Modular robotic decentralized force / position optimal control method with event-triggered mechanism

Abstract

The present application relates to a kind of event trigger mechanism modular robot dispersion force / position optimal control method, the method comprises: constructing the equation of state space equation of conversion under the description equation of modular robot joint dynamics model constrained by environment, performance index function and Hamilton-Jacobi-Bellman function are constructed using multi-element information fusion function, then a kind of reasonable event trigger decision mechanism is designed, when meeting event trigger condition, system satisfies Liapunov gradual stabilization, next performance index function is estimated using evaluation neural network, Hamilton-Jacobi-Bellman function is solved using policy iteration algorithm, finally, the optimal force / position tracking control strategy based on event trigger decision mechanism is obtained.

Description

Technical Field

[0001] This invention relates to the field of robot control technology, and in particular to a modular robot distributed force / position optimal control method with an event-triggered mechanism. Background Technology

[0002] Modular robots have attracted widespread attention in the robotics field due to their superior structural flexibility and adaptability compared to traditional robots. To date, modular robots have found wide applications in many extreme situations, such as medical assistance, disaster investigation, disaster relief, and space exploration. The main idea behind modular robots is to decompose a complex robotic system into multiple highly portable and maintainable subsystem modules. Therefore, the design of their controllers must meet modular requirements, meaning that each joint module has an independent controller capable of meeting the operational needs of different task environments and various robot configurations, thus exhibiting advantages not found in traditional robots and improving work efficiency. Force / position control, as an effective method for handling tasks involving robots interacting with their environment, has garnered significant attention in practice. However, ensuring the robustness of the robot system in complex and extreme environments, and comprehensively optimizing tracking performance, computational load, communication bandwidth, and energy consumption, remains a pressing issue. Event-triggered mechanisms are a novel control strategy that executes control operations only when a specific event occurs, unlike traditional periodic control. The core design principle of typical event-triggered mechanisms is to maintain system stability and performance. In other words, sensors only sample the system's state or output and update the control signal when there are certain requirements for system stability and performance. Therefore, event-triggered control can maintain system stability and performance while reducing the waste of computer resources. In practical robot systems, the number of times the controller executes is equal to the number of times the actuator updates. That is, event-triggered control can effectively reduce the number of actuator updates, thereby achieving the control goals of protecting the actuator and saving energy. Therefore, it is necessary to design a controller scheme based on an event-triggered mechanism. Summary of the Invention

[0003] The purpose of this invention is to provide a modular robot distributed force / position optimal control method based on an event-triggered mechanism, which enables the system to quickly return to the desired performance in unstructured environments. By constructing event-triggered conditions and designing event-triggered controllers, the method reduces the waste of limited resources during robot operation, thereby reducing mechanical wear and achieving actual force / position tracking control of the robot.

[0004] To achieve the above objectives, the present invention provides the following solution: A modular robot force / position optimal control method based on an event-triggered mechanism is characterized by the following steps: First, the method constructs the description equations and transformation state-space equations of the modular robot joint dynamics model under environmental constraints; second, it uses a multivariate information fusion function to construct a performance index function and a Hamiltonian-Jacobi-Bellman function; then, it designs a reasonable event-triggered decision mechanism, ensuring Lyapunov asymptotic stability when the event triggering conditions are met; finally, it uses a judgment neural network to estimate the performance index function and employs a policy iteration algorithm to solve the Hamiltonian-Jacobi-Bellman function, thereby obtaining the optimal force / position tracking control strategy based on the event-triggered decision mechanism.

[0005] The method includes the following steps: Step 1, constructing the description equations and transformation state-space equations of the modular robot joint dynamics model under environmental constraints: Establish a dynamic model for the i-th sub-joint system of the modular robot system: The lower right corner label "i" represents the i-th joint; qi, , This represents the angle, speed, and acceleration measurement of the joint; Represents the moment of inertia of the motor; Represents the reduction ratio; Represents control input; Represents the Jacobian matrix; Represents the contact force of the end effector; Nonparametric terms representing friction; This represents external interference; Represents cross-linking coupling terms; , , , These represent the estimated values ​​of Stribeck's relevant parameters for viscous friction, Coulomb friction, and static friction, respectively; the uncertain parameter vector. express ; Represents an uncertain parameter matrix; This represents a saturation function.

