CN116954063A - Gear inspection nonlinear global sliding mode finite time neural network control method - Google Patents
Gear inspection nonlinear global sliding mode finite time neural network control method Download PDFInfo
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Abstract
A gear inspection nonlinear global sliding mode finite time neural network control method comprises the steps of constructing a model-free control frame and defining a tracking error equation based on a mathematical model of an N-joint mechanical arm of a gear inspection robot system; the method comprises the steps of utilizing a radial basis function neural network observer to realize real-time observation compensation of uncertainty parameters and unknown external disturbance of a gear inspection robot system; based on a tracking error equation and a nonlinear function, constructing a finite time convergence nonlinear global sliding mode surface by combining an N-joint mechanical arm inertia matrix of a gear inspection robot system, a tracking error nonlinear function proportional term, a tracking error nonlinear function integral term and a tracking error nonlinear function initial term; design a gear inspection robot system N joint mechanical arm nonlinear global sliding mode finite time neural network controller by adopting a system disturbance self-adaptive approach lawThe method comprises the steps of carrying out a first treatment on the surface of the Verifying that N-joint mechanical arm of gear inspection robot system is targetTrack following test.
Description
Technical Field
The invention relates to the technical field of industrial robot control systems, in particular to a gear inspection nonlinear global sliding mode finite time neural network control method.
Background
The inspection robot is a device with a multi-dimensional autonomous moving and visual system, such as a tunnel inspection robot, an electric inspection robot and a security inspection robot. The gear inspection robot is equipment for detecting a high-precision gear processing technology. The gear inspection robot consists of a multi-joint mechanical arm and a vision system, and a control system of the gear inspection robot can realize real-time track of the multi-joint mechanical arm. However, the gear inspection robot has the problems of low control precision, poor repeated positioning precision and the like due to the uncertainty of external disturbance and uncertainty of self model parameters.
Disclosure of Invention
The present invention has been made in view of the above-described problems occurring in the prior art.
Therefore, the technical problems solved by the invention are as follows: how to solve the problems that the track tracking control precision of the N-joint mechanical arm of the gear inspection robot system is not high, the repeated positioning precision exists and the like.
In order to solve the technical problems, the invention provides the following technical scheme: based on a mathematical model of the N-joint mechanical arm of the gear inspection robot system, constructing a model-free control frame and defining a tracking error equation of the N-joint mechanical arm of the gear inspection robot system; the method comprises the steps that a radial basis function neural network observer is utilized to realize real-time observation compensation on uncertainty parameters and unknown external disturbances of a gear inspection robot system; based on a gear inspection robot system N-joint mechanical arm tracking error equation and a nonlinear function, constructing a finite time convergence nonlinear global sliding mode surface by combining a gear inspection robot system N-joint mechanical arm inertia matrix, a gear inspection robot system N-joint mechanical arm tracking error nonlinear function proportional term, a gear inspection robot system N-joint mechanical arm tracking error nonlinear function integral term and a gear inspection robot system N-joint mechanical arm tracking error nonlinear function initial term; and designing a nonlinear global sliding mode finite time neural network controller tau (t) of an N-joint mechanical arm of the gear inspection robot system by adopting a system disturbance self-adaptive approach law.
As a preferable scheme of the gear inspection nonlinear global sliding mode finite time neural network control method, the invention comprises the following steps:
the gear inspection robot system comprises: the system comprises an image operation center, a high-power camera and an N-joint mechanical arm.
