Mechanical arm iterative learning control method based on high-order all-drive system design

Abstract

The invention discloses a mechanical arm iterative learning control method based on high-order all-drive system design, and belongs to the field of intelligent control. Aiming at angular velocity control of a mechanical arm system, the invention provides the following control scheme: establishing a single-connecting-rod mechanical arm system driven by a direct-current motor; discretizing a continuous-time mechanical arm system into a discrete-time system; representing a discrete time system as a high-order all-drive system with unknown parameters; and designing a high-order all-drive iterative learning control method. According to the mechanical arm iterative learning control method based on the high-order all-wheel-drive system design, more information in previous operation is utilized, the high-order all-wheel-drive system method is combined, high-precision trajectory tracking of the angular speed of a mechanical arm system can be achieved in a finite time interval, and the mechanical arm iterative learning control method has the advantages of being high in practicability and high in practicability. And meanwhile, model information of a known mechanical arm system is not needed, the modeling difficulty is avoided, and practical application is better facilitated.

Description

Technical Field

[0001] The present invention belongs to the field of intelligent control, and more specifically, relates to an iterative learning control method for a robotic arm based on a high-order full-drive system design. Background Art

[0002] In recent years, with the rapid development of materials science, electronic technology and mechanical engineering, robotic arms have been increasingly used in industrial automation, agricultural harvesting, medical rehabilitation and other fields. As the application scenarios of robotic arms continue to become more refined and complex, the requirements for robotic arm control accuracy are also constantly increasing. However, faced with many complex factors such as the nonlinear dynamic characteristics of the robotic arm system, the uncertainty of dynamic parameters and possible external interference, successfully achieving high-precision trajectory tracking control of the robotic arm has become a challenging task.

[0003] As is well known, modern control theory relies on the state space representation of dynamic systems, which shows great advantages in dealing with both linear and nonlinear systems. However, most first-order nonlinear differential equation models are derived from the augmentation of higher-order physical models, and these mathematical transformations can cause the first-order system states to couple with each other. Therefore, the controllability analysis of the transformed first-order nonlinear system becomes more complicated. In addition, due to the increase in the system dimension, the full drive characteristics of the original physical system may be destroyed, which seriously complicates the design and analysis of the controller. In order to overcome these difficulties, Academician Duan Guangren proposed the theory of high-order full drive system (HOFAS), which aims to establish a control algorithm based on the original full drive system. The core idea of ​​the HOFAS theory is to use the full drive characteristics to eliminate all nonlinear dynamics. Therefore, the desired constant linear closed-loop system can be obtained, and then the theory and technology of linear system analysis and design can be applied. It has been proven to be a control-oriented framework that opens up a new direction for dealing with more general nonlinear systems.

[0004] HOFAS theory has a wide range of applications, because all-wheel drive systems are widely used in practice. In recent years, Academician Duan Guangren has made great contributions to the improvement of HOFAS theory. However, it is worth noting that the early HOFAS theory mainly focuses on the asymptotic stability or asymptotic tracking of the relevant HOFAS in infinite time, while in fact many control tasks are completed in a finite time interval, and the asymptotic convergence performance along the time direction cannot guarantee the complete tracking of the system in a finite time interval.

[0005] In fact, the control tasks of the robot arm in a limited time interval are often repetitive. For example, when the robot arm system on the automobile production line performs tasks such as handling, assembly, spraying, and welding, the robot arm performs the same task for each car on the production line and repeats the same installation action. In this case, a large amount of system information is contained in the previous operation data. If the control system can draw on previous control experience, it will help improve system performance. As a typical learning control method, iterative learning control (ILC) is an effective control strategy for dealing with repeatable systems. It can improve the current control performance of uncertain systems by making full use of past control experience. Therefore, it is of great significance to study the iterative learning control theory based on the HOFAS model. Summary of the invention

[0006] The present invention discloses an iterative learning control method for a robotic arm based on a high-order all-wheel drive system design. The technical problem to be solved is to utilize the design concept of the high-order all-wheel drive system to design an iterative learning control method for the robotic arm system without the need for a known accurate system model, so as to achieve complete tracking control of the robotic arm angular velocity to the desired angular velocity.

