Man-machine sharing control method for exogenous input system under Nash equilibrium

Abstract

The invention belongs to the technical field of man-machine cooperative control, and particularly relates to a man-machine sharing control method for an exogenous input system under Nash equilibrium, which comprises the following steps of: constructing a man-machine sharing control system model with exogenous input items, and setting a cost function of man-machine parties; a man-machine non-cooperative differential game model is considered, an information structure of man-machine interaction meets a closed-loop perfect state mode, a control target is Nash equilibrium between cost functions of the two parties, and a Nash equilibrium solution form of human and machine control input and an algorithm of control gain and additional items are provided; based on fuzziness and uncertainty of human input, constructing an adaptive observer, and combining a Lyapunov equation to obtain a human input estimation gain and an updating law of an additional item; the real-time Nash equilibrium solution of man-machine sharing control in an exogenous input system is provided while the influence of exogenous input on the system state is restrained, and the method has high scientific significance and application value.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of human-machine collaborative control, and particularly relates to a human-machine shared control method for an exogenous input system under Nash equilibrium. BACKGROUND

[0002] Human-machine shared control, which is based on the advantages of accurate and stable machine control and the advantages of strong environmental perception and understanding of human beings and the ability of human beings to make judgments based on incomplete information, is widely used in control scenes such as rehabilitation medicine, auxiliary driving, deep sea exploration, etc. In order to achieve high-performance control effect and fully utilize the control advantages of human beings and machines, the current method mostly adopts a method of allocating control weights to execute the human-machine shared control task. However, when the control purposes of human beings and machines are inconsistent, how to design a reasonable control weight allocation method to coordinate the conflict of the control objectives of human beings and machines while having good control efficiency is a crucial problem in the current field of human-machine shared control. Nash equilibrium is an important theoretical framework in game theory, which gives a balanced state in which each game player cannot unilaterally change his own strategy to obtain higher income. The concept of multiple game players in Nash equilibrium is highly consistent with human beings and machines participating in system control together. The introduction of the concept of Nash equilibrium provides an optimization scheme for mathematically modeling the conflict between the game of human-machine control input, and provides a theoretical basis for the design of control strategies.

[0003] However, in most control scenes, especially in complex environments, there are a large number of disturbances or other external inputs acting on the control system, which are summarized as exogenous input terms. Most current human-machine shared control based on Nash equilibrium does not consider the exogenous input terms when modeling, which directly affects the control effect, and because the human control input has fuzziness and unmeasurability, there is a difference between the control target and the machine, and the control parameters of human beings cannot be directly measured. Therefore, the application proposes a human-machine shared control method for an exogenous input system under Nash equilibrium. SUMMARY

[0004] The purpose of the application is to provide a human-machine shared control method for an exogenous input system under Nash equilibrium, which decouples real-time control input in the form of human interaction force into a control law containing control gain and additional terms and related to system state, constructs an adaptive observer to estimate the control gain and additional terms of human beings, and formulates a control input strategy of the machine in the case that the human-machine shared control system is affected by exogenous input, so as to suppress the influence of exogenous input on the system state, realize real-time Nash equilibrium between different cost functions of human beings and machines, and improve the control performance of the human-machine shared control system in complex environments.

[0005] The technical scheme adopted by the application is as follows:

[0006] A human-machine shared control method for exogenous input systems under Nash equilibrium.

[0007] Step 1: Construct a human-machine shared control framework based on Nash equilibrium, wherein the information acquisition structure of both the human and machine conforms to the closed-loop perfect state pattern. The human-machine shared control framework includes:

[0008] By integrating the inputs of human interaction and automatic control systems as the control inputs of the human-machine shared control system, a state-space equation containing exogenous input terms is constructed for the human-machine shared control system.

[0009] The assumptions of the human-machine shared control framework are declared; the cost functions for both humans and machines are defined, referencing the form of a linear quadratic form.

[0010] Establish a tactile channel for human-computer interaction;

[0011] Determine the form of the Nash equilibrium solution for a human-machine shared control system containing exogenous inputs;

[0012] Then, by solving the coupled Riccati equations, the control input gain and additional terms of the machine are obtained;

[0013] Step 2: Design a method for estimating the control gain and additional terms of human input. The real-time human control input in the form of decoupled interaction force is a control law with the same form as the Nash equilibrium solution. Construct an adaptive input observer, define the state space equation of the estimation error, select an appropriate Lyapunov function, and obtain the update law of the estimated human control input gain and additional terms.