As a preferable scheme of the gear inspection nonlinear global sliding mode finite time neural network control method, the invention comprises the following steps:
the gear inspection robot system N joint mechanical arm mathematical model:
wherein, the left side of the equation is respectively: n-joint mechanical arm inertia force item of gear inspection robot systemCentrifugal force and coriolis force item of N-joint mechanical arm of gear inspection robot system>Gravity item G (q (t)) n×1 Friction force item of N-joint mechanical arm of gear inspection robot system>External disturbance term τ d (t)∈R n×1 ；M(q(t))∈R n×n For gear inspection robot system N joint arm inertial matrix, +.>The centrifugal force matrix and the coriolis force matrix of the N-joint mechanical arm of the gear inspection robot system are adopted; the right side of the equation is the control force term tau (t) epsilon R of the N-joint mechanical arm of the gear inspection robot system n×1 ；
Based on the mathematical model of the N-joint mechanical arm of the gear inspection robot system, a model-free control frame is constructed:
wherein m (q (t))εR n×n The model-free frame controller of the N-joint mechanical arm of the gear inspection robot system has no physical meaning parameter adjusting gain matrix,d(t)∈R n×1 for the uncertainty parameter and unknown external disturbance of the gear inspection robot system, the method is defined as follows:
defining the tracking error of the N joint mechanical arm of the gear inspection robot system as follows:
e(t)＝q * (t)-q(t)
wherein ,q* (t) is a target track of the N-joint mechanical arm of the gear inspection robot system, q (t) is an actual track of the N-joint mechanical arm of the gear inspection robot system, and e (t) is a tracking error of the N-joint mechanical arm of the gear inspection robot system;
taking a second-order differential from the tracking error of the N-joint mechanical arm of the gear inspection robot system to obtain:
wherein ,is the second order derivative of e (t); />Is q * Second order differentiation of (t); />Is the second order derivative of q (t);
defining an N-joint mechanical arm tracking error equation of the gear inspection robot system:
as a preferable scheme of the gear inspection nonlinear global sliding mode finite time neural network control method, the invention comprises the following steps:
defining the radial basis function network observer:
w * ＝argmin(d(t))
h(x)＝[h 1 (x) h 2 (x) … h n (x)]
when x-o n ||≤h n ：
When h n <||x-o n ||≤2h n ：
When 2h n <||x-o n ||：
h n (x)＝0
wherein ,is the estimated value of the uncertainty parameter and the unknown external disturbance of the gear inspection robot system, w * Is the optimal weight of the radial basis function neural network observer, and h (x) isThe hidden layer function of the radial basis function network observer, x is the input of the radial basis function network observer, o n Is the center of the radial basis function neural network observer; h is a n Is the radial basis function neural network observer bandwidth.
As a preferable scheme of the gear inspection nonlinear global sliding mode finite time neural network control method, the invention comprises the following steps:
defining the limited time convergence nonlinear global sliding mode surface:
s(t)＝[s 1 (t) s 2 (t) … s n (t)] T
k gnp ＝diag[k 1gnp k 2gnp … k ngnp ] T
k gni ＝diag[k 1gni k 2gni … k ngni ] T
k＝diag[k 1 k 2 … k n ] T
fal[e(t)，γ，η]
＝[fal[e 1 (t)，γ，η] fal[e 2 (t)，γ，η] … fal[e n (t)，γ，η]] T
fal[e(0)，γ，η]
＝[fal[e 1 (0)，γ，η] fal[e 2 (0)，γ，η] … fal[e n (0)，γ，η]] T
wherein ,kgnp fal[e(t),γ,η]Is a nonlinear function proportional term k of tracking error of an N-joint mechanical arm of a gear inspection robot system gnp Is a proportionality coefficient of the material, is the nonlinear function integral term k of the tracking error of the N-joint mechanical arm of the gear inspection robot system gni Is the integral coefficient, k is the feedback gain, k gnp fal[e(0),γ,η]The method is an initial item of a nonlinear function of tracking error of an N-joint mechanical arm of the gear inspection robot system;
taking first-order differentiation of the limited-time convergence nonlinear global sliding mode surface:
defining the finite time as follows:
when |e (t) | > η:
when |e (t) | < η:
wherein ,ts Is a finite convergence time and C is an arbitrary constant.
