Gravity amplitude The desired formation offset is set to... (Unit: rad). The initial values ​​for the simulation system state and neural network weights are: , , , , All elements are initialized to .

[0095] Other parameters are designed as follows: communication radius Controlling saturation boundary Number of hidden layer neurons in the ADP network Learning rate , , RNN identification learning rate Discount factor Disturbance attenuation level State penalty weight Control weight Disturbance penalty weight The simulation lasted for 500 seconds, and the ADP algorithm started from the initial moment.

[0096] The simulation results are shown in Figures 3–7. Figure 3 shows the formation control performance, where Figures 3(a) and 3(c) show the position and velocity tracking curves of the manipulators, respectively. It can be seen that all single-arm manipulators can effectively track the given leader signal. Figures 3(b) and 3(d) show the position tracking error and velocity consistency error, respectively. The errors converge rapidly after ADP is started, verifying the effectiveness of formation control. Figure 4 shows the convergence curve of RNN estimation error, where Figure 4(a) shows the position estimation error and Figure 4(b) shows the velocity estimation error. It can be seen that after applying the RNN system identification model, the estimation error converges rapidly to a small range within 10 seconds, verifying the effectiveness of the model in identifying unknowns. Figure 5 shows the communication maintenance verification, where Figure 5(a) shows the distance curve between manipulators and Figure 5(b) shows the communication barrier error curve. It can be seen that throughout the entire control process, the maximum neighbor distance is always kept within the communication radius D = 5.0, verifying the effectiveness of the communication barrier function. Figure 6 shows the input constraint verification diagram, where Figure 6(a) is the actual control input curve and Figure 6(b) is the auxiliary variable curve. It can be seen that the control input of all manipulators is always kept within the saturation limit ±3 N·m, without the need for additional projection or clipping operations. Figure 7 shows the convergence curve of the ADP three-network weights, where Figures 7(a), 7(b), and 7(c) are the weights of the Critic, u-Action, and w-Action networks, respectively. It can be seen that the weights of the three networks converge to the convergence target region within 50 seconds, verifying the effectiveness of distributed online learning.

[0097] Example 2 This embodiment provides a distributed optimal control system for a multi-single-arm robotic arm system, including: Modeling module: Used to construct state dynamics models of multiple single-arm manipulators. The model is identified by an RNN system, and the unknown velocity dynamics are approximated online using input-output data to obtain the RNN estimated state. Communication barrier module: used to estimate the state definition speed consistency error using the RNN, design the communication barrier function according to the communication maintenance constraint, transform the consistency error of the multi-arm manipulator, and obtain the transformed communication barrier error; Augmented System Construction Module: Used to construct an optimal control framework for augmented systems and zero-sum games based on communication barrier error and velocity consistency error; Adaptive Dynamic Programming Control Module: Based on the zero-sum game optimal control framework, it introduces an adaptive dynamic programming algorithm, designs a three-network structure, designs the execution-evaluation network update law, and designs an approximate optimal controller. Online update control module: used to achieve near-optimal control by updating the weights of the three networks online based on the near-optimal controller.

[0098] Example 3 This embodiment also provides an electronic device, including: one or more processors, one or more memories, and one or more computer programs; wherein, the processor is connected to the memory, and the one or more computer programs are stored in the memory. When the electronic device is running, the processor executes the one or more computer programs stored in the memory to cause the electronic device to perform the method described in Embodiment 1.

[0099] It should be understood that in this embodiment, the processor can be a central processing unit (CPU), or it can be other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor can be a microprocessor or any conventional processor, etc.

[0100] Memory may include read-only memory and random access memory, and provides instructions and data to the processor. A portion of memory may also include non-volatile random access memory. For example, memory may also store information about the device type.

[0101] In the implementation process, each step of the above method can be completed by the integrated logic circuits in the processor hardware or by software instructions.

[0102] The method in Embodiment 1 can be directly implemented by a hardware processor, or implemented by a combination of hardware and software modules within the processor. The software modules can reside in readily available storage media in the art, such as random access memory, flash memory, read-only memory, programmable read-only memory, electrically erasable programmable memory, or registers. This storage medium is located in memory; the processor reads information from the memory and, in conjunction with its hardware, completes the steps of the above method. To avoid repetition, a detailed description is not provided here.

[0103] Those skilled in the art will recognize that the units and algorithm steps described in connection with the various examples of this embodiment can be implemented in electronic hardware or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this invention.

[0104] Example 4 This embodiment also provides a computer-readable storage medium for storing computer instructions, which, when executed by a processor, complete the method described in Embodiment 1.

[0105] Example 5 This embodiment also provides a computer program product, including software code, wherein the program in the software code performs the steps described in Embodiment 1 of the present invention.

[0106] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A distributed optimal control method for a multi-single-arm robotic arm system, characterized in that, include: Construct a state-dynamic model for a multi-arm manipulator and obtain the state estimated by RNN; The RNN is used to estimate the state definition speed consistency error. A communication barrier function is designed based on the communication maintenance constraint. The consistency error of the multi-arm manipulator is transformed to obtain the transformed communication barrier error. Based on communication barrier error and velocity consistency error, an optimal control framework for augmented systems and zero-sum games is constructed. Based on the zero-sum game optimal control framework, we introduce an adaptive dynamic programming algorithm and design a three-network structure, design the execution-evaluation network update law and an approximate optimal controller; Based on the approximate optimal controller, near-optimal control is achieved by updating the weights of the three networks online.

