Iterative learning control system and method for robot device based on quasi-newton method

Abstract

The application discloses a kind of mechanical arm device iterative learning control system and method based on quasi-newton method, target trajectory determination module in the system is used to determine the expected target trajectory of the mechanical arm device, nonlinear equation determination module is used to determine the nonlinear equation related to mechanical arm nonlinear system, pose acquisition module is used to obtain the position of the mechanical arm device under current iteration, control module is used to update the control input of the mechanical arm device when next iteration according to the expected target trajectory of the mechanical arm system, control input under current iteration, position output under current iteration and gain matrix, the mechanical arm device is controlled.The application can make that mechanical arm is in finite time period at any time to the trackable target trajectory Realize high-precision tracking.

Description

Technical Field

[0001] This invention belongs to the field of robot control technology, and in particular relates to an iterative learning control system and method for a robotic arm device based on the quasi-Newton method. Background Technology

[0002] Currently, high-precision tracking control of robotic arms has received widespread attention in practical applications. With the increasing complexity of system structures and the rising demands for autonomous control of robotic arms, designing high-precision control algorithms using intelligent control methods has become a trend. In practical applications, robotic arms often need to repeatedly and accurately track the required signal trajectory within a limited range to complete specific tasks. Therefore, iterative learning control methods have been introduced into the design of tracking control algorithms for robotic arms. Iterative learning control methods are driven by human learning, utilizing experience from previous tracking stages to gradually improve tracking accuracy. This method has achieved significant progress in both the theory and application of industrial control. Summary of the Invention

[0003] In view of this, the present invention proposes an iterative learning control system and method for a robotic arm device based on the quasi-Newton method. This method applies the quasi-Newton method to nonlinear iterative learning control problems, enabling the nonlinear robotic arm device to achieve high-precision tracking of the trajectory of a target that can be tracked.

[0004] The specific technical solution of the present invention is as follows:

[0005] An iterative learning control system for a robotic arm device based on the quasi-Newton method includes a target trajectory determination module, a nonlinear equation determination module, a pose acquisition module, and a control module.

[0006] The target trajectory determination module is used to set the expected target trajectory of the robotic arm device;

[0007] The nonlinear equation determination module is used to determine the nonlinear equations related to the robotic arm device;

[0008] The pose acquisition module is used to acquire the position output of the robotic arm device in the current iteration;

[0009] The control module is used to perform real-time control of the robotic arm device based on the expected target trajectory, the control input under the current iteration, the position output under the current iteration, and the selected gain matrix.

[0010] Furthermore, the robotic arm device has the following dynamic characteristics:

[0011]

[0012] Where, x k(t), u k (t) and y k (t) represents the state, control input, and position output of the robotic arm at time t in the k-th iteration, respectively, where t∈{0,1,2,…,N} is the running time and N is the running period. Let f(·) be the number of iterations, f(·) represent the relationship between the state and the control input, and h(·) represent the relationship between the position output and the state.

[0013] Furthermore, the nonlinear equation can be obtained in the following way:

[0014] Based on the dynamic system of the robotic arm, the relationship between input and output can be expressed by the following functions g1, g2, ... g N describe:

[0015] y k (1)=h[x k (1)]=h[f(x k (0),u k (0))]=g1[x k (0),u k (0)]

[0016] y k (2)=h[x k (2)]=h[f(x k (1),u k (1))]=g2[x k (0),u k (0),u k (1)]

[0017]

[0018] y k (N)=h[x k (N)]=h[f(x k (N-1),u k (N-1))]

[0019] =g N [x k (0),u k (0),u k (1),…,u k (N-1)]

[0020] The initial state is x k (0) = x0 is independent of the iteration index; therefore, the nonlinear robotic arm device can be represented by the following function:

[0021] y k =g(u k),g(·)=[g1(·),g2(·),…,g N (·)] T

[0022] Here, g(·) depends on f(·), h(·), and x0, representing the relationship between the position output and the control input. The nonlinear iterative learning control problem is reformulated as a nonlinear algebraic equation. Therefore, the desired input u is sought. d Drive dynamic system to track desired output y d The iterative learning control task becomes finding a solution that satisfies the following nonlinear algebraic equation:

[0023] F(u k )=g(u k )-y d =0

[0024] Where F(·) represents a nonlinear function that depends on f(·), h(·), x0, and y. d The control input sequence u for the kth iteration k In the k-th attempt to solve the nonlinear equation, it becomes an unknown variable, and the ideal control input sequence u d Is it satisfying F(u) d The exact solution for ) = 0.

[0025] Furthermore, the control module includes: a control quantity determination unit and a position control unit; wherein,

[0026] The control quantity determination unit is used to control the robotic arm device to execute the next iteration process based on the expected target trajectory, the control input under the current iteration, the position output under the current iteration, and the selected gain matrix, and determines the control input of the robotic arm device using the following formula:

[0027] u k+1 =u k +L(u k )e k

[0028] Where L(·) represents the learning gain, and the learning gain L(u) is selected based on the quasi-Newton method. k )=g′(u k ) -1 , g(·) represents the relationship between position output and control input, which can be obtained through the dynamic characteristics of the robotic arm device, and g′ represents the derivative of the function g; Let be the augmented vector of the control input in k iterations, and T denote the transpose of the vector. y is the augmented vector controlling the input in the (k+1)th iteration; d (t) represents the expected target trajectory of the robotic arm device, e k =y d-y k , This is the augmented vector of the expected target trajectory. This is the augmented vector of the position output after k iterations.

[0029] The position control unit is used to determine the position output of the robotic arm device in the next iteration based on the control input and the initial input vector for the next iteration using the following formula:

[0030] y k+1 =g(u k+1 )

[0031] in, Let g(·) be the augmented vector of the position output in the (k+1)th iteration, and g(·) represent the relationship between the position output and the control input, which can be obtained through the dynamic characteristics of the robotic arm device.

[0032] This invention also provides an iterative learning control method for a robotic arm device based on the quasi-Newton method, comprising the following steps:

[0033] S1: Set the expected target trajectory for the robotic arm device;

[0034] S2: Obtain the nonlinear system model information of the robotic arm device and transform the nonlinear system into nonlinear equations;

[0035] S3: Obtain the position output of the robotic arm device in the current iteration;

[0036] S4: Based on the expected target trajectory of the robotic arm, the control input and position output of the current iteration, and the selected gain matrix, update the control input of the robotic arm for the next iteration, and control the robotic arm to execute the next iteration process. The learning gain L(u) is selected based on the quasi-Newton method. k ) = F ′ (u k ) -1 =g ′ (u k ) -1 , where F ′ Let F(u) denote the derivative of the function F. k )=g(u k )-y d ,e k =-F(u k ), where g(·) represents the relationship between position output and control input, which can be obtained through the dynamic characteristics of the robotic arm device. Therefore, the update algorithm for the iterative learning control scheme is:

[0037] u k+1 =u k +L(u k )e kk = 1, 2, ...

[0038] S5: Repeat steps S3-S4 until the expected target trajectory is tracked.

[0039] Furthermore, step S2, which transforms the nonlinear system into nonlinear equations, includes the following steps:

[0040] S2-1: Definition

[0041] u k =[u k (0)u k (1)…u k (N-1)] T

[0042] y k =[y k (1)y(2)…y k (N)] T

[0043] S2-2: Based on the dynamic system of the robotic arm device, the relationship between control input and position output can be expressed by functions g1, g2, ... g N describe:

[0044] y k (1)=h[x k (1)]=h[f(x k (0),u k (0))]=g1[x k (0),u k (0)]

[0045] y k (2)=h[x k (2)]=h[f(x k (1),u k (1))]=g2[x k (0),u k (0),u k (1)]

[0046]