As a preferable scheme of the gear inspection nonlinear global sliding mode finite time neural network control method, the invention comprises the following steps:
defining the system disturbance self-adaptive approach law:
wherein delta is the system disturbance self-adaptive approach law adjusting gain, and the self-adaptive rate is thatβ 1 ，β 2 ，…，β n Is to regulate the parameter gain, and the weight of the Chinese medicine>
As a preferable scheme of the gear inspection nonlinear global sliding mode finite time neural network control method, the invention comprises the following steps:
based on the radial basis function neural network observer, the limited time convergence nonlinear global sliding mode surface and the system disturbance self-adaptive approach law, a model-free control framework is used for designing a nonlinear global sliding mode finite time neural network controller tau (t) of an N-joint mechanical arm of a gear inspection robot system:
when |e (t) | > η:
when |e (t) | < η:
the invention has the beneficial effects that: (1) The method is based on a mathematical model of the N-joint mechanical arm of the gear inspection robot system, a model-free control frame is constructed, and a tracking error equation of the N-joint mechanical arm of the gear inspection robot system is defined; on the basis, a radial basis neural network observer is provided to realize the uncertainty compensation of the system; (2) Constructing a finite time convergence nonlinear global sliding mode surface by utilizing an inertial matrix of an N-joint mechanical arm of the gear inspection robot system, a tracking error nonlinear function proportional term, a nonlinear function integral term and a nonlinear function initial term of the N-joint mechanical arm of the gear inspection robot system, and enhancing the control robustness; (3) And a controller is designed by adopting a system disturbance self-adaptive approach law, so that the self-adaptability of an approach stage is realized.
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In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings that are needed in the description of the embodiments will be briefly described below, it being obvious that the drawings in the following description are only some embodiments of the present invention, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
wherein ：
FIG. 1 is a control schematic diagram of a gear inspection nonlinear global sliding mode finite time neural network control method according to an embodiment of the invention;
fig. 2 is a schematic diagram of tracking target tracks (aim 1) of a dual-joint mechanical arm of a gear inspection robot system and track tracking of a nonlinear global sliding mode finite time neural network control method (NGSMFTNNC) according to an embodiment of the present invention;
fig. 3 is a schematic diagram of tracking target tracks (aim 2) of a dual-joint mechanical arm of a gear inspection robot system and track tracking of a nonlinear global sliding mode finite time neural network control method (NGSMFTNNC) according to an embodiment of the present invention;
fig. 4 is a schematic diagram of tracking target tracks (aim 1) of a dual-joint mechanical arm of a gear inspection robot system and track tracking of a neural network control method (NNFC) based on a model according to a gear inspection nonlinear global sliding mode finite time neural network control method according to an embodiment of the invention;
fig. 5 is a schematic diagram of tracking target tracks (aim 2) of a dual-joint mechanical arm of a gear inspection robot system and track tracking of a neural network control method (NNFC) based on a model according to the non-linear global sliding mode finite time neural network control method of the gear inspection according to an embodiment of the invention;
Detailed Description
The technical scheme of the invention is further described in detail below with reference to the attached drawings.
So that the manner in which the above recited objects, features and advantages of the present invention can be understood in detail, a more particular description of the invention, briefly summarized above, may be had by reference to the embodiments, some of which are illustrated in the appended drawings. All other embodiments, which can be made by one of ordinary skill in the art based on the embodiments of the present invention without making any inventive effort, shall fall within the scope of the present invention.
In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present invention, but the present invention may be practiced in other ways other than those described herein, and persons skilled in the art will readily appreciate that the present invention is not limited to the specific embodiments disclosed below.
Further, reference herein to "one embodiment" or "an embodiment" means that a particular feature, structure, or characteristic can be included in at least one implementation of the invention. The appearances of the phrase "in one embodiment" in various places in the specification are not necessarily all referring to the same embodiment, nor are separate or alternative embodiments mutually exclusive of other embodiments.