[0006] Only when the joint angles are measurable can the modular robot system reach the desired state. The system state is defined as... =[ ] T =[ qi ] T The transformed state-space representation is obtained as follows: The "i" in the lower right corner represents the i-th joint; Indicates the joint angle state; Indicates the joint velocity state; Represents the physical coefficients of mechanical devices; The model represents the integration of uncertainties in the joint dynamics of a modular robot, including frictional nonlinearity and approximation errors, as well as coupling and cross-linking terms. This represents the known terms of the modular robot joint dynamics model.

[0007] This represents an externally inputted unknown information item; Step two: Construct the performance index function and the Hamilton-Jacobi-Bellman function using a multivariate information fusion function. Based on the modular robot state-space equation, the multivariate information fusion function is constructed as follows: Wherein, the lower right corner label "i" represents the i-th joint; si represents the multivariate information fusion function; e qi represents the tracking error; eτi represents the velocity error; kqi represents the constraint torque tracking error. Both represent the control gain of the multivariate information fusion function.

[0008] Construct the optimal performance index function based on the multi-source information fusion function: Where si(t) represents the fusion error function; the initial value is s0(t) = s(0); The effect function representing the fusion force / position error at time t, given initial values. ; Gi represents the upper bound of the uncertain terms in the model; Gi represents the known terms in the model. Represents the gain coefficient; It represents the upper bound of unknown external input information items.

[0009] Based on the constructed performance metric function, if it exists And it is continuously differentiable, with local Lyapunov equations:

[0010] in, Represents a performance metric function; right partial derivatives ; The relevant functional expressions represent the desired acceleration, actual velocity, and constraint torque error. ; Matrix Qa and Ra are positive definite matrices; Combining the Bellman optimization strategy, the optimal performance index function Satisfies Hamilton's equations: The optimal force / position control law for the modular robot system is obtained as follows: in, This represents the optimal force / position control strategy; The given positive definite matrix represents the force / position tracking control strategy; This represents the model function related to the inertia matrix.

[0011] Step 3: Design a reasonable event-triggered decision-making mechanism: Design an event-triggered decision-making mechanism: in, The sampling state represents the event-triggered decision-making mechanism; the interval function is defined. To obtain reasonable event triggering conditions; tl represents the previous sampling time; tl+1 represents the control time when switching is about to occur; The optimal control strategy for the event-triggered decision-making mechanism.

[0012] Based on the optimal control law of the event-triggered decision-making mechanism and the Hamiltonian equation, the Hamiltonian equation for the optimal problem under the event-triggered decision-making mechanism is obtained as follows:

[0013] Regarding the state of auxiliary variables The designed tracking control law is Lipschitz continuous and has a constant. The following inequalities must be satisfied:

[0014] Based on the Bellman optimality principle, the optimal performance index function Satisfies Hamilton's equations: Step 4: Design the optimal force / position tracking control strategy based on an event-triggered decision-making mechanism: Based on the approximation performance of neural networks, the optimal performance index function for approximating neural networks is evaluated:

[0015] in, This represents the ideal weights of the neural network; Indicates the activation function; This represents the residual error. The gradient of the evaluation neural network based on the event-triggered decision-making mechanism with respect to the corresponding state si is:

[0016] in, , , These are the partial derivatives of the performance index function, the activation function, and the residual error, respectively. Ideal weights for a neural network. Wi Since it cannot be predicted in advance, a local evaluation neural network approximates the result.

[0017] in, The approximate weights of the neural network are used to represent the force / position control strategy of the robot based on the event-triggered mechanism.

