Flexible joint robot neural network adaptive iterative learning control method

Abstract

The invention discloses a neural network adaptive iterative learning control method for a flexible joint robot, and the method comprises the steps: S1, building a constrained flexible joint robot, and initializing a system state, sampling time and control parameters; s2, compensating input saturation constraint; s3, calculating a system tracking error, and constructing an expected error trajectory; and S4, defining an error variable, and designing a neural network adaptive iterative learning controller. According to the method, the uncertainty of the flexible joint robot is estimated and compensated through the neural network, the error convergence precision is improved, by constructing the quadratic fraction type symmetric constraint Lyapunov function, it is guaranteed that the system output is always within the constraint range, the transient performance of the system is improved, and the reliability of the system is improved. According to the method, the flexible joint robot can safely and stably run in an iterative change task, when the number of iterations is increased, the tracking error is consistently converged to zero, and the method has the advantages of less required priori knowledge, no need of an accurate system model, high control precision and the like.

Description

Technical Field

[0001] The invention relates to the technical field of flexible joint robot control, and in particular to a neural network adaptive iterative learning control method for a flexible joint robot. Background Art

[0002] Flexible joint robots have a series of advantages such as light weight, low energy consumption, high flexibility, and good physical adaptability and safety. However, the flexible joint robot is an underactuated system with strong coupling and unknown uncertainty. The existence of its joint elasticity leads to oscillation, especially the various complex uncertainties in practice seriously affect the control performance of the robot. At the same time, due to the flexible structure in the flexible shutdown robot, the connecting rod will deform during operation, which makes it impossible to obtain an accurate mathematical model of the flexible joint robot, increasing the difficulty of controller design.

[0003] Compared with other control methods, the adaptive iterative learning control method contains the advantages of iterative learning control and adaptive control methods, requires less prior knowledge, does not require an accurate system model, and can indirectly improve the control performance by updating the estimation of unknown control parameters. Due to the repeatability of the flexible joint robot's operation tasks, the adaptive iterative learning method can gradually improve the robot's tracking performance by using the previous information of the control input and error. In actual industrial operations, due to the existence of flexible links, the initial state of the flexible joint robot will change, and there are limitations on the repeatability of the system, making it difficult to meet the iterative initial state consistency conditions. At the same time, due to the complexity of the production process, such as in the production mode of multiple varieties and small batches, the robot's work tasks are not necessarily completely repeated. When the iterative task is changed, the previous learning information will become invalid. Even if the task has a small change, the system needs to restart the learning process.

[0004] Therefore, for flexible joint robots with input and output constraints, it is very meaningful to design a method that can estimate and compensate for the uncertainty of flexible joint robots, relax the restrictions on initial conditions and iterative change tasks, achieve high-precision tracking control, and ensure the operational safety of flexible joint robots. Summary of the invention

[0005] The purpose of the present invention is to provide a neural network adaptive iterative learning control method for a flexible joint robot to solve the problems raised by the above background technology.

[0006] To achieve the above object, the present invention provides the following technical solution: a neural network adaptive iterative learning control method for a flexible joint robot, comprising the following steps:

[0007] S1: Establish a constrained flexible joint robot, initialize the system state, sampling time and control parameters;

[0008] S2: Compensation input saturation constraint;

[0009] S3: Calculate the system tracking error and construct the expected error trajectory;

[0010] S4: Define the error variable and design a neural network adaptive iterative learning controller.

[0011] Furthermore, the specific method in S1 is as follows:

[0012] The dynamic model of the flexible joint robot with input and output constraints is established as follows:

[0013]

[0014] in, Indicates the number of iterations; and They are The angles of the connecting rod and the motor at the iteration; and It is Angular acceleration of the connecting rod and the motor at the iteration; and are the inertia of the connecting rod and the motor respectively; is the spring stiffness; is the acceleration due to gravity; is the mass of the connecting rod; is the length from the joint to the center of gravity of the connecting rod; It is in At the iteration, the control torque has input saturation; is the actual control input; is a sine function;

[0015] make , , , ,Mode It can be written as:

[0016]

[0017] in, , , and yes , , and The derivative of

[0018] The control torque with input saturation is expressed as:

[0019]

[0020] in, and Represent the maximum and minimum values ​​of the control input respectively.