[0007] The purpose of the present invention is achieved through the following technical solutions:

[0008] The present invention discloses an iterative learning control method for a robotic arm based on a high-order all-wheel drive system design, which mainly aims at the difficulty in establishing an accurate model of the robotic arm, and designs an iterative learning control method based on a high-order all-wheel drive system design to achieve the purpose of high-precision tracking control of the robotic arm system.

[0009] The present invention discloses a method for iterative learning control of a robotic arm based on a high-order all-wheel drive system design, the method comprising the following steps:

[0010] Step 1: Establish a single-link robotic arm system driven by a DC motor;

[0011] Step 2: discretize the continuous-time robotic arm system into a discrete-time system;

[0012] Step 3, represent the discrete-time system as a high-order all-wheel drive system with unknown parameters;

[0013] Step 4: Design an iterative learning control method for high-order all-wheel drive.

[0014] Furthermore, the single-link robot arm system driven by a DC motor described in step 1 is:

[0015]

[0016] Where t represents continuous time;

[0017] ωk (t) Represents angular displacement (rad), angular velocity (rad / s) and angular acceleration (rad / s 2 ),u k (t) is the driving torque, which is the input of the system;

[0018] J is the moment of inertia of the joint (N·m), defined as J=Mι 2 +(1 / 3)mι 2 κ k (t) = (m + 2M) g ι (ω k (t)-sin(ω k (t))) / 2J is the model mismatch error;

[0019] f is the damping coefficient, M is the weight at the arm end, g is the acceleration of gravity, m is the mass, and ι is the length.

[0020] Furthermore, the step 2 of discretizing the continuous-time robot system into a discrete-time system mainly includes the following steps:

[0021] make So Using the forward difference operator Where h represents the sampling period, s represents the discrete time, and the continuous time system is transformed into the following discrete time system:

[0022]

[0023] in,

[0024] x k (s) represents the angular velocity at the sth moment of the kth iteration;

[0025] y k (s+1) represents the output of the system at the sth moment of the kth iteration, i.e., the angular velocity;

[0026] κ k (s)=(m+2M)gι(ω k (s)-sin(ω k (s))) / 2J;

[0027] ω k (s) represents the angular displacement at the sth moment of the kth iteration.

[0028] Furthermore, the step 3 of expressing the discrete-time system as a high-order all-wheel drive system with unknown parameters mainly includes the following steps:

[0029] make Then the discrete-time system is represented as a high-order all-wheel drive system with unknown parameters:

[0030]

[0031] Among them, p(x k (s),ω k (s)) and φ k (s)It is difficult to obtain its true value in practice.

[0032] Furthermore, the iterative learning control method for designing a high-order all-wheel drive described in step 4 mainly includes the following steps:

[0033] Step 4.1: Design the iterative learning control law of the high-order all-wheel drive as:

[0034]

[0035] in, Represents φ k The estimated value of (s), is a constant, A i , i=0,1,…,τ-1, is any given τ constant, v k (s) is called the learning control input;

[0036] Step 4.2: The update law for design parameter estimation is:

[0037]

[0038] in, 0<η≤2;

[0039] Step 4.3: Design the update law for learning control input as:

[0040] v k (s) = v k-1 (s)+L v (s)e k-1 (s+1),

[0041] Among them, L v (s) indicates learning gain;

[0042] Step 4.4: The iterative learning control method for high-order all-wheel drive is

[0043]

[0044] Wherein, formula (4) represents the reset algorithm, represents the parameter estimate for the initial iteration, and ε is a small positive constant.

[0045] Beneficial effects:

[0046] 1. The present invention discloses an iterative learning control method for a robotic arm based on a high-order all-wheel drive system design. It utilizes more information from previous operations and combines the high-order all-wheel drive system method to design an iterative learning control method based on a high-order all-wheel drive system design. It can obtain complete tracking of the angular velocity of the robotic arm system in a limited time interval and achieve high-precision trajectory tracking control.

