Hybrid Pareto differential game-based modular robot approximate optimal tracking control method under cooperative competition framework
By employing a hybrid Pareto differential game method within a cooperative-competitive framework, the control accuracy and robustness issues of modular robots under uncertain perturbations were addressed. This resulted in improved stability and robustness under maximum perturbation conditions, optimized control accuracy, reduced energy consumption, and overcame the curse of dimensionality.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-12-31
- Publication Date
- 2026-03-27
AI Technical Summary
Modular robots suffer from low control accuracy and poor robustness under uncertain disturbances. Existing technologies, such as H-infinity control, have an inherent trade-off between stability and optimality. Solving the HJI equations is subject to the curse of dimensionality. Furthermore, multi-agent cooperative control frameworks are insufficient.
A hybrid Pareto differential game approach under a cooperative-competitive framework is adopted. A dynamic model is established through the Newton-Euler iterative method, a global cost function and a Hamiltonian function are constructed, an evaluation neural network is used to approximate the optimal control law, a weight update mechanism is designed, and perturbations are handled by combining Pareto game and zero-sum competitive game.
It achieves improved system stability and robustness under maximum disturbance conditions, optimized control precision, reduced energy consumption, solved the curse of dimensionality problem, and provides real-time high-precision trajectory tracking control.
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Figure CN121742218A_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The present application relates to the technical field of robot control algorithm, and particularly relates to a modular robot approximate optimal tracking control method based on mixed Pareto differential game in a cooperative-competitive framework. BACKGROUND
[0002] As a kind of reconfigurable system with standard modules and interfaces, modular robots can flexibly adjust their own configurations according to task requirements. Each joint module integrates communication, sensing, driving and control units, showing adaptability and multifunctionality that traditional robots lack. Trajectory tracking control is the core application of this kind of robot, aiming to achieve high-precision motion trajectory tracking to complete complex tasks. However, in practical applications, external disturbances (such as load changes and environmental disturbances) are inevitable, often causing the system state to deviate from the expected output, severely restricting tracking accuracy and system reliability.
[0003] When the system dynamics and disturbances are known, model predictive control can achieve optimal performance, but disturbances are usually unknown, making this method unsuitable. Disturbance estimation and compensation methods (such as observer design) approximate disturbances, but inaccurate estimation can introduce additional errors, disrupting the balance between stability and optimality. In this context, H-infinity optimal control, as an important branch of robust control, is widely used. Its core idea is to minimize the impact of disturbances on system performance by setting a maximum disturbance boundary. However, this approach inherently involves a trade-off: expanding the disturbance boundary can enhance system stability and suppress disturbances, but it will lead to a conservative control strategy, sacrificing dynamic response performance and control optimality; conversely, if optimal performance is pursued, the system's stability under maximum disturbance may be compromised.
[0004] Further, the effective implementation of H-infinity control strategy highly depends on solving the Hamilton-Jacobi-Isaacs equation (HJI equation) of nonlinear systems. This solving process faces significant theoretical challenges. Traditional solving methods such as dynamic programming suffer from the "curse of dimensionality" problem in practical applications, which leads to explosive computational complexity as the number of joint modules increases (i.e., the growth of system dimension), making it impossible to obtain optimal solutions in real time, resulting in control strategy lag. To overcome this numerical difficulty, the adaptive dynamic programming (ADP) method was proposed, which uses neural networks (such as critic networks) to approximate the optimal cost function or control strategy, bypassing the difficulty of directly solving the HJI equation through data-driven methods. However, for modular robots, a multi-agent system, the control process involves cooperation between multiple joint controllers. Each controller minimizes its own cost while also considering the joint cost function to achieve Pareto equilibrium. Existing ADP methods still have deficiencies in effectively integrating this "cooperation" among multiple controllers and addressing the "competition" mechanism of disturbances.
[0005] In summary, the main problems existing in the prior art are low control accuracy and poor robustness, which are caused by the inherent trade-off of H-infinity control, the dimension disaster challenge of HJI equation solving, and the lack of multi-agent cooperative control framework. SUMMARY
[0006] The purpose of the present application is to provide a modular robot approximate optimal tracking control method based on hybrid Pareto differential game under a cooperative competition framework, to solve the problem of low control accuracy and poor robustness of modular robots under uncertain disturbances in the prior art, and to achieve tracking accuracy while handling external disturbances, improve system stability and energy efficiency.
