Neural adaptive position tracking control method and device for single-link manipulator system

Abstract

The present invention relates to a neural adaptive position tracking control method and device for a single-link manipulator system. Taking into account the unmodeled dynamics and random disturbances of input and state, a single-link manipulator system is established. Information is acquired through the single-link manipulator system, and the single-link manipulator system is converted into a random non-strict feedback nonlinear system. This system is then converted into a random non-strict feedback nonlinear system without time-varying output constraints using nonlinear mapping technology. A radial basis function neural network, an adaptive regulation law, and a controller are designed. The dynamic changes of the adaptive regulation law in the controller are calculated and fed back to the corresponding controller, and a corresponding control signal is calculated. The control signal acts on the final single-link manipulator system, thereby enabling the system output to accurately track a reference signal and achieve the desired control target. The present invention can ensure good performance and stability during the operation of the single-link manipulator system.

Description

Technical Field

[0001] The present invention relates to the field of mechanical control, and in particular to a neural adaptive position tracking control method and device for a single-link manipulator system. Background Art

[0002] With the rapid development of science and technology, robotics has gradually emerged as an indispensable component of human progress. Robots, with their wide range of applications, high flexibility, and ability to operate in extreme environments, are leading the wave of technological innovation. Within this field, robotic arms, as a key technology, are widely used in machinery manufacturing, aerospace, medicine, and atomic energy, playing a key role in automated production.

[0003] Typically, a robot consists of three main parts: an actuator, a drive mechanism, and a control system. While performing its tasks, the robot interacts with the external environment and collects target position information through visual sensors. The control system issues instructions based on the information acquired, driving the robotic arm to contact the workpiece and perform various operations, such as grinding, drilling, polishing, and grasping. The robot, with its compliant control characteristics, can meet actual operational requirements in terms of both precision and strength, significantly expanding its application range and operational safety. Although robots excel in application and safety, the control system is often subject to various motion restrictions when handling different tasks. These restrictions can affect the performance of the controller, causing the robot system to become unstable or even crash during operation, making it difficult to perform tasks as planned.

[0004] The accuracy of the control algorithm in a manipulator control system directly impacts the accuracy of manipulator control. Current control algorithms, such as those based on backstepping, often assume that the virtual control signal from the previous state is known, which limits the controller's applicability. Furthermore, descriptions of external disturbances often assume that these disturbances are deterministic. However, in actual operational environments, the disturbances experienced by different manipulators or operating environments are random and diverse. Therefore, to better meet practical engineering requirements, the entire system should be modeled under a randomized scenario.

[0005] In a real working environment, the movement of the manipulator's end effector needs to be restricted by the object being operated and the environment, which may include spatial constraints, obstacle avoidance requirements, or other operational restrictions. The existence of such constraints may directly affect the performance of the controller and the working effect of the manipulator, such as the perception and control of complex situations and the stability of the entire control system. At the same time, due to the accuracy limitations of the sensors, various errors will always appear in system modeling, such as measurement noise, modeling errors, etc. These errors are collectively referred to as unmodeled dynamics. Unmodeled dynamics are also an issue that needs attention. During the movement of the manipulator, failure to fully consider the unmodeled dynamics of the external environment may lead to a decline in controller performance. Taking into account the differences in random disturbances to different manipulators and operating environments, external disturbances should be described more accurately during the modeling process. Summary of the Invention

[0006] Therefore, the technical problem to be solved by the present invention is to overcome the problems in the prior art of system modeling that do not consider the unmodeled dynamics, the output is limited and constrained, and random disturbances affect the performance of the controller. To solve the above technical problems, the present invention provides a neural adaptive position tracking control method for a single-link manipulator system, comprising the following steps:

[0007] Establishing a single-link manipulator system, wherein the single-link manipulator system is composed of a coupled angular motor rotor position dynamic subsystem, an angular velocity dynamic subsystem, and a motor armature current dynamic subsystem;

[0008] The single-link manipulator system is converted into a random non-strict feedback nonlinear system and input and state unmodeled dynamic terms are added. At this time, the random non-strict feedback nonlinear system is composed of an angular motor rotor position dynamic subsystem, an angular velocity dynamic subsystem, a motor armature current dynamic subsystem, a state unmodeled dynamic subsystem, and an input unmodeled dynamic subsystem coupled;

[0009] The time-varying output constraint of the random non-strict feedback nonlinear system is converted into a time-invariant output constraint by a nonlinear mapping technology, and the random non-strict feedback nonlinear system without time-varying output constraint is used as the final single-link manipulator system;

[0010] The final single-link manipulator system is subjected to neural network adaptive control, wherein the neural network adaptive control includes designing a radial basis function neural network and an adaptive regulation law and a controller. Preferably, the single-link manipulator system is established by the following formula (1):

[0011]

[0012] represents the angular motor rotor position, and y represents the system output, where represents the angular velocity, represents angular acceleration, I represents the motor armature current, is the derivative of I, ΔI represents the current disturbance, L is the armature inductance, R is the armature resistance, K B is the back electromotive force coefficient, U represents the input control voltage, J is the motor rotor inertia, m is the connecting rod mass, Q is the load mass, d is the connecting rod length, δ is the load radius, g is the gravity coefficient, B is the viscous friction coefficient at the joint, K τ is the coefficient that characterizes the electromechanical torque coupling, and the angular motor rotor position is constrained in the interval (-k1(t), k2(t)), k1(t) and k2(t) are positive functions, k 11 <|k1(t)|≤k 12 , k 21 <|k2(t)|≤k 22 , k 11 , k 12 , k 21 , k 22 are known positive constants, |k1(t)| and |k2(t)| represent the absolute values ​​of k1(t) and k2(t), respectively.

