Optimization Method for Manipulator Model Based on Adaptive Sliding Mode Observer

Abstract

The present invention belongs to the technical field of robot control, and particularly relates to a method for optimizing a manipulator model based on an adaptive sliding mode observer, including obtaining a first non-linear manipulator model by Newton-Euler method according to the position signal of the manipulator and unknown external disturbances, processing the first non-linear manipulator model into a model determined part and a model uncertain part in state space; approximating the model uncertain part with a radial basis function neural network to obtain a second non-linear manipulator model; constructing an adaptive sliding mode observer for the second non-linear manipulator model by using a sliding mode control method and a second radial basis function neural network, and calculating an estimated value of the approximation result by using the adaptive sliding mode observer; compensating the estimated value of the approximation result into the first non-linear manipulator model to eliminate the influence of unknown external disturbances on the manipulator and optimize the first non-linear manipulator model.

Description

Technical Field

[0001] The present invention belongs to the technical field of robot control, and in particular relates to a robot arm model optimization method based on an adaptive sliding mode observer. Background Art

[0002] As we all know, the robotics industry is an important indicator of a country's manufacturing and technological advancements. Due to its application areas encompassing industrial manufacturing, resource exploration and development, disaster relief, medical services, home entertainment, military, and aerospace, countries around the world attach great importance to the research and development and production of the robotics industry, investing significant funds and manpower to make robots more intelligent and achieve leapfrog, continuous upgrades and iterations of robotic products. Robot control technology, as one of the core technologies of the robotics industry, influences its development. As the support for robotics technology, the robotic arm, with its continuous technological advancements, simply considering the application of the robotic arm model while ignoring the time-varying and uncertain nature of the robotic arm model itself, no longer meets the control requirements. Therefore, optimizing the robotic arm model to obtain a precise model by taking into account its time-varying and uncertain nature is a critical issue that needs to be addressed in robotic control systems.

[0003] Currently, the optimization methods proposed for the robotic arm model mainly include using intelligent algorithms, such as neural networks or fuzzy theory, to approximate the robotic arm model, and by transforming the model into a certain part and an uncertain part, and then using an observer based on an adaptive robust control algorithm to estimate the uncertain part of the model online, and then compensate for the corresponding part. However, there is a problem of large computational complexity when optimizing the model through intelligent algorithms, and there is a problem of slow model optimization speed when estimating the model online through an observer based on an adaptive robust control algorithm, and at the same time, problems such as environmental noise and measurement noise will be generated, which has a poor effect on the optimization of the robotic arm model. Summary of the Invention

[0004] In order to solve the shortcomings of the existing optimization of the manipulator model, such as poor effect, slow response speed and large amount of calculation, the present invention proposes a manipulator model optimization method based on an adaptive sliding mode observer, comprising:

[0005] S1: Based on the position signal of the manipulator and the unknown external disturbance, the first nonlinear manipulator model is constructed and divided into the model-determined part and the model-uncertain part:

[0006] S11: Obtain the first nonlinear manipulator model using the Newton-Euler method based on the manipulator's position signal and unknown external disturbances:

[0007]

[0008]

[0009]

[0010]

[0011]

[0012] Among them, is the inertia matrix, is the Coriolis force and centripetal force, is the undisturbed part of the inertia matrix, is the disturbed part of the inertia matrix, is the undisturbed part of the Coriolis force and centripetal force, is the gravity torque, is the disturbed part of the Coriolis force and centripetal force, is the undisturbed part of the gravity torque, is the disturbed part of the gravity torque, is the acceleration signal of the -th degree of freedom of the robotic arm, is the velocity signal of the -th degree of freedom of the robotic arm, is the total disturbance part of the -th degree of freedom of the first non-linear robotic arm model, is the unknown disturbance of the -th degree of freedom of the first non-linear robotic arm model, is the control torque of the -th degree of freedom of the robotic arm, where n represents the number of degrees of freedom of the robotic arm.

[0013] S12: Perform state-space processing on the first non-linear robotic arm model according to the position signal of the robotic arm, and process the first non-linear robotic arm model into a model-determined part and a model-uncertain part :

[0014] The state vector of the first non-linear robotic arm model is:

[0015]

[0016] The state-space equation of the first non-linear robotic arm model is:

[0017]

[0018]

[0019]

[0020]

[0021] Among them, is the state vector of the th degree of freedom of the first non-linear robotic arm model, is the position vector of the th degree of freedom of the robotic arm, is the velocity vector of the th degree of freedom of the robotic arm, is the velocity vector of the th degree of freedom of the robotic arm, is the acceleration vector of the th degree of freedom of the robotic arm, is the position signal of the th degree of freedom of the robotic arm, is the velocity signal of the th degree of freedom of the robotic arm, is the undisturbed part of the gravitational torque, is the undisturbed part of the Coriolis force and centripetal force, is the undisturbed part of the inertia matrix, is the first model determination part of the th degree of freedom of the first non-linear robotic arm model is the second model determination part of the th degree of freedom of the first non-linear robotic arm model, is the model uncertainty part of the th degree of freedom of the first non-linear robotic arm model, where n represents the number of degrees of freedom of the robotic arm, is the total disturbance part of the th degree of freedom of the first non-linear robotic arm model).