[0018] The Hamiltonian function based on the event-triggered mechanism is derived as follows:

[0019] Where eich is the estimated residual of the approximate event-triggered Hamiltonian function. Design update strategy mechanism: in, It is used to evaluate the weight update strategy of neural networks.

[0020] In fact, the estimated residual eich of the approximate event-triggered Hamiltonian function is equal to zero or in a small neighborhood near zero. To achieve the ideal approximation, i.e., eich = 0, a multi-objective golden search strategy is used to optimize the weights of the RBF-based evaluation neural network, making the estimated residual eich approach zero. The fitness function is defined as follows: fnes = exp(||eich ||) Step size update iteration: Sti (t+1)=T.Sti (t)+C1 .cos(r1) .(pipb (t)-Wiz (t))+C2 .sin(r2) .(pipgb (t)-Wiz (t)) Where Sti represents the update step size of the search strategy; C1 and C2 are random numbers between [0, 2], and r1 and r2 represent random numbers between (0, 1); pipb represents the local optimum; pipgb represents the global optimum; and T represents the transformation operator of the search strategy, i.e. tmax represents the maximum number of iterations; Wizp(t) represents the weight position.

[0021] Iterative strategy for evaluating the Wizp(t) weight positions in a neural network: Wizp (t+1)=Wizp (t)+Sti (t+1) Based on Lyapunov's stability theorem and event-triggered decision-making mechanisms, event-triggered conditions that enable system stability are designed for a modular robot joint module subsystem with n degrees of freedom: Where λmin (Qa) and λmax (Qa) represent the minimum and maximum eigenvalues, respectively; Eetif is the event triggering condition. Attached Figure Description

[0022] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0023] Figure 1 This invention provides the principle of a modular robot force / position optimization control method based on an event-triggered mechanism, as provided in an embodiment of the present invention.

[0024] Figure 2 The flowchart illustrates a modular robot force / position optimization control method based on an event-triggered mechanism, as provided in this embodiment of the invention. Detailed Implementation

[0025] like Figure 1As shown, a multivariate information fusion function is obtained by subtracting the joint signals actually output by the modular robotic arm system from the desired joint position and desired external force. Then, the conditions for the event triggering mechanism are designed, and the current state variable is updated based on whether the event triggering conditions are violated. The optimized weight update rate of the evaluation neural network is obtained by using a multi-objective golden search strategy and an approximate Hamiltonian function. Under the continuous updating of the neural network weights, an approximate performance index function is obtained through iterative steps. This yields a modular robot force / position control strategy based on the event triggering mechanism. This control strategy is then input into the modular robot joint module subsystem to control the position of the robot's end effector and the contact force generated between it and the unknown environment.

[0026] like Figure 2 As shown, the optimal force / position tracking control strategy based on an event-triggered decision-making mechanism proposed in this invention first requires constructing a description equation for the joint dynamics model of a modular robot under environmental constraints; then, using actual position information and contact force information, a multivariate information fusion function is designed to construct a performance index function; next, based on the event-triggered decision-making mechanism, the performance index function under event triggering is approximated by a neural network, and finally, the optimal force / position tracking control strategy for the modular robot based on the event-triggered decision-making mechanism is obtained.

[0027] 1. Establishment of modular robot joint dynamics model Establish a dynamic model for the i-th sub-joint system of the modular robot system: The "i" in the lower right corner represents the i-th joint; , , Represents the angle, speed, and acceleration of the joint; Imi represents the moment of inertia of the motor; γi represents the reduction ratio; τi represents the control input; Represents the Jacobian matrix; fie represents the end effector contact force; Nonparametric terms representing friction; δi represents external interference; δi represents cross-linking coupling terms. , , , These represent the estimated values ​​of Stribeck's relevant parameters for viscous friction, Coulomb friction, and static friction, respectively; the uncertain parameter vector. express ; Represents an uncertain parameter matrix; This represents a saturation function.