[0007] To achieve the above purpose, the technical scheme adopted by the present application is as follows: The modular robot approximate optimal tracking control method based on hybrid Pareto differential game under a cooperative competition framework comprises the following steps: S1: Establish a dynamic model of the modular robot, construct a dynamic equation by Newton-Euler iteration method and handle uncertainty, and generate state variables and disturbance terms; S2: Construct a global cost function and a Hamilton function based on the state variables and the disturbance terms; S3: Derive a control law using a judgment neural network and a hybrid Pareto game according to the global cost function and the Hamilton function, and design a weight update mechanism; S4: Based on the control law, verify the control performance through a modular robot platform experiment.
[0008] Further, the S1 specifically comprises: Based on the Newton-Euler iteration method, the nominal dynamic equation of the modular robot is established, which includes the inertia matrix, the Coriolis force matrix and the gravity torque matrix; The nominal dynamic equation is decomposed into dynamic equations of multiple joint subsystems, and each joint subsystem dynamic equation includes a coupling cross-linking term for representing the mutual influence between joints; The dynamic equation of the joint subsystem is processed for uncertainty by separating the known parameters and unknown parameters through the estimated value and the deviation value, to generate a disturbance term containing model estimation deviation and coupling effect; The system state variable is defined as the combination of the position vector and the velocity vector, and the dynamic equation after processing the uncertainty is converted into a state space equation, which includes the system state variable and the disturbance term.
[0009] Further, the coupling cross-linking term is represented as , the value of which depends on the position, velocity and acceleration parameters of each joint; The estimated value and the bias value, the separation process comprising: the inertia matrix, the Coriolis force and the centrifugal force matrix and the gravity torque matrix are respectively decomposed into estimated value and estimated bias value.
[0010] Further, S2 specifically comprises: Based on the system state variable and the disturbance term, a global cost function containing a speed tracking error term, a control input energy term and a disturbance suppression term is constructed, and the parameters of the global cost function contain a weight matrix and a decay gain; Based on the Bellman optimality principle, a Hamilton function is constructed, which contains the instantaneous cost function and the gradient information of the global cost function; Based on the Hamilton function, the global optimal cost function is established by the minimax optimization principle.
[0011] Further, S3 specifically comprises: The optimal cost function is approximated by a critic neural network, and the critic neural network contains weight parameters and activation functions; Based on the output of the critic neural network, the optimal control law and the disturbance control law of the hybrid Pareto game are derived; A weight update law is designed to adjust the weight parameters of the critic neural network.
[0012] Further, the weight parameters of the critic neural network are adjusted by the gradient descent method to minimize the Hamilton function approximation error.
[0013] Further, the hybrid Pareto game includes a Pareto cooperative game and a zero-sum competitive game, wherein the Pareto cooperative game is used to realize multi-controller collaborative optimization, and the zero-sum competitive game is used to deal with the worst disturbance.
[0014] Further, the design weight update law is based on the gradient descent method, including calculating the gradient of the Hamilton function approximation error with respect to the weight parameters, and updating the weight parameters in the negative gradient direction.
[0015] Another object of the present application is to provide a computer readable storage medium storing a computer program, which is executed by a processor to implement the approximate optimal tracking control method for modular robots based on hybrid Pareto differential game.
[0016] Another object of the present application is to provide an electronic device comprising a memory and a processor, the memory being used to store a computer program, and the processor running the computer program to make the electronic device execute the approximate optimal tracking control method for modular robots based on hybrid Pareto differential game.
[0017] The application provides a modular robot approximate optimal tracking control method based on a hybrid Pareto differential game under a cooperative competition framework. 1. The robustness is significantly improved. The application successfully breaks through the inherent trade-off relationship between stability and optimality in H-infinity control. By introducing a zero-sum game mechanism, the disturbance is regarded as an antagonistic participant, and a critic neural network is used to solve the worst disturbance strategy of the HJI equation in real time. This innovation enables the system to remain stable under the condition of maximum disturbance, significantly enhancing the anti-interference ability and robustness of the system.