[0047] y k (N)=h[x k (N)]=h[f(x k (N-1),u k (N-1))]

[0048] =g N [x k (0),u k (0),u k (1),…,uk (N-1)]

[0049] S2-3: The initial state is denoted as x k (0) = x0 is independent of the iteration index, and the nonlinear system is represented by the following function:

[0050] y k =g(u k ),g(·)=[g1(·),g2(·),…,g N (·)] T

[0051] Where g(·) depends on f(·), h(·) and x0;

[0052] S2-4: Solve the following nonlinear algebraic equation:

[0053] F(u k )=g(u k )-y d =0

[0054] u k In the k-th attempt to solve the nonlinear algebraic equation, it becomes an unknown variable, and the ideal control input sequence u is... d Is it satisfying F(u) d The exact solution for ) = 0.

[0055] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0056] This invention provides an iterative learning control system and method for a robotic arm device based on the quasi-Newton method. The system includes a target trajectory determination module to determine the expected target trajectory of the robotic arm device, a nonlinear equation determination module to determine the nonlinear equations related to the nonlinear system of the robotic arm, a pose acquisition module to acquire the position output of the robotic arm device in the current iteration, and a control module to update the control input of the robotic arm device for the next iteration based on the expected target trajectory, the control input in the current iteration, the position output in the current iteration, and the selected gain matrix, thereby controlling the robotic arm device. Through this method, this invention enables a robotic arm device with nonlinear dynamics to achieve high-precision tracking of a trackable target trajectory within a finite time period. Attached Figure Description

[0057] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the accompanying drawings used in the embodiments will be briefly introduced below. The features and advantages of the present invention can be more clearly understood by referring to the accompanying drawings. The accompanying drawings are schematic and should not be construed as limiting the present invention in any way. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0058] Figure 1 A schematic diagram of the structure of the iterative learning control system for a robotic arm device based on the quasi-Newton method provided in an embodiment of the present invention;

[0059] Figure 2 A flowchart of an iterative learning control method for a robotic arm device based on the quasi-Newton method, provided for an embodiment of the present invention.

[0060] Figure 3 This is the curve showing the change of tracking error with iteration index k in Embodiment 1 of the present invention.

[0061] 1-Target trajectory determination module, 2-Nonlinear equation determination module, 3-Pose acquisition module, 4-Control module, 41-Control quantity determination unit, 42-Position control unit. Detailed Implementation

[0062] To better understand the above-mentioned objectives, features, and advantages of the present invention, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be noted that, unless otherwise specified, the embodiments of the present invention and the features thereof can be combined with each other.

[0063] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein, and therefore the scope of protection of the invention is not limited to the specific embodiments disclosed below.

[0064] This invention provides an iterative learning control system for a robotic arm device based on the quasi-Newton method, such as... Figure 1 As shown, it includes: a target trajectory determination module 1, a nonlinear equation determination module 2, a pose acquisition module 3, and a control module 4; wherein,

[0065] The target trajectory determination module 1 is used to determine the expected target trajectory of the robotic arm device. Specifically, the expected target trajectory is the reference trajectory that the robotic arm ultimately expects to run, which is a preset value and is a target pre-input by the user according to the tracking requirements;

[0066] Nonlinear equation determination module 2 is used to determine the nonlinear equations associated with the nonlinear system of the robotic arm. Specifically, it is for a robotic arm device with the following nonlinear dynamics:

[0067]

[0068] Where t∈{0,1,2,…,N} is the running time, and N is the running period. x is the number of iterations; k (t), u k (t) and yk (t) represents the state, control input, and position output of the robotic arm at time t in the k-th iteration, f(·) represents the relationship between the state and the control input, and h(·) represents the relationship between the position output and the state. Meanwhile, the expected target trajectory of the robotic arm is y. d (t). Without loss of generality, the initial state of the robotic arm is x. k (0) = x0, definition