Referring to fig. 1, for an embodiment of the present invention, a gear inspection nonlinear global sliding mode finite time neural network control method is provided, and the method organically and uniformly designs a gear inspection robot system N-joint mechanical arm mathematical model, a radial basis neural network observer, a finite time convergence nonlinear global sliding mode surface, and a system disturbance adaptive approach law, by using the method, referring to fig. 1, a control block diagram of the gear inspection nonlinear global sliding mode finite time neural network control method of the present invention specifically includes:
s1: based on a mathematical model of the N-joint mechanical arm of the gear inspection robot system, a model-free control frame is constructed, and a tracking error equation of the N-joint mechanical arm of the gear inspection robot system is defined.
The gear inspection robot system comprises: the system comprises an image operation center, a high-power camera and an N-joint mechanical arm.
The gear inspection robot system N joint mechanical arm mathematical model:
wherein, the left side of the equation is respectively: n-joint mechanical arm inertia force item of gear inspection robot systemCentrifugal force and coriolis force item of N-joint mechanical arm of gear inspection robot system>Gear inspection robot systemGravity term G (q (t)) n×1 Friction force item of N-joint mechanical arm of gear inspection robot system>External disturbance term τ d (t)∈R n×1 ；M(q(t))∈R n×n For gear inspection robot system N joint arm inertial matrix, +.>The centrifugal force matrix and the coriolis force matrix of the N-joint mechanical arm of the gear inspection robot system are adopted; the right side of the equation is the control force term tau (t) epsilon R of the N-joint mechanical arm of the gear inspection robot system n×1 。
Based on the mathematical model of the N-joint mechanical arm of the gear inspection robot system, a model-free control frame is constructed:
wherein m (q (t))εR n×n Parameter adjustment gain matrix without physical meaning for N-joint mechanical arm model-free frame controller of gear inspection robot system, d (t) epsilon R n×1 For the uncertainty parameter and unknown external disturbance of the gear inspection robot system, the method is defined as follows:
defining the tracking error of the N joint mechanical arm of the gear inspection robot system as follows:
e(t)＝q * (t)-q(t
wherein ,q* (t) is the target track of the N-joint mechanical arm of the gear inspection robot system, q (t) is the actual track of the N-joint mechanical arm of the gear inspection robot system, and e (t) is the tracking error of the N-joint mechanical arm of the gear inspection robot system.
Taking a second-order differential from the tracking error of the N-joint mechanical arm of the gear inspection robot system to obtain:
wherein ,is the second order derivative of e (t); />Is q * Second order differentiation of (t); />Is the second order derivative of q (t).
Defining an N-joint mechanical arm tracking error equation of the gear inspection robot system:
s2: and the radial basis function neural network observer is utilized to realize real-time observation compensation of the uncertainty parameters and unknown external disturbance of the gear inspection robot system.
Defining the radial basis function network observer:
w * ＝argmin(d(t))
h(x)＝[h 1 (x) h 2 (x) … h n (x)]
when x-o n ||≤h n ：
When h n <||x-o n ||≤2h n ：
When 2h n <||x-o n ||：
h n (x)＝0
wherein ,is the estimated value of the uncertainty parameter and the unknown external disturbance of the gear inspection robot system, w * Is the optimal weight of the radial basis function network observer, h (x) is the hidden layer function of the radial basis function network observer, x is the input of the radial basis function network observer, o n Is the center of the radial basis function neural network observer; h is a n Is the radial basis function neural network observer bandwidth.
S3: based on a gear inspection robot system N-joint mechanical arm tracking error equation and a nonlinear function, a gear inspection robot system N-joint mechanical arm inertia matrix, a gear inspection robot system N-joint mechanical arm tracking error nonlinear function proportional term, a gear inspection robot system N-joint mechanical arm tracking error nonlinear function integral term and a gear inspection robot system N-joint mechanical arm tracking error nonlinear function initial term are combined to construct a finite time convergence nonlinear global sliding mode surface.