[0028] Only when the joint angles are measurable can the modular robot system reach the desired state. The system state is defined as... =[ ] T =[ qi ] T Obtain the transformed state-space representation: The "i" in the lower right corner represents the i-th joint; Indicates the joint angle state; Indicates the joint velocity state; Represents the physical coefficients of mechanical devices; The model represents the integration of uncertainties in the joint dynamics of a modular robot, including frictional nonlinearity and approximation errors, as well as coupling and cross-linking terms. This represents the known terms of the modular robot joint dynamics model.

[0029] This represents an externally inputted unknown information item; 2. Construct performance index functions and Hamilton-Jacobi-Bellman functions using a multivariate information fusion function: Based on the modular robot state-space equation, the multivariate information fusion function is constructed as follows:

[0030] Wherein, the lower right corner label "i" represents the i-th joint; si represents the multivariate information fusion function; e qi represents the tracking error; eτi represents the velocity error; kqi represents the constraint torque tracking error. Both represent the control gain of the multivariate information fusion function.

[0031] Construct the optimal performance index function based on the multi-source information fusion function:

[0032] Where si(t) represents the fusion error function; the initial value is s0(t) = s(0); The effect function representing the fusion force / position error at time t, given initial values. ; Gi represents the upper bound of the uncertain terms in the model; κi represents the known terms in the model; and θi represents the gain coefficient.

[0033] Based on the constructed performance metric function, if it exists And it is continuously differentiable, with local Lyapunov equations:

[0034] in, Representative performance index function partial derivatives with respect to si ;:vi represents the relevant functional expression for the desired acceleration, actual velocity, and constraint torque error. ; Matrix Qa and Ra are positive definite matrices; Combining the Bellman optimization strategy, the optimal performance index function Satisfies Hamilton's equations: The optimal force / position control law for the modular robot system is obtained as follows:

[0035] in, This represents the optimal force / position control strategy; The force / position tracking control strategy corresponds to the input... A positive definite matrix; This represents the model function related to the inertia matrix.

[0036] 3. Design a reasonable event-triggered decision-making mechanism: Design an event-triggered decision-making mechanism: in, The sampling state represents the event-triggered decision-making mechanism; the interval function Eei(t) is defined to obtain reasonable event triggering conditions; tl represents the previous sampling time; tl+1 represents the control time when the switch is about to take place; The optimal control strategy represents the event-triggered decision-making mechanism. Based on the optimal control law of the event-triggered decision-making mechanism and the Hamiltonian equation, the Hamiltonian equation for the optimal problem under the event-triggered decision-making mechanism is obtained: Regarding the state of auxiliary variables The designed tracking control law is Lipschitz continuous and has a constant. The following inequalities must be satisfied:

[0037] Based on the Bellman optimality principle, the optimal performance index function Satisfies Hamilton's equations:

[0038] 4. Design an optimal force / position tracking control strategy based on an event-triggered decision-making mechanism: Based on the approximation performance of neural networks, the optimal performance index function for approximating neural networks is evaluated:

[0039] in, This represents the ideal weights of the neural network; Indicates the activation function; This represents the residual error. The gradient of the evaluation neural network based on the event-triggered decision-making mechanism with respect to the corresponding state si is: in, , , These are the partial derivatives of the performance index function, the activation function, and the residual error, respectively. Ideal weights for a neural network. Wi Since it cannot be predicted in advance, a local evaluation neural network is used to approximate the result.

[0040] in, The approximate weights of the neural network are used to represent the force / position control strategy of the robot based on the event-triggered mechanism.

[0041] The Hamiltonian function based on the event-triggered mechanism is derived as follows:

[0042] Here, eich is the estimated residual of the approximate event-triggered Hamiltonian function.