[0022] S2: Use the first radial basis function neural network to approximately approximate the uncertainty part of the first non-linear robotic arm model, and replace the uncertainty part of the first non-linear robotic arm model with the approximation result to obtain the second non-linear robotic arm model, including:

[0023] Among them, is the velocity vector of the l-th degree of freedom of the robotic arm, is the acceleration vector of the l-th degree of freedom of the robotic arm, is the state vector of the l-th degree of freedom of the second non-linear robotic arm model, is the th degree of freedom of the robotic arm, is the first model determination part of the th degree of freedom of the second non-linear robotic arm model is the second model determination part of the th degree of freedom of the second non-linear robotic arm model, is the approximation result of the first radial basis function neural network for the uncertain part of the l-th degree of freedom of the first non-linear manipulator model is the first radial basis function neural network for the first non-linear manipulator model at the uncertain part of the degree of freedom model weight factor matrix after approximation is the first radial basis function neural network for the first non-linear manipulator model at the uncertain part of the degree of freedom error after approximation, n represents the number of degrees of freedom of the manipulator is the maximum approximation error value constant of the first radial basis function neural network for the degree of freedom of the manipulator model

[0024] S3: Using the sliding mode control function and the second radial basis function neural network, construct the adaptive sliding mode observer corresponding to the second non-linear manipulator model:

[0025] S31: Use the second radial basis function neural network to construct an observer for the second non-linear manipulator model;

[0026] S32: Use the sliding mode control function and the observer described in step S31 to construct a sliding mode observer for the difference between the estimated value of the state vector of the second non-linear manipulator model and the actual value output by the second non-linear manipulator model;

[0027] S33: According to the difference between the estimated value of the second non-linear manipulator model and the actual value of the second non-linear manipulator model described in step S32, and the difference between the weight factor matrix after approximation of the uncertain part of the first non-linear manipulator model by the first radial basis function neural network and the weight factor matrix of the second radial basis function neural network, adaptively update the weight factor matrix of the second radial basis function neural network in the sliding mode observer to obtain the adaptive sliding mode observer:

[0028]

[0029] [[ID=3�]]where is the estimated value of the state vector of the second non-linear manipulator model by the adaptive sliding mode observer is the estimated value of the velocity vector of the l-th degree of freedom of the manipulator by the adaptive sliding mode observer [[ID=४४]] is the estimated value of the acceleration vector of the l-th degree of freedom of the manipulator by the adaptive sliding mode observer is the estimated value of the velocity vector of the degree of freedom of the manipulator by the adaptive sliding mode observer ​​​​The estimated value, is the determined part of the first model of the l-th degree of freedom of the second non-linear robotic arm model by the adaptive sliding mode observer The estimated value, is the determined part of the second model of the l-th degree of freedom of the second non-linear robotic arm model by the adaptive sliding mode observer The estimated value, is the weight factor matrix of the second radial basis function neural network, is the radial basis function of the second radial basis function neural network, is the sliding mode control function of the adaptive sliding mode observer, is the maximum approximation error value constant of the robotic arm model by the first radial basis function neural network for the degree of freedom, and are the parameters of the adaptive sliding mode controller respectively, and n represents the number of degrees of freedom of the robotic arm:

[0030] Wherein, the and Satisfy:

[0031]

[0032] Wherein, is the maximum approximation error value constant of the robotic arm model by the first radial basis function neural network for the <H degree of freedom;

[0033] The weight factor matrix of the second radial basis function neural network includes:

[0034]

[0035]

[0036]

[0037] Wherein, is the adaptive change rate of the weight factor matrix of the second radial basis function neural network, is the weight factor matrix after approximation by the first radial basis function neural network at time t and the weight factor matrix of the second radial basis function neural network The difference between, is the weight factor matrix after approximation by the first radial basis function neural network at the initial time and the weight factor matrix of the second radial basis function neural network The difference between, and are learning factors, is the estimated value of the position vector of the degree of freedom of the second non - linear manipulator model by the adaptive sliding - mode observer and the difference between the position vector output by the second non - linear manipulator model and the actual value, is the difference between the estimated value of the velocity vector of the degree of freedom of the second non - linear manipulator model by the adaptive sliding - mode observer and the velocity vector output by the second non - linear manipulator model and the actual value, is the estimated value of the state vector of the degree of freedom of the second non - linear manipulator model by the adaptive sliding - mode observer and, is the radial basis function of the second radial basis function neural network of the adaptive sliding - mode observer, e represents the base of the natural logarithm, and are integration variables. and are integration variables.

[0038] S4: Calculate the estimated value of the approximation result by using the adaptive sliding - mode observer, and compensate the estimated value of the approximation result into the first non - linear manipulator model in step S1:

[0039] The estimated value of the approximation result is:

[0040]

[0041] is the weight factor matrix of the second radial basis function neural network in the adaptive sliding - mode observer, is the radial basis function of the second radial basis function neural network.

[0042] Preferably, the radial basis functions of the first radial basis function neural network or the second radial basis function neural network are the same Gaussian function:

[0043]

[0044]

[0045]

[0046]

[0047] where X is the state vector of the manipulator model, is the radial basis function of the radial basis function neural network, [[ID=6③]]is the radial basis function of the radial basis function neural network of the degree of freedom, represents the radial basis function of the $i$-th neural node in the radial basis function neural network of the $l$-th degree of freedom, represents the set of receptive field centers of the $i$-th neural node in the radial basis function neural network of the $l$-th degree of freedom, is the center of the $m$-th receptive field of the $i$-th neural node in the radial basis function neural network of the $l$-th degree of freedom, where $m$ is the number of receptive field centers of the $i$-th neural node in the radial basis function neural network of the $l$-th degree of freedom, represents the number of neural nodes in the radial basis function neural network of the $l$-th degree of freedom, represents the radial basis function of the $i$-th neural node in the radial basis function neural network of the $l$-th degree of freedom width of the Gaussian mode, where is or .