[0013] Preferably, the conversion of the single-link manipulator system into a random non-strict feedback nonlinear system comprises the following steps:

[0014] The single-link manipulator system is converted into a random non-strict feedback nonlinear system by formula (2);

[0015]

[0016] Where x1, x2 and x3 represent the angular motor rotor position state variable, angular velocity state variable and motor armature current state variable of the random non-strict feedback nonlinear system, respectively. x3=I, are the derivatives of x1, x2, and x3 respectively; R is the armature resistance, K B is the back-electromotive force coefficient, U is the input control voltage, μ is the system input of the random non-strict feedback nonlinear system without adding the unmodeled dynamic terms, where μ = U; L is the armature inductance, I is the motor armature current, ΔI is the current disturbance, and Q is the load mass;

[0017] Based on the random non-strict feedback nonlinear system, random disturbance terms, input and state unmodeled dynamic terms are added, and the corresponding random non-strict feedback nonlinear system (3) is described as follows

[0018]

[0019] Considering the existence of random disturbances, inputs and unmodeled state dynamics in random non-strict feedback nonlinear systems, let L=0.05,K B =0.5, R=0.5, ΔI=0.1x1sin(x2x3), dx1 represents the Ito differential of x1, dx2 represents the Ito differential of x2, dx3 is the Ito differential of x3, dw represents the random perturbation term, ξ∈R 3 represents the state with unmodeled dynamics, ζ=[ζ1,ζ2] T ∈R 2 represents the input of the unmodeled dynamics, u represents the input of the unmodeled dynamic subsystem, It represents the output of the input unmodeled dynamic subsystem and is also the system input of the random non-strict feedback nonlinear system after the unmodeled dynamic term is added. w is the r-dimensional standard Brownian motion defined on the complete probability space (Ω, F, P), where Ω is the sample space, F is the σ algebra, and P is the probability measure.

[0020] Preferably, the time-varying output constraint of the random non-strict feedback nonlinear system is converted into a time-invariant output constraint by a nonlinear mapping technique, and the random non-strict feedback nonlinear system without time-varying output constraint is used as the final single-link manipulator system:

[0021] The time-varying output constraint of the random non-strict feedback nonlinear system is converted into a time-invariant output constraint by the nonlinear mapping technology described in the following formula;

[0022]

[0023] The angular velocity state variable and the motor armature current state variable are converted by nonlinear mapping technology based on hyperbolic tangent function and are defined as s2 and s3 respectively, which are equivalent to x2 and x3 in the random non-strict feedback nonlinear system.

[0024] The angular motor rotor position state variable is converted into the following form through nonlinear mapping technology based on hyperbolic tangent function:

[0025]

[0026] Similarly, the reference signal y d After nonlinear mapping technology, it is converted into the following form:

[0027]

[0028] Preferably, the neural network adaptive control includes designing a radial basis function neural network and an adaptive regulation law and controller, including the following steps:

[0029] Step 1: The visual sensor of the final single-link manipulator system captures the angular motor rotor position of the operation target as the reference signal y d ;

[0030] Step 2: The reference signal y d The nonlinear mapping technology is used to convert the information and make a difference with the current angular motor rotor position state information s1 of the final single-link manipulator system to obtain the error z1 between the two, and the dynamic equation is differentially solved;

[0031] Step 3: Use radial basis function neural network to approximate the unmodeled dynamic terms and coupling terms in the final single-link manipulator system, and transform the state information s1 of the angular motor rotor position dynamic subsystem, the angular motor rotor position of the operation target and its first-order derivative As the input of the radial basis function neural network, the output is the radial basis function neural network of the angular motor rotor position dynamic subsystem And contains the corresponding accuracy level error ε1(S1);

[0032] Step 4: Use the two signals output by the radial basis function neural network and Establishing radial basis function neural network weights Adaptive regulation law in is the estimated value of λ1, yes The derivative of

[0033] Step 5: Using the adaptive regulation law Given the corresponding given parameters κ1, a1, Υ1, σ1, design the virtual controller α1;

[0034] Step 6: Using the virtual controller α1 and the adaptive regulation law The angular velocity state information s2 of the angular velocity dynamic subsystem is processed to obtain the control error signal z2 corresponding to the virtual controller of the angular motor rotor position dynamic subsystem, and the radial basis function neural network corresponding to the angular velocity dynamic subsystem is input to establish the radial basis function neural network weights. Adaptive regulation law in is an estimate of λ2, yes The derivative of ; and given the corresponding given parameters κ2, a2, Υ2, σ2, design the virtual controller α2;