[0043] Design update strategy mechanism: in, This is the evaluation strategy for updating the weights of the neural network. In fact, the estimated residual eich of the approximate event-triggered Hamiltonian function is equal to zero or in a small neighborhood near zero. To achieve the ideal approximation, i.e., eich = 0, a multi-objective golden search strategy is used to optimize the weights of the RBF-based evaluation neural network, making the estimated residual eich approach zero. The fitness function is defined as follows: fnes = exp(||eich ||) Step size update iteration: Sti (t+1)=T.Sti (t)+C1 .cos(r1) .(pipb (t)-Wiz (t))+C2 .sin(r2) .(pipgb (t)-Wiz (t)) Where Sti represents the update step size of the search strategy; C1 and C2 are random numbers between [0, 2], and r1 and r2 represent (0, 1). Random numbers between; pipb represents the local optimum; pipgb represents the global optimum; T represents the transformation algorithm of the search strategy. son, that is , t max represents the maximum number of iterations; Wizp(t) represents the position of the weight.

[0044] Iterative strategy for evaluating the Wizp(t) weight positions in a neural network: Wizp (t+1)=Wizp (t)+Sti (t+1) Based on Lyapunov's stability theorem and event-triggered decision-making mechanisms, event-triggered conditions that enable system stability are designed for a modular robot joint module subsystem with n degrees of freedom: Where λmin (Qa) and λmax (Qa) represent the minimum and maximum eigenvalues, respectively; Eetif is the event triggering condition.

[0045] This invention presents a modular robot distributed force / position optimal control method based on an event-triggered decision-making mechanism. Unlike time-triggered strategies with fixed-period updates, this method is aperiodic, which can address the limitations of existing technologies where resources are constrained. It ensures high-precision operation while reducing computational burden and motor consumption, thus providing stability and accuracy for modular robot operation. Specific examples are used to illustrate the principles and implementation methods of this invention. The descriptions of these embodiments are merely for understanding the method and core ideas of this invention; furthermore, those skilled in the art will recognize that modifications may be made to the specific implementation methods and application scope based on the ideas of this invention. Therefore, the content of this specification should not be construed as limiting the invention.