[0014] Step 3: Design the algorithm flow for human-machine shared control of the exogenous input system based on Nash equilibrium, and output the real-time control strategy and system state of the machine under Nash equilibrium.

[0015] Preferably, in step 1:

[0016] The state-space equations of the human-machine shared control system containing exogenous inputs are as follows:

[0017]

[0018] Where, ξ∈R n It is the system state, A∈R n×n It is the system matrix, B∈R n×m The input matrix is ​​u∈R m It is the input of the automated system, f∈R m It is the control exerted by humans, c∈R mThis represents exogenous inputs, which are the sum of disturbances and other inputs that affect the system, excluding those from humans and machines.

[0019] Preferably, in step 2:

[0020] The human-machine shared control framework is based on the following assumptions:

[0021] Both the human and machine cost functions are modeled as linear quadratic functions, and both the human and the machine will minimize their respective cost functions as the control objective.

[0022] Due to the subjectivity and ambiguity of human control in actual control scenarios, the cost functions of humans and robots differ, which is reflected by the different weight matrices in their respective cost functions.

[0023] The information acquisition structure between humans and machines satisfies the closed-loop perfect state pattern. The information acquisition structure η between humans and machines... i (t), i∈{a,h} satisfies η i (t)={ξ(s),0≤s≤t},t∈[0,∞];The system state information at any time and the control strategies of humans and machines are known to both humans and machines;

[0024] The state-space equations of a human-machine shared control system containing exogenous inputs and the control strategy set γ for both humans and machines. i ∈Γ i i∈{a,h} satisfies the Lipschitz condition on ξ,u,f,c;

[0025] The cost function for humans and machines is:

[0026]

[0027] Among them, Q h ∈R m×m and Q a ∈R m×m It is a positive semi-definite matrix, which represents the weights of human and machine control precision, and indicates the degree of importance that humans and machines attach to control precision.

[0028] R a and R h R represents the weights of the robot's and human's inputs to themselves, respectively; ah R represents the evaluation weight of the robot on human input, while R ha These represent the evaluation weights of human input to the robot.

[0029] Preferably, in step 1, the human-machine interaction tactile channel is a tactile channel in the form of a joystick, steering wheel, or wearable device. The machine directly inputs control strategies through the automatic control system, and the human inputs control strategies through the tactile channel in the form of interactive force, and obtains force feedback of the machine's input strategy through the tactile channel. The machine measures the human's interactive force through the tactile channel. The human and machine complete real-time interaction of their control strategies through the tactile channel. At the same time, the real-time system state is known to both the human and the machine. The information acquisition structure of the human and the machine satisfies the closed-loop perfect information (closed-loop perfect state) model. The closed-loop perfect information model is more in line with the scenario of a human and machine jointly controlling the system. Each player understands the current system state and the strategies of other players, and adjusts their strategies throughout the game, reducing the inefficiency caused by information asymmetry and avoiding the occurrence of the prisoner's dilemma.

[0030] Preferably, in step 1: Nash equilibrium provides a reasonable control strategy design method in the case of conflicting individual goals. In Nash equilibrium, each controller, knowing the strategies of other controllers, has no incentive to unilaterally change its own control strategy. The Nash equilibrium of the cost functions of the human and machine in the closed-loop perfect information mode is as follows:

[0031] J a (ξ,u * ,f * )≤J a (ξ,u,f * )

[0032] J h (ξ,u * ,f * )≤J h (ξ,u * f)

[0033] The Nash equilibrium solution of the human-machine shared control system containing exogenous input terms is:

[0034]

[0035] Control gain K a ,K h The following Riccati equation was obtained through calculation:

[0036]

[0037] in,

[0038]

[0039] Additional item m a ,m hThe following Riccati equation was obtained through calculation:

[0040]

[0041] in,

[0042]

[0043] Preferably, in step 2, the control gain K for human input is designed. h and additional items m h The estimation methods include:

[0044] Decouple interactive force forms of real-time human control input;

[0045] Construct an adaptive input observer;

[0046] Determine Lyapunov candidate functions;

[0047] Declare human input to estimate gain and estimated additional items The underlying assumptions;

[0048] The update law for the estimated human control gain and additional terms is obtained.