[0021] Furthermore, the specific method in S2 is as follows:

[0022] Design a function of the form hyperbolic tangent To compensate for the input saturation nonlinearity, as follows:

[0023]

[0024] in, is the hyperbolic tangent function, About The natural exponential function of About The natural exponential function of

[0025] Then, the control torque with input saturation is expressed as:

[0026]

[0027] in, , , yes The absolute value of yes 's boundary;

[0028] Then, by using the mean value theorem of differential calculus, we get:

[0029]

[0030] in, , , is a positive constant, and ;

[0031] choose ,Mode It can be written as:

[0032]

[0033] General Substitution ,get:

[0034]

[0035] General Substitute into the formula ,Mode It can be written as:

[0036]

[0037] The nonlinear state coordinate transformation is defined as follows:

[0038]

[0039] in, , , and is the variable of the nonlinear state coordinate transformation, is the cosine function;

[0040] Through coordinate transformation ,Mode It can be written as:

[0041]

[0042] in, , Abbreviated as , , is the unknown gain constant, , , and yes , , and The derivative of

[0043] because , , , and are all unknown bounded normal numbers, so we can know Bounded, there is an upper bound ,satisfy At the same time, due to is an unknown bounded positive constant, so, is an unknown bounded constant, and there is a lower bound ,satisfy ,in is an unknown constant greater than 0.

[0044] Furthermore, the method for calculating the system tracking error in S3 is as follows:

[0045] Defining Output Tracking Error and state error , , for

[0046]

[0047] in, is the reference trajectory of iterative changes, , and They are The first, second and third derivatives of ;

[0048] According to the formula Japanese style , the error dynamic model of the flexible joint robot can be obtained as follows:

[0049]

[0050] in, , , and yes , , and The first derivative of ; yes The fourth-order derivative of .

[0051] Furthermore, in S3, a smooth fourth-order expected error trajectory is constructed to deal with the initial state problem, where the expected error trajectory The construction conditions are as follows:

[0052]

[0053]

[0054] in, is the access point time, and is the initial value of the expected error trajectory and its derivative, and is the initial value of the state error and its derivative of the flexible joint robot, and is the expected error trajectory and its derivative at the access point The value at , ;

[0055] The fourth-order expected error trajectory is constructed as:

[0056]

[0057] in, is the time period for one iteration;

[0058] Transition trajectory Designed for:

[0059]

[0060] in, , and based on the construction conditions and get:

[0061]

[0062] in, , , , is the initial value of the output tracking error and its derivative; it is expected that the error trajectory is smooth and differentiable, and the initial state and error value of the system are arbitrarily bounded values.

[0063] Furthermore, the method for defining the error variable in S4 is as follows:

[0064] definition , for

[0065]

[0066] in, , and yes The first, second and third derivatives of ;

[0067] and will Defined as:

[0068]

[0069] in, , The selection should make is the Hurwitz polynomial, is the independent variable of the polynomial. From the definition of the expected error trajectory, we know ;

[0070] right The derivative is:

[0071]

[0072] in, , yes The derivative of yes The fourth derivative of ;

[0073] The quadratic fractional constrained Lyapunov function is constructed as:

[0074]

[0075] in, is the error constraint constant;

[0076] Pair Taking the derivative, we get:

[0077]

[0078] in, ;

[0079] General Substitution We can get:

[0080]

[0081] in, .

[0082] Furthermore, the method for designing a neural network adaptive iterative learning controller in S4 is as follows:

[0083] S401: Designing Neural Networks to Approximate and Compensate for Unknown Continuous Functions :

[0084]

[0085] in, is the ideal neural network weight, is the input variable of the neural network, is the approximate error, satisfying ; is the activation function, abbreviated as , which is in the following form:

[0086]

[0087] in, , , and All are constant parameters;

[0088] General Substitution We can get:

[0089]

[0090] in, is a positive constant and ;

[0091] S402: Design combination adaptive law update and :

[0092]

[0093]

[0094] in, , They are and The estimation error of , , and They are and In the and The estimated value at the iteration; and yes and The first derivative of , , , are all normal numbers; , , , ;

[0095] S403: Design a neural network adaptive iterative learning controller as follows:

[0096]

[0097] in, is a normal number.