[0069] u k =[u k (0)u k (1)…u k (N-1)] T

[0070] y k =[y k (1)y(2)…y k (N)] T

[0071] Based on the dynamic system of the robotic arm, the relationship between input and output can be expressed by the following functions g1, g2, ... g N describe:

[0072] y k (1)=h[x k (1)]=h[f(x k (0),u k (0))]=g1[x k (0),u k (0)]

[0073] y k (2)=h[x k (2)]=h[f(x k (1),u k (1))]=g2[x k (0),u k (0),u k (1)]

[0074]

[0075] y k (N)=h[x k (N)]=h[f(x k (N-1),u k (N-1))]

[0076] =g N [x k (0),u k (0),u k(1),…,u k (N-1)]

[0077] The initial state is x k (0) = x0 is independent of the iteration index; therefore, the nonlinear robotic arm device can be represented by the following function:

[0078] y k =g(u k ),g(·)=[g1(·),g2(·),…,g N (·)] T

[0079] Here, g(·) depends on f(·), h(·), and x0, representing the relationship between the position output and the control input. The nonlinear iterative learning control problem is reformulated as a nonlinear algebraic equation. Therefore, the desired input u is sought. d Drive dynamic system to track desired output y d The iterative learning control task becomes finding a solution that satisfies the following nonlinear algebraic equation:

[0080] F(u k )=g(u k )-y d =0

[0081] Where F(·) represents a nonlinear function that depends on f(·), h(·), x0, and y. d The control input sequence u for the k-th iteration k In the k-th attempt to solve the nonlinear equation, it becomes an unknown variable, and the ideal control input sequence u d Is it satisfying F(u) d The exact solution for ) = 0.

[0082] The pose acquisition module 3 is used to acquire the position output of the robotic arm in the current iteration. Specifically, the current position of the robotic arm can be acquired by installing a sensor device on the robotic arm.

[0083] Control module 4 is used to control the robotic arm device by updating the control input of the robotic arm device for the next iteration based on the expected target trajectory, the control input of the current iteration, the position output of the current iteration, and the selected gain matrix. In a specific implementation, in the high-precision tracking iterative learning control system provided in this embodiment of the invention, control module 4 may specifically include: a control quantity determination unit 41 and a position control unit 42; wherein, the control quantity determination unit 41 is used to control the robotic arm device to execute the next iteration process based on the expected target trajectory, the control input, the position output of the current iteration, and the selected gain matrix, and determines the control input of the robotic arm device for the next iteration using the following formula:

[0084] uk+1 =u k +L(u k )e k

[0085] Where L(·) represents the learning gain, and the learning gain L(u) is selected based on the quasi-Newton method. k ) = g ′ (u k ) -1 g(·) represents the relationship between position output and control input, which can be obtained through the dynamic characteristics of the robotic arm device. ′ The derivative of the function g is represented. Let be the augmented vector of the control input in k iterations, and T denote the transpose of the vector. y is the augmented vector controlling the input in the (k+1)th iteration; d (t) represents the expected target trajectory of the robotic arm device, e k =y d -y k , This is the augmented vector of the expected target trajectory. Let be the augmented vector of the position output after k iterations; the position control unit 42 is used to determine the position output of the robotic arm device in the next iteration according to the control input and initial input vector of the robotic arm device in the next iteration by the following formula:

[0086] y k+1 =g(u k+1 )

[0087] in, Let T be the augmented vector of the position output after k+1 iterations, where T represents the transpose of the vector, and g(·) represents the relationship between the position output and the control input, which can be obtained through the dynamic characteristics of the robotic arm device.

[0088] In other words, the robotic arm obtains the control input for the next iteration based on the control input and position output of the current iteration, updates and adjusts its own position output, and ultimately achieves tracking of the expected target trajectory, i.e., lim k→∞ y k (t)=y d (t).