[0049] In step 2, the interactive force-based real-time human control input is:

[0050]

[0051] Where K h ,m h Control gains and additional parameters input by humans cannot be directly measured;

[0052] The adaptive input observer is:

[0053]

[0054] in Γ is a positive definite diagonal matrix. Estimated values ​​input by humans;

[0055]

[0056] in Estimates of the control gain and additional terms input by humans. Considered to be related to the system's exogenous input c, written as Define the gain estimation error as Additional gain error is

[0057] The state-space equation for the estimation error is:

[0058]

[0059] The Lyapunov candidate function is:

[0060]

[0061] Where α is a constant greater than 0, and tr represents the trace of the matrix;

[0062] Find the conditions that satisfy the condition that the first-order partial derivative of the Lyapunov candidate function with respect to time is less than 0. The renewal law:

[0063]

[0064] Under this update law, It is bounded, and as t→∞, Established;

[0065] Human input estimation gain and estimated additional items The underlying assumptions are:

[0066] As t→∞ This holds true, where ξ and c are continuous excitation signals;

[0067] therefore Established, The update law can be used to update And the estimated value Converging to its true value K h M h ;

[0068] The update law for the estimated human control gain and additional terms is:

[0069]

[0070] Step 3, which designs the algorithm flow for human-machine shared control of an exogenous input system based on Nash equilibrium, includes:

[0071] Step 31: Initialize the system state ξ and the system state estimate. Based on the control task, set the system control matrix A, input matrix B, and exogenous input term c; set the initial estimated values ​​for human control gain and additional term gain. Set the initial values ​​K for machine control gain and additional gain. a ,m a Assign the weight matrix Q to the human and machine cost functions. a Q h ,R a,R h ,R ah ,R ha With the estimated parameters Γ,α;

[0072] Step 32: Based on the current K a , Numerical solution of K using gradient descent method a The coupled Riccati equations yield a new K a According to the current m a , K a , The gradient descent method is used to numerically solve for m. a The coupled Riccati equations are as follows, yielding a new m a ;

[0073]

[0074]

[0075] Step 321: Initialize gradient descent parameters

[0076] Set the convergence tolerance (tol), gradient descent step size (step_size), maximum number of iterations (max_iter), and K. a Initial guess matrix, m a Initial guess vector;

[0077] Step 322: Construct the gradient descent iterative method

[0078] When the number of iterations is less than the maximum number of iterations max_iter:

[0079] Take gradient

[0080]

[0081] Step 323: Update K using gradient descent a and m a

[0082] Get K a _new and ensure its symmetry:

[0083] K a _new'=K a +step_size×grad_K a

[0084]

[0085] Get m a _new:

[0086] m a _new=m a +step_size×grad_m a

[0087] Step 324: Check convergence, if ||K a _new-K a ||≤tol and||m a _new-m a If ||≤tol, then let K a =K a _new, m a =m a _new, output K a ,m a Find the numerical solution; otherwise, proceed to steps 2-5.

[0088] Step 325: Obtain K a _new is defined as K a m a _new is defined as m a Return to step 323; when the number of iterations exceeds max_iter, end the loop and output K. a ,m a Numerical solution;

[0089] Step 33: Based on the current The value of the system state ξ and the state error Associative update law

[0090]

[0091] Update human control gain and additional gain

[0092] Step 34: Update the machine input u in the Nash equilibrium form * =-R a -1 B T (K a ξ+m a ) and human-estimated input Output machine control input Update the adaptive observer to obtain a new estimate of the system state.

[0093]

[0094] Step 35: Utilize the tactile channel to obtain the actual human input f, and combine it with the machine's control input u. * Using the system state-space equations Update the system status and output the system status ξ.

[0095] We obtain the real-time machine control input and system state that satisfy the Nash equilibrium of the cost function between humans and machines under the exogenous input system.

[0096] The technical effects achieved by this invention are as follows:

[0097] This invention proposes a human-machine shared control method for exogenous input systems based on Nash equilibrium. By enabling the control strategies of both the human and machine to achieve Nash equilibrium during the control process, it effectively balances system stability and individual control costs, thereby improving overall control efficiency. This invention also constructs an adaptive observer to estimate the human control gain and additional term gain, enhancing the system's adaptability to human input. Furthermore, it provides a Nash equilibrium solution for the machine control strategy under the influence of exogenous inputs, enabling the system to effectively suppress the effects of external inputs, ensuring stable operation and control accuracy of the control system, and improving the control performance of the human-machine shared control system under a game theory framework in complex environments. Attached Figure Description

[0098] Figure 1 This is a flowchart illustrating a human-machine shared control method for an exogenous input system based on Nash equilibrium according to the present invention.