[0035] Step 7: Then, the motor armature current state information s3 of the motor armature current dynamic subsystem is subtracted from the virtual controller α2 obtained by analyzing the angular velocity dynamic subsystem to obtain the error signal z3 of the motor armature current dynamic subsystem, and the error signal z3 is input into the radial basis function neural network corresponding to the motor armature current dynamic subsystem. The weights of the radial basis function neural network are respectively established. and the adaptive regulation law of the regularization signal θ and in and are the estimated values ​​of λ3 and M, respectively. yes The derivative of yes The derivative of , and given the corresponding given parameters κ3, a3, Υ3, σ3, Υ4, σ4, design the actual radial basis neural network adaptive controller u;

[0036] Step 8: Continue to compare the angular position state at the next moment with the state of the operation target, return to step 1, and continue the loop.

[0037] Preferably, the radial basis function neural network is established as follows:

[0038] For any continuous function P1(S1):R 7 →R, any given compact set and any positive constant There exists an ideal constant weight vector and a radial basis function vector Make

[0039]

[0040] Established, of which l>1 is the number of nodes in the radial basis function neural network, Defined as a Gaussian function of the form

[0041]

[0042] Among them, μ 1j and σ 1j Gaussian basis functions The width and center of the approximation error ε1(S1) satisfies ||S1-μ 1j || represents S1-μ 1j The Euclidean norm of the optimal weight vector The definition is as follows

[0043]

[0044] Preferably, the adaptive regulation law of the angular motor rotor position dynamic subsystem And the virtual controller α1 is designed as follows:

[0045]

[0046] in X1=[s1,ω1] T , And v represents the dynamic signal, ω1 represents the expected tracking trajectory after nonlinear mapping transformation, represents the derivative of ω1, ω2 represents the output of the first-order filter in the dynamic subsystem of the angular motor rotor position of the final single-link manipulator system, and a1, Υ1, σ1 and κ1 represent the designed positive constants.

[0047] Preferably, the adaptive regulation law of the angular velocity dynamic subsystem And the virtual controller α2 is designed as follows:

[0048]

[0049] in X2=[s1,s2,ω2] T , And v represents the dynamic signal, ω2 represents the output of the first-order filter in the dynamic subsystem of the angular motor rotor position of the final single-link manipulator system, represents the derivative of ω2, ω3 represents the output of the first-order filter in the angular velocity dynamic subsystem of the final single-link manipulator system, and a2, Υ2, g0, σ2 and κ2 represent designed positive constants.

[0050] Preferably, the radial basis function neural network weights and the adaptive regulation law of the regularization signal θ And the controller u is designed as follows:

[0051]

[0052] in X3=[s1,s2,s3,ω3] T , represents the controller intermediate variable, and v represents the dynamic signal, ω3 represents the output of the first-order filter in the final single-link manipulator system angular velocity dynamic subsystem, represents the derivative of ω3, and a3, Υ3, Υ4, ψ, σ3, σ4 and κ3 represent designed positive constants.

[0053] Preferably, a neural adaptive position tracking control device for a single-link manipulator system comprises:

[0054] A construction module is used to establish a single-link manipulator system, wherein the single-link manipulator system is composed of a coupled angular motor rotor position dynamic subsystem, an angular velocity dynamic subsystem, and a motor armature current dynamic subsystem;

[0055] A conversion module, configured to convert the single-link manipulator system into a random non-strict feedback nonlinear system and add input and state unmodeled dynamic terms;

[0056] a processing module, configured to convert the time-varying output constraints of the random non-strict feedback nonlinear system into time-invariant output constraints through a nonlinear mapping technique, and use the random non-strict feedback nonlinear system without time-varying output constraints as the final single-link manipulator system;

[0057] A control module performs neural network adaptive control on the final single-link manipulator system, wherein the neural network adaptive control includes designing a radial basis function neural network and an adaptive regulation law and a controller.

[0058] The above technical solution of the present invention has the following beneficial effects compared with the prior art:

[0059] The single-link manipulator system described in the present invention takes into account the input unmodeled dynamics and state unmodeled dynamics when establishing the system, and uses the hyperbolic tangent function as a nonlinear mapping to transform the time-varying output constraint manipulator system with unmodeled dynamic factors into a new single-link manipulator system without time-varying constraints, which can overcome random disturbances and improve the applicability of the single-link manipulator system.