[0047] 2. The invention discloses an iterative learning control method for a robotic arm based on a high-order all-wheel drive system design. Compared with the traditional high-order all-wheel drive system method, it does not require the model information of the known robotic arm system, thus bypassing the modeling difficulties and being more conducive to practical applications.

[0048] After reading the specific embodiments of the present invention in conjunction with the accompanying drawings, other features and advantages of the present invention will become more clear. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 This is a flow chart of the iterative learning control method for a robotic arm based on a high-order all-wheel drive system design proposed by the present invention;

[0050] Figure 2 This is a diagram showing the angular velocity tracking effect of the iterative learning control method for a robotic arm based on a high-order all-wheel drive system design proposed by the present invention;

[0051] Figure 3 Iterative convergence diagram of tracking error of the iterative learning control method for the manipulator based on the high-order all-wheel drive system design proposed by the present invention; DETAILED DESCRIPTION

[0052] In order to better illustrate the purpose and advantages of the present invention, the invention is further described in detail below in conjunction with embodiments and corresponding drawings.

[0053] See also Figure 1 As shown, the present embodiment discloses a method for iterative learning control of a robotic arm based on a high-order all-wheel drive system design, comprising the following steps:

[0054] Step 1: Build a single-link robotic arm system driven by a DC motor:

[0055]

[0056] Where t represents continuous time;

[0057] ω k (t) Represents angular displacement (rad), angular velocity (rad / s) and angular acceleration (rad / s 2 ),u k (t) is the driving torque, which is the input of the system;

[0058] J is the moment of inertia of the joint (N·m), defined as J=Mι 2 +(1 / 3)mι 2 κ k (t) = (m + 2M) g ι (ω k (t)-sin(ω k (t))) / 2J is the model mismatch error;

[0059] f is the damping coefficient, M is the weight at the arm end, g is the acceleration of gravity, m is the mass, and ι is the length.

[0060] Step 2: Discretize the continuous-time robotic arm system into a discrete-time system.

[0061] make So Using the forward difference operator Where h represents the sampling period, s represents the discrete time, and the continuous time system is transformed into the following discrete time system:

[0062]

[0063] in,

[0064] x k (s) represents the angular velocity at the sth moment of the kth iteration;

[0065] y k (s+1) represents the output of the system at the sth moment of the kth iteration, i.e., the angular velocity;

[0066] κ k (s)=(m+2M)gι(ω k (s)-sin(ω k (s))) / 2J;

[0067] ω k (s) represents the angular displacement at the sth moment of the kth iteration.

[0068] Step 3: Represent the discrete-time system as a high-order all-wheel drive system with unknown parameters.

[0069] make Then the discrete-time system is represented as a high-order all-wheel drive system with unknown parameters:

[0070]

[0071] Among them, p(x k (s),ω k (s)) and φ k (s)It is difficult to obtain its true value in practice.

[0072] Step 4: Design an iterative learning control method for high-order all-wheel drive.

[0073] Specifically:

[0074] Step 4.1: Design the iterative learning control law of the high-order all-wheel drive as:

[0075]

[0076] in, Represents φ k The estimated value of (s), is a constant, A i , i=0,1,…,τ-1, is any given τ constant, v k (s) is called the learning control input;

[0077] Step 4.2: The update law for design parameter estimation is:

[0078]

[0079] in, 0<η≤2;

[0080] Step 4.3: Design the update law for learning control input as:

[0081] v k (s) = v k-1 (s)+L v (s)e k-1 (s+1),

[0082] Among them, L v (s) indicates learning gain;

[0083] Step 4.4: The iterative learning control method for high-order all-wheel drive is

[0084]

[0085] Wherein, formula (1d) represents the reset algorithm, represents the parameter estimate for the initial iteration, and ε is a small positive constant.

[0086] The parameter values ​​of the robot arm used in the embodiment are given in Table 1.