[0099] Figure 2 This is a schematic diagram of the human-computer interaction tactile channel of a preferred embodiment of the present invention;

[0100] Figure 3 This is a schematic diagram of a human-machine shared control scenario according to a preferred embodiment of the present invention;

[0101] Figure 4 This is a comparison chart of human input and its estimated value in the example;

[0102] Figure 5 This is a diagram showing the changes in the machine control strategy that satisfies the real-time Nash equilibrium of the cost functions of both the human and machine in the embodiment.

[0103] Figure 6 This is a comparison diagram of human and machine control inputs and their combined inputs in the embodiments;

[0104] Figure 7 This is a graph showing the change in trajectory tracking error in the embodiment. Detailed Implementation

[0105] To make the objectives and advantages of this invention clearer, the invention will be specifically described below with reference to embodiments. It should be understood that the following text is merely used to describe one or more specific embodiments of the invention and does not strictly limit the scope of protection specifically claimed by the invention.

[0106] likeFigure 1 As shown, a human-machine shared control method for an exogenous input system under Nash equilibrium is presented.

[0107] Step 1: Construct a human-machine shared control framework based on Nash equilibrium, wherein the information acquisition structure of both the human and machine conforms to the closed-loop perfect state pattern. The human-machine shared control framework includes:

[0108] By integrating the inputs of human interaction and automatic control systems as the control inputs of the human-machine shared control system, a state-space equation containing exogenous input terms is constructed for the human-machine shared control system.

[0109] The assumptions of the human-machine shared control framework are declared; the cost functions for both humans and machines are defined, referencing the form of a linear quadratic form.

[0110] Establish a tactile channel for human-computer interaction;

[0111] Determine the form of the Nash equilibrium solution for a human-machine shared control system containing exogenous inputs;

[0112] Then, by solving the coupled Riccati equations, which are first-order nonlinear ordinary differential equations, the control input gain and additional terms of the machine are obtained.

[0113] Step 2: Design a method for estimating the control gain and additional terms of human input. The real-time human control input in the form of decoupled interaction force is a control law with the same form as the Nash equilibrium solution. Construct an adaptive input observer, define the state space equation of the estimation error, select an appropriate Lyapunov function, and obtain the update law of the estimated human control input gain and additional terms.

[0114] Step 3: Design the algorithm flow for human-machine shared control of the exogenous input system based on Nash equilibrium, and output the real-time control strategy and system state of the machine under Nash equilibrium.

[0115] In this embodiment, the human-machine shared control method based on exogenous input system of Nash equilibrium is applied to the trajectory tracking control scenario of a robotic arm. The human-machine shared control system is considered as follows:

[0116] A human operator and a robot jointly control a robotic arm to track a given desired trajectory. This embodiment assumes the robotic arm has ideal pose control capabilities, achieving precise joint position control. Considering the robotic arm can accurately track the desired trajectory, the dynamic effects of the robotic arm are ignored. The pose control expression for the robotic arm is as follows:

[0117]

[0118] Where M d ∈Rn×n Let C be the inertia matrix. d ∈R n×n Let x ∈ R be the damping matrix. n The position of the robotic arm. For speed, For acceleration, u∈R n For the input of the robot automation system, f∈R n It is the control exerted by humans;

[0119] The state-space equations of the human-machine shared control system containing exogenous inputs are as follows:

[0120]

[0121] in, ξ∈R n It is the system status. A∈R n×n It is a system matrix. B∈R n×m It is the input matrix;

[0122] I n×n and 0 n×n Represents the n-dimensional identity matrix and the zero matrix; u∈R m It is the input of the automated system;

[0123] The pose control of the robotic arm, which is controlled by human force, needs to be transformed into a control stabilization problem, given the target trajectory x. d Target state The state error of the robotic arm's trajectory tracking control is ξ e =ξ-ξ d The state-space equations for the pose control of the robotic arm are rewritten as the state-space equations for the trajectory tracking task:

[0124]

[0125] in, This represents exogenous inputs, which are the sum of disturbances and other inputs that affect the system, excluding those from humans and machines.

[0126] Preferably, in step 2:

[0127] The human-machine shared control framework is based on the following assumptions:

[0128] Both the human and machine cost functions are modeled as linear quadratic functions, and both the human and the machine will minimize their respective cost functions as the control objective.

[0129] Due to the subjectivity and ambiguity of human control in actual control scenarios, the cost functions of humans and robots differ, which is reflected by the different weight matrices in their respective cost functions.