[0060] Based on radial basis function neural networks and the inequality properties of Gaussian functions, the system functions and control gains, including the angular motor rotor position, angular velocity, and armature current, are effectively processed in each recursive step. This enables adaptive regulation of the system output, accurately tracks the reference signal, and stably operates on the control target. This improves the performance and efficiency of the single-link manipulator system. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] In order to make the content of the present invention more clearly understood, the present invention is further described in detail below based on specific embodiments of the present invention in conjunction with the accompanying drawings, wherein

[0062] Figure 1 It is a schematic diagram of the principle flow of the present invention;

[0063] Figure 2 It is a comparison diagram of the tracking effect of the present invention;

[0064] Figure 3 This is a tracking error effect diagram of the present invention;

[0065] Figure 4 This is a control signal u effect diagram of the present invention;

[0066] Figure 5 The adaptive regulation law of the present invention Adaptive change curve graph;

[0067] Figure 6 The adaptive regulation law of the present invention Adaptive change curve graph. DETAILED DESCRIPTION

[0068] The present invention is further described below with reference to the accompanying drawings and specific embodiments so that those skilled in the art can better understand the present invention and implement it. However, the embodiments are not intended to limit the present invention.

[0069] Example 1

[0070] Reference Figure 1 As shown, the present invention is a neural adaptive position tracking control method for a single-link manipulator system, comprising the following steps:

[0071] S1: Establish a single-link manipulator system, which is composed of a coupled angular motor rotor position dynamic subsystem, an angular velocity dynamic subsystem, and a motor armature current dynamic subsystem;

[0072] The single-link manipulator system is established by the following formula (1):

[0073]

[0074] represents the angular motor rotor position, and y represents the system output, where represents the angular velocity, represents angular acceleration, I represents the motor armature current, is the derivative of I, ΔI represents the current disturbance, L is the armature inductance, R is the armature resistance, K B is the back electromotive force coefficient, U represents the input control voltage, J is the motor rotor inertia, m is the connecting rod mass, Q is the load mass, d is the connecting rod length, δ is the load radius, g is the gravity coefficient, B is the viscous friction coefficient at the joint, K τ is the coefficient that characterizes the electromechanical torque coupling, and the angular motor rotor position is constrained in the interval (-k1(t), k2(t)), k1(t) and k2(t) are positive functions, k 11 <|k1(t)|≤k 12 , k 21 <|k2(t)|≤k 22 , k 11 , k12 , k 21 , k 22 are known positive constants, |k1(t)| and |k2(t)| represent the absolute values ​​of k1(t) and k2(t), respectively.

[0075] S2: converting the single-link manipulator system into a random non-strict feedback nonlinear system and adding input and state unmodeled dynamic terms. At this time, the random non-strict feedback nonlinear system is composed of the angular motor rotor position dynamic subsystem, angular velocity dynamic subsystem, motor armature current dynamic subsystem, state unmodeled dynamic subsystem, and input unmodeled dynamic subsystem coupled;

[0076] The single-link manipulator system is converted into a random non-strict feedback nonlinear system by formula (2);

[0077]

[0078] Where x1, x2 and x3 represent the angular motor rotor position state variable, angular velocity state variable and motor armature current state variable of the random non-strict feedback nonlinear system, respectively. x3=I, are the derivatives of x1, x2, and x3 respectively; R is the armature resistance, K B is the back-electromotive force coefficient, U is the input control voltage, μ is the system input of the random non-strict feedback nonlinear system without adding the unmodeled dynamic terms, where μ = U; L is the armature inductance, I is the motor armature current, ΔI is the current disturbance, and Q is the load mass;

[0079] Based on the random non-strict feedback nonlinear system, random disturbance terms, input and state unmodeled dynamic terms are added, and the corresponding random non-strict feedback nonlinear system (3) is described as follows

[0080]

[0081] Considering the existence of random disturbances, inputs and unmodeled state dynamics in random non-strict feedback nonlinear systems, let L=0.05,K B =0.5, R=0.5, ΔI=0.1x1 sin(x2x3), dx1 represents the Ito differential of x1, dx2 represents the Ito differential of x2, dx3 is the Ito differential of x3, dw represents the random disturbance term, ξ∈R 3 represents the state with unmodeled dynamics, ζ=[ζ1,ζ2] T ∈R 2 represents the input of the unmodeled dynamics, u represents the input of the unmodeled dynamic subsystem, It represents the output of the input unmodeled dynamic subsystem and is also the system input of the random non-strict feedback nonlinear system after the unmodeled dynamic term is added. w is the r-dimensional standard Brownian motion defined on the complete probability space (Ω, F, P), where Ω is the sample space, F is the σ algebra, and P is the probability measure.

[0082] S3: converting the time-varying output constraint of the random non-strict feedback nonlinear system into a time-invariant output constraint by using a nonlinear mapping technique, and using the random non-strict feedback nonlinear system without time-varying output constraint as the final single-link manipulator system;

[0083] The time-varying output constraint of the random non-strict feedback nonlinear system is converted into a time-invariant output constraint by the nonlinear mapping technology described in the following formula;

[0084]

[0085] The angular velocity state variable and the motor armature current state variable are converted by nonlinear mapping technology based on hyperbolic tangent function and are defined as s2 and s3 respectively, which are equivalent to x2 and x3 in the random non-strict feedback nonlinear system.

[0086] The angular motor rotor position state variable is converted into the following form through nonlinear mapping technology based on hyperbolic tangent function:

[0087]

[0088] Similarly, the reference signal y d After nonlinear mapping technology, it is converted into the following form:

[0089]

[0090] S4: Performing neural network adaptive control on the final single-link manipulator system, wherein the neural network adaptive control includes designing a radial basis function neural network and an adaptive regulation law and a controller.