[0018] 2. The control accuracy is comprehensively optimized. By constructing a hybrid Pareto game framework, the cooperative optimization between multiple controllers is realized. Each joint controller minimizes its own cost function while considering the overall system performance through the Pareto equilibrium mechanism. This cooperative and competitive mode enables the system to achieve approximate optimal tracking control under the condition that the L2 gain is not greater than γ, significantly improving the trajectory tracking accuracy and effectively suppressing the speed tracking error.
[0019] 3. The dimension disaster problem is effectively overcome. The adaptive dynamic programming method is adopted, which approximates the optimal cost function through the critic neural network, successfully avoiding the computational complexity problem of directly solving the HJI equation. The introduction of the weight update law enables the system to learn and adapt to dynamic changes online, fundamentally solving the dimension disaster challenge caused by the increase in the number of joints, and providing a feasible solution for real-time control of complex modular robot systems.
[0020] 4. The system comprehensive performance is improved. Experimental verification results show that the control torque output of the application is more continuous and smooth, not only maintaining the system's asymptotic stability, but also significantly reducing the energy loss of each joint. The test data of the two-degree-of-freedom modular robot platform confirm that this method ensures high-precision tracking while achieving energy optimization, providing technical support for the long-term stable operation of modular robots in complex environments.
[0021] In summary, the application innovatively combines hybrid Pareto differential game and adaptive dynamic programming, achieving comprehensive improvement in robustness, control accuracy, real-time performance, and energy efficiency, and providing a complete solution for modular robot control systems. BRIEF DESCRIPTION OF DRAWINGS
[0022] Figure 1 The flowchart of the method of the application. DETAILED DESCRIPTION
[0023] In order to make the purpose, technical scheme and advantages of the present application clearer, the present application is further described in detail below in combination with the drawings and examples. It should be understood that the specific examples described herein are only used to explain the present application and are not used to limit the present application. In addition, the technical features involved in each embodiment of the present application described below can be combined with each other as long as they do not conflict with each other.
[0024] The present embodiment provides a modular robot approximate optimal tracking control method based on hybrid Pareto differential game under cooperative competition framework, as shown in Figure 1 The present embodiment provides a modular robot approximate optimal tracking control method based on hybrid Pareto differential game under cooperative competition framework, as shown in S1: Establishing a dynamic model of the modular robot, constructing a dynamic equation by Newton-Euler iteration method and processing uncertainty, and generating state variables and disturbance terms; S2: Constructing a global cost function and a Hamilton function based on the state variables and the disturbance terms; S3: Deriving a control law by using a judgment neural network and a hybrid Pareto game according to the global cost function and the Hamilton function, and designing a weight updating mechanism; S4: Verifying the control performance through a modular robot platform experiment based on the control law.
[0025] The present embodiment provides a modular robot approximate optimal tracking control method based on hybrid Pareto differential game under cooperative competition framework, as shown in The modular robot system is composed of multiple joint modules, and each joint is equipped with an independent controller. In order to achieve optimal tracking performance, the present application proposes a modular robot approximate optimal tracking control method based on hybrid Pareto differential game under cooperative competition framework, the core idea of which is that each joint controller is regarded as a participant in the Pareto game, and the overall performance optimization is achieved through mutual cooperation between the controllers to form a Pareto equilibrium; at the same time, when facing system uncertainty disturbance, a zero-sum game mechanism is introduced to ensure that the optimal performance can still be maintained under the condition of maximum disturbance. This hybrid framework effectively solves the problem of mutual restriction between control accuracy and robustness.
[0026] 1. Establishing a dynamic model of the modular robot, constructing a dynamic equation by Newton-Euler iteration method and processing uncertainty, and generating state variables and disturbance terms. Through accurate modeling and uncertainty processing, a basis reflecting the system dynamics is provided for the control strategy.