Defining the limited time convergence nonlinear global sliding mode surface:
s(t)＝[s 1 (t) s 2 (t) … s n (t)] T
k gnp ＝diag[k 1gnp k 2gnp … k ngnp ] T
k gni ＝diag[k 1gni k 2gni …k ngni ] T
k＝diag[k 1 k 2 … k n ] T
[fal[e(t),γ,η]
＝[fal[e 1 (t),γ,η] fal[e 2 (t),γ,η] … fal[e n (t),γ,η]] T
fal[e(0)，γ，η]
＝[fal[e 1 (0)，γ，η] fal[e 2 (0)，γ，η] … fal[e n (0)，γ，η]] T
/>
wherein ,kgnp fal[e(t),γ,η]Is a nonlinear function proportional term k of tracking error of an N-joint mechanical arm of a gear inspection robot system gnp Is a proportionality coefficient of the material, is the nonlinear function integral term k of the tracking error of the N-joint mechanical arm of the gear inspection robot system gni Is the integral coefficient, K is the feedback gain, K gnp fal[e(0),γ,η]The method is an initial term of a nonlinear function of tracking error of an N-joint mechanical arm of the gear inspection robot system.
Taking first-order differentiation of the limited-time convergence nonlinear global sliding mode surface:
defining the finite time as follows:
when |e (t) | > η:
/>
when |e (t) | < η:
wherein ,ts Is a finite convergence time and C is an arbitrary constant.
S4: and designing a nonlinear global sliding mode finite time neural network controller tau (t) of an N-joint mechanical arm of the gear inspection robot system by adopting a system disturbance self-adaptive approach law, and verifying the stability of the controller tau (t).
Defining the system disturbance self-adaptive approach law:
wherein delta is the system disturbance self-adaptive approach law adjusting gain, and the self-adaptive rate is thatβ 1 ，β 2 ，…，β n Is to regulate the parameter gain, and the weight of the Chinese medicine>
Based on the radial basis function neural network observer, the limited time convergence nonlinear global sliding mode surface and the system disturbance self-adaptive approach law, a model-free control framework is used for designing a nonlinear global sliding mode finite time neural network controller tau (t) of an N-joint mechanical arm of a gear inspection robot system:
when |e (t) | > η:
when |e (t) | < η:
the Lyapunov function is:
wherein ,βn >0，/>
Referring to fig. 1, which is a control schematic diagram of a gear inspection nonlinear global sliding mode finite time neural network control method, the method of the invention is further described, and the main control diagram process is as follows: firstly, constructing a model-free control frame based on a mathematical model of an N-joint mechanical arm of a gear inspection robot system and defining a tracking error equation of the N-joint mechanical arm of the gear inspection robot system; secondly, constructing a radial basis neural network observer and a limited time convergence nonlinear global sliding mode surface based on an N-joint mechanical arm tracking error equation of the gear inspection robot system; finally, the controller τ (t) is designed with a system disturbance adaptive approach law.
Preferably, the embodiment also needs to explain that, compared with the prior art, the invention discloses a gear inspection nonlinear global sliding mode finite time neural network control method, which aims to track the target track of an N-joint mechanical arm of a gear inspection robot system by adopting a finite time convergence nonlinear global sliding mode, predict system disturbance in real time by using a radial basis neural network observer, and then achieve adaptive dynamic response by using a system disturbance self-adaptive approach law. The method is based on a model-free control framework, and adopts the combination of observer compensation and sliding mode control, so that the problems of low control precision and poor repeated positioning precision are solved.
Referring to fig. 2 to 5, there is provided test verification of a gear inspection nonlinear global sliding mode finite time neural network control method, including:
in order to verify and explain the technical effects adopted in the method, in the embodiment, a neural network control method (NNFC) based on a model is selected to be compared with the method of the invention, and the test results are compared by a scientific demonstration means to verify the true effects of the method.