Claims

1. A modular robot force / position optimal control method based on an event-triggered mechanism, characterized in that, This method first constructs the descriptive equations and state-space equations of the modular robot joint dynamics model under environmental constraints; secondly, it uses a multivariate information fusion function to construct the performance index function and the Hamilton-Jacobi-Bellman function; then, it designs a reasonable event-triggered decision mechanism, ensuring that the system satisfies Lyapunov asymptotic stability when the event triggering conditions are met; next, it uses a judgment neural network to estimate the performance index function, and employs a policy iteration algorithm to solve the Hamilton-Jacobi-Bellman function; finally, it obtains the optimal force / position tracking control strategy based on the event-triggered decision mechanism. The method includes the following steps: Step 1: Construct the state-space equations describing the joint dynamics model of the modular robot under environmental constraints and the transformation equations: Establish a dynamic model for the i-th sub-joint system of the modular robot system: The "i" in the lower right corner represents the first... One joint; , This represents the angle, speed, and acceleration measurement of the joint; Represents the moment of inertia of the motor; Represents the reduction ratio; Represents control input; Represents the Jacobian matrix; Represents the contact force of the end effector; Nonparametric terms representing friction; This represents external interference; Represents cross-linking coupling terms; , , , These represent viscous friction, Coulomb friction, and static friction, respectively, and are estimated values ​​of Stribeck's relevant parameters. Uncertain parameter vector express ; Represents an uncertain parameter matrix; Represents a saturation function; Only when the joint angles are measurable can the modular robot system reach the desired state; the system state is defined as... =[ ]T=[qi ]T, obtain the transformed state-space representation: The bottom right corner is marked with " "represents the first One joint; Indicates the joint angle state; Indicates the joint velocity state; Represents the physical coefficients of mechanical devices; The model represents the integration of uncertainties in the joint dynamics of a modular robot, including frictional nonlinearity and approximation errors, as well as coupling and cross-linking terms. This represents the known terms of the modular robot joint dynamics model; This represents an externally inputted unknown information item; Step two: Construct the performance index function and the Hamilton-Jacobi-Bellman function using a multivariate information fusion function. Based on the transformed state-space representation, the multi-source information fusion function is constructed as follows: The "i" in the lower right corner represents the first... One joint; Represents a multi-source information fusion function; Represents tracking error; Represents speed error; Represents the constraint torque tracking error: Both represent the control gain of the multivariate information fusion function; Construct the optimal performance index function based on the multi-source information fusion function: in, Represents the fusion error function; initial value represent The effect function of fusion force / position error at time t, given initial values. ; This represents the upper bound of the uncertainty term in the model; Representative known terms of the model; Represents the gain coefficient; This represents the upper bound of the unknown information item from external input; Based on the constructed performance metric function, if it exists And it is continuously differentiable, with local Lyapunov equations: in, Represents a performance metric function; right partial derivatives ; The relevant functional expressions represent the desired acceleration, actual velocity, and constraint torque error. ; Matrix Qa and Ra are positive definite matrices; Combining the Bellman optimization strategy, the optimal performance index function Satisfies Hamilton's equations: The optimal force / position control law for the modular robot system is obtained as follows: in, This represents the optimal force / position control strategy; The given positive definite matrix represents the force / position tracking control strategy; Represents the model function related to the inertia matrix; Step 3: Design a reasonable event-triggered decision-making mechanism: Design an event-triggered decision-making mechanism: in, The sampling state represents the event-triggered decision-making mechanism; the interval function is defined. In order to obtain reasonable things Triggering conditions; Represents the previous sampling time; This indicates the moment when control is about to switch; Representative event touches The optimal control strategy for the decision-making mechanism; Based on the optimal control law of the event-triggered decision-making mechanism and the Hamiltonian equation, the Hamiltonian equation for the optimal problem under the event-triggered decision-making mechanism is obtained as follows: Regarding the state of auxiliary variables The designed tracking control law is Lipschitz continuous and has a constant constant. The following inequalities must be satisfied: Based on the Bellman optimality principle, the optimal performance index function Satisfies Hamilton's equations: Step 4: Design the optimal force / position tracking control strategy based on an event-triggered decision-making mechanism: Based on the approximation performance of neural networks, the optimal performance index function for approximating neural networks is evaluated: in, This represents the ideal weights of the neural network; Indicates the activation function; Represents residual error; based on events The evaluation neural network for the event-triggered decision-making mechanism approximates the gradient of the optimal performance index function relative to the corresponding state si. in, , , These are the partial derivatives of the performance index function, activation function, and residual error, respectively; and the ideal weights of the neural network. Since it cannot be predicted in advance, a local evaluation neural network is used to approximate the result. in, The approximate weights of the neural network are used to represent the force / position control strategy of the robot based on the event-triggered mechanism. The Hamiltonian function based on the event-triggered mechanism is derived as follows: in, It is an approximate estimated residual of the event-triggered Hamiltonian function; Design update strategy mechanism: in, It is used to evaluate the weight update strategy of the neural network; In fact, the estimated residual eich of the approximate event-triggered Hamiltonian function is equal to zero or in a small neighborhood near zero; in order to achieve the ideal approximation effect, i.e. The weights of the RBF-based evaluation neural network are optimized using a multi-objective gold search strategy, which improves the estimation of residuals. To approach zero, define the fitness function as follows: Step size update iteration: in, Indicates the update step size of the search strategy; , It is a random number between [0, 2]. , Represents a random number between (0, 1); Indicates the local optimal position; Indicates the globally optimal position; The transformation operator representing the search strategy, i.e. , t `max` represents the maximum number of iterations; Wizp ( t () indicates the position of the weight; Evaluate the position of neural network weights Iteration strategy: According to Lyapunov's stability theorem and event-triggered decision-making mechanisms, regarding n The modular robot joint module subsystem with degrees of freedom is designed with event triggering conditions that ensure system stability, namely: in, , These represent the minimum and maximum eigenvalues, respectively. This is the condition for triggering the event.

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