[0098] Compared with the prior art, the present invention has the following beneficial effects:

[0099] The flexible joint robot neural network adaptive iterative learning control method of the present invention ensures the output tracking accuracy of the flexible joint robot under any initial state and iterative change task, and improves the industrial production efficiency. It uses a neural network to estimate and compensate for the uncertainty of the flexible joint robot, improves the error convergence accuracy, and by constructing a quadratic fractional symmetric constraint Lyapunov function, ensures that the system output is always within the constraint range, improves the transient performance of the system, and enables the flexible joint robot to operate safely and stably in iterative change tasks. When the number of iterations increases, the tracking error converges to zero uniformly. The present invention has the advantages of less required prior knowledge, no need for an accurate system model, and high control accuracy. The control performance can be gradually improved by utilizing the repeatability of the flexible joint robot operation task and the previous information of the control input and error. By constructing the expected error trajectory in the form of a fourth-order differentiable polynomial, the problem of inconsistent initial state caused by the flexible link and the problem of iterative change of tasks under different production modes are solved. The constraint neural network adaptive iterative learning control method proposed by the present invention relaxes the restrictions on initial values ​​and operation tasks, realizes high-precision tracking control, and expands the application scope of iterative learning. BRIEF DESCRIPTION OF THE DRAWINGS

[0100] Figure 1 It is a simulation block diagram of trajectory tracking control of a flexible joint robot according to an embodiment of the present invention;

[0101] Figure 2 is an output tracking performance diagram of the flexible joint robot during the first iteration of an embodiment of the present invention;

[0102] Figure 3 is an output tracking performance diagram of the flexible joint robot in the seventh iteration of an embodiment of the present invention;

[0103] Figure 4 It is a control input diagram at the seventh iteration under the constraint control of an embodiment of the present invention;

[0104] Figure 5 is an error tracking performance diagram of the embodiment of the present invention at the seventh iteration;

[0105] Figure 6 is the maximum tracking error of the system in each iteration of the embodiment of the present invention;

[0106] Figure 7 It is a flow chart of the control method of the present invention. DETAILED DESCRIPTION

[0107] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0108] The embodiment of the present invention uses MATLAB / Simulink and Solidworks to simulate the trajectory tracking control of the flexible joint robot. The block diagram is as follows: Figure 1 Based on Figure 1 The simulation block diagram and the proposed constrained neural network adaptive iterative learning controller are used to simulate the trajectory tracking control of the flexible joint robot in the Simulink environment.

[0109] See also Figure 2-7 This embodiment provides a neural network adaptive iterative learning control method for a flexible joint robot with symmetric output constraints, comprising the following steps:

[0110] S1: Establish a constrained flexible joint robot, initialize the system state, sampling time and control parameters; the process is as follows:

[0111] The dynamic model of the flexible joint robot with input and output constraints is established as follows:

[0112]

[0113] in, Indicates the number of iterations; and They are The angles of the connecting rod and the motor at the iteration; and It is Angular acceleration of the connecting rod and the motor at the iteration; and are the inertia of the connecting rod and the motor respectively; is the spring stiffness; is the acceleration due to gravity; is the mass of the connecting rod; is the length from the joint to the center of gravity of the connecting rod; It is in At the iteration, the control torque has input saturation; is the actual control input; is a sine function;

[0114] make , , , ,Mode It can be written as:

[0115]

[0116] in, , , and yes , , and The derivative of

[0117] The control torque with input saturation is expressed as:

[0118]

[0119] in, and Represent the maximum and minimum values ​​of the control input respectively.