In order to verify the self-adaptability of the method of the invention in the uncertainty compensation, global robustness and approaching stage relative to the traditional method, a nonlinear global sliding mode finite time neural network control method (NGSMFTNNC) is adopted in the embodiment, and the real-time measurement comparison is carried out on the output track and the tracking error of the N-joint mechanical arm of the gear inspection robot system respectively by the tracking target tracks (aim and aim) of the double-joint mechanical arm of the gear inspection robot system and a model-based neural network control method (NNFC) because of the uncertainty external disturbance and the uncertainty of the model parameters of the gear inspection robot, which causes the problems of low existing control precision, poor repeated positioning precision and the like.
Test environment: referring to fig. 1, the N-joint mechanical arm of the gear inspection robot system is operated on a simulation platform to simulate and track target tracks (aim 1 and aim) of the two-joint mechanical arm of the gear inspection robot system, and the target tracks are tested by a nonlinear global sliding mode finite time neural network control method (NGSMFTNNC) and a model-based neural network control method (NNFC) respectively, so as to obtain test result data. All tests are performed by starting automatic test equipment and realizing simulation test of a comparison method by using MATLAB software programming, and simulation data are obtained according to experimental results; each method tests 3 groups of data, each group of data is sampled for 10s, each group of data input track and tracking error are obtained through calculation, and the calculation error is compared with the expected target track input through simulation.
Referring to fig. 2 to 5, track trace diagrams of the present invention are compared between a track target track (aim and aim) of a dual-joint mechanical arm of a gear inspection robot system, a nonlinear global sliding mode finite time neural network control method (NGSMFTNNC) and a model-based neural network control method (NNFC).
Double-joint mechanical arm parameters: connecting rod 1 mass m 1 Length l of connecting rod 1 =1 kg 1 Distance l of centroid to joint 1 =1m c1 1/2m, connecting rod 1 moment of inertia I 1 =1/12 kg·m, connecting rod 2 mass m e Distance l of link 2 to joint 2 =3 kg ce =1m, connecting rod 2 moment of inertia l e =2/5 kg·m, centroid and joint 2 angle δ e Coefficient of friction e =0 1 = -7/12, gravitational acceleration e 2 ＝9.81。
Referring to fig. 2 to 5, m (q (t))= [2 3]，k 1gnp ＝5，k 2gnp ＝0.02，k 1gni ＝0.001，k 2gni ＝10，k 1 ＝1，k 2 ＝2，η＝3，γ＝0.5，β 1 ＝0.05，β 2 As is readily seen in fig. 2 and 3, the nonlinear global sliding mode finite time neural network control method (NGSMFTNNC) can effectively track the target trajectories (aim and aim 2), but the model-based neural network control method (NNFC) cannot track, and has a large tracking error.
In summary, the gear inspection nonlinear global sliding mode finite time neural network control method provided by the invention is superior to other methods in steady state error, and is characterized in that: the nonlinear global sliding mode surface and the self-adaptive approach law are converged in limited time, the problems of low control precision and poor repeated positioning precision are solved, in addition, the uncertainty problem of a model is solved without a model frame, and the neural network is compensated.
It should be appreciated that embodiments of the invention may be implemented or realized by computer hardware, a combination of hardware and software, or by computer instructions stored in a non-transitory computer readable memory. The methods may be implemented in a computer program using standard programming techniques, including a non-transitory computer readable storage medium configured with a computer program, where the storage medium so configured causes a computer to operate in a specific and predefined manner, in accordance with the methods and drawings described in the specific embodiments. Each program may be implemented in a high level procedural or object oriented programming language to communicate with a computer system. However, the program(s) can be implemented in assembly or machine language, if desired. In any case, the language may be a compiled or interpreted language. Furthermore, the program can be run on a programmed application specific integrated circuit for this purpose.
Furthermore, the operations of the processes described in the present invention may be performed in any suitable order unless otherwise indicated herein or otherwise clearly contradicted by context. The processes (or variations and/or combinations thereof) described herein may be performed under control of one or more computer systems configured with executable instructions, and may be implemented as code (e.g., executable instructions, one or more computer programs, or one or more applications), by hardware, or combinations thereof, collectively executing on one or more processors. The computer program includes a plurality of instructions executable by one or more processors.