[0091] The radial basis function neural network is established as follows: For any continuous function P1(S1):R 7 →R, any given compact set and any positive constant There exists an ideal constant weight vector and a radial basis function vector Make

[0092]

[0093] Established, of which l>1 is the number of nodes in the radial basis function neural network, Defined as a Gaussian function of the form

[0094]

[0095] Among them, μ 1j and σ 1j Gaussian basis functions The width and center of the approximation error ε1(S1) satisfies ||S1-μ 1j || represents S1-μ 1j The Euclidean norm of the optimal weight vector The definition is as follows

[0096]

[0097] The visual sensor of the final single-link manipulator system captures the angular motor rotor position of the operation target as the reference signal y d ;

[0098] The reference signal y d The nonlinear mapping technology is used to convert the information and make a difference with the current angular motor rotor position state information s1 of the final single-link manipulator system to obtain the error z1 between the two, and the dynamic equation is differentially solved;

[0099] The radial basis neural network is used to approximate the unmodeled dynamic terms and coupling terms in the final single-link manipulator system, and the state information s1 of the angular motor rotor position dynamic subsystem and the angular motor rotor position of the operation target are converted into and its first-order derivative As the input of the radial basis function neural network, the output is the radial basis function neural network of the angular motor rotor position dynamic subsystem And contains the corresponding accuracy level error ε1(S1);

[0100] Because of the particularity of the final single-link manipulator system, the unmodeled dynamic nonlinear terms and coupling terms include all states, here X1=[s1,ω1] T , v represents the dynamic signal, ω1 represents the expected tracking trajectory after nonlinear mapping transformation, represents the derivative of ω1, ω2 represents the output of the first-order filter in the dynamic subsystem of the angular motor rotor position of the final single-link manipulator system, S 1j represents the jth element in S1, X 1j represents the jth element in X1. Based on the inequality relationship, the properties of the Gaussian function can be applied as follows:

[0101]

[0102] Among them, μ 1j and σ 1j Gaussian basis functions width and center.

[0103] Two signals output by radial basis function neural network and Establishing radial basis function neural network weights Adaptive regulation law in is the estimated value of λ1, yes The derivative of

[0104] Using the adaptive regulation law Given the corresponding given parameters κ1, a1, Υ1, σ1, design the virtual controller α1; the adaptive regulation law of the angular motor rotor position dynamic subsystem And the virtual controller α1 is designed as follows:

[0105]

[0106] in X1=[s1,ω1] T , And v represents a dynamic signal, a1, Υ1, σ1 and κ1 represent design positive constants.

[0107] Using the virtual controller α1 and the adaptive regulation law The angular velocity state information s2 of the angular velocity dynamic subsystem is processed to obtain the control error signal z2 corresponding to the virtual controller of the angular motor rotor position dynamic subsystem; the radial basis function neural network corresponding to the angular velocity dynamic subsystem is input, and the output is the radial basis function neural network of the angular velocity dynamic subsystem. And contains the corresponding accuracy level error ε2(S2);

[0108] Because of the particularity of the final single-link manipulator system, the unmodeled dynamic nonlinear terms and coupling terms include all states, here X2=[s1,s2,ω2] T , v represents the dynamic signal, ω2 represents the output of the first-order filter in the dynamic subsystem of the angular motor rotor position of the final single-link manipulator system, represents the derivative of ω2, ω3 represents the output of the first-order filter in the final single-link manipulator system angular velocity dynamic subsystem, S 2j represents the jth element in S2, X 2j represents the jth element in X2. Based on the inequality relationship, the properties of the Gaussian function can be applied as follows:

[0109]

[0110] Among them, μ 2j and σ 2j Gaussian basis functions width and center.

[0111] Establishing radial basis function neural network weights Adaptive regulation law in is an estimate of λ2, yes The derivative of ; and given the corresponding given parameters κ2, a2, Υ2, σ2, design the virtual controller α2;

[0112] The adaptive regulation law of the angular velocity dynamic subsystem And the virtual controller α2 is designed as follows:

[0113]

[0114] in X2=[s1,s2,ω2] T , And v represents a dynamic signal, a2, Υ2, g0, σ2 and κ2 represent design positive constants.

[0115] Then the motor armature current state information s3 of the motor armature current dynamic subsystem is subtracted from the virtual controller α2 obtained by analyzing the angular velocity dynamic subsystem to obtain the error signal z3 of the motor armature current dynamic subsystem, which is input into the radial basis function neural network corresponding to the motor armature current dynamic subsystem, and the output is the radial basis function neural network of the last order subsystem. And contains the corresponding accuracy level error ε3(S3);

[0116] Because of the particularity of the final single-link manipulator system, the unmodeled dynamic nonlinear terms and coupling terms include all states, here X3=[s1,s2,s3,ω3] T , v represents the dynamic signal, ω3 represents the output of the first-order filter in the final single-link manipulator system angular velocity dynamic subsystem, represents the derivative of ω3, S 3j represents the jth element in S3, X 3j represents the jth element in X3. Based on the inequality relationship, the properties of the Gaussian function can be applied as follows:

[0117]

[0118] Among them, μ 3j and σ3j Gaussian basis functions width and center.