[0027] Firstly, the nominal dynamic equation of the modular robot is established based on the Newton-Euler iteration method, which includes the inertia matrix, the Coriolis force matrix and the gravity torque matrix. The nominal dynamic equation of the modular robot is established based on the Newton-Euler iteration method, which accurately describes the inertia characteristics, velocity-dependent forces and gravity effects of the robot. The nominal dynamic equation of the modular robot is established as follows: (1) in, These represent the inertia matrix, Coriolis force and centrifugal force matrix, and gravitational torque matrix of the robot system, respectively. These represent the position vector, velocity vector, and acceleration vector of the robot link, respectively. It represents the control torque.
[0028] Secondly, the nominal dynamic equation is decomposed into dynamic equations for multiple joint subsystems. Each joint subsystem's dynamic equation includes coupling and cross-linking terms to characterize the interactions between joints. Considering the special structure of the modular robot, the overall system needs to be decomposed into multiple joint subsystems for analysis. The dynamic model of the modular robot system can be represented as composed of independent joint subsystems with coupling and cross-linking terms, separating the position vectors. ,speed acceleration variables Each subsystem of a modular robot system in joint space can be represented as: (2) in, For vectors The i-th element; It is a matrix Separation of variables; This represents the coupling and cross-linking terms between joint subsystems. This decomposition allows for the study of the motion characteristics of each joint individually, while simultaneously utilizing the coupling and cross-linking terms... Let's consider the interactions between joints.
[0029] Then, uncertainty processing is applied to the dynamic equations of the joint subsystem. Known and unknown parameters are separated by estimated and bias values, generating a perturbation term that includes model estimation bias and coupling effects. The separation process involves decomposing the inertia matrix, Coriolis force and centrifugal force matrices, and gravitational moment matrix into estimated and bias values, respectively. In practical applications, because modular robots need to change their configuration according to task requirements, their dynamic parameters are often difficult to obtain precisely. To solve this problem, the uncertainties of the system are extracted and processed, and the dynamic model is rewritten, resulting in: (3) in To The estimated value, For matrix The estimated deviation value, This represents the uncertain disturbance of the system. This representation method can clearly distinguish between the known and unknown parts, which facilitates the design of subsequent robust control strategies.
[0030] By extracting the uncertainty of the modular robotic system, the following rewritten dynamics equation can be obtained: (4) wherein, is an imprecisely modeled term.
[0031] Finally, the system state variable is defined as the combination of the position vector and the velocity vector, and the dynamics equation after processing the uncertainty is converted into a state space equation, which includes the system state variable and the disturbance term.
[0032] In order to facilitate the controller design, the above dynamics equation is converted into a state space equation form. The state of the modular robotic system is defined as , the state space equation can be obtained as follows: (5) wherein (6) are the global drift dynamics function, the global control input function and the global uncertain disturbance function of the system respectively, each of which is expressed as: (7) The above modeling process effectively avoids the decrease of control accuracy caused by model error, and through the explicit expression of coupling term and disturbance term, it lays a solid foundation for subsequent robust control strategy and improves the applicability of the system in actual disturbance environment.
[0033] 2. Construct a global cost function and a Hamilton function based on the state variable and the disturbance term. Through a multi-objective optimization framework, the balance between tracking accuracy, energy consumption and disturbance resistance is achieved, providing a theoretical basis for the derivation of the subsequent optimal control law.
[0034] First, based on the system state variable and the disturbance term, a global cost function containing a velocity tracking error term, a control input energy term and a disturbance suppression term is constructed, and the parameters of the global cost function include a weight matrix and a decay gain. A global cost function that can fully reflect the performance requirements of the system is constructed. This function needs to consider multiple goals such as tracking accuracy, control energy consumption and disturbance suppression, and its expression is: (8) wherein the extended control input is represents the global utility function of the robotic system, i.e. the instantaneous cost function; is the velocity tracking error of the system; is a positive definite matrix; is a decay gain.