[0087] Table 1 Setting of robot arm parameter values

[0088] Damping coefficient f Arm end lifting weight M Gravity acceleration g Mass m Length <![CDATA[3kg·m 2 / s]]> 2kg <![CDATA[9.8m / s 2 ]]> 1kg 0.5m

[0089] The desired angular velocity is r(t)=(t 3 -8t 2+16t)rad / s, where t represents continuous time and the sampling time is 0.01s. The simulation time is 4s. In the simulation, set ω k (0) = 0 rad, x k (0)=0rad / s,u0(s)=0N·m,L v (s) = 0.02, The other parameters are η=0.02, μ=1, τ=2, A0=0.08, A1=0.5. The iterative learning control method for a robotic arm based on a high-order full-drive system design disclosed in the present invention is applied. Figure 2 This is the angular velocity tracking effect diagram. Figure 3 is the iterative convergence diagram of the tracking error. Figure 2 and Figure 3 It can be seen that the method disclosed in the present invention can obtain effective control effect, and the angular velocity of the system can track the desired angular velocity with high precision.

[0090] The specific description above further illustrates the purpose, technical solutions and beneficial effects of the invention in detail. It should be understood that the embodiments are only used to explain the invention and are not used to limit the scope of protection of the invention. Any modifications, equivalent replacements, improvements, etc. under the same principles and concepts as the invention should be included in the scope of protection of the invention.

Claims

1. A robotic arm iterative learning control method based on a high-order all-wheel drive system design, characterized in that: The method comprises the following steps: Step 1: Establish a single-link robotic arm system driven by a DC motor; Step 2: discretize the continuous-time robotic arm system into a discrete-time system; Step 3, represent the discrete-time system as a high-order all-wheel drive system with unknown parameters; Step 4: Design an iterative learning control method for high-order all-wheel drive.

2. The method according to claim 1, characterized in that: The single-link robotic arm system driven by a DC motor as described in step 1 is: Where t represents continuous time; ω k (t) Represents angular displacement (rad), angular velocity (rad / s) and angular acceleration (rad / s 2 ),u k (t) is the driving torque, which is the input of the system; J is the moment of inertia of the joint (N·m), defined as J=Mι 2 +(1 / 3)mι 2 κ k (t) = (m + 2M) g ι (ω k (t)-sin(ω k (t))) / 2J is the model mismatch error; f is the damping coefficient, M is the weight at the arm end, g is the acceleration of gravity, m is the mass, and ι is the length.

3. The method according to claim 1, characterized in that: Discretizing the continuous-time robotic arm system into a discrete-time system as described in step 2 mainly includes the following steps: make So Using the forward difference operator Where h represents the sampling period, s represents the discrete time, and the continuous time system is transformed into the following discrete time system: in, x k (s) represents the angular velocity at the sth moment of the kth iteration; y k (s+1) represents the output of the system at the sth moment of the kth iteration, i.e., the angular velocity; k k (s)=(m+2M)gι(ω k (s)-sin(ω k (s))) / 2J; ω k (s) represents the angular displacement at the sth moment of the kth iteration.

4. The method according to claim 1, characterized in that: The step 3 of representing the discrete-time system as a high-order all-wheel drive system with unknown parameters mainly includes the following steps: make Then the discrete-time system is represented as a high-order all-wheel drive system with unknown parameters: Among them, p(x k (s),ω k (s)) and φ k (s)It is difficult to obtain its true value in practice.

5. The method according to claim 1, characterized in that: The iterative learning control method for designing a high-order all-wheel drive described in step 4 mainly includes the following steps: Step 4.1: Design the iterative learning control law of the high-order all-wheel drive as: in, Represents φ k The estimated value of (s), is a constant, A i , i=0,1,…,τ-1, is any given τ constant, v k (s) is called the learning control input; Step 4.2: The update law for design parameter estimation is: in, Step 4.3: Design the update law for learning control input as: v k (s)=v k-1 (s)+L v (s)e k-1 (s+1), Among them, L v (s) indicates learning gain; Step 4.4: The iterative learning control method for high-order all-wheel drive is Among them, formula (4) represents the reset algorithm, represents the parameter estimate for the initial iteration, and ε is a small positive constant.

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