[0048] The present invention has at least the following beneficial effects:

[0049] In the present invention, considering the influence of usage time, corrosion degree of the robotic arm, and lubrication degree of the joints among different robotic arms, the first non-linear robotic arm model is divided into a deterministic part and an uncertain part. According to the principle of the radial basis function neural network, the uncertain part of the first non-linear robotic arm model is approximately approximated, which can suppress the influence of most disturbances on the robotic arm. By using a sliding mode control function and a second radial basis function neural network, an adaptive sliding mode observer corresponding to the second non-linear robotic arm model is constructed. Through the adaptively updated second neural network weight factor in the adaptive sliding mode observer, the approximated part in the second non-linear robotic arm model can be quickly estimated, the approximation error generated after the first radial basis function neural network approximates the uncertain part of the first non-linear robotic arm model is eliminated, and by feeding back to the first non-linear robotic arm model, the robotic arm model is optimized to eliminate the influence of external disturbances on the robotic arm model. The sliding mode function can accelerate the convergence speed during the estimation of the adaptive sliding mode observer and reduce the computational amount. Through the method of the present invention, the influence of various disturbances on the robotic arm model is effectively suppressed, and the response speed of the robotic arm model optimization is improved by designing an adaptive weight factor matrix, and the computational amount is reduced. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 is a flowchart of the method of the present invention;

[0051] Figure 2 is a schematic diagram of the optimization control process of the present invention;

[0052] Figure 3It is a diagram of the model optimization method in the embodiment of the present invention;

[0053] Figure 4 It is a diagram of the trajectory curve tracking of the robotic arm joint 1 in the embodiment of the present invention;

[0054] Figure 5 It is a diagram of the trajectory curve tracking of the robotic arm joint 2 in the embodiment of the present invention;

[0055] Figure 6 It is a diagram of the estimated curve of the uncertain part of the robotic arm joint 1 model in the embodiment of the present invention;

[0056] Figure 7 It is a diagram of the estimated curve of the uncertain part of the robotic arm joint 2 model in the embodiment of the present invention. Detailed implementation manners

[0057] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, those of ordinary skill in the art can implement the present invention without creative efforts, and all belong to the protection scope of the present invention.

[0058] Embodiment 1

[0059] As Figure 1 、 Figure 2 、 Figure 3 shown, the robotic arm model optimization method based on an adaptive sliding mode observer proposed by the present invention includes the following steps:

[0060] 1: According to the position signal of the robotic arm and the unknown external disturbance, construct a first non-linear robotic arm model and divide it into a model-determined part and a model-uncertain part:

[0061] 1.1. Obtain the first non-linear robotic arm model through the Newton-Euler method according to the position signal of the robotic arm and the unknown external disturbance:

[0062]

[0063]

[0064]

[0065]

[0066]

[0067] Among them, is the inertia matrix, is the Coriolis force and centripetal force, is the undisturbed part of the inertia matrix, is the disturbed part of the inertia matrix, is the undisturbed part of the Coriolis force and the centripetal force, is the gravity torque, is the disturbed part of the Coriolis force and the centripetal force, is the undisturbed part of the gravity torque, is the disturbed part of the gravity torque, is the acceleration signal of the th degree of freedom of the robotic arm, is the velocity signal of the th degree of freedom of the robotic arm, is the total disturbance part of the th degree of freedom of the first non - linear robotic arm model, is the unknown disturbance of the th degree of freedom of the first non - linear robotic arm model, is the control torque of the th degree of freedom of the robotic arm. n represents the number of degrees of freedom of the robotic arm, and the value of n depends on the number of active joints of the robotic arm in the first non - linear robotic arm model. If the robotic arm of the first non - linear robotic arm model has one joint, it means the first non - linear robotic arm model has one degree of freedom. is the parameter that comes with the robotic arm when it leaves the factory, or the parameter artificially adjusted by those skilled in the art according to the required robotic arm effect is the control input signal of the user. q is the motion trajectory of the robotic arm under the condition of inputting the control torque of the robotic arm again. is the motion velocity of the robotic arm obtained by differentiating the motion trajectory q of the robotic arm, and the motion acceleration of the robotic arm is obtained by differentiating the motion velocity of the robotic arm. , in the present invention, only the model expression of the th degree of freedom is shown. Creating a robotic arm model through the Newton - Euler method is a commonly used technical means by those skilled in the art, and the dynamic equation of the robotic arm is obtained by transforming the classical robotic arm dynamic equation considering the factors of unknown external disturbances.