Further, the method may be implemented in any type of computing platform operatively connected to a suitable computing platform, including, but not limited to, a personal computer, mini-computer, mainframe, workstation, network or distributed computing environment, separate or integrated computer platform, or in communication with a charged particle tool or other imaging device, and so forth. Aspects of the invention may be implemented in machine-readable code stored on a non-transitory storage medium or device, whether removable or integrated into a computing platform, such as a hard disk, optical read and/or write storage medium, RAM, ROM, etc., such that it is readable by a programmable computer, which when read by a computer, is operable to configure and operate the computer to perform the processes described herein. Further, the machine readable code, or portions thereof, may be transmitted over a wired or wireless network. When such media includes instructions or programs that, in conjunction with a microprocessor or other data processor, implement the steps described above, the invention includes these and other different types of non-transitory computer-readable storage media. The invention also includes the computer itself when programmed according to the methods and techniques of the present invention. A computer program can be applied to the input data to perform the functions described herein to convert the input data to generate output data that is stored to the non-volatile memory. The output information may also be applied to one or more output devices such as a display. In a preferred embodiment of the invention, the transformed data represents physical and tangible objects, including specific visual depictions of physical and tangible objects produced on a display.
The above description is merely of preferred embodiments of the present invention, and the scope of the present invention is not limited to the above embodiments, but all equivalent modifications or variations according to the present disclosure will be within the scope of the claims.
Claims (7)
1. A gear inspection nonlinear global sliding mode finite time neural network control method is characterized in that: the method comprises the following steps:
s1, constructing a model-free control frame based on a mathematical model of an N-joint mechanical arm of a gear inspection robot system and defining a tracking error equation of the N-joint mechanical arm of the gear inspection robot system;
s2, utilizing a radial basis function neural network observer to realize real-time observation compensation of uncertainty parameters and unknown external disturbances of the gear inspection robot system;
s3, based on a gear inspection robot system N-joint mechanical arm tracking error equation and a nonlinear function, constructing a finite time convergence nonlinear global sliding mode surface by combining a gear inspection robot system N-joint mechanical arm inertia matrix, a gear inspection robot system N-joint mechanical arm tracking error nonlinear function proportional term, a gear inspection robot system N-joint mechanical arm tracking error nonlinear function integral term and a gear inspection robot system N-joint mechanical arm tracking error nonlinear function initial term;
s4, designing a nonlinear global sliding mode finite time neural network controller tau (t) of an N-joint mechanical arm of the gear inspection robot system by adopting a system disturbance self-adaptive approach law.
2. The gear inspection nonlinear global sliding mode finite time neural network control method according to claim 1, wherein the method is characterized by comprising the following steps: in step S1, the gear inspection robot system includes: the system comprises an image operation center, a high-power camera and an N-joint mechanical arm.