[0119] Two signals output by radial basis function neural network and Establish the weights of radial basis function neural network respectively and an adaptive algorithm for the regularization signal θ and As follows, and are the estimated values ​​of λ3 and M, respectively. yes The derivative of yes The derivative of :

[0120]

[0121] where a3, σ3, ψ, σ4, Υ3, and Υ4 represent adaptive design constants, and v represents the dynamic signal. Represents the controller intermediate variable, P θ =(1+|θ|) 4 , θ represents the regularization signal, and |θ| represents the absolute value of θ. Using the adaptive regulation law established in this step and the corresponding given positive parameter κ3, the actual controller u is designed as follows:

[0122]

[0123] Continue to compare the angular position state at the next moment with the state of the operation target, return to step 1, and continue the loop.

[0124] Reference Figure 2 and Figure 3 As shown, the solid line represents the actual trajectory y, and the dotted line represents the tracking trajectory y d , the tracking error effect is the difference between the actual output trajectory y and the expected trajectory y d Through the simulation experiment of this embodiment, the output trajectory meets the constraints in the probability sense, the control target can be well achieved, the tracking error can be kept in a small range of 0, and the tracking effect is good.

[0125] Reference Figure 4 As shown, through the simulation experiment of this embodiment, the control signal u is bounded, which ensures the tracking performance of the system.

[0126] Reference Figure 5 and Figure 6 As shown, the parameters in the simulation experiment of this embodiment are adjusted Adaptive change curve.

[0127] From the above simulation experiment results, it can be concluded that the robot can achieve the expected goals very well.

[0128] Example 2

[0129] Based on Example 1, this example introduces a neural adaptive position tracking control device for a single-link manipulator system, comprising:

[0130] A construction module is used to establish a single-link manipulator system, wherein the single-link manipulator system is composed of a coupled angular motor rotor position dynamic subsystem, an angular velocity dynamic subsystem, and a motor armature current dynamic subsystem;

[0131] A conversion module, configured to convert the single-link manipulator system into a random non-strict feedback nonlinear system and add input and state unmodeled dynamic terms;

[0132] a processing module, configured to convert the time-varying output constraints of the random non-strict feedback nonlinear system into time-invariant output constraints through a nonlinear mapping technique, and use the random non-strict feedback nonlinear system without time-varying output constraints as the final single-link manipulator system;

[0133] A control module performs neural network adaptive control on the final single-link manipulator system, wherein the neural network adaptive control includes designing a radial basis function neural network and an adaptive regulation law and a controller.

[0134] Those skilled in the art will appreciate that the embodiments of the present application can be provided as methods, systems, or computer program products. Therefore, the present application can adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment in combination with software and hardware. Moreover, the present application can adopt the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to magnetic disk storage, CD-ROM, optical storage, etc.) that contain computer-usable program code.

[0135] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 a process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0136] These computer program instructions may also be stored in a computer readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 a process or multiple processes and / or boxes Figure 1 The function specified in one or more boxes.

[0137] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions executed on the computer or other programmable device for implementing the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0138] Obviously, the above embodiments are merely examples for clarity of explanation and are not intended to limit the implementation methods. Those skilled in the art will appreciate that other variations or modifications can be made based on the above description. It is not necessary and impossible to enumerate all implementation methods here. Obvious variations or modifications arising therefrom remain within the scope of protection of the present invention.

Claims

1. A neural adaptive position tracking control method for a single-link manipulator system, characterized in that: The following steps are involved: Establishing a single-link manipulator system, wherein the single-link manipulator system is composed of a coupled angular motor rotor position dynamic subsystem, an angular velocity dynamic subsystem, and a motor armature current dynamic subsystem; The single-link manipulator system is converted into a random non-strict feedback nonlinear system and input and state unmodeled dynamic terms are added. At this time, the random non-strict feedback nonlinear system is composed of an angular motor rotor position dynamic subsystem, an angular velocity dynamic subsystem, a motor armature current dynamic subsystem, a state unmodeled dynamic subsystem, and an input unmodeled dynamic subsystem coupled; The random non-strict feedback nonlinear system is: ， in, 、 and are the angular motor rotor position state variable, angular velocity state variable, and motor armature current state variable of the random non-strict feedback nonlinear system, respectively. for The Ito differential, for The Ito differential, for The Ito differential, is a random disturbance term, For states where dynamics is not modeled, is the input unmodeled dynamics, is the input to the unmodeled dynamic subsystem, is the output of the input unmodeled dynamic subsystem, and is also the system input of the random non-strict feedback nonlinear system after adding the unmodeled dynamic term. is defined in the complete probability space on dimensional standard Brownian motion, is the sample space, yes Algebra, is a probability measure; The time-varying output constraint of the random non-strict feedback nonlinear system is converted into a time-invariant output constraint by a nonlinear mapping technology, and the random non-strict feedback nonlinear system without time-varying output constraint is used as the final single-link manipulator system; Performing neural network adaptive control on the final single-link manipulator system, wherein the neural network adaptive control includes designing a radial basis function neural network and an adaptive regulation law and a controller; Adaptive controller for: ， in, is the error signal of the motor armature current dynamic subsystem, Represents the controller intermediate variable, , , is the state information of the dynamic subsystem of the angular motor rotor position, is the angular velocity state information of the angular velocity dynamic subsystem, is the motor armature current state information of the motor armature current dynamic subsystem, represents the output of the first-order filter in the final single-link manipulator system angular velocity dynamic subsystem, 、 To adjust the parameters, is the output signal of the radial basis neural network, , represents the regularization signal, express The absolute value of , and Indicates a design positive constant.