[0130] The information acquisition structure between humans and machines satisfies the closed-loop perfect state pattern. The information acquisition structure η between humans and machines... i (t), i∈{a,h} satisfies η i (t)={ξ(s),0≤s≤t},t∈[0,∞];The system state information at any time and the control strategies of humans and machines are known to both humans and machines;

[0131] The state-space equations of a human-machine shared control system containing exogenous inputs and the control strategy set γ for both humans and machines. i ∈Γ i i∈{a,h} satisfies the Lipschitz condition on ξ,u,f,c;

[0132] The cost function for humans and machines is:

[0133]

[0134] Among them, Q h ∈R m×m and Q a ∈R m×m It is a positive semi-definite matrix, which represents the weights of human and machine control precision, and indicates the degree of importance that humans and machines attach to control precision.

[0135] R a and R h R represents the weights of the robot's and human's inputs to themselves, respectively; ah R represents the evaluation weight of the robot on human input, while R ha These represent the evaluation weights of human input to the robot.

[0136] Preferably, in step 1, the human-machine interaction tactile channel is a tactile channel in the form of a joystick, steering wheel, or wearable device. The machine directly inputs control strategies through the automatic control system, and the human inputs control strategies through the tactile channel in the form of interactive force, and obtains force feedback of the machine's input strategy through the tactile channel. The machine measures the human's interactive force through the tactile channel. The human and machine complete real-time interaction of their control strategies through the tactile channel. At the same time, the real-time system state is known to both the human and the machine. The information acquisition structure of the human and the machine satisfies the closed-loop perfect information (closed-loop perfect state) model. The closed-loop perfect information model is more in line with the scenario of a human and machine jointly controlling the system. Each player understands the current system state and the strategies of other players, and adjusts their strategies throughout the game, reducing the inefficiency caused by information asymmetry and avoiding the occurrence of the prisoner's dilemma.

[0137] like Figure 2 As shown, in this embodiment, the human-machine interaction tactile channel is a single-degree-of-freedom joystick. The human inputs control strategies through force on the joystick, and the machine directly inputs its control strategies through its automatic control system. The joystick measures the human's interaction force and applies resistance representing the machine's control strategy. The human and machine complete real-time interaction of their control strategies by sensing the interaction force on the joystick.

[0138] Nash equilibrium provides a rational control strategy design method in situations of conflicting individual goals. In a Nash equilibrium state, each controller, knowing the strategies of other controllers, has no incentive to unilaterally change its own control strategy. The Nash equilibrium of the cost functions of the human and machine in a closed-loop perfect information model is as follows:

[0139] J a (ξ,u * ,f * )≤J a (ξ,u,f * )

[0140] J h (ξ,u * ,f * )≤J h (ξ,u * f)

[0141] The Nash equilibrium solution of the human-machine shared control system containing exogenous input terms is:

[0142]

[0143] Control gain K a ,K h The following Riccati equation was obtained through calculation:

[0144]

[0145] in,

[0146]

[0147] Additional item m a ,m h The following Riccati equation was obtained through calculation:

[0148]

[0149] in,

[0150]

[0151] Preferably, in step 2, the control gain K for human input is designed. h and additional items m h The estimation methods include: decoupling the interactive force form of real-time human control input; constructing an adaptive input observer; determining Lyapunov candidate functions; and declaring the human input estimation gain. and estimated additional items The assumptions are: to obtain the update law for the estimated human control gain and additional terms.

[0152] In step 2, the real-time human control input in the form of interactive force is:

[0153]

[0154] Where K h ,m h Control gains and additional parameters input by humans cannot be directly measured;

[0155] The adaptive input observer is:

[0156]

[0157] in Γ is a positive definite diagonal matrix. Estimated values ​​input by humans;

[0158]

[0159] in Estimates of the control gain and additional terms input by humans. Considered to be related to the system's exogenous input c, written as Define the gain estimation error as Additional gain error is

[0160] The state-space equation for the estimation error is:

[0161]

[0162] The Lyapunov candidate function is:

[0163]

[0164] Where α is a constant greater than 0, and tr represents the trace of the matrix;

[0165] Find the conditions that satisfy the condition that the first-order partial derivative of the Lyapunov candidate function with respect to time is less than 0. The renewal law:

[0166]

[0167] Under this update law, It is bounded, and as t→∞, Established;

[0168] Human input estimation gain and estimated additional items The underlying assumptions are:

[0169] As t→∞ This holds true, where ξ and c are continuous excitation signals;

[0170] therefore Established, The update law can be used to update And the estimated value Converging to its true value K h M h ;

[0171] The update law for the estimated human control gain and additional terms is:

[0172]

[0173] In this embodiment, the target trajectory x d Set to:

[0174]

[0175] The weight parameters of the cost function are set as shown in Table 1. The setting of these weights indicates that both the human and the machine have a strong desire to stabilize the trajectory tracking error. The initial values ​​and related parameters of the system are shown in Table 2.