[0089] The iterative learning control system for a robotic arm device provided in this embodiment of the invention comprises a target trajectory determination module that determines the expected target trajectory of the robotic arm device, a nonlinear equation determination module that determines the nonlinear equations related to the nonlinear system of the robotic arm, a pose acquisition module that acquires the position output of the robotic arm in the current iteration, and a control module that updates the control input of the robotic arm device for the next iteration based on the expected target trajectory, the control input in the current iteration, the position output in the current iteration, and the selected gain matrix, thereby controlling the robotic arm device. This ensures that the robotic arm device with nonlinear dynamics can achieve high-precision tracking of the trackable expected target trajectory at any given time.

[0090] Based on the same inventive concept, embodiments of the present invention also provide an iterative learning control method for a robotic arm device based on a quasi-Newtonian method, such as... Figure 2 As shown, it includes the following steps:

[0091] S1: Determine the expected target trajectory of the robotic arm device. Specifically, the expected target trajectory is the reference trajectory that the robotic arm ultimately expects to run. It is a preset value, which is a target input by the user according to the tracking requirements.

[0092] S2: Obtain the nonlinear system model information of the robotic arm device and transform the nonlinear system into nonlinear equations. Specifically, for a robotic arm device with the following nonlinear dynamics:

[0093]

[0094] Where t∈{0,1,2,…,N} is the running time, and N is the running period. x is the number of iterations; k (t), u k (t) and y k (t) represents the state, control input, and position output of the robotic arm at time t in the k-th iteration, f(·) represents the relationship between the state and the control input, and h(·) represents the relationship between the position output and the state. Meanwhile, the expected target trajectory of the robotic arm is y. d (t). Without loss of generality, the initial state of the robotic arm is x. k (0) = x0, definition

[0095] u k =[u k (0)u k (1)…u k (N-1)] T

[0096] y k =[y k (1)y(2)…y k (N)]T

[0097] Based on the dynamic system of the robotic arm, the relationship between input and output can be expressed by the following functions g1, g2, ... g N describe:

[0098] y k (1)=h[x k (1)]=h[f(x k (0),u k (0))]=g1[x k (0),u k (0)]

[0099] y k (2)=h[x k (2)]=h[f(x k (1),u k (1))]=g2[x k (0),u k (0),u k (1)]

[0100]

[0101] y k (N)=h[x k (N)]=h[f(x k (N-1),u k (N-1))]

[0102] =g N [x k (0),u k (0),u k (1),…,u k (N-1)]

[0103] The initial state is x k (0) = x0 is independent of the iteration index; therefore, the nonlinear robotic arm device can be represented by the following function:

[0104] y k =g(u k ),g(·)=[g1(·),g2(·),…,g N (·)] T

[0105] Here, g(·) depends on f(·), h(·), and x0, representing the relationship between the position output and the control input. The nonlinear iterative learning control problem is reformulated as a nonlinear algebraic equation. Therefore, the desired input u is sought. d Drive dynamic system to track desired output y dThe iterative learning control task becomes finding a solution that satisfies the following nonlinear algebraic equation:

[0106] F(u k )=g(u k )-y d =0

[0107] Where F(·) represents a nonlinear function that depends on f(·), h(·), x0, and y. d The control input sequence u for the k-th iteration k In the k-th attempt to solve the nonlinear equation, it becomes an unknown variable, and the ideal control input sequence u d Is it satisfying F(u) d The exact solution for ) = 0.

[0108] S3: Obtain the position output of the robotic arm device in the current iteration;

[0109] S4: Based on the expected target trajectory of the robotic arm, the control input and position output of the current iteration, and the selected gain matrix, update the control input of the robotic arm for the next iteration, and control the robotic arm to execute the next iteration process. The learning gain L(u) is selected based on the quasi-Newton method. k ) = F ′ (u k ) -1 =g ′ (u k ) -1 , where F ′ Let F(u) denote the derivative of the function F. k )=g(u k )-y d ,e k =-F(u k ), where g(·) represents the relationship between position output and control input, which can be obtained through the dynamic characteristics of the robotic arm device. The algorithm for iterative learning of the control scheme is then:

[0110] u k+1 =u k +L(u k )e k k = 1, 2, ...