2. The neural adaptive position tracking control method for a single-link manipulator system according to claim 1, characterized in that: The single-link manipulator system is established by the following formula (1): ， represents the angular motor rotor position, represents the system output, where , represents the angular velocity, represents the angular acceleration, represents the motor armature current, yes The derivative of Indicates current interference, is the armature inductance, is the armature resistance, is the back electromotive force coefficient, Indicates the input control voltage, , , , is the motor rotor inertia, is the mass of the connecting rod, is the load mass, is the connecting rod length, is the load radius, is the gravity coefficient, is the viscous friction coefficient at the joint, is the coefficient that characterizes the electromechanical torque coupling, and the angular motor rotor position is constrained in the interval , and is a positive function, , , , , , is a known positive constant, and Respectively and The absolute value of .

3. The neural adaptive position tracking control method for a single-link manipulator system according to claim 1, characterized in that: The conversion of the single-link manipulator system into a random non-strict feedback nonlinear system comprises the following steps: The single-link manipulator system is converted into a random non-strict feedback nonlinear system by formula (2); ， in 、 and They represent the angular motor rotor position state variable, angular velocity state variable, and motor armature current state variable of the random non-strict feedback nonlinear system, respectively. , , , 、 、 They are 、 、 The derivative of is the armature resistance, is the back electromotive force coefficient, Indicates the input control voltage, represents the system input of the random non-strict feedback nonlinear system without the unmodeled dynamic terms, where ; is the armature inductance, represents the motor armature current, Indicates current interference, is the load mass; Based on the random non-strict feedback nonlinear system, random disturbance terms, input and state unmodeled dynamic terms are added. Considering the existence of random disturbances, input and state unmodeled dynamic terms in the random non-strict feedback nonlinear system, let , , , , , , , and the corresponding random non-strict feedback nonlinear system is obtained.

4. The neural adaptive position tracking control method for a single-link manipulator system according to claim 3, characterized in that: The time-varying output constraints of the random non-strict feedback nonlinear system are converted into time-invariant output constraints through nonlinear mapping technology: The time-varying output constraint of the random non-strict feedback nonlinear system is converted into a time-invariant output constraint by the nonlinear mapping technology described in the following formula; ， After the angular velocity state variable and the motor armature current state variable are converted by the nonlinear mapping technology based on the hyperbolic tangent function, they are defined as and , which is similar to the form of random non-strict feedback nonlinear system and The corresponding state variables of the angular motor rotor position are converted into the following form through nonlinear mapping technology based on hyperbolic tangent function: ， Similarly, the reference signal After nonlinear mapping technology, it is converted into the following form, where , Represents the expected tracking trajectory after conversion by nonlinear mapping technology: 。 5. The neural adaptive position tracking control method for a single-link manipulator system according to claim 3, characterized in that: The neural network adaptive control is performed on the final single-link manipulator system, and the neural network adaptive control includes designing a radial basis function neural network and an adaptive regulation law and a controller, and includes the following steps: Step 1: The visual sensor of the final single-link manipulator system captures the angular motor rotor position of the operation target as a reference signal ; Step 2: The reference signal The current angular motor rotor position state information of the final single-link manipulator system is converted by nonlinear mapping technology and combined with the current angular motor rotor position state information of the final single-link manipulator system. Make the difference and get the error between the two , and perform differential solutions to the dynamic equations; Step 3: Use radial basis function neural network to approximate the unmodeled dynamic terms and coupling terms in the final single-link manipulator system, and convert the state information of the angular motor rotor position dynamic subsystem into The target angle of the operation is the motor rotor position and its first-order derivative As the input of the radial basis function neural network, the output is the radial basis function neural network of the angular motor rotor position dynamic subsystem , and contains the corresponding accuracy level error ; Step 4: Use the two signals output by the radial basis function neural network and , establish the radial basis function neural network weights Adaptive regulation law ,in yes The estimated value of yes The derivative of Step 5: Using the adaptive regulation law , given the corresponding given parameters , , , , design a virtual controller ; Step 6: Utilize the Virtual Controller and adaptive regulation law , the angular velocity state information of the angular velocity dynamic subsystem Processing is performed to obtain the control error signal corresponding to the virtual controller of the angular motor rotor position dynamic subsystem , input the radial basis function neural network corresponding to the angular velocity dynamic subsystem, and establish the radial basis function neural network weights Adaptive regulation law ,in yes The estimated value of yes The derivative of ; and given the corresponding given parameters , , , , design a virtual controller ; Step 7: Then the motor armature current state information of the motor armature current dynamic subsystem The virtual controller obtained by analyzing the angular velocity dynamic subsystem The error signal of the motor armature current dynamic subsystem is obtained by subtraction , input the radial basis function neural network corresponding to the motor armature current dynamic subsystem, and establish the radial basis function neural network weights and regularization signal Adaptive regulation law and ,in and They are and The estimated value of yes The derivative of yes The derivative of , and the corresponding given parameters are given by , , , , , , designing a practical radial basis function neural network adaptive controller ; Step 8: Continue to compare the angular position state at the next moment with the state of the operation target, return to step 1, and continue the loop.