[0176] Table 1

[0177]

[0178] Table 2

[0179]

[0180] Taking the above as an example, the human-machine shared control task in this embodiment is designed as follows: humans and machines jointly participate in completing the one-dimensional path tracking control of the robotic arm, such as... Figure 3 As shown; the control strategies of both parties constitute the real-time Nash equilibrium of the cost function, and the exogenous input c of the system is a function related to the target path. Simulation verification was performed using Simulink, with the simulation duration set to t. f =100s.

[0181] Although humans intend to reduce control errors, human control inputs lack stability and precision compared to machine control inputs. Furthermore, there is a reaction time lag between visually observing the system state, the brain generating a control strategy, and finally the limbs applying control. In this embodiment, the human control input f is set as: the optimal input of the same system under linear quadratic optimal control multiplied by a gain of 0.6 and a delay of 0.2 seconds.

[0182] Step 3, which designs the algorithm flow for human-machine shared control of an exogenous input system based on Nash equilibrium, includes:

[0183] Step 31: Initialize the system state ξ and the system state estimate. Based on the control task, set the system control matrix A, input matrix B, and exogenous input term c; set the initial estimated values ​​for human control gain and additional term gain. Set the initial values ​​K for machine control gain and additional gain. a ,m a Assign the weight matrix Q to the human and machine cost functions. a Q h ,R a ,R h ,R ah ,R ha With the estimated parameters Γ,α;

[0184] Step 32: Based on the current K a , Numerical solution of K using gradient descent method a The coupled Riccati equations yield a new K a According to the current m a , K a , The gradient descent method is used to numerically solve for m. a The coupled Riccati equations are as follows, yielding a new ma ;

[0185]

[0186] Step 321: Initialize gradient descent parameters

[0187] Set the convergence tolerance tol = 1e-6, the gradient descent step size step_size = 1e-2, and the maximum number of iterations max_iter = 300, K a Initial guess matrix m a Initial guess vector m a =[1,1];

[0188] Step 322: Construct the gradient descent iterative method

[0189] When the number of iterations is less than the maximum number of iterations max_iter:

[0190] Take gradient

[0191]

[0192] Step 323: Update K using gradient descent a and m a

[0193] Get K a _new and ensure its symmetry:

[0194] K a _new'=K a +step_size×grad_K a

[0195]

[0196] Get m a _new:

[0197] m a _new=m a +step_size×grad_m a

[0198] Step 324: Check convergence, if ||K a _new-K a ||≤tol and||m a _new-m a If ||≤tol, then let K a =K a _new, m a =m a _new, output Ka ,m a Find the numerical solution; otherwise, proceed to steps 2-5.

[0199] Step 325: Obtain K a _new is defined as K a m a _new is defined as m a Return to step 323; when the number of iterations exceeds max_iter, end the loop and output K. a ,m a Numerical solution;

[0200] Step 33: Based on the current The value of the system state ξ and the state error Associative update law

[0201]

[0202] Update human control gain and additional gain

[0203] Step 34: Update the machine input under the Nash equilibrium form Compared with human estimation input Output machine control input Update the adaptive observer to obtain a new estimate of the system state.

[0204]

[0205] Step 35: Utilize the tactile channel to obtain the actual human input f, and combine it with the machine's control input u. * Using the system state-space equations Update the system status and output the system status ξ.

[0206] We obtain the real-time machine control input and system state that satisfy the Nash equilibrium of the cost function between humans and machines under the exogenous input system.

[0207] In this invention, Figure 4 This example illustrates the changes between the human input and its estimated value in this embodiment. The estimated human input is labeled f_hat. As the control process progresses, the estimated human input gradually approaches the actual human input, demonstrating the human control gain error. and additional gain error The convergence property of the property is thus utilized. Substituting the Riccati equation into the solution of the machine's control strategy is reasonable.

[0208] Figure 5This demonstrates the changes in the machine control strategy u that satisfies the real-time Nash equilibrium of the cost functions of both the human and machine in this embodiment.