[0068] 1.2: Perform state - space processing on the first non - linear robotic arm model according to the position signal of the robotic arm, and process the first non - linear robotic arm model into a model - determined part and a model - uncertain part :

[0069] Differentiating the position signal of the robotic arm can obtain the velocity signal of the current position of the robotic arm. According to the velocity signal and the position signal, the current state of the robotic arm can be determined. Therefore, the position signal and the velocity signal of the robotic arm are used as the state vector of the first non - linear robotic arm model: ​

[0070] The state vector of the first non - linear robotic arm model is:

[0071]

[0072] The state - space equation of the first non - linear robotic arm model is:

[0073]

[0074]

[0075]

[0076]

[0077] Wherein, is the state vector of the th degree of freedom of the first non - linear robotic arm model, is the position vector of the th degree of freedom of the robotic arm, is the velocity vector of the th degree of freedom of the robotic arm, is the velocity vector of the th degree of freedom of the robotic arm, is the acceleration vector of the th degree of freedom of the robotic arm, is the position signal of the th degree of freedom of the robotic arm, is the velocity signal of the th degree of freedom of the robotic arm, is the undisturbed part of the gravitational torque, is the undisturbed part of the Coriolis force and centripetal force, is the undisturbed part of the inertia matrix, is the first model - determining part of the th degree of freedom of the first non - linear robotic arm model is the second model - determining part of the th degree of freedom of the first non - linear robotic arm model, is the model - uncertainty part of the th degree of freedom of the first non - linear robotic arm model, n represents the number of degrees of freedom of the robotic arm, is the total disturbance part of the th degree of freedom of the first non - linear robotic arm model, serves as the state vector of the Tth degree of freedom of the first non - linear robotic arm model, which contains the position information and velocity information of the th degree of freedom of the first non - linear robotic arm model, and the specific representation form has been given in (2). of the above.

[0078] 2: Use the first radial basis function neural network to analyze the uncertain part of the first nonlinear manipulator model Approximate approximation, using the approximation result to replace the uncertain part of the first nonlinear manipulator model , obtaining the second nonlinear manipulator model includes:

[0079] 2.1 Determine the radial basis function of the first radial basis function neural network:

[0080]

[0081]

[0082]

[0083] in, The first nonlinear manipulator model The state vector of degrees of freedom, is the radial basis function of the first radial basis function neural network, represents the radial basis function of the i-th neural node in the first radial basis function neural network, represents the set of receptive field centers of the i-th neural node in the first radial basis function neural network, is the center of the mth receptive field of the ith neural node in the first radial basis function neural network, m is the number of receptive field centers of the ith neural node in the first radial basis function neural network, represents the number of neural nodes in the first radial basis function neural network, Represents the radial basis function of the i-th neural node in the first radial basis function neural network The width of the Gaussian pattern, in this embodiment, It is set by those skilled in the art according to experimental requirements, i is set by those skilled in the art according to experimental requirements, and m is set by those skilled in the art according to experimental requirements. It is set up according to experimental requirements for those skilled in the art. In the present invention, a radial basis function neural network is created for each degree of freedom of the robotic arm. Therefore, the value of n depends on the number of joints of the robotic arm in the robotic arm model. At the same time, the radial basis function used in the present invention is not limited to this one. According to the characteristics of the radial basis function neural network, those skilled in the art should understand that in addition to the radial basis function recorded in the present invention, the remaining functions that meet the basic characteristics of the radial basis function can also implement the present invention. In particular, in the present invention, the state vector of the first nonlinear robotic arm model is to input a control torque to the first nonlinear robotic arm model. After that, for the position signal output by the first non-linear manipulator model, the derivative of the position signal is taken to obtain the velocity signal of the first non-linear manipulator model. The position signal and velocity signal of the first non-linear manipulator model are the state vectors of the manipulator model.

[0084] 2.2 Use the first radial basis function neural network to approximate the uncertain part of the first non-linear manipulator model and replace the uncertain part of the first non-linear manipulator model with the approximation result to obtain the second non-linear manipulator model, including:

[0085]

[0086] ,

[0087] where, is the velocity vector of the l-th degree of freedom of the manipulator, is the acceleration vector of the l-th degree of freedom of the manipulator, is the state vector of the second non-linear manipulator model, is the velocity vector of the -th degree of freedom of the manipulator, is the model-determined part of the -th degree of freedom of the second non-linear manipulator model is the model-determined part of the -th degree of freedom of the second non-linear manipulator model, is the approximation result of the first radial basis function neural network for the uncertain part of the l-th degree of freedom of the first non-linear manipulator model , is the weight factor matrix after approximation of the first radial basis function neural network for the model uncertain part of the -th degree of freedom of the first non-linear manipulator model , is the radial basis function of the first radial basis function neural network, is the error after approximation of the first radial basis function neural network for the uncertain part of the -th degree of freedom of the first non-linear manipulator model , n represents the number of degrees of freedom of the manipulator, is the maximum approximation error value constant of the first radial basis function neural network for the -th degree of freedom of the manipulator model, The value is independently designed by those skilled in the art according to the experimental accuracy. According to the principle of the radial basis function neural network, the uncertain part in the first non-linear manipulator model is approximately approximated, which can suppress the influence of most disturbances on the manipulator. Since approximating the non-linear function by using the radial basis function neural network is a commonly used technical means in the art, it will not be described here. Approximating the uncertain part of the first non-linear manipulator model by the first radial basis function neural network is mainly by using the difference between the output of the linear manipulator model and the output value of the first non-linear manipulator as the uncertain part of the first non-linear manipulator model. An initial weight factor is designed for the first radial basis function neural network, and an approximation error will be obtained. , continuously adjust the weight factor of the first neural network , so that the approximation error is less than the set threshold until. The linear manipulator model is the standard manipulator model without any external disturbance. , when approximating the first non-linear manipulator by the first radial basis function neural network, an approximation error will be generated. The difference between the manipulator trajectory (position signal) output by the first radial basis function neural network and the rated value (expected value) is the approximation error. By adding the manipulator trajectory (position signal) output by the first radial basis function neural network and the approximation error, it represents the rated value (expected value). For example, set A1 as the rated output state vector of the linear manipulator model. There is a non-linear manipulator model that is affected by position interference, and its actual output state vector is A2. By A1 - A2, the uncertain part B1 of the non-linear manipulator model is obtained. After approximate approximation by the radial basis function neural network, the approximation part B2 of B1 and the approximation error C1 are obtained. B1 = B2 + C1. In the present invention, B1 is equivalent to , B2 is equivalent to , C1 = , so in the present invention, the first non-linear manipulator model and the second non-linear manipulator are actually the same in essence, but only different in expression. When a same control torque is input to the first non-linear manipulator model and the second non-linear manipulator model, the output results of both are the same. Therefore, for the first non-linear manipulator model and the second non-linear manipulator model, except for the different representation methods of the model uncertain part, the remaining model determined parts and state vectors are correspondingly equal.

