Iterative learning control method, device and medium for single-link robot arm system

Abstract

The embodiment of the specification provides a kind of single connecting rod mechanical arm system iterative learning control method, device and medium, wherein, method includes: single connecting rod mechanical arm system is modeled, and discrete sampling period is set;Desired output trajectory of mechanical arm is discretely sampled, and desired output sequence is obtained;Actual control input signal is discretely processed to actual control input signal, and then actual output trajectory of mechanical arm is obtained, and actual output sequence is obtained according to discrete sampling period;Error sequence is obtained according to actual output sequence and desired output sequence, and error value is calculated, whether error value meets preset convergence condition is judged, if not, iterative learning control gain is calculated, and control input signal of next iteration is updated according to error sequence, iterative learning control gain and iterative learning control law, until error value meets preset convergence condition, stop iteration.

Description

TECHNICAL FIELD

[0001] The present document relates to the technical field of mechanical arm control, and particularly relates to an iterative learning control method of a single-link mechanical arm system, equipment and a medium. BACKGROUND

[0002] With the rapid development of intelligent manufacturing, artificial intelligence and other new technologies, the control system in the industrial internet has become a research hotspot in recent years. The mechanical arm is an automated mechanical device that is most widely used in the field of robot technology, and has a wide range of applications in industrial manufacturing, medical treatment and space exploration. The common working mode of the mechanical arm is to continuously repeat the operation in the same operating interval, such as carrying, cutting, etc. In the real production process, some unexpected events inevitably occur, such as product falling, equipment failure, etc. In order to ensure the safety of personnel and equipment, production should be stopped immediately at this time, which leads to the random change of the operating interval of the intelligent production system.

[0003] With the increasing diversity and complexity of industrial production processes, dynamic systems with strong coupling, strong nonlinearity and uncertainty are increasing. It is more and more difficult to obtain an accurate mathematical model, and due to the existence of system uncertainty and external disturbance, the original mathematical model is easily invalidated, so that the traditional control method based on the model cannot complete the high-speed and accurate tracking task. Compared with the traditional control method, the iterative learning control has many advantages, such as: the prior knowledge requirement of the controlled system is relatively low, it can iteratively determine the control input, so as to track the given reference signal in a fixed time interval. However, the iterative learning control still has many problems. For example: most of the proposed iterative learning control methods require that the learning trajectory must be strictly the same in the iteration domain. If the control target or task specification changes, no matter how small the change is, the controlled system must relearn. In actual projects, due to the change of the control target or task specification, the reference trajectory changes, and when the reference trajectory is no longer a constant set in the iteration domain, the traditional iterative learning control technology will not work. Therefore, a variable desired trajectory iterative learning control method for the random change of the operating interval of the mechanical arm is needed, which can effectively overcome the control problem of the mechanical arm when the reference trajectory changes and the operating interval changes randomly. SUMMARY

[0004] One or more embodiments of the present specification provide an iterative learning control method of a single-link mechanical arm system, comprising:

[0005] S1. Model the single-link mechanical arm system as a linear discrete system, and set the discrete sampling period of the linear discrete system;

[0006] S2. Discretely sampling the acquired desired output trajectory of the robot arm according to the discrete sampling period to obtain a desired output sequence;

[0007] S3. Discretely sampling the acquired initial control input signal of the robot arm according to the discrete sampling period to obtain an actual control input signal;

[0008] S4. Obtaining an actual output trajectory of the robot arm according to the actual control input signal of the robot arm, and discretely sampling the actual output trajectory according to the discrete sampling period to obtain an actual output sequence;

[0009] S5. Obtaining an error sequence according to the actual output sequence and the desired output sequence, calculating an error value according to the error sequence, and judging whether the error value meets a preset convergence condition, if yes, stopping iteration; if not, continuing to perform S6;

[0010] S6. Calculating an iterative learning control gain according to the convergence condition, updating the control input signal in the next iteration according to the error sequence, the iterative learning control gain and an iterative learning control law, and repeating S4-S6 until the error value meets the preset convergence condition, and stopping iteration.