2. The distributed optimal control method for a multi-arm robotic system according to claim 1, characterized in that, The construction of the state dynamics model for the multi-arm manipulator includes: Construct the standard dynamic equations for a single-arm robotic arm that follows the robotic arm; Algebraic graph theory is introduced to establish a communication topology between multiple single-arm robotic arms; The motion model of the multi-arm manipulator is transformed to obtain the state-space equation containing unknown velocity dynamics and bounded external disturbances. Constructing an ideal RNN model to theoretically reconstruct the unknown velocity dynamics; Based on the ideal RNN model, construct an actual RNN estimation model and define the state estimation error; Design an adaptive weight update law for the RNN to ensure that the position state estimation error, velocity state estimation error, and weight estimation error are uniformly bounded.

3. The distributed optimal control method for a multi-arm robotic system according to claim 1, characterized in that, The process involves using the RNN to estimate the state and define the velocity consistency error, designing a communication barrier function based on communication maintenance constraints, and transforming the consistency error of the multi-arm manipulator to obtain the transformed communication barrier error, including: Define the relative position error between robotic arms and introduce the desired position offset; Construct a communication barrier function that satisfies the communication preservation constraint; Based on RNN estimation, a speed consistency error is defined. By combining the communication topology adjacency relationship, the barrier functions of each link are weighted and aggregated to obtain a unified communication barrier error.

4. The distributed optimal control method for a multi-arm robotic system according to claim 1, characterized in that, The optimal control framework for augmented systems and zero-sum games, based on communication barrier error and velocity consistency error, includes: The communication barrier error vector and the velocity consistency error vector are combined to construct an augmented state vector; Using the RNN estimation results, the velocity dynamics are reconstructed, an augmented system is established, a comprehensive perturbation vector containing barrier error, reconstruction error, and RNN model estimation error is constructed, and the comprehensive perturbation is proved to be bounded. By taking the integrated disturbance as the system control input, the control problem of the augmented system with disturbance is transformed into a two-person zero-sum optimal control problem between the controller and the disturbance, and an infinite time-domain performance index function is defined. Design a non-quadratic control input penalty function that adapts to actuator input saturation constraints; We construct the Hamiltonian function and obtain the analytical solution of the HJI equation and the game equilibrium based on the Bellman optimization principle.

5. A distributed optimal control method for a multi-arm robotic system according to claim 1, characterized in that, Based on the zero-sum game optimal control framework, an adaptive dynamic programming algorithm is introduced, and a three-network structure is designed for execution. Evaluation of network update laws and near-optimal controllers includes: A three-layer neural network approximation architecture is constructed to approximate the optimal performance index function, control channel auxiliary variable, and optimal perturbation law, respectively. Construct a u-Action network, handle actuator input saturation constraints, and configure the weight update law; Construct the Action control execution network, handle saturation constraints of the actuator inputs, and configure the weight update law; Construct an Action perturbation execution network to approximate the worst-case optimal perturbation law and configure the corresponding weight update law.

6. The distributed optimal control method for a multi-arm robotic system according to claim 1, characterized in that, The step of achieving near-optimal control by updating the weights of the three networks online, based on the near-optimal controller, includes: The auxiliary variables output by the u-Action network are transformed into the actual control inputs using hyperbolic tangent transform. Substitute the actual control input into the actual RNN estimation model and update the RNN estimation state; Based on the updated RNN estimated state, the communication barrier error and velocity consistency error are recalculated, and the augmented state is updated. The updated augmented state is input into the Critic network, the approximate Hamiltonian residual is calculated, and the Critic network weights are updated. Based on the updated Critic network weights, update the target auxiliary variable of the u-Action network and the target perturbation of the w-Action network respectively; Each sampling time point is iterated in a loop until Critic, u Action, w Action: Network weights converge to steady-state values.

7. A distributed optimal control system for a multi-single-arm robotic arm system, characterized in that, include: Modeling module: Used to construct state dynamics models of multiple single-arm manipulators. The model is identified by an RNN system, and the unknown velocity dynamics are approximated online using input-output data to obtain the RNN estimated state. Communication barrier module: used to estimate the state definition speed consistency error using the RNN, design the communication barrier function according to the communication maintenance constraint, transform the consistency error of the multi-arm manipulator, and obtain the transformed communication barrier error; Augmented System Construction Module: Used to construct an optimal control framework for augmented systems and zero-sum games based on communication barrier error and velocity consistency error; Adaptive Dynamic Programming Control Module: Based on the zero-sum game optimal control framework, it introduces an adaptive dynamic programming algorithm, designs a three-network structure, designs the execution-evaluation network update law, and designs an approximate optimal controller. Online update control module: used to achieve near-optimal control by updating the weights of the three networks online based on the near-optimal controller.

8. An electronic device, comprising: A memory and a processor, wherein the memory is used to store computer programs; and the processor is used to execute, when the computer programs are invoked, a distributed optimal control method for a multi-single-arm robotic system as described in any one of claims 1 to 6.

9. A computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements a distributed optimal control method for a multi-arm robotic system according to any one of claims 1 to 6.

10. A computer program product, wherein the computer program product comprises a computer program that, when executed by a processor, implements a distributed optimal control method for a multi-arm robotic system according to any one of claims 1 to 6.

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