[0088] 3: Adopt a sliding mode control function and a second radial basis function neural network to construct an adaptive sliding mode observer corresponding to the second non-linear manipulator model:

[0089] 1): Adopt a second radial basis function neural network to construct an observer for the second non-linear manipulator model:

[0090]

[0091]

[0092] The estimated value of the state vector of the second non - linear manipulator model for the degree of freedom of the observer, The estimated value of the position vector of the manipulator for the degree of freedom of the observer, For the manipulator of the observer The estimated value of the velocity vector of the degree of freedom, Is the estimated value of the velocity vector of the l - th degree of freedom of the manipulator by the observer, Is the estimated value of the acceleration vector of the l - th degree of freedom of the manipulator by the observer, Is the first model determination part of the second non - linear manipulator model for the degree of freedom, Is the second model determination part of the second non - linear manipulator model for the degree of freedom, Is the weight factor matrix of the second radial basis function neural network, Is the radial basis function of the second radial basis function neural network. n represents the number of degrees of freedom of the manipulator. The simplest way to establish an observer for a model is to establish an expression identical to the model expression, so that the model can be observed. However, in the present invention, an observer similar to the expression of the second non - linear manipulator model is established by combining the second radial basis function neural network. In order to make the observation result more accurate, the present invention does not consider the uncertain terms in the second non - linear manipulator. In order to maintain the function of the observer, in the observer Is the same as the first model determination part of the first non - linear manipulator model / second non - linear manipulator model, Is the same as the second model determination part of the first non - linear manipulator model / second non - linear manipulator model, = 。

[0093] 2): Use the sliding - mode control function and the observer described in step 1) to construct a sliding - mode observer. Use the sliding - mode control method to obtain the sliding - mode control function of the observer according to the difference between the estimated value of the state vector of the second non - linear manipulator model by the observer described in step 1) and the actual value of the state vector output by the second non - linear manipulator model. Construct a sliding - mode observer according to the observer and the sliding - mode control function;

[0094]

[0095] Among them, and Satisfy:

[0096]

[0097] Among them, is the estimated value of the state vector of the second non - linear manipulator model by the adaptive sliding - mode observer, is the estimated value of the velocity vector of the l - th degree of freedom of the manipulator by the adaptive sliding - mode observer ; is the estimated value of the acceleration vector of the l - th degree of freedom of the manipulator by the adaptive sliding - mode observer ; is the estimated value of the velocity vector of the -th degree of freedom of the manipulator by the adaptive sliding - mode observer ; is the estimated value of the determined part of the l - th degree of freedom model of the second non - linear manipulator model by the adaptive sliding - mode observer ; is the estimated value of the determined part of the l - th degree of freedom model of the second non - linear manipulator model by the adaptive sliding - mode observer ; is the weight factor matrix of the second radial basis function neural network, is the radial basis function of the second radial basis function neural network, is the sliding - mode control function of the adaptive sliding - mode observer, is the sliding - mode control function of the adaptive sliding - mode observer, is the maximum approximation error value constant of the first radial basis function neural network for the -th degree of freedom of the manipulator model, and are the parameters of the adaptive sliding - mode controller respectively. n represents the number of degrees of freedom of the manipulator. The sliding - mode function designed in the present invention is mainly based on the idea of sliding - mode control and adopts the function to realize the estimation control of the second non - linear manipulator model by the sliding - mode observer, so that it can converge rapidly at the boundary value.