[0011] One or more embodiments of the present specification provide an electronic device, comprising:

[0012] a processor; and a memory arranged to store computer-executable instructions that, when executed, cause the processor to implement the steps of the iterative learning control method of the single-link robot arm described above.

[0013] One or more embodiments of the present specification provide a storage medium for storing computer-executable instructions that, when executed, implement the steps of the iterative learning control method of the single-link robot arm described above.

[0014] The beneficial effects of the present application are as follows:

[0015] The present application can effectively overcome the control problem of the robot arm when the reference trajectory iteratively changes and the running interval randomly changes by controlling the single-link robot arm through the iterative learning control method. The present application can be applied to a system that completes other trajectory tracking tasks when the desired trajectory iteratively changes, can improve the working efficiency of the system, reduce the running time of the system, and thus reduce the consumption of energy and the cost of production.

[0016] The above description is only a summary of the technical solutions of the present application. In order to enable one skilled in the art to better understand the technical means of the present application and to implement the same according to the contents of the description, and in order to enable the above and other purposes, characteristics and advantages of the present application to be more apparent and easy to understand, the specific embodiments of the present application are described below. BRIEF DESCRIPTION OF DRAWINGS

[0017] In order to more clearly illustrate the technical solutions in the one or more embodiments of the present application or the prior art, the drawings needed in the embodiment or prior art description will be briefly introduced below. Obviously, the drawings in the following description are only some embodiments described in the present application, and those skilled in the art can obtain other drawings according to these drawings without any creative labor.

[0018] Figure 1 A flow chart of an iterative learning control method of a single-link robot arm system provided by one or more embodiments of the present application;

[0019] Figure 2 A specific flow chart of an iterative learning control method of a single-link robot arm system provided by one or more embodiments of the present application;

[0020] Figure 3 A tracking error index of one or more embodiments of the present application under a single-link robot arm model;

[0021] Figure 4 The expected trajectory of one or more embodiments of the present application under a single-link robot arm model when the iteration number is 1, 44, 80 times;

[0022] Figure 5 A graph of the actual output trajectory tracking the expected trajectory when the iteration number is 10, 40 times under a single-link robot arm model of one or more embodiments of the present application;

[0023] Figure 6 A random value graph of the running interval of the actual output trajectory under a single-link robot arm model of one or more embodiments of the present application;

[0024] Figure 7 A structural schematic diagram of an electronic device provided by one or more embodiments of the present application. DETAILED DESCRIPTION

[0025] In order to make the person in the art better understand the technical solutions in one or more embodiments of the present specification, the technical solutions in one or more embodiments of the present specification will be clearly and completely described in the following with reference to the drawings in one or more embodiments of the present specification. Obviously, the described embodiments are only a part of the embodiments of the present specification, rather than all the embodiments. Based on one or more embodiments of the present specification, all other embodiments obtained by those skilled in the art without creative labor should belong to the protection scope of the present document.

[0026] Method embodiment

[0027] According to the embodiment of the present application, an iterative learning control method of a single-link robot arm system is provided, Figure 1 is the flow chart of the iterative learning control method of the single-link robot arm system of the embodiment of the present application, as Figure 1 shown, the iterative learning control method of the single-link robot arm system according to the embodiment of the present application specifically comprises:

[0028] S1. Model the single-link robot arm system as a linear discrete system, and set the discrete sampling period of the linear discrete system.

[0029] The model of the single-link robot arm system is represented as:

[0030]

[0031] ξ i = (m + 2M)gl [θ i -sin (θ i )] / 2J;

[0032] J = Ml 2 +(1 / 3)ml 2 ;

[0033] wherein, represents the acceleration of the robot arm, represents the speed of the robot arm, θ i represents the angular displacement of the robot arm, ξ i represents the model mismatch error due to linear approximation, J represents the moment of inertia of the joint, u i represents the control input, m represents the mass of the robot arm, M represents the tip load of the robot arm, l represents the length of the robot arm, f represents the damping coefficient, and g represents the gravitational acceleration.

[0034] Model the above single-link robot arm system as a nonlinear continuous linear discrete system composed of a state equation and an output equation, which can be represented by the following formula:

[0035]

[0036] wherein:

[0037] wherein, l represents the number of iterations.