3. The gear inspection nonlinear global sliding mode finite time neural network control method according to any one of claims 1-2, which is characterized by comprising the following steps: in step S1, the mathematical model of the N-joint mechanical arm of the gear inspection robot system is as follows:
wherein, the left side of the equation is respectively: n-joint mechanical arm inertia force item of gear inspection robot systemCentrifugal force and coriolis force item of N-joint mechanical arm of gear inspection robot system>Gravity item G (q (t)) n×1 N-joint mechanical arm friction force item of gear inspection robot systemExternal disturbance term τ d (t)∈R n×1 ；M(q(t))∈R n×n For gear inspection robot system N joint arm inertial matrix, +.>The centrifugal force matrix and the coriolis force matrix of the N-joint mechanical arm of the gear inspection robot system are adopted; the right side of the equation is the control force term tau (t) epsilon R of the N-joint mechanical arm of the gear inspection robot system n×1 ；
Based on the mathematical model of the N-joint mechanical arm of the gear inspection robot system, a model-free control frame is constructed:
wherein m (q (t))εR n×n Parameter adjustment gain matrix without physical meaning for N-joint mechanical arm model-free frame controller of gear inspection robot system, d (t) epsilon R n×1 For the uncertainty parameter and unknown external disturbance of the gear inspection robot system, the method is defined as follows:
defining the tracking error of the N joint mechanical arm of the gear inspection robot system as follows:
e(t)＝q * (t)-q(t)
wherein ,q* (t) is a target track of the N-joint mechanical arm of the gear inspection robot system, q (t) is an actual track of the N-joint mechanical arm of the gear inspection robot system, and e (t) is a tracking error of the N-joint mechanical arm of the gear inspection robot system;
taking a second-order differential from the tracking error of the N-joint mechanical arm of the gear inspection robot system to obtain:
wherein ,is the second order derivative of e (t); />Is q * Second order differentiation of (t); />Is the second order derivative of q (t);
defining an N-joint mechanical arm tracking error equation of the gear inspection robot system:
4. a gear inspection nonlinear global sliding mode finite time neural network control method according to any one of claims 1 to 3, characterized in that: in step S2, the radial basis function network observer is defined:
w * ＝argmin(d(t))
h(x)＝[h 1 (x) h 2 (x)…h n (x)]
when x-o n ||≤h n ：
When h n <||x-o n ||≤2h n ：
When 2h n <||x-o n ||：
h n (x)＝0
wherein ,is the estimated value of the uncertainty parameter and the unknown external disturbance of the gear inspection robot system, w * Is the optimal weight of the radial basis function network observer, h (x) is the hidden layer function of the radial basis function network observer, x is the input of the radial basis function network observer, o n Is the center of the radial basis function neural network observer; h is a n Is the radial basis function neural network observer bandwidth.
5. A gear inspection nonlinear global sliding mode finite time neural network control method according to any one of claims 1 to 3, characterized in that: in step S3, defining the limited time convergence nonlinear global sliding mode surface:
s(t)＝[s 1 (t) s 2 (t)…s n (t)] T
k gnp ＝diag[k 1gnp k 2gnp …k ngnp ] T
k gni ＝diag[k 1gni k 2gni …k ngni ] T
k＝diag[k 1 k 2 …k n ] T
wherein ,kgnp fal[e(t),γ,η]Is a nonlinear function proportional term k of tracking error of an N-joint mechanical arm of a gear inspection robot system gnp Is a proportionality coefficient of the material, is a nonlinear function integral term of tracking error of an N-joint mechanical arm of a gear inspection robot system,/-joint mechanical arm>Is->The variable factors, gamma and eta are the parameter-adjusting gain, k gni Is the integral coefficient, k is the feedback gain,k gnp fal[e(0),γ,η]the method is an initial item of a nonlinear function of tracking error of an N-joint mechanical arm of the gear inspection robot system;
taking first-order differentiation of the limited-time convergence nonlinear global sliding mode surface:
defining the finite time as follows:
when |e (t) | > η:
when |e (t) | < η:
wherein ,ts Is a finite convergence time and C is an arbitrary constant.
6. The gear inspection nonlinear global sliding mode finite time neural network control method according to any one of claims 1 to 5, wherein the method is characterized by comprising the following steps of: in step S4, defining the adaptive approach law of system disturbance:
wherein delta is the system disturbance self-adaptive approach law adjusting gain, and the self-adaptive rate is thatβ 1 ，β 2 ，…，β n Is to regulate the parameter gain, and the weight of the Chinese medicine>
7. The gear inspection nonlinear global sliding mode finite time neural network control method according to any one of claims 1 to 6, wherein the method is characterized by comprising the following steps: in step S4, based on the radial basis function neural network observer, the limited time convergence nonlinear global sliding mode surface, and the system disturbance adaptive approach law, a model-free control framework is used to design a gear inspection robot system N-joint mechanical arm nonlinear global sliding mode finite time neural network controller τ (t):
when |e (t) | > η:
when |e (t) | < η:
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