[0098] 3): According to the difference between the estimated value of the second non - linear manipulator model by the sliding - mode observer described in step 2) and the actual value of the state vector output by the second non - linear manipulator model, and the difference between the weight factor matrix of the first radial basis function neural network after approximating the uncertain part of the first non - linear manipulator model and the weight factor matrix of the second radial basis function neural network, adaptively update the weight factor matrix of the second radial basis function neural network in the sliding - mode observer to obtain the adaptive sliding - mode observer:

[0099]

[0100] Among them, and Satisfy:

[0101]

[0102] Wherein, is the estimated value of the state vector of the second non - linear manipulator model by the adaptive sliding - mode observer, is the estimated value of the velocity vector of the l - th degree of freedom of the manipulator by the adaptive sliding - mode observer ; is the estimated value of the acceleration vector of the l - th degree of freedom of the manipulator by the adaptive sliding - mode observer ; is the estimated value of the velocity vector of the -th degree of freedom of the manipulator by the adaptive sliding - mode observer ; is the estimated value of the determined part of the l - th degree of freedom model of the second non - linear manipulator model by the adaptive sliding - mode observer ; is the estimated value of the determined part of the l - th degree of freedom model of the second non - linear manipulator model by the adaptive sliding - mode observer ; is the weight factor matrix of the second radial basis function neural network, is the radial basis function of the second radial basis function neural network, is the sliding - mode control function of the adaptive sliding - mode observer, is the sliding - mode control function of the adaptive sliding - mode observer, is the maximum approximation error value constant of the l - th degree of freedom of the manipulator model by the first radial basis function neural network ; and are the parameters of the adaptive sliding - mode controller respectively, n represents the number of degrees of freedom of the manipulator. Wherein, is the maximum approximation error value constant of the l - th degree of freedom of the manipulator model by the first radial basis function neural network, n represents the number of degrees of freedom of the manipulator, the value of is independently designed by those skilled in the art according to the experimental accuracy, and are set artificially by those skilled in the art. According to the radial basis function neural network combined with the sliding - mode control method, and the output state vector of the non - linear manipulator, an adaptive weight factor matrix is designed, thereby constructing an adaptive sliding - mode observer. Through the adaptive sliding - mode observer, the approximation part in the second non - linear manipulator model can be quickly estimated, and the approximation error generated after the first radial basis function neural network approximates the first non - linear manipulator model can be eliminated. At the same time, The adaptive weight factor matrix for estimation and the weight factors of the second neural network have the same essential content but different names, because the adaptive sliding mode observer is actually based on the second neural network.

[0103] The weight factor matrix of the second radial basis function neural network is:

[0104]

[0105]

[0106]

[0107] Among them, is the adaptive change rate of the weight factor matrix of the second radial basis function neural network, is the weight factor matrix approximated by the first radial basis function neural network at time t and the weight factor matrix of the second radial basis function neural network the difference between, is the weight factor matrix approximated by the first radial basis function neural network at the initial time and the weight factor matrix of the second radial basis function neural network the difference between, and are learning factors, is the estimated value of the position vector of the degree of freedom of the second nonlinear robotic arm model by the adaptive sliding mode observer and the position vector output by the second nonlinear robotic arm model the difference between, is the estimated value of the velocity vector of the degree of freedom of the second nonlinear robotic arm model by the adaptive sliding mode observer and the velocity vector output by the second nonlinear robotic arm model the difference between, is the estimated value of the state vector of the degree of freedom of the second nonlinear robotic arm model by the adaptive sliding mode observer the estimated value of, is the radial basis function of the second radial basis function neural network, e represents the base of the natural logarithm, and are integration variables, and are learning factors artificially set by those skilled in the art according to the required experimental results is the weight factor matrix approximated by the first radial basis function neural network at the initial time and the weight factor matrix of the second radial basis function neural network The difference is that when a person skilled in the art inputs a value identical to the weight factor matrix in this case it is 0. Of course, a person skilled in the art can also randomly input values. The designed adaptive weight factor matrix improves the response speed of the manipulator model optimization and reduces the computational amount.

[0108] 4: Calculate the estimated value of the approximation result using the adaptive sliding mode observer, and compensate the estimated value of the approximation result into the first nonlinear manipulator model to eliminate the influence of unknown external disturbances on the manipulator (eliminate the uncertain terms in the manipulator model ):

[0109] The estimated value of the approximation result is:[[]]

[0110]

[0111] Compensate the estimated value of the approximation result into the first nonlinear manipulator model:

[0112]

[0113] to obtain an accurate manipulator model through sliding:[[]]

[0114]

[0115] Sliding is the state vector of the accurate manipulator model (including the position vector and velocity vector of the manipulator), is the position vector of the manipulator, is the velocity vector of the manipulator, is the control torque of the manipulator, is the acceleration vector of the manipulator, is the first determined part of the accurate manipulator model, is the second determined part of the accurate manipulator model, is the weight factor matrix of the second radial basis function neural network in the adaptive sliding mode observer, is the radial basis function of the second radial basis function neural network, which also represents the adaptive sliding mode observer's response to the weight factor matrix of the first radial basis function neural network The estimated value of 1~5 is provided by the present invention. It can be concluded from the technical content that when the external interference is a continuous interference signal, the optimization method of the design of the present invention can continuously compensate the first nonlinear manipulator model as time changes, thereby suppressing the external interference. When the unknown external interference of the present invention is constant, the first nonlinear manipulator model can also be compensated once by the present invention. When the external interference of the present invention is discrete, the first nonlinear manipulator model can also be compensated periodically by the present invention.

[0116] Preferably, the radial basis functions of the first radial basis function neural network or the second radial basis function neural network are both the same Gaussian function:

[0117]

[0118]

[0119]

[0120] Among them, X is the state vector of the robot model, is the radial basis function of the radial basis function neural network, For the Radial basis function of the radial basis function neural network with degrees of freedom, represents the radial basis function of the i-th neural node in the l-th degree of freedom radial basis function neural network, Indicates the The set of receptive field centers of the i-th neural node in the radial basis function neural network with degrees of freedom, For the The center of the mth receptive field of the ith neural node in the radial basis function neural network, where m is the The number of receptive field centers of the ith neural node in the radial basis function neural network with degrees of freedom, Indicates the Degrees of freedom is the number of neural nodes in the radial basis function neural network, Indicates the Radial basis function of the i-th neural node in the radial basis function neural network The width of the Gaussian mode, where for or .