[0038] S2. Discretely sampling the acquired desired output trajectory of the robot arm according to the discrete sampling period to obtain a desired output sequence.

[0039] Setting the sampling period T of the nonlinear continuous single-link robot arm system, the discrete sequence after sampling is The corresponding discrete time sequence is

[0040] Acquiring the iteratively changing desired trajectory y d,l (t) of the single-link robot arm, discretely sampling the iteratively changing desired trajectory y d,l (t) according to the sampling period T to obtain an iteratively changing desired trajectory sequence y Defining the sequence as y d,l (k);

[0041] The running interval of the desired output trajectory y d,l (t) of the robot arm is [0, N The running interval of the actual output trajectory y i,l (t) is [0, N l ]; N l Changes randomly at each iteration, and

[0042] S3. Discretizing the acquired initial control input signal of the robot arm according to the discrete sampling period to obtain an actual control input signal.

[0043] Acquiring the initial control input signal u i,l (t) of the robot arm, defining the sequence as Applying the initial control input signal to the controlled system.

[0044] S4. Obtaining the actual output trajectory of the robot arm according to the actual control input signal of the robot arm, discretely sampling the actual output trajectory according to the discrete sampling period to obtain an actual output sequence.

[0045] Obtaining the actual control input signal u i,l (t) of the controlled system according to the iterative learning control law, and inputting it into the controlled system to obtain the actual output trajectory y i,l (t);

[0046] According to the set sampling period, the expected trajectory y i,l (t) is discretely sampled to obtain an actual output trajectory sequence The sequence is defined as y i,l (k).

[0047] S5. According to the error sequence obtained from the actual output sequence and the expected output sequence, an error value is calculated, and it is determined whether the error value meets a preset convergence condition. If yes, the iteration is stopped; if no, S6 is continued to be executed.

[0048] The error sequence obtained from the actual output sequence and the expected output sequence is specifically as follows:

[0049] A modified actual output trajectory sequence function is constructed, which is as follows:

[0050]

[0051] According to the modified actual output trajectory sequence and the iteratively changed expected trajectory sequence y d,l (k), a modified tracking error sequence is obtained:

[0052]

[0053] S6. According to the convergence condition, an iterative learning control gain is calculated, and according to the error sequence, the iterative learning control gain and the iterative learning control law, the control input signal in the next iteration is updated, and S4-S6 are repeatedly executed until the error value meets the preset convergence condition, and the iteration is stopped.

[0054] The convergence condition is specifically as follows:

[0055] ‖I-C(k+1)B(k)L(k+1)‖≤γ<1;

[0056] Wherein, L(k+1) is the iterative learning control gain.

[0057] Figure 2 A specific flowchart of an iterative learning control method of a single-link robot arm system provided for one or more embodiments of the present specification is as follows: Figure 2As shown, first, step 1 is to set a discrete sampling period for the mechanical arm. Step 2 is to obtain the desired output trajectory of the machine arm and to perform discrete sampling thereon. Step 3 is to obtain the initial control input signal for controlling the mechanical arm and to perform discrete sampling processing thereon. Step 4 is to obtain the actual control input of the mechanical arm and to obtain the actual output speed of the mechanical arm, and to sample the same. Step 5 is to calculate the error sequence between the sampled output sequence according to step 4 and the desired trajectory sequence. Step 6 needs to judge whether the error meets the convergence condition, if yes, stop iteration; if not, go to step 7, calculate the iterative learning control gain according to the convergence condition. Finally, step 8 updates the control input voltage in the next iteration according to the error sequence, the iterative learning control gain and the iterative learning control law, and repeats steps 4-8.

[0058] The iterative learning control law is calculated according to the tracking error sequence and the iterative learning control gain L(k+1), specifically as follows:

[0059]

[0060] By Figure 3 The trend chart of the tracking error index can see that the tracking error index reaches a bounded value within a limited number of iterations, and when the number of iterations is 30, the tracking error index is basically in a bounded state, that is, the output trajectory of the single-link mechanical arm can effectively track the iteratively changing desired trajectory with small error. Since the desired trajectory to be tracked by the present application is iteratively changed, Figure 4 represents the desired trajectory when the number of iterations is 1, 44 and 80, that is, the desired trajectory of each iteration is different. Figure 5 represents the actual output trajectory of the single-link mechanical arm when the number of iterations is 10 and 40, which tracks the desired trajectory at the same number of iterations. Figure 6 represents the running time of the actual output trajectory of the single-link mechanical arm.