[0209] Figure 6 It demonstrates the control inputs of humans and machines, as well as their combined inputs. It shows that under the current cost function, where both humans and machines have a strong desire to stabilize trajectory tracking errors, when human control input alone is insufficient to achieve high-precision trajectory tracking, the robot will compensate for the control inputs to reduce trajectory tracking errors.

[0210] Figure 7 This embodiment demonstrates the trajectory tracking error ξ. e The changes in these values ​​indicate how the trajectory tracking error changes when the cost functions of both the human and machine satisfy Nash equilibrium.

[0211] The above description is merely a preferred embodiment of the present invention. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention. Structures, devices, and operating methods not specifically described or explained in this invention are implemented according to conventional methods in the art unless otherwise specified or limited.

Claims

1. A human-machine shared control method for an exogenous input system under Nash equilibrium, characterized in that: Step 1: Construct a human-machine shared control framework based on Nash equilibrium, wherein the information acquisition structure of both the human and machine conforms to the closed-loop perfect state pattern. The human-machine shared control framework includes: By integrating the inputs of human interaction and automatic control systems as the control inputs of the human-machine shared control system, a state-space equation containing exogenous input terms is constructed for the human-machine shared control system. The assumptions of the human-machine shared control framework are declared; the cost functions for both humans and machines are defined, referencing the form of a linear quadratic form. Establish a tactile channel for human-computer interaction; Determine the form of the Nash equilibrium solution for a human-machine shared control system containing exogenous inputs; Then, by solving the coupled Riccati equations, the control input gain and additional terms of the machine are obtained; Step 2: Design a method for estimating the control gain and additional terms of human input. The real-time human control input in the form of decoupled interaction force is a control law with the same form as the Nash equilibrium solution. Construct an adaptive input observer, define the state space equation of the estimation error, select an appropriate Lyapunov function, and obtain the update law of the estimated human control input gain and additional terms. Step 3: Design the algorithm flow for human-machine shared control of the exogenous input system based on Nash equilibrium, and output the real-time control strategy and system state of the machine under Nash equilibrium.

2. The human-machine shared control method for an exogenous input system under Nash equilibrium according to claim 1, characterized in that: In step 1: The state-space equations of the human-machine shared control system containing exogenous inputs are as follows: Where A represents the system state, A∈R n×n The system moment ξ∈R n Array, B∈R n×m The input matrix is ​​u∈R m It is the input of the automated system, f∈R m It is the control exerted by humans, c∈R m This represents exogenous inputs, which are the sum of disturbances and other inputs that affect the system, excluding those from humans and machines.

3. The human-machine shared control method for an exogenous input system under Nash equilibrium according to claim 2, characterized in that: In step 2: The human-machine shared control framework is based on the following assumptions: Both the human and machine cost functions are modeled as linear quadratic functions, and both the human and the machine will minimize their respective cost functions as the control objective. The information acquisition structure between humans and machines satisfies the closed-loop perfect information model. The information acquisition structure η between humans and machines... i (t), i∈{a,h} satisfies η i (t)={ξ(s),0≤s≤t},t∈[0,∞];The system state information at any time and the control strategies of humans and machines are known to both humans and machines; The state-space equations of a human-machine shared control system containing exogenous inputs and the control strategy set γ for both humans and machines. i ∈Γ i i∈{a,h} satisfies the Lipschitz condition on ξ,u,f,c; The cost function for humans and machines is: Among them, Q h ∈R m×m and Q a ∈R m×m It is a positive semi-definite matrix, which represents the weights of human and machine control precision, and indicates the degree of importance that humans and machines attach to control precision. R a and R h R represents the weights of the robot's and human's inputs to themselves, respectively; ah R represents the evaluation weight of the robot on human input, while R ha These represent the evaluation weights of human input to the robot.

4. The human-machine shared control method for an exogenous input system under Nash equilibrium according to claim 3, characterized in that: In step 1, the human-machine interaction tactile channel is a tactile channel in the form of a joystick, steering wheel, or wearable device. The machine directly inputs control strategies through the automatic control system, and the human inputs control strategies through the tactile channel in the form of interactive force. The human obtains force feedback of the machine's input strategy through the tactile channel. The machine measures the human's interactive force through the tactile channel. The human and the machine complete real-time interaction of their control strategies through the tactile channel. At the same time, the real-time system status is known to both the human and the machine. The information acquisition structure of the human and the machine satisfies the closed-loop perfect information model.