[0121] Example 2

[0122] like Figure 4 、 Figure 5 、 Figure 6 、 Figure 7As described above, the robotic arm model identification method based on an adaptive sliding mode observer proposed by the present invention is applied to a two-degree-of-freedom robotic arm system, where:

[0123]

[0124]

[0125]

[0126]

[0127] ,

[0128]

[0129]

[0130] The trajectories of Joint 1 and Joint 2 are given as:

[0131]

[0132] where, is the given position signal.

[0133] External disturbance is defined as: the disturbance applied to Joint 1 , and the disturbance applied to Joint 2 . The control torque is designed as:

[0134]

[0135] .

[0136] The experimental results prove the effectiveness of the robotic arm model optimization method based on the adaptive sliding mode observer. It can not only accurately estimate the uncertain part of the nonlinear robotic arm model within a finite time and compensate for it, thereby optimizing the robotic arm model and suppressing the influence brought by external disturbances. By designing an adaptive weight factor, the weight of the adaptive sliding mode observer can be actively adjusted, reducing the response time of the observer, improving the optimization speed of the robotic arm model, and reducing the computational amount. It should be noted that the sliding mode function can accelerate the convergence speed during the estimation of the adaptive sliding mode observer and reduce the computational amount. The robotic arm model optimization method based on the adaptive sliding mode observer described in the present invention can also be extended to handle the model optimization problems of other industrial control systems.

[0137] In consideration of the influence of the usage time, the corrosion degree of the robotic arm, and the lubrication degree of the joints among different robotic arms, the present invention divides the first non-linear robotic arm model into a deterministic part and an uncertain part. According to the principle of the radial basis function neural network, the uncertain part of the model in the first non-linear robotic arm model is approximately approximated, which can suppress the influence of most disturbances on the robotic arm. By using a sliding mode control function and a second radial basis function neural network, an adaptive sliding mode observer corresponding to the second non-linear robotic arm model is constructed. Through the second neural network weight factor updated adaptively in the adaptive sliding mode observation, the approximated part in the second non-linear robotic arm model can be quickly estimated, the approximation error generated after the approximation of the first non-linear robotic arm model by the first radial basis function neural network is eliminated, and by feeding it back to the first non-linear robotic arm model, the robotic arm model is optimized, and the influence of external disturbances on the robotic arm model is eliminated. The sliding mode function can accelerate the convergence speed during the estimation of the adaptive sliding mode observer and reduce the calculation amount. By the method of the present invention, the influence of various disturbances on the robotic arm model is effectively suppressed, and the response speed of the optimization of the robotic arm model is improved by designing an adaptive weight factor matrix, and the calculation amount is reduced.

[0138] Although the embodiments of the present invention have been shown and described, those of ordinary skill in the art can understand that various changes, modifications, substitutions, and variations can be made to these embodiments without departing from the principle and spirit of the present invention. The scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. An optimization method for a robotic arm model based on an adaptive sliding mode observer, characterized in that, It includes the following steps: S1: Based on the position signal of the robotic arm and the unknown external disturbance, construct a first non-linear robotic arm model and divide it into a model determination part and a model uncertainty part; S2: Use the first radial basis function neural network to approximately approximate the model uncertain part D(X l ) l , and replace the model uncertain part D(X l ) l with the approximation result to obtain the second non-linear manipulator model; D(X l ) l represents the model uncertain part of the l-th degree of freedom of the first non-linear manipulator model; S3: Adopt a sliding mode control function and a second radial basis function neural network to construct an adaptive sliding mode observer corresponding to the second non-linear robotic arm model; The S3 includes: S31: Adopt a second radial basis function neural network to construct an observer for the second non-linear robotic arm model; S32: Use the sliding mode control function and the observer in step S31 to construct a sliding mode observer based on the difference between the estimated value of the state vector of the second non-linear robotic arm model and the actual value output by the second non-linear robotic arm model; S33: According to the difference between the estimated value of the second non-linear robotic arm model and the actual value of the second non-linear robotic arm model in step S32, and the difference between the weight factor matrix after the first radial basis function neural network approximates the uncertainty part of the first non-linear robotic arm model and the weight factor matrix of the second radial basis function neural network, adaptively update the weight factor matrix of the second radial basis function neural network in the sliding mode observer to obtain an adaptive sliding mode observer; S4: Use the adaptive sliding mode observer to calculate the estimated value of the approximation result and compensate the estimated value of the approximation result into the first non-linear robotic arm model in step S1.

2. The method for optimizing the manipulator model based on the adaptive sliding mode observer according to claim 1, wherein The S1 includes: Among them, X l is the state vector of the l-th degree of freedom of the first non-linear manipulator model, represents the velocity vector of the l-th degree of freedom of the manipulator, is the acceleration vector of the l-th degree of freedom of the manipulator, is the velocity signal of the l-th degree of freedom of the manipulator, is the undisturbed part of the gravitational torque, is the undisturbed part of the Coriolis force and the centripetal force, is the undisturbed part of the inertia matrix, F l (X l ) is the first model determination part of the l-th degree of freedom of the first non-linear manipulator model, is the second model determination part of the l-th degree of freedom of the first non-linear manipulator model, D(X l ) l is the model uncertainty part of the l-th degree of freedom of the first non-linear manipulator model, n represents the number of degrees of freedom of the manipulator, is the total disturbance part of the l-th degree of freedom of the first non-linear manipulator model; G l (X l ) is the inverse matrix of, is the control torque of the l-th freedom of the manipulator.