[0035] The design of this function embodies the core idea of the cooperative-competitive framework: to guarantee the tracking performance of each joint (cooperation) and to optimize the energy consumption of the whole system (competition). When constructing the cost function, the values of the weight matrix Q and are needed to be chosen reasonably. Generally speaking, the larger the value of Q matrix is, the stronger the system's ability to suppress tracking error is, but it may lead to a large control amount; while the larger the value of matrix is, the more stringent the system's restriction on control energy consumption is, but it may affect the tracking performance. The selection of the decay gain γ also needs to be balanced, a larger γ value can enhance the robustness of the system, but it may reduce the system's ability to suppress disturbances.
[0036] Then, based on the Bellman optimality principle, a Hamilton function is constructed, which contains the instantaneous cost function and the gradient information of the global cost function. Based on the Bellman optimality principle, a Hamilton function is constructed to solve the optimal control problem. Taking the infinite operator of formula (8), the Hamilton function is as follows: (9) Where, is the expected acceleration vector, and the extended global control input matrix is .
[0037] Finally, based on the Hamilton function, a global optimal cost function is established by the minimax optimization principle. In order to ensure the existence of the optimal cost function, it is assumed that the system's gain is not greater than the set . This assumption is reasonable in the actual system, because it corresponds to the boundedness of the system's energy gain. The global optimal cost function is as follows: (10) The global optimal cost function satisfies the following conditions: (11) This function satisfies the Bellman optimality principle, ensuring that the control strategy can still achieve long-term optimal performance under disturbances. Its derivation relies on the extreme value condition of the Hamilton function =0), which embodies the mathematical correlation between the current state and future performance Therefore, in this step, the weight matrix Q and in the cost function can be flexibly adjusted, which not only guarantees high tracking accuracy (cooperative mechanism), but also optimizes energy consumption and robustness through the decay gain γ (competitive mechanism), solving the problem that stability and optimality are difficult to be considered in traditional methods.
[0038] 3. Derive the control law using the critic neural network and the mixed Pareto game according to the global cost function and Hamiltonian function, and design the weight update mechanism. The mixed Pareto game includes a Pareto cooperative game and a zero-sum competitive game, wherein the Pareto cooperative game is used to achieve multi-controller collaborative optimization, and the zero-sum competitive game is used to deal with the worst disturbance case. Through neural network approximation and real-time learning, the curse of dimensionality is overcome, and approximate optimal control is achieved.
[0039] According to the Bellman optimality principle , the approximate optimal tracking control law of each subsystem based on the mixed Pareto game can be obtained as: (12) (13) The above control law is theoretically optimal, but it is often difficult to directly implement in practical applications because it depends on solving complex Hamilton-Jacobi-Bellman-Exponential equations. In order to overcome this difficulty, the original problem is transformed, and formulas (8), (12), and (13) are substituted into formula (9) to obtain the coupled Hamilton-Jacobi-Bellman-Exponential equations of the system: (14) In order to solve the curse of dimensionality, a critic neural network is introduced to approximate the optimal cost function, which includes weight parameters and activation functions. The approximation process adjusts the weight parameters through gradient descent method to minimize the Hamiltonian function approximation error. Since the globally optimal cost function in the coupled Hamilton-Jacobi-Bellman-Exponential equations (formula (14)) cannot be directly obtained, a critic neural network is used to approximate it: (15) wherein, represents the ideal critic neural network weight; is the activation function of the neural network; denotes the approximation error of the neural network.
[0040] By taking the derivative of the neural network, the gradient information of the cost function can be obtained, and the powerful approximation ability of the neural network is used to handle complex nonlinear relationships. Taking the gradient of formula (15), we get: (16) wherein .
[0041] According to formula (16), we get: (17) (18) Substitute (17) and (18) into (9), we have (19) where, is the approximation error of the critic neural network.
[0042] Since the ideal weight is unknown, we approximate it as (20) Take the partial derivative of (20), we have (21) Based on the output of the critic neural network, derive the optimal control law and disturbance control law of the hybrid Pareto game. The hybrid Pareto game includes a Pareto cooperative game and a zero-sum competitive game, wherein the Pareto cooperative game is used to achieve multi-controller collaborative optimization, and the zero-sum competitive game is used to deal with the worst disturbance case. According to formulas (17), (18), and (21), the approximate optimal tracking control strategy and the worst disturbance control law are obtained: (22) (23) Substitute the approximate control strategy (22) and (23) into the Hamilton function (19), we have (24) Define the approximation error of the Hamilton function as (25) where, according to formulas (19) and (24), we have .