[0061] Figure 3 、 Figure 4 、 Figure 5 and Figure 6 The linear discrete model of the single-link mechanical arm used is as follows:

[0062]

[0063] Wherein:

[0064] The desired trajectory is:

[0065]

[0066] Here, ∈ represents a quantity that changes with the number of iterations, thus making the entire desired trajectory iteratively change. θ i,l (t) represents the angular displacement of the robotic arm. This represents the speed of the robotic arm, which needs to be discretely sampled before it can be used in actual single-link robotic arms. Let θ be the initial time for each iteration. i,l (t)=0m, g = 9.8 m / s 2 This represents the acceleration due to gravity; f = 3 kg·m 2 / s represents the damping coefficient, m = 1kg represents the mass of the robotic arm, M = 2kg represents the tip load of the robotic arm, l = 0.5m represents the length of the robotic arm, J = Ml 2 +(1 / 3)ml 2 ξ represents the moment of inertia of the joint. i =(m+2M)gl[θ i -sin(θ i ] / 2J represents the model mismatch error caused by linear approximation. The expected trajectory's running interval is t = 4s, and the sampling period is T = 0.1s. According to the convergence condition ||IC(k+1)B(k)L(k+1)||≤γ<1, let the iterative learning control gain L(k+1)=0.1·e -(k+1) / 100 Tracking error index

[0067] The beneficial effects of this invention are as follows:

[0068] This invention controls a single-link robotic arm using an iterative learning control method when the desired trajectory changes iteratively and the operating range changes randomly. This effectively overcomes the control problem of the robotic arm when the reference trajectory changes iteratively and the operating range changes randomly. This invention can be applied to systems that complete other trajectory tracking tasks when the desired trajectory changes iteratively, thereby improving system efficiency, reducing system running time, and thus reducing energy consumption and production costs.

[0069] Device Example 1

[0070] This invention provides an electronic device, such as... Figure 7 As shown, it includes: a memory 70, a processor 72, and a computer program stored in the memory 70 and executable on the processor 72. When the computer program is executed by the processor 72, it performs the following method steps:

[0071] S1. Model the single-link robotic arm system as a linear discrete system and set the discrete sampling period of the linear discrete system;

[0072] S2. Discretely sampling the acquired desired output trajectory of the robot arm according to the discrete sampling period to obtain a desired output sequence;

[0073] S3. Discretizing the acquired initial control input signal for controlling the robot arm according to the discrete sampling period to obtain an actual control input signal;

[0074] S4. Obtaining an actual output trajectory of the robot arm according to the actual control input signal of the robot arm, and discretely sampling the actual output trajectory according to the discrete sampling period to obtain an actual output sequence;

[0075] S5. Obtaining an error sequence according to the actual output sequence and the desired output sequence, calculating an error value according to the error sequence, and judging whether the error value meets a preset convergence condition; if yes, stopping iteration; if not, continuing to perform S6;

[0076] S6. Calculating an iterative learning control gain according to the convergence condition, updating the control input signal in the next iteration according to the error sequence, the iterative learning control gain, and an iterative learning control law, and repeatedly performing S4-S6 until the error value meets the preset convergence condition, and stopping iteration.

[0077] Device embodiment two

[0078] The embodiment of the application provides a computer readable storage medium, and information transmission is implemented by a program stored on the computer readable storage medium.