[0111] S5: Perform multiple iterations until the target trajectory is tracked.

[0112] Example 1

[0113] The following is a simulation case of an iterative learning control system and method for a robotic arm device based on the quasi-Newton method provided by this invention. Consider a robotic arm device with the following nonlinear dynamics:

[0114]

[0115] in, Indicates the angular position of the robotic arm. Indicates joint torque. The disturbance torque is represented by 0, m0 and l represent the mass and length of the manipulator, respectively, M0 represents the mass of the tip load, J represents the moment of inertia of the joint, and g represents the acceleration due to gravity. The parameters are set as follows: m0 = 2 kg, M0 = 4 kg, l = 0.5 m, g = 9.8 m / sec. 2 .

[0116] The following model is obtained through discretization:

[0117]

[0118] Among them, x1(t)=θ(t), x2(t)=θ(t+1), u(t)=τ(t), y(t)=θ(t), T s The sampling period is 0.01 seconds, t∈[0,1,…100], and the initial values ​​are x1(0)=0, x2(0)=0.

[0119] Tracking trajectory is defined as

[0120]

[0121] Where, θ b =0, τ0=tT s / (t f -t0), t0=0,t f =1.

[0122] The termination rule of the iterative algorithm is

[0123] An iterative learning control algorithm based on the quasi-Newton method is adopted. Figure 3 The figure shows the change in tracking error with the iteration index k, illustrating that the position output of the robotic arm device can achieve tracking of the expected target trajectory.

[0124] In this invention, unless otherwise explicitly specified and limited, the terms "installation," "connection," "linking," and "fixing," etc., should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral part; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; they can refer to the internal communication of two components or the interaction between two components. Those skilled in the art can understand the specific meaning of the above terms in this invention according to the specific circumstances.

[0125] In this invention, unless otherwise explicitly specified and limited, "above" or "below" the second feature can include direct contact between the first and second features, or contact between the first and second features through another feature between them. Furthermore, "above," "over," and "on top" of the second feature includes the first feature directly above or diagonally above the second feature, or simply indicates that the first feature is at a higher horizontal level than the second feature. "Below," "below," and "under" the second feature includes the first feature directly below or diagonally below the second feature, or simply indicates that the first feature is at a lower horizontal level than the second feature.

[0126] In this invention, the terms "first," "second," "third," and "fourth" are used for descriptive purposes only and should not be construed as indicating or implying relative importance. The term "multiple" refers to two or more unless otherwise expressly defined.

[0127] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A robot device iterative learning control system based on a quasi-Newton method, characterized by, The target trajectory determination module, the nonlinear equation determination module, the pose acquisition module, and the control module are included. The target trajectory determination module is configured to set an expected target trajectory of the robotic arm device. The nonlinear equation determination module is configured to determine a nonlinear equation related to the robotic arm device. The pose acquisition module is configured to acquire a position output of the robotic arm device at a current iteration. The control module is configured to control the robotic arm device in real time according to the expected target trajectory, a control input at the current iteration, the position output at the current iteration, and a selected gain matrix. The robotic arm device has the following dynamic characteristics: wherein x k (t), u k (t) and y k (t) represent the state, control input and position output of the robot arm device at time t in the kth iteration, respectively, t e {0, 1, 2, …, N} is the running time, N is the running period, is the iteration number, f(·) represents the relationship between the state and the control input, and h(·) represents the relationship between the position output and the state. The nonlinear equation is obtained in the following manner: According to the dynamic system of the robot arm, the relationship between the input and the output is given by the functions g1, g2,... g N Description: Initial state is x k (0) = x0 is independent of the iteration index, so the nonlinear manipulator device is represented by the function: y k = g(u k ), g(·) = [g1(·), g2(·),..., g N (·)] T where g(·) depends on f(·), h(·) and x0, representing the relationship between the position output and the control input, the nonlinear iterative learning control problem is reformulated as a nonlinear algebraic equation, and thus, finding the desired input u d drives the dynamic system to track the desired output y d the iterative learning control task becomes finding a solution to the following nonlinear algebraic equation: F(u k ) = g(u k ) - y d = 0 where F(·) represents a nonlinear function that depends on f(·), h(·), x0, and y d the control input sequence uk k becomes an unknown variable in the kth attempt to solve the nonlinear equation, the ideal control input sequence uk d is the exact solution that satisfies F(uk d ) = 0.