[0043] Define the approximation error of the critic neural network weight as (26) According to formulas (19), (24), and (25), we have (27) In order to ensure the real-time performance of the control system, a weight update law is designed to adjust the weight parameters of the critic neural network. The designed weight update law is based on the gradient descent method, including calculating the gradient of the Hamilton function approximation error with respect to the weight parameters, and updating the weight parameters in the negative gradient direction. According to the gradient descent method, take the partial derivative of the objective function to obtain the weight update law of the critic neural network as (28) The optimal tracking control strategy (22) and the worst disturbance control law (23) are updated based on (28).
[0044] The neural network approximation strategy significantly reduces computational complexity, avoids the curse of dimensionality, and makes the control torque output continuous and smooth, thus maintaining the asymptotic stability of the system and reducing joint energy loss.
[0045] 4. Based on the control law, conduct experimental verification using a modular robot platform, collect data, and analyze the control performance.
[0046] To verify the practical effectiveness of this method, a complete experimental platform was constructed for testing. The experimental platform employs a two-degree-of-freedom modular robot system, with carefully selected hardware configurations. The power unit uses a Maxon 218014 DC motor, which has a rated voltage of 48V and a rated torque of 190mNm, coupled with a 100:1 harmonic reducer to provide sufficient power support for the system. The measurement system employs a dual encoder configuration: a Maxon 500-line incremental encoder is used for position detection on the motor side, while a Netzer 19-bit high-precision absolute encoder is used on the link side. This configuration ensures both measurement accuracy and sufficient reliability.
[0047] A joint torque sensor with a rated torque of 20 Nm is embedded at the end of the joint module for real-time monitoring of the control effect. The entire system is driven by a linear power amplifier manufactured by Quanser, and data acquisition is completed through a QPIDe data acquisition card, ensuring the accuracy and real-time performance of signal transmission.
[0048] During the experiment, we first calibrated and initialized the system to ensure that all sensors and actuators were functioning correctly. Then, we generated control signals using the proposed method and collected position, velocity, and torque data in real time. To comprehensively evaluate the method's performance, we designed various test scenarios, including performance tests under different trajectory tracking tasks and different disturbance conditions.
[0049] Experimental results demonstrate that this method maintains superior control performance even under external disturbances and model uncertainties. Specifically, the speed tracking error is significantly reduced, the control torque output is smooth and continuous, and the system maintains stable operation under various conditions. These results fully validate the effectiveness of this method in improving system robustness and control accuracy.
[0050] In summary, this invention, through the organic combination of the above-mentioned steps, forms the following core advantages: improved accuracy, with precise modeling of the dynamic model and neural network approximation strategy ensuring minimal speed tracking error; enhanced robustness, with a hybrid game mechanism under a cooperative and competitive framework enabling the system to remain stable under disturbances; optimized energy efficiency, with the smoothness of control torque and synergistic optimization of energy consumption extending the system's lifespan; and outstanding practicality, with experiments verifying the reliability of the method in real-world scenarios, providing a comprehensive solution for modular robots.
[0051] This embodiment provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the modular robot approximate optimal tracking control method based on hybrid Pareto differential game.
[0052] This embodiment provides an electronic device, including a memory and a processor. The memory stores a computer program, and the processor runs the computer program to enable the electronic device to execute the modular robot approximate optimal tracking control method based on hybrid Pareto differential game.
[0053] Embodiments of the present invention may be provided as methods, systems, or computer program products. Therefore, the present invention may take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.
[0054] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.
[0055] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1The function specified in one or more boxes.
[0056] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.
[0057] Contents not described in detail in this specification are prior art known to those skilled in the art. It is hereby indicated that the above description is intended to help those skilled in the art understand this invention, but does not limit the scope of protection of this invention. Any equivalent substitutions, modifications, improvements, or simplifications of the above descriptions that do not depart from the essential content of this invention fall within the scope of protection of this invention.