[0120] S2: Compensate for input saturation constraints. The process is as follows:

[0121] Design a function of the form hyperbolic tangent To compensate for the input saturation nonlinearity, as follows:

[0122]

[0123] in, is the hyperbolic tangent function, About The natural exponential function of About The natural exponential function of

[0124] Then, the control torque with input saturation is expressed as:

[0125]

[0126] in, , , yes The absolute value of yes 's boundary;

[0127] Then, by using the mean value theorem of differential calculus, we get:

[0128]

[0129] in, , , is a positive constant, and ;

[0130] choose ,Mode It can be written as:

[0131]

[0132] General Substitution ,get:

[0133]

[0134] General Substitute into the formula ,Mode It can be written as:

[0135]

[0136] The nonlinear state coordinate transformation is defined as follows:

[0137]

[0138] in, , , and is the variable of the nonlinear state coordinate transformation, is the cosine function;

[0139] Through coordinate transformation ,Mode It can be written as:

[0140]

[0141] in, , Abbreviated as , , is the unknown gain constant, , , and yes , , and The derivative of

[0142] because , , , and are all unknown bounded normal numbers, so we can know Bounded, there is an upper bound ,satisfy At the same time, due to is an unknown bounded positive constant, so, is an unknown bounded constant, and there is a lower bound ,satisfy ,in is an unknown constant greater than 0.

[0143] S3: Calculate the system tracking error and construct the expected error trajectory. The process is as follows:

[0144] Defining Output Tracking Error and state error , , for

[0145]

[0146] in, is the reference trajectory of iterative changes, , and They are The first, second and third derivatives of ;

[0147] According to the formula Japanese style , the error dynamic model of the flexible joint robot can be obtained as follows:

[0148]

[0149] in, , , and yes , , and The first derivative of ; yes The fourth derivative of ;

[0150] The adaptive iterative learning control in the embodiment of the present invention is an effective control method to achieve high precision in repetitive operation tasks; however, there is a problem of repeated positioning drift in practice, which affects the control accuracy of the actual robot and even affects the industrial processing efficiency; in the traditional iterative learning control design, the iterative initial state consistency condition is a common restriction condition, namely:

[0151]

[0152] in, , , and They are , , and exist The value of , , and They are , , and exist The value at time;

[0153] However, due to the limitation of repeated positioning accuracy and the influence of unpredictable factors during the operation of the flexible joint robot, this constraint is difficult to meet. In order to alleviate the problem of repeated positioning of the initial value during the operation of the flexible joint robot, the present invention constructs a smooth fourth-order expected error trajectory for the flexible joint robot that performs iterative tasks, effectively handles the initial state problem, and does not need to reconstruct the expected error trajectory when the iterative task changes, so the amount of calculation is significantly reduced.

[0154] Expected Error Trajectory The construction conditions are as follows:

[0155]

[0156]

[0157] in, is the access point time, and is the initial value of the expected error trajectory and its derivative, and is the initial value of the state error and its derivative of the flexible joint robot, and is the expected error trajectory and its derivative at the access point The value at , ;

[0158] The fourth-order expected error trajectory is constructed as:

[0159]

[0160] in, is the time period for one iteration;

[0161] Transition trajectory Designed for:

[0162]

[0163] in, , and based on the construction conditions and get:

[0164]

[0165] in, , , , is the initial value of the output tracking error and its derivative; it is expected that the error trajectory is smooth and differentiable, and the initial state and error value of the system are arbitrarily bounded values;

[0166] S4: Define the error variable and design a neural network adaptive iterative learning controller. The process is as follows:

[0167] S401: Define the error variable as:

[0168] definition , for

[0169]

[0170] in, , and yes The first, second and third derivatives of ;

[0171] and will Defined as:

[0172]

[0173] in, , The selection should make is the Hurwitz polynomial, is the independent variable of the polynomial. From the definition of the expected error trajectory, we know ;

[0174] right The derivative is:

[0175]

[0176] in, , yes The derivative of yes The fourth derivative of ;

[0177] The quadratic fractional constrained Lyapunov function is constructed as:

[0178]

[0179] in, is the error constraint constant;

[0180] Pair Taking the derivative, we get:

[0181]

[0182] in, ;

[0183] General Substitution We can get:

[0184]

[0185] in, ;

[0186] S402: Designing Neural Networks to Approximate and Compensate for Unknown Continuous Functions :

[0187]

[0188] in, is the ideal neural network weight, is the input variable of the neural network, is the approximate error, satisfying ; is the activation function, abbreviated as , which is in the following form:

[0189]

[0190] in, , , and All are constant parameters;

[0191] General Substitution We can get:

[0192]

[0193] in, is a positive constant and ;

[0194] S403: Design combination adaptive law update and :

[0195]

[0196]

[0197] in, , They are and The estimation error of , , and They are and In the and The estimated value at the iteration; and yes and The first derivative of , , , are all normal numbers; , , , ;

[0198] S403: Design a neural network adaptive iterative learning controller as follows:

[0199]

[0200] in, is a normal number.

[0201] according to Figure 7 , firstly, the initial state and parameters of the flexible joint robot are given, and the parameters of the flexible joint robot system are , , , , and The number of iterations is set to , the cycle of each iteration is .

[0202] The iterative change reference trajectory is set to ,in , , is the current iteration number. The initial state of the system is: , , , , The expected trajectory error is taken as the access point .

[0203] The parameters of the constrained neural network adaptive iterative learning controller and the combined adaptive law are set as: , , , , , , , and . The constraints are , , The control input is subject to saturation constraints, with upper and lower bounds of and , the neural network parameters are , , , .

[0204] from Figure 2 and Figure 3 It can be seen that under the control method proposed in the present invention, the angle of the connecting rod is always within the constraint range. At the same time, as the number of iterations increases, the connecting rod angle asymptotically converges to the iteratively changing connecting rod angle trajectory. Figure 4 The control input is shown when the input is saturated. Figure 5 and Figure 6The performance indicators of error tracking performance and control method are given respectively. The output error converges quickly to the desired error trajectory. The maximum error value decreases with the increase of iteration number and always remains within the constraint range. The simulation results show that the proposed constrained neural network adaptive iterative learning control method is effective. Moreover, with the increase of iteration number, the tracking accuracy of the flexible joint robot gradually improves and finally converges to the desired link angle trajectory.

[0205] In summary: The flexible joint robot neural network adaptive iterative learning control method provided by the present invention ensures the output tracking accuracy of the flexible joint robot under any initial state and iterative change tasks, and improves industrial production efficiency. It uses a neural network to estimate and compensate for the uncertainty of the flexible joint robot, improves the error convergence accuracy, and constructs a quadratic fractional symmetric constrained Lyapunov function to ensure that the system output is always within the constraint range, improves the transient performance of the system, and enables the flexible joint robot to operate safely and stably in iterative change tasks. When the number of iterations increases, the tracking error converges to zero uniformly.

[0206] The above description is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field can make equivalent replacements or changes according to the technical scheme and inventive concept of the present invention within the technical scope disclosed by the present invention, which should be covered by the protection scope of the present invention.

Claims

1. A neural network adaptive iterative learning control method for a flexible joint robot, characterized in that: The following steps are involved: S1: Establish a constrained flexible joint robot, initialize the system state, sampling time and control parameters; S2: Compensation input saturation constraint; S3: Calculate the system tracking error and construct the expected error trajectory; S4: Define the error variable and design a neural network adaptive iterative learning controller.

2. A method for adaptive iterative learning control of a flexible joint robot using a neural network as claimed in claim 1, characterized in that: The specific method in S1 is as follows: The dynamic model of the flexible joint robot with input and output constraints is established as follows: ； in, Indicates the number of iterations; and They are The angles of the connecting rod and the motor at the iteration; and It is Angular acceleration of the connecting rod and the motor at the iteration; and are the inertia of the connecting rod and the motor respectively; is the spring stiffness; is the acceleration due to gravity; is the mass of the connecting rod; is the length from the joint to the center of gravity of the connecting rod; It is in At the iteration, the control torque has input saturation; is the actual control input; is a sine function; make , , , ,Mode It can be written as: ； in, , , and yes , , and The derivative of The control torque with input saturation is expressed as: ； in, and Represent the maximum and minimum values ​​of the control input respectively.