2. The mechanical arm device iterative learning control system according to claim 1, wherein, The control module includes a control quantity determination unit and a position control unit; wherein, The control quantity determination unit is configured to determine a control input of the robotic arm device according to the expected target trajectory, the control input at the current iteration, the position output at the current iteration, and the selected gain matrix, and to control the robotic arm device to perform a next iteration process, by the following formula: u k+1 = u k + L(u k )e k where L(·) denotes the learning gain, which is selected based on a quasi-Newton method k ) = g ′ (u k ) -1 , g(·) denotes the relationship between the position output and the control input, which is obtained through the dynamic characteristics of the robot arm device, g ′ denotes the derivative of the function g; is the augmented vector of the control input at the kth iteration, T denotes the transpose of the vector, is the augmented vector of the control input at the k+1th iteration; y d (t) is the expected target trajectory of the robot arm device, e k = y d -y k , is the augmented vector of the expected target trajectory, is the augmented vector of the position output at the kth iteration, The position control unit is configured to determine a position output of the robotic arm device at the next iteration according to the control input of the robotic arm device at the next iteration and an initial input vector, by the following formula: y k+1 = g(u k+1 ) wherein is the position output augmented vector for the k+1 iteration, T denotes the transpose of a vector, g(·) denotes the relationship of the position output and the control input, which is obtained by the dynamic characteristics of the robot arm device.

3. A control method for an iterative learning control system using the robot device of claim 1 or 2, characterized by, The method includes the following steps: S1: setting an expected target trajectory of the robotic arm device; S2: acquiring nonlinear system model information of the robotic arm device, and converting the nonlinear system into a nonlinear equation; S3: acquiring a position output of the robotic arm device at a current iteration; S4: updating the control input of the robot device for the next iteration based on the expected target trajectory of the robot device, the control input for the current iteration, the position output for the current iteration, and the selected gain matrix k ) = F ′ (u k ) -1 = g ′ (u k ) -1 , wherein F ′ denotes the derivative of the function F, F(u k ) = g(u k ) - y d , e k = -F(u k ), g(·) denotes the relationship between the position output and the control input, which is obtained by the dynamic characteristics of the robot device, and the algorithm of the iterative learning control format is: u k+1 = u k + L(u k )e k , k = 1, 2,... S5: repeating steps S3-S4 until tracking of the expected target trajectory is completed.

4. The control method according to claim 3, characterized by, The step S2 of converting the nonlinear system into a nonlinear equation includes the following steps: S2-1: defining u k = [u k (0)u k (1)…u k (N-1)] T y k = [y k (1) y(2)... y k (N)] T S2-2: According to the dynamic system of the robot arm device, the relationship between the control input and the position output is given by functions g1, g2,... g N Description: S2-3: Initial state is x k (0) = x0, and the nonlinear system is represented by a function: y k = g(u k ), g(·) = [g1(·), g2(·),..., g N (·)] T wherein g(·) depends on f(·), h(·), and x0; S2-4: solving the solution of the following nonlinear algebraic equation: F(u k ) = g(u k ) - y d = 0 u k In the kth attempt to solve the nonlinear algebraic equation becomes an unknown variable, the ideal control input sequence u d is the exact solution that satisfies F(u d ) = 0.

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