6. The neural adaptive position tracking control method for a single-link manipulator system according to claim 5, characterized in that: The radial basis function neural network is established as follows: For any continuous function , any given compact set and any positive constant , there exists an ideal constant weight vector and a radial basis function vector Make Established, of which , is the number of nodes of the radial basis function neural network, is defined as a Gaussian function of the form: , in, and Gaussian basis functions Width and center, approximation error satisfy , express The Euclidean norm of the optimal weight vector The definition is as follows .

7. The neural adaptive position tracking control method for a single-link manipulator system according to claim 5, characterized in that: Adaptive Regulation Law of the Rotor Position Dynamic Subsystem of an Angle Motor and virtual controllers The design is as follows: ， ， in , , ,and Represents a dynamic signal, represents the desired tracking trajectory after nonlinear mapping transformation, express The derivative of represents the output of the first-order filter in the dynamic subsystem of the angular motor rotor position of the final single-link manipulator system, , , and Indicates a design positive constant.

8. The neural adaptive position tracking control method for a single-link manipulator system according to claim 5, characterized in that: Adaptive Regulation Law of Angular Velocity Dynamic Subsystem and virtual controllers The design is as follows: ， ， in , , ,and Represents a dynamic signal, represents the output of the first-order filter in the dynamic subsystem of the angular motor rotor position of the final single-link manipulator system, express The derivative of represents the output of the first-order filter in the angular velocity dynamic subsystem of the final single-link manipulator system, , , , and Indicates a design positive constant.

9. The neural adaptive position tracking control method for a single-link manipulator system according to claim 5, characterized in that: The radial basis function neural network weights and regularization signal Adaptive regulation law 、 The design is as follows: ， ， in , , , Represents a dynamic signal, represents the output of the first-order filter in the final single-link manipulator system angular velocity dynamic subsystem, express The derivative of , , , Indicates a design positive constant.

10. A neural adaptive position tracking control system for a single-link manipulator system, characterized in that: include: A construction module is used to establish a single-link manipulator system, wherein the single-link manipulator system is composed of a coupled angular motor rotor position dynamic subsystem, an angular velocity dynamic subsystem, and a motor armature current dynamic subsystem; a conversion module for converting the single-link manipulator system into a random non-strict feedback nonlinear system and adding input and state unmodeled dynamic terms, wherein the random non-strict feedback nonlinear system is composed of a coupling of an angular motor rotor position dynamic subsystem, an angular velocity dynamic subsystem, a motor armature current dynamic subsystem, a state unmodeled dynamic subsystem, and an input unmodeled dynamic subsystem; The random non-strict feedback nonlinear system is: ， in, 、 and are the angular motor rotor position state variable, angular velocity state variable, and motor armature current state variable of the random non-strict feedback nonlinear system, respectively. for The Ito differential, for The Ito differential, for The Ito differential, is a random disturbance term, For states where dynamics is not modeled, is the input unmodeled dynamics, is the input to the unmodeled dynamic subsystem, is the output of the input unmodeled dynamic subsystem, and is also the system input of the random non-strict feedback nonlinear system after adding the unmodeled dynamic term. is defined in the complete probability space on dimensional standard Brownian motion, is the sample space, yes Algebra, is a probability measure; a processing module, configured to convert the time-varying output constraints of the random non-strict feedback nonlinear system into time-invariant output constraints through a nonlinear mapping technique, and use the random non-strict feedback nonlinear system without time-varying output constraints as the final single-link manipulator system; A control module performs neural network adaptive control on the final single-link manipulator system, wherein the neural network adaptive control includes designing a radial basis function neural network and an adaptive regulation law and a controller; Adaptive controller for: ， in, is the error signal of the motor armature current dynamic subsystem, Represents the controller intermediate variable, , , is the state information of the dynamic subsystem of the angular motor rotor position, is the angular velocity state information of the angular velocity dynamic subsystem, is the motor armature current state information of the motor armature current dynamic subsystem, represents the output of the first-order filter in the final single-link manipulator system angular velocity dynamic subsystem, 、 To adjust the parameters, is the output signal of the radial basis neural network, , represents the regularization signal, express The absolute value of , and Indicates a design positive constant.

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