3. A method for adaptive iterative learning control of a flexible joint robot using a neural network as claimed in claim 2, characterized in that: The specific method in S2 is as follows: Design a function of the form hyperbolic tangent To compensate for the input saturation nonlinearity, as follows: ； in, is the hyperbolic tangent function, About The natural exponential function of About The natural exponential function of Then, the control torque with input saturation is expressed as: ； in, , , yes The absolute value of yes 's boundary; Then, by using the mean value theorem of differential calculus, we get: ； in, , , is a positive constant, and ; choose ,Mode It can be written as: ； General Substitution ,get: ； General Substitute into the formula ,Mode It can be written as: ； The nonlinear state coordinate transformation is defined as follows: ； Among them, , , and is the variable of the nonlinear state coordinate transformation, is the cosine function; Through coordinate transformation ,Mode It can be written as: ； in, , Abbreviated as , , is the unknown gain constant, , , and yes , , and The derivative of because , , , and are all unknown bounded normal numbers, so we can know Bounded, there is an upper bound ,satisfy At the same time, due to is an unknown bounded positive constant, so, is an unknown bounded constant, and there is a lower bound ,satisfy ,in is an unknown constant greater than 0.

4. A method for adaptive iterative learning control of a flexible joint robot using a neural network as claimed in claim 3, characterized in that: The method for calculating the system tracking error in S3 is as follows: Defining Output Tracking Error and state error , , for ； in, is the reference trajectory of iterative changes, , and They are The first, second and third derivatives of ; According to the formula Japanese style , the error dynamic model of the flexible joint robot can be obtained as follows: ； in, , , and yes , , and The first derivative of ; yes The fourth-order derivative of .

5. A neural network adaptive iterative learning control method for a flexible joint robot as claimed in claim 4, characterized in that: In S3, a smooth fourth-order expected error trajectory is constructed to deal with the initial state problem, where the expected error trajectory The construction conditions are as follows: ； ； in, is the access point time, and is the initial value of the expected error trajectory and its derivative, and is the initial value of the state error and its derivative of the flexible joint robot, and is the expected error trajectory and its derivative at the access point The value at , ; The fourth-order expected error trajectory is constructed as: ； in, is the time period for one iteration; Transition trajectory Designed for: ； in, , and based on the construction conditions and get: ； in, , , , is the initial value of the output tracking error and its derivative; it is expected that the error trajectory is smooth and differentiable, and the initial state and error value of the system are arbitrarily bounded values.

6. A method for adaptive iterative learning control of a flexible joint robot using a neural network as claimed in claim 5, characterized in that: The method for defining error variables in S4 is as follows: definition , for ； in, , and yes The first, second and third derivatives of ; and will Defined as: ； in, , The selection should make is the Hurwitz polynomial, is the independent variable of the polynomial. From the definition of the expected error trajectory, we know ; right The derivative is: ； in, , yes The derivative of yes The fourth derivative of ; The quadratic fractional constrained Lyapunov function is constructed as: ； in, is the error constraint constant; Pair Taking the derivative, we get: ； in, ; General Substitution We can get: ； in, .

7. A neural network adaptive iterative learning control method for a flexible joint robot as claimed in claim 6, characterized in that: The method for designing a neural network adaptive iterative learning controller in S4 is as follows: S401: Designing Neural Networks to Approximate and Compensate for Unknown Continuous Functions : ； in, is the ideal neural network weight, is the input variable of the neural network, is the approximate error, satisfying ; is the activation function, abbreviated as , which is in the following form: ； in, , , and All are constant parameters; General Substitution We can get: ； in, is a positive constant and ; S402: Design combination adaptive law update and : ； ； in, , They are and The estimation error of , , and They are and In the and The estimated value at the iteration; and yes and The first derivative of , , , are all normal numbers; , , , ; S403: Design a neural network adaptive iterative learning controller as follows: ； in, is a normal number.

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