Claims
1. A modular robot approximate optimal tracking control method based on hybrid Pareto differential game within a cooperative competition framework, characterized in that... Includes the following steps: S1: Establish a modular robot dynamics model, construct dynamic equations and handle uncertainties through the Newton-Euler iteration method, and generate state variables and disturbance terms; S2: Construct the global cost function and Hamiltonian function based on state variables and disturbance terms; S3: Based on the global cost function and Hamiltonian function, derive the control law using a judgment neural network and a hybrid Pareto game, and design a weight update mechanism; S4: Based on the control law, the control performance is experimentally verified through a modular robot platform.
2. The modular robot approximate optimal tracking control method based on hybrid Pareto differential game as described in claim 1, characterized in that, S1 specifically includes: The nominal dynamic equations of the modular robot are established based on the Newton-Euler iterative method. The nominal dynamic equations include the inertia matrix, the Coriolis force matrix, and the gravitational torque matrix. The nominal dynamic equation is decomposed into dynamic equations for multiple joint subsystems. The dynamic equation of each joint subsystem includes coupling and cross-linking terms to characterize the mutual influence between joints. Uncertainty processing is performed on the dynamic equations of the joint subsystem, and known and unknown parameters are separated by estimated and deviation values to generate a perturbation term that includes model estimation bias and coupling effect; The system state variables are defined as a combination of position vectors and velocity vectors. The dynamic equations after handling uncertainties are transformed into state-space equations, which include system state variables and disturbance terms.
3. The modular robot approximate optimal tracking control method based on hybrid Pareto differential game as described in claim 2, characterized in that: The coupling crosslinking term is represented as: Its value depends on the position, velocity, and acceleration parameters of each joint; The separation process of the estimated value and the deviation value includes: decomposing the inertia matrix, Coriolis force and centrifugal force matrix and gravitational moment matrix into estimated values and estimated deviation values, respectively.
4. The modular robot approximate optimal tracking control method based on hybrid Pareto differential game as described in claim 1, characterized in that, S2 specifically includes: Based on the system state variables and disturbance terms, a global cost function is constructed that includes a velocity tracking error term, a control input energy term, and a disturbance suppression term. The parameters of the global cost function include a weight matrix and a decay gain. A Hamiltonian function is constructed based on the Bellman optimality principle. The Hamiltonian function contains gradient information of the instantaneous cost function and the global cost function. Based on the Hamiltonian function, a globally optimal cost function is established using the minimax optimization principle.
5. The modular robot approximate optimal tracking control method based on hybrid Pareto differential game as described in claim 1, characterized in that, S3 specifically includes: The optimal cost function is approximated by an evaluation neural network, which includes weight parameters and an activation function. Based on the output of the evaluation neural network, the optimal control law and the disturbance control law of the hybrid Pareto game are derived. A weight update law is designed to adjust the weight parameters of the evaluation neural network.
6. The modular robot approximate optimal tracking control method based on hybrid Pareto differential game as described in claim 5, characterized in that: The evaluation neural network approximation method adjusts the weight parameters using gradient descent to minimize the Hamiltonian function approximation error.
7. The modular robot approximate optimal tracking control method based on hybrid Pareto differential game as described in claim 1 or 5, characterized in that: The hybrid Pareto game includes Pareto cooperative game and zero-sum competitive game, wherein the Pareto cooperative game is used to achieve multi-controller collaborative optimization, and the zero-sum competitive game is used to handle the worst-case perturbation.
8. The modular robot approximate optimal tracking control method based on hybrid Pareto differential game as described in claim 5, characterized in that: The design weight update law, based on the gradient descent method, includes calculating the gradient of the Hamiltonian function approximation error relative to the weight parameters, and updating the weight parameters in the direction of the negative gradient.
9. A computer-readable storage medium, characterized in that: It stores a computer program that, when executed by a processor, implements the modular robot approximate optimal tracking control method based on hybrid Pareto differential game as described in any one of claims 1-8.
10. An electronic device, characterized in that: It includes a memory and a processor, wherein the memory is used to store computer programs and the processor runs the computer programs to enable the electronic device to perform the modular robot approximate optimal tracking control method based on hybrid Pareto differential game as described in any one of claims 1-8.