[0079] S1. Modeling a single-link robot arm system as a linear discrete system, and setting a discrete sampling period of the linear discrete system;

[0080] S2. Discretely sampling the acquired desired output trajectory of the robot arm according to the discrete sampling period to obtain a desired output sequence;

[0081] S3. Discretizing the acquired initial control input signal for controlling the robot arm according to the discrete sampling period to obtain an actual control input signal;

[0082] S4. Obtaining an actual output trajectory of the robot arm according to the actual control input signal of the robot arm, and discretely sampling the actual output trajectory according to the discrete sampling period to obtain an actual output sequence;

[0083] S5. Obtaining an error sequence according to the actual output sequence and the desired output sequence, calculating an error value according to the error sequence, and judging whether the error value meets a preset convergence condition; if yes, stopping iteration; if not, continuing to perform S6;

[0084] S6. Calculate the iterative learning control gain according to the convergence condition, update the control input signal at the next iteration according to the error sequence, the iterative learning control gain and the iterative learning control law, and repeat S4-S6 until the error value meets the preset convergence condition, and stop iteration.

[0085] The computer readable storage medium in the embodiment includes, but is not limited to, ROM, RAM, magnetic disk or optical disk, etc.

[0086] Finally, it should be noted that: the above embodiments are only used to illustrate the technical solutions of the present application, but not to limit them; although the present application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that: it can still modify the technical solutions recorded in the foregoing embodiments, or make equivalent replacement for part or all of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present application.

Claims

1. A method of iterative learning control of a single-link robot system, characterized by, Comprising: S1. modeling a single-link robot arm system as a linear discrete system, setting a discrete sampling period of the linear discrete system; The single-link robot arm system model is represented as: ； ； ； wherein, represents the acceleration of the robot arm, represents the velocity of the robot arm, represents the angular displacement of the robot arm, represents the model mismatch error due to linear approximation, represents the moment of inertia of the joint, represents the control input, represents the mass of the robot arm, represents the tip load of the robot arm, represents the length of the robot arm, represents the damping coefficient, represents the gravitational acceleration; The single-link robot arm system is modeled as a linear discrete system composed of a state equation and an output equation, which can be represented by the following formula: Wherein: ； S2. Discretely sampling the obtained desired output trajectory of the robot arm according to the discrete sampling period to obtain a desired output sequence; ； wherein denotes the number of iterations; S3. Discretely sampling the obtained initial control input signal of the robot arm according to the discrete sampling period to obtain an actual control input signal; S4. According to the actual control input signal of the robot arm, the actual output trajectory of the robot arm is obtained, and the actual output trajectory is discretely sampled according to the discrete sampling period to obtain an actual output sequence; S5. According to the actual output sequence and the desired output sequence, an error sequence is obtained, and an error value is calculated according to the error sequence. If the error value meets the preset convergence condition, the iteration is stopped; if not, S6 is continued to be executed; S6. According to the convergence condition, the iterative learning control gain is calculated, and the control input signal in the next iteration is updated according to the error sequence, the iterative learning control gain and the iterative learning control law. Repeat S4-S6 until the error value meets the preset convergence condition, and stop iteration. The method of step S2 is specifically:

2. The method of claim 1, wherein, The error sequence is obtained according to the actual output sequence and the desired output sequence, and the error sequence is specifically: Setting a sampling period for a nonlinear continuous single-link robot arm system , the discrete sequence after sampling is , the corresponding discrete-time sequence is .

3. The method of claim 1, wherein, a desired output trajectory of the robot arm an operating interval of ; an actual output trajectory an operating interval of ; is changed randomly at each iteration, and .

4. The method of claim 3, wherein, The modified actual output trajectory sequence function is constructed as follows: The convergence condition is specifically as follows: ； According to the modified actual output trajectory sequence and the iteratively changed desired trajectory sequence a modified tracking error sequence is obtained: 。 5. The method of claim 4, wherein, Comprising: ； wherein, is the iterative learning control gain.

6. The method of claim 5, wherein, The iterative learning control law is computed as a function of the sequence of tracking errors and an iterative learning control gain The iterative learning control law is computed as a function of the sequence of tracking errors 。 7. An electronic device, comprising: A processor; And a memory arranged to store computer executable instructions that, when executed, cause the processor to implement the steps of the iterative learning control method of the single-link robot arm as claimed in any one of claims 1 to 6. For storing computer executable instructions, which when executed, implement the steps of the iterative learning control method of the single-link robot arm as claimed in any one of claims 1 to 6.

8. A storage medium, characterized by ​

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