3. The method for optimizing the manipulator model based on the adaptive sliding mode observer according to claim 1, wherein Replacing the uncertain part D(X l ) l of the first non-linear robotic arm model with the approximation result to obtain a second non-linear robotic arm model includes: in, is the velocity vector of the lth degree of freedom of the manipulator, is the acceleration vector of the first degree of freedom of the manipulator, X l is the state vector of the lth degree of freedom of the second nonlinear manipulator model, is the velocity vector of the first degree of freedom of the manipulator, F l (X l ) is the first model determination part of the first degree of freedom of the second nonlinear manipulator model, is the second model determination part of the first degree of freedom of the second nonlinear manipulator model, The first radial basis function neural network is used to determine the uncertainty part D(X) of the first degree of freedom of the first nonlinear manipulator model. l ) l The approximation result of The first radial basis function neural network is used to calculate the uncertainty part D(X) of the first nonlinear manipulator model's first degree of freedom. l ) l The weight factor matrix after approximation, δ l (X l ) is the uncertainty part D(X) of the first radial basis function neural network for the first nonlinear manipulator model. l ) l The error after approximation, n represents the number of degrees of freedom of the robot arm, G is the maximum approximation error constant of the first radial basis function neural network to the lth degree of freedom of the manipulator model; l (X l )for The inverse matrix of is the control torque of the first freedom of the manipulator, is the radial basis function of the first radial basis function neural network.

4. The method for optimizing the manipulator model based on the adaptive sliding mode observer according to claim 3, characterized in that The adaptive sliding mode observer includes: Wherein, is the estimated value of the state vector of the second non - linear manipulator model by the adaptive sliding - mode observer, is the position vector of the l - th degree of freedom of the manipulator, is the estimated value of the position vector of the l - th degree of freedom of the manipulator by the observer, represents the velocity vector of the l - th degree of freedom of the manipulator, is the estimated value of the velocity vector of the l - th degree of freedom of the manipulator by the adaptive sliding - mode observer of, is the estimated value of the acceleration vector of the l - th degree of freedom of the manipulator by the adaptive sliding - mode observer of, is the estimated value of the velocity vector of the l - th degree of freedom of the manipulator by the adaptive sliding - mode observer of, is the estimated value of the first model - determining part F l (X l ) of the l - th degree of freedom of the second non - linear manipulator model by the adaptive sliding - mode observer, is the estimated value of the second model - determining part of the l - th degree of freedom of the second non - linear manipulator model by the adaptive sliding - mode observer, is the estimated value of G l (X l ) by the adaptive sliding - mode observer, is the control torque of the l - th freedom of the manipulator, is the weight factor matrix of the second radial basis function neural network, is the radial basis function of the second radial basis function neural network, is the sliding - mode control function of the adaptive sliding - mode observer, and are the parameters of the adaptive sliding - mode controller respectively, and n represents the number of degrees of freedom of the manipulator.

5. The method for optimizing the manipulator model based on the adaptive sliding mode observer according to claim 4, wherein The said and meet the following requirements: Among them, is the maximum approximation error value constant of the first radial basis function neural network for the l-th degree of freedom of the robotic arm model.

6. The method for optimizing the manipulator model based on the adaptive sliding mode observer according to claim 4, characterized in that The weight factor matrix of the second radial basis function neural network includes: Among them, is the adaptive change rate of the weight factor matrix of the second radial basis function neural network, is the weight factor matrix approximated by the first radial basis function neural network at time t and the weight factor matrix of the second radial basis function neural network The difference between them, is the weight factor matrix approximated by the first radial basis function neural network at the initial time and the weight factor matrix of the second radial basis function neural network The difference between them, and are learning factors, is the estimated value of the position vector of the l-th degree of freedom of the second non-linear robotic arm model by the adaptive sliding mode observer and the position vector output by the second non-linear robotic arm model The difference between the actual values, is the estimated value of the velocity vector of the l-th degree of freedom of the second non-linear robotic arm model by the adaptive sliding mode observer and the velocity vector output by the second non-linear robotic arm model The difference between the actual values, is the estimated value of the state vector X of the l-th degree of freedom of the second non-linear robotic arm model by the adaptive sliding mode observer l The estimated value of, is the radial basis function of the second radial basis function neural network. e represents the base of the natural logarithm, and τ and u are integration variables.

7. The method for optimizing the manipulator model based on the adaptive sliding mode observer according to claim 1, wherein The estimated value of the approximation result is: Among them, is the estimated value of the state vector of the second non-linear robotic arm model by the adaptive sliding mode observer, is the weight factor matrix of the second radial basis function neural network in the adaptive sliding mode observer, is the radial basis function of the second radial basis function neural network.

8. The method for optimizing the manipulator model based on the adaptive sliding mode observer according to claim 1, characterized in that, The radial basis functions of the first radial basis function neural network or the second radial basis function neural network are the same Gaussian function.

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