5. The human-machine shared control method for an exogenous input system under Nash equilibrium according to claim 4, characterized in that: In step 1: Under Nash equilibrium, each controller, knowing the strategies of other controllers, has no incentive to unilaterally change its own control strategy; the Nash equilibrium of the cost functions of the human and machine in the closed-loop perfect information model is as follows: The Nash equilibrium solution of the human-machine shared control system containing exogenous input terms is: Control gain K a ,K h The following Riccati equation was obtained through calculation: in, Additional item m a ,m h The following Riccati equation was obtained through calculation: in, 6. The human-machine shared control method for an exogenous input system under Nash equilibrium according to claim 5, characterized in that: In step 2, the control gain K for human input is designed. h and additional items m h The estimation methods include: Decouple interactive force forms of real-time human control input; Construct an adaptive input observer; Determine Lyapunov candidate functions; Declare human input to estimate gain and estimated additional items The underlying assumptions; The update law for the estimated human control gain and additional terms is obtained.

7. The human-machine shared control method for an exogenous input system under Nash equilibrium according to claim 6, characterized in that: In step 2, the interactive force-based real-time human control input is: Where K h ,m h Control gains and additional parameters input by humans cannot be directly measured; The adaptive input observer is: in Γ is a positive definite diagonal matrix. Estimated values ​​input by humans; in Estimates of the control gain and additional terms input by humans. Considered to be related to the system's exogenous input c, written as Define the gain estimation error as Additional gain error is The state-space equation for the estimation error is: The Lyapunov candidate function is: Where α is a constant greater than 0, and tr represents the trace of the matrix; Find the conditions that satisfy the condition that the first-order partial derivative of the Lyapunov candidate function with respect to time is less than 0. The renewal law: Under this update law, It is bounded, and as t→∞, Established; Human input estimation gain and estimated additional items The underlying assumptions are: As t→∞ This holds true, where ξ and c are continuous excitation signals; therefore Established, The update law can be used to update And the estimated value Converging to its true value K h M h ; The update law for the estimated human control gain and additional terms is:

8. The human-machine shared control method for an exogenous input system under Nash equilibrium according to claim 7, characterized in that: Step 3, which designs the algorithm flow for human-machine shared control of an exogenous input system based on Nash equilibrium, includes: Step 31: Initialize the system state ξ and the system state estimate. Based on the control task, set the system control matrix A, input matrix B, and exogenous input term c; set the initial estimated values ​​for human control gain and additional term gain. Set the initial values ​​K for machine control gain and additional gain. a ,m a Assign the weight matrix Q to the human and machine cost functions. a Q h ,R a ,R h ,R ah ,R ha With the estimated parameters Γ,α; Step 32: Based on the current K a , Numerical solution of K using gradient descent method a The coupled Riccati equations yield a new K a According to the current m a , K a , The gradient descent method is used to numerically solve for m. a The coupled Riccati equations are as follows, yielding a new m a ; Step 321: Initialize gradient descent parameters Set the convergence tolerance (tol), gradient descent step size (step_size), maximum number of iterations (max_iter), and K. a Initial guess matrix, m a Initial guess vector; Step 322: Construct the gradient descent iterative method When the number of iterations is less than the maximum number of iterations max_iter: Take gradient Step 323: Update K using gradient descent a and m a Get K a _new and ensure its symmetry: K a _new'=K a +step_size×grad_K a Get m a _new: m a _new=m a +step_size×grad_m a Step 324: Check convergence, if ||K a _new-K a ||≤tol and||m a _new-m a If ||≤tol, then let K a =K a _new, m a =m a _new, output K a ,m a Find the numerical solution; otherwise, proceed to steps 2-5. Step 325: Obtain K a _new is defined as K a m a _new is defined as m a Return to step 323; when the number of iterations exceeds max_iter, end the loop and output K. a ,m a Numerical solution; Step 33: Based on the current The value of the system state ξ and the state error Associative update law Update human control gain and additional gain Step 34: Update the machine input under the Nash equilibrium form Compared with human estimation input Output machine control input Update the adaptive observer to obtain a new estimate of the system state. Step 35: Utilize the tactile channel to obtain the actual human input f, and combine it with the machine's control input u. * Using the system state-space equations Update the system status and output the system status ξ. We obtain the real-time machine control input and system state that satisfy the Nash equilibrium of the cost function between humans and machines under the exogenous input system.

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